Allen's
Astrophysical
Quantities
Fourth Edition
Allen's
Astrophysical
Quantities
Fourth Edition
Arthur N. Cox
Editor
AIP
eR~
'Springer
ArthurN. Cox
Theoretical Division
Los Alamos National Laboratory MS B288
P.O. Box 1663
Los Alamos, NM 87545
USA
anc@ lanl.gov
Cover illustration: An international team of astronomers, led by Dr. Wendy Freedman of the Observatories of the Carnegie
Institution of Washington, Robert Kennicutt of the University of Arizona, and Jeremy Mould of the Australian National
University observed this spiral galaxy NGC 4414 on 13 different occasions over the course of two months.
(AURA/STScJJNASA)
In 1995, the majestic spiral galaxy NGC 4414 was imaged by the Hubble Space Telescope as part of the HST Key Project on
the Extragalactic Distance Scale. Images were obtained with Hubble's Wide Field Planetary Camera 2 (WFPC2) through three
different color filters. Based on their discovery and careful brightness measurements of variable stars in NGC 4414, the Key
Project astronomers were able to make an accurate determination of the distance to the galaxy.
The resulting distance to NGC 4414, 19.1 megaparsecs or about 60 million light-years, along with similarly determined
distances to other nearby galaxies, contributes to astronomers' overall knowledge of the rate of expansion of the universe. The
Hubble constant (Ho) is the ratio of how fast galaxies are moving away from us to their distance from us. This astronomical
value is used to determine distances, sizes, and the intrinsic luminosities for many objects in our universe, and the age of the
universe itself.
Library of Congress Cataloging-in-Publication Data
Cox,Arthur
Allen 's astrophysical quantities/editor, Arthur Cox.
p. cm.
Includes bibliographical references.
Additional material to this book can be downloaded from http://extras.springer.com.
1. Astrophysical-Tables.
QB461.A7685. 1999
523.01'021-dc21
1. Cox, Arthur N.
98-53154
ISBN 978-1-4612-7037-9
ISBN 978-1-4612-1186-0 (eBook)
DOI 10.1007/978-1-4612-1186-0
Printed on acid-free paper.
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Preface
This handbook is the result of compilations and writing of ninety authors who have worked over a
period of nine years to revise the famous Allen's Astrophysical Quantities. The need for such a
revision had been known since shortly after the last edition edited by C.W. Allen in 1972. Even
though his 1973 edition remained in print through the late 1980s, Allen himself called for help in
revising the book in that third edition Preface. His death unfortunately prevented any revision, and
only a few attempts known to me were made by interested astronomers. By 1990, with the third
edition completely outdated, Arlo Landolt convinced the American Institute of Physics that they should
undertake extensive revisions of the Allen book. How my name came up, in late 1990, I do not know,
but once friends discovered I had been solicited by the AlP, they all encouraged me to find the various
astrophysics experts to prepare this new edition, published jointly by the AlP and Springer-Verlag.
The task of finding suitable authors and anonymous referees for the chapters was made easier by
the help of Peter Boyce at the American Astronomical Society and its publications board. Chairpersons
Caty Pilachowski, Hugh Van Horn, Jim Liebert, and Bob Hanisch suggested and helped recruit many
contributors. Numerous AAS officials, especially Roger Bell, helped me and the authors interface with
AlP and Springer.
The basic structure of the earlier Allen editions has been followed, but many changes were
necessary. For example, radio astronomy was represented by Allen with a page-long table of sources
and a few supplementary ones plus some data about solar radio emission. Today a complete chapter is
necessary, and even that does not seem to be as much as the author and I would have liked to include.
Other advances in astrophysics have required us to include new chapters for infrared, ultraviolet, X-ray,
and gamma-ray and neutrino astronomy. The explosion in observations of our solar system has resulted
in a great expansion in information about these nearby bodies, as well as for our Sun itself. Later in the
development of this book we found that we needed to add a chapter about stellar evolution because the
level of understanding essentially the entire lives of stars had matured enormously. Most dramatically,
modem large telescopes have revealed huge quantities of data about galaxies, galaxy clusters, and their
exotic emissions. Three separate chapters cover different aspects of this material. A much expanded
Cosmology chapter was needed to include our current understanding of the structure of the Universe.
Finally, we have added many supplemental tables including an attempt to list the world's largest optical
telescopes, with the help of Kari Parker, that surely will be out of date soon.
While writing the chapters, many authors found that they needed some specialists to supply and
even write sections that were beyond their current knowledge. These section authors are not given in
the table of contents, but only at the start of the sections where they contributed. Thanks are due to
these scientists who have supplied important information that we found relevant, often rather late in
the book development. Their submissions could easily merit a mention in the table of contents, but the
complicated process of assembling this greatly revised handbook and keeping its structure in control
has resulted in this special format.
Readers must realize that a project that involves ninety otherwise very busy astrophysicists is bound
to be uneven. Some authors were able to get their material to me as early as mid-1992, while others
were not even solicited by me for last-minute data until mid-1998. Our plan to include updates to
a uniform date for all chapters could not be carried out because of its complexity, but some data as
recent as the summer of 1999 are included. Readers are invited to contact individual authors directly
for details. Our hope is that we have adequately pointed the way to the extensive literature for each
subject.
v
vi I PREFACE
Some astrophysicists have already decided to adopt our carefully compiled data as standard for their
own special lists. This is reasonable, since this new Allen edition has been prepared by the world's
experts in the various areas of astrophysics. One thing we have learned is that definitive data depend
on interpretations for those last little details, and the best source for the most current and accurate data
is always the experts. We hope our authors are these.
The contents of this new edition of Allen will be available in electronic form with many
tables and graphs "live" for interactive searching, correlating, interpolating, and so forth. The
electronic version will be available by subscription and kept up-to-date on the publisher's web site
(www.springer-ny.com) and will also be available as a CD-ROM for use on a Windows PC. At the
minimum, these electronic data will greatly assist in future editions.
Every publishing undertaking ends with regrets that some things could not be included. Thus
all should realize that our book is a good reference book, but it still misses, for example, the newly
published definitive NIST physical constants, the recent discovery of a satellite around the asteroid (45)
Eugenia, the growing list of brown dwarf candidates, a new and unexpected class of intrinsic variable
(Gamma Doradus) stars, and the latest gamma burst explosions now optically detected from the far
reaches of our Universe. The organization of these new astrophysical quantities into an additional
concise revised-again edition awaits future generations of authors, I hope as skilled and dedicated as
ours.
Los Alamos, New Mexico
October 1999
Arthur N. Cox
anc@lanl.gov
Contents
Preface
v
Contributors
xv
Introduction
1
1.1
1.2
1.3
Arthur N. Cox
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Astronomical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Astronomical and Astrophysical Journals ... . . . . . . . . . . . . . . . . . . . . . . . .
2.1
2.2
2.3
2.4
2.5
2.6
Arthur N. Cox
Mathematical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Astronomical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Astronomical Constants Involving Time . . . . . . . . . . . . . . . . . . . . . . . . . . .,
Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,
Electric and Magnetic Unit Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . .,
1
1
2
2
General Constants and Units
2
Atoms and Molecules
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
Werner Diippen
Online Databases and Other Sources
Elements, Atomic Mass, and Solar-System Abundance . . . . . . . . . . . . . . . . . .
Excitation, Ionization, and Partition Functions . . . . . . . . . . . . . . . . . . . . . . .
Ionization Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electron Affinities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Atomic Cross Sections for Electronic Collisions . . . . . . . . . . . . . . . . . . . . . .
Atomic Radii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Particles of Modem Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plasmas
27
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Spectra
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
Charles Cowley, Wolfgang L Wiese, Jeffrey Fuhr, and Ludmila A. Kuznetsova
Online Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Terminology for Atomic States, Levels, Terms, etc. . . . . . . . . . . . . . . . . . . . .
Electronic Configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spectrum Line Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relative Strengths Within Multiplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wavelengths and Wave Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Atomic Oscillator Strengths for Allowed Lines . . . . . . . . . . . . . . . . . . . . . . .
Nuclear Spin and Hyperfine Structure: Low-Level Hyperfine Transitions . . . . . . .
Forbidden Line Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
7
7
8
12
13
17
22
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27
28
31
35
35
35
43
44
45
47
53
53
54
57
60
65
68
69
78
79
viii / CONTENTS
4.10
4.11
4.12
4.13
Spectra of Diatomic Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Energy Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Selection Rules: Dipole Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Radiation
5
J.J. Keady and D.P. Kilcrease
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
Radio Astronomy
Robert M. HjeUming
6
95
95
100
102
106
109
11 0
114
114
115
117
117
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Atmospheric Window and Sky Brightness . . . . . . . . . . . . . . . . . . . . . . . . . ..
Radio Wave Propagation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Radio Telescopes and Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Radio Emission and Absorption Processes. . . . . . . . . . . . . . . . . . . . . . . . . ..
Radio Astronomy References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
121
121
123
125
128
131
140
Infrared Astronomy
A. T. Tokunaga
Useful Equations; Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
7.1
7.2 Atmospheric Transmission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Background Emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
7.3
7.4 Detectors and Signal-to-Noise Ratios. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Photometry ().. < 30 JLm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
7.5
7.6 Photometry ().. > 30 JLm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Infrared Line List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7
7.8 Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
7.9 Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
7.10 Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
7.11 Extragalactic Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
143
143
144
146
148
149
154
155
158
161
163
164
6.1
6.2
6.3
6.4
6.5
6.6
7
Radiation Quantities and Interrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Refractive Index and Average Polarizability . . . . . . . . . . . . . . . . . . . . . . . . ..
Absorption and Scattering by Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Photoionization and Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
X-Ray Attenuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Absorption of Material of Stellar Interiors . . . . . . . . . . . . . . . . . . . . . . . . . ..
Absorption of Material of the Solar Photosphere . . . . . . . . . . . . . . . . . . . . . ..
Solar Photoionization Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Free-Free Absorption and Emission ...... . . . . . . . . . . . . . . . . . . . . . . ..
Reflection from Metallic Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Visual Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
83
85
87
89
8
8.1
8.2
8.3
8.4
8.5
Ultraviolet Astronomy
Terry J. Teays
Ultraviolet Wavelengths. . . . . . . . . . . . . . . .
Ultraviolet Astronomy Satellite Missions .... .
Significant Atlases and Catalogs. . . . . . . . . . .
Interstellar Extinction in the Ultraviolet . . . . . .
Commonly Observed Ultraviolet Emission Lines.
169
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169
170
172
174
175
CONTENTS
/
ix
8.6
8.7
Ultraviolet Spectral Classification . . . . . . . . . . . . . . . . . . . . . . . .
Ultraviolet Spectrophotometric Standards . . . . . . . . . . . . . . . . . . .
178
180
9.1
9.2
9.3
9.4
9.5
9.6
9.7
X-Ray Astronomy
Frederick D. Seward
Useful Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . .
Characteristic X-Ray Transitions . . . . . . . . . . . . . . . . . . . . . . ..
. .....
Emission Mechanisms and Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transmission of X-Rays Through the Interstellar Medium . . . . . . . . . . . . . . . . .
Cosmic X-Ray Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diffuse Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
X-Ray Astronomy Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
183
183
184
184
194
198
203
205
9
10
V-Ray and Neutrino Astronomy
R.E. Lingenfelter and R.E. Rothschild
10.1 Continuum Emission Processes . . . . . . . . . . . . . . . . .
10.2 Line Emission Processes . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3 Scattering and Absorption Processes . . . . . . . . . . . . . . . . . . .
10.4 Astrophysical v-Ray Observations . . . . . . . . . . . . . . . . . . . .
10.5 Neutrinos in Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . .
10.6 Current Neutrino Observatories . . . . . . . . . . . . . . . . . . . . . .
11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11
11.12
11.13
11.14
11.15
11.16
11.17
11.18
11.19
11.20
11.21
11.22
11.23
11.24
11.25
207
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Earth
Gerald Schubert and Richard L. Walterscheid
Oblate Ellipsoidal Reference Figure . . . . . . .
Mass and Moments of Inertia . . . . . . . . . . .
Gravitational Potential and Relation to Products of Inertia . . . . . . . . . . . .
Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rotation (Spin) and Revolution About the Sun . . . . . . . . . . . . . . . . . . .
Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Geoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solid Body Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Geological Time Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Glaciations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plate Tectonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Earth Crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Earth Interior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Earth Atmosphere, Dry Air at Standard Temperature and Pressure (STP)
Composition of the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . .
Water Vapor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Homogeneous Atmosphere, Scale Heights and Gradients . . . . . . . . .
Regions of Earth's Atmosphere and Distribution with Height . . . . . . .
Atmospheric Refraction and Air Path. . . . . . . . . . . . . . . . . . . . . .
Atmospheric Scattering and Continuum Absorption . . . . . . . . . . . . .
Absorption by Atmospheric Gases at Visible and Infrared Wavelengths .
Thermal Emission by the Atmosphere . . . . . . . . . . . . . . . . . . . . .
Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Night Sky and Aurora . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
207
208
213
216
235
237
239
240
240
241
243
244
245
245
246
246
248
251
252
252
255
257
258
259
259
260
262
265
268
270
271
279
I
x
CONTENTS
11.26 Geomagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
11.27 Meteorites and Craters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
282
285
Planets and Satellites
David J. Tholen, Victor G. Tejfel, and Arthur N. Cox
12.1 Planetary System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
12.2 Orbits and Physical Characteristics of Planets. . . . . . . . . . . . . . . . . . . . . . . ..
12.3 Photometry of Planets and Asteroids. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
12.4 Physical Conditions on Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.5 Names, Designations, and Discoveries of Satellites . . . . . . . . . . . . . . . . . . . . .
12.6 Satellite Orbits and Physical Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
12.7 Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.8 Planetary Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
293
293
294
298
300
302
303
308
311
Solar System Small Bodies
Richard P. Binzel, Martha S. Hanner, and Duncan I. Steel
13.1 Asteroids or Minor Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
13.2 Comets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.3 Zodiacal Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
13.4 Infrared Zodiacal Emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
13.5 Meteoroids and Intetplanetary Dust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
14
315
315
321
328
331
333
SUD
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
14.10
14.11
14.12
14.13
14.14
14.15
15
William C. Livingston
339
Basic Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 340
Interior Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . .. 341
Solar Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
Photospheric-Chromospheric Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 348
Spectral Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Spectral Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 353
Limb Darkening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 355
C o r o n a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
Solar Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
Granulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 364
Surface Magnetism and its Tracers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 364
Sunspots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 367
Sunspot Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
Flares and Coronal Mass Ejections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 373
Solar Radio Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
Normal Stars
John S. Drilling and Arlo U. Landolt
15.1 Stellar Quantities and Interrelations.
15.2 Spectral Classification. . . . . . . . .
15.3 Photometric Systems . . . . . . . . .
15.4 Stellar Atmospheres. . . . . . . . . .
15.5 Stellar Structure . . . . . . . . . . . .
381
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381
383
385
393
395
CONTENTS
16
/
xi
Stars with Special Characteristics
J. Donald Fernie
397
Variable Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Cepheid and Cepheid-Like Variables. . . . . . . . . . . . . . . . . . . . .. . . . . . . ..
Variable White Dwarf Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Long-Period Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rotating Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
T Tauri Stars ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Flare Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wolf-Rayet and Luminous Blue Variable Stars . . . . . . . . . . . . . . . . . . . . . . ..
Be Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Characteristics of Carbon-Rich Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Barium, CH, and Subgiant CH Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Hydrogen-Deficient Carbon Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Blue Stragglers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Peculiar A and Magnetic Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Galactic Black Hole Candidate X-Ray Binaries. . . . . . . . . . . . . . . . . . . . . . ..
Double Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
398
399
400
406
406
407
408
409
410
413
415
416
417
418
419
420
422
424
Cataclysmic and Symbiotic Variables
W.M. Sparks. S.G. Starrfield. E.M. Sion. S.N. Shore. G. Chanmugam.
and R.F. Webbink
17.1 Types of Cataclysmic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
17.2 Types of Symbiotic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
429
429
447
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
16.10
16.11
16.12
16.13
16.14
16.15
16.16
16.17
16.18
17
18
Supernovae
J. Craig Wheeler and Stefano Benetti
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
18.10
19
19.1
19.2
19.3
19.4
19.5
19.6
19.7
Spectral Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Older Population, Type Ia Supernovae. . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Young Population Supernovae. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
SN 1987A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Characteristic Spectral Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Radio Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Polarization.............................................
Supernova Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Old Supernovae, Historical Supernovae, and Supernova Remnants . . . . . . . . . . ..
Radioactive Decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
451
451
452
454
460
463
466
466
467
468
468
Star Populations and the Solar Neighborhood
Gerard F. Gilmore and Michael Zeilik
471
The Nearby Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 471
The Brightest Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
Stellar Populations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 478
Star Counts at High Latitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 480
Vertical Stellar Density Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 481
Main Sequence Field Stellar Luminosity Function. . . . . . . . . . . . . . . . . . . . .. 485
White Dwarf Luminosity Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 485
xii / CONTENTS
19.8
19.9
19.10
19.11
20
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
20.9
20.10
20.11
20.12
20.13
20.14
20.15
20.16
20.17
20.18
20.19
20.20
21
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9
21.10
22
Luminosity Class Distribution for Nearby Field Stars . . . . . . . . . . . . . . . . . . "
Mass Density in the Solar Neighborhood . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stellar Mass Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solar Motion and Kinematics of Nearby Stars . . . . . . . . . . . . . . . . . . . . . . . .
486
487
488
493
Theoretical Stellar Evolution
Arthur N. Cox, Stephen A. Becker, and W. Dean Pesnell
Basic Equations of Stellar Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stellar Nuclear Energy Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Stellar Opacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Electron Conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Element Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Mixing in Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Pre-Main-Sequence Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Main-Sequence Population I Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Main-Sequence Population II Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Stellar Winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Stellar Evolution Tracks: Massive and Intermediate-Mass Stars . . . . . . . . . . . . ..
Evolution to Red Giant Branch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Horizontal Branch Evolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Red Giant Mass-Loss Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Asymptotic Giant Branch Evolution ..... . . . . . . . . . . . . . . . . . . . . . . . ..
White Dwarfs and Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Binary Star Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Theory Versus Observation in the HR Diagram . . . . . . . . . . . . . . . . . . . . . . "
499
500
502
503
505
506
506
506
507
508
509
509
509
511
514
514
515
518
518
519
520
Circumstellar and Interstellar Material
John S. Mathis
Overview of the Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Galactic Interstellar Extinction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Abundances in Interstellar Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Line Emissions from the ISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
H2 and Molecular Clouds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Neutral Gas; Clouds; Depletions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hn Regions, Ionized Gas, and the Galactic Halo. . . . . . . . . . . . . . . . . . . . . ..
Planetary Nebulae (PNe) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cosmic Rays (Excluding Photons and Neutrinos) . . . . . . . . . . . . . . . . . . . . . .
523
523
527
529
530
532
534
536
538
540
541
Star Clusters
Hugh C. Harris and William E. Harris
545
22.1 Open Clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 545
22.2 Globular Clusters in the Milky Way. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 554
22.3 Globular Clusters in Other Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562
/
xiii
Milky Way and Galaxies
Virginia Trimble
23.1 Milky Way Galaxy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
23.2 Normal Galaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
569
569
576
CONTENTS
23
24
24.1
24.2
24.3
24.4
24.5
24.6
24.7
24.8
24.9
24.10
24.11
25
25.1
25.2
25.3
25.4
25.5
25.6
25.7
25.8
25.9
25.10
25.11
25.12
25.13
25.14
25.15
26
26.1
26.2
26.3
26.4
26.5
26.6
26.7
26.8
26.9
26.10
Quasars and Active Galactic Nuclei
Belinda J. Wilkes
Introduction.............................................
The TYPes of Active Galactic Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Catalogs and Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Commonly Measured Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Emission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Absorption Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spectral Energy Distributions (SEDs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Luminosity Functions and the Space Distribution of Quasars. . . . . . . . . . . . . . . .
BL Lacs, HPQs, and OVVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Low-Luminosity Active Galactic Nuclei (LLAGN) . . . . . . . . . . . . . . . . . . . . .
AGN Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Clusters and Groups of Galaxies
Neta A. Bahcall
Typical Properties of Clusters and Groups of Galaxies . . . . . . . . . . . . . . . . . . .
Cluster Catalogs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Catalog of Nearby Rich Clusters of Galaxies . . . . . . . . . . . . . . . . . . . . . . . .
Cluster Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cluster Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
cD Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Luminosity Function of Galaxies in Clusters . . . . . . . . . . . . . . . . . . . . . . . .
Mass Function of Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
X-Ray Emission from Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Sunyaev-Zeldovich Effect in Clusters . . . . . . . . . . . . . . . . . . . . . . . . . .
Clusters and Large-Scale Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Groups of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quasar-:-Cluster Association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Clusters as Gravitational Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Recent Results
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613
614
615
617
620
625
627
627
628
630
632
633
637
639
640
640
Cosmology
Douglas Scott, Joseph Silk, Edward W. Kolb, and Michael S. Turner
Friedmann-Robertson-Walker Metric and Distance Measures . . . . . . . . . . . . . .
The Age of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conversion Factors for the Early Universe . . . . . . . . . . . . . . . . . . . . . . . . . .
Other Useful Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cosmological Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Friedmann-Lemaitre Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Epochs of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Age Limits .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cosmological Tests: Ho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cosmological Tests: qO . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . .
585
585
586
591
593
595
601
602
605
607
608
608
643
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644
646
647
648
649
650
650
652
653
653
XIV
I
26.11
26.12
26.13
26.14
26.15
26.16
26.17
26.18
26.19
26.20
27
27.1
27.2
27.3
27.4
27.5
27.6
27.7
27.8
27.9
CONTENTS
Other Cosmological Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 654
Primordial Nucleosynthesis and Neutrinos. . . . . . . . . . . . . . . . . . . . . . . . . .. 654
Power Spectrum of Density Fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . .. 655
Structure Formation Scales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 656
Cosmic Microwave Background Anisotropies. . . . . . . . . . . . . . . . . . . . . . . .. 658
Large-Scale Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 659
Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660
Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 661
Intergalactic Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 662
Extragalactic Diffuse Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 663
Incidental Tables
Alan D. Fiala, William F. van Altena, Stephen T. Ridgway, and Roger W. Sinnott
The Julian Date. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Standard Epochs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Reduction for Precession . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Solar Coordinates and Related Quantities . . . . . . . . . . . . . . . . . . . . . . . . . ..
Constellations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Messier Objects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Optical and Infrared Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
The World's Largest Optical Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . ..
667
668
669
670
672
674
677
687
689
Index
701
667
Contributors
This list of the contributors gives the institution where the author did the bulk of the writing of the chapter
or section for this handbook. For those authors who participated only in a topic section, that subject is
briefly indicated.
Chapter 1
Arthur N. Cox
Los Alamos National Laboratory
David P. Kilcrease
Los Alamos National Laboratory
Sarah Stevens-Rayburn
Space Telescope Science Institute
Astrophysical Journals
Chapter 6
Robert M. Hjellming
National Radio Astronomy Observatory
Chapter 2
Arthur N. Cox
Los Alamos National Laboratory
Chapter 7
Alan T. Tokunaga
University of Hawaii
Alan D. Fiala
United States Naval Observatory
Astronomical Constants, General and Time
Chapter 8
Terry J. Teays
Goddard Space Fight Center
Chapter 3
Werner Dappen
University of Southern California
Chapter 9
Fredrick D. Seward
Smithsonian Astrophysical Observatory
Chapter 4
Charles R. Cowley
University of Michigan
Chapter 10
Richard E. Lingenfelter
University of California-San Diego
Wolfgang L. Wiese
National Institute of Standards and Technology
Jeffrey Fuhr
National Institute of Standards and Technology
Richard E. Rothschild
University of California-San Diego
Ludmila A. Kuznetsova
Moscow State University
Thomas J. Bowles
Los Alamos National Laboratory
Neutrino Observatories
Chapter 5
John J. Keady
Los Alamos National Laboratory
Wick C. Haxton
University of Washington
Neutrino Observations
xv
xvi / CONTRIBUTORS
Chapter 11
Gerald Schubert
University of California-Los Angeles
Pierre Demarque
Yale University
Solar Model
Richard L. Walterscheid
The Aerospace Corporation
David B. Guenther
St. Mary's University
Solar Model
David Crisp
Jet Propulsion Laboratory/California Institute
of Technology
Earth Atmosphere Scattering, Absorption,
Emission
Chapter 12
David J. Tholen
University of Hawaii
Victor G. Tejfel
Fessenkov Astrophysical Institute
Arthur N. Cox
Los Alamos National Laboratory
Glenn S. Orton
Jet Propulsion Laboratory/California Institute
of Technology
Physical Conditions on Planets
DanPascu
United States Naval Observatory
Names, Designations, and Discoveries of
Satellites, Satellite Orbits and Physical
Elements
Frank Hill
National Solar Observatory
Solar Oscillations
Eugene Avrett
Harvard-Smithsonian Center for Astrophysics
Photospheric Model
Oran R. White
High Altitude Observatory
Solar Spectral Lines
Heinz Neckel
Hamburger Sternwarte
Solar Spectral Energy Distribution
A. Keith Pierce
National Solar Observatory
Solar Limb Darkening
Serge Koutchmy
Institut d' Astrophysique
Solar Corona
Robert F. Howard
National Solar Observatory
Solar Rotation
Chapter 13
Richard P. Binzel
Massachusetts Institute of Technology
Richard Muller
Observatoire Pic du Midi
Granulation
Martha S. Hanner
Jet Propulsion Laboratory/California Institute
of Technology
Peter V. Foukal
Cambridge Research and Instrumentation, Inc.
Surface Magnetism and Tracers
Duncan I. Steel
University of Salford, UK
Sami Solanki
Institute of Astronomy, ETH-Zentrum
Surface Magnetism and Tracers, Sunspots
Chapter 14
William C. Livingston
National Solar Observatory
Jack B. Zirker
National Solar Observatory
Surface Magnetism and Tracers
CONTRIBUTORS /
xvii
Karen L. Harvey
Solar Physics Research Corporation
Sunspot Statistics
Peter S. Conti
University of Colorado
Wolf-Rayet and Luminous Blue Variable Stars
Peter Wilson
University of Sydney
Sunspot Statistics
Arne Slettebak
Ohio State University
Be Stars
Stephen W. Kahler
United States Air Force Research Laboratory
Flares, CMEs
Myron Smith
Computer Science Corporation
Be Stars
Timothy Bastian
National Radio Astronomy Observatory
Solar Radio Emission
Cecilia S. Bambaum
University of California-Berkeley
Characteristics of Carbon-rich Stars
Chapter 15
John S. Drilling
Louisiana State University
Arlo U. Landolt
Louisiana State University
Normal Stars
James W. Liebert
University of Arizona
White Dwarf Spectral Classification
Edward M. Sion
Villanova University
White Dwarf Spectral Classification
Chapter 16
J. Donald Fernie
David Dunlap Observatory
Douglas S. Hall
Vanderbilt University
Variable Stars, Rotating Variables, Flare Stars
Paul A. Bradley
Los Alamos National Laboratory
Variable White Dwarf Tables
Gibor S. Basri
University of California-Berkeley
T Tauri Stars
Kenneth R. Brownsberger
University of Colorado
Wolf-Rayet and Luminous Blue Variable Stars
William Dean Pesnell
Nomad Research, Inc.
Barium, CH, and Subgiant CH Stars
Warrick Lawson
Australian Defence Force Academy
Hydrogen Deficient Carbon Stars
Peter J. T. Leonard
Goddard Space Flight Center
Blue Stragglers
KaiyouChen
Los Alamos National Laboratory
Pulsars
John Middleditch
Los Alamos National Laboratory
Pulsars
Jonathan E. Grindlay
Harvard College Observatory
Galactic Black Hole Candidate X-Ray Binaries
Chapter 17
Warren M. Sparks
Los Alamos National Laboratory
Sumner G. Starrfield
Arizona State University
Edward M. Sion
Villanova University
Steven N. Shore
Indiana University South Bend
xviii / CONTRIBUTORS
Ganesh Chanmugam
Louisiana State University
Ronald F. Webbink
University of lllinois
Chapter 18
J. Craig Wheeler
University of Texas
William E. Harris
McMaster University
Chapter 23
Virginia Trimble
University of California-Irvine and University
of Maryland
Stefano Benetti
European Southern Observatory
Chapter 24
Belinda J. Wilkes
Smithsonian Astrophysical Observatory
Chapter 19
Gerard F. Gilmore
Cambridge University
Chapter 2S
Neta A. Bahcall
Princeton University
Michael Zeilik
University of New Mexico
Chapter 20
Arthur N. Cox
Los Alamos National Laboratory
Stephen A. Becker
Los Alamos National Laboratory
Chapter 26
Douglas Scott
University of British Columbia
Joseph Silk
University of California-Berkeley
Edward W. Kolb
Fermi National Accelerator Laboratory
William Dean Pesnell
Nomad Research, Inc.
Barium, CH, and Subgiant CH Stars
Michael S. Turner
The University of Chicago
Chapter 21
John S. Mathis
University of Wisconsin
Chapter 27
Alan D. Fiala
United States Naval Observatory
Donald P. Cox
University of Wisconsin
Cosmic Rays Excluding Photons and Neutrinos
William F. van Altena
Yale University
Jonathan F. Ormes
Goddard Space Flight Center
Cosmic Rays Excluding Photons and Neutrinos
Chapter 22
Hugh C. Harris
United States Naval Observatory
Stephen T. Ridgway
National Optical Astronomy Observatory
Roger W. Sinnott
Sky and Telescope
Karl Parker
Sky and Telescope
Largest Optical Telescopes
Chapter
1
Introduction
Arthur N. Cox
1.1
Background. . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Astronomical Symbols . . . . . . . . . . . . . . . . . .
2
1.3
Astronomical and Astrophysical Journals . . . . . . .
2
1.1 BACKGROUND
This handbook is a revision of the third edition of Allen's Astrophysical Quantities [1], published in
1973, with further printings in 1976, 1981, and 1983. An attempt has been made to follow the original
format, but the great advances in astronomical and astrophysical subfields have made this very difficult.
More modern styles have been adopted, and many more subjects have been included. However, the
original concept to present a rather concise, but still extensive, listing of astrophysical quantities has
been retained. It is expected that scientists can use this book for quick information and also for key
references to more detailed data sources.
One concept was that this handbook be a companion to A Physicist's Desk Reference, the second
edition of Physics Vade Mecum, edited by Herbert L. Anderson. That book also has a long author list,
and its currently planned revision will undoubtedly include even more.
To allow for space to present information for newly developed astronomical and astrophysical
subfields, some more classical material has been deleted. Reference to the older Allen editions might
be necessary.
The current fields are so extensive that we needed 90 authors. They are indicated either as
chapter authors or authors of individual sections. All were asked to present their information using
the electronic editing language M1EX 2e , so that the submissions to the publisher could be almost
camera ready. Not all authors could completely comply with this policy, and the editor, with help from
the publisher, occasionally needed to reformat the material. With so many involved, including the
copyeditors, it is easy to see why it is important to keep the presentation style as consistent as possible.
One hope is that the electronic files now available for this book can be revised in the coming years,
and an updated version can be published more easily. With the extensive use of the World Wide Web
1
2/1
INTRODUCTION
by so many scientists, it is conceivable that individual chapters can be updated after some years and
made available there. At least future revisions should be easier to produce based on the very great
efforts over most of eight years by all the authors.
The editor requested authors to update their information to about the end of 1997 or later.
Obviously this has not been completely successful. For questions and corrections, readers should
consult individual authors, mostly since no one single individual can know more than a fraction of the
knowledge of the entire area of astronomy and astrophysics.
Just a small part of the Allen introduction chapter has been retained here.
1.2 ASTRONOMICAL SYMBOLS
The standard symbols for astronomical objects and zodiacal areas are given in Table 1.1.
Table 1.1. Sun, Moon, planetary, zodiacal, and orbit symbols [1, 2].
Symbol
*
,
~
0
4{'
y
€9
:!:=
/
"""
n
Name
Star
Mercury
Mars
Saturn 2
Neptune 2
Aries (0°)
Cancer (90°)
Libra (180°)
Sagittarius (240°)
Aquarius 2 (300°)
Ascending Node
Autumnal Equinox
Symbol
Name
Symbol
0
Sun
Venus
Jupiter
Uranus
Pluto
«:
9
4
0
I?
8
~
~
-t5
~
U
l'
Taurus (30°)
Leo (120°)
Libra 2 (180°)
Capricornus (270°)
Aquarius 3 (300°)
6
h
W
t)
:n:
I1lJ
In
~
}{
Name
Moon
Earth
Saturn
Neptune
Pluto 2
Gemini (60°)
Virgo (150°)
Scorpio (210°)
Aquarius (300°)
Pisces (330°)
Descending Node
Vernal Equinox
References
1. Rahtz, S. & Rose, K. ftp to sunsite.unc.edu in directory publpackageslfeX/cmastro
2. Schmitt, P. 1992, ftp to sunsite.unc.edu in directory pub/packageslfeX/astro
1.3
ASTRONOMICAL AND ASTROPHYSICAL JOURNALS
by Sarah Stevens-Rayburn
The names of 51 journals thought to be of interest to readers with an astronomy and astrophysics
background is given together with their first publication dates and the current publisher. Many of
these journals are now available electronically on the World Wide Web. Note that the older European
journals, Annales d'Astrophysique, Bulletin o/the Astronomical Institutes o/the Netherlands, Bulletin
Astronomique, Journal des Observateurs, Zeitschrift jUr Astrophysik, and a few other smaller ones have
been discontinued and have been replaced by Astronomy and Astrophysics.
1.3 ASTRONOMICAL AND ASTROPHYSICAL JOURNALS
Acta Astronomica
1925
Acta Astronomica Sinica = Tien wen hsueh
pao
Acta Astrophysica Sinica = Tien t i wu Ii
hsueh pao
Acta Cosmologica
Annual Review of Astronomy and Astrophysics (ARA&A)
Annual Review of Earth and Planetary Sciences
The Astronomical Journal (AJ)
1953
/
3
1973
1963
Warsaw: Copernicus Foundation for Polish
Astronomy
Beijing, China: Science Press Beijing: K' 0
hsueh ch'u pan she
Beijing, China: Science Press Beijing: K'o
hsueh ch'u pan she
Krakow: Uniwersytet Jagiellonski
Palo Alto, Calif.: Annual Reviews, Inc.
1973
Palo Alto, Calif.: Annual Reviews. Inc.
1894
Chicago: University of Chicago Press for the
American Astronomical Society
Berlin: Wiley-VCH
Berlin: Springer. on behalf of the Board of
Directors
Berlin: Springer on behalf of the Board of
Directors
Les Ulis, France: EDP Sciences on behalf of
the Board of Directors
Bristol: Institute of Physics Publishing Ltd.
for the Royal Astronomical Society
1981
Astronomische Nachrichten
Astronomy and Astrophysics (A&A)
1823
1869
The Astronomy and Astrophysics Review
(A&A Rev)
Astronomy & Astrophysics Supplement series
(A&AS)
Astronomy & Geophysics The Journal of
the Royal Astronomical Society (continues
QJRAS, 1960-1996)
Astronomy Letters (continues Soviet Astronomy Letters, 1975-1992)
1989
Astronomy Reports (continues Soviet Astronomy, 1974-1992, which continues Soviet
Astronomy AJ, 1957-1973)
The Astrophysical Journal (ApJ)
1993
The Astrophysical Journal Supplement series
(ApJS)
Astrophysical Letters & Communications
(Astrophys. Lett) (continues Astrophysical
Letters, 1967-1987)
Astrophysics
1954
Astrophysics and Space Science (Ap&SS)
Astrophysics Reports: Publications of the
Beijing Astronomical Observatory (continues Publications of the Beijing Astronomical Observatory, 1987-1994)
Astrophysics Reports: Publications of the
Beijing Astronomical Observatory (Supplement series)
Baltic Astronomy: An International Journal
1968
1994
Boletin / Asociacion Argentina de Astronomia
1958
1970
1997
1993
1895
1987
1965
Moscow: Maik NaukalInterperiodica Publishing, distributed by the AlP (translation
of Pisma v astronomicheskii zhurnal)
Moscow: Maik NaukalInterperiodica Publishing, distributed by the AlP (translation
of Astronomicheskii zhurnal)
Chicago: University of Chicago Press for the
American Astronomical Society
Chicago: University of Chicago Press for the
American Astronomical Society
New York: Gordon and Breach
New York: Consultants Bureau (translation of
Astrofizika)
Dordrecht: Kluwer Academic
Beijing, China: Beijing Astronomical Observatory, Chinese Academy of Sciences
1997
Beijing, China: Beijing Astronomical Observatory, Chinese Academy of Sciences
1992
Vilnius: Institute of Theoretical Physics and
Astronomy
La Plata: La Asociacion
4/1
INTRODUCTION
Bulletin of the Astronomical Society of India
Celestial Mechanics and Dynamical Astronomy (continues Celestial Mechanics,
1973
1989
Hyderabad: Astronomical Society of India
Dordrecht: Kluwer Academic
Chinese Astronomy and Astrophysics (continues Chinese Astronomy, 1977-1980)
Earth, Moon, and Planets (continues The
Moon and Planets, 1978-1983, which continues The Moon, 1969-1977)
Experimental Astronomy
Icarus
International Journal of Modem Physics, D
Gravitation, Astrophysics, Cosmology
The Irish Astronomical Journal
Journal for the History ofAstronomy
Journal ofAstrophysics and Astronomy
Journal of Geophysical Research. A, Space
Physics (J. Geophys. Res. A) (continues in
part Journal of Geophysical Research, -
1981
Kidlington, Oxford; Elsevier Science
1984
Dordrecht: Kluwer Academic
1989
1962
1992
Dordrecht: Kluwer Academic
Orlando: Academic Press
Singapore: World Scientific
1950
1970
1980
1949
Sheffield: IAJ Editorial Board
Cambridge: Science History Publications
Bangalore: Indian Academy of Sciences
Washington, DC: American Geophysical
Union
1991
Washington,
Union
1907
1872
Toronto: Royal Astronomical Society of
Canada
Firenze: Societa Astronomica Italiana
1940
Observatory, S.A.: The Society
1931
Edinburgh: Blackwell Science for the Royal
Astronomical Society
1869
1877
London: Macmillan Magazines Ltd.
Chilton, Didcot, Oxon: Editors of The Observatory
Kidlington, Oxford: Elsevier Science Ltd.
1969-1988)
1949)
Journal of Geophysical Research. E, Planets
(J. Geophys. Res. E) (continues in part
Journal of Geophysical Research, -1990)
The Journal of the Royal Astronomical Society of Canada (JRASC)
Memorie della Societa Astronomica Italiana
(Mem. Soc. Astron. Italiana)
Monthly Notes of the Astronomical Society of
Southern Africa
Monthly Notices of the Royal Astronomical
Society (MNRAS) (continues Monthly Notices of the Astronomical Society of London, 1927-1931)
Nature
The Observatory
Planetary and Space Science (Planet. Space
Sci.)
Publications / Astronomical Society of Australia (continues Proceedings of the Astronomical Society of Australia, 1967-1994)
Publications of the Astronomical Society of
Japan (PASJ)
Publications of the Astronomical Society of
the Pacific (PASP)
Revista Mexicana de Astronomia y Astrofisica
1959
Science
1883
DC: American Geophysical
1995
Australia: Published for the Astronomical
Society of Australia by CSIRO, Australia
1949
Tokyo: Astronomical Society of Japan
1889
Chicago: University of Chicago Press for the
Astronomical Society of the Pacific
Mexico D.E: Instituto de Astronomia, Universidad Nacional Autonoma de Mexico
Washington: American Association for the
Advancement of Science
1974
1.3 ASTRONOMICAL AND ASTROPHYSICAL JOURNALS
Solar Physics (Sol. Phys.)
Southern Stars
1967
1934
Space Science Reviews (Space Sci. Rev)
Zvaigznota debess
1962
1958
/
5
Dordrecht: Kluwer Academic
Wellington. N.Z.: Royal Astronomical Society of New Zealand
Dordrecht: Kluwer Academic
Riga: Zinatne
REFERENCES
1. Allen, C.W. 1973, Astrophysical Quantities (Ath1one Press, London)
Chapter
2
General Constants and Units
Arthur N. Cox
2.1
2.1
Mathematical Constants
7
2.2
Physical Constants
8
2.3
General Astronomical Constants
12
2.4
Astronomical Constants Involving Time
13
2.5
Units . . .
2.6
Electric and Magnetic Unit Relations.
..
17
MATHEMATICAL CONSTANTS [1-3]
Constant
Number
7r
27r
47r
7r 2
3.1415926536
6.283 185 3072
12.5663706144
9.8696044011
1.7724538509
2.7182818285
vrr
eore
mod = M = loge
I/M=lnlO
2
..ti
v'3
00
0.434294481 9
2.302585 093 0
2.0000000000
1.4142135624
1.732050 807 6
3.1622776602
7
Log
0.497149872 7
0.7981798684
1.099209864 0
0.9942997454
0.2485749363
0.434294481 9
0.6377843113 - 1
0.3622156887
0.301 0299957
0.1505149978
0.238 5606274
0.500 000 000 0
22
8/2
GENERAL CONSTANTS AND UNITS
Constant
In rr
e1r
Euler constant y
1 radian
Number
1.144 729 885 8
23.1406926328
0.577 215 6649
rad = 57?295 779 513 1
= 3437~74677078
= 206 264~'806 25
1° =0~0174532925
I' = O!"lldOOO 290 888 2
1/1 = O!"lldOOO 004 848 1
Log
0.058 703 021 2
1.364 376 3538
0.7613381088- 1
1.7581226324
3.5362738828
5.3144251332
0.241877 3676 - 2
0.463 726 1172 - 4
0.6855748668 - 6
Square degrees on a sphere = 129600/rr = 41252.96125.
Square degrees in a steradian = 32400/rr 2 = 3282.806 35.
. d'IStn'b'
tior GaUSSlan
utlon
1~ exp
uv2rr
(x2
)
-2
2u
.
Probable error/Standard error = r/u = 0.6744897502.
Probable error/Average error = r/rJ = 0.8453475394.
u/rJ = 1.253314137.
p = (r/u)/..ti = 0.4769362762.
2.2
PHYSICAL CONSTANTS [4,5]
These fundamental physical constants, mostly in SI units from [5], are the latest available. A revision
by Cohen and Taylor is expected by the end of 1998. For many values, the standard error of the last
digits follows in parentheses. In the formulations the electron charge e is in esu and e in emu = e/c.
Fundamental constants
Speed of light (exact)
Gravitation constant
Standard acceleration of gravity (exact)
Planck constant
Planck mass
Planck length
Planck time
Elementary charge
Mass of electron
c
c2
G
gn
= 2.99792458 X 108 ms- 1
= 8.98755179 x 10 16 m2 s-2
= 6.67259(85) X 10- 11 m3 kg- 1 s-2
= 9.80665 ms- 1
2rrli = h = 6.6260755(40) X 10-34 Js
Ii = 1.054572 66(63) x 10-34 J S
(Iic/G)I/2 = 2.17671(14) x 10-8 kg
(IiG/c 3 )1/2 = 1.61605(10) x 10-35 m
(IiG/c 5 )1/2 = 5.39056(34) x 10-44 s
e = 4.803206 8(15) x 10- 19 C
e = 1.60217733(49) x 10-20 emu
e 2 = 23.070796 x 10-20 in esu
e4 = 5.3226161 x 10-38 in esu
me = 9.1093897(54) x 10-31 kg
= 5.48579903(13) X 10-4 u
2.2 PHYSICAL CONSTANTS
Mass of unit atomic weight
( 12C = 12 scale)
Boltzmann constant
e
Gas constant 2C scale)
Joule equivalent (chemical, exact) [4]
Avogadro constant
Loschmidt constant
Volume of gram-molecule at STP
(T = 273.15 K, P = 101 325 Pa)
Standard atmosphere pressure (exact)
Ice point
Triple point (H20)
Faraday
Atomic constants
Rydberg constant for IH
Rydberg constant for infinite nuclear mass
2rr2mee4/ch3
Fine structure constant
2rre 2/ hc
Radius for first Bohr orbit
(infinite nuclear mass) h 2/4rr 2m ee 2
Time for (2rr) -1 revolutions in first
Bohr orbit m!/2a 3/ 2e- 1 = h 3/8rr 3m ee 4
Frequency of first Bohr orbit
Area of first Bohr orbit
Electron speed in first Bohr orbit
Atomic unit of energy
(Hartree = 2 Rydbergs) e 2 /ao = 2chRoo
Energy of Rydberg
(often adopted as atomic unit)
Atomic unit of angular momentum h /2rr
Classical electron radius e 2 / moc 2
SchrOdinger constant for fixed nucleus
SchrOdinger constant for 1H atom
/
9
u = 1.6605402(10) x 10-27 kg
k = 1.380658(12) x 10-23 JK- 1
= 8.617385(73) x 10-5 eVK- 1
10-8 ergl/2 K-l/2
R = 8.314510(70) JK- 1 mol- 1
= 1.987216 calK-l mol- 1
= 82.05783(70)
cm3 atmK- 1 mol- 1
= 4.184 J cal- 1
NA = 6.0221367(36) x 1023 mol- 1
no = 2.686763(23) x 1025 m- 3
NA/no = Vo = 22.41410(19) x 10-3
m3 mol- 1
Po = 1013 250 dyn cm- 2
= 760mmHg
0° C = 273.150 K
= 273.160K
NM/C = 96485.309(29) C mol- 1
k 1/ 2
= 1.175014 x
RH = 10967758.306(13) m- 1
1/ RH = 911.7633450 A
Roo = 10973731.534(13) m- 1
1/ Roo = 911.2670534 A
cRoo = 3.289841950 x 1015 s-1
a = 7.29735308(33) x 10-3
l/a = 137.0359895(61)
a 2 = 5.325 13620 x 10-5
ao = 0.529177249(24) x 10- 10 m
1"0
= 2.4188844 x
10- 17 s
= 6.5796837 x
1015 s-1
rra5 = 8.79735670 x 10-21 m2
2.1876914 x 106 ms- 1
4.3597482(26) x 10- 18 J
27.2113961(81) eV
2.1798741(13) x 10- 18 J
= 13.605698 1(40) eV
Ii = 1.05457266(63) x 10-34 kgm2s- 1
1= 2.81794092(38) x 10- 15 m
8rr2meh-2 = 1.63819748 x 1027 erg- 1 cm- 2
= 1.63730578 x 1027 erg-l cm- 2
ao1"OI =
=
=
ryd =
10 /
2
GENERAL CONSTANTS AND UNITS
Hyperfine structure splitting of I H
VH
ground state
Doublet separation in IH atom
(1/16)RHa 2 [1 + a/7f + (5/8 - 5.946/7f 2 )a 2 ]
Reduced mass of electron in IH atom
me(mp/mH)
Mass of IH atom
Mass of proton
Mass of neutron
Mass of deuteron
Mass energy of unit atomic mass
Rest mass energy of electron
Mass ratio proton/electron
Specific electron charge
Quantum of magnetic flux
Quantum of circulation
Compton wavelength
Band spectrum constant
(moment of inertia/wave number)
Atomic specific heat constant
C2/C
= h/k
Electron magnetic moment
Proton magnetic moment
Gyromagnetic ratio of proton
corrected for diamagnetism of H20
Magnetic moment of 1 nuclear magneton
/Le
/Lp
Yp
he/47fmpc
Atomic unit of magnetic moment
2/LB/a
Magnetic moment per mole of 1 Bohr
magneton per molecule
Zeeman displacement
3/47fme c (e in emu)
in frequency
= 0.365 866231 cm- I
= 1.096839 36x 1010 s-I
= 9.1044313 x
=
=
= 4.799216 X
/LB
= he/47fmec
1420.405751768 x 106 s-I
10-31 kg
1.6735344 x 10-27 kg
1.007825050(12) u
= 1.6726231(10) x 10-27 kg
= 1.007276470(12) u
= 1.6749286(10) x 10-27 kg
= 1.008664 904(14) u
= 3.3435860(20) x 10-27 kg
= 2.013 553 214(24) u
uc2 = 1.4924191 x 10- 10 J
= 931.4942(28) MeV
mec2 = 8.1871111 x 10- 14 J
= 0.51099906(15) MeV
= 1836.152701(37)
e/me = 1.75881962 x 107 emu g-I
e/me = 5.2728086 x 10 17 esu g-I
hie = 1.37951077 x 10- 17 erg s esu- I
hc / e = 4.135 669 2 x 10-7 gauss cm2
h/me = 7.2738962 erg s g-I
h/mec = 2.42631058(22) x 10- 12 m
h/27fmec = 3.86159323(35) x 10- 13 m
h/87f 2c = 27.992774 x 10-40 g cm
Magnetic moment of 1 Bohr magneton
1/2 5/2 -I
I
/LB='i.ame ao t'o
=
/Ln
IO- II sK
= 9.2740154(31) x
10-21
I
erg gauss= 1.001159652193(1O)/LB
= 1.521032202(15) x 1O-3/LB
= 2.67522128(81) x 104
rad S-I gauss- I
= 5.0507866(17) x 10- 24
erg gauss- I
= 2.5417478 x 10- 18 erg gauss- l
= 5584.9388 erg gauss- I mol- l
= 4.6686437(14) x 10-5
cm- I gauss- l
= 1.39962418(42) x 106
s-l gauss- l
2.2 PHYSICAL CONSTANTS
The electron-volt and photons [5]
Wavelength associated with 1 eV
Wave number associated with 1 e V
Frequency associated with 1 eV
Energy of 1 eV
Photon energy associated with unit
wavenumber
Photon energy associated with
wavelength A
Speed of 1 e V electron
(2 x 108 (e/mec»1/2
Speed2
Wavelength of electron of energy V in e V
h(2me E O)-1/2V- I / 2
Temperature associated with 1 eV
Eo/k
Temperature associated with 1 eV
in common logs = (Eo/ k) log e
Temperature associated with 1 kilo-kayser
in common logs = 1<P(hc/ k) loge
Energy of 1 e V per molecule
Radiation constants
Radiation density constant
87l' 5k4 /15c 3 h 3
Stefan-Boltzmann constant = ac/4
First radiation constant
(emittance) = 27l' hc 2
First radiation constant (radiation density)
Second radiation constant = hc/ k
Wien displacement law constant
c2/4.965 11423
Some general constants [1,5]
Density of mercury (00 C, 760 mmHg)
Ratio, grating to Siegbahn scale
of X-ray wavelengths [5]
Lattice spacing of Si (in vacuum, 22.50 C)
Molar volume of Si
Maximum density of water
Cesium resonance frequency
(defining the SI second) [6]
=
So =
=
V() =
Eo =
=
hc =
AO
/
11
12398.4282 x 10- 10 m
8065.53851 cm- I
8.065 538 51 kilo-kayser
2.41798836(72) x 1014 s-I
1.602177 33(49) x 10- 19 J
0.0734986176 ryd
1.9864480 x 10-23 J
= 1.9864480 x 1O-8 /A erg (A in A)
= 5.93096892 x
= 3.517 639 23
=
lOS m s-I
x lOll m 2 s-2
263 x 10-8 ) cm
V- I / 2 (12.264
= 11604.45 K
= 5039.75 K
= 624.8493 K
= 23060.0542 cal mol- I
a = 7.56591(25) x 10- 15
ergcm-3 K-4
u = 5.67051(19) x 10-5
erg cm-2 K- 4 s-I
CJ = 3.7417749(22) x 10-5
erg cm2 s-I
87l' hc = 4.9924870 x 10- 15 erg cm
C2 = 1.438769(12) cm K
= 0.2897755
= 13.395080 g cm- 3
Ag/ As = 1.002077 89(70)
[As (Cu Kal) = 1.537400 kXu]
= 0.543 101 96(11) x 10-9 m
= 12.058 817 9(89) cm3 mol- I
= 0.999972 g cm-3
= 9192631770 Hz
12 / 2
2.3
GENERAL CONSTANTS AND UNITS
GENERAL ASTRONOMICAL CONSTANTS
by Alan D. Fiala
Astronomical unit of distance
Parsec (= 206264.806 AU)
Light (Julian) year
Light time for 1 AU [6]
Solar mass
Solar radius
Solar radiation
Earth mass
Earth mean density
Earth equatorial radius [6]
= mean Sun-Earth distance
= semimajor axis of Earth orbit [2, 6].
AU = 1.495978706 6 x lOll m.
pc = 3.085 677 6 x 10 16 m.
= 3.261 5638 light (Julian) year.
= 9.460730472 x 1015 m.
= 499.004 783 70 s = 0.00577551833 d.
M0 = 1.9891 x 1030 kg.
'R0 = 6.95508 ± 0.00026 x 108 m.
£0 =3.845(8) x 1033 ergs-I.
Me = 5.9742 x 1024 kg.
Pe = 5.515 g cm- 3.
= 6378.136 km.
Galactic pole (J2000.0)
GY3 = 192?85948123
83
Direction of galactic center (J2000.0)
Solar motion toward galactic center [7]
toward direction of galactic rotation
vertically up in north direction
Galactic rotation [8]
Sun's equatorial horizontal parallax [6]
Moon's equatorial horizontal parallax
at mean distance
Constant of nutation [6]
Constant of aberration [6]
21l' x 206265 x AU
= +27?12825120
+ 27°7'41 ~'704
81 = -28?93617242
GYI = 266.40499625
17h45m37~ 1991
-28°56' 1O~'221
U = 10.00 ± 0.36 km s-1
V = 5.23 ± 0.62 kms- i
w= 7.17±0.38kms- 1
Ro = 7.66 ± 0.32 kpc
Vcirc =
237 ± 12 kms- 1
= 8~'794144(3)
= 4.263521 x 10-5 rad
= 3422~'608
12h51m26~2755
=
=
9~'2025
20~'495 52
ct(1 - e2 )1/2
t = sidereal year, e = Earth orbital
eccentricity
Gaussian gravitational constant k
in n 2 a 3 = k 2 (1 + m), where m = mass
of planet in solar units, n = mean daily in AU
motion, and a = semimajor axis
(a defining constant)
k/86400 = 21l' /(sidereal year in sec)
Heliocentric gravitational constant = AU3(k')2
Semimajor axis of Earth orbit in tenns of AU
k = 0.01720209895 rad
= 3548~'187 607
= 0?985 607 668 6
k' = 1.990 983675 x 10-7 rad,
for use with seconds of time
= 1.32712440 x 1026 cm2 S-i
= 1.00000105726665 AU
2.4
ASTRONOMICAL CONSTANTS INVOLVING TIME
Mass ratios [6,9]
Me/Mrt.
M0/ M e
M 0 /(M e +Mrt.}
Obliquity of ecliptic (fixed ecliptic of J2000.0)
/
13
= 81.30059
= 332946.05
= 328900 56(2}
E = 23°26'21~'4119
2.4 ASTRONOMICAL CONSTANTS INVOLVING TIME [6]
by Alan D. Fiala
The basic unit of time is the Systeme International (SI) second which is defined to be the duration
of 9 192631 770 cycles of one of the hyperfine transitions of the ground state of l33Cs. Based on
this defined unit, International Atomic Time (TAl) is formed from statistical analysis of individual
frequency standards and time scales based on atomic clocks in many countries. It was introduced in
January 1972, and is a coordinate time scale.
Universal Time (UT) is the measure of time used for all civil time keeping, and conforms closely
to the mean diurnal motion of the Sun. It is directly related to sidereal time by means of an adopted
numerical formula. It does not refer to the motion of the Earth and is not precisely related to the hour
angle of the Sun.
UTO is the uncorrected observed rotational time scale derived from observation of sidereal time at a
particular station. When this time scale is corrected for the shift in longitudes caused by polar motion,
it is designated UTI. This still contains the variable rotation of the Earth and is generally implied when
the symbol .oUT" is used without qualification.
Coordinated Universal Time (UTC) is the time scale distributed by radio signals, satellites,
communication media, as the basis for civil time keeping around the world. UTC is maintained within
0.9 second of UTI by the introduction of leap seconds. UTC differs from TAl by an integer number of
seconds, which difference changes when leap seconds are introduced.
Dynamical time represents the independent variable of the equations of motion of the bodies in the
Solar System. It depends on the theory of relativity being used, as does the transformation between
barycentric and geocentric time scales. In the transformation, the constants can be chosen so that
the timescales have only periodic variations with respect to each other. The dynamical time scale
for apparent geocentric ephemerides was chosen to be unique and independent of the theories; the
barycentric timescales are theory dependent.
Terrestrial Dynamical Time (TDT), or Terrestrial Time (TT), is the idealized time on the geoid
of the Earth and is approximated as being equal to TAl + 32.184 seconds. Terrestrial Time is a
continuation of Ephemeris TIme (ET), beginning 1977 Jan. 1.0 TAl. The relationship between UT
and TT changes according to the variations in the rotation of the Earth.
Barycentric Dynamical Time (TDB) is the relativistically transformed time for referring equations
of motion to the barycenter of the Solar System. It is defined to contain only periodic variations with
respect to TDT.
The time scales Geocentric Coordinate TIme (TCG) and Barycentric Coordinate Time (TCB) are
the time-like arguments appropriate for coordinate systems defined with respect to the geocenter of the
Earth and the barycenter of the Solar System, respectively, including all relativistic transformations
from terrestrial time.
Up to 1984, the tropical year was used as the basis of time for reference systems and the Besselian
year was used as the epoch for such reference frames, thus designated, for example, as B 1950.0. Since
1984, the Julian Century has been used as the time unit for reference frames and the standard epoch is
then designated as, for example, J2000.0.
14 / 2
GENERAL CONSTANTS AND UNITS
Sidereal time is defined by the hour angle of the equinox. The relationship between Greenwich
Mean Sidereal Time (GMST) and UTt is specified by an adopted equation, which is often considered
to be the definition of UTI. At 0 hours UTI:
GMST
= 24110.54841 + 8640184~812866Tu + 0~093104T; -
6.2 x 1O-6 T,;
seconds of time, where Tu = du /36525, du is the number of days of Universal Time elapsed since JD
2451545.0 UTt (2000 January 1, 12 hrs UTI), taking on values ±0.5, ±1.5, etc.
The ratio of mean sidereal time to UTI is
r'
= 1.002737909350795 + 5.900 6 x
1O- 11 T - 5.9 x 10- 15 T2,
where T is the number of Julian centuries elapsed since JD 2451 545.0.
The ratio of UTI to mean sidereal time is
l/r'
= 0.997269566329084 -
5.8684 x 1O- 11 T
+ 5.9 x
1O- 15 T 2•
The relationships between time scales in seconds of time are:
TT = TDT = ET = TAl + 32.184,
.6.T = ET - UT = TDT - UT = TT - UT,
.6.AT = TAl - UTC,
DUT", .6.UT = UTI - UTC,
TDB=TDT+P,
TCG - TT = 6.9692904 x lO- lO (J D - 2443144.5) x 86400,
TCB - TCG = 1.480813 x 10-8 (1 D - 2443144.5) x 86400 + Ve· (x - Xe)c- 2 + P,
TCB - TDB = 1.550506 x 1O- 8 (J D - 2443144.5) x 86400,
P = 0.0016568 sin(35 999.37T + 357.5) + 0.0000224 sin(32 964.5T + 246)
+ 0.000013 8 sin (7 1 998.7T + 355) + 0.000004 8 sin(3 034.9T + 25)
+ 0.000004 7 sin(34 777.3T + 230),
where T is the elapsed time from J2ooo.0 measured in Julian centuries and the coefficients are rounded
at their last digits [6, 10, 11]. Arguments are in degrees. Here Xe and Ve denote the barycentric position
and velocity of the Earth's center of mass, the difference (x - Xe) is the vector distance of the observer
from this center of mass, and c is the speed of light.
2.4.1
Reduction of Time Scales
The variations in the Earth's rotation rate have resulted in differences between time based on it and
that based on planetary orbits. The differences between the ephemeris and the (generally slower)
universal time are given in Tables 2.1 and 2.2 for the last 130 years. For dates back to 1620, see the
Astronomical Almanacs [12]. Even earlier to the year 1500 B.C., one can find a table in the Canon of
Lunar Eclipses [13]. Before 1884, .6.T = ET - UT, after 1984, .6.T = TDT - UT, and after 1989, the
differences are for exactly 1 Jan. 0" UTC.
2.4 ASTRONOMICAL CONSTANTS INVOLVING TIME
Table 2.1. Reduction of time scales from 1870 to 1974.
Year
t:..T
Year
t:..T
Year
t:..T
Year
t:..T
Year
t:..T
1870
1875
1880
1885
1890
+1.61
-3.24
-5.40
-5.79
-5.87
1895
1900
1905
1910
1915
-6.47
-2.72
+3.86
+10.46
+17.20
1920
1925
1930
1935
1940
+21.16
+23.62
+24.02
+23.93
+24.33
1945
1950
1955
1960
1965
+26.77
+29.15
+31.07
+33.15
+35.73
1970
1971
1972
1973
1974
+40.18
+41.17
+42.23
+43.37
+44.49
Table 2.2. UTe leap seconds since 1971 and staning at the given date.
Year
t:..T
Year
t:..T
Year
t:..T
Year
t:..T
1972, Jan. 1
1972, July 1
1973, Jan. I
1974, Jan. 1
1975, Jan. I
1976, Jan. I
10
11
12
13
14
15
1977, Jan. 1
1978,Jan.l
1979, Jan. 1
1980, Jan. 1
1981, July 1
1982, July 1
16
17
18
19
20
21
1983, July 1
1985, July I
1988, Jan. 1
1990, Jan. 1
1991, Jan. 1
22
23
24
1992, July 1
1993, July 1
1994, July 1
1996, Jan. 1
1997, July 1
27
28
29
30
31
25
26
Day
1 day = 24 hours = 1440 minutes = 86400 SI seconds
Period of rotation of Earth (referred to fixed stars)
In mean sidereal time
In mean solar time
1 day of mean sidereal time
1 day of mean solar time
Rate of rotation
Year
1 Julian year = 365.25 days
= 86164.09054 SI seconds.
= 23h56m04~090 549.
= 0.99726956633 of mean solar time.
= 1.002737909 35 of mean sidereal time.
= 15~/041 067178 66910 s-I.
= 7.29211510 x 10-5 rads- I .
= 8766 hours = 525960 minutes = 31557600 SI seconds
Tropical (equinox to equinox)
Sidereal (fixed star to fixed star)
Anomalistic (perihelion to perihelion)
Eclipse (Moon's node to Moon's node)
Gaussian (Kepler's law for a = 1)
Julian (based on Julian calendar)
Gregorian (based on Gregorian calendar)
d
d
h
m
s
365.242 1897
365.25636
365.25964
346.62005
365.25690
365.25
365.2425
365
365
365
346
365
365
365
05
06
06
14
06
06
05
48
09
13
52
09
45.19
10
53
52
56
49
12
/
15
16 / 2
GENERAL CONSTANTS AND UNITS
Calendar Julian Dates (see Chapter 27 also)
1900 January 0.5 = JD 2415020.0,
1925 January 0.5 = JD 2424151.0,
1950 January 0.5 = JD 2433 282.0,
2000 January 0.5 = JD 2451 544.0,
2050 January 0.5 = JD 2469 807.0,
2100 January 0.5 = JD 2488 069.0.
Length of the month
Synodic (new Moon to new Moon)
Tropical (equinox to equinox)
Sidereal (fixed star to fixed star)
Anomalistic (perigee to perigee)
Draconic (node to node)
Orbit of the Moon about the Earth
Sidereal mean motion of Moon
Mean distance of Moon from Earth
d
d
h
m
s
29.53059
27.32158
27.32166
27.55455
27.21222
29
27
27
27
27
12
07
07
13
05
44
43
43
18
05
03
05
12
33
36
2.661699489 x 10-6 rads- l
3.844 x 10 * 5 kIn
60.27 Earth radii
0.002570 AU
57' 02~'608
Equatorial horizontal parallax
at mean distance
3422~'608
Mean distance of center of Earth
from Earth-Moon barycenter
4.671 x 103 kIn
Mean eccentricity
0.05490
Mean inclination to ecliptic
5?145396
Mean inclination to lunar equator
60 41'
Limits of geocentric declination
±29°
Saros = 223lunations = 19 passages of Sun through node = 6585l days
6798 days
Period of revolution of node
Period of revolution of perigee
3232 days
Mean orbital speed
1023 ms- l =0.000591 AU day-l
Mean centripetal acceleration
0.00272 m s-2 = 0.0003 g.
Precession
Annual rates of precession (T in centuries from J2000.0)
general precession in longitude
lunisolar precession in longitude
planetary precession
geodesic precession (relativistic nonperiodic Coriolis effect)
50~'290966
50~'387 784
-O~'OI8 862 3
1~'92T.
+ O~'0222226T,
+ O~'OO4 926 3T,
-
O~'047 612 8T,
2.5 UNITS I
17
2.5 UNITS
The seven SI base units are: meter (m), kilogram (kg), second (s), ampere (A), Kelvin (K), mole (mol),
and candela (cd) [14]. All other units are derived from these. Units used with SI are: the time units of
minute (min), hour (h), and day (d); the plane angle units of radian (rad), degree e), minute ('), and
(arc)second ("); the solid angle unit, steradian (sr); the volume unit liter; (L); the mass unit metric ton
(t); and the land area hectare (ha). Other experimentally determined units used with SI are: the special
energy unit (eV), and the atomic mass unit (u).
Units used in astronomy and astrophysics are often not standard but unique to the special subfield.
This procedure is followed for many chapters in this book. They are frequently defined at the beginning
of each chapter.
Table 2.3 gives the SI unit prefixes.
Table 2.3. The SI prefixes.
Factor
1024
1021
1018
1015
1012
109
106
103
102
101
Prefix
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deka
Symbol
Factor
Prefix
Symbol
Y
10- 1
10-2
10-3
10-6
10-9
10- 12
10- 15
10- 18
10-21
10- 24
deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto
d
c
m
Z
E
P
T
G
M
k
b
da
/.t
n
p
f
a
z
y
Unconventional (nonstandard) units sometimes used in astronomy and astrophysics are listed
below.
Length
Angstrom unit
Micron
Foot
Inch
Mile
Nautical mile [2]
Area
Square foot
Acre
Bam
A = 10- 8 cm = 10- 10 m
J.L
= J.Lm = 10-4 cm = 10-6 m
ft = 30.4800 cm = 12 in
in = 2.540 000 cm
= 1.609 344 km = 5280 ft
1.853 km
6080 ft
=
tt2 =
=
929.03 cm
= 4046.85 m 2 =43560 ft2
= 10-24 cm2
18 I 2
GENERAL CONSTANTS AND UNITS
Volume
Cubic foot
Fluidounce
Mass
Kilogram (SI unit)
Pound avoirdupois
Pound troy and apothecary
Grain (all systems)
Carat
Slug
Ton = tonne
Metric ton
Energy
louIe (SI unit)
Calorie [4] (exact)
Kilowatt-hour
British thermal unit
Therm
Foot-pound
Kiloton of TNT
Power
Watt (SI unit)
British horse-power
Force de cheval
Force
Newton (SI unit)
Poundal
Pound weight
Slug
Gram weight
Acceleration
Standard gravity
Gravity (equator)
Gravity (pole)
Speed
Mile per hour
Knot
ft3 = 28316.8 cm3
=
=
=
=
=
6.229 British gallons
7.481 US gallons
480 minims (British and US)
28.413 cm3 (British)
29.574 cm3 (US)
kg = lO00g
British lb = 453.59237 g = 7000 grains
US lb = 453.59243 g = 7000 grains
= 373.242 g = 5760 grains
= 0.064 7989 g
=0.2000g
= 14.594 kg
= 2240lb
= 1.016047 x 106 g
= 106 g
1 = 107 erg
cal = 4.1841 = 4.184 x 107 erg
= 3600 x 103 1
= 8.6042 x lOS cal
BTU = 1055 1 = 252.0 cal
= 100000 BTU
= 1.35582 x 107 erg
= 4.184 x 1019 erg -
= 107 ergls = 1 s-1
= 745.7W
= 735.5W
N=
=
=
=
=
lOS dyn
1.3825 x lQ4 dyn
4.4482 x lOS dyn
14.594 kg
980.665 dyn
1 gal = 1 em s-2
g = 978.031 em s-2 = 32.09 ft s-2
g = 983.217 em s-2 32.26 ft s-2
=
= 44.704 cms- 1 = 1.4667 fts- 1
= 51.47 cms- 1
2.5 UNITS /
Pressure
Pascal (SI unit)
Barye (occasionally called Bar)
Bar
Millibar
Atmosphere (standard)
Millimeter of mercury (= 1 Torr)
Inch of mercury
Pound per square inch
Density
Kilogram/cubic meter (SI unit)
Density of water (4° C)
Density of mercury (0° C)
Solar mass/cubic parsec
STP gas density
where /.LO is molecular weight
Temperature
Degree scales (Kelvin K,
Celsius (centigrade) C, Fahrenheit F)
Temperature comparisons
Triple point of natural water
Viscosity (dynamic)
Poise
SI unit
Viscosity (kinematic)
Stokes
SIunit
Frequency
Hertz
Kayser (a wave number unit)
Rydberg frequency
Frequency in first Bohr orbit
Frequency of free electron
in magnetic field 'H. (gauss)
Plasma frequency associated
with electron density Ne in cm-3 )
= 10 dyn cm- 2 =
/.Lb
= 1.000 dyn cm-2
10 /.Lb
bar =
=
=
mb =
=
atm =
1.000 x 106 dyn cm- 2
0.986923 atm
1.0197 x 103 g-weight cm-2
10-3 bar = 103 /.Lb
103 dyn cm-2
1.013 250 x 106 dyn cm- 2
= 760 mmHg = 1013.25 mb
mmHg = 1333.22 dyn cm-2
= 0.0013158 atm
= 3.38638 x 104 dyn cm- 2
= 0.033421 atm
= 6.8947 x 104 dyn cm- 2
= 0.068046 atm
=
=
=
=
=
1.000 X 10-3 g cm-3
0.999972 g cm- 3
13.5951 g cm- 3
6.770 x 10-23 g cm-3
4.4616 x 1O-5 /.LO g cm- 3
K = deg C = 1.8 deg F
0° C = 273.150 K = 32° F
100° C = 373.150 K = 212° F
= 273.160 K = 0.010° C
P = 1 g cm- 1 s-l = 0.1 Pas
Nsm- 2 = 10gcm- 1 s-l
= 1 cm2 s-l
m2 s-l = 10000 cm2 s-l
Hz =
cm- 1 =
c Roo =
2c Roo =
=
cycle s-l
cHz~ 3 x 10 10 Hz
3.28984 x 1015 Hz
6.5797 X 1015 Hz
2.7993 x 106 'H. Hz
,,1
1/2
= 8.979 x hr Ne
Hz
19
20 / 2
GENERAL CONSTANTS AND UNITS
Angular velocity (= 21l' frequency)
Unit of angular velocity
1" of arc per tropical year
I" of arc per day
Angular velocity of Earth on its axis
Mean angular velocity of Earth in its orbit
= 1 rad s-I =
= 1.5363147
= 5.6112695
= 7.2921152
= 1.9909867
Momentum
Linear momentum, SI unit
= lOS g cm s-I = 1 kg m s-I
= 2.73093 x 10- 17 gcm s-I
mc
Angular momentum
SI unit
Electron momentum in first Bohr orbit
Quantum unit
Homogeneous sphere angular momentum
(R
radius, M
mass,
w = angular velocity)
Angular momentum of solar system
=
=
Luminous intensity
Luminous intensity is defined
as the luminous emission per sterad
Candela (SI unit)
Star, mv = 0, outside Earth atmosphere
= 107 g cm2 s-I = 1 kg m2 s-I
= 1.993 x 10- 19 g crn s-I
Ii = 1.0546 x 10-27 erg s
= (2/5)R 2 Mw
= 3.148 x
= flux from 1 cd into 1 sr
= flux from (1/601l') crn2 of
black body at 2044 K
= 1.470 x 10-3 W
Lumen of maximum visibility radiation
at 5550 A
therefore 1 W at 5550 A
Jansky
= 680 lumens
= 10-23 ergs cm-2 s-1 Hz- 1
= 10-26 W m- 2 Hz- I
Luminous energy
Talbot (SI unit)
Lambert
IOS0 g cm-2 S-I
cd = (1/60) luminous intensity
of 1 projected cm2
black body at the
temperature of melting
platinum (2044 K)
= 2.45 x 1029 cd
Luminous flux
Lumen (both SI and CGS unit)
Surface brightness
Stilb
21l' Hz
x 1O- 13 rads- 1
x 10- 11 rad s-I
x 10-5 rad s-1
x 10-7 rad s-I
= 1 lumerg (CGS unit)
= 1 lumen second
sb
= 1 cd cm- 2 = 1l' lambert
= 1 lumen cm- 2 SCi
= (1/1l') cd cm-2
= 1000 millilambert
== 1 lumen cm- 2 for a perfectly
diffusing surface
2.5 UNITS / 21
Apostilb
Nit (SI unit)
Candle per square inch
Foot-lambert
= 0 star per square degree outside
atmosphere
1mv
= 0 star per square degree inside clear
unit airmass
1mv
Luminous emittance (of a suiface)
Lumen per square meter (SI unit)
Illuminance (light received per unit suiface)
Phot (CGS unit)
Lux (SI unit)
Foot-candle
Star, mv = 0, outside Earth atmosphere
= 1 lumen m- 2 for a perfectly\
diffusing surface
= 10-4 lambert
= 10-4 sb = cd m- 2
= 0.487 lambert = 0.155 stilb
= 1.076 x 10-3 lambert
= 343 x 10-4 stilb
= 0.84 x 10-6 stilb
= 0.84 x 10-2 nit
= 2.63 x 10-6 lambert
= 0.69 x 10-6 stilb
= 10-4 lumen cm- 2
=
Ix =
=
=
=
=
1 lumen cm- 2
1 lumen m- 2 = 10-4 phot
1 m-candle
10.76 lux = 1.076 x 10-3 phot
1 lumen ft- 2
2.54 x 10- 10 phot
Electrical units
The general inter-relations between electric
and magnetic units are given in Sec. 2.6
Electrical charge
Coulomb (SI unit)
Electron charge
Electrical potential
Volt (SI unit)
Potential of electron at first Bohr orbit distance
Ionization potential from first Bohr orbit
Electric field
Volt per meter (SI unit)
Nuclear field at first Bohr orbit
Resistance
Ohm (SI unit)
Electric current
Ampere (SI unit)
Current in first Bohr orbit
C = 2.997925 x 109 esu = 0.10 emu
= -6.24151 x 10 18 electrons
e = -4.803 25 x 10- 10 esu
e = -1.60218 x 10- 19 C
V = 3.33564 x 10- 3 esu = 108 emu
= 27.211 volt = 0.090767 esu
= 13.606 volt = 0.045384 esu
= 3.33564 x 10-5 esu = 106 emu
= 5.1402 x 1011 voltm- 1
= 1.7152 x 107 esu
Q= 1.11265 x 1O- 12 esu= 109 emu
A = 2.997 925 x 109 esu = 0.10 emu
= -6.24151 x 10 18 electrons s-1
= 1.054 x 10-3 A
= 3.160 x 106 esu
22 / 2
GENERAL CONSTANTS AND UNITS
Electric dipole moment
Coulomb-meter (SI unit)
Dipole moment of nucleus and electron in
first Bohr orbit
Cm
Magnetic field
Ampere-turn per meter (SI unit)
Gauss (in free space)
Gamma
. umt
. (me1/2 a -1/2 .0-1)
A tomlc
O
Field at nucleus due to electron in first Bohr orbit
am!/2aol/2.0-1, .0 = W01 = 2.4189 x 10- 17 s
1
ILB(mel m p )
Earth magnetic moment
Radioactivity
Curie [4]
Roentgen
2.6
1011 esu = 10 emu
x 10- 29 Cm
x 10- 18 esu
= 1 oersted =
y
=
=
=
79.58 amp-tumm- 1
10-5 oersted
1.715 x 107 gauss
1.252 x 105 oersted
=
104 gauss
= 1 weberm- 2
ILB
= (l/41l") 1010 emu = 0.02654 esu
= 2.541 x 10- 18 erg gauss- 1
= 0.9274 x 10-20 erg gauss- 1
ILK
= 5.051
1/2 5/2 -1
zame a o .0
Nuclear magneton
Rad
= 0.8478
= 2.5417
= 41l" x 10-3 oersted [emu]
= 3.767 x 108 esu
Magnetic flux density, Magnetic induction
Tesla (SI unit)
Magnetic moment
Weber-meter (SI unit)
. umt
. (me1/2 a 5/2 .0-1)
A tomlc
O
Bohr magneton, magnetic moment of
electron in first Bohr orbit
= 2.9979 x
= 7.98
X
10-24 erg gauss- 1
x 1025 emu
= 3.700 x 1010 disintegrations s-1
= exposure to radiation producing
2.082 x 109 ion pairs in
0.001293 g of air = I esu cm- 3
= 2.58 x 10-4 C kg- 1
= 10- 2 Jkg- 1
ELECTRIC AND MAGNETIC UNIT RELATIONS
Table 2.4 on pages 24 and 25 is adapted from the previous Astrophysical Quantities edition. Many of
these quantities are now superseded by the SI units, but the older esu and emu units are still frequently
used for special cases in astrophysics.
For the SI units, the permittivity (EO) and permeability (ILO) of free space are defined to be exact as
(l/41l"c 2 ) x 1011 Fm- 1 = 8.854187817 ... Fm- 1 and 41l" x 10-7 N A -2, respectively. Here F is the
farad capitance unit, N is the newton force unit, and A is the ampere current unit.
2.6 ELECTRIC AND MAGNETIC UNIT RELATIONS / 23
REFERENCES
1. Astrophysical Quantities. I, §7
2. Astrophysical Quantities, 3, §1O
3. Abramowitz, M. & Stegun, I.A. 1965, Handbook of
Mathematical Functions, (Dover, New York), p. 2
4. Anderson, H.L. 1989, A Physicist's Desk Reference, the
second edition of Physics Vade Mecum (American Institute of Physics, New York)
&
Taylor,
B.N.
1998,
5. Cohen,
E.R.,
http://physics.nist.gov/cuulReferencelversioncon.html
6. Seidelmann, p.K. 1992, Explanatory Supplement to the
Astronomical Almanac (University Science Books, Mill
Valley, CA)
7. Dehnen, W, & Binney, J.J. 1998, MNRAS, 298, 387
8. Metzger, M.R., Caldwell, J.A., & Schechter, P.L. 1998,
AJ, 115,635
9. Standish M. 1995, Report of the IAU WGAS SubGroup on Numerical Standards, in Highlights ofAstronomy edited by Appenzeller (Kluwer Academic, Dordrecht)
10. Fairhead L., Bretagnon, P. & Lestrade, J.E 1998, IAU
Symposium 128 (Kluwer, Dordrecht) p. 419
II. Hirayama, Th. et al. 1987, Proc. lAG Symposia I.,
IUGG XIX General Assembly, Vancouver
12. Astronomical Almanacs (USNO, GPO)
13. Liu, Bao-Lin, & Fiala, A.D. 1992, Canon of Lunar
Eclipses 1500 B.C.-A.D. 3000 (Willmann-Bell, Richmond)
14. Nelson, R.A. 1998, Physics today, BGll
24 /
2
GENERAL CONSTANTS AND UNITS
Table 2.4. Electric and
Quantity
SI symbol and unit
Charge
Q
coulombC
= c x 10- 1 esu
Current
I
ampere A
= c x 10- 1 esu
Potential, EMF
V
volt V
= (l/c) x 10- 12 esu
Electric field
£
volt/m
= (l/c) x 1O- 14esu
Resistance
R
ohmQ
= (l/c 2 ) x 109 esu
Resistivity
p
ohmm
= (l/c 2 ) x 10- 11 esu
Conductance
G
siemens, mho
= c 2 x 10-9 esu
Conductivity
a
mho/m
= c 2 x 10- 11 esu
Capitance
C
farad F
= c 2 x 10-9 em
Electric flux
\11
coulombC
= 4rrc x 10- 1 esu
Electric flux density, displacement
D
coulomb/m2
= 4rrc x 10-5 esu
Polarization
P
coulomb/m2
= c x 10-5 esu
coulomb/m
= c x 10 1 esu
Electric dipole moment
in esu
Permittivity, dielectric constant
E
farad/m
= 4rrc 2 x 10- 11 esu
Permittivity of free space
EO
(1/4rrc 2 ) x 1011 F/m
= 1 esu
Inductance
L
henry H
= (l/c 2 ) x 109 esu
Magnetic pole strength
m
weberWb
= (l/4rrc) x 108 esu
Magnetic flux
<I>
weberWb
= (l/c) x 108 esu
Magnetic field
1i
ampere turn/m
= 4rrc x 10-3 esu
Magnetomotive force, magnetic potential
:F
ampere turn AT
= 4rrc x 10- 1 esu
Magnetic dipole moment
M
weberm
= (l/4rrc) x 10 10 esu
Electromagnetic moment
m
ampere m 2
Mag. flux density, induction
B
tesla T
= (l/c) x 104 esu
Intensity of magnetization
J
weber/m2 T
= (l/4rrc) x 10 16 esu
Magnetic energy density
Permeance
Bx1i
joule/m3
A
henry H
= (l/4rrc 2 ) x 109 esu
l/henry
= 4rrc 2 x 10-9 esu
Reluctance
Permeability
JL
henry/m
= (l/4rrc 2 ) x 107 esu
Permeability of free space
JLO
4rr x 10- 7 H/m
= (l/c 2 ) esu
2.6
/
25
T
I
001
1
000
1
ELECTRIC AND MAGNETIC UNIT RELATIONS
magnetie units.
Dimensions
in emu, etc.
ESU
EMU
L
M
T
112
112
112
112
-1
= 106 emu
312
312
112
-112
= 109 emu
-1
0
= 10- 1 emu
= 10- 1 emu
= 108 emu
esu
JL emu
SI
K
L
M
T
112
112
312
112
112
112
112
0
-1
112
112
-112
-112
1
-1
1
o
-1
1
1
-1
2
-1
1
1
-1
1/e2 -2 -1
3
2
1
-1
1/e2 -3 -1
3
2
-1
o
o
o
o
2
-1
1/e2 -2 -1
4
2
-2
-1
liz
-1
-2
-2
-112 lie
-112 lie
112 e
112 e
L
M
2
-3-1
1
-3-1
e2
2
1 -3 -2
e2
3
-3 -2
= 1011
= 10-9 emu
= 10- 11 emu
o
= 10-9 emu
1
o
o
o
o
312
112
-1
112
112
112
0
-112
lie
0
0
112
112
112
-1
112 -312
112 -312
112 312
112
112
112
0
-2
0
-2
0
0
-112 lie
-112 lie
-112 lie
1
0
1
1
2
1/e2
-3 -1
4
2
= 4:rr x
= 4:rr
10- 1 emu
1
o
x 10-5 emu
= 10-5 emu
= 10 emu
o
= 4:rr x 10- 11 emu
-1
-1
-1
1
0
-1
-1
0
1
-2
-2
o
0
-1
= O/e2 ) emu
= 109 em
= O/4:rr) x 108 emu
= 108 maxwell (Mx)
= 4:rr x 10-3 oersted (Oe)
= 4:rr x 10- 1 gilbert (Gb)
= (1/4:rr)
-1
o
2
112
112
112
312
112
112
112
112
0
112
112
112
= 104 gauss (Gs)
= O/4:rr) x 104 emu
= 40:rr Gs Oe
= 4:rr x
10-9 GblMx
= (l/4:rr)
= 1 emu
0
-2
-2
-1
-112 312
-112 312
112 -112
112 112
o
0
e2
2
1 -2 -2
112
112
112
112
-1
112 e
112 e
-112 lie
-112 lie
2
-2 -1
2
1 -2 -1
-1
-1
-1
x 1010 emu
x 109 Mx/Gb
x 107 emu
1
1/e2
= 103 emu
= (1/4:rr)
1
-1
1
-2
0
112 512
-112 -112
-112 -112
1 -2
0-1
0
-2
0
2
0 -2
0
2
-1
1
1-1
-1
0
112
112
112
-1
-112 lie
-1
-1
1 -2
o
o
o
-1
1
0
-1
0
1
e2
001
3
1 -2 -1
2
001
o
o
1 -2 -1
1 -2 -1
1 -2
2
e2
0
-2-2
1/e2 -2 -1
e2
0
0
-1
0
o
2
2
1 -2 -2
Chapter 3
Atoms and Molecules
Werner Dappen
3.1
3.1
Online Databases and Other Sources. . . . . . . . ..
27
3.2
Elements, Atomic Mass, and Solar-System Abundance
28
3.3
Excitation, Ionization, and Partition Functions . . ..
31
3.4
Ionization Potentials. . . . . . . . . . . . . . . . . . ..
35
3.5
Electron Affinities . . . . . . . . . . . . . . . . . . . ..
35
3.6
Atomic Cross Sections for Electronic Collisions . ..
35
3.7
Atomic Radii. . . . . . . . . . . . . . . . . . . . . . ..
43
3.8
Particles of Modem Physics . . . . . . . . . . . . . ..
44
3.9
Molecules. . . . . . . . . . . . . . . . . . . . . . . . ..
45
3.10
Plasmas. . . . . . . . . . . . . . . . . . . . . . . . . ..
47
ONLINE DATABASES AND OTHER SOURCES
The National Institute of Standards and Technology (NIST) gives access to extensive
physical and atomic data (http://physics.nist.gov).
The Plasma Laboratory of the Weizmann Institute (http://plasma-gate.weizmann.ac.il) and the Southwest Research Institute
(http://espsun.space.swri.edulspacephysics/www.atomic.html) provide, besides their own data. many
useful links to other databases. For astrophysical applications, among the most extensive databases
are those of the Harvard-Smithsonian Center for Astrophysics (http://cfa-www.harvard.edulamp/data)
(giving, e.g., searchable access to the data by R.L. Kurucz and R.L. Kelly) and of the Opacity Project
(http://astro.u-strasbg.fr/OP) (with monochromatic opacities, collision strengths, and other atomic
data). A further source of important data is the Iron Project (http://www.am.qub.ac.uk/projects/iron).
Gary Ferland's Web Page (http://www.pa.uky.edulgary/cloudy) has references to CLOUDY ("Photoionization Simulations for the Discriminating Astrophysicist"), which contains pointers to the atomic
27
28 I
3
ATOMS AND MOLECULES
databases they use and maintain (e.g., http://www.pa.uky.edulverner/atom.html. "Atomic Data for Astrophysics"). The CHIANTI group (http://www.solar.nrl.navy.miUchianti) has installed a database
with information suitable for extreme-UV applications. The Particle Data Group (http://pdg.lbl.com)
makes available periodically its newest releases of particle properties. Other sources of information
are the recent Atomic, Molecular, and Optical Physics Handbook [1], the results of the work of the
Collaborative Computational Project No. 7 (United Kingdom) [2], and the Handbook of Chemistry
and Physics [3].
3.2
ELEMENTS, ATOMIC MASS, AND SOLAR-SYSTEM ABUNDANCE
Atomic masses (weighted by the fractional abundances of the stable isotopes in normal terrestrial
composition [4]) are scaled to 12C = 12.00. Standard values abridged to five significant digits are
given (from the International Union of Pure and Applied Chemistry (IUPAC); see [5]). For some
elements, atomic masses can be accurately measured to seven or more significant figures. IUPAC
regularly publishes these values irrespective of interest to any user. For many users, however, it is often
desirable that the published data remain valid over an extended period, which is helpful for textbooks
and numerical tables derived from atomic-mass data. IUPAC has recognized this need and approved
the use of the designation standard to its abridged atomic-mass table, with the hope that the quoted
values may survive for at least a decade.
The solar-system abundances (formerly denoted as cosmic abundances) are expressed logarithmically on a scale for which H is 12.00 dex. The intention is that they express cosmic abundance [6].
Thus, abundances are taken mainly from meteorites and the Sun's photosphere. In both cases, values by
number are quoted. The agreement between meteoritic and solar data has improved remarkably since
the 1970s. Discrepancies have mostly gone away as the solar values-thanks especially to improved
transition probabilities and other atomic data-have become more accurate [6]. The two principal exceptions are'the solar photospheric Li and Be abundances that are smaller than the meteoritic ones by
2.15 and 0.27 dex, respectively. The reason is that these elements are destroyed by nuclear reactions at
the bottom of the solar convection zone. For most other elements the agreement is better than ±0.04
dex (for this, and exceptions, see [6]). In the case of iron, a previous controversy has been solved: the
solar and meteoritic values agree now [7]. For details on isotopic abundances, see [1] and [4].
The group abundance ratios given in Table 3.1 are derived from Table 3.2. The H ratio is set to 100.
Table 3.1. Group abundance ratios.
Element group
Number
Mass
Stripped
electrons
H
He
C,N,O,Ne
Other
100
9.8
0.145
0.013
100
39
2.19
0.44
100
20
1.1
0.21
Total
109.96
141.63
121.3
The composition by mass [2] is as follows:
fraction of H, X
fraction of He, Y
fraction of other atoms, Z
0.707 ±2.5%
0.274±6%
0.0189 ± 8.5%
3.2 ELEMENTS, ATOMIC MASS, AND SOLAR-SYSTEM ABUNDANCE / 29
Mean atomic mass of cosmic material
Mean atomic mass per H atom
Mean atomic mass for fully ionized cosmic plasma
1.30
1.41
0.62
Table 3.2. Atomic 1NJSses and solar-system abundances.
Log abundance [2]
Symbol
[1]
Atomic
number
Atomic
mass
Hydrogen
Helium [3]
Lithium
Beryllium
Boron
H
He
Li
Be
B
1
2
3
4
5
1.0079
4.0026
6.941
9.0122
10.811
Carbon
Nitrogen
Oxygen
Auorine
Neon
C
N
0
F
Ne
6
7
8
9
10
12.011
14.007
15.999
18.998
20.180
8.56"
8.05"
8.93"
4.48
8.09
8.56
8.05
8.93
4.56
8.()9<i
Sodium
Magnesium
Aluminum
Silicon
Phosphorus
Na
Mg
Al
Si
P
11
12
13
14
15
22.990
24.305
26.982
28.086
30.974
6.31
7.58
6.48
7.55
5.57
6.33
7.58
6.47
7.55
5.45
Sulphur
Chlorine
Argon
Potassium
Calcium
S
CI
Ar
K
Ca
16
17
18
19
20
32.066
35.453
39.948
39.098
40.078
7.27
5.27
6.56d
5.13
6.34
7.21
5.5
6.56d
5.12
6.36
Scandium
Titanium
Vanadium
Chromium
Manganese
Sc
Ti
V
Cr
Mn
21
22
23
24
25
44.956
47.88
50.942
51.996
54.938
3.09
4.93
4.02
5.68
5.53
3.10
4.99
4.00
5.67
5.39
Iron [2]
Cobalt
Nickel
Copper
Zinc
Fe
Co
Ni
Cu
Zn
26
27
28
29
30
55.847
58.933
58.693
63.546
65.39
7.51
4.91
6.25
4.27
4.65
7.54
4.92
6.25
4.21
4.60
Gallium
Germanium
Arsenic
Selenium
Bromine
Ga
Ge
As
Se
Br
31
32
33
34
35
69.723
72.61
74.922
78.96
79.904
3.13
3.63
2.37
3.35
2.63
2.88
3.41
Krypton
Rubidium
Strontium
yttrium
Zirconium
Kr
Rb
Sr
Zr
36
37
38
39
40
83.80
85.468
87.62
88.906
91.224
3.23
2.40
2.93
2.22
2.61
2.60
2.90
2.24
2.60
Niobium
Molybdenum
Technetium
Ruthenium
Rhodium
Nb
Mo
Tc
Ru
Rh
41
42
43
44
45
92.906
95.94
98.906
101.07
102.91
1.40
1.96
1.42
1.92
1.82
1.09
1.84
1.12
Element
Y
Meteoritic
12.{)()"
10.99"
3.31
1.42
2.8
Solar
12.00
1O.wh
1.16
1.15
2.6c
30 / 3
ATOMS AND MOLECULES
Table 3.2. (Continued.)
Element
Symbol
[l]
Atomic
number
Atomic
mass
Log abundance [2]
Meteoritic
Solar
Palladium
Silver
Cadmium
Indium
Tin
Pd
Ag
Cd
In
Sn
47
48
49
50
106.42
107.87
112.41
114.82
118.71
1.70
1.24
1.76
0.82
2.14
1.69
O.94c
1.86
1.66c
2.0
Antimony
Tellurium
Iodine
Xenon
Cesium
Sb
Te
I
Xe
Cs
51
52
53
54
55
121.76
127.60
126.90
131.29
132.91
1.04
2.24
1.51
2.23
1.12
1.0
Barium
Lanthanum
Cerium
Praseodymium
Neodymium
Ba
La
Ce
Pr
Nd
56
57
58
59
60
137.33
138.91
140.12
140.91
144.24
2.21
1.20
1.61
0.78
1.47
2.13
1.22
1.55
0.71
1.50
Promethium
Samarium
Europium
Gadolinium
Terbium
Pm
Sm
Eu
Gd
Tb
61
62
63
64
65
146.92
150.36
151.96
157.25
158.93
0.97
0.54
1.07
0.33
1.00
0.51
1.12
-0.1
Dysprosium
Holmium
Erbium
Thulium
Ytterbium
Dy
Ho
Er
Tm
Yb
66
67
68
69
70
162.50
164.93
167.26
168.93
170.04
1.15
0.50
0.95
0.13
0.95
1.1
0.26c
0.93
O.OOC
1.08
Lutetium
Hafnium
Tantalum
Thngsten
Rhenium
Lu
Hf
Ta
W
Re
71
72
73
74
75
174.97
178.49
180.95
183.85
186.21
0.12
0.73
0.13
0.68
0.27
0.76c
0.88
Osmium
Iridium
Platinum
Gold
Mercury
Os
Ir
Pt
Au
Hg
76
77
78
79
80
190.2
192.22
195.08
196.97
200.59
1.38
1.37
1.68
0.83
1.09
1.45
1.35
1.8
1.01 c
Thallium
Lead
Bismuth
Polonium
Astatine
Tl
Ph
Bi
Po
At
81
82
83
84
85
204.38
207.2
208.98
209.98
209.99
0.82
2.05
0.71
0.9c
1.85
Radon
Francium
Radium
Actinium
Thorium
Rn
Fr
Ra
Ac
Th
86
87
88
89
90
222.02
223.02
226.03
227.03
232.04
0.08
0.12
Protactinium
Uranium
Neptunium
Plutonium
Americium
Pa
U
Np
Pu
Am
91
92
93
94
95
231.04
238.03
237.05
239.05
241.06
46
-0.49
1.11 c
< -0.45c
3.3 EXCITATION, IONIZATION, AND PARTITION FUNCTIONS I 31
Table 3.2. (Continued.)
Element
Symbol
[l]
Atomic
number
Atomic
mass
Curium
Berkelium
Californium
Einsteinium
Fermium
Cm
Bk
Cf
Es
Fm
96
97
98
99
100
244.06
249.08
252.08
252.08
257.10
Mendelevium
Nobelium
Lawrencium
Md
No
Lr
101
102
103
258.10
259.10
262.11
Log abundance [2]
Meteoritic
Solar
Notes
aBased on solar data.
bBased on stellar observations and solar models [1, 3, 4].
cUncertain.
dBased on other astronomical data.
References
1. IUPAC 1969, Comptes Rendus XXV Conference, p. 95
2. Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53, 197;
Grevesse, N., & Noels, A. 1993, in Origin and Evolution· of the Elements,
edited by N. Prantzos, E. Vangioni, & M. CasSIS (Cambridge University
Press, Cambridge), p. 15
3. Christensen-Dalsgaard, J., Diippen, W., & the GONG Team 1996, Science,
272, 1286
4. Biemont, E., Baudoux, M., Kurucz, R.L., Ansbacher, W., & Pinnington,
E.H. 1991, A&A, 249, 539
5. Kosovichev, A.G., Christensen-Dalsgaard, J., Diippen, W., Dziembowski,
W.A., Gough, D.O., & Thompson, M.J. 1992, MNRAS, 259,536
3.3 EXCITATION, IONIZATION, AND PARTITION FUNCTIONS
3.3.1 Introduction
Finding the occupation of individual levels of atoms and ions and the fractions of ions of any given
chemical element in a plasma is a complex task. The difficulty arises from the interaction of the
plasma with the atoms. Therefore, in principle, the problems of modified atoms and of their statistical
occupation should be solved simultaneously and self-consistently. The typical task of quantumstatistical mechanics consists of the calculation of a density operator (ensemble) for the system of all
particles. The partition function, i.e., the trace over the density operator, not only gives the occupation
of all states, but it also leads to a thermodynamical potential.
It is evident that various approximations are necessary before this procedure can be carried out.
One such approximation consists of treating the motion of the heavy particles (nuclei, atoms, ions)
according to classical mechanics. Once the heavy particles are separated out, quantum-mechanical
electrons remain. In the treatment of electrons, we find a bifurcation into two distinct classes of
approach, the "chemical picture" and the ''physical picture." While in the more conventional chemical
picture, bound configurations (atoms, ions, and molecules) are introduced and treated as new and
independent species, only fundamental particles (electrons and nuclei) appear in the physical picture.
In the chemical picture, reactions between the various species occur. Thus the thermodynamical
equilibrium must be sought among the stoichiometrically allowed set of concentration variables by
means of a maximum entropy (or minimum free-energy) principle. In contrast, the physical picture
32 I 3
ATOMS AND MOLECULES
has the aesthetic advantage that there is no need for a minimax principle. The question of bound states
is dealt with implicitly through the Hamiltonian describing the interaction between the fundamental
particles.
It is obvious that these self-consistent approaches require extensive analytical and numerical work.
For a recent realization of the chemical-picture approach, see, e.g., [8-10]. For the physical picture, the
most detailed work so far was done as part of the OPAL opacity project [11-14]. In the OPAL project,
the physical picture was not only used to model excitation and ionization processes, but for the first time
also to yield the highly accurate thermodynamic quantities needed in computations of stellar models
[15]. The book by Ebeling et al. [16] contains further information and references on the physical
picture. The most recent addition to the set of stellar equations of state is based on the formalism
of the path integral in the framework of the Feynman-Kac representation. This formalism leads to a
virial expansion of the thermodynamic functions in the power of the total density of a Coulomb plasma
([17,18], and references therein).
For many lower-density applications, especially stellar spectroscopy, adequate qualitative and
quantitative information can be extracted from simpler considerations, in which atoms are assumed to
have an unperturbed structure. In this case, excitation fractions are given by the Boltzmann factor, and
the ionization degree follows from the Saba equation, which is the mass-action law for the ionization
reaction. The Saba equation contains the internal partition functions for bound systems. A fundamental
theoretical flaw of this approximate approach is that isolated atoms would have infinite partition
functions because of their infinite number of excited states. Many heuristic recipes to truncate partition
functions exist. However, only the physical picture comes to a satisfactory solution, which then can
often be used to justify the intuitive concepts [19]. In many cases, neglecting all excited states, that is,
assuming ground-state-only internal partition functions, is a reasonable approximation. The following
simple treatment of excitation, ionization, and partition functions is, with reasonable care, still very
useful for many qualitative and semiquantitative astrophysical applications.
3.3.2
Approximate Methods and Results
For practical applications, a useful introduction to the statistical mechanics of plasmas is the book by
Eliezer et al. [20]. The number of atoms existing in various atomic levels 0, 1,2, ... when in thermal
eqUilibrium at temperature T is approximately described by the Boltzmann distribution
N2/Nl = (g2/gl)exp(-Xl,2/kT),
N2/ N
= (g2/ U) exp( -
XO,2/ kT).
Numerically
log(N2/ Nl) = log(g2/gt} - Xl2(5040/T)
(X12 in eV),
where N is the total number of atoms per cm3 , No, NI, and N2 are the numbers of atoms per cm3 in
the zero and higher levels, gO, g). and g2 are the corresponding statistical weights, XI,2 is the potential
difference between levels 1 and 2, and U is the partition function.
The degree of ionization in conditions of thermal eqUilibrium is given by the Saba equation
Ny+!
U Y +!2 (27fm)3/2(kT)5/2
- N Pe = - U
3
exp(-xY,Y+l/kT).
y
Numerically
y
h
3.3 EXCITATION, IONIZATION, AND PARTITION FUNCTIONS /
or
NY+l
)
log ( ~Ne
= -XY,Y+le -
23 log
33
e + 20.9366 + log (2UY+l)
--u;- ,
where Ny and Ny + 1 are the numbers of atoms per cm3 in the Y and Y + 1 stages of ionization (Y = 1,
neutral; Y = 2nd, 1st ion; etc.), Ne is the number of electrons per cm3 , Pe is the electron pressure in
dyncm- 2, XY,Y+I the ionization potential in eV from the Y to the Y + 1 stage of ionization, e = 5040
KIT, Uy and UY+I are the partition functions, and the factor 2 represents the statistical weight of an
electron.
The degree of ionization, when ionizations are caused by electron collisions and recombinations
are radiative, can be approximately given by
NY+I/Ny
= SlOt,
where the effect of both collisional ionizations from state of ionization Y + 1 and of recombinations
of Y + 2 in the abundance of ions in Y + 1 is neglected, and the possibility of multiple-ionization
events is excluded. In the formula, S is the collision ionization coefficient (such that SNeNy = rate of
collisional ionization, see Sec. 3.6), and a is the recombination coefficient (such that aNeNY+l = rate
of recombination, see Chap. 5).
Detailed calculations of partition functions are given by Irwin [21] (atoms and molecules) and
Sauval and Tatum [22] (molecules). However, for the approximate purposes of this section, the
partition function may simply be regarded as the effective statistical weight of the atom or ion under
existing conditions of excitation. Except in extreme conditions it is approximately equal to the weight
of the lowest ground term. The ground term weight gO is therefore given and this can normally be
extrapolated along the isoelectronic sequences to give the approximate partition function for any ion.
The partition functions, given in Table 3.3 in the form log U for e = 1.0 and 0.5, are not intended
to include the concentration of terms close to each series limit. The part of the partition function
associated with these high-n terms is dependent on both T and Pe. This part is usually negligible unless
the atom concerned is mainly ionized in which case the high-n terms may be counted statistically with
the ion.
Lowering of XY,Y+I in the Saba equation to allow for the merging of high-level spectrum lines
gives [23]
~XY,Y+I
= 7.0 x
-7
10
1/3 2/3
Ne
Y
,
with ~X in eV and Ne in cm- 3 , and where Y is the charge on the Y
+ 1 ion.
Table 3.3. Partition junction [1-3].
Y=II
Y =1
logU
logU
Element
1
2
3
4
5
6
7
8
9
III
go
Y=ill
8 = 1.0
8=0.5
go
8 = 1.0
8=0.5
go
H
He
Li
Be
B
2
1
2
1
6
0.30
0.00
0.32
0.01
0.78
0.30
0.00
0.49
0.13
0.78
1
2
1
2
1
0.00
0.30
0.00
0.30
0.00
0.00
0.30
0.00
0.30
0.00
1
2
1
2
C
9
4
9
6
0.97
0.61
0.94
0.75
1.00
0.66
0.97
0.77
6
9
4
9
0.78
0.95
0.60
0.92
0.78
0.97
0.61
0.94
1
6
9
4
IlM
IlM
F.
Il 7'1
Il 7<;
0
N
0
F
1\1"
34 / 3
ATOMS AND MOLECULES
Table 3.3. (Continued.)
Y =1
Y=II
10gU
Element
go
Y=ill
10gU
0=1.0
0=0.5
gO
0=1.0
0=0.5
go
11
12
13
14
15
Na
Mg
Al
Si
P
2
1
6
9
4
0.31
0.01
0.77
0.98
0.65
0.60
0.15
0.81
1.04
0.79
1
2
1
6
9
0.00
0.31
0.00
0.76
0.91
0.00
0.31
0.01
0.77
0.94
6
1
2
1
6
16
17
18
19
20
S
Cl
AI
K
Ca
9
6
1
2
1
0.91
0.72
0.00
0.34
0.07
0.94
0.75
0.00
0.60
0.55
4
9
6
1
2
0.62
0.89
0.69
0.00
0.34
0.72
0.92
0.71
0.00
0.54
9
4
9
6
1
21
22
23
24
25
Sc
Ti
V
Cr
Mn
10
21
28
7
6
1.08
1.48
1.62
1.02
0.81
1.49
1.88
2.03
1.51
1.16
15
28
25
6
7
1.36
1.75
1.64
0.86
0.89
1.52
1.92
1.89
1.22
1.13
10
21
28
25
6
26
27
28
29
30
Fe
Co
Ni
Cu
Zn
25
28
21
2
1.43
1.52
1.47
0.36
0.00
1.74
1.76
1.60
0.58
0.03
30
21
10
1
2
1.63
1.46
1.02
0.01
0.30
1.80
1.66
1.28
0.18
0.30
25
28
21
10
1
31
32
34
36
37
38
39
Ga
Ge
Se
Kr
Rb
Sr
Y
6
9
9
1
2
1
10
0.73
0.91
0.83
0.00
0.36
0.10
1.08
0.77
1.01
0.89
0.00
0.7
0.70
1.50
1
6
4
6
1
2
1 + 15
0.00
0.64
0.00
0.70
0.62
0.00
0.34
1.18
0.66
0.00
0.53
1.41
2
1
9
9
6
1
10
40
48
50
56
57
70
82
'h:
Cd
Sn
Ba
La
Yb
Pb
21
1
9
1
10
1
9
1.53
0.00
0.73
0.36
1.41
0.02
0.26
1.99
0.02
0.88
0.92
1.85
0.21
0.54
28
2
6
2
21
2
6
1.66
0.30
0.52
0.62
1.47
0.30
0.32
1.91
0.30
0.61
0.85
1.71
0.31
0.40
21
1
1
1
10
References
I. Astrophysical Quantities, I, §15; 2, § 15
2. Cayrel, R., & Jugaku, J. 1963, Ann. d'Astrophys., 26, 495
3. Bolton, C.T. 1970, ApJ, 161, 1187
The degree of ionization in the material of stellar atmospheres is given in Table 3.4, relating gas
pressure Pg• electron pressure Pe , and temperature T. The data are averaged from [24] (rather high
heavy-element abundance) and [25] (rather low heavy-element abundance).
3.6 ATOMIC CROSS SECTIONS FOR ELECTRONIC COLLISIONS / 35
Table 3A. log Pg.
E> and T
10gPe
E>
T (K)
-2
-1
0
1
2
3
4
5
3.4
0.1
50400
0.2
25200
0.4
12600
0.6
8400
0.8
6300
1.0
5040
1.2
4200
1.4
3600
-1.9
-0.8
+0.27
1.27
2.27
3.28
4.28
5.59
-1.8
-0.74
+0.29
1.30
2.30
3.30
4.31
5.30
-1.70
-0.70
+0.31
1.33
2.34
3.35
4.43
5.87
-1.67
-0.66
+0.35
1.47
2.98
4.87
6.84
8.66
-1.54
-0.01
+1.90
3.87
5.65
7.0
8.7
10.4
+0.78
2.57
3.9
5.2
6.7
8.3
10.0
11.8
+2.0
3.1
4.5
6.0
7.7
9.4
11.2
13.2
+2.4
3.9
5.3
6.7
8.5
10.4
12.4
14.4
IONIZATION POTENTIALS
Table 3.5 gives the energy in eV required to ionize each element to the next stage of ionization. I
(Y = 1) denotes the neutral atom, II the first ion, etc. Dividing lines between shells and subshells are
added to assist interpolation. Part of the data is based on an especially accurate compilation for selected
ions [6-20], made available by the National Institute of Standards and Technology (NIST. see Sec. 3.1
for online access). If the data are given in wave numbers, the currently recommended conversion factor
to energy is 1 eV = 8065.541 cm- 1 [26].
3.5
ELECTRON AFFINITIES
Electron affinity is the energy difference between the lowest state of the atom (or molecule or ion)
and the lowest state of the corresponding negative ion (see Table 3.6). It is positive for those atoms or
molecules that form stable negative ions. Regarding the astrophysically important H-, it was thought
earlier that a second stable state exists [27]. Later, however, it was proven rigorously that there is only
one stable state [28, 29].
3.6 ATOMIC CROSS SECTIONS FOR ELECTRONIC COLLISIONS
Definitions of symbols are presented below:
Q
v
2
7rao
Ne,Na,Nj
L=vQ
NeL
NeNaL
Pc
Atomic cross section [= Q(v)].
Precollision electron velocity.
Atomic unit cross section = 8.797 X 10- 17 cm2 •
Electron, atom, ion densities (per cm3 ).
Collision rate for each atom per unit N e.
Collision rate per atom (or ion).
Collision rate per cm3 .
Collisions encountered by an electron per cm at 0° C and 1 mm Hg.
pressure, then Q = 2.828 X 10- 17 Pc = 0.32157ra5Pc.
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
11
2
3
4
5
6
7
8
9
10
I
Zn
Cr
Mn
Fe
Co
Ni
Cu
V
n
Ca
Sc
Ar
K
Cl
P
S
F
Ne
Na
Mg
Al
Si
0
Be
B
C
N
Li
H
He
Atom
13.59844
24.58741
5.39172
9.32263
8.29803
11.26030
14.53414
13.61806
17.42282
21.56454
5.13908
7.64624
5.98577
8.15169
10.48669
10.36001
12.96764
15.75962
4.34066
6.11316
6.56144
6.8282
6.7463
6.76664
7.43402
7.9024
7.8810
7.6398
7.72638
9.39405
54.41778
75.640 18
18.21116
25.15484
24.38332
29.6013
35.11730
34.97082
40.96328
47.2864
15.03528
18.82856
16.34585
19.7694
23.3379
23.814
27.62967
31.63
11.87172
12.79967
13.5755
14.66
16.4857
15.63999
16.1878
17.083
18.16884
20.29240
17.96440
II
122.454
153.897
37.931
47.888
47.449
54.936
62.708
63.45
71.620
80.144
28.448
33.493
30.203
34.79
39.61
40.74
45.806
50.913
24.757
27.492
29.311
30.96
33.668
30.652
33.50
35.19
36.841
39.723
m
217.713
259.366
64.492
77.472
77.413
87.140
97.12
98.91
109.265
119.99
45.142
51.444
47.222
53.465
59.81
60.91
67.27
73.489
43.267
46.71
49.16
51.2
54.8
51.3
54.9
55.2
59.4
IV
340.22
392.08
97.89
113.9O
114.24
126.21
138.40
141.27
153.83
166.77
65.03
72.59
67.8
75.02
82.66
84.50
91.65
99.30
65.28
69.46
72.4
75.0
79.5
75.5
79.9
82.6
V
489.98
552.06
138.12
157.17
157.93
172.18
186.76
190.49
205.27
220.42
88.05
97.03
91.01
99.4
108.78
111.68
119.53
128.1
90.64
95.6
99.1
103
108
103
108
VI
667.03
739.29
185.19
207.28
208.50
225.02
241.76
246.49
263.57
280.95
114.20
124.32
117.56
127.2
138.0
140.8
150.6
161.18
119.20
124.98
131
134
139
136
VII
871.41
953.91
239.10
264.25
265.96
284.66
303.54
309.60
328.75
348.28
143.46
154.88
147.24
158.1
170.4
173.4
184.7
194.5
151.06
160
164
167
175
vm
Stage of ionization
1103.1
1195.8
299.9
328.1
330.1
351.1
372.1
379.6
400.1
422.5
175.8
188.5
180.0
192.1
205.8
209.3
221.8
233.6
186.2
193
199
203
IX
Table 3.5. Ionization potentials (electron volts) [1-20].
1362.2
1465.1
367.5
398.8
401.4
424.4
447.5
455.6
478.7
503.8
211.3
225.2
215.9
230.5
244.4
248.3
262.1
276.2
224.6
232
238
X
1648.7
1761.8
442.0
476.4
479.5
504.8
529.3
539.0
564.7
591.9
249.8
265.1
255.1
270.7
286.0
290.2
305
321
266
274
XI
1963
2086
523
561
564
592
618
629
657
688
292
308
298
314
331
336
352
369
311
XII
2304
2438
612
652
657
686
715
727
757
788
336
355
344
361
379
384
401
412
xm
2673
2817
707
750
756
787
818
831
863
896
384
404
392
411
430
435
454
XIV
(I)
tTl
c::t'"
(')
t'"
tTl
0
~
t:I
>
Z
(I)
a:
~
0
UJ
.......
UJ
0'1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
F
Ne
Na
Mg
Al
Si
p
S
C1
Ar
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
0
H
He
Li
Be
B
C
N
Atom
3070
3224
809
855
862
895
927
941
975
1011
435
457
444
464
484
490
XV
3494
3658
918
968
974
1009
1044
1060
1097
1136
489
512
499
520
542
XVI
3946
4121
1034
1087
1094
1131
1168
1185
1224
1266
547
571
557
579
xvn
4426
4611
1157
1213
1221
1260
1299
1317
1358
1402
607
633
619
xvrn
5129
1288
1346
1355
1396
1437
1456
1500
1546
671
698
4934
XIX
5470
5675
1425
1486
1496
1539
1582
1602
1648
1698
738
XX
6034
6249
1569
1634
1644
1689
1734
1756
1804
1856
XXI
6626
6851
1721
1788
1799
1846
1894
1919
1970
XXll
7246
7482
1879
1950
1962
2010
2060
2088
XXllI
Stage of ionization
Table 3.5. (Continued.)
7895
8141
2045
2119
2131
2182
2234
XXIV
8572
8828
2218
2295
2310
2363
XXV
9278
9544
2398
2478
2495
XXVI
10030
10280
2560
2660
xxvn
10790
11050
2730
xxvrn
W
......:J
w
til
Z
-
0
....
....til
t""
t""
0
(J
n
Z
....
0
::0
n~
trl
t""
tI1
0
::0
'11
til
Z
0
....~
n
CI'.l
trl
til
til
0
(J
::0
....3:n
0
~
0'1
38 I 3
ATOMS AND MOLECULES
Table 3.5. (Continued.)
Stage of ionization
Atom
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
Ga
Ge
As
Se
Br
Kr
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
Cs
Ba
La
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
TI
Pb
Bi
Po
At
5.99930
7.900
9.8152
9.75238
11.81381
13.99961
4.17713
5.69484
6.217
6.63390
6.75885
7.09243
7.28
7.36050
7.45890
8.3369
7.57624
8.99367
5.78636
7.34381
8.64
9.0096
10.45126
12.12987
3.8939
5.21170
5.5770
.5387
5.464
5.5250
5.55
5.6437
5.6704
6.1500
5.8639
5.9389
6.0216
6.1078
6.18431
6.25416
5.42585
6.82507
7.89
7.98
7.88
8.7
9.1
9.0
9.22567
10.43750
6.10829
7.41666
7.289
8.41671
9.3
II
m
IV
V
VI
VII
vm
IX
X
20.514
15.935
18.633
21.19
21.8
24.360
27.285
11.0:30
12.24
13.13
14.32
16.16
15.26
16.76
18.08
19.43
21.49
16.908
18.870
14.632
16.531
18.6
19.131
21.21
23.157
10.004
11.06
10.85
10.55
10.73
10.90
11.07
11.241
12.09
11.52
11.67
11.80
11.93
12.05
12.176
13.9
14.9
16
18
17
17
17
18.563
20.5
18.756
20.428
15.032
16.69
19
20
30.71
34.224
28.351
30.820
36
36.95
40
42.89
20.52
22.99
25.04
27.13
29.54
28.47
31.06
32.93
34.83
37.48
28.03
30.503
25.3
27.96
33
32.123
35
64
45.71
50.13
42.944
47.3
52.5
52.6
57
61.8
34.34
38.3
46.4
46
50
48
53
56
59
54.4
40.734
44.2
37.41
42
46
46
49
87
93.5
62.63
68.3
59.7
64.7
71.0
71.6
77.0
81.5
50.55
61.2
55
60
65
62
68
72
116
112
127.6
81.7
88.6
78.5
84.4
90.8
93
99
102.6
68
80
92
97
90
89
94
98
103
140
144
147
155.4
103.0
111.0
9.2
106
116
117
125
126.8
170
174
179
184
192.8
126
136
122.3
129
140
142
153
212
207
212
218
224
230.9
150
162
146.2
155
161
163
187
243
250
242
250
257
263
277.1
177
191
19.177
20.198
21.624
~
110
115
115
120
125
130
137
100
100
100
95
100
100
105
130
140
145
145
150
155
165
170
120
120
120
115
120
120
130
135
155
160
170
180
175
185
190
200
210
145
145
145
140
145
150
155
160
180
185
195
205
210
210
220
230
240
250
160
165
165
160
170
175
180
190
23.68
25.05
20.959
23.3
22
24
26
25
27
28
30
34.2
29.83
31.937
25.56
27
29
n
72.28
56
58.75
lOS
36.72
38.95
~
57.45
70.7
81
82
74
80
80
85
~
33.3
33
35
38
40
39
41
44
46
50.7
42.32
45.3
38
41
45
48
51
54
57
55
58
61
64
68.8
56.0
61
51
61
64
68
72
75
73
77
81
84
88.3
73
78
66
57
62
62
66
!.!!L.
79
83
88
92
96
94
98
103
107
112
91
100
105
110
115
120
115
120
125
130
140
120
125
l35
140
145
140
150
155
160
145
155
160
165
175
170
175
185
3.6 ATOMIC CROSS SECTIONS FOR ELECTRONIC COLLISIONS / 39
Table 3.S. (Continued.)
Stage of ionization
Atom
86
87
88
89
90
91
92
93
94
95
Rn
Fr
Ra
Ac
Th
Pa
U
Np
Pu
Am
10.74850
4
5.27892
5.17
6.08
5.89
6.19405
6.2657
6.06
5.993
II
ill
IV
V
21
22
10.147
12.1
11.5
29
33
34
20
20.0
44
43
46
49
28.8
55
59
58
62
65
VI
67
71
76
76
80
84
VII
Vill
IX
X
97
84
89
95
94
100
104
110
115
105
110
115
115
120
165
135
140
125
130
140
140
190
195
155
165
145
155
160
References
1. Astrophysical Quantities, 1, §16; 2, §16; 3, §16
2. Lotz, W. 1966, Ionisierungsenergien von Ionen H his Ni (lost. Plasrnaphys, Miinchen)
3. Moore, C.E. 1970, Ionization Potentials, NSRDS-NBS 34, Washington
4. Finkelnberg, W., & Humbach, W. 1955, Naturwiss., 42, 35
5. Handbook of Chemistry and Physics, 77th ed. (CRC, Boca Raton, FL, 1996)
6. Martin, W.e. 1987, Phys. Rev. A, 36, 3575 (He I)
7. Martin, w.e., Kaufman, V., & Musgrove, A. 1993, J. Phys. Chem. Ref Data, 22,1179 (011)
8. Martin, w.e., & Zalubas, R. 1981, J. Phys. Chem. Ref Data, 10, 153 (Na I-XI)
9. Martin, W.C., & Zalubas, R. 1980, J. Phys. Chem. Ref Data, 9, 1 (Mg I-XII)
10. Martin, W.C., & Zalubas, R. 1979, J. Phys. Chem. Ref Data, 8,817 (AI I-XIII)
11. Martin, W.C., & Zalubas, R. 1983, J. Phys. Chem. Ref Data, 12, 323 (Si I-XIV)
12. Martin, w.e., Zalubas, R., & Musgrove, A. 1985, J. Phys. Chern. Ref Data, 14, 751 (PI-XV)
13. Martin, W.C. Zalubas, R., & Musgrove, A. 1990, J. Phys. Chem. Ref Data, 19, 821 (S I-xvI)
14. Sugar, J., & Corliss, C. 1985, J. Phys. Chem. Ref Data, 14, Supp!. No.2 (K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni)
15. Sugar, J., & Musgrove, A. 1990, J. Phys. Chem. Ref Data, 19, 527 (I-XXIX)
16. Sugar, J., & Musgrove, A. 1995, J. Phys. Chem. Ref Data, 24, 1803 (Zn I-XXX)
17. Sugar, J., & Musgrove, A. 1993, J. Phys. Chem. Ref Data, 22,1213 (Gel-XXXII)
18. Sugar, J., & Musgrove, A. 1991, J. Phys. Chem. Ref Data, 20,859 (KrI-xxxvI)
19. Sugar, J., & Musgrove, A. 1988, J. Phys. Chem. Ref Data, 17, 155 (Mo I-XLII)
20. Martin, W.C., Zalubas, R., & Hagan, L. 1978, Nat!. Stand. Ref. Data Ser. (Nat!. Bur. Stand., U.S.) 60 (Rare-Earth
Elements)
21. Cohen, E.R., & Taylor, B.N. 1988, J. Phys. Chern. Ref. Data, 17,1795
Table 3.6. Electron affinities [1-2].
Atom
Electron
affinity (eV)
Atom
Electroo
affinity (eV)
H
He
Li
Be
B
+0.754
-0.3
+0.618
-0.4
+0.277
Na
Mg
Al
Si
P
+0.479
-0.4
+0.441
+1.385
+0.747
C
N
0
0F
Ne
+1.263
-0.2
+1.461
-6.7
+3.401
-0.7
S
CI
Br
I
K
Ca
+2.077
+3.612
+3.48
+3.17
+0.501
+0.018
Molecule
Electron
affinity (eV)
02
03
OH
SH
C2
C3
+0.451
+2.1028
+1.82767
+2.314
+3.269
+1.981
CN
NH2
NO
N02
N03
CH
+3.862
+0.771
+0.026
+2.273
+3.951
+1.238
References
\
1. Astrophysical Quantities, 1, § 17; 2, § 17; 3, § 17
2. Handbook of Chemistry and Physics. 77th ed. (CRC, Boca Raton, FL, 1996)
40 I
3
3.6.1
Ionization Cross Section
ATOMS AND MOLECULES
The classical cross section of atoms for ionization by electrons [30] is
Ql
= 4mraJ-1-
XE
(1 - !)
,
E
where X is the ionization energy in rydbergs (Ry), E the electronic energy before collision in Ry, and n
the number of optical electrons.
The general approximation for cross sections of atoms for ionization by electrons (see, [30-33]) is
Ql
2
1
mraJ
= mrao-F(Y,
E/x) = -2- q
X~
X
= 1.63 x 1O-14n (l/x;v)(x/E)F(Y, E/x),
where Y is the charge on the ionized atom (or next ion stage) and XeV is the ionization energy in
eY. The function F(Y, E/x) is given and also q = (X/E)F(Y, E/x), which is sometimes called the
reduced cross section in Table 3.7. The Y = 1 and Y = 2 values are from experiment and Y = 00
from calculation. About ±1O% accuracy may be expected for hydrogenic ions. In other cases ±0.3
dex may be expected. Other empirical forms have been suggested (see, e.g., [34-36]).
Table 3.7. Numericalfunctions F(Y. ~/X) and q(Y. E/X).
E/X
F(c1assical)
F(l. E/X)
F(2. ~/X)
F(OO.E/X)
= 4(1 -
q(c1assical)
q(l. ~/X)
q(2. E/X)
q(oo. E/X)
= 4(X/E)(l- X/E)
X/E)
1.0
1.2
1.5
2.0
3
5
10
0.00
0.0
0.00
0.00
0.67
0.31
0.53
0.74
1.33
0.78
1.17
1.54
2.00
1.60
2.02
2.56
2.67
2.9
3.3
3.8
3.20
4.6
4.7
5.0
3.60
6.4
6.4
6.4
0.00
0.00
0.00
0.00
0.56
0.26
0.44
0.62
0.89
0.52
0.78
1.03
1.00
0.80
1.01
1.28
0.89
0.97
1.09
1.28
0.64
0.92
0.94
1.00
0.36
0.64
0.64
0.64
The maximum ionization cross section for the classical case is
Qmax
= mraJx-2
atE
= 2X·
The value of Qmax is approximately the same in actual cases but the maximum occurs near E
The rate of ionization by electrons (see [30-32]) is
Ll
= VQ1.
The neutral atom approximation (with kT < ionization energy) gives
Ll = 1.1 x 1O-8nTl/2xc11O-5040Xev/T cm3 s-l.
The coronal ion approximation (with kT < ionization energy) gives
Ll = 2.1 x 1O-8nTl/2Xe11O-5040xev/T cm3 s-l.
= 4X.
3.6 ATOMIC CROSS SECTIONS FOR ELECTRONIC COLLISIONS 1 41
3.6.2
Excitation Cross Section (permitted Transitions)
An approximation for Qex, the excitation cross section of an atom (see [30,37]), is given. The
approximation applies fairly well when I::!.n 2: 1 (notation of Chap. 5). For I::!.n = 0 the approximation
tends to be small:
Qex
=
8n
2 f
-nao-b
.J3
EW
= 1740na5)..2(WIE)fb
= 1.28 x 10- 15 (fIE W)b cm2 ,
where f is the oscillator strength, W is the excitation energy in Ry (= 0.09121).. with ).. in JLm), and E
is the electron energy before collision, also in Ry. See Table 3.8.
Table 3.8. Numerical/actors b and bW IE.
1.0
1.2
1.5
2.0
3
5
10
30
100
b, neutral atoms
b, ions
0.00
0.20
0.03
0.20
0.06
0.20
0.11
0.20
0.21
0.24
0.33
0.33
0.56
0.56
0.98
0.98
1.33
1.33
b WI E, neutral atoms
bW/E, ions
0.00
0.20
0.03
0.17
0.04
0.13
0.06
0.10
0.07
0.08
0.07
0.07
0.06
0.06
0.03
0.03
0.01
0.01
E/W
The maximum excitation cross section is as follows:
• The neutral atom approximation gives
• The ion approximation gives
The rate of excitation (see [34,35,37]) is
L
= vQe=x170
x
·
10-4
f
Tl/2WeV
1O-5040Wev/ T P(WlkT)
'
where WeV and Ware the excitation energy in eV and in ergs (with 11600Wev 1kT = WI kT) and
P(W1kT) is tabulated from [37] (see Table 3.9).
Table 3.9. Numerical/actors
pew I kT) and WI kT.
P(WlkT)
WlkT
< 0.01
0.01
0.02
0.05
Neutral atoms
Ions
0.29E] (WlkT)a
1.16
0.96
0.70
1.16
0.98
0.74
42 / 3
ATOMS AND MOLECULES
Table 3.9. (Continued.)
P(W/kT)
W/kT
0.1
0.2
0.5
I
2
5
10
>10
Neutral atoms
Ions
0.49
0.33
0.11
0.10
0.063
0.035
0.023
0.55
0.40
0.26
0.22
0.21
0.20
0.20
O.066/(W/ kT) 1/2
0.20
Note
a E 1( ) is the first exponential integral.
The tabulated P(W j kT) are too small when the total quantum number of Chap. 5 is unchanged.
The approximations quoted should be replaced by quantum calculations when available (see
[30,38-40]). A Coulomb approximation for ions [41] gives b = geff(2L + l)jgl (L in Chap. 5).
The tabulations of geff, the effective Gaunt factor, range from 0.5 to 0.9.
3.6.3 Deexcitation Cross Sections
Deexcitation cross sections Q21 are related to excitation cross sections Q12 (2 being the upper level)
through
where E"2 = E"l + W, and g2 and gl are statistical weights.
The deexcitation rate L21 and excitation rate LI2 are related by
3.6.4 Excitation Cross Sections (Forbidden Transitions)
The collision strength Q for each line is defined by (see [33,42])
Qf = rrQjglk~
= rra5QjglE"
h2 Q
= - - 2 - - 2 =4.21Qjglv 2 ,
4rrm glv
where kv j2rr is the wave number of the incident electron (then k~ in atomic units = E" in Ry), v is the
electron velocity, gl is the statistical weight of the initial (lower) level, and Qf is the forbidden line
cross section for atoms in this level. Then QI2(excitation) = Q21 (deexcitation).
3.6.5
Collision Strengths: Extensive Databases
Crude recipes to estimate the order of magnitude of collision strengths (for allowed and forbidden
transitions) can be found in older references [43]. In recent years, however, a wealth of accurate
3.7 ATOMIC RADII / 43
collision strengths have been obtained for a very large number of transitions. They are based on
extensive UV and IR emission-line observations and on theoretical calculations. Data are available,
e.g., from the Opacity Project, the Iron Project, and the Harvard-Smithsonian Center for Astrophysics
(see Sec. 3.1 for information about online access of these sources).
3.6.6 Total Atomic Cross Section (Elastic and Inelastic)
An approximation for the total cross section is (see [31, 32, 44])
Q ~ 1801l"a6J../E1/2
(J.. in /.Lm, E in Ry),
where J.. is the wavelength of the strongest low-level lines.
3.6.7 Ionic Collision Cross Section
Cross section for collision deflection of at least a right angle (see [45])
QJ
= 1l"(Y -
1)2(e2/mv2)2
= IT(Y -
1)2(e2 /2EhcR)2
= 1l"a6(Y - 1)2/E2 (E in Ry),
where Y - 1 is the ionic charge.
The effective ionic collision cross section is usually concerned with the more distant collision
involving deflections much less than a right angle. These increase the effective Q by a factor depending
logarithmically on the most distant collisions that enter the integration and also on the circumstances.
The factor is usually between 10 and 50 (see Sec. 3.10). We may write a general approximation:
Q(effective) ~ 201l"a6(Y - 1)2 /E2.
3.7 ATOMIC RADII
Atomic radii are defined through the closeness of approach of atoms in the formation of molecules
and crystals. The radius r so derived is approximately that of maximum radial density in the charge
distribution of neutral atoms (see Table 3.10). For ions the appropriate radius measures to the point
where the radial density falls to 10% of its maximum value. The atomic mass divided by the atomic
volume (4/3)1l"r 3 gives the density of the more compact solids. 2r is approximately the gas-kinetic
diameter of monoatomic molecules.
Table 3.10. Atomic radii [1-5].
Atom
r (A)
Ion [3]
r (A)
Atom
r (A)
H
He
Li
Be
B
0.7
1.2
1.58
1.06
0.83
H-
1.8
S
Cl
Ar
K
Ca
1.05
1.02
1.6
2.37
1.97
Li+
Be2+
B3+
0.68
0.39
0.28
Ion [3]
r (A)
Atom
r (A)
Ion [3]
r (A)
S2-
Cl-
1.70
1.67
1.82
1.52
1.14
1.2
1.82
2.54
2.3
1.44
Br-
K+
Ca2+
Br
Kr
Rb
Sr
Ag
Rb+
sr2+
Ag+
1.66
1.32
1.29
44 /
3
ATOMS AND MOLECULES
Table 3.10. (Continued.)
Atom
rCA)
Ion [3)
rCA)
Atom
rCA)
Ion [3)
rCA)
Atom
rCA)
Ion [3)
rCA)
C
N
0
F
Ne
0.77
0.70
0.66
0.62
1.3
C4+
N 30 2F-
0.22
1.92
1.26
1.19
Sc
Ti
Y
Cr
Mn
1.64
1.46
1.39
1.28
1.26
Sc3+
Ti4+
y4+
0.89
0.75
0.61
1.09
0.76
2.06
0.81
1.6
1.62
1.4
2.00
2.73
Cd2+
Sn4+
1-
Mn2+
Cd
Sn
I
Xe
Cs
Cs+
1.81
1.27
1.25
1.29
1.28
1.39
Fe2+
Co2+
Ni2+
Cu+
Zn2+
2.24
1.38
1.44
1.57
Ba2+
1.49
Au+
Hg2+
1.51
1.16
1.91
1.62
1.43
1.09
1.08
Na
Mg
Al
Si
P
Na+
Mg2+
A13+
Si4+
p3-
1.16
0.86
0.67
0.47
2.3
Fe
Co
Ni
Cu
Zn
0.75
0.79
0.83
0.91
0.77
Ba
Pt
Au
Hg
References
1. Astrophysical Quantities, I, §19; 2, §19; 3, §19
2. Teatum, E., Gschneidner, K., & Waber, J. 1960, Los Alamos Scientific Laboratory, Report No. LA-2345
3. Shannon, R.D. 1976, Acta Cryst., A32, 751
4. Allen, EH., Kennard, 0., Watson, D.G., Brammer, L., Orpen, A.G., & Taylor, R. 1987,1. Chern. Soc. Perkin /l,
SI
5. Alcock, N.W. 1990, Bonding and Structure: Structural Principles in Inorganic and Organic Chemistry, (Ellis
Horwood, New York)
3.8
PARTICLES OF MODERN PHYSICS
A representative selection of particles is given in Table 3.11. Hadrons include mesons, nucleons, and
baryons. Possible proton decay is not included. I denotes the isotopic spin, J the spin, and P the
parity. The lifetime is that in free space. In the column labeled "Decay" are given the main decay
products. The mean life r for Wand Z bosons is given as the linewidth f (rf ~ h).
Table 3.11. Selected particles o/modem physics [1-3].
Name
Symbol
Charge
Mass
(amu)
JP
Mean life
(s)
1I
1
r=2.IGeV
r = 2.5 GeV
Decay
Bosons
Gauge bosons
Photon
W
y
W
Z
Z
0, I
0
+1,-1
0
0.000
86.24
97.90
+1, -1
0
+1, -I
0.14984
0.14490
0.53015
000-
2.603 x 10- 8
0.83 x 10- 16
1.237 x 10- 8
JLv
I
Ih
s
0
0.53438
Ih
0-
0.892 x 10- 10
,,+,,- ,,,0,,0
L
0
0.53438
Ih
0-
5.38 x 10-8
"eo," JLV, 3,,0
Mesons
,,-mesons (pion)
n+,Jr,,0
K meson (kayon)
K(j,KKO
KO
00
eV,etc.
e+e-, etc.
yy
/Lv, ",,0
Fermions
Leptons
e Neutrino
JL Neutrino
T Neutrino
Electron, Positron
JL meson (muon)
T meson (tauon)
Ve
vI'
VT
e
JL
T
0
0
0
-1,+1
-1,+1
-1,+1
< 5 x 10- 8
< 5 x 10-4
<0.2
0.0005486
0.1134
1.915
Ih
Ih
Ih
Ih
Ih
Ih
00
00
00
00
2.197 x 10-6
(3.4 ± 0.5) x 10- 13
evv
evii
3.9 MOLECULES / 45
1Bble 3.11. (Continued.)
Name
Symbol
Charge
p
n
+I, -1
A
Nonstrange baryons
Proton
Neutron
Mass
(amu)
Mean life
(s)
1.007275
1.008664
lil
lil
Ih+
Ih+
0.932 x 103
0
+1,-1
0
-1,+1
1.1976
1.2768
1.2802
1.2854
0
Ih+
Ih+
Ih+
Ih+
2.632 x 10- 10
0.800 x 10- 10
< 10- 19
1.482 x 10- 10
p",-, n,..O, etc.
p,..O, fill" + , etc.
Ay, etc.
fill" - , etc.
0
Strangeness-} baryons
A
};+
};+
};O
};O
};-
};-
Strangeness-2 baryons
Decay
00
pe - v
SO
SO
8-
8-
0
-1,+1
1.411 6
1.4185
lil
lil
Ih+
Ih+
2.90 x 10- 10
1.641 x 10- 10
A"'O, etc.
A,..-. etc.
n-
-1,+1
1.795
0
3h+
0.819 x 10- 10
AK-, etc.
-1,+1
2.450
0
Ih+
2.3 x 10- 13
AK-,etc.
Strangeness-3 baryons
!Or
Nonstrange charmed baryons
Ac
Ac
Composite particles
IH
2H
0
a
Hydrogen (251/2)
Deuterium (251/2)
Deuteron
a particle
0
0
+I
+2
1.00782
2.01410
2.0\355
4.00140
00
00
00
00
References
1. Astrophysical Quantities, 1, §20; 2, §20; 3, §20
2. Barnett, R.M. et al. 1996, Rev. Mod. Phys.• 68, 611
3. Barnett. R.M. et al. 1996. Phys. Rev.. D54. 1
3.9
MOLECULES
Some definitions follow:
NA, NB, NAB
mAB
ro
Do
gO
We, WeXe
IP
UA,UB
QAB
I
Number of atoms A, B, and molecules AB per cm3 .
Reduced mass = mAmB/(mA + mB)'
Internuclear distance (lowest state).
Dissociation energy (lowest state).
Electronic statistical weight (lowest state), or
Multiplicity, = 2S + 1 for 1: states, = 2(2S + 1) for other states.
= 1 for heteronuclear molecules, = 2 for homonuclear molecules.
Vibrational quantum number.
Rotational constants [46,47].
Energy change = heB = h 2/87r 2 1= h 2/87r 2mABr;.
Vibrational constants.
Ionizational potential.
Atomic partition functions (Sec. 3.3).
Molecular partition function, = QrotQvibQeI. each term dimensionless.
Moment of inertia, = m ABr;.
46 / 3
ATOMS AND MOLECULES
Molecular diameters (diatomic) are
~ 3ro ~ 3.4A.
Molecular dissociation is represented by
Numerically,
log(NANB/NAB) = 20.2735 + ~ log mAB
+ ~ log T
- 5040D/T + log(UAUB/QAB)
with min amu, Din eV, N in cm- 3 ,
Qrot
= kT/uhcBv = (T/1.439 K)uBv ,
Bv = Be - OIe(V +
i),
Qvib = ""
~ exp (1.439
T K [We V
Qel
= Lgel exp ( el
-
WeXe(V
2)
+
v)]
,
1.439 K )
T
Tel,
with Bv , We, Tel (= electronic excitation energy) in em-I.
The main ground-level constants are given in Tables 3.12 and 3.13, but upper level constants
[46, 47] are required for dissociation calculations.
Table 3.12. Diatomic molecules [l-3].Q
Molecule
gO
u
H2
H2+
He2
DH
DO
C2
CH
CH+
CO
CO+
1
4
1
1
2
1
4
1
1
2
2
2
2
1
2
1
1
1
1
CN
2
1
2
3
4
3
4
4
3
2
1
2
2
1
1
2
2
1
1
1
N2
N+
2
NH
NO
02
02+
OH
OH+
MgH
AlH
AIO
SiH
1
2
4
I
Be
ae
(em-I)
We
(em-I)
WeXe
(em-I)
TO
(A)
IP
(em-I)
60:85
30.2
3.06
1.68
4401
2321
15.426
12.02
1.78
1.82
14.46
14.18
1.93
1.977
0.412
0.017
0.018
0.53
0.49
0.018
0.019
2367
1886
1855
2859
2740
2170
2214
121
66.2
22.22
49.4
11.8
13.3
63.0
1.131
13.29
15.16
0.741
1.052
3.42
8.28
6.296
3.465
4.085
11.092
8.338
0.504
0.504
2.002
0.923
6.452
6.003
0.930
0.930
6.856
6.859
1.232
1.205
1.243
1.120
9.77
7.0
12.15
10.64
1.128
1.115
14.01
26.8
7.76
9.759
8.713
3.47
6.497
5.116
6.663
4.392
5.09
1.34
6.462
7.002
7.001
0.940
7.467
7.997
7.997
0.948
0.948
0.967
1.90
1.998
1.932
16.699
1.672
1.445
1.691
18.91
16.79
5.826
0.017
0.017
0.019
0.649
0.017
0.016
0.020
0.724
0.749
0.185
2068
2359
2207
3282
1904
1580
1905
3738
3113
1495
13.09
14.32
16.10
78.35
14.08
11.98
16.26
84.88
78.52
31.89
1.172
1.098
1.116
1.036
1.151
1.208
1.116
0.970
1.029
1.730
14.17
15.58
27.1
13.63
9.26
12.07
24.2
12.90
3.06
5.27
3.06
0.972
10.042
0.973
6.391
0.641
7.500
0.186
0.006
0.219
1683
979
2042
29.09
6.97
1.648
1.618
1.520
Do
(eV)
4.4781
2.6507
ob
mAB
(amu)
(eV)
9.53
8.04
3.10 PLASMAS / 47
Table 3.12. (Continued.)
go
SiO
SiN
SO
CaR
CaO
ScO
TiO
2
3
2
1
2
6
VO
crO
FeO
YO
zrO
LaO
a
I
4
2
6
2
IP
mAB
(amu)
Be
(em-I)
8.26
4.5
5.359
1.70
4.8
6.96
6.87
10.177
9.332
10.661
0.983
11.423
11.797
11.994
0.727
0.731
0.721
4.276
0.445
0.513
0.535
0.005
0.006
0.006
0.097
0.003
0.003
0.003
1242
1151
1149
1298
732
965
1009
5.97
6.47
5.63
19.10
4.81
4.20
4.50
1.510
1.572
1.481
2.003
1.822
11.43
1.620
6.4
6.4
4.4
4.20
7.29
7.85
8.23
12.173
12.229
12.438
13.556
13.579
14.343
0.548
0.541
0.513
0.388
0.423
0.353
0.004
0.005
0.004
0.002
0.002
0.001
lOll
4.86
6.75
8.71
2.93
4.90
2.22
1.589
1.615
8.2
1.790
1.712
1.825
4.95
DO
Molecule
(eV)
Q!e
(em-I)
We
(em-I)
WeXe
(em-I)
898
965
861
970
812
rO
(eV)
10.29
5.86
Notes
a See Sec. 4.11 for further molecular data and references.
bThe lowest electronic state supports no bound state. However, the ground-state energy (as a function of
nuclear separation) has a potential well. Its depth is De = 0.0009 eV.
References
1. Astrophysical Quantities, 1, §21; 2, §22; 3, §21
2. Herzberg, G. 1950, Spectra of Diatomic Molecules (Van Nostrand, New York)
3. Huber, K.P., & Herzberg, G. 1979, Molecular Spectra and Molecular Structure IV. Constants of Diatomic
Molecules (Van Nostrand, New York)
Table 3.13. Selected polyatomic molecules [1-2].
Molecule
IP
(eV)
(eV)
(A)
H2O
N2 0
CO2
NH3
Cf4
HCN
12.61
12.89
13.77
10.15
13.0
13.91
5.11
1.68
5.45
4.3
4.4
5.6
3.5
4.0
3.8
3.0
3.5
D
Diameter
References
1. Astrophysical Quantities, 1, §21; 2, §22; 3, §21
2. Herzberg, G. 1966, Electronic Spectra of Polyatomic Molecules (Van Nostrand, New York)
3.10
PLASMAS
Some definitions follow:
Ne , Ni, Np , N
Zj
L
T,B,p
A
Electron, ion, proton, total heavy-particle densities.
Charge on i ion (denoted Yj - 1 in other sections).
Characteristic size (e.g., diameter) of plasma.
Temperature, magnetic field, density.
Mass in amu.
48 / 3
ATOMS AND MOLECULES
The Debye length, electron screening, the distance from an ion over which Ne can differ appreciably
from Li NiZi is
with T in K and Ne in cm- 3 .
The plasma oscillation frequency is
Vpl
= (Ne2/rrme)I/2 = 8.978 x 103 N~/2s-2
(in cgs).
The gyrofrequency for electrons is
Vgy
= (e/2rrmec)B
= 2.7994 x 106 B s-l,
and for ions is
Vgy
= (Ze/2rrmic)B
= 1.535 x lo3Zi B/A s-l,
with B in G.
The gyroradius for electrons is
a e = mev1. c/ eB
= 5.69 x 1O-8v1.B cm
:::::2.21 x 1O-2 T 1/ 2 jBcm,
and for ions is
al = miV1.cjZieB
= 1.036 x 1O-4v1.AjZiB cm
::::: 0.945Tl/2Al/2jZiB cm,
where v1. is the velocity normal to B.
The most probable thermal velocity for electrons is
v
and for atoms and ions is
v
= (2kT jme)I/2
= 5.506 x loST1/2 cm/s,
= (2kT jm)I/2
= 1.290 x 104(T j A)I/2 cm/s.
For rms velocities increase v by the factor.../'J12 = 1.225.
The velocity of sound is
comparable with thermal velocity.
The Alfven speed (magnetohydrodynamic or hydromagnetic wave) is
VA
= Bj(4rrp)I/2 =
0.282Bjp l/2.
3.10 PLASMAS / 49
The phase velocity is cO + 4npc 2I B2)1/2.
The electron drift velocity in crossed magnetic and electric fields is 108 E.LI B cm/s, with E.L in
V/cm and B in G.
The electron drift velocity in magnetic and gravitational fields is
megcleB = 5.686 x 1O-8g 1B cm/s,
with g in cm/s2 and B in G.
The collision radius p for right-angle deflection of electrons by an ion is
PO
= Zje2Imev;:::::
= 8.3 x
~Zle2lkT
1O-4 ZtlT
cm.
The corresponding collision cross section is
The cross section for all electron collisions with an ion is
with
In A
= In(dlc) =
ld
p- 1 dp
and where c is the minimum of p in circumstances and d is the maximum of p in circumstances.
c is the largest of
Ci
or
= 8.3 X
C2 = 1.06
10-4 Z11 T cm from the right-angle definition
1O-6 T -l/2 cm
X
from electron size.
d is the smallest of
dl
= N- 1/ 3 cm
d2
=
D
d3
=
1.8 x 105 T 1/2 Iv
or
or
from ion spacing
= 6.9T 1/ 2N- 1/ 2
(the Debye length)
for collisions giving free-free absorption of frequency v radiation.
The most general approximation for A is
In A
= 9.00 + 3.45 log T
- 1.15 log N e .
The collision cross section for neutral atoms and molecules is ::::: 10- 15 cm2 .
The collision frequency for electrons is Nl vex(cross section) = 2.5(ln A)NeT- 3 / 2 Zj s-l.
The collision frequency for ions with ions is 8 x 1O-2 (ln A)NeA -1/2T- 3/ 2 s-l.
The mean free path of electrons among charged particles is 4.7 x IOST 2 NIl NI2 cm.
The mean free path of electrons among neutral particles is 10 15 N- 1 cm.
Zf
50 / 3
ATOMS AND MOLECULES
The electrical resistivity [48] is
T/
= 8 x lO l2 (1n A)T-3/ 2
= 9 x 1O-9 (1n A)T-3/ 2
(emu)
(esu) ,
applying when the energy gains during free path < kT.
The thermal conductivity [48-50] is 1.0 x 1O-6 T5/2 ergcm- l s-l K- l .
The life of a magnetic field in a plasma is
'f
= 47CL 2/T/
= 1.5 x
(T/inemu)
1O- 12 L 2 (ln
A)-IT 3 / 2 s.
For approximate parameters for some plasmas, see Table 3.14.
Table 3.14. Approximate parameters for some plasmas. a Values are logarithmic.
Interstellar. f
Definition
Quantity
Unit
log
log
log
log
log
cm
cm- 3
cm- 3
K
G
L
Ne
N
T
B
Ion.b
Intpl.c
0Cor.d
o Rev.e
HIg
Huh
7.0
5.5
11.0
3.0
-1.0
13.0
0.5
0.5
5.0
-5.0
10.0
8.0
8.0
6.0
0.0
7.0
12.5
16.5
3.7
0.0
19.5
-3.0
0.0
2.0
-5.0
19.5
0.0
0.0
4.0
-5.0
s-1
6.8
4.2
8.0
10.2
2.5
4.0
cm
-0.6
3.0
-0.3
-3.6
3.2
2.7
6.4
0.7
6.4
3.2
1.4
-1.8
1.4
-1.8
Debye length
i log Ne
0.7 + i log T - i log Ne
Gyro freq.
Electron
Ion
6.4+ log B
3.2 + log B
s-1
s-1
5.4
2.2
1.4
-1.8
Collision freq.
Electron
1.7 + log Ne - ~ log T
s-1
2.2
-5.9
3.2
8.7
-1.8
-4.3
0.2 + log Ne - ~ log T
s-1
1.2
-7.4
-0.8
7.2
-5.8
-5.8
6.3 + ~ log T
esu
10.8
13.8
15.3
11.9
9.3
12.3
-14.6+ ~log T
emu
-10.1
-7.1
-5.6
-9.0
-11.6
-8.6
5.7 + 210g T -log Ne
15.0-10g N
cm
cm
6.2
4.0
15.2
14.5
9.7
7.0
0.6
-1.5
12.7
15.0
13.7
15.0
cm
cm
0.8
2.5
5.8
7.5
1.3
3.0
0.1
1.8
4.3
6.0
5.3
7.0
cmls
7.5
6.1
7.3
5.1
7.8
6.3
cmls
5.7
6.7
7.2
6.0
5.2
6.2
5.4
-2.1
19.4
11.9
15.9
8.4
6.5
-1.0
29.9
22.4
31.9
24.4
Plasma freq.
Ion
Electrical
conductivity
Mean free path
Ion
Neutron
Gyroradius
Electron
Proton
4.0+
Sound v
i
i
11.3 - i log N + log B
4.2+ i log T
B decay
-13.1 +2 log L+ ~log T
Alfv~n
v
-1.7 + log T -log B
0.0 + log T - log B
s
yr
Notes
aFor spectral emission from high-temperature plasmas, see Chap. 14.
3.10 PLASMAS I 51
blon. denotes ionosphere.
cIntpl. denotes interplanetary space.
d 0 Cor. denotes solar corona.
e 0 Rev. denotes solar reversing layer.
f Interstellar denotes interstellar space.
8H I denotes the H I region.
hH II denotes the H II region.
ACKNOWLEDGMENT
The author was supported in part by Grant No. AST-9315112 of the National Science Foundation.
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6. Anders, E., & Grevesse, N. 1989. Geochim. Cosmochim. Acta 53.197; Grevesse, N .• & Noels, A. 1993.
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Prantzos, E. Vangioni, and M . Casse (Cambridge University Press, Cambridge), p. 15 .
7. Biemont, E., Baudoux, M., Kurucz, R.L., Ansbacher,
W., & Pinnington, E.H. 1991, A&A, 249, 539
8. Hummer. D.G., & Mihalas, D. 1988, ApJ, 331. 794
9. Mihalas, D., Dii.ppen W., & Hummer, D.G. 1988, ApJ,
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10. Dippen. W., Anderson, L.S., & Mihalas, D. 1987, Api,
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11. Rogers. F.J. 1981. Phys. Rev. A, 24. 1531
12. Rogers. F.J. 1986, ApJ, 310, 723
13. Iglesias, C.A., & Rogers, F.J. 1991.ApJ. 371, L73
14. Rogers, FJ., & Iglesias, C.A. 1992.ApJS.401, 361
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17. Alastuey, A., & Perez, A. 1992, Europhys. Len., 20,19
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25. Aller. L.H. 1961, Stellar Atmospheres, edited by J.
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29. Hill, R.N. 1977, J. Math. Phys., 18, 2316
30. Bely. 0., & Van Regemorter, H. 1970, ARA&A, 8, 329
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33. Seaton, MJ. 1962, Atomic and Molecular Processes,
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Chapter 4
Spectra
Charles Cowley, Wolfgang L. Wiese,
Jeffrey Fuhr, and Ludmila A. Kuznetsova
4.1
4.1
Online Database . . . . . . . . . . . . . . . ..
...
53
4.2
Tenninology for Atomic States, Levels, Tenus, etc.
54
4.3
Electronic Configurations
57
4.4
Spectrum Line Intensities
60
4.5
Relative Strengths Within Multiplets . . . . . . . . ..
65
4.6
Wavelengths and Wave Numbers . .
68
4.7
Atomic Oscillator Strengths for Allowed Lines. . .
69
4.8
Nuclear Spin and Hyperfine Structure:
Low-Level Hyperfine Transitions . . . . . . . . . . ..
78
4.9
Forbidden Line Transition Probabilities . . . . . . .
79
4.10
Spectra of Diatomic Molecules . . ..
..
83
4.11
Energy Levels . . . . . . . . . . . . . . . . . . . . . .
85
4.12
Transitions. . . . . . . . . . . . . . . . . . . . . . .
87
4.13
Selection Rules: Dipole Radiation
89
. .
....
..........
ONLINE DATABASE
Extensive data and references are available online through the Internet [1]. A comprehensive, critically
evaluated database, whose address is given below, is maintained by the National Institute of Standards
and Technology (NIST). Files of special relevance to atomic spectroscopy are the Atomic Spectroscopic
53
54 / 4
SPECTRA
Database by J.R. Fuhr, W.C. Martin, A. Musgrove, J. Sugar, and W.L. Wiese, Bibliographic Database
on Atomic Transition Probabilities by J .R. Fuhr and H.R. Felrice, and Program of the NIST Atomic
Data Centers by W.L. Wiese and W.C. Martin. The unifonn resource locator, or URL, is currently
http://physics.nist.govlPhysRefData/contents.html. File names and locations are subject to change.
The above files might be found by first "opening" http://physics.nist.gov/ and following the appropriate
links, or simply by doing a network search for the keywords "NIST atomic data."
4.2
TERMINOLOGY FOR ATOMIC STATES, LEVELS, TERMS, ETC.
The angular momenta of atoms are vector quantities describing the orbital angular momenta (I, L),
the spin (s, S), and the sum of the two (j, J). Lowercase letters are used for individual electrons,
and uppercase letters refer to corresponding sums (e.g., L = L I). The magnitudes of these
vectors are specified by quantum numbers usually written with lightface italic symbols. For example,
III = ,.j1(1 + 1)11. Spectroscopists often interchange the meaning of the vector quantities and the
associated quantum numbers, and say, for example, that L is the sum of the I's, although the relation is
only valid for the vector quantities. This loose usage is convenient and is followed here. Spectroscopic
levels are typically described by quantum numbers based on LS (Russell-Saunders) coupling. For
other coupling schemes, see [2) and [3). Often, levels are expressed as mixtures of LS terms, where
the leading component is the single LS tenn that best describes the level.
Orbital angular momentum (or azimuthal quantum number), L = vector sum of orbital angular
momenta I of individual electrons. The unit is h/27r == Ii, and the designations are
L (or I)
0
1
2345678
9
Designation (L)
Designation (I)
S
s
P
P
DFGHIKL
d
f g h
k
I
M
N
0
m
n
0
10
11
12
Q
q
13
R
r
14
15
T
t
u
u
Spin angular momentum, S = vector sum of s for individual electrons. The multiplicity of terms
= 2S + 1.
The effects of the atomic nucleus on atomic structure, including nuclear spin I, are treated in a
separate section below.
Total angular momentum quantum number, J = vector sum L+S (in LS coupling). In j j coupling,
j = vector sum I + s for each electron, and J = L j. The total angular momentum J is said to be a
"good quantum number," independent of the coupling scheme.
Electron shells are described by the principal quantum number n as follows:
n
123
4
5
6
7
Shell designation
K
N
0
P
Q
L
M
Only the magnitude of an angular momentum (e.g., ILl) and one of its components (e.g., L z )
are observables. The z component is chosen arbitrarily. Quantum numbers corresponding to these z
components are designated, for example, by m" ML, or M J = M. If the atom is in a magnetic field, it
is convenient to choose the z direction along the field, so the m's have been called magnetic quantum
numbers.
4.2 TERMINOLOGY FOR ATOMIC STATES, LEVELS, TERMS, ETC.
/
55
Maximum values of various quantum numbers are limited as follows:
I
~
n - 1;
s
= 1;
1 ~ S + L;
S~1na;
ML ~ L;
Ms ~ S;
M~
1;
L~II+12+···+lna'
where there are na electrons in open shells.
Interpretation of a typical symbol for an atomic level, e.g., 2 p 3
Principal quantum number of outer electrons = 2; i.e., L shell.
Three outer electrons with I = 1.
Multiplicity = 2, whence S =
Orbital momentum L = 2.
1 = 11, whence statistical weight g = 21 + 1 = 4.
The level is odd (omitted when level is even).
1.
Possible 1 values for given L and S:
Singlets
Doublets
Triplets
Quartets
Quintets
Sextets
Septets
The magnetic quantum numbers are usually not indicated unless the level is split by a magnetic
field. In the absence of such a perturbation, the energies of all levels with a given 1 are the same, and
are therefore (21 + 1)-fold degenerate.
Classical atomic spectroscopists have used the following hierarchial scheme to describe energy
states, combinations thereof, and transitions among such states, as given in Table 4.1.
Table 4.1. Hierarchy of designations.
Atomic
division
State
Level
Term
Statistical
weight g
Specification
Specified by L, S, J, M, or L, S, ML, MS
Specified by L, S, J, e.g., 4S11
1
Group oflevels specified by L, S
2J
(2S
+I
+ 1)(2L + 1)
Transition
Component (of line)
Line
Multiplet
56 / 4
SPECTRA
Table 4.1. (Continued.)
Atomic
division
Polyad
Configuration
Statistical
weightg
Specification
Group of terms from one parent term, and
with same multiplicity or S
Specified by n and I of all electrons
Transition
Supermultiplet
See text
Transition array
Nowadays, spectroscopists rarely use the tenn polyad. Very complicated level structures arise with
the filling of the 3d (iron group), 4d (palladium group), 5d (platinum group), 4f (lanthanides), and Sf
(actinides) subshells. Johansson refers to a subconfiguration for all of the levels that result from the
addition of an electron (nl) to a parent tenn. For example, if we use S p and L p to designate the spin
and orbital angular momentum of the parent, 3d2 (sp L p)nl has five subconfigurations corresponding to
the five allowed tenns from d 2 • Similarly, 3d4 (sp L p)nl would have 16 subconfigurations. He uses the
tenn supermultiplet to mean all transitions between levels belonging to subconfigurations of opposite
parity [4].
4.2.1
Terms from Various Configurations
Table 4.2 gives the multiplicities and orbital angular momenta of the various tenns arising in LS
coupling from the configurations listed [2,3]. When a tenn can appear more than once, the number of
possible tenns is written below the symbol. Complete shells s2, p6, d 10, f 14, etc., give rise to only 1S
tenns. They need not be considered for possible tenns due to outer electrons.
Electrons with the same n and I are said to be equivalent. Tenns arising from complementary
numbers of equivalent electrons are the same; e.g., tenns from p2 and p4 are the same, since six
electrons complete the p shell.
The total weight of an electron configuration may be written [2]
Here, Wi is the number of (equivalent) electrons with angular momentum Ii. A number of examples
are given below. If a single electron with angular momentum I is added to a parent with Lp and Sp,
the total weight of the resulting tenns of both resulting multiplicities is
g
= (4Sp + 2)[(b + 1)2 -
a 2 ],
where b = ILp + 11 and a = ILp -II.
Often, atomic energy levels are not well described by a single electronic configuration. In such
cases, configuration interaction or configuration mixing is said to occur.
Table 4.2. Allowed terms for equivalent electrons.
Configuration
Terms
Total weight
Equivalent s electrons
2
4.3 ELECTRONIC CONFIGURATIONS / 57
Table 4.2. (Continued.)
Configuration
Total weight
Terms
Equivalent p electrons
2pO
p5
p4
p
p2
p3
6
2PDO
15
20
4S0
Equivalent d electrons
d
d2
d3
d9
d8
d7
2D
ISDG
3PF
2PDFGH
d4
d6
ISDFGl
10
45
120
2
22
3PDFGH
2
d5
2
2
210
5D
252
2SPDFGHI
3 2 2
2FO
f
f2
f3
f13
fl2
f11
ISDGI
3PFH
2PDFGHIKL O 4SDFGI O
f4
flO
ISDFGHIKLN
f5
2 2 22
24
f9
423
3pDFGHIKLM
2
2pDFGHIKLMNOO
f8
4SPDFGHIKLMO
2344332
2002
6pFH O
5SPDFGHIKL
7F
2SPDF GHIKLMNOQO 4SPDFGHIKLMN O 6pDFGHIO
8,sO
ISPDFGHIKLMNQ
4648473422
f7
1001
5SDFGl
3243422
457675532
f6
14
91
364
3pDFGHIKLMNO
659796633
2571010997542
3003
3 2 322
3432
226575533
4.3 ELECTRONIC CONFIGURATIONS
Tables 4.3 and 4.4 give the electronic configurations for ground-level atoms [5]. The inner core of
electrons is not explicitly shown for heavier elements. Extensive tabulations of energy levels are
available [6,7].
Thble 4.3. Ground-level co1!figurations_
L
K
Atom
Is
H I
He 2
2
2s
M
N
---
0
2p 3s 3p 3d 4s 4p 4d 5s
I
Ground
level
2SIf2
ISo
Li 3
2
Be 4
B 5
2
2
2
2
C
N
6
7
2
2
2
2
2
3
0
8
2
2
4
F
9
2
2
5
2SIf2
2p O
1f2
ISo
3 PO
4 s?1f2
3PI
2pO
tIf2
0
N
Atom
4f
p
Q
5s 5p 5d 5f 6s 6p 6d 7s
Ag 47
I
Cd 48
2
Ground
level
2S If2
ISO
In 49
2 I
2pO
Sn 50
Sb 51
2 2
2 3
4.si\f2
I
Te 52
53
2 4
2 5
2pO
Xe 54
2 6
Cs 55
2 6
1f2
3 PO
3 P2
11f2
2S If2
ISo
58 / 4
SPECTRA
'nIble 4.3. (ContinuetL)
K
L
Atom
Is
2s 2p
Ne 10
2
2
6
Na 11
2
2
6
2 1
10
Necore
Ar 18
2pO
)lh
2 6
2
2
Ca 20
Sc 21
1
2D)lh
2
3
2
2
4Fllh
5
5
1
2
6S21h
Fe 26
6
2
Co 27
Ni 28
7
8
2
2
4F41h
10
1
2S Ih
11 22
V 23
18
Cr 24
Mn2S
Cu 29
Areore
2
2
6
2 6
Ge 32
28
2 3
Se 34
Br 35
2 4
2 5
Kr 36
2
2
6
2pO
Ih
2 2
As 33
Rb 37
2 6
Nb 41
10
2pO
)lh
2 6
2 6
M042
Te 43
Ru 44
Rh 45
Pd46
Kreore
4
5
2
2
3P2
Sm62
Eu 63
6
7
2
2
Gd64
7
2
Th6S
9
2
Dy66
10
Ho 67
11
2
2
Er 68
Tm69
12
13
2
2
Yb 70
Lu 71
14
14
2
2
SD4
Hf72
14 2 6
3F4
Ta 73
W 74
ISo
31'0
3~
ISo
2
4
1
6Dlh
5
5
7
8
10
1
2
6~lh
1
4F41h
6~lh
4[0
71h
ISo
3F2
6S21h
Os 76
lr 77
6
7
2
2
4F)lh
Pt 78
9
Au 79
14 2 6 10
SD4
2SIh
2
2 1
HS 80
81
2pO
Ih
2 2
2 3
46+32
Rn86
2 6
U 92
Soo
3D]
n
Ra 88
Ae 89
Th90
Pa 91
3H6
2D)lh
2
Fr 87
SIs
2Fflh
5
Pb 82
Bi 83
7Fo
9~
4F)lh
46+22
SI4
s~lh
2
2
3F2
ISo
6HO
21h
3
4
2 4
2 5
SFs
4/0
41h
2
Po 84
At 85
7S3
IG~
2
ISo
2D)lh
2
1
2D)lh
2
Re 75
2S Ih
2
2
36
Nd 60
Pm61
4s?lh
Sr 38
Y 39
Zr40
3Po
7S3
ISo
2
2 6
Ground
level
2
2
3F2
2
2 1
Zn30
Ga 31
8
1
ISo
2
2
Ba 56
3
ISo
Q
58 5p 5d 5f 6s 6p 6d 78
Ce 58
2S Ih
2 6
6
4f
Pr 59
4s?lh
2 4
2 5
C\ 17
19
2pO
Ih
Atom
p
0
N
La 57
ISo
2 2
2 3
P
K
Ground
level
2S Ih
1
AI 13
16
0
ISo
2
S
---
38 3p 3d 4s 4p 4d 58
Mg 12
Si 14
15
N
M
14 2 6 10
3Po
4s?lh
2pO
)lh
3~
ISo
1 2S Ih
2 6
46+32
2
2
3
ISo
ISo
2
2 2D)lh
3F2
2
2 4KSlh
sLg
2
4.3 ELECTRONIC CONFIGURATIONS / 59
Table 4.4. Transuranic elements.
p
0
Q
Ground
Atom
5f
6s
6p
93
94
95
4
6
7
2
2
2
6
6
6
2
2
2
96
97
7
9
2
2
6
6
2
2
6Ho
Cf
98
10
Es
99
11
2
2
6
6
2
2
4]0
Pm
Md
No
100
101
12
13
2
2
2
6
6
2
2Fo
102
103
14
14
2
2
6
2
2
2 D 3 1f2
Np
Pu
Am
Cm
Bk
Lr
7s
6d
6
level
6 L S lf2
7 FO
S~lf2
9Do
7 1.12
7 1.12
2
S]s
3H6
3 1.12
ISO
Table 4.5 of first ions (Sc II, etc.), is restricted to those ions whose ground levels differ from those
of the preceding atom. Table 4.5 gives outer and incomplete shells only.
Table 4.5. First ions.
Element
Configuration
Sc
Ti
3d4s
3d 24s
V
3d4
3d 5
3dS4s
3d6 4s
Cr
Mn
Fe
Co
Ni
Cu
Ground
level
3 01
500
6 S21/2
3d B
3d9
7 S3
3 F4
202 1/2
3d l0
ISo
Zr
4d 2Ss
Nb
Mo
4d4
4d 5
Tc
4d5 Ss
Ru
4 F41/2
Rh
4d 7
4d B
Pd
4d9
202 1/2
La
Ce
4FII/2
604 '12
Element
4FII/2
5 00
6 S21/2
7 S3
3F4
Configuration
5d 2
4/Sd 2
Sm
4/36s
4/46s
4/56s
4/ 66s
Eu
Gd
4/76s
4/75d6s
Th
Dy
4/9 6s
4/106s
Ho
4/116s
Pr
Nd
Pm
Er
4/ 12 6s
Tm
4/136s
Yb
4/ 14 6s
Ground
level
4HO
3 1/2
Element
3F2
W
9~
Au
Sd lO
7H~
Th
6tJ27s
5/ 27s 2
4FII/2
Pa
U
5/ 37s 2
Np
S/57s
4[0
4'12
Pu
S/67s
5/77s
6[8 1/2
5[~
2
3F
2SI/2
SFI
60 1/2
Pt
7Hf
BFI/2
4H61/2
5d36s
Sd4 6s
Ground
level
Sd 56s
5d6 6s
5d7 6s
5d9
5[2
6[3 1/2
1000
21/2
Ta
Configuration
Re
Os
Ir
Am
7 S3
604 1/2
5 F5
202 1/2
ISO
3H4
7Hf
BFI/2
9~
60 / 4
4.4
4.4.1
SPECTRA
SPECTRUM LINE INTENSITIES
Definitions
We use the symbol
"dimensionless."
g
Ii!)
to mean "dimensionally equal to" or "has dimensions of";
~
0 means
= (dimensionless) statistical weight for a level = 2J + 1. Subscripts denote levels.
f = (dimensionless) oscillator strength, or simply f value. Unless otherwise stated, this
is the absorption oscillator strength fabs, related to the emission oscillator strength
fern (which is often taken to be negative) by glfabs = -g2fern. Here, gl and g2 are
the statistical weights of the lower level and upper level, respectively.
gf = weighted oscillator strength = glf12 = -g2izl. gf is symmetrical between
emission and absorption.
A = Einstein's A ~s-l; spontaneous transition probability (for a downward transition).
B12, B21 = Einstein's B; induced transition probability upward and downward.
Bu v =
probability of transition where U v is the radiation energy density at the frequency
v of the transition. Then Buv ~s-l. The B coefficients are sometimes defined with
specific intensity Iv, whence BIv ~s-l.
S = line strength. Sum of the matrix elements of the electric dipole operator li!)e 2 JxJ 2 •
Also used for higher-order radiation (see below).
Yel = classical damping constant (~S-l). Yel is the full width at half maximum (FWHM)
in units of circular frequency (w = 2rrv) of an absorption line due to a classical
oscillator.
Y'2 = reciprocal mean life of level 2
= LI A21 + LI B2IU(V21) + L3 B23U(V23)+ collision terms, where level 1 is below
and level 3 is above 2.
Y = damping constant = VI + Y'2 for transition 1 -+ 2. It is convenient to define damping
constants Yv and VA, for use when profiles are expressed in frequency or wavelength
units. Then Yv/v = n/)... = Y /w.
O'v = atomic cross section (~cm2) near an absorption line. Note: O'A = O'v. Traditionally,
O'v is written in terms of y, not Yv. Often a v or a v is used for atomic cross sections.
NI = number of atoms per unit volume in level 1 (the lower level).
K = NIO'v, the line absorption coefficient, which must be corrected for stimulated
emission: Keorr = K[l- exp(-hv/kT)].
vo = frequency at line center.
Ri, Rc = Initial and final radial wave functions of the active electron. For bound levels, Ri,C ~
cm- 3/ 2. Commonly, rRi,C == Pi,(, where r = radius.
0' = proportional to radial transition moment (see below), not related to O'v or O'A'
S = multiplet strength, scale as given in Table 4.9.
E = energy emitted due to spontaneous, bound-bound transitions in all directions, per
unit volume and time.
8Ry = photon energy in rydbergs (e 2 /2ao = 2rr2m e e 4 / h 2 ).
n* = effective principal quantum number; describes the energy of an atomic level.
4.4 SPECTRUM LINE INTENSITIES / 61
4.4.2 Formulas
For a spectral line that arises from a transition between levels a L S J and a' L' S' J', the line strength for
a dipole transition is defined as
S=
L
L
I(aLSJ Mlexq la' L' S' J' M') 12
(4.1)
l{aLSJ MlerC~l)la'L'S' J'M')1 2 .
(4.2)
MM'q
=
MM'q
Here, a and a' stand for unspecified quantum numbers. q runs from 1 to 3 for the three components of
the position vector of the active electron, or equivalently, the three components of the spherical tensor
of rank 1, rC~l). The C's are proportional to the spherical harmonics of corresponding order:
Consider a simple electronic transition, where there is a single active optical electron (L pi
~ L pi'), where L p stands for the orbital angular momentum of the parent. The greater of I and I'
is usually written I>. In a nonrelativistic, single-configuration approximation, the line strength can be
written with the help of two Wigner 6 - j symbols [2]:
S = (2J
x
r{~p i, ~ r (10
+ 1)(2J' + 1)(2L + 1)(2L' + 1)
{~, ~
2,
I>
00
Rjr Rfr2 dr
y
The line strength S is often taken to be in atomic units (e = ao = me = 1), but that is not the case in
the following relations (the B's used here are defined with energy density; we use m == me):
g2 A 21
8rr h v 3
= g2~B21
8rr h v 3
= gl ~B12
= 3Yc1g1J12 = -3Yc1g2hl =
=
64rr 4
3hJ...3 S12 or 21
8rr 2e 2v 2
3 gI/12,
me
8rr 2e 2v 2
8rr 2e 2
Ycl = 3mc3 = 3mCA 2 '
gJ
mhv
= glf12 = -g2hl = --2
g1 B 12 =
rre
8rr 2mv
3h 2 S12,
e
8rr 3
gl B12 = g2 B 21 = 3h 2 S12,
E
f
N28rr 2e 2hv3
3
gI/12
me
= N2 A 21 hv = -g2
= N2
8rr 2e 2hv3
3
(-hi)
me
8rr 2e 2h
= N2 mJ...3 (-hi),
(Tv
rre2
dv = -Jabs,
me
2
Kv
Y
= -rre
Jabsme
4rr2 (v -
NJ
-1
~ cm ,
vO)2 + (y /4rr)2
62 I 4
SPECTRA
f
nl)2
(I p(l»2
( Rn'l'
= > ll'
(1
2
=
* =
nnl
1
412 _ I
>
2e2 A2
">..0 = - 2 .Jl. Ntfabs,
mc YA.
7re2
,,>..dA = --2A~fabsNl'
mc
(notation of [2]),
(Rnl)2
n'l' ,
ZJ Xion +XHXp -
Xnl
.
The effective principal quantum number n* may be defined for each level with excitation Xnl. The
core, or parent excitation, Xp, if present, must be added to the ionization energy Xion. For example, the
2s22p2(1 D)3s level of N I at 12.36 eV (99663 cm- 1) is built on an excited parent in N II. Therefore,
in calculating n*, one must add Xp = 1.90 eV to the (first) ionization energy 14.53 eV of N I.
4.4.3 Numerical Relations
The following relations are based on the above formulas, which are derived from an approximate,
nonrelativistic radiation theory. The numerical factors are given only to four figures. Physical constants
are from [8]. Note that the line strength S is in atomic units in the following:
= 303.8S/)' = 1.499 x 1O-16g2AA2 (A in A, A in s-I),
= 0.003292gfA = 4.936 x 1O-19g2AA3 (A in A, A in s-I),
g2A = 2.026 x 1018 S/A3 = 2.678 x 10geiyS
= 0.6670 x 10 16 gflA 2 (A in A, A in s-I),
gf
S
7re 2/mc = 0.02654cm2 s-I,
Yel = 2.223 x 1015 /A 2 s-1
87rhv 3
7re 2/mc 2 = 8.853 x 10- 13 cm,
(A in A),
3
3
/c = 87rh/A = 0.1665/A (A in A),
e2 = 6.460 x 10-36 cm2 esu2 •
a5
3
4.4.4 Forbidden Transitions: Electric Quadrupole (E2)
and Magnetic Dipole (MI)
In astronomical usage, a line is called ''forbidden'' when it violates the rules for an electric dipole
(E1)-induced transition. The lines are designated with a bracket notation, e.g., [0 III] for transitions
among the low-level, even-parity states of doubly ionized oxygen. El transitions with as ¥= 0 occur
frequently and in the astronomical literature are often written with a single bracket. For example,
4.4 SPECTRUM LINE INTENSITIES / 63
Pp
the transition 2s2 1So-2s2p 3
at A1909 is written C III]. Such a transition is sometimes called
semiforbidden, or spinforbidden. In complex spectra the rule against intercombination of multiplicities
is violated so frequently that this notation is not particularly useful, and it is rarely employed. In the
formulas below, ex is the fine structure constant (~O), and u is the wave number of the photon (~cm -I ).
The gyromagnetic ratio of the electron spin has been assumed to be 2.000 [2]. For magnetic dipole
radiation,
g2 A 21
=
41l' 2 he 2 u 3
3 2 2
m
C
= 2.6974 x
L
1(y J MIJJI)
qMM'
L
lO-llu 3
+ S~I) IY' J' M'} 12
1(y J MIJJI)
+ S~l) IY' J' M'} 12.
qMM'
For electric quadrupole radiation, we show the explicit sum over i electrons. These sums are
implicit in the symbols JJI) and S~I) above. In practice, only one electron is important. We have
641l'4 e 2a 4 u 5
g2 A21 =
=
5h 0
1
L
l(yJ Mlr?C~2)(i)IY' 1'M'} 12
qMM'i
1.1200 x 1O-22u 5
L
l(yJ Mlr?C~2)(i)IY' J' M'}12.
qMM'i
4.4.5
Selection Rules
Selection rules for atomic transitions are summarized in Table 4.6, including rules for LS coupling.
When levels are not accurately described by single values of L and S, rules involving these quantum
numbers are no longer valid. However, even in complex atoms it is often the case that transitions that
violate the LS selection rules are weak. Configuration interaction can cause the selection rule on 111
to be violated. An example is found in Si I, >..5621.61 of multiplet 17.01 [9]. This appears to be a jump
from 3p4s to 3p4f (111 = 3). The transition occurs because the 3p4s configuration is mixed with
3p3d.
Table 4.6. Selection rules for atomic transitions. a
Electric Dipole (E 1)
AI = ±l, parity change
L!.n arbitrary
L!.J = 0 ± I, J = 0.,.. J = 0
L!.L=O,±l, L=O+L=O
L!.S=O
Magnetic Dipole (M 1)
L!.J = 0, ±l, J = 0.,.. J = 0
L!.M=O,±l
L!.l
0, L!.n = 0, for all electrons
L!.S, L!.L =0
=
64 / 4
SPECTRA
1Bble 4.6. (ContinuetL)
Electric Quadrupole (E2)
aJ =O,±I,±2, 0 ~O,! ~ !,O ~ 1
al = 0, ±2, no parity change
an arbitrary
aM=O,±I,±2
as = 0,
aL = 0, ± I, ±2,
L = 0
~
L = 0, 1
Note
a Rules for L and S hold for LS coupling, while those
for J are independent of the coupling conditions.
4.4.6
Radial Integrals and Related Calculations
The Coulomb approximation [10, 11] to the radial integral for a single electron is still of heuristic
interest. It uses the effective principal quantum numbers n*. Let Z be the charge seen by the active
electron at large distances from the nucleus. Z = 1 for a neutral species, 2 for a first ion, etc. Set
a = (Z/n*). The nonnalizations of the wave functions in the Coulomb approximation are
N=~
n*
r(n
Z
+ 1 + 1)r(n -I)
,
where r is the gamma function. We shall use numbers 1 and 2 to distinguish upper and lower levels in
the relations below (as above, I> means the greater of the two values, It and 12):
U=
*
1
v'41; -
1
*
Nl(nl,11)N2(n2,h)
(2a l)nj (2a2)ni
max
p
*+*+2LG p LCp (al + a2)nt n2
p=o q=o
q (1)Cq (2).
The coefficients G and C are easily obtained from recurrence relations:
Co = 1,
.
Ck(I)=-
(-nj-Ij+k-1)(lj-nj+k)al+a2
k
Go = r(nj + ni + 2),
2aj
Gk =
.
Ck-l(I),
i = 1,2,
Gk-l
---:--.....,;.;..~--
nj +ni +2-k
For integral n*'s the coefficients C are 0 for k above n-I-l. Then, if the sum includes all nonvanishing
terms, the results are identical with those well known for hydrogen and hydrogenlike ions. The
Coulomb approximation usually gives good results when n:1 > 1 + 1 with max < nj + ni - 1.
Useful tables are given in [11].
Kurucz and Bell [12] have made extensive calculations of radial integrals for complex atoms using
scaled Thomas-Fermi-Dirac potentials. Results from the international "Opacity Project" are becoming
available [13].
4.4.7 Sum Rules
The Kuhn-Thomas-Reiche f -sum rule states
4.5 RELATIVE STRENGTHS WITHIN MULTIPLETS / 65
where the summations are for level 1 below the selected level 2, and 3 above that level (including
an integral over continuum). z is the number of atomic or ionic electrons. hI is negative and hence
for upward transitions L3 123 ~ z. The rule is rigorous for nonrelativistic quantum mechanics, but
the sum includes physically unrealistic states. Restricted and approximate forms of the sum rule are
of more practical importance, as for more complex spectra where the lines concerned are mainly the
lowest members of their series and contain most of the total oscillaator strength.
The Wigner-Kirkwood rule for a one-electron jump [2] is
"
__ ! 1(21 - I} for 1 -+ 1 - I,
~f- 3 2/+1
" f = ! (l + 1)(21 + 3)
for 1 -+ 1 + 1
~
3
2/+1
(l is the orbital quantum number); for example,
Lf = -!,
Lf=I,
Lf=-~,
Lf
p -+ ns,
s -+ np,
d -+ np,
p -+ nd.
= I~,
'"'"
The above rule may sometimes be used for complex spectra, but it applies precisely for hydrogen.
The J file and J group sum rules refer to a transition array, e.g., sp -++ pp. A J file refers to
all transitions that begin or end on a specified level. Let all line strengths S(y' L' s' J', y LSJ} within
a transition array be entered in an i x f matrix, with i being the number of initial levels and f the
number of final levels. A J file is any single row or column in this matrix. The J file sum rule states
that
L S(y' L' S' 1', y LSJ} ()( 2J' + 1
1
and
L S(y' L' S' J', y LSJ} ()( 2J + 1.
l'
These two rules are independent of the coupling conditions, but apply only to simple transition arrays,
where either the moving electron has no equivalent congeners or the electron configuration with the
summed J or J' values does not contain equivalent electrons.
A J group consists of all lines in a transition array connecting a level with a given J (e.g., initial)
with one with a given J' (e.g., final). The J group sum rule states that the sum of the strengths of the
lines in a J group are independent of the coupling conditions.
4.5
RELATIVE STRENGTHS WITHIN MULTIPLETS
Table 4.9 gives the relative strengths of lines in multiplets. The notation used here is for LS-coupling
multiplets for a transition LS J -+ L' S' J'. It is important to note that the relative strengths apply
much more generally to any case where two angular momenta, say iI, and h, couple to a third
i3, where h commutes with the dipole operator er [2]. As a result of this generality, these same
relative intensity tables may be used for lines in a hyperfine "multiplet" by the following substitution
of quantum numbers: J -+ F, L -+ J, and S -+ I, where F is the total angular momentum including
the nuclear spin I. Similarly, the relative intensities of what were once called "supermultiplets" may
66 I 4
SPECTRA
be computed by making the following exchange: I -+ L, L -+ 1, and S -+ Lp. Here, we assume a
single optical electron with angular momentum 1 that couples to a parent core with angular momentum
Lp. It therefore turns out that tables [14] giving relative multiplet strengths are unnecessary.
The entries are all proportional to
(21' + 1)(21 + I)W 2(LL' I I'; IS) = (21' + 1)(21 + 1)
{~, ~
I
L'
}2
Table 4.7. Normal multiplets SP, P D, DF, etc.
Jm
Jm
Jm
Jm
Jm
-I
-2
-3
-4
XI
Jm -3
Jm -2
Jm - I
Jm -4
2:1
YI
x2
Y2
x3
2:2
Y3
X4
2:3
Y4
where the W is a Racah coefficient, and the symbol on the right is a Wigner 6 - j symbol [2]. We
normalize so that the sum of the entries for a given multiplet is S = (2S + 1) (2L + 1)(2L' + 1). The
entries are therefore proportional to the line strengths as defined above and do not contain wavelengthdependent factors. Therefore, they are only approximately proportional to relative line intensities in
real (LS-coupling) multiplets.
The following qualitative rules describing the intensities in LS multiplets are of practical value.
The most intense lines are those where L and I change in the same sense, for example, I -+ I + 1
while L -+ L + 1. These strong lines are called the principal, or sometimes diagonal, lines of the
multiplet. In Tables 4.7 and 4.8, their intensities are called Xl, X2, X3, •••• The intensity of the strongest
line on the (principal) diagonal is called XI, and it belongs to the line involving the largest I value,
called 1m below. With a few exceptions that may be seen in Table 4.9, the intensities diminish down
the diagonal. Lines that falloff the main diagonal are called satellite, or off-diagonal, lines. There
are two kinds of multiplets to consider, the symmetrical ones (P -+ P, D -+ D, etc.), and "normal
multiplets" (L -+ L + 1, such as S -+ P or P -+ D). Since the line strength factors are independent
of which level is upper and which is lower, we are free to choose 1m to belong to the largest L. For
the symmetrical multiplets, we call the intensities of the lines for which 1m -+ 1m - 1, YI, those for
which 1m - 1 -+ 1m - 2, Y2, etc. Lines with identical intensities fallon the complementary side
of the diagonal, as shown below. In normal multiplets, there are a second series of satellites with
1m - 1 -+ 1m - 2, etc., which are designated Zh etc. We remark that in a breakdown of LS coupling,
the weaker lines typically deviate more strongly from the LS intensities, so that a calculation in LS
coupling may yield reasonable results for a line on the main diagonal, but could be badly off for a
satellite.
Table 4.8. Symmetrical multiplets P P, DD, etc.
Jm
Jm - I
Jm -2
Jm -3
Jm
Jm - I
xI
YI
x2
Jm -2
Jm -3
Y2
x3
Y3
Y3
X4
YI
Y2
4.5
RELATIVE STRENGTHS WITHIN MULTIPLETS
/
Table 4.9. Intensities in LS-coupling multiplets.
Multiplicity
3
2
s=
Xl
Xl
X2
X3
Xl
X2
X3
Xl
X2
x3
X4
Xs
Yl
Y2
Y3
Y4
Ys
10
11
SP
15
18
21
24
27
30
33
3.00
4.00
2.00
5.00
3.00
1.00
6.00
4.00
2.00
7.00
5.00
3.00
8.00
6.00
4.00
9.00
7.00
5.00
10.00
8.00
6.00
11.00
9.00
7.00
12.00
10.00
8.00
13.00
11.00
9.00
9
18
27
36
45
54
63
72
81
90
99
9.00
10.00
4.00
11.25
2.25
12.60
1.60
1.00
14.00
1.25
2.25
15.43
1.03
3.60
16.88
0.88
5.00
18.33
0.76
6.43
19.80
0.67
7.87
21.27
0.61
9.33
22.75
0.55
10.80
2.00
3.75
3.00
5.40
5.00
7.00
6.75
8.57
8.40
10.13
10.00
11.67
11.57
13.20
13.13
14.73
14.67
16.25
16.20
15
30
45
60
75
90
105
120
135
150
165
15.00
18.00
10.00
21.00
11.25
5.00
24.00
12.60
5.00
27.00
14.00
5.25
30.00
15.43
5.60
33.00
16.88
6.00
36.00
18.33
6.43
39.00
19.80
6.88
42.00
21.27
7.33
45.00
22.75
7.80
2.00
3.75
3.75
5.40
6.40
5.00
7.00
8.75
6.75
8.57
10.97
8.40
10.13
13.13
10.00
11.67
15.24
11.57
13.20
17.33
13.13
14.73
19.39
14.67
16.25
21.45
16.20
0.25
0.60
1.00
1.00
2.25
3.00
1.43
3.60
6.00
1.88
5.00
9.00
2.33
6.43
12.00
2.80
7.88
15.00
3.27
9.33
18.00
3.75
10.80
21.00
PP
PD
DD
25
50
75
100
125
150
175
200
225
250
275
25.00
28.00
18.00
31.11
17.36
11.25
34.29
17.29
8.00
5.00
37.50
17.50
6.25
1.25
40.74
17.88
5.14
0.22
2.22
44.00
18.38
4.37
5.00
47.27
18.94
3.81
0.14
8.00
50.56
19.56
3.38
0.49
11.11
53.85
20.21
3.03
0.95
14.29
57.14
20.89
2.75
1.50
17.50
2.00
3.89
3.75
5.71
7.00
5.00
7.50
10.00
8.75
5.00
9.26
12.86
12.00
7.78
11.00
15.63
15.00
10.00
12.73
18.33
17.86
12.00
14.44
21.00
20.63
13.89
16.15
23.64
23.33
15.71
17.86
26.25
26.00
17.50
35
70
105
140
175
210
245
280
315
350
385
35.00
40.00
28.00
45.00
31.11
21.00
50.00
34.29
22.40
14.00
55.00
37.50
24.00
14.00
7.00
60.00
40.74
25.71
14.40
6.22
65.00
44.00
27.50
15.00
6.00
70.00
47.27
29.33
15.71
6.00
75.00
50.56
31.20
16.50
6.11
80.00
53.85
33.09
17.33
6.29
85.00
57.14
35.00
18.20
6.50
2.00
3.89
3.89
5.71
7.31
5.60
7.50
10.50
10.00
7.00
9.26
13.54
13.89
11.38
7.78
11.00
16.50
17.50
15.00
10.00
12.73
19.39
20.95
18.29
12.00
14.44
22.24
24.30
21.39
13.89
16.15
25.06
27.58
24.38
15.71
17.86
27.86
30.80
27.30
17.50
Yl
Y2
Y3
Y4
s=
9
8
12
Zl
Z2
Z3
Xl
X2
X3
X4
Xs
7
9
Yl
Y2
Y3
s=
6
6
Yl
Y2
s=
5
3
Yl
Zl
s=
4
67
68 / 4
SPECTRA
Table 4.9. (Continued.)
2
4
3
Zl
Xl
0.29
0.40
0.50
1.00
1.00
0.74
1.71
2.40
2.22
X2
x3
X4
x5
X6
X7
Yl
Y2
Y3
Y4
Y5
Y6
Y7
Zl
Z2
Z3
Z4
Z5
Z6
Z7
4.6
9
10
11
1.00
2.50
4.00
5.00
5.00
1.27
3.33
5.71
8.00
10.00
1.56
4.20
7.50
11.11
15.00
1.85
5.09
9.33
14.29
20.00
2.14
6.00
11.20
17.50
25.00
FF
98
147
196
245
294
343
392
441
490
539
49.00
54.00
40.00
59.06
41.17
31.11
64.17
42.67
28.90
22.40
69.30
44.36
27.56
17.50
14.00
74.45
46.20
26.74
14.40
7.62
6.22
79.62
48.12
26.25
12.25
4.37
0.87
84.81
50.13
25.98
10.67
2.50
3.50
90.00
52.18
25.88
9.45
1.36
0.49
7.88
95.20
54.28
25.90
8.48
0.67
1.60
12.60
100.41
56.41
26.00
7.70
0.26
3.06
17.50
13.19
20.68
23.33
22.00
17.50
10.50
15.00
23.82
27.30
26.25
21.39
13.13
16.80
26.92
31.18
30.33
25.00
15.40
18.59
30.00
35.00
34.30
28.44
17.50
2.00
3.94
3.89
63
126
189
252
315
378
441
504
567
630
693
63.00
70.00
54.00
77.00
59.06
45.00
84.00
64.17
48.21
36.00
91.00
69.30
51.56
37.50
27.00
98.00
74.45
55.00
39.29
27.00
18.00
lO5.oo
79.62
58.50
41.25
27.50
16.88
9.00
112.00
84.81
62.05
43.33
28.29
16.50
7.50
119.00
90.00
65.63
45.50
29.25
16.50
6.88
126.00
95.20
69.23
47.73
30.33
16.71
6.60
133.00
100.41
72.86
50.00
31.50
17.06
6.50
2.00
3.94
3.94
5.83
7.62
5.79
7.70
11.14
10.94
7.50
9.55
14.55
15.71
13.71
9.00
11.38
17.88
20.25
19.25
15.63
10.13
13.19
21.15
24.62
24.38
21.21
16.00
10.50
15.00
24.38
28.88
29.25
26.25
20.63
13.13
16.80
27.57
33.04
33.94
30.95
24.69
15.40
18.59
30.74
37.14
38.50
35.44
28.44
17.50
0.06
0.17
0.21
0.30
0.56
0.50
0.45
1.00
1.29
1.00
0.62
1.50
2.25
2.50
1.88
0.81
2.05
3.33
4.29
4.50
3.50
1.00
2.63
4.50
6.25
7.50
7.87
7.00
1.20
3.23
5.73
8.33
10.71
12.60
14.00
1.41
3.86
7.00
10.50
14.06
17.50
21.00
Yl
Y2
Y3
Y4
Y5
Y6
Xl
8
7
49
X2
X3
X4
x5
x6
X7
s=
6
0.11
Z2
Z3
Z4
Z5
s=
5
5.83
7.50
5.60
7.70
10.94
10.50
7.00
9.55
14.26
15.00
12.60
7.78
11.38
17.50
19.25
17.50
13.13
7.00
FG
WAVELENGTHS AND WAVE NUMBERS
Angstrom units (A) and microns (micrometers, JLm) are used for wavelengths in the tables presented
in the following sections. Astronomers often indicate wavelengths in angstrom units by the A symbol.
Wavelengths may be truncated after the last unit of an angstrom or they may be rounded off. We have
4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES
j
69
tried to follow the latter procedure here, but there is no uniformity in the literature. Thus a line of Ca I
at 4226.73 A might be called either >..4226 or >..4227. Wave numbers are almost always given in units
of cm- i , although reciprocal microns are occasionally used. Common symbols for wave numbers are
v, ii, and a.
Many workers use the SI unit nanometer (nm) for wavelengths, 1 nm = 10 A. Wavelengths here
are given "in air" for (air) wavelengths greater than 2000 A. Air and vacuum wavelengths are related
by the index of refraction of air, n: Avacuum = nAair. An extensive tabulation [15] is based on Edlen's
formula for n,
n
= I + 6432.8 x
-8
10
2949810
8
2
10 - a
+ 146 x
+ 41
25540
OS
2'
x I - a
where a is the wave number in em-i. This formula suffices for conversions from air to vacuo when no
more than eight-figure accuracy is desired [16]. For shorter wavelengths reciprocal wave numbers, or
"vacuum wavelengths" are used. With the advent of space astronomy, some workers have suggested
the exclusive use of vacuum wavelengths, but this has not been adopted here.
Reader and Corliss [17] give a modem table of wavelengths of the chemical elements. They include
lines that are suitable for use in calibration of most spectrographs. Extensive references to wavelength
standards are given by Wiese and Martin [18].
4.7
ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES
Atomic hydrogen is considered separately here, in the nonrelativistic approximation in Table 4.10.
Exact numerical values have been available from the early days of quantum mechanics [19]; they
remain of heuristic as well as of practical value. For most cases of astrophysical interest, it is
permissible to ignore the electron spin in hydrogen. Each level with a given I is then (21 + 1)- rather
than 2(21 + I)-fold degenerate, and the weight of all states belonging to a principal quantum number
n is n 2 rather than 2n 2 • The corresponding partition junction at low temperatures is then I and not 2;
this must be used in the Boltzmann and Saba formulas when absorption or emission coefficients are
calculated. Authors sometimes use a notation that is valid if spin is ignored with statistical weights that
take spin into account [19,20]. Transitions may be designated nl ~ n'I', e.g., Is ~ 2p for Lyman ex
in absorption. If spin is ignored, then the line strength S = I> (R~?,)2. The values for S in [20] and [21]
allow for the spin degeneracy and are twice this value. The Einstein coefficients, line strengths, and f
values must be defined in such a way that the intensities or equivalent widths of lines do not depend
on whether spin is included in the level-counting scheme. For example, consider the equivalent width
W{ of a weak hydrogen absorption line when light passes through a uniform slab of thickness H. If
we use the Boltzmann formula to express the population of the lower level Ni as a function of the total
population of neutrals NT, we have
W{
=
rre 2
g'fik
-2A5NT-I-I-[1 - exp(hvjkT)]e-xi/kT H.
me
u(T)
'lltble 4.10. Radial integrals and absorption oscillator strengths Jor hydrogen.
Line
La
LfJ
Ly
Transition
Wavelength (A)
(Rn'I' )2
nl
Jabs
Is-2p
Is-3p
Is04p
1215.67
1025.72
972.54
1.66479
0.266968
0.092771
0.4162
0.07910
0.02899
70 / 4
SPECTRA
Table 4.10. (Continued.)
(R,,'I')2
Line
Transition
Wavelength (A)
Ha
Ha
Ha
2s-3p
2p-3s
2p-3d
6562.74
6562.86
6562.81
9.3931
0.8806
22.5434
0.4349
0.01359
0.6958
Hp
Hp
Hp
2s-4p
2p-4s
2p-4d
4861.29
4861.35
4861.33
1.6444
0.1462
2.9231
0.1028
0.003045
0.1218
labs
,,1
The factor [1 - exp(h v j kT)] allows for stimulated emission.
Spin doubles the value of all statistical weights and the partition function u(T). Therefore, the sum
of the gf's for transitions including spin must be double the corresponding sum of the gf's with spin
ignored (g, = 21 + 1), in order to keep W{ the same.
We use the convention that when a double subscript is written for an I or A value, the first subscript
belongs to the initial level. A few authors follow a convention from atomic spectroscopy that the lower
level is written first. Spin is ignored in calculating the absorption I values in Table 4.10 condensed
from [21].
It is also possible to ignore the I degeneracy of hydrogen, so that only transitions of the form n ~ n'
are considered. Let n and I be the initial levels and let n' and I' be the final ones. Then one defines
average values of A as follows:
Ann' = (ljn 2 )
L(21 + I)Anl-+n'I',
II'
For example,
~ ( IA 3s-+2p + 3A3p-+2s + 5A3d-+2p)'
A similar definition holds for the absorption Inn" but with the weights for the initial, lower level. Thus:
A32 =
123 =
!(lf2s-+3p
+ 3/2p-+3s + 3/2p-+3d).
Data for the major series in hydrogen from [21] are given in Table 4.11.
Table 4.11. Average Einstein A's and absorption I's.
Line
Transition
Wavelength (A)
La
Lp
Ly
Llimit
Ha
Hp
Hy
HI!
HE
HS
Hlimit
Pa
Pp
Py
1-2
1-3
1-4
1-00
2-3
2-4
2-5
2-6
2-7
2-8
2-00
3-4
3-5
3-6
3-00
1215.67
1025.72
792.54
911.8
6562.80
4861.32
4340.46
4101.73
3970.07
3889.05
3646
18751.0
12818.1
10938.1
8204
PIimit
A (s-l)
4.699
5.575
1.278
labs
X
lOS
107
107
0.4162
7.910 X 10-2
2.899 X 10-2
4.410 X
8.419 X
2.530 X
9.732 X
4.389 X
2.215 X
107
106
106
loS
loS
loS
0.6407
0.1193
4.467 X
2.209 X
1.270 X
8.036 X
X
X
8.986 X 106
2.201 X 106
7.783 X loS
10-2
10-2
10-2
10- 3
0.8421
0.1506
5.584 X 10-2
4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES / 71
Table 4.11. (Continued.)
Line
Transition
Wavelength (A)
Ba
4-5
BfJ
By
Blimit
4-6
40512.0
26252.0
21655.0
14584
4-7
4-00
A (s-I)
2.699
7.711
3.041
X
X
X
Jabs
106
105
105
1.038
0.1793
6.549 X 10- 2
In Table 4.12 for La and Ha , the additional states and lines due to electron spin are shown explicitly.
The levels are designated with quantum numbers n,l, s, L, S, and J (appropriate to LS coupling).
Wavelengths and levels are from [22]. The f and A values were generated from the expression
for the line strength given above, using L p = 0 in the appropriate 6 - j symbol, and the numerical
constants from [8]. Use of these constants accounts for small differences with other tabulated values.
For example, our sum of the gf values for the two La lines is 0.8321, while twice the value for Is-2p
given above is 0.8324.
In Table 4.13, multiplet numbers are mostly from [23]. They are labeled with u when the ultraviolet
table [24] is used. The values of log(gf) given without explicit references were derived from [25].
Asterisks preceding the wavelengths indicate blends, in which case the gf is for the blend as a whole.
Accuracy assessments are indicated by letters [21]. References for the table are collected separately at
its end. Uncertainties in the range of 25%-50% are indicated by the letter D, those from 10%-25% by
a C, 3%-10% by B, 1%-3% by A, and within 1% by AA. The letter E is used for accuracies below
50%. The same scheme is followed for other sources when accuracy estimates are available.
Table 4.12. La and Ha transitions with doublet structure.
XI (em-I)
X2 (em-I)
glJI2
2p 2PI/2
2p 2 P3/2
0
0
82258.913
82259.279
0.2774
0.5547
3p 2 PI/2
3p 2P3/2
3s 2SI/2
3s 2SI/2
3d 2D3/2
3d 2D3/2
3d 2D5/2
82258.949
82258.949
82258.913
82259.279
82258.913
82259.279
82259.279
97492.205
97492.313
97492.215
97492.215
97492.313
97492.313
97492.349
0.2898
0.5796
0.02717
0.05434
1.391
0.2782
2.504
Wavelength (A)
Lower
Upper
1215.6737
1215.6683
Is 2SI/2
Is 2SI/2
6562.2720
6562.7256
6562.7520
6562.9099
6562.710 I
6562.8675
6562.8520
2s 2SI/2
2s 2SI/2
2p 2PI/2
2p 2P3/2
2p 2 PI/2
2p 2P3/2
2p 2P3/2
g2A21 x 10- 8 (s-I)
12.51
25.03
0.4485
0.8970
0.04204
0.08408
2.153
0.4305
3.875
Table 4.13. Atomic oscillator strengths Jor allowed lines.
Multiplet
Line
Atom
Transition
Hell,
Li llI,
BeIv,
B v, etc.
Hydrogen-like ions have nearly the same J values as those for hydrogen.
See discussion in [I] and [2] for Sc xXI-Ni XXVIII for higher-order effects.
HeI
Is2_ls2p
Is 2-ls3p
Is2_ls4p
No.
2u
3u
4u
Designation
IS_I pO
IS_I pO
IS_I pO
Ji - Jk
0-1
0-1
0-1
A (A)
584.33
537.03
522.21
log(gf)
-0.5588
-1.134 I
-1.5249
Accuracy
AA
AA
AA
Reference
[3]
[3]
[3]
72 I 4
SPECTRA
1Bble 4.13. (Continued.)
Multiplet
Atom
Transition
Hel
Is2s-ls2p
No.
(Cont.)
1s2s-ls3p
Is2s-1s4p
1s2p-ls3s
Is2p-1s4s
Is2p-ls3d
Is2p-ls4d
1s2p-1s5d
2
4
3
5
10
45
12
47
11
46
14
48
18
51
Is3s-1s3p
Is3s-1s4p
Line
Designation
Jj -J"
3S_3pO
IS_I pO
3S_3pO
IS_I pO
3S_3pO
IS_I pO
3pO_3S
IpO_IS
3pO_3S
IpO_IS
3pO_3D
IpO_ID
3 pO_3D
IpO_ID
3 pO_3D
I pO_I D
3S_3pO
IS_I pO
3S_3pO
IS_I pO
1-0, 1,2
0-1
1-0, 1,2
0-1
1-0, 1,2
0-1
0, 1,2-1
1-0
0, 1,2-1
1-0
0, 1,2-1,2,3
1-2
0, 1,2-1,2,3
1-2
0, 1,2-1,2,3
1-2
1-0,1,2
0-1
1-0, 1,2
0-1
A (A)
*10830
20581
*3889
5016
*3188
3965
*7065
7281
*4713
5048
*5876
6678
*4472
4922
*4026
4388
*42947
74355
*12527
15084
log(gf)
Accuracy Reference
0.2088
-0.4243
-0.7135
-0.8200
-l.1119
-l.3085
-0.2037
-0.8373
-l.0216
-l.5873
0.7397
0.3285
0.0436
-0.4427
-0.3737
-0.8866
0.4270
-0.2032
-0.8234
-0.8419
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
Lil
2s-2p
2s-2p
2S_2pO
2S_2pO
Ih-Ilh
Ih-Ih
6708
6708
-0.0012 AA
-0.3023 AA
[3]
[3]
Bell
2s-2p
2s-2p
1 2S_2pO
1 2S_2pO
Ih-Ilh
Ih-Ih
3130
3131
-0.1772 AA
-0.4783 AA
[3]
[3]
CI
2p3s-2p3p
2 p 2_2s2 p 3
2p2_2p3s
2p 2_2p3d
2p3s-2p3p
2p3s-2p4p
2p3s-2p4p
3 pO_3D
31u 3p_3 sO
3u 3p_3DO
2u 3p_3pO
u7 3p_3DO
10 I pO_IS
6 3pO_3p
11 I pO_I P
12 I pO_I D
l3 IpO_IS
2pO_2p
2pO_2S
2pO_2D
2pO_2S
2pO_2D
2S_2pO
2pO_2S
2pO_2D
2D_2FO
CII
2s 22p-2s2p 2
2s 22p-2s2p 2
2s 22p-2s2p2
2p-3s
2p-3d
3s-3p
3p--4s
3p-3d
3d-4f
lu
2u
3u
4u
5u
2
4
3
6
Cm
2s 2-2s2p
2s 2-2s3p
2s3s-2s3p
lu IS_I pO
2u IS_1 pO
1 3S_3pO
2-3
2-1
2-3
2-2
2-3
1-0
2-2
1-1
1-2
1-0
10691
0.345
945.6 -0.118
1561 -0.521
1657 -0.285
1278 -0.403
8335 -0.437
4772 -l.866
5380 -l.615
5052 -l.304
4932 -l.658
B
C+
A
A
BB+
C
B
B
B
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
Ilh-Ilh
IIh-Ih
IIh-2Ih
Ilh-Ih
Ilh-21h
lh-llh
Ilh-Ih
Ilh-2lh
21h-3 1h
904.1
1037
1336
858.6
687.3
6578
3921
7236
4267
0.224
-0.310
-0.341
-l.284
0.082
-0.026
-0.232
0.298
0.717
B
B
B
B
B
B
B
B
C+
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
0-1
0-1
1-2
977.0
386.2
4647
-0.1200 A+
-0.634
B
B+
0.070
[3]
[3]
[3]
4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES I 73
Table 4.13. (Continued.)
Line
Multiplet
-h
log(gf)
Accuracy
-0.419
-0.721
-0.391
-0.194
A
A
AA
[3]
[3]
[3]
[3]
40.27
-0.1891
AA
[3]
1112-2112
2112-3 112
l1/;rllh
21h-lIh
1199.6
8680
8629
4152
-0.285
0.346
0.Q75
-1.981
B+
B+
B
C+
[3]
[3]
[3]
[3]
~1
915.6
1085
5679.6
3995
500.2
-0.782
-1.071
0.250
0.215
0.592
B+
B+
A
B+
C+
[3]
[3]
[3]
[3]
[3]
991.6
991.5
4097
4515
-0.357
-1.317
-0.057
0.221
B
B
B
B
[3]
[3]
[3]
[3]
1-0. 1.2
1-2
765.1
247.2
*3481
4058
-0.2140
-0.486
0.238
-0.088
A+
B
B
B
[3]
[3]
[3]
[3]
2S_2pO
2S_2pO
2S_2pO
2S_2pO
1h-11/2
Ih-Ih
1h-1/2.11/2
1h-11/2
1239
1243
*209.3
4604
-0.505
-0.807
-0.321
-0.278
A
A
A
A
[3]
[3]
[3]
[3]
NYI
Is 2-ls2p
IS_lpO
~1
28.79
-0.1712
AA
[3]
01
2p4_2p 33s
3 p_3SO
Atom
Transition
CIY
2s-2p
2s-2p
2s-3p
3s-3p
CY
Is 2-ls2p
NI
2p 3_2p 2 3s
2p 23s-2p 23p
Designation
Ji
2S_2pO
2S_2pO
2S_2pO
2S_2pO
1h-11h
Ih-Ih
Ih-Ih.11h
1h-11h
IS_lpO
~1
2u
1
8
6
4sO_4p
4p_4Do
2p_2pO
4 p_4 sO
3 p_3pO
2p3p-2p3d
2u
lu
3
12
19
Nm
2s 2 2p-2s2p 2
2s 22p_2s2 p2
3s-3p
2s2p3s-2s2p3p
lu 2pO_2D
lu 2pO_2D
1 2 S_2 pO
3 4pO_4D
NIY
2s2_2s2p
2s 2-2s3p
2s3s-2s3p
2s3p-2s3d
lu IS_I pO
2u IS_lpO
1 3S_3pO
3 1 pO_ID
Ny
2s-2p
2s-2p
2s-3p
3s-3p
lu
lu
2u
2p 23s-2p 24p
NIl
2s 22p2_2s2 p 3
2s 22p 2_2s2 p 3
2p3s-2p3p
OIV
I
3p_3DO
3pO_3D
IpO_ID
3D_3Fo
1-1
2-3
1-2
~
1Ih-21h
11h- 11/2
1h-11/2
21h-3 1/2
~1
~1
1548
1551
*312.4
5801
Reference
3p_3Do
5sO_5 P
3sO_3p
3sO_3p
5p_5Do
4sO_4p
4sO_4p
4p_4DO
4p_4sO
4pO_4D
2-1
2-3
2-3
1-2
1-2
3-4
11/2-21/2
11/2-2112
21fr3 1/2
21/2-11/2
21h-3 1/2
1302
988.8
7772
8446
4368
6158
430.2
834.5
4649
3749
4119
-0.585
-0.634
0.369
0.236
-1.983
-0.409
-0.139
-0.268
0.307
-0.105
0.433
A
B
A
B
C
B+
B+
B+
B+
B+
B+
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
2p3s-2p3p
2p3p-2p3d
lu
2u
2
14
3p_3DO
3p_3 pO
3 pO_3 D
3p_3Do
2-3
2-2
2-3
2-3
835.3
703.9
3760
3715
-0.358
-0.293
0.162
0.149
A
A
C+
C+
[3]
[3]
[3]
[3]
2p-3d
2s 22p-2s2p 2
2s2p3s-2s2p3 p
5u 2pO_2D
lu 2pO_2D
3 4pO_4D
llh-21/2
llh-21/2
21h-3 1h
238.6
790.2
3386
0.258
-0.401
0.148
B
B
B
[3]
[3]
[3]
2p 33s-2p 34p
2p 33p_2p 34d
2p 3_2p 23d
2s 2 2 p 3_2s2 p 4
2p 23s-2p 23p
2p 23p-2p 23d
Om
lu
lu
2u
1
)..(A)
2u
5u
1
4
5
10
3u
lu
1
3
20
2p 33s-2p 33p
OIl
No.
2s 22 p 2_2s2 p 3
74 / 4
SPECTRA
Table 4.13. (Continued.)
Multiplet
Atom
Transition
No.
Ov
2s 2-2s2p
2s 2-2s3p
2p3s-2p3p
2p3p-2p3d
lu 'S-' pO
2u 'S-' pO
4 3pO_3D
Ov,
2s-2p
2s-2p
2s-3p
3s-3p
lu 2S_2pO
lu 2S_2pO
2u 2S_2pO
I 2S_2pO
o VII
Is 2-ls2p
NeI
2p5 3s-2p 5 3p
II
Designation
3S_3 pO
'S_'pO
Line
Jj - Jk
A(A)
log(gf)
Accuracy
0-1
0-1
2-3
1-2
629.7
172.2
4124
4159
-0.2905
-0.407
-0.066
-0.356
A+
B
B
B
[3]
[3]
[3]
[3]
'h-lih
'/z-'h
'f:z-lih
'/z-lih
1032
1038
150.1
3811
-0.576
-0.879
-0.451
-0.349
A
A
AA
[3]
[3]
[3]
[3]
0-1
21.60
-0.1584
AA
[3]
2-3
6402
0.345
B
2'12-2'12
3694
0.09
D
Reference
Nell
2p4 3s-2p4 3p
4p_4pO
NevI
2p-3d
2pO_2D
1'/z-2'h
122.7
0.313
D
[3]
NevIl
2s 2-2s2p
'S_'pO
0-1
465.2
-0.410
C
[3]
NevIll
2s-2p
2S_2pO
'f:z-lih
770.4
-0.689
B+
[3]
NeIX
Is 2-ls2p
'S_'pO
0-1
13.45
-0.141
A
[3]
NaI
3s-3p
3s-3p
3s-4p
3p-4s
3p-5s
2S_2pO
'f:z-I'h
'/z-'h
'f:z-lih
I'/z-'h
1'12-'12
lih-'h
li/z-2'h
lih-2'h
li/z-2'h
5890
5896
3302
11404
6161
5153
8195
5688
4983
0.104
-0.197
-1.736
-0.163
-1.23
-1.732
0.51
-0.46
-0.962
A
A
C
C
C
C
C
C
C
[3]
[3]
0-1
2-1
I"'{}
2-1
2-3
1-2
0, I, 2"'{}, 1,2
2852
5184
11828
3337
3838
8807
*2780
0.29
-0.158
-0.27
-1.l0
0.414
-0.08
0.73
D
B
D
C
B
D
C
2796
2937
2798
*4481
9218
0.09
-0.23
-0.43
0.973
0.26
C
C
D
C
C
3p~s
3p-3d
3p-4d
3p-5d
MgI
3s 2-3s3p
3s3p-3s4s
3s3p-3s5s
3s3p-3s3d
3s3p-3 p 2
I 2S_2pO
2 2S_2pO
3 2pO_2S
5 2pO_2S
8 2pO_2S
4 2pO_2D
6 2pO_2D
9 2pO_2D
lu
2
6
4
3
7
6u
'S-' pO
3pO_3S
lu
2u
3u
4
2S_2pO
2pO_2S
2pO_2D
2D_2FO
2 S_2 pO
'/z-lih
lih-'h
1'12-1'12
1'12,2'12-2'12,3'12
'h-lih
'pO_'S
3pO_3S
3 pO_3D
'pO_'D
3 pO_3 P
MgIl
3s-3p
3p-4s
3p-3d
3d-4f
4s-4p
MgIX
2s 2-2s2p
'S_'pO
0-1
368.1
-0.493
B
Mgx
2s-2p
2s-3p
2S_2pO
2S_2pO
'/z-lih
'/z-lih
609.8
57.88
-0.775
-0.377
B
B
MgXI
Is 2-ls2p
'S_'pO
0-1
9.169
-0.128
B
3p-4s
4s-5p
3p-3d
2pO_2S
2S_2pO
2pO_2D
1'12-'12
'f:z-lih
lih-2'h
3962
6696
3093
-0.34
-1.343
0.263
C
C
C
All
1
5
3
[4]
[4]
[4]
4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES / 75
Table 4.13. (Continued.)
Multiplet
Designation
Ji -it
A (A)
log(gf)
Accuracy
2u
4u
IS_1 pO
3pO_3S
0-1
2-1
1671
1862
0.263
-0.192
B
B
lu
2
2S_2pO
2S_2pO
If2-Ilf2
If2-Ilf2
1855
5696
0.047
0.235
B
B
2s 2-2s2p
IS_1 pO
0-1
332.8
-0.55
C
3p2-3p4s
lu
43u
3
3u
4
5
6
3 p_3 pO
ID_lpO
IS_lpO
3p_3DO
3pO_3D
3 pO_3 P
3pO_3S
2-2
2-1
0-1
2-3
2-3
2-2
2-1
2516
2882
3906
2217
12031
10827
10585
-0.241
-0.151
-1.092
-0.55
0.41
0.16
-0.19
C
C
C
C
D
D
D
Atom
Transition
No.
AlII
3s 2-3s3p
3s3p-3s4s
Al III
3s-3p
4s-4p
Alx
Sil
Line
3s 2 3 p2-3s3 p3
3 p4s-3p4p
Reference
[4]
[4]
[4]
[4]
Sill
4s-4p
3d-4f
3s 23p-3s3 p 2
3s 23p-3s3p2
3p-3d
3p-4s
3p-4d
2
3
lu
5u
4u
2u
6u
2S_2pO
2D_2FO
2pO_2D
2 pO_2 P
2pO_2D
2 pO_2S
2pO_2D
llz-Ilf2
2 If2-3If2
llz-Ilf2
Ilf2-11f2
111z-21f2
Ilf2-1f2
Ilf2-2 1f2
6347
4131
1808
1195
1265
1534
992.7
0.23
0.463
-2.14
0.49
0.52
-0.28
-0.15
C
C
D
D
D
C
D
Si III
3s 2-3s3p
3s4s-3s4p
2u
2
4
IS_lpO
3 S_3 pO
IS_1 pO
0-1
1-2
0-1
1207
4553
5740
0.22
0.292
-0.16
B
C
D
[5]
Silv
3s-3p
3s-4p
4s-4p
lu
2u
I
2S_2pO
2S_2pO
2S_2pO
llz-llf2
llz-Ilf2
llz-Ilf2
1394
457.8
4089
O.oI
B
D
B
[5]
-1.34
0.195
[4]
SixI
2s 2-2s2p
IS_lpO
0-1
303.3
-0.576
C
SixII
2s-2p
2S_2pO
llz-Ilf2
499.4
-0.845
B
[6]
SI
3p 34s-3p 34p
5S0_5 P
2-3
9213
0.42
D
[4]
SII
3s 2 3p 3_3s3p4
lu
4S0_4P
Illz-2 112
1260
-1.31
C
SIV
3p-4s
5u
2pO_2S
Ilf2- 112
554.1
-0.425
C
Sv
3s 2-3s3p
3s3p-3s3d
lu
3u
IS_1 pO
3pO_3D
0-1
0, 1, 2-1, 2, 3
786.5
*661.5
0.165
0.802
B
B
KI
4s-4p
4s-5p
llz-llf2
1/Z-1lf2
7665
4044
0.135
-1.915
B
C
Cal
4s 2-4s4p
4s4p-4s5s
4s4p-4s6s
4s4p-4s4d
4s4p-4s5d
4s4p-4s6d
4s4p-4p 2
3d4s-3d4p
0-1
2-1
2-1
2-3
2-3
2-3
2-2
3-3
4227
6162
3974
4455
3644
3362
4303
5589
0.243
-0.089
-0.906
0.26
-0.306
-0.578
0.276
0.21
B
C
C
C
C
C
C
D
1 2S_2pO
3 2S_2pO
2
3
6
4
9
11
5
21
IS_1 pO
3pO_3S
3pO_3S
3pO_3D
3 pO_3D
3pO_3D
3pO_3p
3D_3 DO
76 I 4
SPECTRA
Table 4.13. (Continued.)
Multiplet
Atom
Transition
Call
4s~p
3d~p
4p-5s
4~
SCI
Til
3d24s-3d24p
3d 34s-3d 34p
3d 34s-3d 24s4p
Till
VI
Designation
Jj -Jk
A. (A)
log(gf)
Accuracy
1
2
3
4
2S_2pO
2D_2pO
2pO_2S
2pO_2D
Ih- llh
21h-llh
I1h- 1h
llh-2 1h
3934
8542
3737
3179
0.135
-0.365
-0.15
0.51
e
e
e
e
12
14
15
16
6
4F_4GO
4F_4DO
2 F_2 GO
2F_2FO
2D_2pO
4 1h-5 1h
41h-31h
5672
0.49
4744
0.42
5521
0.29
5482
0.27
4082 -0.57
No.
38 5F_5GO
42 5 F_5 FO
145 5 p_S DO
12 3 F_3 FO
24 3F_3GO
110 3F_3GO
2
7
4F_4 GO
4F_4FO
4 F_4 FO
21
22
27
88
109
14
29
41
125
114
6D_6 pO
6D_6FO
6 D_6 DO
4H_4HO
4 F_4 GO
4F_4 GO
6D_6pO
4D3FO
6Fo_6F
6GO_6H
3d24s_3d 24p
3d 3-3d24p
~4s-3~4p
3d44s-3d 34s4p
3d 34s4p-3d 34s5s
3d 34s4p-3d34s4d
Line
31h~lh
3 1h-3 1h
2 1h-llh
5-6
5-5
~
~
4-5
3~
31~lh
41~lh
41~lh
41h-31h
41h-51h
41~lh
6 112-6 112
41h-5 1h
41h-51h
4112-3 112
31~lh
5 1h-5 1h
6 112-7112
4982
4533
4617
3999
3371
5036
0.504
0.476
0.389
-0.056
0.13
0.130
3361
3235
3323
0.28
0.336
-0.183
4460 -0.15
4379
0.58
4112
0.408
4269
0.65
4545
0.45
3185
0.69
3704
0.18
4091
0.33
5193
0.29
0.97
3695
VII
3d 34s-3d 34p
11 3 p_S DO
5 3F_3Do
25 S p_S DO
2-3
4-3
~
3903
3557
4202
en
3d S4s-3dS4p
7S_7 pO
Ss_SpO
5G_SHO
5 D-S FO
7S_7 pO
SG_S GO
3-4
2-3
6-7
4-5
3-4
6-6
4254 -0.114
5208
0.158
0.67
3964
4351 -0.44
3579
0.409
0.318
3744
41~lh
4041
3807
4031
2795
0.285
0.19
-0.47
0.53
3820
3581
4384
4272
4046
3816
0.119
0.406
0.200
-0.164
0.280
0.237
3d44s2-3d44s4p
3d S4s-3d44s4p
Mnl
3d64s-3~4p
3d s4s2-3dS4s4 p
Fel
3d74s-3d7 4p
7
38
22
4
43
5
6
2
lu
6 D_6 DO
6D_6FO
6S_6pO
6S_6pO
20 5F_SDO
23 5 F_S GO
41 3F_SGO
42 3F_3GO
43 3 F_3 FO
45 3 F_3 DO
4112-5 112
21h-31h
2112-3 112
5-4
5-6
4-5
4-5
~
4-3
-0.89
-0.17
-1.75
Reference
[4]
D
D
D
D
e
e+
e+
e+
B
e
e+
e
e+
e+
ee
B
eee
ee
eeB
B
D
B
B
D-
e
B
B
e+
B
e+
e
B+
B+
B+
B+
B+
B
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[2]
[2]
[2]
[2]
[2]
[7]
4.7 ATOMIC OSCILLATOR STRENGTHS FOR ALLOWED LINES / 77
Table 4.13. (Continued.)
Multiplet
Atom
Transition
No.
Fel
(Cont.)
3d 6 4s 2-3d 6 4s4p
4 5 D_5 DO
5 5 D_5 FO
68 5p_5DO
152 7DO_7 D
3d74s-3d 64s4p
3d6 4s4p-3d6 4s5s
Designation
Line
Jj -It
A (A)
log(gf)
Accuracy
4-4
4-5
3-4
5-5
3860
3720
4529
4260
-0.710
-0.431
-0.822
0.077
B+
B+
B+
B
[2]
[2]
[2]
[7]
Reference
Fe II
3d 6 4s-3d6 4p
27
38
4p_4Do
4 F_4 DO
2112-3 112
4112-3 112
4233
4584
-2.00
-2.02
C
D
[2]
[2]
COl
3d 84s-3d 84p
22
23
35
5
28
4F_4GO
4F_4FO
2F_2Fo
4F_4 GO
2F_2GO
4112-5 112
4112-4112
3 112-3 112
4112-5 112
3 112-4112
3454
3405
3569
3466
4121
0.38
0.25
0.37
-0.70
-0.32
C+
C+
C
C
C
[2]
[2]
[2]
[2]
[2]
19
35
7
25
111
17
130
143
162
194
3 D_3 FO
3-4
2-3
4-5
3-4
5-5
3-3
2-2
4-5
3-4
3-4
3415
3619
3233
3051
5018
3374
4855
5081
5084
5081
-0.06
-0.04
-0.90
-0.12
-0.08
-1.76
0.00
0.13
0.03
0.30
C
C
C
C+
D
C
D
D
DD-
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
112-1112
2112-1112
1112-2112
3248
5106
5218
-0.056
-1.50
0.26
C
D
D
3d 74s2_3d 74s4p
3d 84s-3d74s4p
Nil
3d 94s-3d 94p
3d 84s 2-3d 84s4p
3d94s-3d 84s4 p
3d 84s4p-3d 84s5s
3d 84s4p-3d 84s4d
3d 94p-3d 94d
ID_IFo
3F_3GO
3 D_3 FO
5 FO_5 F
3D_5FO
3 pO_3 P
3FO_3G
3DO_3F
I FO_IG
CuI
4s-4p
3d 94s 2-3dI04p
4p-4d
1 2S_2pO
2 2D_2pO
7 2pO_2D
Znl
4s4p-4s4d
4s4p-4s4d
4
6
3 pO_3D
IpO_ID
2-3
1-2
3345
6362
0.30
0.158
B
C
SrI
5s 2-5s5p
2
IS_lpO
~1
4607
0.283
C
SrIl
5s-5p
5d-6s
1 2S_2pO
3 2pO_2S
112-1112
1112-112
4078
4306
0.151
-0.11
C
D
Bal
6s 2-6s6p
2
IS_I pO
~1
5536
0.215
C
BaIl
6s-6p
5d-6p
6p-6d
2
4
2S_2pO
2D_2pO
2pO_2D
112-1112
2112-1112
1112-2112
4554
6142
4131
0.163
-0.08
0.441
C
D
C
3 pO_3S
~1
1-2
2-1
4047
4348
5461
-0.81
-0.92
-0.185
D
D
C
2-1
4058
-0.18
D
HgI
6s6p-6s7s
Pbl
6p2-6p7s
3p_3 pO
References
1. Martin, G.A., Fuhr, I.R., & Wiese, W.L. 1988, J. Phys. Chern. Ref Data, 17, Suppl. 3
2. Fuhr, I.R., Martin, G.A., & Wiese, W.L. 1988, J. Phys. Chem. Ref Data, 17, Suppl. 4
3. Wiese, W.L., Fuhr, I.R., & Deters, T.M. 1996, J. Phys. Chern. Ref Data Monograph, 7; and other data to be published
4. Wiese, W.L., Smith, M.W., & Miles, B.M. 1969, Atomic Transition Probabilities, Sodium Through Calcium, NSRDSNBS, 22
5. Morton, D.C. 1991, ApJS, 77,119
6. Wiese, W.L., Smith, M.W., & Glennon, B.M. 1966, Atomic Transition Probabilities, H Through Ne, NSRDS-NBS, 4
7. O'Brian, T.R., Wickliffe, M.E., Lawler, I.E., Whaling, W., & Brault, I.W. 1991, J. Opt. Soc. Am., 88,1185
78 / 4
SPECTRA
4.8 NUCLEAR SPIN AND HYPERFINE STRUCTURE:
LOW-LEVEL HYPERFINE TRANSITIONS
The angular momentum, or spin, of the ground levels of nuclei [26] can be of importance in atomic
spectra and structure. Nonzero spins result from unpaired nucleons and occur for some isotopes of most
elements. In elements with odd Z, the most abundant isotope will have a nonzero spin, so hyperfine
structure is most important for these species. However, secondary (odd-N) isotopes of even-Z elements
may make a significant contribution to the overall line shape.
If the spin I is taken into account, the total angular momentum of an atomic level is F = J + I.
The vectors J and I are added using the same rules as when L and S are added to form J. The quantum
numbers F and 1 play analogous roles to J and S. Thus, for a given J and 1 there are 2I + 1 values of
F if J > I, and 2J + 1 if 1 > J. The number of elementary states belonging to a level with a given
F is 2F + 1, corresponding to the number of possible values of M F, the projection of F on the z axis
in units of h. When there should be no ambiguity, MF may be written without the subscript M.
Nuclear spin broadens spectral lines and adds 2I + 1 additional states to an atomic system. The
first factor, known as hyperfine splitting, may usually be ignored if the resultant width is much smaller
than that due to other broadening mechanisms, such as pressure or Doppler broadening. The additional
atomic states cancel in the Boltzmann and Saba formulas and usually are not accounted for explicitly.
The splitting of atomic levels due to nuclear spin (Il.EM) may be augmented (Il.EQ) if the nucleus
has an electric quadrupole moment [27]:
+ 1) - J(J + 1) - 1(1 + 1)] == !AC,
= B[C(C + 1) - jJ(J + 1)/(1 + 1)].
Il.EM = !A[F(F
Il.EQ
Values of A and B are given by [28].
Nuclear mass effects may be treated as follows. Let P be the momentum of the nucleus with mass
M, and let Pi be the momentum of the ith electron. The kinetic energy is then
p2
E= 2M
We can eliminate P using P
+ Li Pi =
E =
P~
+ ~2~'
I
0, whence
(2~ + 2~) ~pr+ ~ .~.Pi ·Pj·
I
I,J>I
The first term is called the normal mass shift and gives rise to well-known displacements of lines
in very light elements [29]. The second term, called the specific mass shift, is difficult to calculate [27]
but may be measured in the laboratory. It can be significant even for heavy atoms [30].
Finally, nuclear volume, field effects, or isotope shifts occur because the potential at small r
departs from a pure llr dependence due to the finite size of the nucleus. Astrophysically important
consequences have been documented [31].
While the hyperfine width is difficult to calculate, the relative intensities of lines in a hyperfine
multiplet follow readily from the quantum theory of angular momentum. The relative line strengths
are written simply with a Wigner 6 - j symbol:
S(J'I F'
~ J/ F) ex (2F + 1)(2F' + 1) {
i,
~
F}2
J'
The relative intensities are identical to those discussed for LS coupling, and the tables of Sec. 4.5
may be used with the substitutions J -+ F, S -+ I, and L -+ J.
4.9 FORBIDDEN LINE TRANSITION PROBABILITIES I 79
The celebrated 21-cm line in atomic hydrogen is an example of a pure magnetic dipole transition.
Similar transitions occur in ionized 3He, as well as in deuterium. Results are summarized in Table 4.14,
with 1986 constants and transition frequencies from [32]. The formula for magnetic dipole radiation
simplifies in this case to
Here, S~l) is a spherical tensor, analogous to cf.!), which operates in electron spin space. Quantum
numbers Sn and Se describe the spin states of the nucleus and electron. For I H I and 3He II, g F' = 3,
while for 2H I it is 4. The sums over M, M', and q are 3/4 for I H I and 3He II and 4/3 for 2H 1.
The numerical coefficient is 4.01367 x lO-42 v 3 (cgs). We have neglected the magnetic moment of
the nucleus. The ground state orbital functions are not indicated, since they contribute only a trivial
multiplicative factor of unity.
4.9
FORBIDDEN LINE TRANSITION PROBABILITIES
Most of the lines in Table 4.15 are forbidden in the sense that they involve no change in parity. A
few intersystem lines are included. Both magnetic dipole (Ml) and electric quadrupole (E2) lines are
possible at the same wavelength in many cases. The dominant radiation is indicated, but the A value
is for the sum over all mechanisms, including electric dipole radiation (for intersystem lines). When
both magnetic dipole and electric quadrupole transitions are permitted by their selection rules, the
Einstein A coefficient for the magnetic dipole will usually dominate for optical transitions. Generally,
AmI Aq ~ 3 X lOll la 2 , where a is the wave number of the transition. Typical A values for electric
dipole transitions are 105 times larger than their magnetic dipole congeners. Accuracy estimates
from [33-36] are indicated where available. The notation is the same as in Sec. 4.7.
Table 4.14. Hyperfine transitions.
IHI
2HI
3Hen
I
F'
F
v (Hz)
A21 (s-I)
1/2
I
1/2
Il/2
I
0
1/2
0
1.420405752 x 109
3.273843523 x 108
8.665 649 867 x 109
2.876 x 10- 15
4.695 x 10- 17
6.530 x 10- 13
Table 4.15. Forbidden and intercombination lines.
Atom
Array
He I]
[e I]
en]
e III]
[NI]
Is 2-1s2p
2p2
2s 22p-2s2 p 2
2s2_2s2p
2p 3
Designation
lower-upper
IS_3 pO
ID_1S
2pO_4p
IS_3 pO
4S0_2DO
4sO_2DO
Ji-Jk
0-1
2-'{}
Il/2-21/2
0-1
Il/:z-Il/2
Ili2-21/2
A (A)
591.4
8727
2325.4
1908.7
5198
5200
A (s-I)
Accuracy
1.76 x 10+2
0.634
52.6
114
2.26 x 10- 5
5.77 x 10-6
B
B
B+
e
B
MI
or E2
Reference
[1]
E2
Ml
E2
[2]
[2]
[2]
[2]
[2]
80 / 4
SPECTRA
Table 4.15. (Continued.)
Atom
Array
[Nil]
2p2
Nil]
NIlI]
NIY]
[01]
[011]
[0 Ill]
Om]
OIY]
OY]
[FlY]
[Ne Ill]
2s 22p2_2s2p3
2s 22p2_2s2p 3
2s 22p-2s2p 2
2s 2-2s2p
2p4
2p 3
2p2
2s 22p2_2s2 p 3
2s 22p2_2s2 p 3
2s 2 p_2s2p2
2s 2-2s2p
2p2
2p4
Designation
lower-upper Jj-h
ID_IS
3p_I S
3p_I S
3p_ID
3p_ID
3p_ID
3p_3p
3p_3p
3p_3p
3 p_5So
3 P_5S0
2pO_4p
IS_3 pO
ID-IS
3p_I S
3p_I S
3p_ID
3p_ID
3p_ID
3p_3p
3p_3p
3p_3p
2DO_2pO
2Do_2pO
2Do_2pO
2Do_2pO
4sO_2pO
2sO_2 pO
4sO_2DO
4 sO_2 DO
ID_ 1S
3p_1D
3p_1D
3p_1D
3p_3p
3p_3p
3p_3p
3 p_5sO
3p_5sO
2pO_4p
IS_3 pO
3p_1D
ID-IS
3p_I S
3P_ 1S
3p_1D
3p_1D
3p_1D
3p_3p
3p_3p
3p_3p
2-0
2-0
1-0
1-2
2-2
0-2
1-2
0-2
0-1
2-2
1-2
lih-2lh
0-1
2-0
2-0
1-0
2-2
1-2
0-2
1-0
2-0
2-1
2lh-lih
1112-1112
2112-112
11h-lh
lih-lih
11h-lh
lih-2lh
lih-lih
2-0
1-2
2-2
0-2
1-2
0-2
0-1
2-2
1-2
1112-2112
0-1
2-2
2-0
2-0
1-0
2-2
1-2
0-2
1-0
2-0
2-1
A (A)
5755
3071
3063
6548
6583
6527
121.8/Lm
76.45/Lm
205.3/Lm
2143
2139
1749.7
1486
5577
2958
2972
6300
6364
6392
145.5/Lm
44.06/Lm
63.19/Lm
7320
7331
7319
7330
2470
2470
3729
3726
4363
4959
5007
4931
51.81/Lm
32.66/Lm
88.18/Lm
1666
1661
1401.2
1218.3
4060
3342
1794
1815
3869
3967
4012
36.02/Lm
1O.86 /Lm
15.55/Lm
A (s-I)
1.17
1.40 x
3.15 x
9.20 x
2.73 x
5.45 x
7.40 x
9.69 x
2.07 x
1.27 x
5.49 x
3.08 x
1.02 x
1.26
2.42 x
7.54 x
5.65 x
1.82 x
8.60 x
1.75 x
1.34 x
8.91 x
9.91 x
5.34 x
5.19 x
8.67 x
5.22 x
2.12x
3.06 x
1.78 x
1.71
6.21 x
1.81 x
2.41 x
9.76 x
3.17 x
2.62 x
5.48 x
2.20 x
1.47 x
3.68 x
9.25 x
2.72
1.88
2.02
0.159
4.92 x
9.60 x
l.l5 x
2.19 x
5.97 x
MI
Accuracy orE2
B
B
B
B
B
B
B
C
B
BBc+
B
B+
10-4 c+
10- 2 B+
10-3 B+
10- 3 B+
10-7 B+
10-5 B+
10- 10 c+
10-5 B+
10- 2 B
10- 2 B
10- 2 B
10- 2 B
10-2 c+
10- 2 c+
10- 5 C
10-4 C
B
10-3 B
10- 2 B
10-6 c+
10-5 B+
10- 11 B+
10-5 B+
10+2 B
10+2 B
10+3
10+3 B
10- 2 B
B
B
A
A
10-2 A
10-6 B+
10- 3 B+
10-8 B
10- 3 A
10-4
10-2
10-4
10- 3
10-7
10-6
10- 13
10-6
10+2
10+ 1
102
10+3
E2
E2
MI
MI
MI
E2
MI
E2
E2
E2
E2
MI
MI
MI
E2
MI
E2
MI
E2
E2
E2
E2
MI
MI
E2
MI
E2
MI
MI
E2
MI
E2
MI
MI
E2
E2
MI
MI
MI
E2
MI
E2
MI
Reference
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[3]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
4.9 FORBIDDEN LINE TRANSITION PROBABILITIES / 81
Table 4.15. (Continued.)
Atom
[NeIv]
Array
2p 3
Designation
lower-upper
2DO_2pO
2 DO_2 pO
2DO_2pO
2DO_2pO
4S0_2 pO
4S0_2pO
4S0_2DO
4S0_2DO
2DO_2pO
[Nev]
Nev]
Si III]
[S I]
[S II]
[S III]
2p2
2s 2 2p2_2s2 p 3
2s 2 2 p 2_2s2 p 3
3s 2-3s3p
3p4
3p 3
3p2
SIll]
3s 3 p2_3s3 p 3
[CI III]
[CI IV]
3p 3
3p2
[ArIII]
3p4
ID_1S
3p_ID
3p_ID
3p_ID
3p_3p
3p_3p
3p_3p
3 P_5S0
3 p_5sO
IS_3 pO
ID_1S
2Do_2pO
2 DO_2 pO
2Do_2pO
2DO_2pO
4 sO_2 pO
4sO_2pO
4 SO_2 DO
4S0_2DO
ID_1S
3p_I S
3p_I S
3p_ID
3p_ID
3p_ID
3p_3p
3p_3p
3p_3p
3 P_5S0
3 p_5sO
4sO_2Do
ID-1S
3p_ID
3p_ID
ID-1S
3p_I S
3p_ I S
3p_ID
3p_ID
3p_ID
3p_3p
3p_3p
3p_3p
Ji-Jk
2lh-llh
ll/:z--llh
2lh-Ih
Ilh-lh
llh-llh
Ilh-lh
llh-2lh
ll/:z--llh
Ilh-lh
2-0
2-2
1-2
0--2
1-2
0--2
0--1
2-2
1-2
0--1
2-0
2lh-Ilh
Ilh-Ilh
2 1/:z-- lh
Ilh-lh
llh-llh
Ilh-lh
1l/:z--21h
I Ih-IIh
2-0
2-0
1-0
2-2
1-2
0--2
1-2
0--2
0--1
2-2
1-2
ll/:z--llh
2-0
1-2
2-2
2-0
2-0
1-0
2-2
1-2
0--2
1-0
2-0
2-1
A (A)
4714
4724
4716
4726
1602
1602
2424
2422
4726
2973
3426
3345
3300
MI
A (s-I)
0.380
0.421
0.105
0.372
1.23
0.499
4.12 x
5.76 x
0.372
2.89
0.351
0.126
2.44 x
4.59 x
14.33 JLm
9.008 JLm 5.12 x
1.28 x
24.25 JLm
6.06 x
1146
2.37 x
1137
1.67 x
1892
7725
1.53
10320
0.179
10287
0.133
7.79 x
10370
0.163
10336
4069
0.225
9.06 x
4076
2.60 x
6716
8.82 x
6731
2.22
6312
1.05 x
3797
3722
0.796
5.76 x
9531
2.21 x
9069
5.82 x
8830
2.07 x
18.71 JLm
4.61 x
12.00 JLm
4.72 x
33.48 JLm
7.32 x
1729
2.66 x
1713
4.83 x
5538
2.80
5323
7.23 x
7531
0.179
8046
2.59
5192
4.17 x
3005
3.91
3109
0.314
7136
8.23 x
7751
2.15 x
8036
5.17 x
21.83 JLm
6.369 JLm 2.37 x
8.992JLm 3.08 x
Accuracy
B
B
B
B
B
10-4
10- 3
10-5
10- 3
10- 9
10- 3
10+3
10+3
10+4
B
c+
C
B
B
B
B
B
A
B+
A
or E2
Reference
MI
MI
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[I]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[I]
[ I]
[3]
[I]
[I]
[ I]
[ I]
[ I]
[I]
[I]
[I]
[ I]
[ I]
E2
MI
MI
MI
E2
MI
MI
E2
MI
MI
E2
MI
E2
MI
E2
E2
10-2
10- 2
10-4
10-4
10- 2
10-2
10-2
10-6
10- 3
10- 8
10-4
103
103
10- 3
10-2
10-2
10- 2
10-5
10- 3
10-6
10- 2
MI
E2
E2
MI
MI
E2
E2
E2
E2
MI
MI
MI
E2
MI
E2
MI
MI
E2
MI
MI
E2
E2
MI
MI
MI
E2
MI
E2
MI
[ 1]
[ I]
[I]
[I]
[I]
[I]
[I]
[ I]
[3]
[3]
[I]
[I]
[I]
[ I]
[ I]
[ I]
[I]
[I]
[I]
[I]
[ I]
[I]
[ I]
82 I 4
SPECTRA
'Dable 4.15. (Continued.)
Atom
Array
[ArIV]
3p 3
[ArV]
[Arx]
3p2
2 p5
[ArXIV]
[Klv]
2p
3p4
[Cav]
[CaxII]
[CaxIII]
[Caxv]
3p4
2p5
2p4
2p2
[Fell]
3d64s-3d7
3d64s-3d54s 2
3d7 -3d64s
[Fe III]
3d6
[Fe IV]
[Fe v]
3d5
)d4
[Fe VI]
3d 3
[Fe VII]
3d2
[Fe x]
[Fe XI]
3p 5
3p4
[Fe XIII]
3p2
[Fe XIV]
[Fe xv]
3p
3s3p
Designation
lower-upper Jj-J"
2DO_2pO
2 DO_2 pO
2 DO_2pO
2 DO_2pO
4sO_2pO
4sO_2pO
4sO_2DO
4sO_2DO
ID-1S
3p_IS
3p_I S
3p_ID
3p_ID
3p_ID
3p_3p
3p_3p
3p_3p
2 pO_2 pO
21frl lh
llh-llh
21h-Ih
llh-Ih
llh-llh
IIh-Ih
llh-2lh
1Ih-I Ih
2-0
2-0
1-0
2-2
1-2
0--2
1-2
0--2
0--1
llh-Ih
2 pO_2 pO
ID_1S
3p_ID
3p_ID
3p_ID
2 pO_2 pO
3p_3p
3p_3p
3p_3p
6D-4 p
6D_4 F
6D-6S
6D-6 S
4D-2p
4F_4 G
5D_3 F
5D-3 p
4G_4 F
5D-3 p2
5 D-3 F2
4F_4p
4F_2G
3F_3p
3F-ID
lh-llh
2-0
1-2
2-2
2-2
Ilh-Ih
2-1
1-2
0--1
3 1h-21h
41h-4lh
41h-21h
3 1h-21h
Ih-Ih
41h-5 1h
4-4
3-2
5 lh-4lh
3-2
4-4
41h-21h
41h-4lh
4-2
2-2
3-2
11h-lh
1-2
2-1
0--1
1-2
2-2
Ih-llh
1-2
2pO_2pO
3p_ID
3p_3p
3p_3p
3p_3p
3p_ID
2pO_2pO
3 pO_3 pO
A(A)
7237
7171
7331
7263
2854
2868
4711
4740
4626
2786
2691
7006
6435
6133
7.903 1Lm
4.9281Lm
13.09lLm
5533
4412
4511
6795
6102
5309
3328
4087
5446
5694
4890
4416
4287
4359
5528
4244
4658
5270
4907
3895
3891
5677
5176
5276
5721
6087
6375
3987
7892
10747
10798
3389
5303
7059
A (s-I)
0.598
0.789
0.119
0.603
2.11
0.862
1.77 x
2.23 x
3.29
5.69 x
6.55
0.476
0.204
3.50 x
2.72 x
1.24 x
7.99 x
1.06 x
MI
Accuracy or E2 Reference
10-3
10-2
10-2
10-5
10-2
10-6
10-3
10+2
1.04 x 10+2
3.18
0.203
0.838
1.90
4.87 x 10+2
3.19 x 10+2
7.9 x 10+ 1
9.4 x 10+1
0.36
0.46
1.5
1.1
0.12
0.90
0.44
0.40
0.32
0.71
0.74
0.052
0.62
0.050
0.36
0.58
69.2
9.5
4.36 x 10+1
1.4 x 10+ 1
9.86
7.5 x 10+ 1
6.01 x 10+ 1
3.80 x 10+ 1
B
A
E
E
E
E
E
E
D
D
E
D
D
E
D
E
D
D
B
DC+
C+
C+
E
C+
C+
MI
MI
E2
MI
MI
Ml
E2
Ml
E2
E2
Ml
MI
Ml
E2
Ml
E2
MI
MI
[1]
Ml
E2
Ml
Ml
Ml
Ml
Ml
Ml
Ml
MI
Ml
E2
E2
MI
E2
Ml
Ml
E2
Ml
Ml
E2
Ml
E2
MI
Ml
Ml
MI
Ml
Ml
Ml
Ml
Ml
Ml
[4]
[1]
[4]
[4]
[1]
[1]
[1]
[I]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
[I]
[1]
[1]
[1]
[4]
[1]
[4]
[4]
[4]
[4]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
4.10 SPECTRA OF DIATOMIC MOLECULES / 83
Table 4.15. (Continued.)
Atom
Array
[Ni II]
[Ni III]
[Ni XII]
[NiXIII]
3d9_3d 8 (3 F)4s
3d 9_3d 8 (3 P)4s
3d 8
3p 5
3p4
[Nixv]
3p2
[Nixvl]
3p
Designation
lower-upper
Ji-Jk
2D_2F
2D_4p
3F_3p
2pO_2pO
3p_ID
3p_3p
3p_3p
3p_3p
2pO_2pO
2 1h-2 Ih
2 1h-2 Ih
4-2
11h-Ih
1-2
2-1
0-1
1-2
1/2-11/2
).. (A)
6668
4326
6000
4231
3637
5116
6702
8024
3601
A (s-I)
Accuracy
0.099
0.35
0.050
2.37 x 10+2
1.8 x 10+ 1
1.57 x 10+2
5.65 x 10+ 1
2.27 x 10+ 1
1.92 x 10+2
E
E
E
B
E
C+
C+
C+
C+
M1
orE2
Reference
E2
E2
E2
M1
M1
M1
M1
M1
Ml
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
[5]
References
1. Mendoza, C. 1983, in Planetary Nebulae, edited by D.R. Flower, lAU Symposium No. 103 (Reidel, Dordrecht),
p.143
2. Wiese, W.L., Fuhr, 1.R., & Deters, T.M. 1996, J. Phys. Chem. Ref. Data Monograph, 7; and other data to be published
3. Morton, D.C. 1991,ApJS, 77,119
4. Kaufman, v., & Sugar, I. 1986, J. Phys. Chem. Ref. Data SeT., 15,321
5. Fuhr, I.R., Martin, G.A., & Wiese, W.L. 1988, J. Phys. Chem. Ref. Data SeT., 17, Suppl. 4
4.10 SPECTRA OF DIATOMIC MOLECULES
4.10.1
General Remarks
Realistic calculations of astronomical spectra today involve the use of extensive databases such
as HITRAN [37], RADEN [38], or the material assembled by Kurucz [39]. The proceedings of
IAU Commission 14 [40,41] describe these sources and contain additional material, also covering
polyatomic molecules. Recent texts [42,43] treat diatomic molecules.
4.10.2
Approximate Wave Function
It is often assumed that the total wave function of a diatomic molecule may be written as a product
containing electronic, vibrational, rotational, and nuclear spin components: 1/1 = 1/Ie1/lv1/lr1/ln. A more
general situation is considered below. Traditionally, electronic spin is included in 1/Ie, but the nuclear
spin wave functions are written separately. In the simplest cases, 1/Iv and 1/Ir are the functions describing
the quantum oscillator and rotator. The latter are spherical harmonics. Sophisticated treatments of 1/Iv
use realistic potential functions. In general, the rotational function 1/Ir may include electronic angular
momentum. In this case, 1/Ir is described by symmetrical top wave functions [43,44]. For the rotational
functions to have the proper behavior with respect to parity operations, it is often necessary to use linear
combinations of symmetrical top functions.
4.10.3
Quantum Numbers and Notation
Angular momentum vectors L and S have the same meanings as for atoms. These, and other (e.g., J)
angular momenta, are often loosely referred to by the associated quantum numbers (L, S, J).
R or 0 = angular momentum of nuclear (end over end) rotation. R = 0, I, ....
N = total angular momentum apart from spin; formerly called K.
84 / 4
SPECTRA
= total electron spin; (2S + I) is given as a pre-superscript.
= projection of S on internuclear axis (can be positive or negative).
J = total angular momentum exclusive of nuclear spin.
A = component of electron orbital angular momentum along one internuclear axis,
symbolized by 1:: (A = 0), n (A = I), f1 (A = 2), ....
g = IA + 1:: I. A + 1:: is used as a term subscript (e.g., 4n_I/2, 4n3/2).
I = total nuclear spin.
F = total angular momentum including nuclear spin [not F(J); cf. below].
M = projection of vector J (MJ) or F (MF) on the z axis of the laboratory
S
1::
coordinate system.
F(J)
= rotational energy in cm- I , FI, F2, ....
A = spin-coupling constant; tabulated by [45] in footnotes.
Y = AI Bv describes intermediate coupling; smalllYI =* case (b).
v = vibrational quantum number, v = 0, I, . .. .
Te = equilibrium electronic energy (or ''term value") in cm- I .
G(v) = vibrational energy in em-I.
voo = wave number of the 0--0 band of a band system.
+, - describe the parity of electronic wave functions of 1:: states, viz., 1::+ and 1::-,
with respect to reflection in plane of nuclei.
g, u
describe the parity of electronic wave functions in homonuclear diatomic molecules
with respect to inversion of electronic coordinates.
+, - describe the total parity of 1/1e 1/1v 1/1r for rotational levels with respect to inversion of
all coordinates in the laboratory frame.
s, a describe the parity of 1/Ie1/lv1/lr1/ln of homonuclear molecules with respect to exchange
of two nuclei.
4.10.4
Angular Momenta and Hund's Cases [42-44,46,47]
The quantum numbers A, 1::, and g all derive from the projection of vectors and are similar in nature to
the numbers ML, Ms, and MJ of atoms. In the nomenclature of molecular spectroscopy, only positive
values of these projections are commonly used. However, just as in the atomic case, positive and
negative projections occur, and it is often necessary to employ both signs in the theoretical description
of a molecular state.
Case (a): J =L + S + R. The projection ofL, whose absolute magnitude is called A, is well defined,
as is the projection of S, called 1::. Unlike atoms, molecules have their full multiplicity, and A ± 1:: is
.
· e.g., 4n 5/2, 4n 3/2, 4n 1/2, 4n -1/2.
wntten
as a sub
scnpt,
Case (b): L + R = N (formerly called K). N + S = J. Rotational levels, which may be labeled by
the quantum number N, are split into 2S + I sublevels if N > S, and 2N + I sublevels if S > N.
Case (c): L + S = J a . The quantum numbers A and 1:: are not "good," but the projection of Ja on
the internuclear axis, g, is well defined. N + Ja = J, the total angular momentum. Case (c) is common
for heavier molecules.
4.11 ENERGY LEVELS I 85
Case (d): L + R = N as in case (b), but the energy splitting due to spin and orbital angular
momentum is very small. The vector J = S + N does not differ significantly from N, and energy
levels are proportional to BvR(R + 1).
4.11
ENERGY LEVELS
Approximate energy levels (in cm -1) may be calculated from the following formulas:
Bv =
+ G(v) + F(J),
We(v + !) - WeXe(V + !)2 + ... ,
J(J + I)Bv - J2(J + 1)2 D v ,
Be - ae(v + !) + ... ,
Dv
De.
T = Te
G(v) =
F(J) =
~
For accurate work it is necessary to consult relations specialized for individual molecules (see [45]).
Electron spin manifests itself on molecular energy levels in a variety of ways that are not easily
described by general formulas (see [44]). The splitting of 2n levels due to spin, for example, may be
approximately described by the formulas below. Here, F1 and F2 refer to the levels with J = N +
and J respectively. Y = AI B, as above.
!
!,
F1(1) = Bv
F2(J)
= Bv
[(1 +
[(1 +
+ !)2 + Y(Y -
4)A2]
+ ... ,
+ !J4(J + !)2 + Y(Y -
4)A2]
+ ... .
!)2 - A2 - !J4(1
!)2 - A2
Levels with A > 0 are twofold degenerate (±IML I). Rotation can lift this degeneracy, giving rise
to A -doubled pairs of levels with opposite parity. See [42,48] for additional comments and notation
(a, b, c, d, e, f> used to describe rotational levels.
4.11.1
Molecular Constants
Tables 4.16 and 4.17 give the more important constants for selected electronic states of some common
diatomic molecules of astrophysical interest. These constants are sufficient for approximate and
heuristic work. For example, one may use them to locate lower-order bands and define their character
(red or violet degredation). Accurate work would require the use of more elaborate formulas than can
be written with these constants alone. Higher-order constants may be found in the papers cited.
Table 4.16. Selected constants for diatomic molecules. a
State
Te
We
WeXe
Be
ae
De
re (A)
1.599
1.115
3.053
1.994(-2)
1.656(-2)
4.644(-2)
1.03
1.29
0.74
IH2. D8 = 4.478075 eV
C In.. 2p1l"
B IE;t2poX 1Etls0-2
100089.8
91700.0
0.0
2444.66
1357.19
4402.93
65.58
20.15
123.07
31.324
19.984
60.847
86 / 4
SPECTRA
Table 4.16. (Continued,)
State
Te
We
d 3 ng
BIIEt
Bid
c 3 E'!
Ainu
b 3 Eg
a3nu
xlEt
20024.597
15409.139
12082.336
9124.212
8391.408
6435.736
718.318
0.0
1788.2220
1424.119
1407.465
2085.899
1608.199
1470.415
1641.32959
1855.014
WeXe
12C2, Dg
D2ni
b 4 ni
a 4 E+
B2E+
A2ni
X 2 E+
54486.3
44317
(36400)
25753.22
9243.308
0.0
1004.71
1148
(1400)
2160.38
1813.235
2068.648
a'3E+
a 3nr
XIE+
55825.~
48686.70
0.0
1228.60
1743.41
2169.814
x2ni
0.0
3737.761
Be
ae
De
re (A)
0.01907
0. 1175
0.016816
0.01255
0.016969
0.016312
0.0166625
0.01801
6.72(-6)
6.86(-6)
6.319(-6)
6.517(-6)
6.509(-6)
6.196(-6)
6.463(-6)
6.964(-6)
1.27
1.38
1.39
1.21
1.32
1.37
1.31
1.24
= 6.296 eV
16.4574
2.5711
11.4794
18.623
12.060
11.155
11.65195
13.555
1.755523
1.4810
1.463685
1.921
1.616628
1.49864
1.632365
1.82010
12C 14 N, Dg
= 7.74eV
8.78
18.1
(20)
17.74
12.751
13.097
1.162
1.170
0.013
0.016
7(-6)
1.50
1.49
1.96879
1.71562
1.8997832
0.01996
0.01712
0.017372
6.58(-6)
6.129(-6)
6.406(-6)
1.15
1.23
1.17
0.01892
0.01904
0.0175
6.41(-6)
6.36(-6)
6.121(-6)
1.3523
1.20574
1.128
0.7242
19.38(-4)
0.96966
12C 16 0, Dg
10.468
14.36
13.2883
160 I H, Dg
84.8813
= 11.108 eV
1.3446
1.69124
1.9313
= 4.392 eV
18.910g
Note
aUnits are cm- I except as indicated. The power of ten to be applied to the entry for De is shown in parentheses.
References: H2 [1-4]; C2 [5-15]; CO [1,16]; CN [17-21].
References
1. Huber. K.P.• & Herzberg. O. 1979, Molecular Spectra and Molecular Structure N. Constants ofDiatomic Molecules
(Van Nostrand. New York)
2. Dabrowski, I. 1984. Can. J. Phys., 62.1639
3. Abgrall. H .• Roueff. E., Launay. F.• Roucin. J.-Y., & Subtil, J.-L. 1993. J. Mol. Spectrosc.• 1S7, 512
4. Balakrishnan. A .• Smith,
& Stoicheff. B.P. 1992. Phys. Rev. Len.• 68. 2149
5. Douay. M .• Nietmann. R .• & Bernath, P.P. 1988.1. Mol. Spectrosc., 131. 250. 261
6. Prasad. C.V.V.• & Bernath. P.F. 1994,ApJS, 426, 812
7. Davis. S.P., Abrams. M.C .• Phillips. 10., & Rao. M.L.P. 1988. J. Opt. Soc. Am.. B5, 2280
8. Oalehouse. D.C .• Brault, J.W.• & Davis, S.P. 1980.ApJ. 42. 241
9. Simard, B .• & Hackett, P.A. 1991, J. MoL Spectrosc.• 148, 128
10. Phillips, J.O. 1973, ApJS. 26, 313
11. Hocking. W.H.• Gerry, M.C.L., & Merer, A.J. 1979. Can. J. Phys., 57. 54
12. Veseth. L. 1975. Can. 1. Phys.• 53. 299
13. Urdahl. R.S., Bao, Y.. & Jackson. W.M. 1991, J. Chem. Phys. Len., 178,425
14. Amiot. C .• Chauville. J.• & Maillard, J.-P. 1979. J. Mol. Spectrosc.• 75. 19
15. Davis. S.P.• Abrams. M.C .• Sandalphon, X.x.. Brault, J.W., & Rao. M.L.P. 1988, J. Opt. Soc. Am., B5, 1838
16. Eidelsberg. M .• Roncin. J.-Y, LeFloch, A., Launay, F., Letzelter. C .• & Rostas, J. 1987, J. Mol. Spectrosc., 121. 309
17. Ito. H .• Ozaki. Y.• Suzuki. K., Kondow. T., & Kuchitsu. K. 1992, J. Chem. Phys., 96. 4195
18. Huang. Y., Barts. S.A., & Halpern, J.B. 1992.1. Phys. Chem., 96.425
19. Ito, H .• Ozaki. Y.• Nagata, T .• Kondow. T.• & Kuchitsu. K. 1984, Can. J. Phys., 62, 1586
20. Prasad. C.V.V.• & Bernath. P.P' 1992. J. Mol. Spectrosc.• 156, 327
21. Kotlar. A.J .• Field, R.W., Steinfeld, J.I.. & Coxon, J.A. 1980. J. Mol. Spectrosc.• 80. 86
v..
4.12 TRANSITIONS I 87
Table 4.17. Selected constants continued: nO.a
State
TO
We
WeXe
Be
re (A)
ae
De
0.489888
0.063062
6.627(-7)
1.69
0.506223
0.00318
6.97(-7)
1.67
0.003145
6.918(-7)
1.66
48n 16 0, Dg = 6.87 eV
C3 a3
C3 a2
C 3al
B3n2
B3nl
B3nO
bln
A3~4
A3~3
A3~2
E3n2
E3nl
E3nO
dlI;+
ala
x3a3
x3a2
x3al
[19536.63]
[19441.47]
[19341.68]
[16266.797]
[16247.951]
[16255.986]
[14721.14]
[14365.60]
[14193.69]
[14019.43]
[12016.13]
[11925.26]
[11840.15]
[5667.10]
[3448.32]
[202.6177]
[97.8177]
0.0
838.2567
4.7592
[863.563]
919.7593
867.7799
4.2799
3.9422
0.507390
924
5.1
[0.5155]
1023.0585
1018.273
1009.1697
4.8935
4.521
4.5640
0.549320
0.537602
0.535431
1.65
0.003348
0.002916
0.003022
6.337(-7)
5.9(-7)
6.32(-7)
1.60
1.62
1.62
Note
aUnits are cm- l except as indicated. The power of ten to be applied to the entry for De is shown in
parentheses. For no the square brackets indicate that To is given rather than the usual Te. These apply
to the v = 0 vibrational level. The constants We, etc., are the same for the levels split by spin-orbit
interaction. References: TiO [1-4].
References
1. Gustavsson, T., Amiot, C., & Verg~, J. 1991, J. Mol. Spectrosc., 145, 56
2. Hildebrand, D.L. 1976, Chern. Phys. Lett., 44, 281
3. Merer, AJ. 1989,Annu. Rev. Phys. Chern., 40, 407
4. Brandes, G.R., & Galehouse, D.C. 1985, J. MoL Spectrosc., 109, 345
4.12 TRANSITIONS
The upper level is written first, for both absorption and emission. Symbols describing the upper level
have a single prime, while a double prime is used for the lower level.
4.12.1
Rotation and Vibration
Rotational transitions in emission or absorption are assigned to P, Q, and R branches designated as
follows for dipole radiation:
P:
J" ~ l' = J" - 1,
Q:
J" ~ J'
R:
J" ~ l'
= J",
= J" + 1.
Transitions forbidden for electric dipole radiation can give rise to lines in an 0 branch (1" ~ J' =
1" - 2) and an S branch (JII ~ J' = J" + 2).
In case (b), when the spin splitting is small with respect to the rotational separation of the energy
levels, one can have P-, Q-, and R-form branches whose nomenclature depends on N ' and Nil. For
88 / 4
SPECTRA
example, a line in a P-fonn Q branch would arise when J' *+ J", but N" *+ N' = N" - l. It
would be labeled P Q. The branch labels also contain subscripts. The symbol Q Rl2 would designate a
transition in a Q-fonn R branch from a lower level labeled F2 to an upper Fl. See [49] for additional
notation.
A common designation of rotational lines uses the J value of the lower level. Thus R(O) arises
in transitions between J' = 1 and J" = 0 (in absorption from J" = 0 and in emission from
J' = 1). Since J' = 0 *+ J" = 0 is forbidden for electric dipole radiation, Q(O) does not occur.
The corresponding wave number is, however, called the band origin, voo or voo.
Vibrational transitions are designated by the corresponding quantum numbers. For example, the
(0-0) band means a transition from v' = 0 to v" = O. The quantum number for the upper vibrational
state is written first.
4.12.2 Electronic Transitions
In the spectra of diatomic molecules line strengths are defined in the same way as for atomic transitions,
by a sum over the degenerate elementary states of both the upper and lower levels, which are labeled
by M' and M":
SPJ" =
L
i(1/IM'lp.I1/IM"} 12.
M'M"
This "line strength" is symmetrical in the upper and lower levels. The electric dipole moment,
here written as 1£, is the sum of the electric moments (charge times displacement) of the electrons and
nuclei. This vector must be in the fixed or laboratory frame. For convenience, it is transfonned to
the frame of the molecule with the help of Euler angles. In practice, for a given transition, only one
electron is important.
The line strength for an electronic transition may be written as a product of three factors [50,51]
The quantity Re is called the electronic transition moment. Its definition, consistent with the HonlLondon factor S (see below), is such that
IRel = I{A'S':E'lzIA"S":E"}I,
!:!.A = 0,
= I(A'S':E'I (x ± iy)/-hIA"S":E)I,
!:!.A = ±1,
L Sp
JII
= (2 -
8o, A' 80, A" )(2S + 1)(21
+ 1).
This nonnalization [50] holds for absorption or emission. In the fonner case, the value of J on
the right-hand side is J", while in the latter it is J'. The Kronecker 8 functions are zero if A' or A"
is not equal to zero, and are unity otherwise. Consider a given J (J' or J"). It is necessary to sum
the rotational strengths S for all allowed transitions from the (2 - 80,A)(2S + 1) levels with a given
J for which transitions are allowed. Thus the sum extends over more than one energy level in general
and includes lines with the same J that arise from A doubling. If A doubling is present in both upper
and lower levels, the number of allowed lines is exactly twice that which would result if there were
no degeneracy. However, if only one of the upper or lower levels is doubled, the resulting number of
allowed lines is the same as if neither upper nor lower were doubled because of the selection rule on
parity. The sum of these strengths may not equal the theoretical value for low levels where the full spin
multiplicity (oflevels) has not developed [43].
4.13
SELECTION RULES: DIPOLE RADIATION
/
89
The recommended nonnalization follows naturally if the rotational strengths are written with n - j
symbols [47,52]. Thus for Hund's case (a), we have
S = (2J'
+ 1)(2J" + 1) (~
0"
~ 0'
J"
-0"
)2
The symbol in the large parentheses is a Wigner 3 - j symbol. This fonnula also holds for cases
(c) and (d), in the latter instance with the replacement of 0 by A. These cases are of less importance
for molecules of astrophysical interest. For case (b), it is necessary to decouple the electron spin, and
this introduces a 6 - j (curly bracket) symbol:
S = (2J
,+ 1)(2N,+ 1)(2J"+ 1)(2N,,{N'
+ 1) J"
1
S
N"}2
(N'A'
J'
1
A" - A'
N"
-A"
)2
Pure Hund cases are only approximations to the more general description of molecular levels by
intermediate coupling. Intensity fonnulas have been given by various authors, e.g., [53-55], and
Whiting [56] has published a program for the S's consistent with the above summation rules. We
recommend use of the Whiting code for all but I:-I: transitions, which are inherently case (b).
It is often useful to have guides to the rotational structure of electronic transitions. In addition to
the basic reference [44] useful diagrams may be found in [49, 51, 57].
Oscillator strengths and Einstein coefficients are related to S J' J" by the same fonnulas as for atoms
(Sec. 4.4).
4.13
SELECTION RULES: DIPOLE RADIATION
Many selection rules for diatomic molecules can be inferred from the properties of the n - j symbols of
Sec. 4.12; the relevant 3 - j or 6 - j symbol will vanish for the forbidden transition. For example, we
can infer for electric dipole radiation fl.J = 0, ±1 with J = 0 ~ J = O. Similarly, we have fl.0 = 0,
±l for case (a) and fl.A = 0, ±1 for case (b). Case (b) also has fl.N = 0, ±1 and N = 0 ~ N = O.
The 3 - j symbol vanishes if N' = N" while A' = A" = 0; consequently, fl.N = 0 is forbidden for
I: ~ I: transitions [case (b)]. Similarly fl.J = 0 for 0 = 0 ~ 0 = 0 [case (a)].
The total spin operator commutes with the dipole moment; consequently, fl.S is forbidden for
electric dipole radiation. In case (a), where I: is well defined, we also have fl. I: = O.
Symmetry of the electronic wave functions prevent I: + from combining with I: -, while symmetry
of the overall wave functions prevent positive-positive and negative-negative transitions. For
homonuclear molecules gerade-gerade and ungerade-ungerade transitions are prohibited, while
symmetric-antisymmetric rotational transitions cannot occur.
4.13.1
Parameters for Selected Electronic Transitions
Table 4.18 gives parameters for line-strength calculations in a few diatomic band systems of
astrophysical interest. The material is primarily for heuristic use. For detailed calculations it is
necessary to consult the sources cited. Entries are primarily from the RADEN database [38]. The
first three columns identify the systems and give wavelength ranges, following [58]. A very useful
table of persistent band heads is given in [59]. The fourth column contains the band origin for the 0-0
band. The following columns provide information relevant to line-strength calculations. Entries are
for r-centroid [Re(rv'v")] and ab initio [Re(r)] calculations. The fonner are used with Franck~ondon
factors (qv'v") while the latter involve an integration of Re(r) over the vibrational wave functions. The
final column of the table gives square of the transition moment for the 0-0 band, by the two methods,
with vibration included. A superscript a in this column indicates R50 = R;(roo)qoo, while b indicates
R50 = I{v' = OIRe(r)lv" = 0)12.
Comet tail
CO+
",,5015-6450
H4700-6100
H2680-5450
H2800-5900
"i..3 020-3 680
U1950-3400
A 2n-x 2E+
Second
positive
C 3 n u-B 3 n g
First
negative
B 2Et -x 2Et
A 3n_x 3E-
y system
A 2E+_X 2n
MgH
N2
N+
2
NH
NO
44080.5
44200.2
29776.76
25566.04
29671.0
19278.4
17837.8
99120.17
HI 028-1 239
LaO
H2
90203.55
",,955-1674
A 2n_x 2E+
Lyman
B I Et-X lEt
Werner
C Inu-x lEt
B 2E+_X 2E+
H2
20407.6
64 748.48
HI 115-1544 (abs.)
",,2006-2785 (emiss.)
4th positive
A In_x IE+
CO
",,3080-8500
25797.84
H3440-4600
Violet
B2E+ - X 2 E+
eN
1.1091
0.9999
1.0559
0.1639
1.0995
0.6636
1.8424
0.944
1.7270
0.4545
1.184 3
1.1783
0.0037
0.%24
0.1217
0.8937
0.8604
1.1806
0.0422
1.1658
0.1150
1.2062
0.9180
9117.38
Red system
A 2n_x2E+
H4370-15050
23217.5
H4314-4890
(A)
0.7244
1.2938
0.5445
roo
qoo
1.2913
0.9907
1.1313
0.4957
25969.19
CN
CH
Deslandresd'Azambuja
C Ing-A Inu
A 2 6-X 2 n
H3390-4110
19378.44
i..i..3 400-7 850
Swan
d 3ng-Q 3nu
C2
(cm- I )
Ii(J()
Approx. range (A)
System
Molecule
Re(rv'v") = (1.86±0.17)(1...{}.51rv'v")
forrv'v" = 1.05-1.35 A.
Re(r) = 0.887 exp[-3.30(r - 0.95)]
for r = 0.95-1.40 A.
Re(rv'v") = (12.12 ± 0.01)(1-1.63Irv'v"
+0.70rv'v") for rv'v" = 0.97-1.16 A.
Re (r) = 1.051 + 0.203 3r...{}.4646r 2
for r = 0.85-2.65 A.
(Re) = 0.210 ± 0.006.
See (7) for Re(r), r = (1.25-20.0)"0.
Re(rv'v") = (26.8± 1.5)(I-2.8986r v'v"
+2. 749 9r~, v,,"'{}·8597r~, v")
for rv'v" = (1.0-1.20)"0'
See (8) for Re(r), r = (1.6-2.4)"0'
See [2] for R.(r),
r = (1.0-12)"0'
See [6] for Re(r),
r = (1.0-10.0)"0'
Re(rv'v") = 348(-1 + 1.74275rv'v"
-0.9%36r;,v" + 1.8803r~,v")
for rv' v" = 1.6-2.1 A.
(Re) = 1.22
(Re) = 0.280 ± 0.008.
See (2) for R.(r), r = (1.3-4.0)"0'
R.(rv'v") = (0.19±0.03)(1 +0.571rv'v")
forrv'v" = 1.05-1.27 A.
See (3) for R.(r), r = (1.4-4.0)"0'
Re(rv'v") = (0.72 ± 0.02)(I-{J.03rv'v")
for rv'v" = 0.95-1.35 A.
See (3) for Re(r), r = (1.6-4.0)"0'
Re(rv'v") = (2.94 ± 0.15)(1...{}.68rv'v")
for r v'v" = 1.0-1.3 A.
See (4) for R.(r), r = (1.8-8.0)"0'
See [5] for R.(r),
r = (1.4-3.1)"0'
Re(rv'v") = (2.380±0.28)(I-0.52r v'v")
for r v' v" = 1.12-1.50 A.
See [I). Figure of Re(r)
for r = (2.0-3.5)ao.
Recommended electronic
transition moment (e"O)
Table 4.18. Parameters for molecular transition strengths.
(e"O)2
0.0026b
O.044la
0.0463b
0.0031 a
0.326b
0.325a
0.25b
0.24a
1.42a
2.23a
0.D785b
0.0054~
0.0371b
0.00158 b
0.427b
0.0386a
0.0426b
0.442a
0.D78a
0.084b
0.0511 a
0.54b
O.44la
Rfu
>
~
~
()
tr1
"C
en
.f;>.
........
\0
0
),),3863-4278
A 2t;_X 2n
a system;
SiH
no
a system;
ZrO
21631.48
21548.46
21536.36
16033.81
15741.31
15426.78
14163.00
14095.88
14019.43
16722.75
16294.72
17420.2
19334.03
19343.66
19341.68
17840.6
24193.04
32402.39
49358.15
"00 (em-I)
(A)
1.7448
1.7564
0.973
1.6448
0.9950
1.7940
0.3130
1.633 I
0.672
1.6590
0.9152
1.6313
0.7191
1.0080
0.9932
1.5459
0.4092
For band (15.0)
0.000272
1.3107
0.9067
roo
qOO
(Continued.)
0.085a
= 0.52.
See (10). for Re(r)
for r = (2.8-3.8)ao.
2.63b
0.97 b
3.33a
5.24a
4.63 a
0.084a
= 1.83.
= 2.7.
= 2.25.
See (10). for Re(r).
r = (2.8--3.8)"0'
(Re)
(Re)
(Re)
(Re)
Re (r v' v") = (102 ± 25) exp( - 2.57rv' v" )
for r v'v" = 1.58-1.72 A.
0.062I a
O.OlOgb
0.00953a
For (15.0) band
0.000 175a
Re(rv'v") = 1.86-0.8069,v'v"
for rv'v" = 1.30--2.16 A.
Re(rv'v") = (0.42 ± 0.01)(I.0--0.75r v'v")
for r v' v" = 0.8-1.2 A.
See (9) for Re (,)., = (1.3-4.4)ao.
(Re) = 0.25 ± 0.03.
R& (e"O)2
Recommended electronic
transition moment (e"O)
References
I. Chabalowski, C.F., Peyerimhof, S.D., & Buenker, R.1. 1983, J. Chern. Phys., 81. 57
2. van Dishoeck, E. 1987, J. Chern. Phys., 86,196
3. Bauschlicher, C.w., Langhoff, S.R., & Taylor, P.R. 1988, ApJ. 332, 531
4. Kirby, K., & Cooper, D.L. 1989, J. Chern. Phys., 90, 4895
5. Marian, C.M., Larsson, M.• Olsson, B.1., & Sigray, P. 1989, J. Chern. Phys., 130, 361 ApJ. 332, 531
6. Dressler, H., Wolniewicz, L. 1985, J. Chern. Phys., 82, 4720
7. Kirby, K.P., & Goldfield, E.M. 1991, J. Chern. Phys .• 94. 1271
8. Langhoff, S.R., Bauschlicher, C.W., & Partridge. H. 1988, J. Chern. Phys.• 89. 4909
9. Bauschlicher, C.W., & Langhoff, S.R. 1987, J. Chern. Phys., 87, 4665
10. Langhoff, S.R., & Bauschlicher, C.W. 1990, ApJ, 349, 369
b 3 <1>--<l3t;
y system;
),),5110--7600
),),4200--5600
C 4};--X 4};-
YO
d 3t;--<l 3t;
),),4400--7000
A 2n_x 2};+
),),5 700--6 800
),),5 700--8 650
).).4900--5800
),),4050--6 300
YO
A 3<1>_X 3t;
y system;
c I <I>--<l It;
fJ system;
C 3t;_X 3t;
),),2608-4107
OH
),),1750--5350 (bands)
),),1300--1750 (continuum)
SchumannRunge
B 3};;; -X 3};g
A 2};+ -X 2n
02
Approx. range (A)
System
Molecule
Thble 4.18.
\0
-
.........
oz
~
>
o
:::0
ttl
"C
ot"'"
-o
en
ttl
c:t"'"
:::0
oz
ttl
t"'"
ttl
Ii
>-3
w
en
+::0.
92 /
4
SPECTRA
ACKNOWLEDGMENTS
One of our authors (e.R.e.) thanks the following for advice and help of various kinds: P.P. Bernath,
T.M. Dunn, K.T. Hecht, Sveneric Johansson, R.L. Kurucz, W.e. Martin, D.e. Morton, R.W. Nicholls,
L.S. Rothman, R.L. Sears, R.H. Tipping, and E.E. Whiting.
REFERENCES
1. Clark, D. 1996, Student's Guide to the Internet, 2nd ed.
(QUE, Indianapolis). (There are also many other books
that deal with the Internet and its applications.)
2. Cowan, R.D. 1981, The Theory ofAtomic Structure and
Spectra (University of California Press, Berkeley)
3. Martin, WC., Zaiubas, R., & Hagan, L. 1978, Atomic
Energy Levels-The Rare Earths, NSRDS-NBS No. 60
4. Johansson, S., & Cowley, C.R. 1988, J. Opt. Soc. Am.,
58,2664
5. Wiese, WL., & Martin, G.A. 1989, in A Physicist's
Desk Reference, edited by H.L. Anderson (AlP, New
York)
6. Moore, e.E. 1993, in Tables of Spectra of Hydrogen,
Carbon, Nitrogen, and Oxygen Atoms and Ions, edited
by J.W Gallagher (CRC, Boca Raton, FL)
7. Martin, W.e. 1992, in Atomic and Molecular Data for
Space Astronomy, edited by P.L. Smith and W.L. Wiese
(Springer, Berlin)
8. Cohen, E.R., & Taylor, B.N. 1987, Rev. Mod. Phys., 59,
1121
9. Moore, C.E. 1967, Selected Tables of Atomic Spectra,
NSRDS-NBS No.3, Sec. 2
10. Bates, D.R., & Damgaard, A. 1949, PTRSLA, 242,101
11. Oertel, G.K., & Shomo, L.P. 1968, ApJS, 16, 175
12. Kurucz, R.L., & Bell, B. 1995, "Atomic Line List," Kurucz CD-ROM No. 23 (Smithsonian Ap. Obs., Cambridge, MA)
13. Seaton, MJ., Yan, Y., Mihalas, D., & Pradhan, A.K.
1994,MNRAS,266,805
14. Allen, C.W 1976, Astrophysical Quantities, 3rd ed.
(Athlone, London), Sec. 27
15. Coleman, C.D., Bozman, WR., & Meggers, W.P. 1960,
Table of Wavenumbers, NBS Monograph No. 3 (two
volumes)
16. Peck, E.R., & Reeder, K. 1972, J. Opt. Soc. Am., 62,
958
17. Reader, J., & Corliss, C.H. 1991, in HandbookofChemistry and Physics, 72nd ed., edited by R Lide (CRC,
Boca Raton, FL.), p. 10-1
18. Wiese, W.L., & Martin, G.A. 1989, in A Physicist's
Desk Reference, edited by H.L. Anderson (AlP, New
York), p. 97
19. Bethe, H., & Salpeter, E.E. 1957, Quantum Mechanics
ofOne- and Two-Electron Atoms (Academic Press, New
York)
20. Green, L.e., Rush, P.R., & Chandler, e.D. 1957, ApJS,
3,37
21. Wiese, W.L., Smith, M.W., & Glennon, B.M.
1966, Atomic Transition Probabilities, H Through Ne,
NSRDS-NBS4
22. Moore, C.E. 1993, in Tables of Spectra of Hydrogen,
23.
24.
25.
26.
27.
28.
29.
30.
Carbon, Nitrogen, and Oxygen Atoms and Ions, edited
by J.W Gallagher (CRC, Boca Raton, FL.)
Moore, e.E. 1959, A Multiplet Table of Astrophysical
Interest, revised ed., NBS Tech. Note 36
Moore, C.E. 1952, An Ultraviolet Multiplet Table, NBS
Circ. No. 488, 1950
Fuhr, J.R, & Wiese, W.L. 1991, Handbook of Chemistry and Physics, 72nd ed., edited by D.R Lide (CRC,
Boca Raton, FL.), pp. 10-128
Holden, N.E. 1991, in Handbook of Chemistry and
Physics, 72nd ed., edited by D.R. Lide (CRC, Boca Raton, FL.), Sec. 11-128
Cowan, R.D. 1981, The Theory of Atomic Structure
and Spectra (University of California Press, Berkeley),
Chaps. 15 and 17
Landolt-Bomstein, 1952, Zahlenwerte und Funktionen,
6th ed. (Springer, Berlin), Vol. I, Part 5
Cowley, C.R. 1995, A Textbook of Cosmochemistry
(Cambridge University Press, Cambridge), Sec. 11.8
Rosberg, M., Litzen, U., & Johansson, S. 1993, MN-
RAS,262, Ll
31. Leckrone, D.S., Wahlgren, G.M., & Johansson, S. 1991,
ApJ, 377, L37
32. Hinds, E.A. 1988, in The Spectrum of Atomic Hydrogen: Advances, edited by G.W. Series (World Scientific,
Singapore)
33. Fuhr, J.R., Martin, G.A., & Wiese, WL. 1988, J. Phys.
Chern. Ref Data. SeT., 17, Suppl. 4
34. Kaufman, v., & Sugar, J. 1986, J. Phys. Chem. Ref
Data. SeT., 15, 321
35. Morton, D.C. 1991, ApJS77, 119
36. Wiese, WL., Fuhr, I.R., & Deters, T.M., 1996, J. Phys.
Chem. Ref Data Monograph, 7
37. Rothman, L.S., Gamache, R.R, Tipping, R.H., Rinsland, C.P., Smith, M.A.H., Benner, D.C., Malathy Devi,
V., Flaud, I.-M., Brown, L.R, & Toth, RA. 1992, J.
Quant. Spectrosc. Rad. Transf, 48, 469
38. Kuznetsova, L.A. et al. 1993 (Russian) J. Phys. Chem.,
67,11
39. Kurucz, R.L. 1994, in Molecules in the Stellar Environment, Lecture Notes in Physics, edited by U.G.
If1)rgensen (Springer, Berlin), Vol. 428, p. 282; see also
Kurucz CD-ROM No. 15 (Smithsonian Ap. Obs., Cambridge, MA), 1993
40. Parkinson, W.H. 1992, in Atomic and Molecular Data
for Space Astronomy, Lecture Notes in Physics, edited
by P.L. Smith and W.L. Wiese (Springer, Berlin), Vol.
407,p.149
41. If1)rgensen, U.G. 1994, in Molecules in the Stellar Environment, Lecture Notes in Physics, edited by U.G.
If1)rgensen (Springer, Berlin), Vol. 428, p. 29
4.13 SELECTION RULES: DIPOLE RADIATION / 93
42. Bernath, P. 1995, Spectra of Atoms and Molecules (Oxford University Press, Oxford)
43. Zare, R.N. 1988, Angular Momentum (Wiley, New
York)
44. Herzberg, G. 1950, Spectra of Diatomic Molecules, 2nd
edited by (Van Nostrand, New York)
45. Huber, K.P., & Herzberg, G. 1979, Molecular Spectra and Molecular Structure Iv. Constants of Diatomic
Molecules (Van Nostrand-Reinhold, New York)
46. Gordy, W., & Cook, R.L. 1984, Microwave Molecular
Spectroscopy (Wiley, New York)
47. Judd, B. 1975, Angular Momentum Theory for Diatomic
Molecules (Academic Press, New York), see pp. 184186
48. Brown, J.M., Hougen, J.T., Huber, K.-P., Johns, J.W.C.,
Kopp, I., Lefebvre-Brion, H., Merer, A.J., Ramsay,
D.A., Rostas, J., & Zare, R.N. 1975, J. Mol. Spectrosc.,
55,500
49. Tatum, J.B. 1967,ApJS, 24, 3
50. Whiting, E.E., Schadee, A., Tatum, J.B., Hougen, J.T.,
& Nicholls, R.W. 1980, J. Mol. Spectrosc., SO, 249
51. Morton, D.C. 1994, ApJS, 95,301
52. Edmonds, A.R. 1960, Angular Momentum in Quantum
Mechanics (Princeton University Press, Princeton)
53. Schadee, A. 1964, Bull. Astron. Netherlands, 17, 311
54. Kovacs, I. 1969, Rotational Structure in the Spectra of
Diatomic Molecules (Elsevier, Amsterdam)
55. Whiting, E.E., Paterson, J.A., Kovacs, I., & Nicholls,
R.W. 1973, J. Mol. Spectrosc., 47, 84
56. Whiting, E.E. 1973, NASA Tech. Note D-7268
57. Herzberg, G. 1971, The Spectra and Structure of Simple
Free Radicals (Cornell University Press, Ithaca)
58. Rosen, B. 1970, Spectroscopic Data Relative to Diatomic Molecules (Pergamon, New York)
59. Pearse, R.W.B., & Gaydon, A.G. 1976, The Identification of Molecular Spectra, 4th ed. (Chapman and Hall,
London)
Chapter 5
Radiation
J.J. Keady and D.P. Kilcrease
5.1
5.1
Radiation Quantities and Interrelations. . . . . . . ..
95
5.2
Refractive Index and Average Polarizability. . . . ..
100
5.3
Absorption and Scattering by Particles. . . . . . . ..
102
5.4
Photoionization and Recombination . . . . . . . . . .
106
5.5
X-Ray Attenuation . . . . . . . . . . . . . . . . . . . .
109
5.6
Absorption of Material of Stellar Interiors. . . . . ..
110
5.7
Absorption of Material of the Solar Photosphere. ..
114
5.8
Solar Photoionization Rates . . . . . . . . . . . . . ..
114
5.9
Free-Free Absorption and Emission . . . . . . . . ..
115
5.10
Reflection from Metallic Mirrors . . . . . . . . . . ..
117
5.11
Visual Photometry . . . . . . . . . . . . . . . . . . . ..
117
RADIATION QUANTITIES AND INTERRELATIONS
The quantitative concepts of radiation are defined [1] in terms of /, the flux of radiation at a given point
in a given direction across a unit surface normal to that direction per unit time and per unit solid angle.
This is called specific intensity, or simply intensity.
The flux of radiation through a unit surface is the sUrface flux, or flux density,
:F
=
1/
cos
4:71"
e dw,
where e is the angle between the ray and the outward normal and integration is in all directions.
95
96 I 5
RADIATION
The emittance is the flux of radiation emitted from a unit surface,
r
f21r I
=
cos () d w
for isotropic radiation 7t I, where in this case the integration is over the outward hemisphere.
The radiation density is
u
= (lIe)
{ I dw
J4rr
= (47tje)i.
The radiation quantities per unit frequency and wavelength ranges are written lv, 1)., rv, etc.:
I
I).
dA
=
f
Iv dv
=
f
I). dA,
v2
e
= -2
Iv = -Iv,
A
e
A2
AI).
e
= --dv
= -"2dv,
e
v
= vlv,
e
= Av.
The linear absorption coefficient is Ks:
dl jds = -KsI.
The scattering coefficient as. is similar to the absorption coefficient but applies to the radiation
scattered. It is used in the sense that Ks - as represents absorption and transference into heat.
The mass absorption coefficient is Km (the subscript is usually omitted):
dl jds = -PKml,
where P is the density.
The atomic or particle absorption coefficient or cross section is a:
dljds = -Nal,
where there are N atoms or particles per unit volume and a represents the effective area over which the
incident radiation if fully absorbed.
The emission coefficient j is the radiant flux emitted per unit volume and unit solid angle. For
uniform scattering,
j = (a j47t) {
J4rr
I dw,
where the first term represents scattering and the integral represents incident radiation.
For scattering by electrons, atoms, molecules,
where () is the angle between incident and scattered light. I is assumed to be unpolarized, and the
scattered radiation when viewed at the angle () is polarized with intensity proportional to cos 2 () in the
plane of scattering and proportional to I in the direction perpendicular to the plane of scattering.
5.1 RADIATION QUANTITIES AND INTERRELATIONS I 97
The optical thickness or depth is
r =
f
f
Ks ds =
pKm ds.
The source function is
S
= jlKs.
The intensity emitted from an absorbing medium is
1=
f
j exp{-r) ds =
f
S exp{-r) dr.
We show two forms of the Kirchoff law:
(a) In a volume element,
jv
= Ks.vBv{T),
where Bv(T) is blackbody intensity at temperature T.
(b) At a surface element,
Iv
= AvBv{T),
where Av is the fraction of incident radiation absorbed, i.e., I - Av is the reflection coefficient and
analogous to albedo.
The atomic polarizability a is the induced dipole moment per unit electric field (& for a steady or
low-frequency field):
&
= 4a5 L
in I{vnI cRoo)2
n
= 5.927 x
10- 25
= 7.138 x
10-23
L in/{vnlcRoc,)2 cm3
n
L inA~ cm
3
(A in jlm),
n
where vn/cRoo is the frequency in rydbergs of lines connecting the ground level and in is the
corresponding oscillator strength.
For scattering,
as
= (128rr 5 /3)N{vlc)4a 2
= (128rr 5 13A4)Na 2
= 1.3057 x
1020 Na 2 IA 4
(A in jlm).
The index of refraction is n:
n-I=2rrNa
= 1.688 x
lO20a
at STP.
98 / 5
RADIATION
The molecular refraction is
R
n2 - 1 M
41l'
=- - = -Noa,
n2 + 2 p
3
where M is the molecular weight, p is the density, and No is the Avogadro number.
The radiation constants are
Cl
= 21l'hc2 = 3.74177 x 10-5 ergcm2 s-I,
C2
= hc/ k = 1.43877 cmK.
The Stefan-Boltzmann constant is
U
= 21l' 5 k 4J(15c 2 h 3 ) = 1l'4CJ J(l5ci)
= 5.6705 x 10-5 ergcm- 2 s- 1 K- 4 .
The blackbody emittance is
The blackbody intensity is
The radiation density u in a cavity at temperature T is
In a medium of refractive index n,
B
u
= n 2 (u/1l')T 4,
= n 3 (4u/c)T 4 ,
with similar factors applying for the Planck law with nv and n).,.
The photon emission constant is
p
= 41l'~(3)c/c~
= 1.520486 x
where ~ (n) is the Riemann zeta function.
10 11 photonscm- 2 s- 1 K- 3 ,
5.1
RADIATION QUANTITIES AND INTERRELATIONS
/
99
The photon flux from a unit blackbody surface is
Blackbody radiation is unpolarized, hence the intensity of radiation linearly polarized in a specific
direction will be half the value quoted in the formulas.
The Planck function in wavelength units is
(C/4)UA
= rr BA =:FA = 2rrhc2 A-5 /(e hc / HT
=
ClA -5 /(e C2 / AT - 1)
- 1)
(A in cm),
where U A , B A , and:FA are the radiation density, intensity, and emittance for unit wavelength ranges.
The Planck function in frequency units is
The photon distribution law is
NA = 2rrCA -4 /(e C2 / AT - 1),
N v = 2rrc-2v2/(ehv/kT - 1),
where NA and N v are the emittance of photons per squared centimeter per second and per unit
wavelength and frequency ranges, respectively.
The Rayleigh-Jeans distribution (for the red end of the spectrum) is
:FA = 2rrckTA -4 = (Cl/C2)TA -4,
:Fv = 2rrc- 2kTv 2 = 2rrkTA -2.
The Wien distribution (for the violet end of the spectrum) is
:FA
:Fv
= 2rrhc2A-5e-C2/AT = ctA-5e-C2/AT,
= 2rrhc-2v3e-hv/kT.
Wien law: The wavelength of maximum:FA or BA is Amax:
TA max = 0.201405 2C2 = 0.28978 cm K.
The wavelength of maximum photon emission is Am:
TAm
= 0.2550571c2 = 0.36697 cmK.
The frequency of maximum :Fv or Bv is Vm:
Tc/v m
y
= 0.354429Oc2 = 0.50994cmK.
The three numerical constants above are l/y in y
e- Y ), respectively.
= 3(1 -
=
5(1 - e- Y ), y
=
4(1 - e- Y ), and
100 / 5
RADIATION
S.2 REFRACTIVE INDEX AND AVERAGE POLARIZABILITY
The refractive index and polarizability of atomic and molecular gases are given in Tables 5.1 and 5.2,
where n is the refractive index at STP,
n - 1 = A(1
+ BP..2)
(A in Itm),
and a is the polarizability at low frequency.
Table 5.1. Refractive index and polarizability of atomic gases.
a [1]
Atom
(10- 25
em3)
H
He
Li
Be
C
N
0
Ne
Na
Mg
Al
Si
P
S
6.67
2.05
243
56
17.6
11.0
8.03
3.95
236
106
83.4
53.8
36.3
29.0
n (D lines)
A
(units of
10-5)
B
(units of
10- 3)
1.0000350
3.48
2.3
a [1]
Atom
CI
Ar
K
Ca
Se
n
1.0000671
6.6
2.4
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
(10- 25
em3)
21.8
16.4
434
250
169
136
114
68
86
75
68
65
61
71
n(D lines)
A
(units of
10-5)
B
(units of
10- 3)
1.0002837
27.92
5.6
Reference
1. Miller. T.M., & Bederson. B. 1977,Adv. Atom. Mol. Phys. 13. 1
Table 5.2. Refractive index of molecular gases.
B
(units of
10-3)
Molecule
n (D lines)
A
(units of
10-5)
Air
H2
1.0002918
1.0001384
1.000272
1.000297
1.000254
28.71
5.67
13.58
7.52
26.63
5.01
29.06
7.7
516 (rodio fioq.)
~
N2
H2O
Molecule
n (D lines)
CO2
CO
NH3
NO
CI4
1.0004498
1.000334
1.000375
1.000297
1.000441
A
(units of
10-5 )
B
(units of
10- 3)
43.9
32.7
37.0
28.9
6.4
8.1
12.0
7.4
The refractive indices quoted in Table 5.3 are relative to air at 15 0 C. The temperatures of the media
are about 180 C and the temperature coefficients quoted are the change of D-line refractive index for a
10 C temperature rise. Manufacturers' reports must be consulted for indices that are accurate enough
for optical design. The table also gives the spectral limits (A in Itm) within which the absorption is less
than 2.72cm- 1 (i.e., 1 cm transmission> 37%).
)..
0.23
2.2
0.23
4
+0.000014
1.58
1.515
1.499
1.491
1.486
1.483
1.481
1.479
1.476
1.91
1.722
1.683
1.666
1.657
1.652
1.648
1.643
1.626
+0.000005
Extr.
ray
Ord.
ray
0.32
2.2
-0.000001
1.557
1.531
1.522
1.517
1.513
1.511
1.507
1.496
BSC
crown
1.650
1.627
1.616
1.61O
1.605
1.600
DF
flint
0.13
9.0
0.17
3.6
1.663
1.589
1.567
1.558
1.553
1.550
1.548
1.544
1.528
Extr.
ray
0.17
3.6
-0.000006
Quartz
-0.000005
1.651
1.579
1.558
1.549
1.544
1.541
1.539
1.536
1.520
1.42
1.495
1.455
1.442
1.437
1.434
1.432
1.430
1.429
1.424
1.398
1.303
-0.00001
Ord.
ray
Fluorite
CaF2
References
I. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. I, Sec. 34; 2, Sec. 35; 3, Sec. 36
2. Garton, W.R.S. 1966, Adv. Atom. Mol. Phys. 2,93
0.37
2.8
+0.000003
Glass
Note
For information on atmospheric refraction, see Table 5.2.
Limits [2)
Low)..
High)..
Temp.
coef.
IO
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.0
2
5
(~m)
Calcite
Table 5.3. Refractive indices of optical media [1,2).
0.16
21
-0.000003
1.550
1.489
1.471
1.463
1.458
1.455
Fused
silica
0.20
17
-0.00004
1.792
1.602
1.568
1.552
1.543
1.538
1.535
1.532
1.526
1.519
1.494
Rock
salt
1.14
< 0.2
-0.00008
1.423
1.358
1.343
1.336
1.332
1.330
1.328
1.325
1.315
Water
VI
o
......
--
><
~
l'
.....
.....
>
tD
N
.....
ol'
>
::0
'"C
tTl
>
o
::0
~
tTl
1::1
>
Z
~
tTl
Z
1::1
-
<:tTl
~
>
(j
::0
'Tl
tTl
:;d
tv
102 / 5
5.3
RADIATION
ABSORPTION AND SCATTERING BY PARTICLES
For scattering of free electrons, U e (Thomson scattering) is [2]
ue
where
8Jl'
=3
e 2)2
( mc2
(1 - 2 mchv2 )
= 0.66524 x
10-24 (1 - 2
hv
mc 2 )
2
cm ,
is the (exponential) scattering coefficient per electron (Sec. 5.1) with the relativistic term
At the high densities and temperatures found in stellar interiors, further corrections due to
correlations and thermal motion may be required [3,4].
For Rayleigh scattering of atoms or molecules,
Ue
2hv/mc 2 .
32Jl'3 (n - 1)2
Us
= 3N
= 3.307 x
A.4
10
18 (n
6 + 3~
6-7~
- 1)28/A.4N cm- I
(A. in ILm),
where N is the number of atoms or molecules per unit volume, n is the refractive index of the medium,
is the linear scattering coefficient, and 8 = (6 + 3M/(6 - 7~) = depolarizing factor [5, 6]. ~ =
0.030 for N2 and 0.054 for 02 [7].
The Rayleigh scattering cross section of an atom or a molecule is
Us
U
(n - 1)2
= 32Jl' 38
a
3A.4
=
N
l.306 x
= 128Jl'5 8a2
3A.4
10 8a /A.4 cm
20
2
2
(A. in ILm),
where the polarizability a = (n - 1)/(2Jl' N).
For atomic scattering at some distance from any absorption line,
Ua
=
8Jl'
3
(~)2
mc 2
("
112V2
2
~
v - v2
2
12
)2,
where 112 is the oscillator strength (1 is the ground level when excitation is low).
For the absorption of small particles (spherical) of radius a in terms of Jl'a 2 [5], the efficiency
factors (Q = u/Jl'a 2) for extinction, scattering, absorption, and radiation pressure are Qext' Qsca,
Qabs, and Qpr, respectively, with
Qext
Qpr
= Qsca + Qabs,
=
Qext - (cose}Qsca,
where (cos e) is the forward asymmetry of scattering [8]. For large objects Qext =2.0 of which l.0 is
intercepted and l.0 scattered with (cos e) = l.0. The extinction coefficient k is related to the complex
dielectric constant E through
E
=
EI
± iE2 =
(n
± ik)2.
Here n is the refractive index and El, E2, n, and k are real. k and n are therefore given by
k}
1
2 + (2)1/2 = E ]1/2
n = _[(E
../i
1
2
,- 1
.
5.3 ABSORPTION AND SCATTERING BY PARTICLES / 103
For measurements performed in vacuum, with 21l' a/A
coefficient is related to the indices of refraction via
Qabs
«
21l'
Qext
---;;- ~ --;- = T
1 everywhere, the measured extinction
24nk
(n 2 - k 2
+ 2) + 4n 2k 2 •
See Tables 5.4-5.10, extinction efficiency factors for various compounds. The mean particle radius for
the spheroids in the amorphous carbon sample was 40 A.
Table 5.4. Extinction efficiency factor Qext for water droplets as a function ofparticle rodius and wavelength [1).
A (p,m)
a = 0.31J,m
1.0 IJ,m
3.0 IJ,m
10.0 IJ,m
A (p,m)
a = 0.31J,m
1.0 IJ,m
3.0 IJ,m
10.0 IJ,m
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.80
2.00
2.10
2.20
2.30
2.50
2.60
2.70
2.75
2.80
2.90
2.95
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.75
3.83
4.00
1.39
1.07
0.80
0.58
0.44
0.35
0.28
0.23
0.18
0.15
0.099
0.067
0.054
0.043
0.035
0.022
0.0127
0.0136
0.0477
0.1754
0.4178
0.458
0.423
0.293
0.159
0.0806
0.0429
0.0264
0.0189
0.0130
0.0114
0.0114
2.79
3.37
3.76
3.90
3.89
3.60
3.41
3.08
2.83
2.56
2.07
1.65
1.45
1.25
1.09
0.69
0.33
0.189
0.297
0.940
1.65
1.74
1.76
1.79
1.93
1.52
1.21
0.944
0.763
0.569
0.497
0.428
2.47
2.13
1.95
2.37
2.68
2.80
2.28
2.04
1.86
1.83
2.09
2.87
3.16
3.51
3.67
3.66
2.61
1.58
1.61
2.58
2.45
2.44
2.49
2.67
2.74
3.14
3.53
3.97
3.99
3.84
3.76
3.58
2.07
1.99
2.05
2.14
2.18
2.05
2.25
2.25
2.01
2.27
2.11
2.13
2.42
2.46
2.28
2.34
1.96
2.26
2.34
2.23
2.21
2.21
2.22
2.24
2.26
2.33
2.42
2.17
1.97
2.38
2.66
2.80
4.50
4.66
4.80
5.00
5.26
5.50
5.80
6.00
6.05
6.40
7.00
7.50
8.00
8.50
9.00
9.50
10.00
10.50
11.00
11.50
12.00
12.50
13.00
13.50
14.00
15.00
16.00
17.50
18.00
20.00
30.00
100.00
0.0182
0.0197
0.0180
0.0131
0.0098
0.0111
0.026
0.076
0.083
0.030
0.022
0.021
0.020
0.020
0.020
0.021
0.025
0.031
0.044
0.063
0.083
0.091
0.103
0.107
0.114
0.123
0.104
0.086
0.080
0.061
0.037
0.014
0.342
0.319
0.291
0.242
0.189
0.162
0.177
0.39
0.419
0.215
0.145
0.120
0.106
0.097
0.091
0.087
0.094
0.112
0.155
0.220
0.286
0.317
0.360
0.376
0.400
0.434
0.371
0.309
0.289
0.223
0.129
0.048
3.02
2.88
2.76
2.56
2.22
1.93
1.50
1.95
2.02
1.95
1.47
1.19
1.02
0.886
0.734
0.596
0.509
0.487
0.547
0.706
0.884
0.992
1.13
1.20
1.29
1.44
1.38
1.30
1.29
1.23
0.528
0.149
2.46
2.26
2.21
2.02
1.85
2.02
2.65
2.40
2.38
2.30
2.73
3.09
3.24
3.30
3.21
2.95
2.50
2.08
1.78
1.83
1.97
2.09
2.20
2.26
2.32
2.42
2.51
2.64
2.71
2.92
2.75
0.758
Reference
1. Irvine, W.R., & Pollack, J.B. 1968, Icarus, 8, 324
Table 5.5. Extinction efficiency factor Qextfor ice particles as afunction ofparticle rodius and wavelength [1).
A (IJ,m)
a = 0.31J,m
1.0 IJ,m
3.01J,m
10.0 IJ,m
0.95
1.00
1.20
1.50
2.00
2.35
0.572
0.49
0.295
0.158
0.063
0.029
2.92
3.80
3.35
2.52
1.52
0.94
2.41
2.66
2.28
1.82
3.10
3.77
2.02
2.08
2.15
2.24
2.35
1.96
A (IJ,m)
3.60
3.80
3.90
4.00
4.10
4.20
a =0.3IJ,m
1.0 IJ,m
3.01J,m
10.0 IJ,m
0.025
0.017
0.018
0.019
0.021
0.023
0.76
0.52
0.46
0.41
0.38
0.35
3.91
3.70
3.51
3.28
3.04
2.84
2.04
2.57
2.63
2.64
2.43
2.30
104 I 5
RADIATION
Table 5.5. Continued.
). (/Lm)
a = 0.3/Lm
1.0/Lm
3.0/Lm
1O.0/Lm
). (/Lm)
a=0.3/Lm
1.0/Lm
3.0/Lm
1O.0/Lm
2.40
2.45
2.50
2.55
2.60
2.625
2.65
2.800
2.85
2.90
2.95
3.00
3.05
3.075
3.10
3.15
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
0.025
0.022
0.019
0.016
0.013
0.012
0.012
0.027
0.066
0.177
0.306
0.377
0.514
0.547
0.511
0.379
0.244
0.151
0.1096
0.0817
0.0608
0.046
0.035
0.029
0.823
0.724
0.626
0.522
0.433
0.397
0.364
0.261
0.360
0.675
0.986
1.151
1.516
1.63
1.69
2.30
2.23
2.10
1.91
1.74
1.50
1.16
0.97
0.85
3.81
3.73
3.58
3.35
3.09
2.96
2.79
1.84
1.68
1.78
1.92
2.00
2.22
2.28
2.36
2.54
2.57
2.62
2.78
2.92
3.14
3.62
3.87
3.94
1.93
2.12
2.46
2.71
2.58
2.36
2.18
2.07
2.31
2.19
2.14
2.14
2.18
2.19
2.20
2.25
2.26
2.26
2.25
2.25
2.36
2.37
2.19
2.06
4.30
4.40
4.50
4.60
4.70
4.80
4.90
5.00
5.70
6.00
6.40
6.70
7.00
8.00
9.00
10.00
11.00
12.00
15.00
20.00
40.00
62.00
100.00
150.00
0.027
0.032
0.036
0.031
0.023
0.Dl8
0.Dl5
0.014
0.026
0.048
0.040
0.039
0.033
0.021
0.019
0.020
0.038
0.039
0.019
0.005
0.017
0.016
0.0027
0.00057
0.34
0.33
0.32
0.28
0.23
0.20
0.17
0.16
0.16
0.23
0.19
0.18
0.15
0.10
0.08
0.07
0.15
0.16
0.076
0.019
0.058
0.055
0.009
0.002
2.67
2.46
2.31
2.17
2.02
1.86
1.73
1.61
1.20
1.31
1.11
1.02
0.92
0.67
0.51
0.33
0.77
1.25
0.80
0.21
0.20
0.18
0.028
0.007
2.16
2.11
2.10
2.10
2.06
2.16
2.27
2.39
2.95
2.73
2.86
2.89
2.96
3.01
2.74
1.76
2.79
3.00
3.58
3.06
1.37
1.02
0.17
0.04
Reference
1. Irvine, W.R., & Pollack, J.B. 1968, Icarus, 8, 324
Table 5.6. Extinction efficiencies for amorphous carbon [I, 2].a
). (/Lm)
Qext/a (em-I)
). (/Lm)
Qext/a (em-I)
). (/Lm)
Qext/a (em-I)
0.12
0.13
0.14
0.15
0.16
0.18
0.20
0.22
0.23
0.25
5.12[5]
3.21[5]
2.02[5]
2.18[5]
1.84[5]
1.47[5]
1.43[5]
1.56[5]
1.63[5]
1.60[5]
0.27
0.30
0.50
0.70
1.00
1.60
2.00
3.13
4.00
5.00
1.49[5]
1.28[5]
7.07[4]
4.81[4]
3.52[4]
2.14[4]
1.69[4]
1.05[4]
7.96[3]
6.06[3]
7.14
10.00
15.40
20.00
30.50
50.80
70.50
101.00
205.00
289.00
4.49[3]
3.18[3]
1.74[3]
1.35[3]
8.80[2]
5.38[2]
4.04[2]
3.17[2]
1.66[2]
1.19[2]
Note
aNumbers in square brackets denote powers of 10.
References
1. Bussoletti, E. et al. 1987, AclAS, 70, 257
2. Maron, M. 1990,ApS&S, 172, 21
5.3 ABSORPTION AND SCATTERING BY PARTICLES /
Table 5.7. Extinction efficiency factor Qextfor graphite as ajunction ofparticie
radius and wavelength [I].a
= O.OIJLm
A (JLm)
a
0.12
0.15
0.18
0.20
0.21
0.215
0.2175
0.22
0.225
0.23
0.24
0.26
0.28
0.30
0.33
0.365
0.4861
0.6562
0.80
1.00
1.40
0.425
0.244
0.512
0.995
1.51
1.25
1.22
Ll7
1.01
0.88
0.63
0.40
0.31
0.25
0.20
0.160
0.093
0.058
0.043
0.030
0.017
= O.OIJLm
0.1 JLm
A (JLm)
a
2.58
2.32
2.49
2.83
2.92
3.03
3.06
3.08
3.11
3.13
3.12
3.02
2.98
3.01
3.09
3.11
3.34
2.65
1.88
1.09
0.45
2.00
3.00
4.00
5.00
6.00
9.00
10.00
11.00
11.52
11.54
12.00
20.00
40.00
60.00
80.00
100.0
200.0
400.0
700.0
1000.0
2000.0
l.oo[ -2]
5.37[ -3]
3.44[-3]
2.43[-3]
1.83[ -3]
4.65[-6]
9.00[-4]
8.21[ -4]
2.98[-3]
8.82[-4]
7.60[-4]
6.91[-4]
6.51[-4]
4.28[-4]
2.77[-4]
1.89[ -4]
5.24[-5]
1.40[ -5]
4.71[-6]
2.33[-6]
5.87[-7]
0.1 JLm
0.19
0.084
0.048
0.032
0.024
1.23[-2]
1.07[-2]
9.61[ -3]
3.13[-2]
1.01[ -2]
8.78[-3]
7.45[-3]
6.87[-3]
4.41[-3]
2.80[-3]
1.9O[ -3]
5.13[-4]
1.29[-4]
4.24[-5]
2.08[-5]
5.22[-5]
Note
aNumbers in square brackets denote powers of 10.
Reference
I. ~ne,B.L. 1985, ApJS, 57, 587
Table 5.S. Extinction efficiencies for silicon carbide [I]. a
A (JLm)
0.10
0.20
0.40
0.78
0.99
1.96
3.09
3.97
4.69
6.02
7.10
8.39
Qext!a (em-I)
A (JLm)
Qext/a (em-I)
A (JLm)
Qext!a (em-I)
3.46[6]
7.65[4]
1.29[4]
8.85[4]
8.13[3]
7.01[3]
4.15[3]
2.55[3]
1.66[3]
6.97[2]
4.83[2]
4.03[2]
9.12
9.90
10.14
10.37
10.61
10.86
ILlI
11.37
11.63
11.90
12.17
12.45
4.24[2]
9.65[2]
1.66[3]
3.06[3]
5.76[3]
9.35[3]
1.37[4]
1.45[4]
1.04[4]
7.30[3]
4.84[3]
3.31 [3]
12.74
13.04
13.34
13.65
13.96
14.29
15.30
22.00
36.90
52.00
103.3
205.3
2.53[3]
1.94[3]
1.50[3]
Ll8[3]
9.69[2]
7.96[2]
5.76[2]
3.23[2]
1.57[2]
9.74[1]
3.79[1]
1.23[1]
Note
aNumbers in square brackets denote powers of 10.
Reference
1. Pegourie, B. 1988, A& A, 194, 335
105
106 / 5
RADIATION
Table 5.9. Extinction efficiency factors Qextfor silicate as afunction ofpanicle
radius and wavelength [1].a
A (JLm)
0.12
0.14
0.16
0.20
0.23
0.30
0.40
0.55
a
= O.OlJLm
0.943
0.51
0.154
0.032
0.0146
1.09[-2)
7.99[-3)
5.76[-3)
0.1 JLm
2.56
2.62
2.67
3.13
3.98
3.41
2.26
0.78
A (JLm)
1.00
1.65
2.00
2.60
3.00
4.00
5.00
6.00
a
= O.OIJLm
3.22[-3]
4.19[-4]
2.25[-4]
9.40[-5]
5.75[-5]
2.06[-5]
8.64[-4]
9.95[-4]
0.1 JLm
0.11
3.18[ -2]
2.31[ -2]
1.67[ -2]
1.46[ -2]
1.14[-2]
1.01[ -2]
1.00[ -2]
Note
aNumbers in square brackets denote powers of 10.
Reference
1. rhr.Une,B.L. 1985, ApJS, 57, 587
Table 5.10. Extinction efficiencies for silicate for A > 6 JLm [1].a
A (JLm)
7.0
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
Qext/a (em-I)
A (JLm)
Qext/a (em-I)
A (JLm)
1.04[3]
3.26[3]
6.75[3]
1.20[4]
1.32[4]
1.20[4]
1.05[4]
8.38[3]
6.80[3]
5.58[3]
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
23.0
25.0
3.74[3]
2.79[3]
3.08[3]
3.70[3]
4.34[3]
4.70[3]
4.62[3]
4.19[3]
3.06[3]
2.57[3]
27.5
30.0
40.0
50.0
80.0
100.0
200.0
500.0
1000.0
2000.0
Qext/a (em-I)
2.10[3)
1.75[3]
9.80[2)
6.15[2]
2.26[2]
1.41[2]
3.40[1]
5.38
1.34
3.36[-1]
Note
aNumbers in square brackets denote powers of 10.
Reference
1. rhr.Une,B.L. 1985, ApJS, 57, 587
5.4
5.4.1
PHOTOIONIZATION AND RECOMBINATION
Photoionization Fit Parameters for Ground States
The following parameters are taken from [9] and are used in the fonnula for the photoionization cross
section:
where ET is the threshold energy in eV and aT is the threshold cross section, divided by 1.0 x
10- 18 cm2 . The fitting coefficients R and s are found in Table 5.11.
5.4 PHOTOIONIZATION AND
RECOMBINATION
/
107
Table S.11. Photoionization cross-section fits [l].
Parent
Resulting ion
ET
aT
R
s
H(2S)
He(IS)
He+(2 S)
Cep)
C+ep)
C2+(IS)
C3+eS)
N~S)
N+(3p)
N 2+(2p)
N3+(IS)
N*(2S)
Oep)
0(3p)
0(3p)
0+ (4S)
0 2+(3 P)
03+ (2p)
04+(IS)
05+ (2S)
Ne(IS)
Ne+(2p)
Ne+(2 P)
Ne+(2 P)
Ne2+(3 P)
Ne2+(3 P)
Ne2+ep)
Ne3+(4S)
Ne4+ep)
Ne5+eS)
Ne5+ep)
H+(IS)
He+(2S)
He2+(IS)
C+(2P)
C 2+(IS)
C 3+(2S)
c4+('S)
N+(3p)
N 2+(2p)
N3+(IS)
N"+(2S)
N5+(IS)
0+ (4S)
O+eD)
0+(2p)
0 2+(3 P)
03+(2p)
04+(IS)
05+ (2S)
06+(IS)
Ne+(2p)
Ne2+(3p)
Ne2+(ID)
Ne2+(IS)
Ne3+(4S)
Ne3+(2D)
Ne3+(2p)
Ne4+ep)
NeS+ep)
Ne6+(IS)
Ne6+(IS)
13.6
24.6
54.4
11.3
24.4
47.9
64.5
14.5
29.6
47.5
77.5
97.9
13.6
16.9
18.6
35.2
54.95
77.4
113.9
138.1
21.6
41.1
42.3
47.99
63.74
68.8
71.5
97.2
126.5
138.1
157.96
6.30
7.83
1.58
12.2
4.60
1.60
0.68
11.4
6.65
2.06
1.08
0.48
2.94
3.85
2.26
7.32
3.65
1.27
0.78
0.36
5.35
4.16
2.71
0.52
1.80
2.50
1.48
3.11
1.40
0.36
0.49
1.34
1.66
1.34
3.32
1.95
2.60
1.00
4.29
2.86
1.63
2.60
1.00
2.66
4.38
4.31
3.84
2.01
0.83
2.60
1.00
3.77
2.72
2.15
2.13
2.28
2.35
2.23
1.96
1.47
1.00
1.15
2.99
2.05
2.99
2.00
3.00
3.00
2.00
2.00
3.00
3.00
3.00
2.00
1.00
1.50
1.50
2.50
3.00
3.00
2.00
2.10
1.00
1.50
1.50
1.50
2.00
2.50
2.50
3.00
3.00
2.10
3.00
Reference
1. Osterbrock, D.E. 1974, Astrophysics o/Gaseous Nebulae (Freeman, San Francisco)
5.4.2 Photoionization of Light Hydrogenic Ions
A semiempirical expression [10] for the photoionization cross section per K -shell electron for
hydrogenic light elements is given by
a=
v
a6
291f2
(_EI)4 (T/f3y)3
3a 2Z5
hv
[1 + ~4
y(y - 2)
y +1
(1 __I_In 11 +- 13)]
exp(-4T/arccot
13
1 - exp(
T/),
-21fT/)
2f3y2
where T/ = [-EI/(hv + El)]1/2. EI is the negative binding energy of the Is electron, v is the electron
velocity, and
13 = ~ =
[(hv
y = (1 -
13 2)-1/2 =
c
+ El)2 + 2(hv + El)mc2]1/2
+ El +mc2
1 + (hv + El)/mc 2,
hv
'" [2(hv
+ Ed/mc2]1/2 '" aZ/T/,
a:::: 1/137.036.
108 / 5
5.4.3
RADIATION
Radiative Recombination
Given an absorption coefficient all for a particular level, microscopic reversibility demands that the
recombination cross section into that same level be given by
gi (hv)2
u(v) = - - - - - all.
gi+l (mcv)2
This is the Milne relation. Here gi is the statistical weight for the particular level or term i in the
recombined ion, gi+ 1 is that of the original ion.
Using the Milne relation and the above analytic form for the photoionization cross section, the
recombination rate coefficient can be expressed as [9]
ai(T)=
4
g.
/--'
v7r gi+I
(m
2k
)3/2
T
eET / kT
E3
t2 aT [REs -2(ET/kT)+(1-R)Es -3(ET/kT)],
m c
where En (x) is the exponential integral function. If s is noninteger, the relation En (x) -+ x n - I r (1 n, x) can be used, where r(a, x) is the incomplete gamma function.
Recombination into excited states is generally at least as, if not more, important than recombination
into the ground state. If the excited state can be approximated as hydrogenic (often a good
approximation), then the cumulative recombination coefficient a(n) for principal quantum number
n and higher is a(n) = L~=n an' and is given in Table 5.12 as a function of temperature for the first
four values of n for Z = 1 [9]. For an arbitrary ionic charge Z, a(n; Z, T) = Za(n; I, T /Z2).
Table S.12. Recombination coejJicients a(n) in cm3 5- 1 for hydrogen [1].
n
1250K
2500K
5000K
lOOOOK
20000K
1
2
3
4
1.74[-12]
1.28[-12]
1.03[-12]
8.65[-13]
1.10[-12]
7.72[-13]
5.99[-13]
4.86[-13]
6.82[-13]
4.54[-13]
3.37[-13]
2.64[-13]
4.18[-13]
2.60[-13]
1.83[-13]
1.37[-13]
2.51[-13]
1.43[-13]
9.50[-14]
6.83[-14]
Reference
1. Osterbrock, D.E. 1974, Astrophysics of Gaseous Nebulae (Freeman, San
Francisco)
Recombination into the nth hydrogenic level can be written as (taking s
= 3 and R = 1)
(m
4 gi
)3/2 Ef
E /kT
an = - - - - --aTe T
EI(ET/kT) .
gi+I 2kT
m 3c2
..;;r
Note that exp(x)EI (x) ~ l/x for x > 5.
The threshold photoionization cross section aT can be obtained from the table of photoionization
cross-section fitting parameters or from the Kramers-Gaunt formula:
aT (Kramers & Gaunt)
= .J3 8h2 3gn
2
3 37r m ce2Z2
where g is the Gaunt factor [11] given in Table 5.13.
= 7.907 x
10- 18
n~ cm2 ,
Z
5.5 X-RAY ATTENUATION /
109
Table 5.13. Bound-free Gaunt/actors/or the hydrogen atom [11.
Configuration
g at absorption edge
g level average
Is
0.80
0.96
0.88
1.14
1.14
0.73
1.3
1.3
0.80
0.89
2s
2p
3s
3p
3d
4s
4p
4d
0.92
0.94
4/
5
6
0.95
0.96
0.97
7
Reference
1. Gaunt, J.A. 1930. Philos. Trans. 229. 163
5.4.4 Dielectronic Recombination
For dielectric recombination into ion X+, with excited state x+* and charge Z, we have the Burgess
formula [12] for the recombination coefficient ad,
ad
where
= 3.0 x 10-3 T- 3/ 2 f A(x)B(Z)exp[-xC(Z)/T] cm3 s-I,
f is the oscillator strength for the transition X+
x = 2[E(X H ) - E(x+)]f[(Z
-+ X+* with T in K and
+ I)Eo],
£0
+ 0.105x +
B(Z) = [Z(Z + 1)5/(Z2 + 13.4)] 1/2,
A(x) =
x 1/ 2 /(1
C(Z) = 1.58 x
5.5
== 27.2 eV,
x > 0.05,
0.015x 2 ),
Z :::: 20,
lOS (Z + 1)/ [1 + 0.015Z 3/(Z + 1)2] ,
xC(Z)/T ;$ 5.0.
X-RAY ATTENUATION
The smoothed fits in Table 5.14 provide an approximate representation ("-' 10% or better) to both the
Henke experimental data [13] and to relativistic calculations [14] for the photoionization cross section
u (1 barn = 10-24 cm2 ). The photon energy E is measured in keY, and
n
logI0[u(barn/atom)]
=L
m=O
am (log 10 E)m.
110 /
5
RADIATION
Table 5.14. Cold material X-ray attenuation (total cross section) fits. a
H
He
C
N
0
Na
Mg
AI
Si
S
Ar
E range (IreV)
n
ao
a}
0.1089-8.0470
8.0470-44.77
0.1086-8.0470
0.0305-0.2885
0.2888-30.000
0.0105-0.4027
0.4031-32.20
0.0305-0.5374
0.5380-30.320
0.0415-0.0708
0.0724-1.079
1.0800-9.886
0.0305-0.0574
0.0576-0.0824
0.0824-1.3113
1.3130-30.921
0.0305-0.0813
0.0815-0.1144
0.1144-1.5680
1.5690-30.000
0.0305-0.1087
0.1089-0.1300
0.1303-1.8470
1.849-30.800
0.0394-0.1740
0.1742-0.1932
0.1996-2.4772
2.479-31.970
0.0504-0.1085
0.1085-0.2497
0.2653-3.2002
3.2033-32.200
5
2
5
3
4
4
4
4
5
5
5
3
3
4
5
4
3
4
5
4
4
4
4
4
4
3
4
4
4
3
4
3
1.000266
-0.1057762
2.596995
3.113512
4.641890
3.653780
4.880570
3.851303
5.087381
2.522877[2]
4.372625
5.551365
1.819299
0.7597808
4.556145
5.664605
1.516313
4.047249[2]
4.713295
5.732064
4.653385
1.704974[3]
4.842629
5.818893
4.862989
-3.287565[2]
5.105629
5.957286
0.1038804
3.766572
5.325805
6.236304
-2.874876
-8.314851[-2]
-3.278818
-3.093789
-2.929378
-2.036035
-2.726891
-2.158767
-2.624299
7.578575[2]
-2.803046
-2.508414
-3.725268
2.040 594[2]
-2.709325
-2.340560
-5.356061
1.227899[3]
-2.629794
-2.167852
1.585146
5.668094[3]
-2.691588
-2.084606
1.407408
-9.238824[2]
-2.701358
-1.944676
0.1580149
-3.816305
-2.604915
-2.427534
a2
1.337216
-5.823671[-2]
-0.5054382
-0.3919827
0.5928674
-0.3171900
0.7451610
-0.3410862
8.701549[2]
-0.7833634
-0.2958825
-0.9686183
2.000915[2]
-0.6249299
-0.6420745
-1.787405
1.261952[3]
-0.4217032
-0.7593566
4.064835
6.305044[3]
0.1273064
-0.8070467
4.580753
-6.359921[2]
-0.2269985
-0.8396531
0.1802517
-1.506623
-0.4119090
-0.1853513
a3
a4
0.6905931
-0.2734547
0.6372270
0.3444271
0.3640990
0.4291417
6.076411[ -2]
0.5485890
-0.1972559
4.394 846[2]
-1.137645
65.19285
-1.125062
0.2357794
4.319780[2]
-1.136888
0.2548878
1.700534
2.337491[3]
0.8214728
0.2611724
2.192223
0.2442756
82.19558
-0.7944890
-0.9611755
-1.261846
0.6971264
0.2465677
6.544871
0.4831536
Note
aNumbers in square brackets denote powers of 10.
See Sec. 5.4 for a semiempirical equation for hydrogen and hydrogenic ion cross sections.
5.6
ABSORPTION OF MATERIAL OF STELLAR INTERIORS
The opacity of stellar interiors is usually expressed as the Rosseland mean of the mass absorption
coefficient K. Tabulations are available [15,16] for a wide range of compositions expressed by X, Y,
and Z. Tables 5.15-5.17 give 10g1OK incm2 g-1 as a function oflog 10 p where density p is in gcm-3
and temperature T in units of 10-6 K. These tables are based on interpolations of data in [15].
5.6 ABSORPTION OF MATERIAL OF STELLAR INTERIORS /
111
Table S.lS. Hydrogen Rosseland mean opacity loglO K [1].
Ta
logp = -10.0
-9.0
-8.0
-7.0
-6.0
0.006
0.007
0.008
0.009
0.010
0.011
0.012
0.014
0.016
0.D18
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
0.060
0.070
0.080
0.090
0.100
0.120
0.150
0.200
0.250
0.300
0.400
0.500
0.600
0.800
1.000
1.200
1.500
2.000
2.500
3.000
4.000
5.000
6.000
8.000
10.00
15.00
20.00
30.00
40.00
60.00
80.00
100.0
-1.67
-0.66
0.18
0.71
0.85
0.76
0.60
0.31
0.12
-0.01
-0.08
-0.15
-0.17
-0.21
-0.27
-0.32
-0.35
-0.37
-0.38
-0.40
-0.40
-0.40
-0.40
-1.41
-0.49
0.33
1.01
1.42
1.56
1.50
1.19
0.89
0.68
0.52
0.30
0.21
0.15
0.07
-0.02
-0.11
-0.18
-0.24
-0.31
-0.35
-0.37
-0.38
-0.39
-0.40
-0.40
-1.00
-0.19
0.54
1.20
1.71
2.05
2.21
2.16
1.91
1.68
1.48
1.17
1.00
0.89
0.78
0.65
0.50
0.35
0.21
0.00
-0.14
-0.22
-0.28
-0.34
-0.37
-0.39
-0.40
-0.40
-0.40
-0.61
0.16
0.82
1.40
1.89
2.27
2.57
2.86
2.86
2.73
2.56
2.25
2.06
1.92
1.78
1.62
1.43
1.21
1.01
0.66
0.39
0.19
0.05
-0.13
-0.26
-0.35
-0.38
-0.39
-0.40
-0.40
-0.40
-0.40
-0.40
-0.13
0.57
1.15
1.65
2.09
2.46
2.77
3.22
3.48
3.57
3.55
3.37
3.19
3.04
2.88
2.67
2.44
2.20
1.97
1.56
1.22
0.94
0.71
0.37
0.07
-0.17
-0.28
-0.33
-0.37
-0.39
-0.39
-0.40
-0.40
-0.40
-0.40
-0.40
Note
-0.40
-0.41
-0.41
-0.41
-0.41
-0.41
-0.40
-0.40
-0.41
-0.41
-0.41
-0.42
-0.42
-0.38
-0.39
-0.40
-0.41
-0.41
-0.42
-0.42
-0.43
-0.44
-0.28
-0.33
-0.36
-0.38
-0.40
-0.41
-0.42
-0.43
-0.44
-0.46
-0.47
-0.49
-5.0
2.36
2.68
2.98
3.47
3.82
4.07
4.23
4.35
4.29
4.15
3.96
3.72
3.46
3.20
2.96
2.53
2.17
1.86
1.60
1.17
0.72
0.26
0.02
-0.13
-0.27
-0.33
-0.36
-0.39
-0.39
-0.40
-0.40
-0.40
-0.40
-0.40
0.00
-0.14
-0.22
-0.31
-0.35
-0.39
-0.41
-0.43
-0.44
-0.46
-0.47
-0.49
aUnits of 106 K.
Reference
1. Iglesias. C.A .• Rogers. EI .• & Wilson. B.O. 1992. ApJ. 397. 717
-4.0
-3.0
-2.0
-1.0
0.0
1.45
1.10
0.62
0.32
0.13
-0.10
-0.21
-0.27
-0.33
-0.37
-0.38
-0.39
1.07
0.79
0.40
0.17
0.02
-0.13
-0.25
-0.31
-0.34
0.85
0.60
0.34
0.07
-0.08
-0.17
1.06
0.68
0.41
0.23
0.49
0.25
-0.07
-0.22
-0.35
-0.40
-0.44
-0.47
-0.49
0.43
0.14
-0.16
-0.29
-0.41
-0.45
-0.48
-0.01
-0.29
-0.42
-0.48
-0.17
-0.35
4.96
5.10
5.07
4.90
2.56
2.11
1.60
1.01
0.61
0.34
0.03
-0.14
-0.22
-0.32
-0.35
-0.37
-0.39
-0.40
-0.40
-0.40
0.60
0.34
0.16
-0.05
-0.17
-0.31
-0.37
-0.41
-0.43
-0.46
-0.47
-0.49
112 /
5
RADIATION
Table 5.16. Helium Rosseland mean opacity 10g1O K [1].
Ta
0.006
0.007
0.008
0.009
0.010
0.011
0.012
0.014
0.016
0.Ql8
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
0.060
0.070
0.080
0.090
0.100
0.120
0.150
0.200
0.250
0.300
0.400
0.500
0.600
0.800
1.000
1.200
1.500
2.000
2.500
3.000
4.000
5.000
6.000
8.000
10.00
15.00
20.00
30.00
40.00
60.00
80.00
100.0
logp
= -10.0
-5.79
-4.95
-4.13
-3.36
-2.71
-2.04
-1.49
-0.82
-0.74
-0.83
-0.88
-0.93
-0.73
-0.53
-0.60
-0.64
-0.66
-0.68
-0.67
-0.67
-0.67
-0.67
-0.68
-0.70
-9.0
-8.0
-5.81
-5.14
-4.43
-3.73
-2.99
-2.31
-1.67
-0.72
-0.33
-0.37
-0.51
-0.72
-0.64
-0.28
-0.20
-0.34
-0.45
-0.52
-0.57
-0.61
-0.62
-0.62
-0.62
-0.65
-0.68
-0.69
-5.71
-5.13
-4.52
-3.94
-3.24
-2.43
-1.76
-0.68
-0.01
0.24
0.19
-0.17
-0.27
0.02
0.39
0.43
0.17
-0.03
-0.16
-0.33
-0.42
-0.46
-0.47
-0.49
-0.56
-0.66
-0.69
-0.69
-0.70
-0.70
-0.70
-0.70
-0.71
-0.71
-0.70
-0.70
-0.70
-0.71
-0.71
-0.71
-0.72
-7.0
-3.15
-2.41
-1.73
-0.65
0.13
0.62
0.86
0.72
0.46
0.52
0.85
1.17
1.19
0.95
0.69
0.35
0.15
0.02
-0.06
-0.15
-0.23
-0.45
-0.59
-0.65
-0.69
-0.69
-0.70
-0.70
-0.70
-0.66
-0.68
-0.69
-0.70
-0.71
-0.71
-0.72
-0.73
-0.74
-6.0
1.49
1.36
1.24
1.34
1.63
1.90
1.98
1.83
1.40
1.11
0.93
0.80
0.63
0.47
0.12
-0.21
-0.42
-0.60
-0.66
-0.68
-0.69
-0.70
-0.70
-0.70
-0.70
-0.53
-0.60
-0.64
-0.68
-0.69
-0.71
-0.72
-0.73
-0.74
-0.76
-0.77
-0.79
-5.0
2.39
2.57
2.69
2.57
2.26
2.03
1.89
1.68
1.48
1.03
0.52
0.13
-0.30
-0.49
-0.58
-0.66
-0.68
-0.69
-0.70
-0.70
-0.70
-0.70
-0.19
-0.36
-0.46
-0.57
-0.63
-0.69
-0.71
-0.72
-0.74
-0.75
-0.77
-0.79
Note
aUnits of 106 K.
Reference
1. Iglesias. e.A.. Rogers, F.J.• & Wilson. B.G. 1992.ApJ. 397, 717
-4.0
3.04
2.83
2.58
2.04
1.45
0.97
0.32
-0.06
-0.28
-0.50
-0.60
-0.64
-0.67
-0.69
-0.70
-0.70
0.43
0.15
-0.05
-0.29
-0.43
-0.59
-0.66
-0.71
~0.73
-0.75
-0.77
-0.79
-3.0
-2.0
-1.0
0.0
2.41
1.91
1.18
0.68
0.32
-0.10
-0.33
-0.46
-0.57
-0.64
-0.67
-0.69
1.58
1.17
0.60
0.22
-0.03
-0.27
-0.47
-0.56
-0.62
1.02
0.68
0.32
-0.05
-0.26
-0.40
0.65
0.34
0.09
0.29
0.04
-0.31
-0.48
-0.63
-0.69
-0.74
-0.77
-0.79
0.24
-0.07
-0.39
-0.54
-0.68
-0.74
-0.77
-0.22
-0.51
-0.64
-0.72
-0.40
-0.57
5.6 ABSORPTION OF MATERIAL OF STELLAR INTERIORS I
113
Table 5.17. Solar composition (X = 0.73, Z = 0.018) Rosseland mean opacity log lO iC [1].
Ta
logp = -10.0
-9.0
-8.0
-7.0
-6.0
0.006
0.007
0.008
0.009
0.010
0.011
0.012
0.014
0.016
0.018
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
0.060
0.070
0.080
0.090
0.100
0.120
0.150
0.200
0.250
0.300
0.400
0.500
0.600
0.800
1.000
1.200
1.500
2.000
2.500
3.000
4.000
5.000
6.000
8.000
10.00
15.00
20.00
30.00
40.00
60.00
80.00
100.0
-1.77
-0.78
0.05
0.55
0.67
0.61
0.47
0.24
0.13
0.04
-0.04
-0.13
-0.12
-0.14
-0.21
-0.26
-0.31
-0.34
-0.35
-0.36
-0.37
-0.36
-0.33
-1.53
-0.62
0.20
0.88
1.27
1.41
1.35
1.06
0.82
0.66
0.54
0.33
0.25
0.25
0.20
0.09
0.00
-0.09
-0.15
-0.22
-0.25
-0.27
-0.26
-0.19
-0.04
-0.20
-1.10
-0.32
0.42
1.08
1.60
1.94
2.08
2.00
1.76
1.56
1.39
1.14
0.97
0.92
0.90
0.81
0.66
0.50
0.38
0.18
0.06
0.00
-0.04
-0.05
0.09
-0.01
-0.24
-0.38
-0.46
-0.62
0.07
0.72
1.30
1.80
2.20
2.48
2.74
2.71
2.56
2.40
2.15
1.97
1.85
1.80
1.74
1.62
1.43
1.25
0.95
0.74
0.60
0.50
0.38
0.38
0.33
0.02
-0.19
-0.40
-0.44
-0.45
-0.44
-0.45
0.00
0.52
1.08
1.59
2.03
2.41
2.71
3.14
3.36
3.42
3.37
3.20
3.06
2.94
2.83
2.73
2.62
2.47
2.29
1.96
1.70
1.51
1.36
1.18
0.99
0.84
0.53
0.24
-0.18
-0.37
-0.40
-0.44
-0.44
-0.44
-0.44
-0.45
-0.46
-0.46
-0.47
-0.47
-0.47
-0.47
-0.43
-0.45
-0.46
-0.47
-0.47
-0.48
-0.48
-0.26
-0.38
-0.43
-0.46
-0.46
-0.47
-0.48
-0.49
-0.50
0.29
-0.03
-0.22
-0.38
-0.43
-0.46
-0.48
-0.49
-0.50
-0.52
-0.54
-0.56
-5.0
2.33
2.65
2.95
3.40
3.71
3.94
4.08
4.16
4.11
4.03
3.92
3.78
3.63
3.47
3.32
3.02
2.76
2.56
2.39
2.15
1.90
1.56
1.25
0.97
0.48
0.05
-0.20
-0.34
-0.38
-0.39
-0.40
-0.45
-0.46
-0.47
0.82
0.50
0.23
-0.11
-0.27
-0.39
-0.44
-0.49
-0.50
-0.52
-0.54
-0.56
Note
aUnits of 106 K.
Reference
1. Iglesias, e.A., Rogers, F.l., & Wilson, B.G. 1992, ApJ, 397,717
-4.0
-3.0
-2.0
-1.0
0.0
3.66
3.12
2.74
2.45
2.03
1.76
1.49
0.93
0.52
0.27
0.05
-0.11
-0.25
-0.36
2.52
2.26
2.06
1.74
1.43
1.15
0.83
0.48
0.26
0.05
2.23
2.03
1.87
1.65
1.29
0.98
0.73
2.10
1.78
1.50
1.24
0.72
0.48
0.11
-0.09
-0.32
-0.42
-0.50
-0.53
-0.55
0.53
0.22
-0.11
-0.28
-0.44
-0.50
-0.54
-0.30
-0.44
-0.51
-0.18
-0.37
4.80
4.93
4.95
4.88
3.93
3.75
3.58
3.44
3.17
2.85
2.42
2.05
1.77
1.34
0.94
0.53
0.05
-0.15
-0.25
-0.29
-0.35
-0.42
-0.44
1.19
0.88
0.64
0.29
0.06
-0.21
-0.32
-0.44
-0.49
-0.52
-0.54
-0.56
114 I 5
RADIATION
The opacity due to electron scattering alone for a completely ionized plasma, with hydrogen mass
fraction X, is given by Ke = 0.200(1 + X) [17].
5.7 ABSORPTION OF MATERIAL OF THE SOLAR PHOTOSPHERE
The Rosseland mean opacity for the solar photosphere including diatomic species is given by
Table 5.18, as loglO K with Kin cm2 g-I. The assumed microturbulent velocity is 2 km/s.
Table 5.18. Solar photospheric Rosseland mean opacity log 10 K [I].
T (10- 6 K)
logp = -10.0
-9.0
-8.0
-7.0
-6.0
-5.0
-4.0
0.0021
0.0030
0.0040
0.0050
0.0062
0.0071
0.0081
0.0093
0.0100
0.0126
0.0158
0.0200
0.0316
0.0398
0.0501
0.0631
0.0708
0.0794
0.0891
0.1000
-5.31
-4.12
-3.42
-2.83
-1.60
-0.70
0.15
0.61
0.66
0.35
0.07
-0.08
-0.17
-0.23
-0.32
-0.36
-0.35
-0.36
-0.37
-0.37
-5.27
-3.66
-2.72
-2.42
-1.34
-0.53
0.33
1.05
1.27
1.24
0.78
0.49
0.20
0.16
-0.03
-0.21
-0.26
-0.28
-0.30
-0.31
-5.16
-3.04
-2.00
-1.74
-0.92
-0.21
0.54
1.29
1.61
2.05
1.73
1.34
0.87
0.83
0.62
0.26
O.ll
0.01
-0.06
-O.ll
-4.95
-2.49
-1.38
-0.92
-0.43
0.19
0.83
1.48
1.79
2.56
2.64
2.35
1.83
1.71
1.54
Ul
0.87
0.66
0.50
0.38
-4.61
-2.14
-0.84
-0.14
0.17
0.65
1.20
1.76
2.03
2.81
3.28
3.29
2.92
2.71
2.50
2.09
1.84
1.61
1.39
1.21
-4.03
-1.94
-0.38
0.47
0.85
U8
1.63
2.11
2.33
3.04
3.63
4.01
3.98
3.80
-3.12
-1.72
-O.ll
0.86
1.43
1.72
2.10
Reference
I. Kurucz, R.L. 1992, Rev. Mexicana Astron. Af., 23, 181
5.8 SOLAR PHOTOIONIZATION RATES
The solar photoionization rates are calculated as [18]
R=
fvooo C1v(v)Fv dv,
where C1v (V) is the photoionization cross section having threshold vo and Fv is the solar flux.
The unattenuated photoionization rate for the quiet and active Sun for some monatomic species, at
heliocentric distance 1 AU, is shown in Table 5.19.
Table 5.19. Solar photoionization rate R in s-1 [1].a
Species
Quiet Sun
Active Sun
Species
Quiet Sun
Active Sun
HH
He
14.
7.3[-8]
5.2[-8]
14.
1.9[ -7]
2.2[-7]
o (IS)
2.0[-7]
2.1[-7]
1.6[-5]
7.5[-7]
9.5[-7]
1.7[-5]
F
Na (expt.)
5.9 FREE-FREE ABSORPTION AND EMISSION /
115
Table 5.19. (Continued.)
Species
Quiet Sun
Active Sun
C (3 P)
C (ID)
C (IS)
N
4.1[-7]
3.6[-6]
4.3[-6]
1.9[-7]
2.1[-7]
1.8[ -7]
1.0[-6]
1.0[-5]
1.2[-5]
6.3[-7]
8.5[-7]
7.4[-7]
o (3p)
o (ID)
Species
Na(theor.)
S(3 P)
S(I D)
S(IS)
Cl
K
Quiet Sun
Active Sun
5.9[-6]
1.1[-6]
1.1[-6]
1.0[-6]
5.7[-7]
2.2[-5]
6.6[-6]
2.6[-6]
2.6[-6]
2.5[-6]
1.5[-6]
2.3[-5]
Note
aNumbers in square brackets denote powers of 10.
Reference
1. Huebner, W.E, Keady, 1.1., & Lyon, S.P. 1992, AP&SS, 195, 1
5.9
FREE-FREE ABSORPTION AND EMISSION
The free-free linear absorption coefficient [19,20] is
4:rr
Z2 e6
g
= - - - -2- . -NeNj
3
Ks
3.J3 hcm
= 1.802 x
= 6.686 x
v
v
(K
in expcm- 1)
1014(Z2g/v3v)NeNj
(v in cm/s)
1O- 18 Z 2 gA 3 NeNi/v
(A in cm),
where v is the electron velocity, g is the Gaunt factor representing the departure from Kramers's theory,
Z is the ionic charge, and Ne and Nj are the electronic and ionic densities in cm- 3 . The mean lIv is
(2m/:rrkT) 1/2, whence
Ks
= 3.692 x
= 1.370 x
108Z2gT-l/2v-3NeNj
1O-23Z2A3gNeNi/TI/2
(A in cm).
The effective linear absorption coefficient K' after allowance for stimulated emission is
K'
= 3.692 x 108 [1 - exp( -hv/ kT)]Z2 gT -l/2 v -3 NeNj.
For small hv/ kT (= 1.438/AT), e.g., for radio waves,
8(:rr)
1/2
-
K' -
-
- 3
6
e6
Z2 g
N N·
c(mkT)3/2 v2 e I
= 0.017 8Z 2gv- 2T- 3/ 2NeNj
= 1.98 x 1O-23Z2gA2NeNjT-3/2
(A in cm).
The Gaunt factor for radio waves is [19,21]
g = 10.6 + 1.90 log lO T - 1.26 log10 Zv.
Gaunt-factor calculations incorporating relativistic effects and electron degeneracy can be found
in [22,23]. The temperature parameter y2 is defined by
y2
= Z] Ry/kT,
2
= Z·J
Zj
1.579 x lOS K
T
=1
(forR),
(T in K).
Zj
=2
(for He),
116 I 5
RADIATION
For -3 :5 10g10 y2 :5 2.0 we list in Table 5.20 approximate Gaunt factors for both hydrogen and
helium, where TJ (defined as the chemical potential divided by kT) is the degeneracy parameter and
u == hv/kT.
Table 5.20. Relativistic thermally averaged free-free Gaunt factors.
logu
1/
-4.0
-3.5
-3.0
-2.0
-1.4
-1.0
-0.7
-0.2
0.0
= -6.0
-2.0
0.0
1.0
2.0
3.0
5.5
4.89
4.26
3.03
2.37
1.95
1.69
1.30
1.17
5.13
4.55
3.97
2.84
2.22
1.85
1.59
1.25
1.13
3.77
3.35
2.95
2.14
1.69
1.42
1.25
1.03
0.96
2.77
2.48
2.18
1.61
1.28
1.10
0.96
0.83
0.80
1.94
1.74
1.54
1.15
0.93
0.80
0.72
0.63
0.62
1.36
1.22
1.09
0.82
0.67
0.58
0.52
0.47
0.46
These smoothed numbers are least accurate ('" 1{}-20%) for large u and small log 10 y2 (~ -3),
improving to a few percent for smaller u and larger 10g10 y2. For larger u, Gaunt factors for hydrogen
and helium can differ significantly [22,23].
When degeneracy is not important (TJ :5 -4, say),
g ~
{
.J3 In (~) , r
1r
u-0 .4
ru
= 1.781
foru« 1,
for u ~ 1.
The free-free emission (bremsstrahlung) per unit solid angle, volume, time, and frequency range is
iv
= K~Bv
(black body)
6 (m )1/2 (hV)
gexp - kT NeNi
16 (1r)1/2 e Z 2
="3
6"
c3m 2 kT
= 5.444 x 1O-39 Z 2gexp (- ;~) T- 1/ 2 N eNi ergcm-3 s-1 sr- 1 Hz- 1 (T in K, N in cm- 3).
The free-free emission from a cosmic plasma is
iv
= 6.2 x 10-39 g exp ( -
;~ ) T- 1/ 2
f N; dV
erg s-1 sr- 1 Hz-I
(T in K, Ne in cm- 3),
where J N; dV (integrated over volume) is called the emission measure.
The integrated free-free emission is
41r
f
iv
641r 1r 1/2 e6Z2 (kT) 1/2
dv = -3hc3 m -;;;
gNeNi
(6")
= 1.426 x
10-27 Z 2 T 1/ 2 gNe Ni ergcm- 3 s-l.
For a completely ionized plasma with solar abundance [24], Li NiNeZl ~ 1.4N;, and thus
41r
f
iv
dv = 2.0 x 10-27 gT I / 2
f
N; dV erg s-l.
5.11 VISUAL PHOTOMETRY /
117
Free-free absorption from neutral atoms: For highly polarizable target atoms, an approximation for
the thermally averaged free-free absorption coefficient valid for long wavelength and low temperature
is [25]
k
=
1.62 x 10- 19 N eN aa l / 2 )..3T(1 -
e-hc/J...kT)
cm- I ,
where Ne(Na ) are the number of free electrons (neutral atoms) per cm3 , a is the polarizability (cm3),
).. is the wavelength (cm), and T is the temperature (K).
The validity criterion is O.633/a < e < 2/a l / 3• where the free-electron kinetic energy e is
measured in Rydbergs and a is in units of
a3.
5.10
REFLECTION FROM METALLIC MIRRORS
In Table 5.21, no attempt has been made to differentiate between different methods of deposition [26].
Table 5.21. Reflectionfrom metallic mirrors.
>..
(tt m)
Ag
AI
Speculum
Hg
Ni
Cu
Au
Si
Pt
Steel
W
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
0.20
0.22
0.24
0.26
0.28
20
25
27
27
23
72
58
61
35
40
42
40
39
34
34
31
29
28
18
27
32
34
34
68
68
68
68
67
20
29
35
37
38
24
27
30
33
36
15
16
18
20
21
0.30
0.32
0.34
0.36
0.38
12
7
63
82
82
83
83
84
44
48
51
54
56
67
69
71
73
39
41
43
45
47
29
30
32
34
36
35
33
33
33
34
65
61
56
50
41
39
40
42
43
45
39
41
46
49
44
23
25
27
30
34
85
86
87
88
89
88
87
58
61
63
65
66
67
74
74
73
73
74
74
75
50
57
61
63
65
67
69
38
42
47
60
74
82
85
34
37
51
84
89
93
35
30
30
30
30
30
30
48
56
59
60
61
63
66
51
55
57
57
56
55
56
38
45
49
52
51
52
53
85
93
96
97
98
70
70
73
82
89
92
70
73
89
92
96
98
95
97
98
99
99
70
74
81
91
95
59
63
77
99
29
28
28
28
28
56
60
87
95
98
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.80
1.00
2.0
5.0
10.0
77
82
85
90
91
92
93
94
95
97
98
98
99
99
78
81
82
82
26
33
38
68
72
82
89
92
64
84
92
96
77
90
93
Reflections in the EUV [27, 28] are strongly dependent on the details of deposition, the age of the
surface. and the reflection angle. No summary can be made.
5.11
VISUAL PHOTOMETRY
Units of visual photometry are given in Chapters 2 and 15. For values of the relative visibility factor K>..
for normal brightness (about 5x 10-4 stilb or greater). the photopic curve (international) (cone vision
118 /
5
RADIATION
at fovea) is given in Table 5.22 [29]. This and the following table are actually one-dimensional tables
so that the last column and first row entry of the first table applies to a wavelength of 3 900 A.
Table 5.22. Relative visibility factors.
)" (A)
3000
4000
5000
6000
7000
0
100
200
300
400
500
600
700
0.0004
0.323
0.631
0.0041
0.0012
0.503
0.503
0.0021
0.0040
0.710
0.381
0.00105
0.0116
0.862
0.265
0.00052
0.023
0.954
0.175
0.00025
0.038
0.995
0.107
0.000 12
0.060
0.995
0.061
0.00006
0.091
0.952
0.032
0.00003
800
900
0.00004
0.139
0.870
0.017
0.000 12
0.208
0.757
0.0082
The equivalent width of the K)" curve is J K)" dJ... = 1068 A.
The mechanical equivalent of light (experimental) [29] is
K)" lumens
== 0.00147 W.
The luminous energy (in lumergs) is 680 J K).,e)., dJ..., where e)., dJ... is the element of energy in joules.
1 lumen (5550 A radiation) = 4.11 x 10 15 photons s-I,
1 nanolambert (5550 A radiation) = 1.31 x 106 photons s-I cm- 2 sr- I .
The number of lumens L entering a telescope of diameter D in cm for a star of visual apparent
magnitude V near the zenith (clear conditions) is
IOgiO L
= 2 IOgiO
D - O.4V - 9.86.
For relative visibility for dark-adapted eyes (about 10-7 stilb or less), the scotopic curve (rod
vision) is given in Table 5.23.
Table 5.23. Relative visibility factors.
)" (A)
0
100
200
300
400
500
600
700
800
900
4000
5000
0.0185
0.900
0.0490
0.000 11
0.040
0.985
0.0300
0.076
0.960
0.0175
0.132
0.840
0.0100
0.212
0.680
0.0058
0.302
0.500
0.0032
0.406
0.350
0.0017
0.520
0.228
0.00087
0.650
0.140
0.00044
0.770
0.083
0.00021
6000
7000
For dark-adapted eyes,
1 lumen at 5100 A (scotopic)
== 0.00058 W.
The quantum thresholds for a single scintillation with most favorable conditions for human eye are
4 quanta in 0.15 s (absorbed) and 60 quanta in 0.15 s (incident).
The threshold intensity for a large steady source [30] is 1.4 x 10- 10 stilb.
The size of the retinal image for l' arc is 4.9 J1,m.
The eye resolving power::::: l' ::::: 5 J1,m at fovea.
5.11 VISUAL PHOTOMETRY I 119
Density of rods and cones in the retina [29]:
Rods 30 x 106 rods/sr = 2.7 rods/(minutes of arc)2,
Cones 1.2 x 106 cones/sr = 0.1 cones/(minutes of arc)2.
The density of cones in the fovea::::: 50 x 106 cones/sr.
The equivalent diameter of the fovea region containing no rods [31] is 10 40'.
The diameters of individual cones are 2 J.£m == 25" (variable).
The diameters of individual rods are 1 J.£m == 12".
The approximate brightness of common objects is given in Table 5.24 [32].
Table 5.24. Object and brightness (stilb).
Candle
Acetylene (Kodak burner)
Welsbach (high-pressure) mantle
Thngsten lamp filament
Sodium vapor lamp
Mercury vapor lamp (high pressure)
Arc crater (plain carbon)
Clear blue sky
Overcast sky
Zenith Sun
0.6
10.8
25
800
70
150
16000
0.2-0.6
0.3-0.7
165000
Table 5.25 gives approximate albedos for common objects.
Table 5.25. Approximate albedos [1. 2].
White cartridge paper
Magnesium oxide (or carbonate)
Black cloth
Black velvet
0.80
0.98
0.012
0.004
References
1. Walsh. 1.W.T. Photometry. 3rd ed. (Dover.
New York). p. 529
2. Houston. R.A. 1924. Treatise on Light
(Longmans. London)
REFERENCES
1. Allen. C.W. 1973. Astrophysical Quantities. 3rd ed.•
Sec. 35 (Athlone Press. London)
2. Allen. C.W. 1973. Astrophysical Quantities. 3rd ed.•
Sec. 37 (Athlone Press. London)
3. Sampson. D.H. 1959. Api. 129. 734
4. Boercker. D.B. 1987. Api. 316. L95
5. van de Hulst, H.C. 1957. Light Scattering by Small Particles (Wiley. Chapman and Hall. New York)
6. Stergis. C.G. 1966. I. Arm. Ten: Phys.• 28. 273
7. Penndorf.R.1957.1. Opt. Soc. Am.. 47. 176
8. Irvine. W.R. 1965. I. Opt. Soc. Am.. 55.16
9. Osterbrock. D.E. 1974. Astrophysics of Gaseous Nebulae (Freeman. San Francisco)
10. Huebner. W.F. 1986. Physics of the Sun. Vol. I. edited
by P. Sturrock (Reidel. Dordrecht)
11. Gaunt. I.A. 1930. Phi/os. Trans .• 229. 163
12. Burgess. A. 1965.ApJ.141. 1588
13. Henke. B.L. et al. 1982. At. Data Nucl. Data Tables.
27. 1
14. Saloman. E.B .• & Hubbell. 1.H. 1986. X-Ray Attenuation Coefficients (Total Cross Sections): Comparison
of the Experimental Data Base with the Recommended
120 I
15.
16.
17.
18.
19.
20.
21.
22.
23.
5
RADIATION
Values of Henke and the Theoretical Values of Scofield
for Energies between 0.1-100 keY, U.S. Dept. of Commerce Report No. NBSIR 86-3431
Iglesias, C.A., Rogers, F.I., & Wilson, B.G. 1992, ApJ,
397,717
Rogers, F.I., & Iglesias, C.A. 1992, ApI, 7, 507
Cox, A.N. 1965, in Stellar Structure, 3rd ed., edited by
L.H. Aller & D.B. McLaughlin (University of Chicago
Press, Chicago), 195
Huebner, W.F., Keady, JJ., & Lyon, S.P. 1992, AP&SS,
195, 1
Allen, C.W. 1973, Astrophysical Quantities, 3rd ed.,
Sec. 43 (Athlone Press, London)
Spitzer, L. 1962, Physics of Fully Ionized Gases, 2nd
ed. (lnterscience, New York), p. 148
Chambe, G., & Lantos, P. 1971, Sol. Phys., 17,97
!toh, N., Nakagawa, M., & Kohyama, Y. 1985, ApJ,
294, 17
Nakagawa, M., Kohyama, Y., & ltob, N. 1987, ApJ
Supp., 63, 661
24. Grevese, N., & Anders. E. 1991. in Solar Interior
and Atmosphere, edited by A.N. Cox, W.C. Livingston,
M.S. Matthews (University of Arizona Press, Tucson),
p. 1227
25. Hyman, H.A., Kivel, B., & Bethe, H.A. 1973, Inverse Neutral Bremsstrahlung for Highly Polarizable
Atoms, AVCO-Everett Research Laboratory Report
No. SAMSO-TR-73-98
26. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed.,
Sec. 45 (Athlone Press, London)
27. Hass, G., & Tousey, R., 1958, J. Opt. Soc. Am., 49, 593
28. Garton, W.R.S. 1966,Adv. Atom. Mol. Phys., 2, 93
29. Allen, C.W. 1973, Astrophysical Quantities. 3rd ed.,
Sec. 46 (Athlone Press. London)
30. Pirenne, M.H. 1961, Endeavour. 20,197
31. Martin, L.C. 1948, Technical Optics (Pitman. London),
pp. 1, 144
32. Walsh, I.W.T. Photometry. 3rd ed. (Dover, New York).
p.529
Chapter 6
Radio Astronomy
Robert M. Hjellming
6.1
6.1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . .
121
6.2
Abnospheric Window and Sky Brightness . . . . . . .
123
6.3
Radio Wave Propagation ...............................
125
6.4
Radio Telescopes and Arrays ............................
128
6.5
Radio Emission and Absorption Processes ............
131
6.6
Radio Astronomy References ............................
140
INTRODUCTION
Radio astronomy is defined by three things. First is the range of frequencies that constitute the
radio windows of the Earth's atmosphere, ranging roughly from 20 MHz to 1000 GHz. Second are
the astronomical objects that emit radio waves with sufficient strength to be detectable at the Earth;
some emit by thennal processes, but most are seen because of the emission from relativistic electrons
(cosmic rays) interacting with local magnetic fields. Third, radio radiation behaves more like waves
than particles (photons), allowing the measurement of both amplitude and phase of the radiation field.
The capability to measure phase gives radio interferometry the capability to do the highest resolution
imaging of astronomical objects currently possible in astronomy.
The variety and number of radio sources is so large that in Table 6.1 we merely summarize a number
of source catalogs devoted to these topics.
121
122 I 6
RADIO ASTRONOMY
Table 6.1. List of radio soun:e catalogs.
1YPe of Source
Contents
4C Radio Survey [1, 2]
Bologna B2 Sky Survey [3-5]
Bologna B3 Sky Survey [6, 7]
20 cm N. Sky Catalog [8]
6 cm Gal. Plane Survey [9]
6 cm South & Tropical Surveys [10, 11]
11 cm All Sky Catalog [12]
11 cm N. Sky Catalog [13]
Bright Galaxies [14]
20 cm Gal. Plane Survey [15]
21 cm Gal. Plane Survey [16]
Galaxy III [17,18]
Atlas of Galactic III [19]
Molecular lines [20, 21]
Pulsars [22]
Opt. Pos. Radio Stars [23]
20 cm Radio Sources 8 > _5° [24,25]
4844 56 cm sources > 2 Jy, _7° !: 8 !: 800
408 MHz, 21.7° !: 8 !: 40°
408 MHz, 37° !: 8 !: 47°
365, 1400,4850 MHz, 0 !: 8 !: 75°
Parkes 64 m, Ibl !: 2°, I = 190° - 360° - 40°
Parkes 64 m, -78° !: 8 !: _10°
Bright sources
6483 sources, Ibl !: 5°,240° !: I !: 357°
All radio data pre-1975, normal galaxies
VLA B Conf. Survey
Eff. 100m, Ibl !: 4°,95° !: I !: 357°
Galaxies, Vradial !: 3000 kmls
21 cm H emission line profiles
Frequencies, other molecular data
Catalog of known pulsars
221 radio stars
1400 MHz sky atlas
References
1. Pilkington, J.D.H., & Scott, P.P. 1965, Mem. R.A.S., 69, 183
2. Gower, J.P'R., Scott, P.F., & Willis D. 1967, Mem. R.A.S., 71, 144
3. Colla, G. et al. 1970, A&AS, 1, 281
4. Colla, G. et al. 1972, A&AS, 7, 1
5. Colla, G. et al. 1973, A&AS, 11,291
6. Fanti, C. et al. 1974, A&AS, 18, 147
7. Ficcara, A., Grueff, G., & Tomesetti, G. 1985, A&AS, 59, 255
8. White, R.L., & Becker, R.H. 1992, ApJS, 79, 331
9. Haynes, R.P., Caswell, J.L., & Simons, L.W.J. 1978, Aust. J. Phys. SuppL, 48,1
10. Griffith, M.R. et al. 1994, ApJS, 90, 179
11. Wright, A.E. et al. 1994, ApJS, 91, III
12. Wall, J.V., & Peacock, J.A. 1985, MNRAS, 216,173
13. Fiirst, E. et al. 1990, A&AS, 85, 805
14. Haynes, R.F., Caswell, J.L., & Simons, L.W.J. 1978, Aust. J. Phys. Suppl., 45, 1
15. Zoonematkermani, S. etal. 1990, ApJS, 74,181
16. Reich, W., Reich, P., & Fiirst, E. 1990, A&AS, 83, 539
17. Tully, R.B. 1988, Nearby GaJoxies Catalog (Cambridge University Press, Cambridge)
18. Huchtmeier, W.K., & Richter, O.-G. 1989, A General Catalog of III Observations of
Galaxies: The Reference Catalog (Springer-Verlag, New York)
19. Hartman, D., & Burton, W.D. 1995, Atlas of Galactic III (Cambridge University Press,
Cambridge)
20. Lovas, F.J. 1992, J. Phys. Chem. Ref. Data, 21,181
21. Lovas, F.J., Snyder, L.E., & Johnson, D.R. 1979, ApJS, 41, 451
22. Taylor, J.H., Manchester, R.N., & Lyne, A.G. 1993, ApJS, 66, 529
23. R6quieme, Y. & Mazurier, J.M. 1991,A&AS, 89, 311
24. Condon, JJ., Broderick, JJ., & Seielstad, G.A. 1989, AI, 97, 1064
25. Condon, J.J., Broderick, JJ., & Seielstad, G.A. 1991, AI, 102, 2041
Other information and images from surveys can be obtained from Internet pages maintained by the
Nationa1 Center for Super Computing Applications (NCSA) Astronomy DigitaJ Image Library (ADIL,
http://imagelib.ncsa.uiuc.edulimagelib.htm1) and the Nationa1 Radio Astronomy Observatory (NRAO,
http://info.aoc.nrao.edu). More extensive radio (and other) cataJogs can be found from Internet pages
for the NASA Astrophysics Data System (http://adswww.harvard.edulindex.htm1).
In Figure 6.1 schematic radio spectra representative of a variety of continuum radio sources
are plotted in the form of flux density (in units of Jy
Jansky
10-23 ergs cm-2 s-1 Hz-I
10-26 W m- 2 Hz-I) as a function offrequency. The sources and spectra in Figure 6.1 are schematic
=
=
=
6.2 ATMOSPHERIC WINDOW AND
SKY BRIGHTNESS
/
123
10'
'va Sun
10'
Sky
Background
10'
Jupiter
(radiation
belts)
10'
10'
3:
roo
,
x
u:
Crab
Pulsar ""'(unpulsed)
M31
10'
10'
10'
BLLac
10"
SS433
Crab Pulsar
Cyg X-3 (non-flaring)
(pulsed)
10-'
10-'
Antares
10
100
1000
10000
Figure 6.1. Radio spectra of various types of sources in the form of flux density as a function of frequency v.
indicators of typical behavior for a wide variety of objects. Major solar-system radio sources are
the active Sun, the quiet Sun, the Earth's Moon, Mars, the surface of Jupiter, and Jupiter's radiation
belts. Stellar system sources are: pulsars, with the pulsed and unpulsed (dashed line) emission from
the Crab pulsar; the partially ionized coronal emission of the red supergiant Antares; and the X-ray
binaries SS433 and Cyg X-3 (quiescent). The optically thick and thin portions of the radio spectrum
of the ionized gas from an HII region is indicated for the Orion Nebula. Cas A is a remnant of a
supernova explosion in our Galaxy; and the Crab nebula spectrum is representative of the relatively
rare plerion, i.e., nebulosities energized by pulsars. The radio spectrum for M31, the Andromeda
nebula, is representative of spiral galaxy behavior. Strong radio galaxies are represented by Cyg A and
Virgo A; BL Lac is a blazar, while 3C273 and 3C295 are strong quasars.
Defining the convention that the spectral index ex is the power law index for the flux density,
Sv ex: va, then positive spectral indices indicate optically thick emission while negative spectral indices
indicate optically thin emission. Spectral indices near zero indicate optically thin emission for thermal
sources, while similarly flat spectra for synchrotron radiation sources indicate optically thick emission
from a wide range of optical depths.
6.2 ATMOSPHERIC WINDOW AND SKY BRIGHTNESS
6.2.1
Atmospheric Window
The low-frequency end of the radio window is set by ionospheric absorption. Since the ionosphere
has diurnal variations, solar cycle variations, variations depending upon the effect of particle storms
impacting the atmosphere, and variations with Earth latitude and longitude, the lowest frequency where
the atmosphere is transparent varies considerably over the range 10 to 30 MHz. From that lowfrequency cut-off, up to about 22 GHz, the Earth's atmosphere does not absorb radio waves, although
variation in the index of refraction affects the phase of incoming radio waves at the higher frequencies.
124 / 6
RADIO ASTRONOMY
I
I
f)'
1 r-
c:
/' 111
I
I
I
-
f'T
c:
o
.L:
\(\
..c:
I
a.
f/)
o
E
.:(
-1mmPWV
- - 8mmPWV
o
0.01
0.1
~
\1 \
\1 \
I
Q)
-
\
I
I
~
I-
I
\
I
I
a.
f/)
I
~ IA" 1'\
I
~
co
I
I
1
I
I
1
10
\
I
I
~
\~
\
I
~
100 1000
o
o
~I
200
I
1/ 1
d
Ii
400
~ ~
II J
600
800
1000
Frequency [GHz]
Wavelength [cm]
Figure 6.2. The radio window for the Earth's atmosphere shown in terms of plots of atmospheric transparency as
a function of both wavelength and frequency. The solid line is for excellent conditions with 1 mm PWV and the
dashed line is for nonnal conditions with 8 mm PWV.
At the lowest frequencies plasma effects in the ionosphere induce variable Faraday rotation in incoming
radio waves.
In Figure 6.2 we plot models for the transparency of the Earth's atmosphere for two values
of precipitable water vapor (PWV), 1 and 8 mm, representing extremely low and normal levels,
respectively.
6.2.2 Surface Brightness and Brightness Temperature
All astronomy is based upon measurements of surface brightness on the celestial sphere: Iv (a, /), t),
where t is time, (a,/» is position specified by right ascension and declination, v is frequency, and
I is the specific intensity which can be any of the four Stokes parameters. The surface brightness
of a black body of temperature T is Bv = (2hv3/c2)(1/[ehv/kT - 1]), where h and k are the
Planck and Boltzmann constants. For small values of h v f kT, the Rayleigh-Jeans approximation is
valid, and Bv(T) ~ 2kT f).. 2; this is valid at longer radio wavelengths. For reasons related to the
antenna measurement equation, radio astronomy often uses brightness temperature rather than surface
brightness to describe measurements, where the brightness temperature is
Tb
==
)..2
2kBv.
(6.1)
Equation (6.1) is often used even when black body or long wavelength approximations are not
applicable. Because of this, the concept of radiation temperature (Tr == [hvf k]/[e hv/ kT - 1]) is
commonly used; where T is a "true" physical temperature.
6.2.3 Sources of Background Radiation
At each wavelength there are sources of background radiation detectable by radio telescopes,
principally the Earth's atmosphere, the cosmic radiation background, and diffuse emission from our
6.3 RADIO WAVE PROPAGATION /
-E
100000
...
1;)
E
100
~
10
0
on
1
....
~o
)(
-
.s:::;
C)
'':::
0.001
co 0.0001
I°
.
0.1
0.01
11
I'I
I I'r
[I
II I
II 11\1
I I I
Earth's II II (
Atmosphere I ItI
( I I
! I \/
't I
,\./
1000
'l'
en
en
CD
c:::
Galactic
. . .Background
10000
0
..
Galactic
e; . ............... a..ackground
..e /'/
100
....................
y
10
1
0.1
°
~O~·
. ./
..
o
I
__ -0·0-0
.
100
Wavelength [cm]
10
g
....
CD
:::l
~
CD
10
a.
E
CD
~
en
en
CD
c:::
1
Cosmic
Bac
1
100
125
-
.c
0)
'':::
co
0.1
Wavelength [cm]
Figure 6.3. Apparent brightness (left) and brightness temperature (right) plotted as a function of wavelength
for: the Earth's atmosphere (dashed line, model; open circle, measurements); cosmic background radiation from
COBE (solid line) and other instruments (filled circles); and galactic background radiation (dotted line).
Galaxy. In Figure 6.3 we plot data and models for these sources of radiation. At wavelengths shorter
than ~ I cm the Earth's atmosphere dominates the background, while above 13 cm the galactic
background dominates. Between 1 and ~ 13 cm the cosmic background dominates. However, in many
cases man-made interference, or solar radio emission, can be more important "background emission,"
particularly at wavelengths longer than 10 cm.
6.3
6.3.1
RADIO WAVE PROPAGATION
Radiators-Absorbers, Fields, and Coupling Equations
Radiation measurement at radio wavelengths allows direct measurement of the amplitude and phase of
electromagnetic fields; this is the reason radiation field analysis in radio astronomy is usually done in
terms of fields.
If we identify a distant point in a radio source with the vector R, and the location of the oscillating
current element with the vector, the fields between the two points are proportional to the propagator [1]
e21rivIR-rl/c
Pv(r)
= IR - rl '
(6.2)
so by Huygens' Principle, and the fact that all radiation appears as if it originates from the celestial
sphere, the field on the celestial sphere at r is the superposition
Ev(r)
=
f
E(R)
e21rivIR-rl/c
IR-rl
dS,
(6.3)
where d S is a surface element on the celestial sphere.
The radiation flux for propagating fields is determined by the real part of the Poynting flux averaged
over time, so (Sr) = (E x H) = Re(EeHcp - Et/JHe)/2 = EeHt/J. The power dP at distance r
126 / 6
RADIO ASTRONOMY
passing through solid angle dO = dA/r 2 is the Poynting flux through dA at distance r. From the
field distribution over the surface of an antenna we compute d P / dO which allows us to calculate the
important properties of antennas. The normalized antenna pattern is defined by
P.(
n
e, t/J
)_
-
dP/do.
(dP /do.)max
(6.4)
so an infinitesimal current element has Pn(e, t/J) = sin2 e. The beam solid angle of an antenna is
Oa = f41r Pn(e, t/J) dO, and the directivity is D = 4rr/o.a [2].
For real antennas we integrate over the collecting surface and from that compute d P / dO. from
which antenna parameters may be computed.
6.3.2
Radio Noise and Detection Limits
The measured quantities for radio telescopes are total power or correlated total power at some point in
the signal path of the electronics. This is one of the sources of the predominance of using temperature
as a measurement variable, because of Nyquist's law which relates the total power Pa to an antenna
temperature Ta by
Pa = 4kTa '&v,
(6.5)
where k.&v is the frequency range (or bandwidth) over which the total power measurement is made.
Pa is the measure of the sum of the power due to radiation sources external to the antenna and the
power generated in the antenna and its electronics system. In modern systems the latter is dominated
by the receiver temperature, but is generally called system temperature (Tsys) which constitutes an
irreducible minimum level of noise in the measured signal. The power being measured is that of a
fluctuating voltage, originally induced by the external electric fields in the form of oscillating currents
in the antenna's collecting surface, which radiate with a focus on either a feed at the prime focus of the
antenna or on one or more subreflectors directed at a feed. The feed absorbs radiation and produces an
output signal which is transferred to an electronic receiver followed (usually) by a complicated series
of amplifiers, frequency converters, and other electronics elements. Then the fluctuating total power
is then measured over a specific frequency range with a bandwidth (.&v), and over a specific time
interval .&t. For a system temperature Tsys the noise component of the measured signal is
.&Tnoise
=
Tsys
~,
v.&v.&t
(6.6)
which indicates how noise changes with bandwidth and integration time. The same principle applies
in the case of interferometry where signals are either added or (almost all the time) correlated (or
multiplied), so it is the correlated power from two antennas that is being measured.
The noise component of the system temperature is usually the limiting factor in the measurements
being made. The fundamental limit to electronic noise temperatures is the quantum limit: h v / k =
O.048vGHz K, where VGHz is the frequency in units of GHz. Real system temperatures must be above
this limit. In the 1990s the state of the art of modern electronics is roughly capable of producing
noise temperatures of 4hv/ k. It is expected that at the beginning of the twenty-first century noise
temperatures will be'" 2hvj k, but it is unlikely that they will ever get very close to the quantum limit.
6.3.3
Effects of Ionosphere, ISM, and Source Environment
Because radio signals are best dealt with by an analysis based upon electric fields, one should think of
radio sources as three-dimensional regions radiating electric fields. Once radiation that will eventually
6.3 RADIO WAVE PROPAGATION /
127
reach a radio telescope on, or near, the Earth is produced, one then must think of propagation
phenomena which affect these fields. Absorption and re-radiation by free electrons, ions, and atomic
or molecular species can change the original radiation field into one modified by many effects. One
can decompose this process into propagation effects: inside radio sources; in the intergalactic and
interstellar medium (IGM and ISM); in the interplanetary medium of the solar system; and in the
Earth's atmosphere and ionosphere.
The ionized component of the intervening medium between a radio source and an observing
telescope affects propagation by introducing time delays and Faraday rotation. The time of arrival
of a pulse of radiation is tpulse = JoL ds / vgroup where L is the propagation path length, ds is a segment
of the line of sight, and vgroup is the group velocity. The delay per unit frequency introduced by the
electron concentration Ne is approximated by
e2
dtpul se '"
-- =
dv
41l'Eomcv
3
lL
0
Neds.
(6.7)
The pulsed emission of radio pulsars allows the measurement of the changing time of arrival of a pulse
with frequency, so the dispersion measure, Dm = JoL Ne ds, is routinely measured for the lines of sight
to pulsars in our galaxy. If coexistent with magnetic fields, the same electrons that cause propagation
delays induce Faraday rotation of the field vectors by an angle tP = i.. 2Rm where i.. is the wavelength.
Rm is the rotation measure, which depends on the product of the local electron density, Ne , and the
component of the magnetic field parallel to the line of sight, BII, and is given by
Rm = 8.1 x 105
f
NeBIl ds
(6.8)
in units of radians/m2, where BII is in Gauss, Ne is in cm- 3, ds is in parsecs, and the integral is over
the path length along the line of sight. An estimate for the magnitude of these effects in can be made
using mean values for the Galactic ISM such as (Ne ) ~ 0.003 cm- 3, BII ~ 2 JLG, and typically
Rm '" -181 cot bl cos(l - 94°) radians/m2, where I and b are the galactic longitude and latitude.
The scattering of radiation from electrons in the ISM, which produces interstellar scintillation,
also has the effect of increasing the apparent size of point sources of radio emission. This effect
produces an angular size due to scintillation which is roughly 7.Si.. 11/5 milliarcsec for Ibl ~ 0.°6,
O.S(I sinbD- 3/ 5i.. 1l / 5 milliarcsec for 0.°6 < Ibl < 4°, 13(1 sinbl)-3/5i.. 11 / 5 milliarcsec for ISo>
Ibl > 4°, and lSi.. 2/.J1 sinbl milliarcsec for Ibl > ISO, where b is the galactic latitude and i.. is the
wavelength in meters.
At long wavelengths, and for source line of sights close to the Sun, the solar corona and solar
wind contribute very strongly to propagation delay, Faraday rotation, and scintillation. This can be
estimated from the above formulas by Ne ~ (1.SSR- 6 + 2.99R- 16 ) x 10 14 m- 3 for R < 4, and
Ne ~ S x lOll R- 2 m- 3 for 4 < R < 20, where R is the radial distance from the center of the Sun.
The scattering size for an unresolved radio source due to the interplanetary medium is approximately
SO(i../ R)2 arcmin where i.. is in meters.
The ionosphere of the Earth is a major, and highly variable, contributor of electrons along the line
of sight that affects the propagation of radio waves at long wavelengths. Figure 6.4 shows typical, but
idealized, distributions of the ionospheric electron density for night and day, during sunspot maximum,
and at temperate latitudes.
The troposphere of the Earth's atmosphere also has the effect of absorbing the radiation from distant
sources. If 10, v is the surface brightness of a source seen from outside the Earth's atmosphere, and t'o,v
is the optical depth at the zenith, then at a zenith angle (z)
I(z , v)
=],0 ,v e-To.vX(z) ,
(6.9)
128 I
6
RADIO ASTRONOMY
1012
Day
~
§.
...
E
8
c: 10 10
0
0
c:
e
t)
CD
F
F1
c: 1011
0
~
c:
E
109
jjj
108
100
1000
Height [km]
Figure 6.4. The electron concentration profile of the Earth's ionosphere for day and night plotted against height
above the Earth's surface, at solar maximum, and at mid-latitudes.
where X (z) is the relative air mass in units of the air mass at the zenith. To first order, X (z) ~ sec(z) =
1/ cos z. For X < 5 the formula X (z) = -0.0045+ 1.00672 sec z-0.OO2234 sec 2 z-O.OOO 624 7 sec3 z
has an error less than 6 x 10-4 • Also, t'o,v ~ 0.12, 0.05, and 0.04 at 20,6, and 2 cm, but can be very
large and variable at mm wavelengths.
Even more important than air mass in affecting radio observations are the delay and scattering
effects in the Earth's troposphere that produce the radio equivalent of seeing disks. However, since
the 1970s radio astronomers have devised algorithms that allow so-called self-calibration of phase
variations produced by the troposphere for radio interferometry measurements with four or more
antennas in an array. Phase self-calibration by interferometric arrays are methods by which one can,
for any observed field with a strong source, solve for the differences in atmospheric phase variations
over each antenna, and then remove these phase variations from interferometric data.
6.4
6.4.1
RADIO TELESCOPES AND ARRAYS
Properties of Antennas
The normalized antenna pattern Pn(O, cp) (Equation (6.4» is used to define many of the important
antenna properties. Although real antenna patterns cannot be exactly described by a mathematical
function, many are close to that for a uniformly illuminated circular aperture of diameter D for which
Pn (0)
=
{2J' ~
r 9) }
T
8m
2,
(6.10)
smO
where Jl is a first-order Bessel function. In Table 6.2 we list various definitions of antenna and source
properties that depend upon the antenna pattern, and give the approximate values for uniform circular
6.4 RADIO TELESCOPES AND ARRAYS /
129
apertures. Since some of the directly measured quantities for radio sources are dependent upon the
antenna pattern, some of these are also listed in Table 6.2 [2].
Table 6.2. Antenna propenies.
Quantity
Definition
Uniform Circular Ap.
Source solid angle
Qs
Effective source solid angle
Q s = fsource Pn (e, t/J) dQ
Surface brightness
(Bv) =
Half power beam width
Pn(E>HPBW)
Beam width at first nulls
Pn(E>BWFN)
Beam solid angle
QA = f4:n: Pn(e, t/J) dQ
= fsource dQ
fmain lobe Bv(e, t/J)Pn dQ
r
Jmain lobe Pn dQ
= 1/2
=0
E>HPBW
E>BWFN
= 1.02(J,./D) = 58°(J,./D)
= 2.44(J,./ D) = 140 (J,./ D)
0
= fmain lobe Pn(e, t/J)dQ
Main beam solid angle
QM
Directivity
4n/QA
Effective area
Ae=J,.2/QA
Aperture efficiency
"A = Ae/(n D2 /4)
Beam efficiency
"M = QM/QA
6.4.2 Major Radio Telescopes and Arrays
There are many tens of radio telescope systems in the world that are, have been, or are about to be,
important in radio astronomy. Many are listed in Table 6.3, where the size of the telescope or array, its
main operational wavelengths, and its type or specialized role may be listed in abbreviated form. For a
complete list of most of these telescopes and arrays, see [3].
Table 6.3. Radio observatories.
Name of Observatoryllnst.
Location
Description
Australia Tel. Nat. Facility
Basovizza-Solar Radio Stn.
Bleien Radio Ast. Obs.
Culgoora, Australia
Parkes, Australia
Trieste, Italy
Zurich, Switzerland
Caltech Submillimeter Obs.
Crawford Hill Obs.
Mauna Kea, Hawaii
Holmdel, New Jersey
Decameter Wave Radio Obs.
Deep Space Network Sta.
Gauribidanur, India
Goldstone, California
Deep Space Network Sta.
Robledo, Spain
Deep Space Network Sta.
Tidbinbilla, Australia
6 km EW Arr. 1 + (6) 22 m; 0.3-24 em
64 rn; 0.7-75 em
10 m; 38-130 em solar
5 rn; 30-300 em solar
7 rn; 10-300 em solar
10.4 rn; 1.3 mm-350 /.Lm
7 m Hom Thnable; 21 em
7 m Thnable; 1.3-3 mm
1.5 km T Arr.; 200-900 em
34 m; 3.6-13 em
70 m; 3.6-13 em
34 m; 3.6-13 em
70 m; 3.6-13 em
34 m; 3.6-13 em
70 m; 3.6-13 em
130 / 6
RADIO ASTRONOMY
1Bble 6.3. (Continued.)
Name of ObservatorylInst.
Location
Description
Dominion Radio Astro. Obs.
Penticton. BC. Canada
Dwingeloo Radio Obs.
Eur. Incoh. Seatt. Fac.
Dwingeloo. Netherlands
Kinma, Sweden
F1eurs Radio 'leI.
Five College Radio Ast. Obs.
Giant Metrewave Radio Tel.
Hat Creek Radio Ast. Obs.
Haystack Obs.
Hiraiso Solar-Terr. Res. Ctr.
Humain Radio Ast. Stn.
F1eurs. NSW. Aus.
Quabbin Res .• Mass.
Pune District, India
Cassel. California
High TIme Resolving 'leI.
Interplanetary Scint. Obs.
Instituto Argentino de Rad.
Inst. de Radio Astron. Mill.
Nanjing. China
Toyakawa, Japan
Parque Pereya Iraola, Arg.
P1ateau de Bore. France
Pico Veleta, Spain
F1eurs. NSW. Aus.
Atibaia, Brazil
600mEW Arc. 49m;21.90em
26 In; 18-21 em
2S m; 6-29 em
32m; 32 em
440 x 120m; 130 em
EW Arc. 325.8m+614m;21 em
13.7 m; 1-7 mm
2S km Irr. Arc. 3645 m; 21-790 em
3+ (3) T Arc. 6m; 1-7 mm
36 m; 0.7-18 em
210m+6m+ I m; 300-950 em
7.5 m; SO em solar
T Arc. 48 4 m; 74 em solar
2 In; 3.2 em solar
100 x 20 m; 92 em
230 m; 17-21 em
0.4 km T Arc. (3) IS m; 1.3-4 mm
30 m; 0.8-4 mm
2.5 m+ 12-Yagi; 6.11.20. 120 em
13.7 m; 0.3-28 em
1.5 m; 4.3 em solar
IS m; 1.3 mm-300 I'm
26m;3-ISOem
1.5 m; CO 2.6 mm Line
26 m; 0.7-90 em
32 m; 1.3-20 em VLBI
T Parab. Cyl.; 74 em
14 m; 0.3-1.3 em
1570 x 12 m EW Cyl. Par.; 36 em
14 m; 30-SO em pulars
26 m; 2.5-SO em
5 km EW Arc. (4) 13 m; em A305 m; A- > 6em
14m;mmA43 In; 1.3-600 em
100 m; 0.7-90 em
12 m; 0.9-7 mm
1-35 km Y Arc. (27) 2S m; 0.7-90 em
SOOO km Arc. 10 2S m; 0.7-90 em VLBI
22mAnt.
0.5 km T Arc. 16 1.2 m, 1.8 em solar
TArcI76m.l90em
45 m, 0.26-3 em
0.7 km T Arc. (5) 10 m, 0.25-1.3 em
32 m; 0.3-1.3 em VLBI
134 km Irr. MERLIN Arc. 7 Ant.:
76 m; 5-200 em
38 x 26 m Par.; 1.3-200 em
38 x 26 m; 17-370 em
2S m; 6-200 em
2S In; 1.3-200 em
2S m; 1.3-2OOem
2S In; 1.3-200 em
13 In; 20-50 em pulsars
2.5 m; 2.5-4 mm
2.5 m; 1.3mm
IPS F1eurs Solar Obs.
ltapetinga Radio Obs.
Westford, Massachusetts
Nakaminato. Ibaraki. Japan
Humain, Belgium
James Clerk Maxwell 'leI.
Kashima Space Res. Ctr.
Kisaruzu College Obs.
Maryland Point Obs.
Staz. Rad. di Medieina
Mauna Kca, Hawaii
Metsahovi Obs. Radio Sta.
Molonglo Obs. Synth. 'leI.
Mount Pleasant Radio Obs.
Metslihovi. Finland
Hoskinstown. NSW. Aus.
Cambridge, 'Thsmania, Aus.
Mullard Radio Ast. Obs.
National Astro. and Ion. Obs.
National Obs. Ast. Center
National Radio Ast. Obs.
Cambridge, England
Arecibo. Puerto Rico
Yebes. Spain
Green Bauk, West Va.
NRAO mm 'lelescope
Very Large Array
Very Long Baseline Array
Netherlands Found. Res. Ast.
Nobeyama Solar Radio Obs.
Kitt Peak, Arizona
Socorro. New Mexico
Nobeyama Radio Obs.
Nobeyama, Japan
Nobeyama, Japan
Noto. Sicily
England
Jockell Bauk, Cheshire
Jockell Bauk, Cheshire
Wardle, Cheshire
Defford, Worchestershire
DarnhaII. Cheshire
Knockin. Shropshire
Pielanere. Cheshire
Jockell Bauk, Cheshire
F1oirac. France
Plateau de Bore. France
Noto Radio Ast. Sta.
Nuffield Radio Ast. Labs.
Obs. de Bordeaux
Obs. de Grenoble
Kashima, Japan
Kisaruza ehiba, Japan
Riverside. Maryland
Medicina, Italy
Socorro. New Mexico
Dwingeloo. Netherlands
Nobeyama, Japan
6.5
RADIO EMISSION AND ABSORPTION PROCESSES
/
131
Table 6.3. (Continued.)
Name of Observatoryllnst.
Location
Description
Obs. fur Solare Astr.
Obs. Radioastron. de Maipu
Ohio State Radio Obs.
Ondrejov Ast. Obs.
Tremsdorf, Germany
Maipu, Chile
Delaware, Ohio
Ondrejov, Czech.
Onsala Space Obs.
Onsala, Sweden
Ooty Radioteleseope
Ooty Synthesis Radiotelescope
Owens Valley Radio Obs.
Ootacamund, India
Purple Mountain Obs.
Purple Mt. Obs. Solar Fac.
Delingha, China
Nanjing, China
Puschino Radio Ast. Sta.
Puschino, Russia
Radioobs. Effelsberg
RATAN-600
Solar Radiospec. Obs.
Sta. de Rad. de Naneay
Effelsberg, Germany
Zelenehukskaya, SU
Ravensburg, Germany
Naneay, Franee
Swedish-ESO Subrnm. Tel.
Tonantzintla Solar Radio Int.
Toyokaya Obs.
La Silla, Chile
Puebla, Mexieo
Toyokawa, Japan
U. of Mieh. Radio Obs.
URAN-l Interferometer
UTR-2Array
Westerbork Synth. Rad. Tel.
YunnanObs.
Dexter, Miehigan
Kharkov, SU
Kharkov, SU
Westerbork, Netherlands
Kunming, China
1.5 + 4 + 10.5 m + Vagi; 3.2-750 em
160 x 73 m; 670 em
100 x 30 m; 1.9 em
3 m; 1.5-3 em solar
7.5 m; 37-120 em solar
7.5 m; 25-300 em solar
20 m; 3.7-270 em
25 m; 30-260 em
530 x 30 m Par. Cyl.; 90 em
(ORT) + 8 23 x 9 m; 90 em
0.4 km T Arr. (4) 10 m; 1.3-3 mm
40 m; 0.7-90 em
Arr. of 2 27 m; 4-30 em
13.7 m; 0.3,1.3 em
1.5 m; 3.2-11 em solar
2 m; 6 em solar
22 m Tel.
Cross-type 1 km decimetrie array
18 acre decimetrie phased array
100 m; 0.6-49 em
0.6 em eircle of 895 elem.; 0.8-30 em
7 m + 8 dipoles; 30-1000 em
161m Parab.; 3.2 em
24 Parab.; 67-200 em solar
16 + 2 Parab.; 67-200 em solar
299 x 40 m; 9-21 em
144 Con. Log. Per.; 380-2000 em
15 m; 0.8-3 rnm
2 1.1 m Parab.; 4 em solar
0.85 m; 3.2 em solar
1.5 m; 8 em solar
2 m; 14 em solar
3 m; 2.8 em solar
3 arrays; 3.2,7.8 em solar
25 m;em>..
Linear Arr, Xed dipoles; 1200-3000 em
T Arr 1800 x 54 m + 900 x 54 m; 1200-3000 em
4 km EW Arr. 10 + (4) 25 m; 6-90 em
2.5,3,3.2, & 10 m; 8.1-130 em
Big Pine, California
6.5 RADIO EMISSION AND ABSORPTION PROCESSES
6.5.1
Source Models and Prediction of Observables
The relationship between the emission and absorption coefficients, which are used to describe
the microphysics of radiation processes, and the theoretical quantities corresponding to the direct
observables, is important in discussing the principle physical processes in radio astronomy. There
are three principal observables: surface brightness Bv (and the related brightness temperature Tb,v),
the integrated flux density Sv for a source with a closed boundary of solid angle Qsource, and Vv the
132 / 6
RADIO ASTRONOMY
coherence (or visibility) function measured by radio interferometers. All are computed as integrals
over the true sky brightness, or specific intensity, lv, and are given by
Jsource Iv dOsource
r
Bv =
Jsource
dO source
(6.11)
'
(6.12)
(where the approximation is valid for the Rayleigh-Jeans limit and most radio wavelengths) and
Vv(u, v)
=
ff
Iv(a, 8)Pn (a - ao,
8 - 80)e- 21ri/A,[Lj-Lk)·[s(a.8)-so(ao.&o)] dO,
(6.13)
where Lj and Lk are vector locations of antennas j and k, and 5 is a unit vector pointing to locations
on the celestial sphere such as (a, 15) or the reference position (ao,80). For a spherically symmetric
brightness distribution the latter equation simplifies to a Hankel transform:
Vv(u, v)
=
f
Iv
«()
P n «()Jo(27rq()27r() d(),
(6.14)
where (Lj - Lk) . (5 - SO)/A = ux + vy + WZ, q = (u 2 + v 2 + w 2 )1/2 '" (u 2
() = (x2 + y2 + z2)1/2 ~ (x2 + y2)1/2.
In Table 6.4 a number of models and the associated observables are listed.
+ v 2 )1/2,
and
Table 6.4. Observables for simple source models.
Tb(8)/ Tb,max
Sv(Jy)
Vv(q)/Sv
Gaussian
e-4 In 2(916s)2
Tb.max(K)8~ (arcsec)
e-(1I' 24In2)(q6s)2
Uniform disk
I, 8 ~ Bu/2
0,8> Bu/2
Tb,max(K)~ (arcsec)
Limb-brightened
28u/(~
Model
(shot glass)
'''Ibin'' ring
-
1360A,2(cm)
196 lA,2(cm)
8 2),
Tb.max(K)~ (arcsec)
98U 2(cm)
2JI (1TqBu)/(1TqBu)a
sin(1TqBu)/(1TqBu)
8 ~Bu/2
0,8> Bu/2
420Tb.max(K)~ (arcsec)
8(8 -Bu/2)
A,2(cm)
JO(1TqBu)
Note
a I n is a Bessel function of order n, and assuming that source is at the center of the field, then
8
rid (d is the distance to the object) and Bu is the half-intensity point in these spherically
symmetric models.
=
The resolution of an instrument of size D is set by diffraction theory to be A/ D, and for radio
astronomy the best resolution of an antenna is determined by its diameter (Dm in units of meters)
and the shortest wavelength it can observe ('" [surface rms]/16). For arrays the size is the maximum
separation of antennas (Dun in units of kIn). Thus
C\
Oresolution
A
,Acm
= - = 34 -
D
Dm
= 2" -Acm
-.
Dun
(6.15)
6.5
RADIO EMISSION AND ABSORPTION PROCESSES
/
133
The resolution of the instrument and the characteristics of the radio source, which we will discuss
in terms of the models in Table 6.4, together with the other parameters determining the sensitivity of
the antenna or array, determine the minimum surface brightness that can be detected. For modern
paraboloid-shape antennas the 50" detection level for flux density during a time interval Lltsec is
O"detection
=
20 Tsys (
2
FK/JyDm
I
.J LlVMHz Lltsec
)
(6.16)
Jy,
where FK/Jy is a fixed, empirically determined constant for each antenna-receiver combination, while
for an array of N antennas of this size,
O"detection
=
2.5Tsys (
2
TJcEaDm
1
.JLl VMHz LltsecN (N -
)
1)/2
Jy,
(6.17)
where TJe is the correlator efficiency (0.82 for 3-level correlations), Ea is the aperture efficiency (~ 0.5
for simple paraboloids, but 0.6--0.7 for specially designed antennas), LlVMHz is the bandwidth in MHz,
and Lltsec is the integration time in seconds.
6.5.2
Thermal Free-Free and Free-Bound Transitions
For thermal bremsstrahlung radiation, the emission and absorption coefficients jvP and KvP are
proportional to p2, where P is the mass density. The source function jv!K v , at radio wavelengths,
is the Planck function for an electron temperature Te. Thermal bremsstrahlung or free-free radiation
processes are caused by interactions between free electrons and positive ions in a partially or fully
ionized plasma. The emission coefficient for free-free emission is given by
jrf,vP = 5.4 x 10-39 N;Tel / 2 gffehv/kTe ~ 7.45 x 10- 39 N;Teo.34v-0.ll,
(6.18)
where we have used
3 1/2 [
Te3/2)] ~
-0.34 -O.ll
17.7 + In ( -v= 1.38 x Te
vaHz
gff(V, Te) = --;-
(6.19)
for the free-free Gaunt factor, with an approximation valid at radio wavelengths [4, 5]. In (6.18)(6.19), Ne is the electron concentration in units of cm- 3 , and Te is the electron temperature. The
Planck function relates the emission and absorption coefficients for black body radiation, i.e.,
SV
3
jv
= -Kv
= -2hv
2C
1
h /kT.
eVe -
1
~
(V)2 ,
== 2kTr (V)2
=
2kTe c
c
(6.20)
where the approximation that the radiation temperature Tr ~ Te is valid for longer radio wavelengths,
but becomes invalid at mm wavelengths.
For bound-free transitions the emission coefficient and Gaunt factor are given by
00
3 2 n - 3gfb(V
= 1
72 x 10-33 Ne2 r.l 'fb .PV
·
e / "
~
,
r.e, n)eI57890/n2Te ,
(6.21)
n=m
where n is the principal quantum number and m is the integer portion of (3.789 89 x 10 15 Hz/v) and
gbf(V, Te, n)
where Un
= n 2 (v/3.289 89 x
= 1+
0.1728(u n - 1)
0.0496(u~ + 1Un + 1)
n(u n + 1)2/3 n(u n + 1)4/3'
10 15 Hz) [6].
(6.22)
134 / 6
6.5.3
RADIO ASTRONOMY
Spectral Lines-Thermal Bound-Bound Transitions
For bound-bound transitions between any two levels with energies En = E 1•...• Eionization and
statistical weights gn. radiation absorption and emission involves photons of energy hVnm = Em - En.
The properties of a line transition are determined by the Einstein coefficients Amn. Bmn. and Bnm.
which are related by
and
(6.23)
The emission and absorption coefficients for line transitions are
(6.24)
and
(6.25)
where 4Jnm (vmn ) and 4Jmn (vmn ) are absorption and emission "line" profile functions. which are usually
equal to each other. Note that in general the source function can be expressed as
Sv
nm
= .ibb,vnm = 2hv2 3 (
Kbb,vnm
c
1
) .
N ngn4Jmn(vmn ) _ 1
N mgm4Jmn(vnm )
(6.26)
If the line is in Local Thermodynamic Equilibrium (LTE) with temperature T. then Nn/Nm
(gn/gm)exp(hvnm/kT) andS
Kbb,LTE,vnm
= Bv so
,/,. ( Vnm ) [1 = hV41l'nm Nm Bnm'f'mn
e -hvnm1kT] .
=
(6.27)
Most of the known spectral lines from molecules in the interstellar medium have been detected at
radio wavelengths. Many are in Table 6.5. For current lists and information about the parameters of
various molecular species see the Internet URL http://spec.jpl.nasa.gov.
18ble 6.5. Known interstellar molecules.
Name of
molecule
Chemical
symbol
Wavelength
region
Date and telescope
of discovery
methyladyne
cyanogen radical
rnethyladyne ion
hydroxyl radical
ammonia
water
formaldehyde
carbon monoxide
hydrogen cyanide
cyanoacetylene
hydrogen
methanol
formic acid
formyl radical ion
CH
CN
CH+
OH
NH3
H2O
H2CO
CO
HCN
HC3N
H2
CH30H
HCOOH
HCO+
4300 A
3875A
4232A
18cm
l.3cm
l.4cm
6.2cm
2.6mm
3.4mm
3.3cm
1013-1108 A
36cm
18cm
3.4mm
1937 - Mt. Wilson 2.5 m
1940 - Mt. Wilson 2.5 m
1941 - Mt. Wilson 2.5 m
1963 - Lincoln Lab. 26 m
1968 - Hat Creek 6 m
1968 - Hat Creek 6 m
1969-NRA043 m
1970 - NRAO 11 m
1970-NRAO 11 m
1970-NRA043 m
1970 - NRL rocket
1970-NRA043 m
1970-NRA043 m
1970-NRAO 11 m
6.5 RADIO EMISSION AND ABSORPTION PROCESSES /
Table 6.5. (Continued.)
Name of
molecule
Chemical
symbol
Wavelength
region
Telescope of
discovery
fonnamide
carbon monosulfide
silicon monoxide
carbonyl sulfide
methyl cyanide
isocyanic acid
methyl acetylene
acetaldehyde
thiofonnaldehyde
hydrogen isocyanide
hydrogen sulfide
methanimine
sulfur monoxide
diazenylium
ethynyl radical
methylamine
NH2CHO
CS
SiO
OCS
CH3CN
HNCO
CH3CCH
CH3CHO
H2CS
HNC
H2S
CH2NH
SO
N2H+
C2H
CH3NH2
dimethyl ether
ethanol
sulfur dioxide
silicon sulfide
vinyl cyanide
methyl fonnate
nitrogen sulfide
cyanamide
cyanodiacetylene
formyl radical
acetylene
cyanoethynyl radical
ketene
cyanotriacetylene
nitrosyl radical
confirmed
ethyl cyanide
cyano-octatetra-yne
methane
nitric oxide
butadiynyl radical
methyl mercaptan
isothiocyanic acid
thioformyl radical ion
protonated carbon dioxide
ethylene
cyanotetraacetylene
silicon dicarbide
propynylidyne
methyl diacetylene
methyl cyanoacetylene
tricarbon monoxide
silane
protonated HCN
(CH3}z0
CH3CH20H
6.5cm
2.0mm
2.3mm
2.7mm
2.7mm
3.4mm
3.5mm
28cm
9.5cm
3.3mm
1.8mm
5.7cm
3.0mm
3.2mm
3.4mm
3.5mm
4.1 mm
9.6mm
2.9-3.5 mm
3.6mm
2.8,3.3 mm
22cm
18cm
2.6mm
3.7mm
3.0cm
3.5mm
infrared
3.4mm
2.9mm
2.9cm
3.7mm
1.9mm
2.7-4.0mm
2.9cm
infrared
2.0mm
2.6-3.5mm
3mm
3mm
3mm
3mm
infrared
many (cm)
many(mm)
many (3 mm)
several (cm)
several (cm)
2cm
infrared
3,2, I mm
1971-NRA043 m
1971 - NRAO II m
1971 - NRAO II m
1971-NRAO II m
1971- NRAO II m
1971- NRAO II m
1971-NRAO II m
1971-NRA043 m
1971 - Parkes 64 m
1971 - NRAO II m
1972 - NRAO II m
1972 - Parkes 64 m
1973 - NRAO II m
1974 - NRAO II m
1974 - NRAO II m
1974-NRAO 11 m
1974 - Tokyo 6 m
1974-NRAO II m
1974-NRAO II m
1975-NRAOllm
1975 - NRAO II m
1975 - Parkes 64 m
1975 - Parkes 64 m
1975 - Texas 5 m
1975 -NRAO II m
1976 - Algonquin 46 m
1976 - NRAO II m
1976 - KPNO 4 m
1976-NRAO II m
1976-NRAO II m
1977 - Algonguin 46 m
1977 - NRAO II m
1990 - FCRAO 14 m
1977 - NRAO II m
1977 - Algonguin 46 m
1977 - KPNO 4 m
1978-NRAO II m
1978-NRAO II m
1979-BTL 7 m
1979-BTL7m
1980-BTL 7 m
1980-BTL7m
1980 - KPNO 4 m
1981 - Algonquin 46 m
1984-BTL 7 m
1984-BTL7m
1984 - Haystack 37 m
1984 - Haystack 37 m
1984 - Haystack 37 m
1984-KPN04m
1984 - NRAO 12 m
1984 - Texas 5 m
1985 -many
1985 -KAO
1985 - KAO
1986 - NRAO 12 m
1990 - CSO 10 m
cyclopropynylidene
hydrogen chloride
protonated water
confirmed
SOz
SiS
CH2CHCN
CH3OCHO
NS
NH2CN
HCSN
HCO
C2H2
C3N
H2CCO
HC7N
HNO
CH3CH2CN
HC9N
C14
NO
C4H
CH3SH
HNCS
HCS+
HOCO+
C214
HCllN
SiC2
C3H
CH3C4H
CH3C3N
C30
Si14
NCNH+
C3H2
H2D+ ?
HCl?
H3 0 +
3,2mm
0.62mm
0.48mm
1.0mm
0.8mm
135
136 I 6
RADIO ASTRONOMY
Table 6.5. (Continued.)
Name of
molecule
Chemical
symbol
Wavelength
region
Telescope of
discovery
pentynylidyne radical
hexatriynyl radical
phosphorus nitride
CSH
radio
radio
3,2,1 mm
1986 - IRAM 30 m
1986 - IRAM 30 m
1986 - NRAO 12 m
1986-FCRAO 14m
1986 - Nobeyama 45 m
1986 - Nobeyama 45 m
1987 - IRAM 30 m
1987 -IRAM 30m
1987 - IRAM 30 m
1987 -IRAM 30m
1987-IRAM30m
1987 - IRAM 30 m
1988 - Nobeyama 45 m
1988 - NRAO 43 m
1989-IRAM 30 m
1989 - Nobeyama 45 m
1989 - NRAO 43 m
1989 - Nobeyama 45 m
1989 - IRAM 30 m
1990 - IRAM 30 m
1990 - NRAO 43 m
1990 - IRAM 30 m
1990 - NRAO 12 m
199O-CSO 10m
1991 - IRAM 30 m
1991-Nobeyama45 m
1991-NRA043 m
1992 - Nobeyama 45 m
1992-NRAO 12 m
1992 - Nobeyama 45 m
1992 - Nobeyama 45 m
1993 - Nobeyama 45 m
1993-CSO
1993-NRAO 12m,CSO
1993 - NRAO 12 m
1993 - NRAO 12 m, CSO
1994 - NRAO 12 m
1995 - NRAO 12 m
1995 - Nobeyama 45 m
1996 - IRAM 30 m
1996 - IRAM 30 m
1996-UKIRT
1997 - NASA 34 m
1997 - NRO, SEST, Haystack
1997 - ISO
acetone
sodium chloride
aluminum chloride
potassium chloride
aluminum ftuoride
methyl isocyanide
cyanomethyl radical
C2S
C3S
(CH3hCO?
NaCI
AICI
KCl
AlF
CH3NC
CH2CN
silicon carbide
propynal
SiC
HCCCHO
phosphorus carbide
propadienylidene
SiC4
CP
H2CCC
butatrienylidene
silicon nitride
silylene (pend. conf.)
carbon suboxide
isocyanoacetylene
sulfur oxide ion
ethinylisocyanide
magnesium isocyanide
protonated HC3NH+
carbon monoxide ion
sodium cyanide
nitrous oxide
magnesium cyanide
prot. formaldehyde
octatetraynyl radical
octatetraynyl radical
protonated hydrogen
hexapentaenylidene
ethylene oxide
hydrogen ftouride
6.5.4
YiH
PN
H2CCCC
SiN
SiH2 ?
HCCN
C20
HCCNC
SO+
HNCCC
MgNC
NC3H+
NH2
CO+
NaCN
CH20+
N20
MgCN
H2COH+
CSH
C7H
Hj
H2C6
C-C2~O
HF
3,7mm
3,7mm
3.4mm
2,3mm
2,3mm
2,3mm
2,3mm
3mm
6.5mm
1.3cm
2mm
8mm
1.6cm
3.5,7.5mm
1.2,3.0mm
3mm
1.4cm
many (3 mm)
1.1,1.4 mm
0.8,1.0mm
3mm
7mm
1.3cm
7mm
1.3,3mm
1.1,0.8,0.64 cm
radio
radio
0.645mm
1.3,O.8mm
3,2.4mm
0.8-4.0mm
2.0-4.0mm
radio
radio
radio
radio
IR-3.67 f.Lm
K-band
K, Q, 3 mm,l mm
121.7 f.Lm
Magneto-Bremsstrahlung Emission and Absorption
The other radiation process of dominant importance in radio astronomy is magneto-bremsstrahlung
emission and absorption which results from the interaction between fast-moving electrons and the
ambient magnetic field. There are three major varieties of magneto-bremsstrahlung emission. When
the moving electrons are very relativistic, the emission process is the very efficient, highly beamed
synchrotron emission which dominates the emission from many galactic and most extragalactic ra-
6.5
RADIO EMISSION AND ABSORPTION PROCESSES
/
137
dio sources. However, in some stars and certain solar system environments, two other magnetobremsstrahlung processes occur when the moving electrons are nonrelativistic or only mildly relativistic. When mildly relativistic (}'Lorentz == (1 - (v/c)2)-1/2 ~ 2-3) electrons undergo interactions
with magnetic fields, the emission process is called gyro synchrotron, which is much less beamed and
much less efficient at producing radio emission than synchrotron processes; however, it tends to be
highly circularly polarized, a characteristic commonly found in stellar radio emission. Even less efficient is the magneto-bremsstrahlung resulting from less relativistic particles, with YLorentz :s 1, which
is called cyclotron or gyro resonance emission. The details of nonrelativistic (cyclotron) and mildly
relativistic (gyro synchrotron) emission and absorption processes are more complicated than the highly
relativistic case. They are summarized by [7], and extensively discussed by [8] and [9].
Much of the analysis of radio source data uses very simple models for the behavior of synchrotron
radiating sources. This section summarizes formulas used in such analysis. We assume that the density
of relativistic electrons can be described by a power law distribution in energy, N(E) = K E-Y in
the energy range E to E + dE, where y is a constant. If these electrons are mixed in with a uniform
distribution of magnetic fields of strength H, which can be described as having uniformly random
directions on a large scale, then the emission and absorption coefficients are given by
jvP = 1.35 x 1O-22 a (y)K H(y+l)/2 (
636
.
:
1018)(Y-l)/2
and
(6.28)
(6.29)
where H is in gauss and all other variables are in cgs units, so that the source function is
_ 2
-jv . 84
S v --
Kv
x 10-30a(y)2y/2H-I/2
-v 5/2 erg s -I cm -3
g(y)
(6.30)
[10]. Table 6.6 gives some of the values of the functions a(y), g(y), the brightness temperature source
function Ts , and the angular size (80) of a uniform source with flux density So and magnetic field HmG
in units of milligauss.
Table 6.6. Incoherent synchrotron emission constants.
Y
1.0
15
2.0
2.5
3.0
4.0
5.0
a(y)
g(y)
a
0.283
0.147
0.103
0.0852
0.0742
0.0725
0.0922
0.96
0.79
0.70
0.66
0.65
0.69
0.83
0.0
0.25
0.50
0.75
1.0
1.5
2.0
T. -1/2 HI/2
sVGHz
1.9
1.0
6.6
4.9
3.6
2.3
1.7
x
x
x
x
x
x
x
mG
1012 K
1012 K
10" K
10" K
10" K
10" K
10" K
e oS-I/2
H- 1/ 4 5/4
0
mG vGHz
0.015 mas
0.021 mas
0.026 mas
0.030 mas
0.035 mas
0.044 mas
0.051 mas
The specific intensity is given by
(6.31)
where dTv = KvP ds in the above integral, which is along the line of sight of length L.
138 / 6
RADIO ASTRONOMY
We see from (6.30) that the important case where jv/Kv is constant occurs if the magnetic field
is unifonn in strength and geometry. Equations (6.28)-(6.30) also tell us that for the optically thick
and thin limits, Iv is proportional to H- 1/ 2v 5/ 2 and K H(y+l)/2 v -(y-l)/2 L, respectively, where L is a
line-of-sight path length. Defining the spectral index a by Sv ex: va, then a 2.5 and -(y - 1)/2 in
the optically thick and thin limits, respectively. The values of a in the latter case for various values of
y are listed in Table 6.6.
The evolution of the relativistic electron energy distributiop N(E, t) is the primary factor in the
evolution or synchrotron radiation sources. In its most general fonn this evolution is described by
=
aN(E, t)
at
+
a[
dE]
aE N(e, t)Tt = r(E, T) - A(E, t),
(6.32)
where r(E, T) and A(E, t) are functions describing particle "injection" and "escape," with escape
time scales T, respectively. Usually r and A are zero, as they will be for all models discussed
below, or applies to only small portions of the radio sources. The equation for evolution of N (E, t) is
supplemented by the energy loss equation:
dE
dt
= q,(E) = _~ _
TJE _
~E2,
(6.33)
where the first two terms are due to losses by ionization in the ambient, medium, and free-free
interaction with this medium. The last tenn, which is usually the most important, includes both energy
loss due to synchrotron radiation and energy loss due to inverse Compton scattering off photons in the
local radiation field. The coefficients of the first two tenns in (6.33) are:
~ ~ 3.33 x 1O-20nH (6.27 + In (m~2 ) ) + 1.22 x 10-20n e (73.4 In (m~2 )
and
TJ
~8x
1O- 16nHne (0.36 + In
(m~2)) ,
- In ne )
(6.34)
(6.35)
where nH is the concentration of neutral hydrogen atoms and ne is the concentration of thermal
electrons.
For synchrotron radiation losses ~synch ~ 2.37 x 10-3 Hi, where Hl.. is the magnetic field
perpendicular to the velocity vector of the radiating relativistic electron. The time scale for synchrotron
losses is tsynch == E/(-dE/dt) = 1/(~synchE) '" (5.1 x 108 /Hi)(mc 2/E) s. Synchrotron radiation
losses dominate in regions with large magnetic fields and low radiation fields.
For inverse Compton losses ~IC ~ 3.97 x 1O-4 urad, where Urad is the radiation energy density.
Inverse Compton losses dominate when brightness temperature approaches Tb ~ 10 12 K. Above 10 12 K
all relativistic electrons loss their energy rapidly due to this process.
For steady-state synchrotron radiation sources where one assumes A(E, t) = A(E), and
N(E, t) = N(E), and aN/at = 0, the relativistic particle energy equation has the solution N(E) =
q,-I(E) J A(E)dE. So if one can assume a power law for the particle injection, A(E) = AoE-Y,
then
(6.36)
The relativistic particle spectra and observable radio spectrum for such steady-state radio sources can
be described by three segments of power laws as shown in Figure 6.5. The principle effect of more
complex models is replacement of the sharp spectral breaks with smooth transitions.
6.5 RADIO EMISSION AND ABSORPTION PROCESSES /
139
a=-(y-l)/2
y
log N(E)
y+ 1
logE
,
ionization losses : free-free losses, synchrotron + inverse
,
: compton losses
,,
a
absorption
/ absorption
a + 112
log
V
Figure 6.5. Relativistic particle (top), and observable flux density (bottom), spectrum for steady-state synchrotron
radiation sources. The changes in slope indicate regions where ionization, free-free, and synchrotron (+ inverse
Compton) losses dominate. By each curve segment is the power law index for the energy and flux density spectra.
External or self-absorption can occur at any point in the flux density spectrum; two possibilities are indicated in
the figure.
A synchrotron radio source with losses only due to synchrotron radiation has an energy loss
equation d(E- l )/dt = {synch which leads to a spectrum described by E = Eo/[1 + {synch(t - to)Eo].
Then if at t = to, N(E) = NoE-Y, then at later times N(E) = NoE-Y(1 - {synchEtV-l for
E < ET(t), and N(E, T) = 0 for E > ET(t), where ET(t) = 1/({syncht). The frequency above
which synchrotron losses dominate is Vb ~ BG:usst~ GHz.
Time-dependent synchrotron radiation source models with complex geometry and complex energy
loss mechanisms require extensive computation. However in the case of simple geometries and only
adiabatic losses the evolution of the flux density of a radio source can be expressed in analytic or nearanalytic equations. For a spherical region which "suddenly" has a distribution of relativistic particles
given by No = KoE-Y and which expands with an outer radius r2(t) the flux density of the source is
described by the quantities in Table 6.7 [11-13]. An analogous model can be expressed for a conical
jet with ejection of adiabatically expanding plasma [13]. The jet ejection parameters are such that at
an initial distance Zo the radius of the cross section of the jet is ro Get Mach number Mo = zo/ ro)
and the relativistic particle density is No. The quantities that determine the flux density for an observer
for whom the jet is oriented at an inclination angle e are in Table 6.7; for a continuous jet Z2 = 00
and Zl = zo; however, a time-dependent jet which starts ejection with velocity V2 at time tstart and
ends ejection with velocity VI at time tstop is described by the same equations with the necessary time
dependence in the limits of integral for the flux density.
Table 6.7. Radio source models-{)niy adiabatic energy losses.
TO
Expanding sphere
Conical jet
E = Eo(r2/ro)-1
H = Ho(r2/ro)-2
K = Ko(r2/ro)-(y+2)
E = Eolr2(Z2)/rOr 2/ 3
H = HO[r2(Z2)/rO]-1
Ko[r(Z2)/rOr 2(y+2)/3
K
= 0.038g(y)(3.5
x 109 )y KoHci Y+ 2)/2 ro
=
same
140 /
6
RADIO ASTRONOMY
Table 6.7. (Continued.)
Expanding sphere
Hr; r > 20)
Hr; r < 20)
Conical jet
=1
= 0.66584 + 0.09089r
- 0.009989r2 + 0.0005208r 3
> 20)
r < 20)
~(r; r
~(r;
- 0.00001268r4 + 0.000000115r 5
,
rv
= rO
( r )-<2Y+3) ( v )-<Y+4)/2
-
rO
-
Vo
-0.65y n-1/2. 5/2 ",,3
Sv -- 142
. e
O,mG vGHz "'mas
r'
v
Sv
r2(t; E cons.)
r2(t; Mom. cons.)
sm(E»
rO
JzZI2<~i 1; 3/ 2 [1 - exp( -r~)H(r~) dl;
r2(t; free exp.)
/
= rO ( iOt )2 5
t )
vo
= SOMO ( ~) 5/2 sin(E»
= rO (~)
= rO ( iO
= 0.78517 + 0.06273r
- 0.007242r2 + 0.0003905 r 3
- 0.00000973r4 + 0.OOOOOOO9r 5
= (~) (~)-<Y+4)/2 [r2(Z2) ]-<7Y+8)/6
x
r2(t; freeexp.)
=1
1/4
r2(t; E cons.) = rO
z )1/2
( Z~
r2(t; Mom. cons.) = ro
(~~) 1/3
Z2
ZI
6.6
= rO G~)
= v2 (t = vI (t -
tstart)
tstop)
RADIO ASTRONOMY REFERENCES
Table 6.8 gives further references for radio astronomy.
Table 6.8. List of radio astronomy references.
Topic
Reference
Radio astronomy research field reviews
Properties of radio telescopes
Interferometry and aperture synthesis
Aperture synthesis
Observation-oriented radio astronomy textbooks
Synchrotron radiation physics
Radio astrophysical theory
General astrophysical theory
(1)
(2)
(3)
[4,5)
[6,7)
(8)
(9)
(10)
References
1. Verschuur, V.L., & Kellermann, K.I. 1988, Galactic and Extragalactic Radio Astronomy (Springer-Verlag, New York)
2. Christiansen, W.N., & Hogbom, I.A. 1985, Radio Telescopes (Cambridge University Press, Cambridge)
3. Thompson, A.R., Moran, I.M., & Swenson, G.w. 1986, Interferometry and Synthesis in Radio Astronomy (Wiley,
New York)
4. Perley, R.A., Schwab, F.R., & Bridle, A.H. 1989, Synthesis Imaging in Radio Astronomy, A.S.P. Conference Series, 6
5. Cornwell, T.I., & Perley, R.A. 1991, Radio Interferometry: Theory, Techniques, and Applications, A.S.P. Conference
Series, 19
6. Rohlfs, K. 1986, Tools of Radio Astronomy (Springer-Verlag, Berlin)
7. Krause, J.D. 1986, Radio Astronomy, 2nd ed. (Cygnus-Quasar Books, Powell)
8. Ginzburg, V.L., & Syrovatskii, S.I. 1965, Ann. Rev. Astron. Astrophys., 3, 297
9. Pacholczyk, A.G. 1970, Radio Astrophysics (W.H. Freeman, San Francisco)
10. Longair, M.S. 1981, High Energy Astrophysics: an informal introduction for students of physics and astronomy
(Cambridge University Press, Cambridge)
6.6 RADIO ASTRONOMY REFERENCES
I
I
141
REFERENCES
1. Clark, B.G. 1989, Synthesis Imaging in Radio Astronomy, A.S.P. Conference Series, 6, p. I
2. Christiansen, W.N., & H6gbom, I.A. 1985, Radio Telescopes (Cambridge University Press, Cambridge)
3. Price, R.M. et al. 1989, Radio Astronomy Observatories
(National Academy Press, Washington, DC)
4. Karzas WJ., & Latter, R. 1961,ApJS, 6,167
5. Hjellming, R.M., Wade, C.M., Vandenberg, N.R., &
Newell, R.T. 1979, AI, 14,1619
6. Aller, L.H. & Liller, W. 1968, Nebulae and Interstellar
Matter, edited by B. Middlehurst & L.H. Aller (Univer-
sity of Chicago Press, Chicago), Chapter 9
7. Dulk,G.A. 1985,ARA&:A.13. 169
8. Kundu. M.R. 1965. Solar Radio Astronomy (Interscience. New York)
9. Zheleznyakov, v.v. 1970. Radio Emission of the Sun
and Planets (Pergamon Press. Oxford)
10. Ginzburg, V.L., & Syrovatskii. S.I. 1965. ARA&:A. 3.
297
11. vander Laan,H. 1966. Nature. 211. 1131
12. Kellermann, K.I. 1966. ApJ. 146.621
13. Hjellming, R.M., & Iohnston. KJ. 1988. ApJ. 328, 600
Chapter 7
Infrared Astronomy
A.T. Tokunaga
7.1
7.1
Useful Equations; Units . . . . . . . . . . . . . . . . .
143
7.2
Atmospheric Transmission. . . . . . . . . . . . . . ..
144
7.3
Background Emission. . . . . . . . . . . . . . . . . ..
146
7.4
Detectors and Signal-to-Noise Ratios. . . . . . . . ..
148
7.5
Photometry (J.. < 30 #Lm) . • . • • . . . . • . . . . • ..
149
7.6
Photometry (J.. > 30 #Lm) . . . . . . . . . • . • . . • .•
154
7.7
Infrared Line List . . . . . . . . . . . . . . . . . . . ..
155
7.8
Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
158
7.9
Solar System . . . . . . . . . . . . . . . . . . . . . . ..
161
7.10
Stars. . . . . . . . . . . . . . . . . . . . . . . . . . . ..
163
7.11
Extragalactic Objects. . . . . . . . . . . . . . . . . ..
164
USEFUL EQUATIONS; UNITS
The Planck function in wavelength units
B).
(J..~m
= 2hc2J.. -5 /(e hc / kAT -
in #Lm; T in K) is
1)
= 1.1910 x 108J..;~/(eI4387.7/).,.mT - 1) Wm- 2 #Lm- 1 sr-I.
The Planck function in frequency units (v in Hz) is
Bv = 2hv3c-2/(ehv/kT - 1)
= 1.4745 x 10-SO v 3 /(e4.79922xIO-IJ v/T _ 1) Wm- 2 Hz-I sr-I.
143
144 / 7
INFRARED ASTRONOMY
The Rayleigh-Jeans approximation (for hv «kT) is
B)" = 2ckT)..-4 = 8.2782 x 103 TP"!m Wm- 2 JLm- l sr- l ,
Bv
= 2c- 2kTv 2 = 3.0724 x
10-40 Tv 2 Wm- 2 Hz- l sr- l .
The Stefan-Boltzmann law is
The wavelength of maximum B)" (Wien law) is
Amax
= 2898/T,
Amax
in JLm.
The frequency of maximum Bv is
Vmax
= 5.878 x 10 10 T,
Vmax
in Hz.
The conversion equations (0 in sr) are F)" = OB)", Fv = OBv, F)" = 3.0 x 1014 Fv/A~m'
Other units are 1 Jansky (Jy) = 10-26 Wm- 2 Hz-l. Units details are given in Table 7.1.
Table 7.1. Units [1-4].
Units
Radiometric name
Astronomical name
Luminosity
Flux
Wsr- I
Wm- 2 sr- 1
Wm- 2 IL m - l ; Wm- 2 Hz-I
Wm-2ILm-1 sr-I; Wm- 2 Hz-I sr- I
Flux
Irradiance;
radiant exitance
Intensity
Radiance
Spectral irradiance
Spectral radiance
Intensity
Flux density
Surface brightness;
specific intensity
References
1. Boyd, R.W. 1983, Radiometry and the Detection of Optical Radiation (Wiley, New
York)
2. Dereniak, B.L., & Crowe, D.G. 1984, Optical Radiation Detectors (Wiley, New York)
3. Wolfe, W.L., & Zissis, G.J. 1985, The Infrared Handbook. rev. ed. (Office of Naval
Research. Washington, DC)
4. Rieke. G.H. 1994. Detection of Light; From the Ultraviolet to the Submillimeter
(Cambridge University Press. Cambridge)
7.2
ATMOSPHERIC TRANSMISSION
The major atmospheric absorbers and central wavelengths of absorption bands are H20 (0.94, 1.13,
1.37, 1.87,2.7,3.2,6.3, A > 16 JLm); C02 (2.0,4.3, 15 JLm); N20 (4.5, 17 JLm); CR4 (3.3,7.7 JLm);
03 (9.6 JLm). See Figures 7.1 and 7.2.
For atmospheric transmission at airborne and balloon altitudes, see [6,11]. For water-vapor
measurements at observatory sites, see [12-14]. For atmospheric extinction, see [2, 15-17].
7.2 ATMOSPHERIC TRANSMISSION I
145
1.0
0.8
C
0
'00
0.6
'E
0.4
C
0.2
u
.;::
1.0
C/)
C/)
ca
.... 0.0
+-'
Q)
.c
c..
en
6
0.8
0.6
0
E
0.4
~
0.2
0.0
N
10
6
20
Wavelength
(~m)
Figure 7.1. Atmospheric transmission from 0.9 to 30 JLm under conditions appropriate for Mauna Kea, Hawaii.
Altitude = 4.2 km, zenith angle = 300 (air mass = 1.15), precipitable water vapor overhead = 1 mm.
AI AA = 300 for 1-6 JLm and 150 for 6-30 JLm. Spectra are calculated by Lord [1]. The infrared filter band
passes are shown as horizontal lines; see Table 7.5 for definitions. Note that the filter transmission is modified by
the atmospheric absorption. For the atmospheric transmission at Kitt Peak, see [2]. For ESO, see [3]. See also [4].
f...
-?flc
".
60
'E
40
C/)
c
ca
....
~
1000
80
0
'00
en
5000
100
·.
·.
::
500
400
w
I ••
..
W
300
250
=1 mm (Mauna Kea)
=5 mm (Kitt Peak)
..
..'" .
..'.' .
.'
.'
.'
..'.'.' · ....
..'.'• ··· ..
'
20
0
.: (......
(~m)
'
'
''
0
5
10
15
20
25
30
35
40
u (em -1)
Figure 7.2. Atmospheric transmission from 0.25 to 3 mm, adapted from [5]. The precipitable water vapor is
denoted by w. See also [6-9]. For the South Pole. see [10].
146 I
7.3
7.3.1
7
INFRARED ASTRONOMY
BACKGROUND EMISSION
Background Emission Sources
Table 7.2 gives the background emission from a ground-based telescope. The main background
emission sources are shown in Figure 7.3. Where specified they are blackbody functions reduced
by a multiplying factor €. In most cases, only the minimum background levels are plotted.
OH
GBT
ZSL
ZE
GBE
SEP
CST
CBR
OH airglow. Average OH emission of 15.6 and 13.8 mag arcsec- 2 at J and H, respectively [18-21].
Ground-based telescope thermal emission, optimized for the thermal infrared and approximated as a 273 K blackbody with € = 0.02. Emission from the Earth's atmosphere at 1.525ILm is shown [22].
Zodiacal scattered light at the ecliptic pole, approximated as a 5 800 K blackbody with € =
3 x 10- 14 (based on data from [23]).
Zodiacal emission from interplanetary dust at the ecliptic pole, approximated as a 275 K
blackbody with € = 7.1 x 10-8 . Based on observations from the Infrared Astronomical
Satellite (IRAS) [24].
Galactic background emission from interstellar dust in the plane of the Galaxy. In the plane of
the Galaxy away from the Galactic Center, it can be approximated by a 17 K blackbody and
€ = 10-3 [25,26].
South ecliptic pole emission as measured by the Cosmic Background Explorer (COBE)
spacecraft [27].
Cryogenic space telescope, cooled to 10 K with € = 0.05.
Cosmic background radiation, 2.73 K blackbody with € = 1.0 [28].
Table 7.2. Combined sky, telescope, and instrument background emission at the 3.0 m IRTF (1).a
Band
A(JLm)
dA
Surface brightness
(mag arcsec- 2)
Band
A(/Lm)
dA
J
H
Ks
K
1.26
1.62
2.15
2.21
0.31
0.28
0.35
0.39
15.9
13.4
14.1
13.7
L
L'
M'
M
3.50
3.78
4.78
4.85
0.61
0.59
0.22
0.62
Surface brightness
(mag arcsec- 2)
4.9
4.5
0.3
-0.7
Note
aTelescope emissivity at the time of the observations was about 7%.
Reference
1. Shure, M. et al. 1994, Proc. SPIE. 2198, 614
7.3.2
OU Emission Spectrum
The OH emission is often given in Rayleigh units. To convert to other units, use the following
equations, with A/Lm in ILm [29]:
1 Rayleigh unit = 10 10 /4K photons s-1 m- 2 sr- 1
= 1.5808 X lO- lO /A/Lm Wm- 2 sr- 1,
7.3 BACKGROUND EMISSION /
147
Frequency (cm-1 )
10000
c:
1000
10
100
1.0
0
'iii
0.8
0.6
0.4
0.2
(J)
'E
(J)
c:
~
l-
0.0
f"
u
Q)
(J)
10° ::-I
...
108
~
tU
(J)
I'
E 106
=l
10-2
')IE
I(J)
10-4
104
-z
~
~
[0"<
«
...o
(J)
c:
0
0
10-6
102
[0>
:>
..c:
a.
-e- 100
1
100
10
Wavelength
(~m)
Figure 7.3. Top: Transmission of the Earth's atmosphere at Mauna Kea (4.2 km), airborne (14 km), and balloon
altitudes (28 km), adapted from [6]. Bottom: Background emission sources. The surface brightness is calculated
from NqJ = fA,."mB).../(hc) = 1.41 x 10 16 fAj;!/(eI4387.7/AjLmT - 1) (A,."m in J.Lm, T in K). The intensity is
derived from A,."mBA = 8.45 x 10-9 N qJ •
~
==
=
=
=:~
1.10
1.15
1.20
1.25
1.45
1.30
1.50
1.55
1.65
1.70
1.60
1.75
1.80
~
1 .95
2.00
2.05
2.10
Wavelength <14m)
2.15
2.20
Figure 7.4. Observed OR airglow spectrum adapted from [30]. See also [19,31-34,29].
148 / 7
INFRARED ASTRONOMY
1 Rayleigh unit/A = 1.5808 x 1O-6 /AJ.tffi Wm- 2 J,Lm- 1 sr- I
= 3.7184 x
1O- 17 /AJ.tffi Wm- 2 J,Lm- 1 arcsec- 2 .
The OR airglow spectrum is given in Figure 7.4.
7.4
DETECTORS AND SIGNAL-TO-NOISE RATIOS
Tables 7.3 and 7.4 list the basic detector types for infrared observations.
Table 7.3. Basic detector types and typical useful wavelength ranges [1-4].
Material
Typea
Si
Ge
HgCdTe
PtSi
InSb
Si:As
PO
PO
PO
SO
PO
mc
Wavelength
range (J.tffi)b
<1.1
< 1.8
1-2.5
1-4
1-5.6
6-27
Material
Typea
Si:Sb
Ge:Be
Ge:Ga
Ge:Ga
GeorSi
mc
PC
PC
PC (stressed)
TO (bolometer)
Wavelength
range (J.tffi)b
14-38
30-50
40-120
120-200
200-1000
Notes
apO = photodiode, PC = photoconductor, SO = Schottky diode, mc = impurity band
conduction photoconductor [also known as blocked impurity band (Bm) photoconductor];
TO = thermal detector.
bThe HgCdTe long-wavelength cutoff is determined by the Hg/Cd ratio and can be
extended to 25 J.tm.
References
1. Rieke, G.H. 1994, Detection of Light: From the Ultraviolet to the Submillimeter
(Cambridge University Press, Cambridge)
2. Fazio, G.G. 1994, Infrared Phys. Technol., 35, 107
3. Herter, T. 1994, in Infrared Astronomy with Arrays, edited by I. McLean (Kluwer
Academic, Dordrecht), p. 409
4. Haller, E.E. 1994, Infrared Phys. Technol., 35, 127
For an object that is distributed over n pixels, the signal photocurrent for photodiodes, photoconductors, and Schottky diodes is [35]
I>s = ATT/GAF>..ll.A/(hc) = ATT/G(ll.A/A)Fv / h electrons s-I,
n
where is is the photocurrent from an individual pixel, A (m 2 ) is the telescope collecting area, T
is the transmission of instrument, telescope, and atmosphere, T/ is the detector quantum efficiency,
G is the photoconductive gain (= 1 for a photodiode; ::::: 0.5 for a photoconductor), ll.A/A is the
fractional spectral bandwidth, F>.. (W m- 2 J,Lm- 1 ) = QsourceB>.. = source flux density, and Fv
(W m- 2 Hz-I) = QsourceBv = source flux density.
The background photocurrent per pixel is
ibg
= ATT/GNtjJll.AQpix electrons s-l,
where NtjJ (photons s-l m- 2 J,Lm- 1 arcsec- 2 ) is the background surface brightness and Qpix (arcsec 2 )
is the solid angle on the sky viewed by one pixel.
7.5 PHOTOMETRY (A. < 30 j.Lm) I
149
The RMS noise per pixel is
[ N r2
+ xG(is + ibg + idc) t ]1/2 electrons,
where N r (electrons) is the detector read noise, idc (electrons s-l) is the detector dark current, t (s) is
the integration time, and x = 1 for a photodiode or !BC photoconductor or x = 2 for a photoconductor.
The signal-to-noise ratio before sky subtraction is
An alternative signal-to-noise ratio equation including the noise introduced by sky subtraction
is [36]:
SIN
= Nobj[Nobj + npix(1 + npixlnbg)(N; + Nbg + Ndc + NJig)]-1 / 2,
where Nobj is the total number of signal electrons from the object (= Lis t), npix is the number of
pixels summed for the object, nbg is the number of pixels summed for the sky subtraction, N r is the
read noise in electrons per pixel, Nbg is the sky background in electrons per pixel (= xGibgt), Ndc is
the dark current in electrons per pixel (= xGidct), and Ndig is the digitization noise in electrons per
pixel (usually negligible).
Table 7.4. Far-infrared heterodyne detectors [1,2].
Type
Schottky diode
Superconducting-insulator-superconducting (SIS)
Wavelength range (J.l.ffi )
100-300
300-3000
References
1. Phillips, T.O. 1988, in Millimetre and Submillimetre Astronomy, edited by R.D.
Wolstencroft and W.B. Burton (Kluwer Academic, Dordrecht), p. 1
2. White, OJ. 1988, in Millimetre and Submillimetre Astronomy, edited by R.D.
Wolstencroft and W.B. Burton (Kluwer Academic, Dordrecht), p. 27
For a heterodyne receiver [37],
where Ts is the source temperature (K), TN is the equivalent Rayleigh-Jeans noise temperature (K) of
the receiver, and f::J. v (Hz) is the channel width of the radio integrator.
7.5 PHOTOMETRY (A. < 30 j.Lm)
There is no common infrared photometric (radiometric) system. As a result, filter central wavelengths,
filter bandwidths, and instrumental responses are different at each observatory, as are the effects of
the atmospheric transmission. The flux density of Vega established by Cohen et al. [38] is presented in
Table 7.5. It is based upon an atmospheric model for Vega and the flux density calibration at 0.555 6 JLm
given by Hayes [39]. It is consistent with ground-based absolute flux density measurements to within
.::: 20" of the measurement errors.
150 / 7
INFRARED ASTRONOMY
Table 7.5. Filter wavelengths, bandwidths, and flux densities for Vega. a
b
Filter
name
Aiso
(/Lm)
D.A c
(/Lm)
V
J
H
Ks
K
0.5556d
1.215
1.654
2.157
2.179
3.547
3.761
4.769
8.756
10.472
11.653
20.130
0.26
0.29
0.32
0.41
0.57
0.65
0.45
1.2
5.19
1.2
7.8
L
L'
M
8.7
N
11.7
Q
FA
(Wm- 2 /Lm- l )
3.44
3.31
l.l5
4.30
4.14
6.59
5.26
2.ll
1.96
9.63
6.31
7.18
x
x
x
x
x
x
x
x
x
x
x
x
10-8
10-9
10-9
10- 10
10- 10
10- 11
10- 11
10- 11
10- 12
10- 13
10- 13
10- 14
Fv
(Jy)
3540
1630
1050
667
655
276
248
160
50.0
35.2
28.6
9.70
N,p
(photons s-I m- 2 /Lm- I )
9.60
2.02
9.56
4.66
4.53
l.l7
9.94
5.06
8.62
5.07
3.69
7.26
x 1010
x
x
x
x
x
x
x
x
x
x
x
1010
109
109
109
109
108
108
107
107
107
106
Notes
aCohen et al. [I] recommend the use of Sirius rather than Vega as the photometric standard for
A > 20 /Lm because of the infrared excess of Vega at these wavelengths. The magnitude of Vega
depends on the photometric system used, and it is either assumed to be 0.0 mag or assumed to be
0.02 or 0.03 mag for consistency with the visual magnitude.
bThe infrared isophotal wavelengths and flux densities (except for Ks) are taken from Table 1
of [1], and they are based on the UKIRT filter set and the atmospheric absorption at Mauna
Kea. See Table 2 of [1] for the case of the atmospheric absorption at Kitt Peak. The
isophotal wavelength is defined by F(Aiso) = J F(A)S(A) dA/ J S(A) dA, where F(A) is the flux
density of Vega and S(A) is the (detector quantum efficiency) x (filter transmission) x (optical
efficiency) x (atmospheric transmission) [2]. Aiso depends on the spectral shape of the source and
a correction must be applied for broadband photometry of sources that deviate from the spectral
shape of the standard star [3]. The flux density and Aiso for Ks were calculated here. For another
filter, K', at 2.11/Lm, see [4].
cThe filter full width at half maximum.
dThe wavelength at V is a monochromatic wavelength; see [5].
References
1. Cohen, M. et al. 1992, AJ, 104, 1650
2. Golay, M. 1974, Introduction to Astronomical Photometry (Reidel, Dordrecht), p. 40
3. Hanner, M.S., et al. 1984,AJ, 89,162
4. Wainscoat, R.J., & Cowie, L.L. 1992, AJ, 103,332
5. Hayes, D.S. 1985, in Calibration of Fundamental Stellar Quantities, edited by D.S. Hayes, et
al., Proc. IAU Symp. No. III (Reidel, Dordrecht), p. 225
Absolute calibration. (a) For 1.2-5 J,tm, see [40]. (b) For 10-20 J,tm, see [41].
Photometric systems and standard star observations. For AAO, 1.2-3.8 J,tm, see [42]; for CIT, 1.23.5 J,tm, see [43]; for ESO, 1.2-3.8 J,tm, see [44]; for ESO, 1.2-4.8 J,tm, see [45]; for IRTF, 10-20 J,tm,
see [46]; for KPNO, 1.2-2.2 J,tm, see [47]; for MSO, 1.2-2.2 J,tm, see [48]; for OAN, 1.2-2.2 J,tm,
see [49]; for SAAO, 1.2-3.4 J,tm, see [50]; for UA, IRTF, WIRO, 1.2-20 J,tm, see [51]; for UKIRT,
1-2.2 J,tm, faint standards, see [52]; for WIRO, 1.2-33 J,tm, see [53].
Color transformations. For JHKLI.!M; SAAO-Johnson, SAAO-ESO, SAAO-AAO, AAO-MSO,
AAO-CIT, see [17]; for JHKLM; ESO-SAAO; ESO-AAO; ESO-MSSSO; ESO-CTIO, see [44]; for
JHK; OAN-CIT, OAN-AAO, OAN-ESO, OAN-Johnson, see [49]; for JHKL; SAAO-ESO, SAAOAAO, SAAO-MSSSO, SAAO-CTIO, see [50]; for JHKL; CIT-AAO, CIT-SAAO, CIT-Johnson,
see [54]; for JHKLM; Johnson-ESO, Johnson-SAAO, see [55]; for JHK; CIT-IRTF, CIT-UKIRT,
CIT-CTIO, CIT-ESO, CIT-KPNO, CIT-HCO, CIT-AAO, CIT-Johnson/Glass, see [56].
Acronyms. AAO = Anglo-Australian Observatory; CIT = California Institute of Technology;
CTIO = Cerro Tololo Inter-American Observatory; ESO = European Southern Observatory; HCO =
7.5 PHOTOMETRY (). < 30/Lm) /
151
Harvard College Observatory (Mt. Hopkins); !RTF = NASA Infrared Telescope Facility; KPNO =
Kitt Peak National Observatory; MSO = Mt. Stromlo Observatory; MSSSO = Mt. Stromlo/Siding
Springs Observatory; OAN = San Pedro Martir National Observatory; SAAO = South African
Astronomical Observatory; UA = University of Arizona; UKIRT = United Kingdom Infrared
Telescope; WIRO = Wyoming Infrared Observatory.
Tables 7.6-7.8 give intrinsic colors and effective temperatures for stars.
Thble 7.6. Intrinsic colors and effective temperatures for the main sequence (class V).a
Spectral type
V-K
J-H
H-K
K-L
09
09.5
BO
Bl
B2
B3
B4
B5
B6
B7
B8
B9
AO
A2
-0.87
-0.85
-0.83
-0.74
-0.66
-0.56
-0.49
-0.42
-0.36
-0.29
-0.24
-0.13
0.00
0.14
0.38
0.50
0.70
0.82
1.10
1.32
1.41
1.46
1.53
1.64
1.96
2.22
2.63
2.85
3.16
3.65
3.87
4.11
4.65
5.28
6.17
7.37
-0.14
-0.13
-0.12
-0.10
-0.09
-0.08
-0.07
-0.06
-0.05
-0.03
-0.03
-0.01
0.00
0.02
0.06
0.09
0.13
0.17
0.23
0.29
0.31
0.32
0.33
0.37
0.45
0.50
0.58
0.61
0.66
0.67
0.66
0.66
0.64
0.62
0.62
0.66
-0.04
-0.04
-0.04
-0.03
-0.03
-0.02
-0.02
-0.01
-0.01
-0.01
0.00
0.00
0.00
0.01
0.02
0.03
0.03
0.04
0.04
0.05
0.05
0.05
0.06
0.06
0.08
0.09
0.11
0.11
0.15
0.17
0.18
0.20
0.23
0.27
0.33
0.38
-0.06
-0.06
-0.06
-0.05
-0.05
-0.05
-0.05
-0.04
-0.04
-0.04
-0.04
-0.03
0.00
AS
A7
FO
F2
F5
F7
GO
02
04
06
KO
K2
K4
K5
K7
MO
Ml
M2
M3
M4
M5
M6
om
0.02
0.03
0.03
0.03
0.04
0.04
0.05
0.05
0.05
0.05
0.06
0.07
0.09
0.10
0.11
0.14
0.15
0.16
0.20
0.23
0.29
0.36
K-L'
0.00
0.01
0.02
0.03
0.03
0.03
0.04
0.04
0.05
0.05
0.05
0.05
0.06
0.07
0.10
0.11
0.13
0.17
0.21
0.23
0.32
0.37
0.42
0.48
K-M
0.00
om
0.03
0.03
0.03
0.03
0.02
0.02
0.01
0.01
0.01
0.00
-0.01
-0.02
-0.04
Tefl
35900
34600
31500
25600
22300
19000
17200
15400
14100
13000
11800
10700
9480
8810
8160
7930
7020
6750
6530
6240
5930
5830
5740
5620
5240
5010
4560
4340
4040
3800
3680
3530
3380
3180
3030
2850
Notes
aColors given in the Iohnson-Glass system as established by Bessell and Brett [1].
References used: 0, B, [2]; A, F, 0, K, [1]; K. M, [3]. Did not use K-M from [2] because
there is a large offset compared to [1]. Approximate uncertainties (one standard deviation):
±0.02 (O-K); ±0.03 (M).
bTeff is an average of values from the following sources: for 0, B, [4]; for B, A, F, 0,
K, [5]; for B, 0, K. [6]; for A, F, [7]; for A, F, 0, K, [8]; for A, F, 0, [9]; for 0, K, [10]; for
K, M, [3]; for M, [11], [7], [12]. Approximate uncertainties (one standard deviation): ±1000
K (09-B2); ±250 K (B3-B9); ±100 K (AO-M6).
References
1. Bessell, M.S., & Brett, I.M. 1988, PASP, 100,1134
152 / 7
INFRARED ASTRONOMY
2. Koomneef, J. 1983, A&A, 128, 84
3. Bessell, M.S. 1991, AJ, 101, 662
4. Vacca, W.O. et aI. 1996,ApJ, 4(;0, 914
5. Popper,D.M. 1980, ARA&A, 18, 115
6. Bohm-Vitense, E. 1981'ARA&A, 19,295
7. Bohm-Vitense, E. 1982,ApJ, 255, 191
8. Blackwell, D.E. et aI. 1991, A&A, 245, 567
9. Fernley, J.A. 1989, MNRAS, 239, 905
10. Bell, R.A., & Gustafsson, B. 1989, MNRAS, 236, 653
11. Jones, H.R.A et aI. 1995, MNRAS, 277, 767
12. Leggett, S.K. et aI. 1996, ApJS, 104, 117
1Bble 7.7. Intrinsic colors and effective temperatures for giant stars (class m). a
Spectral type
V-K
J-H
H-K
K-L
K-L'
K-M
Terf
1.75
2.05
2.15
2.16
2.31
2.50
2.70
3.00
3.26
3.60
3.85
4.05
4.30
4.64
5.10
5.96
6.84
7.80
0.37
0.47
0.50
0.50
0.54
0.58
0.63
0.68
0.73
0.79
0.83
0.85
0.87
0.90
0.93
0.95
0.96
0.96
0.07
0.08
0.09
0.09
0.10
0.10
0.12
0.14
0.15
0.17
0.19
0.21
0.22
0.24
0.25
0.29
0.30
0.31
0.04
0.05
0.06
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.12
0.13
0.15
0.17
0.18
0.20
0.05
0.06
0.07
0.07
0.08
0.09
0.10
0.12
0.14
0.16
0.17
0.17
0.19
0.20
0.21
0.22
0.00
-0.01
-0.02
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07
-0.08
-0.09
-0.10
-0.12
-0.13
-0.14
-0.15
5910
5190
5050
4960
4810
4610
4500
4320
4080
3980
3820
3780
3710
3630
3560
3420
3250
GO
G4
G6
G8
KO
Kl
K2
K3
K4
KS
MO
Ml
M2
M3
M4
M5
M6
M7
Notes
aColors given in the Johnson-Glass system as established by Bessell and Brett in [1].
APf,roximate uncenainties (one standard deviation): ±o.02.
Teff is an average of values from the following sources: for G, K, M, [2]; for K, M, [3];
for G, K, [4]; for G, K, M, [5]. Approximate uncertainties (one standard deviation): ±50 K
(G2-KS); ±70 K (MO-M6). For 0 and B stars, see [6].
References
1. Bessell, M.S., & Brett, J.M. 1988, PASP, 100, 1134
2. Ridgway, S.T. et aI. 1980,ApJ, 235,126
3. Di Benedetto; G.P', & Rabbia, Y. 1987,A&A, 188,114
4. Bell, R.A., & Gustafsson, B. 1989, MNRAS, 236, 653
5. Blackwell, D.E. et aI. 1991, A&A, 245, 567
6. Vacca, W.O. etal. 1996,ApJ, 4(;0, 914
1Bble 7.8. Intrinsic colors and effective temperatures for supergiant stars (class I). a
Spectral type
V-K
J-H
H-K
K-L
Tetf
09
BO
Bl
B2
B3
B4
-0.82
-0.69
-0.55
-0.40
-0.28
-0.20
-0.05
-0.04
-0.03
-0.04
-0.03
-0.01
-0.13
-0.10
-0.06
0.00
0.03
0.01
-0.08
-0.07
-0.07
-0.07
-0.05
-0.01
32500
26000
20700
17800
15600
13900
7.5 PHOTOMETRY ().. < 30 JLffi) / 153
Table 7.8. (Continued.)
Spectral type
V-K
J-H
H-K
K-L
Tetf
B5
B6
B7
B8
B9
AO
Al
A2
A5
G8
KO
Kl
K2
K3lab
K5Iab
MOlab
Mllab
M2Iab
M3Iab
M4Iab
-0.13
-0.07
0.01
0.07
0.13
0.19
0.26
0.32
0.48
0.64
0.75
0.93
1.21
1.44
1.67
1.99
2.15
2.28
2.43
2.90
3.50
3.80
3.90
4.10
4.60
5.20
0.01
0.04
0.06
0.07
0.08
0.09
0.11
0.12
0.13
0.15
0.18
0.22
0.28
0.33
0.38
0.43
0.46
0.49
0.52
0.59
0.67
0.73
0.73
0.73
0.74
0.78
0.00
-0.02
-0.02
-0.02
-0.02
-0.02
-0.01
-0.01
0.02
0.04
0.05
0.06
0.07
0.08
0.09
0.11
0.12
0.13
0.13
0.13
0.14
0.18
0.20
0.22
0.24
0.26
0.02
0.03
0.04
0.05
0.06
0.07
0.07
0.08
0.07
0.06
0.06
0.07
0.07
0.08
0.08
0.09
0.10
0.11
0.12
0.15
0.18
0.20
0.22
0.24
0.26
0.28
13400
12700
12000
11200
10500
9730
9230
9080
8510
7700
7170
6640
6100
5510
4980
4590
4420
4330
4260
4130
3850
3650
3550
3450
3200
2980
MOIb
Mllb
M21b
M31b
M41b
3.80
3.90
4.10
4.60
5.20
0.76
0.76
0.76
0.77
0.81
0.18
0.20
0.22
0.24
0.26
0.12
0.14
0.16
0.18
0.20
MOIa
Mila
M2Ia
M3Ia
M4Ia
3.80
3.90
4.10
4.60
5.20
0.61
0.61
0.61
0.62
0.66
0.18
0.20
0.22
0.24
0.26
0.27
0.29
0.31
0.33
0.35
FO
F2
F5
F8
GO
G3
Notes
aColors given in the Johnson-Glass system as established by Bessell and Brett [I].
References used: For 0, A, [2]; for A, F. G, K. [3]; for K, M. [4]. Approximate
uncertainties (one standard deviation): ±0.03.
bTeff is an average of values from the following references: For O-M. [5]; for 0K, [6]; for O. B. [7]. Approximate uncertainties (one standard deviation): ±1000 K
(09-B2); ±250 K (B3-B9); ±200 K (A-M).
References
1. Bessell. M.S .• & Brett. J.M. 1988, PASP.l00. 1134
2. Whittet, D.C.B., & van Breda, I.G. 1980, MNRAS, 192.467
3. Koomneef. J. 1983.A&A.128. 84
4. Elias. J. et al. 1985. ApJS. 57, 91
5. Schmidt-Kaler, Th. 1982. in Landolt-Biirnstein. New Series, edited by K. Schaifer
& H.H. Voigt (Springer-Verlag. Berlin). Vol. V1I2b. p. 451
6. Bohm-Vitense. E. 1981. ARA&A.19. 295
7. Remie. H .• & Lamers. HJ.G.L.M. 1982. A&A. lOS. 85
154 / 7
INFRARED ASTRONOMY
7.6 PHOTOMETRY (A > 30 jlm)
The primary flux density calibrator for ground-based submillimeter and millimeter observations is
Mars [57]. The main secondary calibrators are Uranus [58,59] and Jupiter [5, 59, 60]. Other secondary
calibrators consist of astronomical sources [59,61].
Instrument details for the IRAS satellite are given in Table 7.9.
Table 7.9. InfraredAstronomical Satellite (IRAS) summary injormation. a
Effective wavelength (#Lm)
12
25
60
100
Bandwidth (FWHM) (#Lm)
'JYpicai detector field of view,
(in scan) x (cross scan) (arcmin)
Point Source Catalog, with 2 coverages,
90% completeness limits (Jy)b
Faint Source Catalog
median 90% completeness limits (Jy)b
7.0
11.15
32.5
31.5
0.76 x 4.55
0.76 x 4.65
1.51 x 4.75
3.03 x 5.05
0.45
0.64
0.18
0.29
0.26
Notes
aIRAS
observations are sensitive to dust with T > 25 K. For IRAS catalogs, see [1, 2].
bCompleteness limits vary according to the amount of sky coverage obtained.
References
1. Infrared Astronomical Satellite (lRAS) Catalogs and Atlases, 1988, ed. Joint IRAS Science Working
Group (U.S. Government Printing Office, Washington, DC), Vols. 1-7
2. The Infrared Processing & Analysis Center (IPAC) WWW Home Page (bttp://www.ipac.caltecb.eduJ) bas
numerous databases and information on IRAS catalogs
The following formulas give the IRAS four-band and two-band fluxes. For galactic sources [62]
Fir(7 - 135/Lm)
= 1.0 x
1O-14(20.653fI2 + 7.538/25
+ 4.578160 + 1.7621100) Wm- 2.
For extragalactic sources [63,64]
Fir(8 - 1000 /Lm)
Ffir(43 - 123 /Lm)
=
=
1.8 x 1O- 14 (13.48fI2
1.26 x 10- 14 (2.58160
+ 5.16/25 + 2.58160 + 1100) Wm-2,
+ fIoo) Wm-2,
where 112, /25, 160, and fIoo are the IRAS flux densities in Jy at 12, 25, 60, and 100 /Lm. These
formulas are approximations based on assumptions about the intrinsic source spectrum and dust
emissivity. It is recommended that the original references be consulted for details.
The luminosity (in solar luminosities) is
where D is in pc and Fir,fir is in W m- 2.
The far-infrared emission-radio emission correlation [65] is
q
where fI.4
GHz
= log{[Ffir/(3.75 x
10 12 Hz)]/it.4 GHz}
is the 1.4 GHz flux density in W m- 2 Hz-I.
= 2.14,
7.7 INFRARED LINE LIST / 155
7.7 INFRARED LINE LIST
Table 7.10 presents data for a sample of infrared lines.
Table 7.10. Selected infrared lines.
A (ttm)a
1.00521
1.01264
1.0833
1.09411
1.11286
1.1290
1.16296
1.16764
1.252
1.25702
1.28216
1.31682
1.47644
1.52647
1.58848
1.61137
1.6189
1.62646
1.64117
1.64400
1.68111
1.68778
1.69230
1.70076
1.73669
1.74188
1.81791
1.87561
1.94509
1.95756
1.9634
2.03376
2.040
2.04065
2.05869
2.06059
2.08938
2.09326
2.1127
2.12183
2.13748
2.14380
2.16612
2.18911
2.20624
2.20897
2.22329
2.24772
2.26311
v (cm-I)a
Species
Transitionb
Referencec
9948.17
9875.18
9231.2
9139.85
8985.84
8857.4
8598.75
8564.28
7987.0
7955.30
7799.34
7594.03
6773.05
6551.08
6295.29
6205.92
6177.0
6148.32
6093.21
6082.73
5948.45
5924.94
5909.12
5879.74
5758.08
5740.94
5500.82
5331.60
5 141.15
5108.40
5093.2
4917.01
4902.0
4900.39
4857.45
4852.99
4786.11
4777.23
4733.4
4712.91
4678.41
4664.61
4616.55
4568.07
4532.59
4527.00
4497.84
4448.96
4418.69
HI
Hell
Hel
HI
Fell
n = 7-3 (Pa.S)
n =5-4
2 p 3p o_2s 3S
n = 6-3 (pay)
b 4 GS/2-z4F3/2
3d 3Do_3p3p
n = 7-5
n = 11-6
3PI _ 3 P2
[1,2,3]
[1,3]
[1,3]
[1,2,3]
[4,5,6]
[2,3,4]
[1,3]
[1,7]
[8,9, 10, 11]
[4,5,6]
[1,2,3]
[3,6]
[1,3]
[1,2,3]
[1,2,3]
[1,2,3]
[12]
[12]
[1,2,3]
[4,5,6]
[1,2,3]
[4,5,6]
[1,7]
[3,6]
[1,2,3]
[3,6]
[1,2,3]
[2,3]
[1,2,3]
[13, 14]
[9, 10, 15]
[14, 16]
[9, 10]
[17]
[3, 18]
[5,6, 18]
[5,6, 16]
[17]
[3,6]
[14, 16]
[18]
[18]
[2,3, 16]
[1,7]
[16, 19,20]
[16, 19,20]
[14, 16]
[14, 16]
[19]
01
Hell
Hell
lSi IX]
[Fe II]
HI
01
Hell
HI
HI
HI
CO
OH
HI
[Fe II]
HI
Fell
Hell
Hel
HI
Fell
HI
HI
HI
H2
lSi VI]
H2
[AlIX]
H3+
Hel
Fell
Fell
H3+
Hel
H2
MgII
MgII
HI
Hell
Nal
Nal
H2
H2
Cal
a 4n-, /2--a 6D9/2
n = 5-3 (PafJ)
4s 3So_3p 3 P
n = 9-6
n = 19-4 (BrI9)
n = 14-4 (8rI4)
n = 13-4 (Br13)
v = 6-3 band head
v = 2--0 Pld(15)
n = 12-4 (BrI2)
a 4n-, /2--a 4F9/2
n = 11-4 (Br11)
c4F9/2-z4F9/2
n = 12-7
4d 3D _ 3p 3p o
n = 10-4 (BrIO)
c 4 F7/2-Z 4 n-, /2
n = 9-4 (Br9)
n = 4-3 (Paa)
n = 8-4 (Br8)
v = 1--0 S(3)
2PI/2-2p3/2
v = 1-0 S(2)
2po 2po
3/2- 1/2
v = 2V2(2)--O; (4, 6, +2}-(3, 3)
2p Ipo_2s IS
c 4FS/2-Z 4F3/2
c 4F3/2-Z 4F3/2
v = 2V2(2)--O; (7, 9, +2}-(6, 6)
4s 3S_3 p 3po
v = 1-0 SO)
5 p 2Pf/2-5s 2SI/2
5p 2Pl/2-5s 2SI/2
n = 7-4 (Bry)
n = 10-7
4p 2Pf/2-4S 2SI/2
4p 2Pl/2-4s 2SI/2
v = I-OS(O)
v = 2-1 SO)
4f 3Ff-4d 3D2
156 I 7
INFRARED ASTRONOMY
Table 7.10. (Continued.)
(em-If
A. (p.mf
II
2.26573
2.29353
2.32265
2.34327
2.34531
2.34950
2.35167
2.35246
2.38295
2.40659
2.41344
2.42373
2.4833
2.49995
2.62587
2.62688
3.0279
3.03920
3.09169
3.133
3.29699
3.41884
3.48401
3.50116
3.52203
3.6246
3.64592
3.661
3.69263
3.7240
3.74056
3.80741
3.8462
3.935
3.95300
4.0045
4.02087
4.03781
4.04900
4.05226
4.17079
4.64931
4.65378
4.65748
4.67415
4.68262
4.69462
5.0531
6.634
6.985
7.642
8.99135
10.51
10.521
12.2786
12.3720
4413.58
4360.09
4305.42
4267.54
4263.84
4256.22
4252.30
4250.87
4196.48
4155.25
4143.47
4125.87
4026.9
4000.08
3808.26
3806.80
3302.6
3290.34
3234.48
3192.0
3033.07
2924.97
2870.26
2856.20
2839.27
2758.9
2742.79
2731.0
2708.10
2685.3
2673.40
2626.46
2600.0
2541
2529.72
2497.2
2487.02
2476.59
2469.75
2467.76
2397.63
2150.86
2148.79
2147.08
2139.43
2135.55
2130.10
1979.0
1507
1432
1309
1112.18
951.5
950.48
814.425
808.283
Species
Transitionb
Referencec
Cal
CO
CO
CO
CO
CO
CO
CO
CO
H2
H2
H2
lSi VII]
H2
HI
H2
[Mgvm]
HI
Hell
OH
HI
Hell
Hell
HI
HI
H2
HI
[Alvl]
HI
H2
HI
H2
H2
[Silx]
H3+
SiO
HI
Hel
Hel
HI
HI
CO
HI
CO
CO
CO
H2
H2
[Nill]
4f 3F:-4d 3D3
[19]
[16]
[16]
[21]
[21]
[21]
[21]
[16]
[16]
[13,14]
[13,14]
[13,14]
[9,10,15]
[14,22]
[2,22]
[14,22]
[8, 9, 10, 15]
[2]
[3]
[23]
[2, 24]
[3,24]
[3,24]
[2,24]
[2,24]
[25,26]
[2,25]
[8-10]
[2,25]
[26]
[2]
[14,27]
[26,27]
[9,10,15]
[28]
[29]
[2,16]
[3,30]
[30]
[2, 16]
[2,16]
[31]
[2, 16]
[31]
[31]
[31]
[14]
[14,26]
[32]
[33]
[9,10]
[33,34]
[33]
[11,32]
[14]
[2]
[Arn]
[NevI]
[Arm]
[SIV]
[COli]
H2
HI
=
II =
II =
II =
II =
II =
II =
II =
II =
II =
II =
II
2-0 band head
3-1 band head
2"'{)R(1)
2"'{)R(0)
2-OP(1)
2-OP(2)
4-2 band head
5-3 band head
1-OQ(l)
1...{)Q(2)
I...{)Q(3)
3PI_3~
II = 1...{)Q(7)
n = 6-4 (Brp)
II = 1"'{)0(2)
21'.0
2po
3/2- 1/2
n = 10-5 (PfE)
n=7-6
II = 1"'{), K=9 multiplet
n = 9-5 (PfB)
n = 25-11
n = 17-10
n = 24-6 (Hu24)
n = 23-6 (Hu23)
II = 0...{) S(15)
n = 19-6 (Hu19)
3PI _3~
n = 18-6 (Hu18)
II = 0...{) S(14)
n = 8-5 (Pfy)
II = 1"'{)0(7)
II = 0...{) S(13)
3PI_3PO
II = "2(1)...{); (1, 0, -1)-(1,0)
1I=2-0bandhead
n = 14-6 (HuI4)
5f3F°-4d 3D
5g IG~f I FO; 5g 3G~f 3 FO
n = ~(Bra)
n = 13-6
II = l"'{)R(1)
n = 7-5 (PfP)
II = 1...{)R(0)
II = 1...{)p(1)
II = 1...{)p(2)
II = 0...{) S(9)
II = 0...{) S(8)
a 2D)/2-<l2DS/2
2po 21'.0
1/2- 3/2
2Pj/2-2PI/2
3PI_3~
21'.0 2po
3/2- 1/2
a 3F3-<l3F4
II = 0...{) S(2)
n =7-6(Hua)
7.7 INFRARED LINE LIST /
Table 7.10. (Continued.)
).. (/Lm)Q
v (cm-I)Q
Species
Transitionb
Referencec
12.8135
780.424
[Nell]
642.7
587.032
534.387
411.256
386.5
354.374
298.67
192.99
174.47
[Nem]
H2
[S m]
[Nev]
[OIV]
H2
[S m]
[Om]
[Nm]
2po 2po
1/2- 3/2
3PI_3P2
v=O-OS(l)
3P2_3PI
3PI_3PO
2PJ/2-2PI/2
v = O-OS(O)
3PI_3PO
[33,34]
15.56
17.0348
18.7130
24.3158
25.87
28.2188
33.482
51.816
57.317
63.1837
77.059
88.355
119.23
119.44
121.898
124.65
145.526
157.741
162.81
205.178
370.415
371.65
609.135
158.269
129.77
113.18
83.872
83.724
82.0358
80.225
68.7162
63.3951
61.421
48.7382
26.9967
26.907
16.4167
[01]
CO
[Om]
OH
OH
[NIl]
NH3
[01]
[CII]
CO
[NIl]
[CI]
CO
[CI]
3~_3pI
2po 2po
3/2- 1/2
3PI_3~
J = 34-33
3PI_3PO
2n3/2 J = 5/2-312
2n3/2 J = 512-312
3P2_3PI
K = 3, J = 4-3, a - s
3PO_3PI
2po 2po
3/2- 1/2
J = 16-15
3PI_3PO
3P2_3PI
J=7~
3PI_3PO
[33]
[l4]
[34,35]
[34,35]
[33]
[14]
[35,36]
[33,35]
[33]
[37]
[37]
[33,35]
[37]
[37]
[33,38]
[37]
[33]
[33]
[37]
[38]
[33]
[39]
[33]
Notes
Q Vacuum wavelengths and frequencies are given.
bTransition shown is (upper level}-{Iower level).
cBecause of space limitations, only a few transitions of each species are shown; see references
for additional lines. Wavelength and frequencies were calculated or obtained from primary
references where possible. For additional information, see [40-45].
References
I. Treffers, R.R. et al. 1976, ApJ, 209, 793
2. Moore, C.E. 1993, in Tables of Spectra of Hydrogen, Carbon, Nitrogen, and Oxygen Atoms
and Ions, edited by J.W. Gallagher (CRC, Boca Raton, FL); van Hoof, P.A.M., private
communication
3. Bashkin, S., & Stoner, J.O. 1975, Atomic Energy Levels and Grotian Diagrams (NorthHolland, Amsterdam); van Hoof, P.A.M., private communication
4. Allen, D.A. et al. 1985, ApJ, 291, 280
5. Johansson,S. 1978,Phy~Scr.,18,217
6. Hamann, F. et al. 1994, ApJ, 422, 626
7. Moore, C.E. 1971, Atomic Energy Levels, NSRDS-NBS Publication No. 35; van Hoof,
P.A.M., private communication
8. Woodward, C.E. et al. 1995,ApJ, 438, 921
9. Greenhouse, M.A. et al. 1993, ApJS, 88, 23
10. Gehrz, R.D. 1988, ARA&A, 26, 377
II. Roche, P.F. et al. 1993, MNRAS, 261, 522
210
12. Hinkle, K.H. 1978,ApJ,
13. Gautier m, T.H. et al. 1976, ApJ, 207, LI29
14. Black, J.H., & van Dishoeck, E.F. 1987, ApJ, 322, 412
15. Reconditi, M., & Oliva, E. 1993, A&A, 274, 662; Oliva, E. et al. 1994, A&A, 288, 457
16. Scoville, N. et al. 1983, ApJ, 275, 201
17. Drossart, P. et al. 1989, Nature, 340, 539; see also Kao, L. et al. 1991, ApJS, 77,317
18. Simon, M., & Cassar, L. 1984, ApJ, 283, 179
19. Kleinman, S.G., & Hall, D.N.B. 1986, ApJS, 62, 501
no,
157
158 I 7
INFRARED ASTRONOMY
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
7.8
Martin, W.C., & Zalubas, R. 1981, J. Phys. Chern. Ref Data Ser., 10, 153
Black, I.H., & Willner, S.P. 1984, ApJ, 279, 673
Davis, D.S. et al. 1982, ApJ, 259, 166
Beer, R. et al. 1972, ApJ, 172,89
Lowe, R.P. et al. 1991, ApJ, 368,195
Sanford, S.A. 1991, ApJ, 376, 599
Knacke, R.E, & Young, B.T. 1981, ApJ, 249, L65
Brand, P.W.I.L. et al. 1989, MNRAS, 236, 929
Oka, T., & Geballe, T.R. 1990, ApJ, 351, L53
Hinkle, K.H. et al. 1976, ApJ, 210, L141
Hamann, E, & Simon, M. 1986, ApJ, 311, 909
Guelachvili, G. 1979, J. Mol. Spectrosc., 75, 251; Mitchell, G.E et al. 1989, ApJ, 341,1020
Wooden, D.H. et al. 1993, ApJS, 88, 477
Genzel, R. 1988, in Millimetre and Submillimetre Astronomy, edited by R.D. Wolstencroft
and W.B. Burton (Kluwer Academic, Dordrecht), p. 223
Kelly, D.M., & Lacy, I.H. 1995, ApJ, 454, L161
Emery, R.I., & Kessler, M.E 1984, in Galactic and Extragalactic Infrared Spectroscopy,
edited by M.E Kessler and I.P. Phillips (Reidel, Dordrecht), p. 289
Stacy, G.J. et al. 1993, Proc. SPIE, 1946,238
Watson, D.M. 1984, in Galactic and Extragalactic Infrared Spectroscopy, edited by M.E
Kessler and I.P. Phillips (Reidel, Dordrecht), p. 195; Townes, C.H., & Melnick, G. 1990,
PASP, 102, 357
Colgan, S.W.I. et al. 1993, ApJ, 413,237
Howe, I.E. et al. 1993, ApJ, 410, 179
H: Wynn-Williams, C.G. 1984, in Galactic and Extragalactic Infrared Spectroscopy, edited
by M.E Kessler and I.P. Phillips (Reidel, Dordrecht), p. 133
H2: Schwartz, R.D. et al. 1987, ApJ, 322, 403; Black, I.H., & van Dishoeck, E.E 1987, ApJ,
322,412
CO: Goorvitch, D. 1994,ApJS, 95, 535
Solar atlases: Livingston, W., & Wallace, L. 1991, An Atlas of the Solar Spectrum in
the Infraredfram 1850 to 9000 cm- 1 (1.1-5.4/Lm), NSO Technical Report No. 91-001
(NOAO, Thcson); Wallace, L., & Livingston, W. 1992, An Atlas of a Dark Sunspot Umbral
Spectrum fram 1970 to 8640 cm- 1 (1.16-5.1 /Lm), NSO Technical Report No. 92-001
(NOAO, Thcson)
Infrared spectra: Iourdain de Muizon, M. et al. 1994, Database of Astronomical Infrared
Spectroscopic Observations (University of Leiden, Leiden)
Infrared wavelength calibration: Outred, M. 1978,1. Phys. Chern. Ref Data Ser., 7, 1; Rao,
K.N. et al. 1966, Wavelength Standards in the Infrared (Academic Press, New York)
DUST
For the infrared interstellar reddening law, see [66--69].
The total to selective absorption ([66-68], for R = Av IE(R - V)
Av IE(1 - K)
Av /E(V - K)
AdE(1 - K)
The color excess ratio
[67]
= 5.82 ± 0.1,
= 1.13 ± 0.03,
= 2.4(A)-1.75
Av IE(H - K)
(for 0.9 <
A
= 3.1) is
=
15.3
± 0.6,
< 6/Lm).
is
E(l - H)/E(H - K)
=
1.70 ± 0.05.
The ratio of visual extinction to silicate band optical depth
A v / t"Si
Av /t"Si
= 19 ± 1
= 11 ± 2
(t"Si) [68,70,71]
(local interstellar medium),
(Galactic Center region).
is
7.8 DUST /
e-o
1ii
:x:
-i
-
~
1crU
+
159
+
J:
Z
>
~1cr-
~
.IRAS
-COBEFIRAS
100
10
A (11m)
Figure 7.5. Emission spectrum of interstellar dust. Adapted from [78]. See also [26,79,80].
The average visual extinction to the Galactic Center region is 34 mag [72] and to individual sources it
ranges from 23 to 35 mag [67].
The extinction cross section per H nucleus in the local interstellar medium [68] is
The interstellar linear polarization [73-75]:
P(A)/ P rnax = exp[ -K In2(Arnax/A)]
P(A) ex: A-{3,
(for A < 2 JLm),
f3 = 1.6 - 2.0 (for 2
< A < 5 JLm),
where P(A) is the percentage polarization, Prnax is the maximum percentage polarization occurring at
Amax, and K = 0.01 ± 0.05 + (1.66 ± 0.09)Arnax.
Table 7.11 and Figure 7.5 present data on the interstellar dust emission. Table 7.12 presents farinfrared dust properties.
Dlble 7.11. Average galactic diffuse emission [1].a
3.5
4.9
12
25
0.21
0.13
0.80
0.41
60
100
140
240
0.88
2.0
3.8
2.5
Note
aFor galactic latitudes _60 to _40 and +40 to +60 . Emission is highly
variable on small spatial scales [1, 2].
References
1. Bernard, J.P. et al. 1994, A&A, 291, 1.5
2. Cutri, R.M., & Latter, W.B., editors, 1993, The First Symposium on the
Infrared Cirrus and Diffuse Interstellar Clouds, ASP Conf. Set. (ASP, San
Francisco), Vol. 58
160 / 7
INFRARED ASTRONOMY
The dust mass estimate from the 100 JLm flux density is
Mdust = 4.81 x 10- 12 /100 D2(eI43.88/Td
-
1) M 0
,
where 1100 is the 100 JLm flux density in Jy, D is the distance in pc, and Td is the dust temperature in
K. The derivation follows from [76], using a mass absotption coefficient of 2.5 m 2 kg- 1 at 100 JLm.
The dust mass absotption coefficient at submillimeter wavelengths is estimated in [68,76,77].
The equilibrium dust temperature of a particle with albedo A at a distance r (in pc) from a source
of luminosity L (in L0) is
Te = 0.612(1 - A)0.25 L 0.25 r -0.5 K.
The nonequilibrium emission from
extremely~mall
particles is discussed in [81-83].
Table 7.12. Galactic dust properties at 140-240 I'm Mean values in the galactic plane (lbl < 1°) [I].a
Inner galaxy
Quantity
Dust temperature (K)
240 I'm optical depth
Total FIR radiance
(Wm- 2 sr- 1 )
Gas-to-dust ratio
FIR luminosity
perHmass (L0/M0)
(270° < t < 350°;
10° < t < 90°)
Outer galaxy
20± I
(5.0 ± 2.0) x 10-3
(3.7 ± 0.3) x 10-5
17± I
(9.5 ± 3.0) x 10-4
(2.4 ± 0.2) x 10-6
19± I
(3.0 ± 1.0) x 10- 3
(2.0 ± 0.2) x 10-5
140±50
3.0±0.3
190±60
0.9±0.1
160±60
2.0±0.2
(90° <
t
< 270°)
Entire galaxy
Note
aData from the Cosmic Background Explorer (COBE) satellite; for additional information, see the COBE
WWW Home Page: http://www.gsfc.nasa.gov/astrolcobelcobe_home.html
Reference
I. Sodroski, T.J. et al. 1994, ApJ, 428, 638
Spectral features of dust and ice in the infrared are listed in Table 7.13.
Table 7.13. Major dust and ice features [1-7].
3.08
3.29,6.2,7.7,
8.65, 11.25
4.62
4.67
6.0
6.85
~9.7
~
11.2
1l.5
~
18
~34
43
Identification
Where observed
H20 ice
Aromatic hydrocarbonsa
Molecular clouds; OH-IR stars
H II regions, planetary nebulae, reflection nebulae,
young and evolved stars, starburst galaxies
Molecular clouds
Molecular clouds
Molecular clouds
Molecular clouds
H II regions, molecular clouds
Circumstellar shells; planetary nebulae
OH-IRstars
H II regions; Galactic center
Planetary nebulae; carbon stars
OH-IRstars
"X-CN"
CO ice
H20 ice
CH30H + other
Amorphous silicates
SiC
H20 ice
Amorphous silicates
MgS (7)
H20 ice
Note
aThe nature of the "aromatic hydrocarbons" is not known precisely [7]; it is commonly assumed
to be polycyclic aromatic hydrocarbons (PAHs).
7.9 SOLAR SYSTEM /
161
References
1. Willner, S.P. 1984, in Galactic and Extragalactic Infrared Spectroscopy, edited by M.P. Kessler
and J.P. Phillips (Reidel, Dordrecht), p. 37
2. Roche, P.P. 1989, in Proc. 22nd ESLAB Symp. on Itifrared Spectroscopy in Astronomy, ESA SP290,p.79
3. Tokunaga, A.T., & Brooke, T.Y. 1990, Icarus, 86, 208
4. Whittet, D.C.B. 1992, Dust in the Galactic Environment (Institute of Physics, Bristol), p. 147
5. Allamandola, LJ. et al. 1989, ApJS, 71, 733
6. Uger, A., & d'Hendecourt, L. 1987, in Polycyclic Aromatic Hydrocarbons and Astrophysics,
edited by A. Uger et al. (Reidel, Dordrecht), p. 223
7. Sellgren, K. 1994, in The First Symposium on the Infrared Cirrus and Diffuse Interstellar Clouds,
edited by R.M. Cutri and W.B. Latter, ASP Conf. Ser. (ASP, San Francisco), Vol. 58, p. 243
7.9 SOLARSYSTEM
The solar colors are [84]
J - H = 0.310,
H - K = 0.060,
K - L = 0.034,
L - M = -0.053,
v-
K
= 1.486.
Solar analogs [85] are 16 eyg B, VB64, HD 105590, HR 2290.
The blackbody temperature of an object without an atmosphere in the solar system is
Tb =
278.8(1 -
A)O.25 r -0.5
K,
where A is the albedo and r is the distance from the Sun in AU.
For thermal emission from asteroids, see [86-88].
For the infrared spectra of planetary atmospheres, see [89-92].
For the infrared spectra of comets, see [93,94].
For near-infrared spectra of satellites, see [95,96].
For near-infrared spectra of asteroids, see [97,98].
The infrared magnitudes and colors of many solar system objects are given in Table 7.14.
'Dlble 7.14. Magnitudes o/selected solar system bodies. Q
Object
Ref.
V(l,O)b
I1Ve
V-J
J-H
H-K
K-L
V-N
11 10
J2 Europa (L)
J2 Europa (T)
13 Ganymede (L)
J3 Ganymede (T)
J4 Callisto
S2 Enceladus
S3 Tethys
S4Dione
S5Rhea
S6 Titan
S8 Iapetus (L)
S8 Iapetus (T)
Ul Ariel
U2Umbriei
U3 Titania
U40beron
[1-4]
[1-5]
[1-5]
[1-5]
[1-5]
[1-5]
-1.68
-1.37
0.15
0.3
5.69
10.26
142e
0.13
0.5
0.1
0.3
0.2
0.0
0.00
-2.24
-2.35
-1.90
-1.44
-1.01
< -0.5
130e
-0.95
1.9
0.7
0.88
0.1
-1.3
2.4
0.6
1.7
2.4
1.3
1.6
0.08
-0.35
-0.53
-0.08
-0.07
0.07
-0.24
-0.16
-0.12
-0.24
-0.38
0.05
-0.13
-0.04
-0.09
-0.14
-0.14
9.29
8.81
0.15
0.35
-0.31
-0.37
-0.10
-0.07
-0.27
-0.05
-0.20
-0.20
-0.05
-0.31
0.4
-0.11
0.21
0.25
0.20
0.20
4.70
3.91
-2.08
1.3
1.2
1.4
1.0
7.26
11.72
152e
[6-8]
[4,6,7]
[4,6,7]
[4,5,8,9]
[4, 10--13]
[13-15]
[13-15]
[4, 16]
[7,9]
[4,7,9]
[7,9]
1.5
1.06
0.9
0.8
1.06
0.2
1.60
0.8
1.20
1.30
1.30
1.35
-1.6
-1.7
V-Q
8.5
6.3
10.4
10.0
10.4
T (K)d
137e
761
162 / 7
INFRARED ASTRONOMY
Table 7.14. (Continued.)
Object
Ref.
V(1,O)b t::..V c V-J
J-H
H-K
Nl Triton
Pluto, Charon
1 Ceres
2 Pallas
3 Juno
4 Vesta
[5,8, 17, 18]
[17, 19-21]
[22-28]
[22-28]
[22-28]
[22-28]
-1.0
-0.76
3.72
4.45
5.73
3.55
1.3
1.3
1.2
1.2
0.31
-0.01
0.31
0.21
1.4
0.17
-0.24
-0.36
0.05
0.04
0.05
0.01
0.30
0.04
0.16
0.22
0.12
K-L
V-N V-Q
10.0
9.9
8.7
8.4
> 8.2
> 9.9
12.8
12.4
12.0
11.2
T (K)d
38d
558
245 h
270h
230h
250h
Notes
a Average magnitude given unless indicated otherwise; (L) = leading hemisphere, (T) = trailing hemisphere.
Approximate filter wavelengths: V (0.55 ~m), J (1.25 ~m), H (1.65 ~m), K (2.2 ~m), L (3.45 ~m), N (10 ~m), Q
(20 ~m); see references for details.
bV(1,O) absolute visual magnitude at a distance of 1 AU from the Earth and 1 AU from the Sun at 0° phase angle.
The apparent visual magnitude of an object is V(r, t::.., a) = V(I, 0) + Ca + 5Iog(rt::..), where r is the heliocentric distance
and t::.. is the geocentric distance (both in AU), C is the phase coefficent in mag deg- 1, and a is the phase angle (deg). The
opposition effect, occurring when a ~ 0°, is not included in this table.
c t::.. V
visual light curve amplitude (peak to peak).
d TB = brightness temperature; TS = surface or subsolar temperature.
=
=
eTB (lO~m).
f TB (100 ~m).
8TB (60~m).
hTS (10 ~m).
RefereDc:es
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7.10
STARS
I
163
7.10 STARS
Molecular features seen in cool stars are listed in Table 7.15.
1Bb1e 7.15. Molecular bands in cool stars [1, 2].
Wavelength
range (ILm)
Selected references
dv
dv
1.5-4.7
1.7-2.5
1.3-3.6
[3,4.5.6.7.8.9]
[3]
[10. II]
CN
C2
A 2n_x2E
b I n,,-x I E+ (Phillips)
A' 3Eg -X' fn" (Ballik-Ramsey)
<4
<2.5
[3.4.6. 12. 13. 14. 15]
[3. 6. 14. 16]
C3,CS
II]
4-5
2-5.7.1.14
2.5-4.14
4-4.2. 8.0-8.3
1.6-2.0.3.1-4.0
3.3-4.0
3.8-4.0
[12. 17, 18]
[13. 15. 16. 19]
[13. 16. 19]
[9.20.21.22.23]
[8.22.24]
[3.22]
[22.23]
Molecule
Bands
CO
H2
H2O
= 1,2,3
= I (quadrapole vib-rot)
11]. 2V2. V2 + II] - V2.
V2 + 11], VI + V2
HCN
C2H2
SiO
OH
CH
CS
V2. 11], 2V2. 3V2. 2VI
11]. vs. VI + Vs
dv = 1.2
dv = 1.2
dv= 1
dv=2
+ V2
References
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For the spectrophotometry of standard stars, see [99-102].
For the infrared star count models, see [103-105].
Useful catalogs are found in [106--109].
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see [119-124].
Figure 7.6 shows the color-color diagram for stars.
164 / 7
INFRARED ASTRONOMY
/
1.5
J:
I
..., 1.0
0.5
0.0
7.11
7.11.1
0.5
H-K
1.0
1.5
Figure 7.6. Color-color diagram for various classes
of stars, adapted from [17]. The dark line indicates
the location of G5 to M6 main sequence dwarf and
giant stars. The dashed lines indicate the boundary
for most carbon-rich stars; the carbon long-period
variable (LPV) stars lie to the right. The oxygenrich (M type) LPV stars fall within the boundary
of the solid line, and the LPV stars with periods
greater than 350 days are to the right and overlap
the carbon-rich LPV stars. The supergiant M stars
(SG) lie in a region below and to the right of the
giant sequence. The arrow indicates the direction of
the interstellar reddening.
EXTRAGALACTIC OBJECTS
Energy Distributions and Colors
Infrared energy distributions of galaxies vary widely. Representative examples may be found
in [125,126]. At least five different physical causes have been identified for the continuum infrared
emission from galaxies:
(a) Photospheric emission from evolved stars (usually dominant in the 1-3 /Lm region) [127, 128]: Mean colors of elliptical galaxies (CIT photometric system): V -K = 3.33 mag; J-H
= 0.69 mag; H-K = 0.21 mag. Molecular absorption bands in elliptical galaxies H20 (1.95 /Lm) =
0.12 mag; CO (2.3 /Lm) =0.16 mag. For additional near-infrared colors, see [129-132].
(b) Dust shells around evolved stars [133]: This is the main cause of 10-12 /Lm emission in
elliptical galaxies, for which /v(l2 /Lm) =0.13/v(2.2 /Lm). Units of /v are Jy.
(c) Emission from interstellar dust [134,135]: Transiently heated "small" grains dominate at about
10 /Lm; "large" grains in thermal equilibrium dominate at 50-100 /Lm. A typical energy distribution
from dust emission in a starburst galaxy normalized to 60 /Lm is /v(l2 /Lm)
=0.035; /v(25 /Lm) =0.18; /v(60 /LID) = 1.0; /v(loo /Lm) = 1.41 [136].
(d) Seyfert nucleus: Seyfert galaxies exhibit infrared emission from dust heated by the central
source, as well as emission from starburst or nonthermal components. Seyfert galaxies tend to be most
prominent at 60 /Lm, but energy distributions vary widely. The IRAS 25-60 /Lm spectral slope has
been found useful for selecting Seyfert galaxies [137, 138].
(e) Blazar component: Nonthermal, approximately power-law emission (fv oc va). Mean values
are a(1 /Lm) = -1.42 ± 0.95; a(10 /Lm) = -1.12 ± 0.47; a(loo /Lm) = -0.88 ± 0.43;
a(l mm) = -0.18 ± 0.42 [139].
For far-infrared colors of extragalactic objects, see [125, 140-143].
7.11 EXTRAGALACTIC OBJECTS /
7.11.2
165
Statistics of Galaxies at Infrared Wavelengths
Galaxy number counts at 2.2 ILIn. The number of galaxies per square degree per magnitude is [144]:
dN /dK
where a
=0.67 for 10 <
K < 17, a
= 4000 x
lOa(K-l7),
=0.26 for 17 <
Luminosity function at 60 /-Lm [125,145],
magnitude interval at 60 /-Lm is
K < 23, and K = 2.2 /-Lmmag.
The density of galaxies per cubic megaparsec per
log(p) = -3.2 - a (log[vLv(60 /Lm)] - 1O.2},
=
=
where vLv(60 /-Lm) is given in units of L 0 , and a 0.8 for 10g[vLv(60 /Lm)] < 10.2 and a
2.0 for
10g[vLv(60 /Lm)] > 10.2. Ho is assumed to be 75 Ian s-1 Mpc-l.
The total infrared energy output of the local universe from 8 to 1000 /-Lm is 1.24 x
108 L0 Mpc- 3 [146],
ACKNOWLEDGMENTS
Many people have helped with their comments and suggestions. I thank in particular the following
persons for valuable comments and contributions to this chapter: E. Beckiin, M. Cohen, D. Cruikshank,
M. Hanner, T. Herter, J. Hora, E. Hu, T. Geballe, I. Glass, R. Knacke, S. Leggett, P. Lena, C. Lonsdale,
S. Lord, J. Mazzarella, J. Pipher, S. Ridgway, K. Robertson, P. Roche, K. Sellgren, M. Simon, G.
Veeder, M. Werner, G. Wynn-Williams, W. Vacca, and D. Van Buren.
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on the Galactic Ecosystem: From Gas to Stars to Dust,
edited by M.R. Haas et aI., ASP Conf. Ser. No. 73,
p. 121
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Impey, C.D., & Neugebauer, G. 1988, AI, 95, 307
Soifer, B.T. et aI. 1989, AI, 98, 766
Mazzarella, I.M. et aI. 1991, AI, 101,2034
Cohen, M. 1992, AI, 103,1734
Walker, H.I. et aI. 1989, AI, 98, 2163
Gardner, I.P. et aI. 1993, ApI, 415, L9
Soifer, B.T. et aI. 1987, ApI, 320, 238
Soifer, B.T., & Neugebauer, G. 1991, AI, 101, 354
Chapter 8
Ultraviolet Astronomy
Terry J. Teays
8.1
8.1
Ultraviolet Wavelengths . . . . . . . . . . . . . . . . .
169
8.2
Ultraviolet Astronomy Satellite Missions . . . . . ..
170
8.3
Significant Atlases and Catalogs . . . . . . . . . . . .
172
8.4
Interstellar Extinction in the Ultraviolet . . . . . . ..
174
8.5
Commonly Observed Ultraviolet Emission Lines ..
175
8.6
Ultraviolet Spectral Classification. . . . . . . . . . ..
178
8.7
Ultraviolet Spectrophotometric Standards. . . . . ..
180
ULTRAVIOLET WAVELENGTHS
The Earth's atmosphere is an efficient absorber of ultraviolet radiation, and so astronomical observations in this wavelength regime are pretty well limited to space-based instruments. As such, I adopt the
nomenclature that "ultraviolet" refers to the wavelengths in the region from the atmospheric cutoff at
~ 3200 A down to 100 A. (The tenns ''far ultraviolet" and "extreme ultraviolet" are frequently used to
refer to the shorter end of the ultraviolet wavelength range, but the usage has not been consistent in the
literature. Generally one thinks of the far ultraviolet as referring to wavelengths shorter than that of the
Lyman limit at 912 A, and the extreme ultraviolet as being the region between 912 and 100 A.) Note
that wavelengths given in this chapter will always be vacuum ones. In the past ultraviolet wavelengths
shorter than 2000 A were expressed as vacuum values, while those longward of this were given with
regard to wavelengths in air. This convention has been continued in the International Ultraviolet Explorer (IUE) Project, but is currently being changed in their newest pipeline processing system, and
eventually the entire archive will make use of only vacuum wavelengths. Newer missions such as the
Hubble Space Telescope (HST) and Extreme Ultraviolet Explorer (EUVE) are using vacuum wavelengths exclusively. This practice conforms to Resolution C15 of the 21st General Assembly of the
International Astronomical Union. Equation (8.1) is the algorithm for calculating the index of refrac169
170 I
8
ULTRAVIOLET ASTRONOMY
tion (n) of standard air as a function of vacuum wavelength. This algorithm was derived by Edlen [1],
and was the one officially adopted by the International Astronomical Union (IAU) [2]. The wavelength
in air is the vacuum wavelength divided by the index of refraction:
-5
n = 1 + 6.4328 x 10
+
2.94981 x 10-2
146 x 108 _ (T2
2554.0 x 10-4
x 108 _ (T2 '
+ 41
(8.1)
where (T represents the wave number in vacuum, expressed in reciprocal A.
8.2
ULTRAVIOLET ASTRONOMY SATELLITE MISSIONS
There have been numerous balloon and rocket flights devoted to ultraviolet astronomy, as well as
various short-term studies, such as those conducted from manned space missions. The first ultraviolet
spectrum of the Sun was obtained in 1946 using a captured V2 rocket, while the first stellar ultraviolet
observations took place during 1955-1957. The first stellar ultraviolet spectrophotometry, by Stecher
and Milligan [3], was accomplished by a rocket-borne instrument, while the first ultraviolet stellar
spectroscopy (i.e., wavelength resolution sufficient to resolve individual spectral lines) was achieved in
a 1965 rocket flight [4]. A balloon-borne stellar spectrograph first examined the very important Mg II
resonance doublet in 1971 [5]. The principal long-term ultraviolet astronomy missions are summarized
in Table 8.1. Note that the extensive number of missions that have been devoted to ultraviolet solar
studies have not been included in the table. The first column in Table 8.1 gives the mission's name
or acronym. OAO-2 stands for the second satellite in the Orbiting Astronomical Observatory series
(the first having failed). It was the first instrument to carry out an extensive survey of the ultraviolet
sky. The fourth satellite in this series was named Copernicus. It made substantial contributions to
our understanding of the interstellar medium, hot stars, and stellar chromospheres. The lU-I mission
(named after the launch vehicle-a Thor Delta) was a European Space Agency (ESA) mission which
had two ultraviolet experiments on board, including the S2/68 Ultraviolet Sky Survey Telescope. lUI's primary legacy is the catalog of ultraviolet fluxes, which is cited in Table 8.2. ANS, the Astronomy
Netherlands Satellite, had one ultraviolet experiment. Though well known for their spectacular success
in planetary encounter missions, each of the two Voyager spacecraft have an ultraviolet spectrometer
(UVS) that has been used for stellar spectroscopy, now that the primary mission objectives are
completed. IUE, the International Ultraviolet Explorer, was a joint project of NASA, ESA, and the
British SERC. It was originally intended for a three-year mission, but it continued to operate for over
18 years. One of the first major international satellites, IUE was operated in real-time from NASA's
Goddard Space Flight Center for 16 hours per day, and from the ESA tracking station near Madrid
for the remaining 8 hours. It is in an eccentric geosynchronous orbit. RiJntgensatellit (ROSAT) is
primarily an X-ray mission, but it has a wide field camera which operates in the ultraviolet wavelength
range and has been used to produce an all-sky survey. The Hubble Space Telescope contains a battery
of instruments, most with a number of configurations, which operate at ultraviolet wavelengths. For
example, the Goddard High Resolution Spectrograph (GHRS) had a number of gratings and echelle
cross-dispersers, which have not been detailed specifically in the table, rather representative ranges
have been listed. These instruments, referred to by their acronyms in Table 8.1, are the GHRS, Faint
Object Spectrograph (FOS), Wide FieldIPlanetary Camera (WFIPC), Faint Object Camera (FOC), High
Speed Photometer (HSP), and the Space Telescope Imaging Spectrograph (STIS).
8.2 ULTRAVIOLET ASTRONOMY SATELLITE MISSIONS I
171
Table 8.1. Major long-term ultraviolet astronomy missions.
Spect.
resol.
Tel.
apert.
Mission
Operational
dates
(cm)
Instrument
OA0-2
I 2J07/68-211 3173
20
20
20
20
20
20
40
30
30
30
30
Photometer
Photometer
Photometer·
Photometer
Photometer
Photometer
Nebular photometer
Vidicon
Vidicon
Vidicon
Vidicon
Spectrometer
Spectrometer
Copernicus
TD-I
8121172-12131180
3/12172-1/9/80
80
27.5
Spectrometer
Spectrometer
Spectrometer
Spectrometer
A (A)
(A)
1430
Reference
[1]
1550
1910
2460
2980
3320
I 200-4 000
1850-3600
1160-1850
12
22
912-1500
0.05
912-1645
1640-3185
1480-3275
0.2
0.01
0.04
Photometer
Spectrophotometer
2740
[2]
[3]
1350-2550
ANS
8/30174-6/14177
22
Photometer
Photometer
Photometer
Photometer
Photometer
ISSO
1800
2200
2500
3300
WE
1/26/78-9/30/96
45
Echelle spectrograph
Spectrograph
1145-3230
1150-3300
0.2
6
[5.6]
HST
4/24/90-
240
OHRS
FOS
WFIPC
1110-3200
1150-7000
I 200-10000
1200-6500
I 150-8000
I 150-10 000
0.01-3.5
1.2-7
[7]
FOe
HSP
STIS
ROSAT
EUVE
6/1190-
6/7/92-
aa
aa
aa
aa
IIf
aa
aa
Wide field camera
Wide field camera
Wide field camera
Wide field camera
Scanning photometer
Scanning photometer
Scanning photometer
Deep survey
Spectrometer
Spectrometer
Spectrometer
[4]
[8]
60-140
112-200
150-220
530-720
[9]
44-360
44-360
400-750
40-385
70-190
140-380
280-760
0.5
1
2
Note
a See text for aperture discussion.
References
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ULTRAVIOLET ASTRONOMY
Wesselius, P.R., van Duinen, RJ., de Jonge, A.R.W., Aalders, J.W.G., Luinge, W., & Wildeman, K.J. 1982, A&AS, 49, 427
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Bowyer (pergamon, New York), p. 409
9. EUVE Guest Observer Center 1992, EUVE Guest Observer Program Handbook (Appendix G of NASA NRA 92-0SS-5)
4.
5.
6.
7.
This configuration will change as a result of servicing missions for HST. The Extreme Ultraviolet
Explorer (EUVE) is still in opemtion at the time of writing. The ROSAT and EUVE missions provided
the first extensive and detailed look at this wavelength regime. HST and EUVE are in low-Earth orbits.
Column 2 of Table 8.1 gives the mission's opemtional dates (the first date is the launch date, and so
science opemtions will have begun somewhat later). Column 3 gives, when applicable, the size of
the telescope objective (in cm) for the satellite or specific instrument. The notation "a" is used for
the ROSAT and EUVE instruments to indicate that the matter of aperture is not as stmightforward
in the case of those instruments. They make use of various types of segmented filter masks which
allow a given instrument to make use of a specific fraction of the aperture. Column 4 indicates
the type of instrument, and column 5 gives the experiment's wavelength range (for spectrogmphic
and spectrophotometric instruments) or the effective and/or centml wavelength (for photometric
instruments). Column 6 gives the approximate avemge spectml resolution (in A) for spectrographic
instruments. (This will, of course, vary with wavelength in each instrument, so the entries in column 6
are intended to be representative only.) Finally, column 7 lists a representative reference which gives
information about the mission.
8.3
SIGNIFICANT ATLASES AND CATALOGS
Table 8.2 gives titles and references for some of the more important catalogs and atlases of ultraviolet
astronomical data.
Table 8.2. Important atloses and catalogs of ultraviolet data.
The Variation of Galactic Interstellar Extinction in the Ultraviolet [1]
Atlas of the Wavelength Dependence of Ultraviolet Extinction in the Galaxy [2]
IUE-ULDA Access Guide No.2: Comets [3]
ANS Ultraviolet Photometry, Catalogue of Point Sources [4]
An Atlas of Extreme Ultraviolet Explorer (EUVE) Sources [5]
IUE Low-Dispersion Spectra Reference Atlas. Part 1. Normal Stars [6]
IUE Ultraviolet Spectral Atlas of Selected Astronomical Objects [7]
Ultraviolet Bright-Star Spectrophotometric Catalogue [8]
Supplement to the Ultraviolet Bright-Star Spectrophotometric Catalogue [9]
Catalogue of Stellar Ultraviolet Fluxes [10]
Ultraviolet Photometry from the Orbiting Astronomical Observatory. XXXII. An Atlas of Ultraviolet
Stellar Spectra [11]
IUE Ultraviolet Spectral Atlas [12]
IUE Ultraviolet Spectral Atlas [13]
The Extreme Ultraviolet Explorer Stellar Spectral Atlas [14]
Spectral Synthesis in the Ultraviolet. I. Far-Ultraviolet Stellar Library [15]
An Atlas of High Resolution IUE Ultraviolet Spectra of 14 Wolf-Rayet Stars [16]
The Hopkins Ultraviolet Telescope Far-Ultraviolet Spectral Atlas ofWolf-Rayet Stars [17]
International Ultraviolet Explorer Atlas of 0 Type Spectra from 1200 to 1900 A [18]
Ultraviolet Spectral Morphology of the 0 Stars. ll. The Main Sequence [19]
P Cygni and Related Profiles in the Ultraviolet Spectra of O-Stars [20]
8.3 SIGNIFICANT ATLASES AND CATALOGS /
Table 8.2. (Continued.)
An Atlas of Ultraviolet P Cygni Profiles [21]
Identification of Lines in the Satellite Ultraviolet: The Spectrum of Tau Scorpii [22]
Spectral Classification with the International Ultraviolet Explorer: An Atlas of B-Type Spectra [23]
The IUE Spectral Atlas of1\vo Normal B Stars: 1r Ceti and v Capricorni (l25-198nm) [24]
Identification Lists of the Far UV Spectra of 7 Solar Chemical Composition Main Sequence Stars in the
Spectral Range B2-B9.5 [25]
A Catalog of 0.2 AResolution Far-Ultraviolet Stellar Spectra Measured with Copernicus [26]
The Copernicus Ultraviolet Spectral Atlas of Vega [27]
The Copernicus Ultraviolet Spectral Atlas of Sirius [28]
Early Type Strong Emission-Line Supergiants of the Magellanic Clouds: A Spectroscopic Zoology [29]
Chromospheric Mg II Emission in A5 to K5 Main Sequence Stars from High Resolution IUE Spectra [30]
Atlas of High Resolution IUE Spectra of Late-Type Stars. 2500-3230 A[31]
The Spectra of Late-Type Dwarfs and Sub-Dwarfs in the Near Ultraviolet. I. Line Identifications [32]
Outer Atmospheres of Cool Stars. VII. High Resolution Absolute Flux Profiles of the Mg II h and k Lines
in Stars of Spectral Types F8 to M5 [33]
UV Fluxes of Pop II Stars [34]
IUE Low Dispersion Observations of Symbiotic Objects [35]
A Far-Ultraviolet Atlas of Symbiotic Stars Observed with IUE. I. The SWP Range [36]
A Spectrophotometric Atlas of White Dwarfs Compiled from the IUE Archives [37]
Ultraviolet Observations of Cataclysmic Variables: The IUE Archive [38]
A Catalogue of Low-Resolution IUE Spectra of Dwarf Novae and Nova-Like Stars [39]
An Atlas of UV Spectra of Supernovae [40]
UV Observations of SN 1987a [41]
International Ultraviolet Explorer Atlas of Planetary Nebulae. Central Stars. and Related Objects [42]
UV Spectra of the Central Stars of Large Planetary Nebulae [43]
A Survey of Ultraviolet Interstellar Absorption Lines [44]
Galactic Interstellar Abundance Surveys with IUE. II. The Equivalent Widths & Column Densities [45]
An Ultraviolet Spectral Atlas of Interstellar Lines toward SN 1987a [46]
IUE UV Spectra of Extra Galactic H II Regions. I. The Catalogue & the Atlas [47]
UV Observations by IUE of 31 Clusters of the LMC [48]
IUE-ULDA Access Guide No.3: Normal Galaxies [49]
An Atlas of Hubble Space Telescope Ultraviolet Images of Nearby Galaxies [50]
An Atlas of Ultraviolet Spectra of Star-Forming Galaxies [51]
IUE-ULDA Access Guide No.4: Active Galactic Nuclei [52]
The Ultraviolet Variability of Seyfert I Galaxies [53]
An Ultraviolet Atlas of Quasar and Blazar Spectra [54]
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195
3. Festou. M.C. 1990. IUE-ULDA Access Guide No.2: Comets (ESA SP-I134)
4. Wesselius. P.R .• van Duinen. R.J .• de Jonge. A.R.W.• Aalders. J.W.G .• Luinge. W.• & Wildeman. K.J.
1982. A &AS. 49.427
5. Shara, M.M .• Bergeron. I.E .• Christian. C.A .• Craig. N .• & Bowyer. S. 1997. PASP.I09. 998
6. Heck. A. 1987. in Exploring the Universe with the WE Satellite. edited by Y. Kondo (Reidel. Dordrecht)
p. 121
7. Wu. C.-C. et al. 1992. IUE Ultraviolet Spectral Atlas of Selected Astronomical Objects. NASA Tech.
Memo. No. 1285
8. Jamar. C .• Macau-Hercot, D .• Monfils. A .• Thompson. G.I .• Houziaux. L.. & Wilson. R. 1976. Ultraviolet
Bright-Star Spectrophotometric Catalogue (ESA. Paris)
9. Macau-Hercot, D .• Jamar. C .• Monfils. A .• Thompson. G.I .• Houziaux. L.. & Wilson. R. 1978. Supplement
to the Ultraviolet Bright-Star Spectrophotometric Catalogue (ESA. Paris)
10. Thompson. G.I.• Nandy. K.. Jamar. D .• Monfils. A.. Houziaux. L.. Camochan. D.J .• & Wilson. R. 1978.
Catalogue of Stellar Ultraviolet Fluxes (Science Research Council. London)
II. Code. A.D .• & Meade. M.R. 1979. ApJS. 39. 195
12. Wu. C.-C. et al. 1983. NASA WE Newslett.• 22. I
13. Wu. C.-C. et al. 1991. NASA WE Newslett.• 43. I
14. Craig. N .• Abbott M .• Finley. D .• Jessop. H .• Howell. S.B.. Mathioudakis. M .• Sommers. J .• Vallerga, J.V.•
& Malina, R.E 1997. ApJS. 113. 131
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15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
8.4
ULTRAVIOLET ASTRONOMY
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Willis, A.J., van der Hucht, KA., Conti, P.S., & Garmany, D. 1986,A&AS, 43, 417
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Walborn, N.R., & Panek, R.J. 1984, ApJ, 286, 718
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Ramella, M., Castelli, E, Malagnini, M.L., Morossi, C., & Pasian, E 1987, A&AS, 69,1
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Rogerson, J.B. 1989, ApJS, 71, 1011
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La Dous, C. 1990, Space Sci. Rev., 52, 203
Benvenuti, P., Sanz Fernandez de Cordoba, L., Wamsteker, W., Macchetto, E, Palumbo, G.e., & Panagia,
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Kirschner, R.P., Sonneborn, G., Crenshaw, D.M., & Nassiopoulos, G.E. 1987,ApJ, 320, 602
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INTERSTELLAR EXTINCTION IN THE ULTRAVIOLET
Since interstellar extinction is significantly stronger in the ultraviolet than at visual wavelengths,
correcting for its effects is very important. The most prominent feature in the ultraviolet extinction
curves is a broad peak centered at ~ 2 175 A.
Equation (S.2) [6] gives some useful analytic functions which can be used to determine AJ.. in the
ultraviolet. Equation (S.2) is broken into three wavelength domains, and is parametrized in terms of a ,
the wave number expressed in microns:
2.70
~
a
~
3.65,
AJ../EB-V
= 1.56 + I.04Sa + [(a _
1.01
4.60)2 + 0.2S0],
(S.2a)
8.5 COMMONLY OBSERVED ULTRAVIOLET EMISSION LINES /
3.65::: a ::: 7.14,
AA/EB-V
= 2.29 + O.848a + [(a
7.14::: a ::: 10,
AA/EB-v
= 16.17 -
3.20a
1.01
_ 4.60)2
+ 0.280]'
+ 0.2975a 2 •
175
(8.2b)
(8.2c)
Savage and Mathis [7] adopt 3.1 for the value of Av /E(R-v), while Seaton [6] uses 3.2. More detailed
information is available in the review by Savage and Mathis [7], and additional references concerning
ultraviolet extinction as a function of location in the sky are cited in Table 8.2.
8.S
COMMONLY OBSERVED ULTRAVIOLET EMISSION LINES
Table 8.3 (which is an expanded version of one given in Wu et al. [8]) gives a list of some of the more
prominent ultraviolet emission lines observed in astronomical objects. The organization of Table 8.3
is as follows. Column 1 gives the wavelength (in A) of the line, using the convention that a reasonably
precise value (to 0.01 A) is given for single lines, while an approximate value is given for lines formed
of closely spaced individual lines of a given element. This value corresponds to the approximate
location of the (blended) line which would be seen in low-resolution spectra, such as those taken in
IUE's low-dispersion mode. In cases where there is a spectral region which contains a large number
of lines due to a single element, then the range of wavelengths is given in column 1. In the cases of
multiple lines, column 4 gives more accurate wavelengths for the individual components that may be
present. Column 2 specifies the ion which is the source of the emission line, while column 3 lists the
type of objects in which this emission line is generally observed. The abbreviations used in column 3
to specify object type are given at the bottom of Table 8.3.
Table 8.3. Emission lines commonly found in ultraviolet spectra.
A (A)O
Ion
lYpe of object where observed b
Individual components in multiplets
538
584.33
834
916
On
Hel
Om
Nn
C
SSO
C
C
537.83,538.26,538.32,539.13
933.4
977.02
1033
1066.66
1085
SVI
Cm
OIV
Arl
Nn
SNR
SNR
SNR
SSO,C
C
1175
Cm
WR, PN, CS, SS
1199
Sm
SSO
1215.67
1240
HI
Nv
1247.38
1256
1279
Cm
Sn
CI
(all sources)
PN, SS, WR, CV, XRB, SN, m,
N,SQ,SNR
SS,WR
SSO
TI,LTS
1299
1304
1309
Si m
01
Si n
sS,m, TI
RS, LTS, N, SQ, C
PN
832.93,833.74,835.29
915.61,915.96,916.02,916.10,916.35,
916.70,916.71
1031.93, 1033.82, 1037.62
1083.99, 1 084.56, 1 084.58, 1085.53,
1085.55, 1085.70, 1085.12
1174.93,1175.26,1175.59,1175.71,
1 175.99, 1 176.37
1190.21, 1194.06, 1194.46, 1197.56,
1200.97,1201.73,1202.13
1 238.82, 1 240.15, 1 242.80
1250.58, 1253.81, 1256.12, 1259.52
1276.48, 1276.75, 1277.19, 1277.25,
1277.28, 1277.46, 1277.51, 1277.55,
1277.72, 1277.95, 1279.06, 1279.23,
1279.50, 1279.89, 1280.14, 1280.33,
1 280.36, 1 280.40, 1 280.60, 1 280.85
1 298.89, 1 298.96
1302.17,1303.49,1304.86,1306.03
1304.37, 1307.64, 1309.28
176 I
8
ULTRAVIOLET ASTRONOMY
Table 8.3. (ContinuetL)
A (A)a
Ion
'IYPe of object where observed b
Individual components in multiplets
1335
CII
1334.53. 1335.31. 1335.66. 1335.71
1342
1371.29
1394
OIV
Ov
SiIV
TI. PN. LTS. RS. WR, ev. N.
SNR.C
CS. SS. WR. XRB
1397-1407
OIV
1402.77
Si IV
1460
CI
PN. LTS. RS. TT. XRB. CV. IV.
N.SQ
TI
1473
SI
RS.LTS
1483.32
1486
1487
1550
NIV
SI
NIV
CIV
~.SS.WR.N
1561
CI
1574.77
1577
1602
1640
Nev
CIll
Nelv
Hell
1641.31
1657
01
1663
o III
1670.79
1710
1718.55
1728.94
1750
AlII
Sill
NIV
SIll
NIll
1760
1815
1814.63
1860
1882.71
1892.03
CII
Si II
NellI
AlIll
Si III
Si III
1900.29
1908.73
SI
CIll
1914.70
1993.62
2321.67
2326
SI
CI
LTS.m
~. LTS.mI. SN. N. SQ. SNR
TI. PN. LTS. mI. SN. N. SQ.
SNR
RS. LTS. SN.mI
TI. PN. LTS. WR. mI. N. SN.
SQ.ELG
RS.LTS
RS.LTS
CII
RS.LTS.SQ
CI
o III
1342.99. 1343.51
~.CS.SS.XRB.SNR
~. LTS. RS. TT. XRB. ev.lV.
N.SQ
PN.SS.N
RS.LTS
PN. SS. WR. N. SNR
TI. PN. LTS. SS. N. WR. CV. m.
XRB. SQ. SNR
C
1393.76.1396.75.1398.13
1397.23. 1399.78. 1401.16. 1404.81.
1407.38
1459.03. 1463.34. 1467.40. 1467.88.
1468.41
1472.97. 1473.02. 1473.01. 1473.99.
1474.38. 1474.57. 1478.50
1485.62. 1487.15
1 486.50. 1 487.89
1548.20.1550.77
1560.31. 1560.68. 1560.71. 1561.05.
1561.34. 1561.37. 1561.44
~.N
SS
~.N.SS
TT. PN. LTS. RS. WR. XRB. SQ.
SNR
RS. LTS. SS. N
C. RS. LTS. TT
1576.48. 1577.30. 1577.89
1 601.50. 1601.68
1640.47. 1640.49
~.
1656.28. 1656.93. 1657.01. 1657.38.
1657.59. 1657.91. 1658.12
1660.81. 1666.15
~.WR
1710.83. 1711.30
WR. SQ. N. LTS.mI. SS.
SNR
m.LTS
PN. WR. XRB. CV. N
SSO
WR. TT. mI. N. SN. SNR
~
TT. PN. RS. LTS
1746.82. 1748.65. 1749.67. 1752.16.
1754.00
1760.47. 1760.82
1808.01. 1816.93. 1817.45
~.N
1 854.72. 1862.79
1906.68. 1908.73. 1909.60
~
2324.21.2325.40.2326.11.2327.65.
2328.84
8.5 COMMONLY OBSERVED ULTRAVIOLET EMISSION LINES /
177
Table 8.3. (Continued.)
Ion
Type of object where observed b
Individual components in multiplets
2328-2414
Fe II
LTS. IT
2328.11.2333.52.2338.73.2344.21.
2344.70.2345.00.2349.02.2359.83.
2365.55.2367.59.2374.46.2381.49.
2382.77.2383.79.2389.36.2394.98.
2396.15.2396.36.2399.97.2405.16.
2405.62.2407.39.2411.25.2411.80.
2414.05
2329.23
2335
2381.13
2424
2471.04
2511.96
2586-2632
Sill
Si II
He II
Ne IV
all
He II
Fe II
RS.LTS
PN
PN
SQ
PN. SN.HIl
PN
LTS. IT. N. MSG
2664.06
2696.92
2724.00
2734.14
2764.62
2783.03
2786.81
2794
2800
Hel
He I
Hel
Hel
Hel
Mgv
Arv
MgIl
MgIl
2829.91
2838
2852.96
2854.48
2869.00
2928.34
2933
2945.97
2950.07
2973.15
2978
3005.36
3024.33
3046
3068
3109
3133.77
3188.67
3204.03
Hel
CII
MgI
Arlv
Arlv
Mgv
MgIl
Hel
MnIl
PN
PN
PN
PN
PN.HIl
PN
PN
PN
PN. LTS. RS. IT.
ELG
PN.HIl
PN
PN.HIl
PN
PN
PN
PN
PN
PN.IT
C
PN
PN
PN
PN
PN
PN
PN. IT. N. LTS
PN
PN
01
NIII
ArIII
alII
am
NIl
ArIII
alII
Hel
He II
2335.12.2335.32.2344.92.2350.89
2422.51.2425.15
2586.65.2599.15.2600.17.2607.87.
2611.41.2612.65.2614.61.2618.40.
2621.19.2622.45,2626.45,2629.08,
2631.83, 2632.11
m. N. SQ.
2798.81,2791.59
2796.35. 2803.53
2837.54. 2838.44
2929.49,2937.36
2973.43,2979.70
3043.91,3048.02
3 063.72. 3071.44
3109.16,3110.06
Notes
aWavelengths (in vacuum) are taken from: Aller. L.H. 1984, Physics o/Thermal Gaseous Nebula (Reidel. Dordrecht);
Kelly. R.L. 1979, Atomic Emission Lines in the Near Ultraviolet; Hydrogen through Krypton. NASA Tech. Memo.
No. 80268; Kelly, R.L. 1987. Atomic and Ionic Spectrum Lines Below 2000 A: Hydrogen through Krypton (American
Chemical Society. New York); Kelly. R.L. & Palumbo. LJ. 1973, Atomic and Ionic Emission Lines Below 2000 Angstroms
(Naval Research Lab.• Washington. DC); Koppen. J.• & Aller. L.H. 1987. in Exploring the Universe with the IUE Satellite.
edited by Y. Kondo (Reidel. Dordrecht). p. 589; and Morton. D.C. 1991. ApJS. 77. 119.
bThe astronomical objects where these lines are frequently seen in emission are noted by the abbreviated code in
column 3. They are: C. comets; CS. carbon stars; CV. cataclysmic variables (N.B. novae have a separate listing); ELG.
emission line galaxies; HIl. H II regions; m. interacting binaries; LTS.late-type stars; MSG. massive supergiants; N. novae;
PN. planetary nebulae; RS. RS CVn stars; SQ. Seyfert galaxies and QSOs; SN. supernovae; SS. symbiotic stars; SSO. solar
system objects; IT. T Tau stars; WR. Wolf-Rayet stars; XRB. low-mass X-ray binaries.
178 / 8
8.6
ULTRAVIOLET ASTRONOMY
ULTRAVIOLET SPECTRAL CLASSIFICATION
Studies of spectral classification of 0 and B stars based on ultraviolet spectra have been made
using Copernicus data and the extensive IUE archive. Low-dispersion spectra were used by Heck
et al. [9], Heck [10], and laschek and laschek [11]. High-dispersion studies have been conducted
by Snow and Morton [12], Walborn and Panek [13], Walborn et al. [14], Walborn and NicholsBohlin [15], Massa [16], Bates and Gilheany [17], Prinja [18], and Rountree and Sonneborn [19]. For
detailed quantitative comparisons, the papers by Massa and Prinja are convenient, because they give
tables and/or figures which show the equivalent widths as a function of spectral type or temperature.
Prinja [18] gives two useful fonnulas relating equivalent widths (Wa) in rnA to effective temperature.
The most sensitive diagnostic for 0 stars temperatures is Si III A1299:
log(Wa )
= 17.89 -
3.43 log Teff.
(3)
For B stars, the Si II ),,1265 is the most sensitive temperature indicator [16]:
log(Wa )
= 20.57 -
4.21 log Teff.
(4)
The infonnation in Table 8.4 is taken from these studies. Table 8.4 gives the approximate
wavelength and identification for classification lines in its first two columns, and summarizes their
changing characteristics as a function of spectral type and luminosity in the final column. (More
accurate wavelengths can be found in Table 8.3.)
Table 8.4. Lines useful for spectral classification of 0 and B stars.
A (A)
Ion
Comments
1175
C
1216
HI
1240
Nv
1247
C
1255
1264
Fev
Si II
1 300
Si III
1310
Si II
1336
CII
1339
OIV
1371
Ov
In low dispersion this blend of six lines (U 1174.933-1176.370) is seen to increase from 04 to a
maximum at B I, and disappears at B6 into the Ly a wing. In high dispersion one can see dramatic P
Cygni profiles for all supergiants from 04 I-BO.5 Ia, for bright giants as late as 09.5, and for giants
as late as OS.
When not affected by interstellar or circumstellar components has a half-width at half-maximum
which increases from lO A at 09 to 100 A at BS.
AI.. 1239, 1243 show wind profiles in most 0 stars. Shows a dependence on luminosity at 09.5, since
the stellar wind effects have declined by then.
Blended with Fe II AI.. 1246.S, 1247.S, and can be severely affected by emission component of
NY J..l240 P Cygni lines in luminous stars. Generally increases in strength from early to late O.
Strongest in early B (BO-Bl), and then slowly declines. The ratio C III 1..1247/0 IV 1..1339 depends
on luminosity class, being higher for more luminous stars. This ratio can be as large as 4 between
supergiants and main-sequence stars at a given temperature (Prinja, R.K. 1990, MNRAS, 246, 392).
The comparison of this line with Si II 1..1265 shows a slight dependence on luminosity class (N.B.:
can be affected by a reseaux mark in high-dispersion IUE spectra).
Decreases from 03 to 07.
Becomes visible at Bl; at B1.5 it is clearly present but weaker than 1..1247; at B2 it is as strong
as J..l247; and by B4 it is much stronger. Continues to increase through B9. Does not show any
luminosity effect.
Probably the most sensitive diagnostic of 0 star temperatures. Increases sharply from 03 to B2, then
levels out in strength from B2 to B5.
Useful diagnostic in B stars. It is weaker than 1..1300 at B2, greater than or equal to 1300 at B3-B4,
and dominates the spectrum at B5-BS.
Doublet, which increases from BO to a maximum at BS. The wind profiles achieve maximum strength
at B I-B2 Ia. There is a very strong interstellar contribution to this line.
Shows a well-defined temperature sequence for luminosity classes I and V in 0 stars, decreasing as
temperature declines. Generally only the 1..1339 line is used in this doublet, since the J..l343 line is
blended with a nearby Si III line (as well as lying in an awkward location in IUE echelle spectra).
This line declines from 03 until it disappears at 07.
III
III
8.6 ULTRAVIOLET SPECTRAL CLASSIFICATION I
179
Table 8.4. (Continued.)
A (A)
Ion
Comments
1400
Si IV
1428
CIII
1430
1453
1485
1527
1533
1550
Fev
Blend
Si"
Si"
Si"
CIV
1608
Fe"
1640
He"
1655
1670
CI
AI"
1718
NIV
1723
AI"
1750
NIII
1859
Al III
1862
AI"
1891
Fe '"
1926
1967
Fe III
Fe III
Blend of the A1394 and AI403 lines of Si IV. In low-dispersion spectra this blended pair is a useful
luminosity indicator for late 0, and a spectral type discriminator for B. First strongly visible in lowdispersion spectra at 07, and gets stronger as surface gravity decreases. In high dispersion, at 06.5
lines display stellar wind effects which increase with luminosity, from none at V to a full P Cyg profile
at Ia. At 09.5 the doublet shows no stellar-wind effect in luminosity classes v-m, but it develops
gradually as a function of luminosity from classes II through Ia. In the B stars, Si IV is strong in BO
and Bl and decreases in strength until it disappears at about B6. The intensity ratio Si IV A1400/C IV
A1550 is very sensitive to the 0 star spectral type, being R:: 1 at 06, and greater than 1 for 06.5-09.7.
(In low dispersion the A1426 and A1428 lines are blended, though they are never especially strong.
They increase from 04 to a maximum at B1.) Especially fine discriminator in the 07-Bl region,
where it can be compared to A1430.
The ratio A1429/A1430 = 1 for this Fe v doublet between 03 and 04, and declines at 05 and later.
In low dispersion, has a maximum at 04 and disappears at BO.
Blend of three lines. First present at B2 and becomes stronger through B9.
Absorption feature becomes prominent in late B.
Absorption feature becomes prominent in late B.
Resonance doublet is one of the most prominent UV lines. Strong in 0 stars, decreasing from 03 to
B2 (in dwarfs) where it disappears. If seen in mid-B, indicates a supergiant. Saturated P Cyg profiles
from 03-06, declining at 07. Continues to show strong wind absorption through 09, becoming
purely photospheric at B1. At the transition type 09.5 there is an increase in strength with luminosity
class.
A large collection of Fe "lines exist in the AA 1~161O region. These blends increase in strength
with increasing luminosity, while showing little temperature effect. In 0 stars there is a noticeable
interstellar component.
Present throughout the 0 star regime, is still strong at BO, still noticeable, but declining in BO.5-B I,
weak at B 1.5, and weak to absent at B2.
Increases in strength as spectral type gets later. It is a prominent line in B5-B9.
Becomes prominent in late B (N.B.: there is frequently a strong interstellar line seen in 0 stars, due
to this ion).
Unsaturated subordinate line which shows P Cyg profiles through 06, then declines in strength with
increasingly later spectral type. It is still strong at BO, much less prominent at BO.5, and weak to
absent at B 1. At BO it is stronger in giants than dwarfs.
Blend. The components are at AA 1719.44, 1721.24, 1721.27, 1724.95, 1724.98. Line strength
increase with luminosity in B stars.
Doublet at AA 1748, 1752. The strength of both lines increases between 03 and 04, and the ratio
A1748/A1752 increases dramatically between 03 and 04. The pair remains distinct through BO, but
starts to weaken at BO.5, and disappears as B1.
Doublet at AA 1855, 1862. Purely interstellar in 0 stars. In B stars increases with increasing luminosity
class. There is a strong wind maximum at B 1-2 la.
Strong in 0 stars. Blended with A1855 in low-resolution spectra. Shows an increased strength with
increased luminosity class.
Present in early B stars. Shows a positive luminosity effect. There are many Fe III lines in this
wavelength region. The use of this line and others below is most generally useful in low-dispersion
spectra.
Similar to A1891.
Similar to A1891.
The ultraviolet is particularly suitable for classifying 0 and B stars, due to the strong fluxes for these
objects in that wavelength regime. Difficulties with classifying OB stars include the contamination of
some lines by strong interstellar components, and the fact that ultraviolet resonance lines are frequently
severely affected by stellar winds. Snow and Morton [12] found that all 0 and B supergiants exhibited
mass loss, with P Cygni profiles being seen to as late as B 1. For bright giants and giants, strong P
Cygni profiles were noted as late as 09.5 and 09, respectively, and all main-noted sequence 0 stars
showed evidence of mass loss. A further complication is that the wind profiles of some B supergiants
have been found to be variable. Exactly how much of the dispersion in wind line strengths is due to
variations in the intrinsic stellar properties, and how much is due to variability or abundance anomalies,
is uncertain [17, 20].
180 / 8
8.7
ULTRAVIOLET ASTRONOMY
ULTRAVIOLET SPECTROPHOTOMETRIC STANDARDS
Spectrophotometric calibration has always been a thorny problem for long-term ultraviolet satellite
missions. Early efforts tended to focus on using hot subdwarfs as reasonably line-free continuum
sources, which were not generally variable, and had very small or negligible interstellar reddening.
The current IUE absolute calibration is based on comparison with the earlier measurements of
some baseline standard stars made by OAO-2 and TO-I, and normalized to the flux values for the
fundamental calibration star, T/ UMa. The stars used were HD 60753, BD + 75° 325, HD 93521,
BD + 33° 2642, and BD + 28° 4211 for the low-dispersion data, while Cas, }.. Lep, and r Sco
were used for the high-dispersion data. It should be noted that both Cas and T/ UMa have shown
some indications of microvariability [21]. A more complete list of IUE standards can be found in [22],
while the HST standards are cited in [23]. More recently a shift has been made to using hot DA (i.e.,
essentially pure helium) white dwarfs as fundamental calibrators. The reasoning behind this is that
the models for these stars are very simple and well understood, as well as being unaffected by spectral
lines. The ruE' Project's Final Archive is making use of white dwarfs for their new absolute calibration.
The EUVE used this approach from the very beginning. The fundamental calibrator that is being used
is G19lB2B. Table 8.5 lists some of the ultraviolet standard stars that have been used in common by
many missions. Columns 1 and 2 give the star's catalog number and common name, while columns 3
and 4 list the star's coordinates. Columns 5 and 6 give the spectral type and visual magnitude, while
column 7 indicates which missions have observed this star for calibration purposes.
s
s
Table 8.5. Selected ultraviolet spectrophotometric standard stars.
CatalogID
Common name
HD 2151
HD3360
BPM 16274
Feige 11
HD 10144
HD 11636
HD 15318
GD50
HZ4
LB227
HZ2
Gl91B2B
HD32630
HD34816
HD35468
HD35580
HD38666
PG0549 + 158
HD45557
HD49798
HD60753
CD -310 4800
HD 61421
HD66811
BD+75° 325
HD 80007
AGK +81 0 266
BD +48 0 1777
HD87901
Feige 34
13 Hyi
~Cas
a Eri
f3Ari
~2 Cet
TJAur
ALep
yOri
Pic
JL Col
GD71
Ie
aCMi
~ Pup
13 Car
a Leo
a(2000)
8(2000)
Sp. Type
V
00:25:45.4
00:36:58.3
00:50:03.2
01:04:21.6
01:37:42.9
01:54:38.3
02:28:09.5
03:48:50.1
03:55:21.7
04:09:28.8
04:12:43.5
05:01:31.0
05:06:30.8
05:19:34.4
05:25:07.8
05:22:22:2
05:44:08.4
05:52:27.5
06:24:13.7
06:48:04.6
07:33:27.3
07:36:30.2
07:39:18.1
08:03:35.1
08:10:49.3
09:13:12.1
09:21:19.1
09:30:46.6
10:08:22.3
10:39:36.7
-77:15:16
+53:53:49
-52:08:17
+04:13:38
-57:14:12
+20:48:29
+08:27:36
-00:58:30
+09:47:19
+17:07:54.4
+11:51:50
+52:45:48
+41:14:04
-13:10:37
+06:20:59
-56:08:04
-32:19:27
+15:53:17
-60:16:52
-44:18:59
-50:35:04
-32:12:45
+05:13:30
-40:00:12
+74:57:58
-69:43:02
+81:43:29
+48:16:26
+11:58:02
+43:06:10
G2IV
B2IV
DA
BOVI
B3Vpe
A5V
B9m
DA
DA
DA
DA
DA
B3V
BO.5IV
B2m
B8-9V
09.5 IV
DA
AOV
sd06
B3IV
08 AI
F5 IV-V
05f
05p
A2IV
sdO
OVI
B7V
DO
2.80
3.68
14.2
12.06
0.46
2.64
4.29
14.06
14.52
15.34
13.86
11.78
3.17
4.29
1.64
6.11
5.17
13.04
5.80
8.30
6.69
10.50
0.38
2.26
9.54
1.68
11.92
10.37
1.35
11.18
Observed by"
H
OTAVI
H
OIH
OCTI
OTI
H
H
H
H
H
VllIE
OTAI
OTAI
OTI
TI
VIH
VIE
TI
VIH
TIH
AI
OCTAl
OCTVIH
OTAVIH
OTI
AIH
AI
OCTAVIH
VIH
8.7 ULTRAVIOLET SPECTROPHOTOMETRIC STANDARDS /
181
Table 8.5. (Continued.)
Catalog ID
HD93521
HD 100889
HD 103287
HZ21
PG 1254 + 223
HZ 44
Grw +70° 5824
HD 120315
HD 121263
HD 122451
HD 125924
HD 128801
HD 137389
HD 137744
BD +33°2642
HD 142669
HD 145454
0153-41
HD 149438
HD 149757
HD 155763
HD 164058
HD 172167
HD 172883
HD 177724
HD 186427
HD 196519
HD 197637
HD 201908
LDS749B
BD +28°4211
G93-48
HD209952
NGC7293
HD214680
HD 214923
PG2309+ 105
Feige 110
Common name
o Crt
yUMa
GD 153
TJUMa
s Cen
fJ Cen
lOra
p
Sco
r Sco
s Oph
s Dra
Y Ora
aLyr
s Aql
16 Cyg B
vPav
aGru
10 Lac
s Peg
GD246
a(2000)
10:48:23.5
11:36:40.8
11.53:49.8
12:13:56.4
12:57:04.5
13:23:35.4
13:38:51.8
13:47:32.4
13:55:32.3
14:03:49.5
14:22:43.0
14:38:48.1
15:22:37.1
15:24:55.7
15:51:59.9
15:56:53.0
16:06:19.5
16: 17:55.4
16:35:52.9
16:37:09.5
17:08:47.1
17:56:30.4
18:36:56.3
18:39:52.7
19:05:24.5
19:41:52.0
20:41:57.1
20:36:00.6
21:05:29.2
21:32:15.8
21:51:11.1
21:52:25.3
22:08:13.9
22:29:38.5
22:39:15.6
22:41:27.7
23:12:35.3
23:19:58.4
1YPe
8(2000)
Sp.
+37:34:13
-09:48:08
+53:41:41
+32:56:31
+22:12:45
+36:08:00
+70:17:09
+49:18:48
-47:17:18
-60:22:23
-08:14:54
+07:54:44
+62:02:50
+58:57:58
+32:56:55
-29:12:50
+67:48:36
-15:35:49
-28:12:58
-10:34:02
+65:42:53
+51:29:20
+38:47:01
+52:11:46
+13:51:48
+50:31:03
-66:45:39
+79:25:49
+78:07:35
+00:15:14
+28:51:52
+02:23:24
-46:57:40
-20:50:13
+39:03:01
+10:49:53
+10:50:27
-05:09:56
09Vp
B9.5 Vn
AOVe
00
DA
sdO
DA
B3V
B2.5 IV
Blm
B2IV
B9
AOpSi
K2m
B2IV
B2IV-V
AOVn
DA
BOV
09.5Vn
B6m
KSm
AOV
AOpHg
AOVn
G1.5 V
B9m
B3
B8Vn
DB
sdOp
DA
B7IV
PNN
09V
B8V
DA
DOp
V
7.04
4.70
2.44
14.68
13.4
11.66
12.77
1.86
2.55
0.61
9.70
8.80
5.98
3.29
10.81
3.88
5.44
13.42
2.82
2.56
3.17
2.22
0.03
6.00
2.99
6.20
5.15
6.78
5.91
14.67
10.51
12.74
1.74
13.51
4.88
3.40
13.10
11.82
Observed by"
TAVIH
IH
IH
H
VIE
VH
H
OCTVIH
OCTAl
H
TAl
TAl
TAl
H
OTAIH
OTAI
TI
VIH
OCTAVI
OCTVIH
OCTAl
H
OCTAVIH
TI
OTAI
IH
TAl
TI
on
H
OTAVIH
H
OCTI
VIH
OCTAl
H
!HE
H
Note
aObservations were made of these standards by many of the ultraviolet astronomy missions, and they
are listed in column 7, where the letters refer to 0 = OAO-2, C = Copernicus, T = TO-I, A = ANS,
V = Voyager UVS, I = ruE, H = HST, E = EUVE.
REFERENCES
Edlen, B. 1953, JOSA, 43, 339
Oosterhoff, P.T. 1957, Trans. IAU, 9, 202
Stecher, T.P., & Milligan, J.E. 1962, ApJ, 136, 1
Morton, D.C., & Spitzer, L. 1966, ApJ, 144, 1
Kondo, Y., Giuli, T., Modisette, J.L., & Rydgren, A.E.
1972,ApJ, 176, 153
6. Seaton, M.J. 1979, MNRAS, 187,73
7. Savage, B.D., & Mathis, J.S. 1979, ARA&A, 17, 73
8. Wu, C.-c. et al. 1992, 1UE Ultraviolet Spectral Atlas
of Selected Astronomical Objects, NASA Tech. Memo.
1.
2.
3.
4.
5.
No. 1285
9. Heck, A., Egret, D., Jaschek, M., & Jaschek, C. 1984,
lUE Low-Resolution Spectra Reference Atlas: Part 1.
Normal Stars (ESA, Paris)
10. Heck, A. 1987, in Exploring the Universe with the IUE
Satellite, edited by Y. Kondo (Reidel, Dordrecht), p. 121
II. Jaschek, C., & Jaschek, M. 1987, The Classification of
Stars (Cambridge University Press, Cambridge)
12. Snow, Jr., T.P., & Morton, D.C. 1976, ApJS, 32, 429
13. Walborn, N.R., & Panek, R.J. 1984, ApJ, 286, 718
182 I
8
ULTRAVIOLET ASTRONOMY
14. Walborn, N.R., Nichols-Bohlin, J., & Panek, R.J. 1985,
IUE Atlas of O-Type Spectra from 1200 to 1900 A,
NASA RP-1155
15. Walborn, N.R., & Nichols-Bohlin, J. 1987, PASP, 99,
40
16. Massa,D.1989,A&A,224,131
17. Bates, B., & Gilheany, S. 1990, MNRAS, 243, 320
18. Prinja, R.K. 1990, MNRAS, 246, 392
19. Rountree, J., & Sonneborn, G. 1991, ApJ, 369, 515
20. Massa, D., Altner, B., Wynne, D., & Lamers,
H.J.G.L.M. 1991, A&A, 242, 188
21. Taylor, B.J. 1984, ApJS, 54, 259
22. P6rez, M.R., Dliversen, N.A., Garhart, M.P., & Teays,
T.J. 1990, in Evolution in Astrophysics: IUE Astronomy
in the Era of New Space Missions, edited by E.J. Rolfe
(ESA, Noordwijk), p. 349
23. Thrnshek, D.A., Bohlin, R.C., Williamson, R.L., Lupie,
D.L., & Koorneef, J. 1990, ApJ, 99, 1243
Chapter 9
X-Ray Astronomy
Frederick D. Seward
9.1
..
183
9.1
Useful Conversions
9.2
Characteristic X-Ray Transitions
184
9.3
Emission Mechanisms and Spectra
184
9.4
Transmission of X-Rays Through the
Interstellar Medium
194
9.5
Cosmic X-Ray Sources.
9.6
Diffuse Background .
9.7
X-Ray Astronomy Missions
..
198
203
..
. . .. . .
205
USEFUL CONVERSIONS
= 1.6021 x 10-9 erg = 1.6021 x 10- 16 J: the kilo-electron-volt.
= 12.398 [A (A)r l : the energy of a photon.
= 0.862T (l07K): the characteristic energy, kT, of a thennal source.
= 2.998 x 1018 [A(A)r l = 2.418 x 1017 E (keV).
= 1.160 x 107 [kT (keV)].
1 (keV)
E (keV)
E (keV)
v (Hz)
T (K)
1/.L1y
= 10-29 ergcm-2 s-I Hz- I = 10-32 W m-2 Hz-I: the micro-Jansky.
Spectra are usually presented as the dependence of spectral irradiance (spectral flux density) I, on
wavelength A (A), frequency v (Hz), or photon energy E (keV or erg). To convert from one to the
other:
h(ergcm- 2 s-I A-I)
= 3.336 x
= 5.034 x
183
1O- 19 v2 (Hz) I v (ergcm- 2 s-I Hz-I)
107 E 2 (erg) Ie(ergcm- 2 s-Ierg-I),
184 / 9
X-RAY ASTRONOMY
= 3.336 x
= 6.626 x
Ie (keYcm- 2 s-I key-I) = 1.509 x
I v (ergcm- 2 S-I Hz-I)
= 5.034 x
N p (photoncm- 2 s-I key-I)
9.2
1O- I9 )..2(A) h(ergcm- 2 s-I A-I)
10-27 Ie (keY cm-2 s-I key-I),
1026 Iv (ergcm- 2 s-I Hz-I)
107)..2 (A) h(ergcm- 2 s-I A-I),
= Ie (keY cm- 2 s-I key-I)E-I(keY).
CHARACTERISTIC X-RAY TRANSITIONS
Energies of absorption edges and emission lines are given in Table 9.1. All energies are in keV.
9.3
EMISSION MECHANISMS AND SPECTRA
9.3.1
Continuum Models
X-ray spectra have historically been compared to three simple models that imply emission from:
(a) high-energy electrons moving in a magnetic field; (b) thermal electrons in an optically thin plasma
with temperature, T > 3 x 107 K; and (c) thermal radiation from an optically thick object. These
spectra are:
(a) Power law,
I (E)
= AE-a ,
a
= spectral index.
(b) Thermal bremsstrahlung,
I(E, T) = AG(E, T)Z2neni(kT)-I/2e-E/kT.
Densities of electrons and positive ions are ne and ni, respectively, and G is the Gaunt factor, a slowly
varying function with increasing value as E decreases [1,2].
When E « kT, G ~ 0.55In(2.25kT/E), and when E "" kT, G ~ (E/kT)-O.4 is an adequate
approximation [3].
When electrons are relativistic, the Gaunt factor can be approximated as
G
= [0.9 + 0.75(kT /mc 2)](E/ kT)-I/4 + 1.9(kT /mc 2)(E/ kT)-I/6 + 3.4(kT /mc 2)2(E/ kT),
an approximation better than 20% in the range (kT /mc 2) :::: I, (E/ kT) :::: 6 [4].
(c) Blackbody radiation,
Early observations were usually well fit using these simple models. Spectra of actual sources are,
of course, more complex. There are emission lines, absorption edges, and, usually, scattering and
absorption in material surrounding, or close to, the sources. Observations with high spectral resolution
and good counting statistics, or those covering a broad spectral range, require more complex models
for good fits [5].
9.3
EMISSION MECHANISMS AND SPECTRA
Table 9.1. Energies of characteristic lines and edges [1].
K series
Z
K(ab)
IH
2He
3Li
4Be
5B
6C
7N
80
9F
lONe
11 Na
12Mg
13 AI
14Si
15 P
16 S
17 CI
18Ar
19K
20Ca
21 Sc
22 Ti
23V
24Cr
25Mn
26 Fe
27 Co
28Ni
29Cu
30Zn
31 Ga
32Ge
33 As
34Se
35Br
36Kr
37Rb
38 Sr
39Y
40Zr
41Nb
42Mo
43Tc
44Ru
45Rh
46Pd
47Ag
48 Cd
49 In
0.0136
0.025
0.055
0.112
0.192
0.283
0.399
0.531
0.687
0.867
1.072
1.305
1.559
1.838
2.142
2.472
2.822
3.202
3.607
4.038
4.496
4.965
5.465
5.989
6.540
7.112
7.709
8.333
8.979
9.659
10.368
11.104
11.868
12.658
13.474
14.322
15.201
16.105
17.037
17.998
18.986
20.002
21.054
22.118
23.224
24.350
25.514
26.711
27.940
K{33
K{3,
Kfh
Ku,
KU2
9.656
10.365
11.099
11.862
12.650
13.467
14.312
15.183
16.082
17.013
17.967
18.949
19.962
21.002
22.070
23.169
24.295
25.452
26.639
27.856
0.052
0.110
0.185
0.277
0.392
0.525
0.677
0.848
1.041
1.253
1.486
1.740
2.013
2.307
2.622
2.957
3.313
3.691
4.090
4.510
4.951
5.414
5.898
6.403
6.929
7.477
8.046
8.637
9.250
9.885
10.542
11.220
11.922
12.648
13.393
14.163
14.956
15.772
16.612
17.476
18.364
19.276
20.213
21.174
22.159
23.170
24.206
1.486
1.739
2.012
2.306
2.620
2.955
3.310
3.687
4.085
4.504
4.944
5.405
5.887
6.390
6.914
7.460
8.026
8.614
9.223
9.854
10.506
11.179
11.876
12.596
13.333
14.095
14.880
15.688
16.518
17.371
18.248
19.147
20.070
21.017
21.987
22.980
23.998
1.067
1.295
1.553
1.829
2.136
2.464
3.190
3.589
4.012
4.460
4.931
5.426
5.946
6.489
7.057
7.648
8.263
8.904
9.570
10.263
10.259
10.976
10.980
11.724
11.718
12.437
12.494
13.282
13.289
14.102
14.110
14.959
14.949
15.822
15.833
16.723
16.735
17.651
17.665
18.603
18.619
19.587
19.605
20.595
20.615
21.631
21.653
22.695
22.720
23.787
23.815
24.907
24.938
26.057
26.091
27.233
27.271
/
185
186 I 9
X - RAY ASTRONOMY
Table 9.1. (Continued.)
K series
Z
50Sn
51 Sb
52 Te
53 I
54Xe
55 Cs
56Ba
57 La
58Ce
59Pr
60Nd
61 Pm
62Sm
63Eu
640d
65Th
66Dy
67Ho
68Er
69Tm
70Yb
71 Lu
72Hf
73 Ta
74W
75Re
76 Os
77 Ir
78Pt
79 Au
80Hg
81 Tl
82Pb
83 Bi
84 Po
85 At
86Rn
87Fr
88Ra
89Ac
90Th
91 Pa
92U
93Np
94Pu
95 Am
96Cm
97Bk
98Cf
K(ab)
29.200
30.491
31.813
33.169
34.582
35.959
37.441
38.925
40.449
41.998
43.571
45.207
46.835
48.515
50.240
51.996
53.789
55.615
57.483
59.390
61.332
63.304
65.351
67.414
69.524
71.662
73.860
76.112
78.395
80.723
83.103
85.528
88.006
90.572
93.112
95.740
98.418
101.147
103.927
106.759
109.649
112.581
115.603
118.619
121.760
124.876
128.088
131.357
134.683
K{33
K{31
K{32
Kal
28.439
29.674
30.939
32.234
33.556
34.913
36.298
37.714
39.163
40.646
42.159
43.705
45.281
46.896
48.547
50.221
51.949
53.702
55.485
57.293
59.141
61.037
62.969
64.938
66.940
68.983
71.065
73.190
75.355
77.567
79.809
82.104
84.436
86.819
89.231
91.707
94.230
%.791
99.415
102.084
104.813
107.576
110.387
28.481
29.721
30.990
32.289
33.619
34.981
36.372
37.795
39.251
40.741
42.264
43.818
45.405
47.030
48.688
50.374
52.110
53.868
55.672
57.506
59.356
61.272
63.222
65.212
67.233
69.298
71.401
73.548
75.735
77.971
80.240
82.562
84.922
87.328
89.781
92.287
94.850
97.460
100.113
102.829
105.591
108.409
111.281
113.725
116.943
120.350
122.733
126.490
127.794
29.104
30.388
31.698
33.036
34.408
35.815
37.251
38.723
40.226
41.767
43.327
44.929
46.566
48.248
49.952
51.715
53.500
55.315
57.204
59.085
60.974
62.956
64.969
67.001
69.089
71.219
73.390
75.606
77.864
80.172
82.530
84.933
87.351
89.846
92.383
94.974
97.622
100.307
103.051
105.849
108.699
111.605
114.587
118.057
120.350
123.960
126.490
130.484
133.290
25.267
26.355
27.468
28.607
29.774
30.968
32.188
33.436
34.714
36.020
37.355
38.718
40.111
41.535
42.989
44.474
45.991
47.539
49.119
50.733
52.380
54.061
55.781
57.523
59.308
61.130
62.990
64.885
66.821
68.792
70.807
72.859
74.956
77.095
79.279
81.499
83.768
86.089
88.454
90.868
93.334
95.852
98.422
100.781
103.300
105.949
108.737
111.676
114.778
Ka2
25.040
26.106
27.197
28.312
29.453
30.620
31.812
33.028
34.273
35.544
36.841
38.165
39.516
40.895
42.302
43.737
45.200
46.692
48.213
49.764
51.345
52.956
54.602
56.267
57.972
59.708
61.476
63.276
65.112
66.978
68.883
70.820
72.792
74.802
76.851
78.930
81.051
83.217
85.419
87.660
89.938
92.271
94.649
%.844
99.168
101.607
104.168
106.862
109.699
19K
20Ca
21 Sc
22 Ti
23V
24Cr
25Mn
26 Fe
27 Co
28Ni
29Cu
30Zn
310a
320e
33 As
34Se
35Br
36Kr
37Rb
38 Sr
39Y
40Zr
41Nb
42Mo
43Tc
44Ru
45Rh
Z
0.400
0.463
0.530
0.604
0.682
0.754
0.842
0.929
1.012
1.100
1.196
1.300
1.420
1.530
1.653
1.794
1.920
2.067
2.216
2.369
2.547
2.698
2.866
3.054
3.236
3.419
L[(ab)
LY3
1.697
1.817
1.936
2.060
2.187
2.319
2.455
2.741
2.890
2.763
2.915
1.286
LP4
0.585
0.654
0.721
0.792
0.866
0.941
1.023
1.107
1.197
1.294
1.388
1.490
1.596
1.706
1.826
1.947
2.072
2.201
2.334
2.473
LP3
L[ series
1.596
1.756
1.866
2.007
2.145
2.307
2.465
2.625
2.795
2.996
3.146
LU(ab)
2.964
3.143
2.302
2.461
2.623
0.350
0.407
0.460
0.520
0.583
0.652
0.721
0.794
0.872
0.952
1.044
1.134
1.249
1.360
1.477
LYI
0.345
0.400
0.458
0.519
0.583
0.649
0.718
0.791
0.869
0.950
1.034
1.125
1.218
1.317
1.419
1.526
1.636
1.752
1.871
1.995
2.124
2.257
2.394
2.536
2.683
2.834
LPI
LII series
L series
Table 9.1. (Continued.)
2.382
2.519
1.542
1.649
1.761
1.876
1.9%
2.120
0.262
0.306
0.353
0.401
0.453
0.510
0.567
0.628
0.694
0.762
0.832
0.906
0.984
1.068
1.155
1.244
1.399
LI'/
0.346
0.403
0.454
0.513
0.574
0.641
0.709
0.799
0.855
0.932
1.021
1.117
1.218
1.325
1.436
1.550
1.675
1.806
1.940
2.079
2.223
2.371
2.520
2.677
2.837
3.003
Lm(ab)
2.835
3.001
2.219
2.367
2.518
LP2
La2
0.341
0.395
0.452
0.511
0.573
0.637
0.705
0.776
0.851
0.930
1.012
1.098
1.188
1.282
1.379
1.480
1.586
1.692
1.694
1.804
1.806
1.922
1.920
2.042
2.040
2.163
2.166
2.289
2.293
2.424
2.554
2.558
2.692
2.696
Lal
LIII series
2.252
2.376
1.482
1.582
1.685
1.792
1.902
2.015
0.260
0.303
0.348
0.395
0.446
0.500
0.556
0.615
0.678
0.743
0.811
0.884
0.957
1.036
1.120
1.204
1.293
Ll
\0
-...l
00
.....
......
>
:;:0
>-l
(")
tr1
'"C
CJ')
I:::)
>
Z
en
~
en
......
>
Z
:t
(")
tr1
0
Z
~
en
......
en
~
......
tTl
UJ
46Pd
47 Ag
48 Cd
49 In
50Sn
51 Sb
52Te
53 I
54Xe
55Cs
56Ba
57 La
58Ce
59Pr
60Nd
61 Pm
62Sm
63Eu
64Gd
65Th
66Dy
67Ho
68Er
69Tm
70Yb
71 Lu
72Hf
Z
3.617
3.806
4.019
4.237
4.465
4.698
4.939
5.188
5.452
5.720
5.955
6.267
6.549
6.846
7.126
7.448
7.737
8.069
8.376
8.708
9.083
9.395
9.776
10.116
10.486
10.867
11.264
LI(ab)
7.485
7.795
8.104
8.422
8.752
9.086
9.429
9.778
10.141
10.509
10.889
5.552
5.808
6.073
6.340
6.615
6.900
3.749
LYJ
4.649
4.851
5.061
5.276
5.497
5.721
4.716
4.926
5.143
5.364
5.591
5.828
6.070
6.317
6.570
6.830
7.095
7.369
7.650
7.938
8.229
8.535
8.845
9.162
6.195
6.438
6.686
6.939
7.203
7.470
7.744
8.024
8.312
8.605
8.904
3.045
3.203
3.367
3.535
3.708
3.886
4.069
4.257
L{J4
3.072
3.234
3.401
3.572
3.750
3.932
4.120
4.313
L{J3
LI series
3.330
3.524
3.727
3.938
4.156
4.381
4.612
4.852
5.100
5.358
5.624
5.891
6.165
6.443
6.722
7.018
7.312
7.624
7.931
8.252
8.621
8.919
9.263
9.618
9.978
10.345
10.739
LII(ab)
5.279
5.530
5.788
6.051
6.321
6.601
6.891
7.177
7.479
7.784
8.100
8.417
8.746
9.087
9.424
9.778
10.142
10.514
3.328
3.519
3.716
3.920
4.130
4.347
4.570
4.800
LYI
4.619
4.827
5.041
5.261
5.488
5.721
5.960
6.205
6.455
6.712
6.977
7.246
7.524
7.809
8.100
8.400
8.708
9.021
2.990
3.150
3.316
3.487
3.662
3.843
4.029
4.220
L{JI
LII series
L series
Table 9.1. (Continued.)
5.588
5.816
6.049
6.283
6.533
6.787
7.057
7.308
7.579
7.856
8.138
4.141
4.330
4.524
4.731
4.935
5.145
2.660
2.806
2.956
3.112
3.272
3.436
3.605
3.780
LTJ
3.173
3.351
3.537
3.730
3.929
4.132
4.341
4.557
4.781
5.011
5.247
5.483
5.724
5.968
6.208
6.466
6.717
6.983
7.243
7.515
7.850
8.071
8.364
8.648
8.943
9.241
9.561
Lm(ab)
4.935
5.156
5.383
5.612
5.849
6.088
6.338
6.586
6.842
7.102
7.365
7.634
7.910
8.188
8.467
8.757
9.047
9.346
3.l7l
3.347
3.528
3.713
3.904
4.100
4.301
4.507
LfJ2
2.838
2.984
3.133
3.286
3.443
3.604
3.769
3.937
4.109
4.286
4.465
4.650
4.839
5.033
5.229
5.432
5.635
5.845
6.056
6.272
6.494
6.719
6.947
7.179
7.414
7.654
7.898
Lal
Lm series
4.272
4.450
4.633
4.822
5.013
5.207
5.407
5.607
5.816
6.024
6.237
6.457
6.679
6.904
7.132
7.366
7.604
7.843
2.833
2.978
3.126
3.279
3.435
3.595
3.758
3.925
La2
4.994
5.176
5.361
5.546
5.742
5.942
6.152
6.341
6.544
6.752
6.958
3.794
3.953
4.124
4.287
4.452
4.632
2.503
2.633
2.767
2.904
3.044
3.188
3.335
3.484
LI
==
><
0
Z
0
:;tI
til
~
>
~
I
><
:;c
1.0
......
00
00
-
8111
82Pb
83Bi
84 Po
85 At
86Rn
87Fr
88Ra
89Ac
90Th
91 Pa
92U
93Np
94Pu
95 Am
96Cm
97Bk
98Cf
BOHg
73Th
74W
75Re
76 Os
17Ir
78Pt
79 Au
Z
11.680
12.098
12.522
12.965
13.424
13.892
14.353
14.846
15.344
15.860
16.385
16.935
17.490
18.058
18.638
19.233
19.842
20.470
21.102
21.756
22.417
23.095
23.793
24.503
25.230
25.971
LI(ab)
19.503
20.094
20.709
21.336
21.979
18.354
11.276
11.672
12.080
12.498
12.922
13.359
13.807
14.262
14.734
15.215
15.708
9.486
9.817
10.158
10.509
10.866
11.233
11.608
11.993
12.388
12.791
13.208
13.635
14.065
14.509
14.973
15.442
15.929
16.423
16.927
17.452
17.986
18.537
19.103
LfJ3
Llseries
L}/'3
15.640
16.101
16.573
17.058
17.553
18.060
14.745
9.211
9.524
9.845
10.174
10.509
10.852
11.203
11.561
11.929
12.304
12.689
13.083
L{34
11.139
11.542
11.955
12.383
12.824
13.273
13.733
14.209
14.698
15.198
15.708
16.244
16.784
17.337
17.904
18.480
19.078
19.692
20.311
20.947
21.596
22.263
22.944
23.640
24.352
25.080
Ln(ab)
10.893
11.284
11.683
12.093
12.510
12.940
13.379
13.828
14.289
14.762
15.245
15.741
16.249
16.768
17.300
17.845
18.405
18.979
19.565
20.164
20.781
21.414
22.061
22.703
23.389
24.070
Ln
9.342
9.671
10.008
10.354
10.706
11.069
11.440
11.821
12.211
12.612
13.021
13.445
13.874
14.313
14.768
15.233
15.710
16.199
16.699
17.217
17.747
18.291
18.849
19.399
19.961
20.557
L{31
Ln series
L series
Thble 9.1. (Continued.)
14.507
14.944
15.397
15.874
16.330
13.661
8.427
8.723
9.026
9.335
9.649
9.973
10.307
10.649
10.992
11.347
11.710
LT/
9.881
10.204
10.531
10.869
11.215
11.564
11.918
12.284
12.657
13.035
13.418
13.817
14.215
14.618
15.028
15.442
15.865
16.300
16.731
17.167
17.614
18.053
18.526
18.990
19.461
19.938
Lm(ab)
15.621
16.022
16.425
16.837
17.252
17.673
18.096
18.529
18.983
14.448
14.839
9.650
9.960
10.274
10.597
10.919
11.249
11.583
11.922
12.270
12.621
12.978
13.338
L/h
8.145
8.396
8.651
8.910
9.174
9.441
9.712
9.987
10.267
10.550
10.837
11.129
11.425
11.725
12.029
12.338
12.650
12.987
13.288
13.612
13.942
14.276
14.615
14.953
15.304
15.652
Lal
Lm series
8.086
8.334
8.585
8.840
9.098
9.360
9.626
9.896
10.171
10.448
10.729
11.014
11.303
11.596
11.893
12.194
12.499
12.807
13.120
13.437
13.757
14.082
14.409
14.740
15.080
15.418
La2
11.117
11.364
11.616
11.887
12.122
12.381
10.620
7.172
7.386
7.602
7.821
8.040
8.267
8.493
8.720
8.952
9.183
9.419
9.662
LI
00
\0
..-
'-
>
~
~
n
ttl
~
en
0
>
Z
til
~
....Ztil
>
n
::t:
ttl
0
Z
~
....til~
....til
ttl
\0
w
190 /
9
X-RAY ASTRONOMY
Table 9.1. (Continued.)
M series
Mv series
MN series
Z
57 La
58Ce
59Pr
60Nd
61 Pm
62Sm
63Eu
640d
65Th
66Dy
67Ho
68Er
69Tm
70Yb
71 Lu
72Hf
73Ta
74W
75 Re
76 Os
77Ir
78Pt
79 Au
80Hg
81 Ti
82Pb
83 Bi
84 Po
85 At
86Rn
87Fr
88Ra
89Ac
90Th
91 Pa
92U
MN(ab)
0.851
0.902
1.004
1.108
1.221
1.280
1.390
1.515
1.578
1.718
1.793
1.871
2.116
2.202
2.291
2.385
2.485
2.586
2.687
3.491
3.728
MfJ
Mv(ab)
Mal
Ma2
1.809
1.775
1.773
2.041
2.122
2.206
2.295
2.389
2.484
2.579
1.980
2.050
2.123
1.975
2.046
2.118
2.270
2.345
2.422
2.265
2.339
2.416
3.332
2.996
3.082
3.170
2.986
3.072
3.159
0.854
0.902
0.949
0.996
1.100
1.153
1.209
1.266
1.325
1.383
1.443
1.503
1.567
1.631
1.697
1.765
1.835
1.906
1.978
2.053
2.127
2.204
2.282
2.362
2.442
2.525
3.145
3.239
3.336
3.552
Reference
1. Woldseth. R. 1973. X-Ray Energy Spectroscopy (Kevex Corp .•
Burlingame. CA)
9.3.2
Line Emission
When the source is "thin" and T < 3 X 107 K, the dominant radiation mechanism is line emission.
Elemental abundances [6] and temperature determine which lines are strongest. In the X-ray band, lines
from H-like and He-like ions and from ions of 0 and Fe are usually prominent. Figures 9.1 through 9.3
show the relative numbers of selected ions as a function of temperature [7]. Collisional eqUilibrium
is assumed. Some sources, however, have ages smaller than the time required to achieve equilibrium.
Young supernova remnants are the most obvious examples. In these cases, the ion populations are quite
different from those expected at the temperature indicated by the continuum radiation. Emission from
such nonequilibrium models has been calculated [8].
9.3 EMISSION MECHANISMS AND SPECTRA /
o
1oJ:
-.3...
C
N
0
S Ar
Ne
Ca
2
I
3
&
&.5
7
LogT
Figure 9.1. Concentration of hydrogen-like ions versus temperature.
JJ
I
LogT
Figure 9.2. Concentration of helium-like ions versus temperature.
8
191
192 I
9
X-RAY ASTRONOMY
o
Fe XVII
Fe IX
-0.5
z
J
I
-1
-1.5
8
8.5
LogT
o
Fe XXV
Fe XVII
-0.5
z
J
I
-1
-1.5
7
7.5
8
LogT
Figure 9.3. Concentration of iron ions versus temperature. Above: low temperatures; below: high temperatures.
9.3
EMISSION MECHANISMS AND SPECTRA
I
193
-21.5
i . -22
-23.5
8
8.5
Lo, T
7
7.5
8
Figure 9.4. Power radiated from a low-density plasma.
Table 9.2 gives the power from a low-density plasma, with solar abundances, in units of 10- 23 ergs
em3 s-l. Figure 9.4 plots these data.
Table 9.2. Power radiatedjrom a low-density plasma [1].
logT
< O.IOkeV
0.10-0.28
0.28-1.00
1.00-3.00
3.0-10.0
5.500
5.600
5.700
5.800
5.900
6.000
6.100
6.200
6.300
6.400
6.500
6.600
6.700
6.800
6.900
22.75
13.71
11.66
9.84
8.69
8.93
8.82
8.25
6.15
3.35
1.75
1.00
0.60
0.37
0.29
0.49
0.92
1.52
1.90
1.96
1.85
1.49
1.08
0.79
0.56
0.42
0.36
0.37
0.45
0.55
0.00
0.02
0.12
0.37
0.79
1.29
1.67
1.82
1.89
1.87
1.85
1.99
2.28
2.51
2.20
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.03
0.09
0.20
0.35
0.52
0.72
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
> 10.0
Total
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
23.24
14.66
13.30
12.11
11.44
12.07
11.98
lU5
8.84
5.81
4.12
3.55
3.59
3.85
3.78
194 I 9
X-RAY ASTRONOMY
Table 9.2. (Continued.)
logT
7.000
7.100
7.200
7.300
7.400
7.500
7.600
7.700
7.800
7.900
8.000
<
O.lOkeV
0.38
0.43
0.34
0.26
0.20
0.16
0.14
0.12
O.lO
0.09
0.08
0.10-0.28
0.28-1.00
1.00-3.00
3.~lO.0
0.53
0.35
0.23
0.18
0.16
0.15
0.14
0.13
0.12
0.12
0.11
1.28
0.67
0.52
0.48
0.47
0.46
0.44
0.43
0.41
0.39
0.37
0.89
0.89
0.80
0.71
0.67
0.65
0.63
0.62
0.62
0.61
0.60
0.03
0.07
0.12
0.20
0.30
0.41
0.55
0.68
0.81
0.93
1.02
>
lO.O
0.00
0.00
0.00
0.00
om
0.02
0.05
0.11
0.20
0.32
0.48
Total
3.11
2.41
2.01
1.83
1.81
1.85
1.96
2.lO
2.26
2.46
2.66
Reference
1. Raymond, J.C. 1992, current version of code described by Raymond, J.C., & Smith, B.W. 1977,
ApJ,35, 419
9.3.3
X-Ray Sources for In-Flight Calibration
The best-known X-ray spectrum is that of the Crab Nebula. It has small angular extent, and for our
purpose, is not time variable (the pulsar contribution is only'" 5% in the soft X-ray band and the diffuse
nebula is probably only slowly decreasing in flux). It has a simple power-law spectral continuum.
The Crab spectrum between 3 and 30 keY is I(E) = (9.7 ± l)E-l.l0±·03 keY cm- 2 s-1 keV- 1 [9].
Below 3 keV this spectrum is decreased by interstellar absorption, which is not well measured. Most
observations fall within the range NH = (2 - 3.5)
1021 atomscm- 2 (Morrison and McCammon
abundances).
Other sources which, because of small angular extent, simple spectra, and constant flux, are suitable for calibration purposes are: the supernova remnant G21.5-0.9, the clusters AI795 and A40I,
and, probably, the white dwarf HZ43. The supernova remnant NI32D in the Large Magellanic Cloud
is in a favorable location (close to the ecliptic pole) and often used, but has a thermal spectrum with
detailed spectral structure.
x
9.4 TRANSMISSION OF X-RAYS THROUGH
THE INTERSTELLAR MEDIUM
The transmission of X-rays through interstellar gas (which is cold and atomic) depends on column
density, usually expressed as the number of hydrogen atoms cm-2 , NH, and elemental composition.
Two models with different elemental composition and absorption cross sections have been used
extensively in the literature: that of Brown and Gould (BG) [10], and that of Morrison and McCammon
(MM) [11]. The BG gas contains H, He, C, N, 0, Ne, Mg, Si, S, and Ar. The MM gas contains these
same elements with updated cross sections [12] plus Ca, Fe, and Ni. Figure 9.5 shows the relative
importance of these elements. At 0.7 keY, for example, half the absorption is in O. At 10 keY, half
the absorption is in Fe. Since very little of the absorption occurs in H, the use of NH is somewhat
misleading. This is sometimes referred to as the number of "equivalent H atoms" cm-2.
9.4.1
Transmission of the MM Gas
Figure 9.6 shows graphs of transmission through the MM gas over a large range of column densities.
Only photoelectric absorption has been considered. Compton scattering will become important at
energies above 5 keY, so 1024 atoms cm- 2 is the highest column density shown. The two prominent
absorption edges are 0 K at 0.53 keY and Fe K at 7.1 keY.
9.4 TRANSMISSION OF X-RAYS I
195
900.
-
500....
N
E
c.J
:; 400.
-
'0
> 300.
..,,:
.
LaJ
b 200.
100.
o. tw::::r::u~0~.1==r:::i::::W:J:IJ::It1.0~:::I:=c::i:I:b;;;;;;;~1o.
PHOTON ENERGY ( keV)
Figure 9.S. X-ray absorption coefficient versus energy for the ISM. The structure is caused by atomic absorption
edges [11].
1
0.9
0.6
0.7
r::
0
0.6
·s
0.5
'iii
UI
UI
r::
<\I
s...
E-<
0.4
0.3
0.2
0.1
0
0.1
1
Pholon Energy
(keV)
10
Figure 9.6. Transmission versus energy for various interstellar medium column densities.
196 / 9
X-RAY ASTRONOMY
I:
0
S
S
a:I
23
U
()
:::;;!
I
I:
0
.s::I'll
22
1-0
0
:::;;!
N
I
S
()
21
I'll
S
.....0
~
:.:
Z
20
QO
..2
0.1
1
E.
(keV)
Figure 9.7. Conversion of the parameter Ea to column density.
9.4.2
Comparison of Different Models
In order to compare published analyses, a conversion between different absorption-measure models
is needed. Table 9.3 gives a comparison between the measured BG and MM column densities. The
conversion is not precise because the BG and MM transmission curves do not have the same shape.
Transmission through the column densities in Table 9.3 cross at '" 0.5, but the BG transmission curve
is steeper at low NH, and the MM curve is steeper at high NH.
In early work, the parameter Ea was used to quantify observed absorption. The transmission Tr
through interstellar gas was expressed as
T.r -- e -(Ea/ E)8/3 .
Figure 9.7 gives the conversion of Ea to MM column density. It is assumed that the measurement
is made over that energy range where Tr drops from 0.8 to 0.2, and there is some ambiguity when the
o or Fe absorption edge falls in this range. The value of the conversion factor at these energies will
depend on the characteristics of the X-ray detector used to make the observation.
Table 9.3. Equivalent transmission column densities for MM and BG gas.
Model
MMgas
8Ggas
Ea
Column
1 x 10 19
0.90 x 1019
0.080
1 x 1020
1.18 x 1020
0.187
1 x 1021
1 x 1022
1.15 x 1021
-0.50
1.25 x 1022
1.41
1 x 1023
0.95 x 1023
3.4
1 x 1024
0.80 x 1024
9.8
9.4 TRANSMISSION OF X-RAYS /
9.4.3
197
Relation to Optical Extinction
An empirical relation between X-ray absorption and optical extinction has been noted. Using diffuse
supernova remnants as calibrators, the relationship to extinction, A v, and to color excess, E B - v, were
found to be:
NH/Av
NH/ EB-V
= 1.9 x
= (5.9
1021 atomscm- 2 mag- 1 [13],
± 1.6)
x
1021 atomscm- 2 mag- 1 [14].
Agreement with Copernicus observations of absorption in atomic (HI) and molecular (H2)
hydrogen is quite good. The average measured column density toward 100 stars (90 closer than
2 kpc) is
ROSAT (Rontgensatellit) observations of bright, strongly absorbed sources have given a measure
of both soft X-ray absorption and of the brightness and extent of dust-scattering halos, a direct relation
between dust and gas. The result is
NH/Av
= 1.79±O.03 x
1021 atomscm- 2 mag- 1 [16].
Table 9.4. Conversion of count rate to millicrab. ILJy. and energy flux.
Satellite
Vela5B
Uhuru
Ariel V
HEAO-I
Einstein
EXOSAT
Tenma
Ginga
ROSAT
ASCA
XTE
BeppoSAX
Chandra
Instrument
survey
survey
Al
A2 (1 keY band)
A4 (channel A)
HRI
!PC
MPC
ME
GSPC(A+B)
LAC
HRI
PSPC
SIS
GIS
PCA
HEXTE
MECS
HPGSPC
PDS
HRC-I
ACIS-I
Crab rate
(counts-I)
40 [1]
947 [2]
403 [3.4]
13 600" [5]
575 [6]
11.2 [7]
120 [8]
684 [8]
1383 [8]
1740 [9]
1640 [10]
10500 [11]
362 [12]
964 [12]
1020 [12]
890 [12]
11800 [12]
200 [12]
328 [12]
334 [12]
210 [12]
1200 [12]
3200 [12]
1 count s-I =
erg cm- 2
coune l
27 ILJy @ 5 keY
1.15 JL1y @ 5 keY
2.70 ILJy @ 5 keY
0.080 ILJy @ 5 keY
4.8 ILJy @ 2 keY
21 ILJy @ 20 keY
23 JL1y @ 2 keY
4.0 JL1Y @ 2 keY
0.79 ILJy @ 5 keY
0.63 JL1y @ 5 keY
0.66 ILJy @ 5 keY
0.104 ILJy @ 5 keY
7.6 ILJy @ 2 keY
2.8 ILJy @ 2 keY
1.07 ILJy @ 5 keY
1.22 ILJy @ 5 keY
0.092 ILJy @ 5 keY
1.2 JL1Y @ 20 keY
3.3 ILJy @ 5 keY
0.71 ILJy @ 20 keY
1.13 ILJy @ 20 keY
2.3 ILJy @ 2 keY
0.34 JL1Y @ 5 keY
4.5 x
1.6 x
5.3 x
2.7 x
2.7 x
6.8 x
1.6 x
2.8 x
1.6 x
2.1 x
2.2 x
2.8 x
3.7 x
1.4 x
3.3 x
3.8 x
3.1 x
9.0 x
8.1 x
7.8 x
9.5 x
2.8 x
1.1 x
10- 10
10- 11
10- 11
10- 12
10- 11
10- 10
10- 10
10- 11
10- 11
10- 11
10- 11
10- 12
10- 11
10- 11
10- 11
10- 11
10- 12
10- 11
10- 11
10- 11
10- 11
10- 11
10- 11
Note
QHEAO-l A 1 rates are cataloged in counts cm -2 s-l; to convert, use area = 3 300 cm2 .
References
1. Priedhorsky, W.C., Terrell, J. & Holt, S.S. 1983, ApJ, 270, 233
2. Forman, W. et aI. 1978, ApJS, 38, 357
Energy range
(keV)
3-12
2--6
2-10
1-20
0.5-3
13-25
0.5-4
0.5-4
1--6
1-20
1-20
2-20
0.5-2.4
0.5-2.4
0.4-12
0.4-12
1-20
12--60
1.3-10
4-34
13-80
0.4-10
0.4-10
198 I 9
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
9.5
9.5.1
X-RAY ASTRONOMY
Warwick, R.W. et al. 1981, MNRAS, 197, 865
McHardy,I.M. et al. 1981, MNRAS, 197, 893
Wood, K.S. et al. 1984, ApJS, 56, 507
Nugent, 1.1. et al. 1983, ApJS, 51, 1
Levine, A.M. et al. 1984, ApJS, 54, 581
Seward, F.D. 1990, ApJS, 73, 781
White, N. 1992, the ME catalog accessed through the HEASARC online database
Koyama, K. et al. 1984, PASJ, 36, 659
Thmer, M.l.L. et al. 1989, PASJ, 41, 345
PIMMS program. 1997, NASAlGSFC HEASARC online software
COSMIC X-RAY SOURCES
AU-Sky Surveys
Sensitive surveys have been completed by Uhuru (2-6 keY) [17]; Ariel V (2-18 keV) [18, 19]; HEAO1 (1-20 keY) [20]; Einstein in the slew mode (0.2-4 keY) [21]; and ROSAT (0.2-2.4 keY) [22]. Table
9.4 gives sensitivities of the survey instruments. Figure 9.8 shows the 842 sources found by HEAO-l.
HEAO-l also covered lower [23] and higher [24] energy bands and, because of its lO-year coverage,
the Vela 5B data are unique [25].
Count rates from these surveys and from other missions can be converted to spectral irradiance
assuming a Crab-like spectrum [a well-known power law (see Sec. 9.3.3) modified by absotption below
3 keY and with no spectral flux below 0.4 keY]. The Crab spectral irradiance at 2,5, 10, and 20 keY is
2750, 1090, 510 and 238 J,£Jy. The energy flux per count listed in Table 9.4 was calculated using a Crablike spectrum, including interstellar absotption. This conversion is reasonable for most sources with
absorbing column> 5 x loW atomscm- 2 • For soft sources and the Einstein and ROSAT detectors,
which have appreciable sensitivity down to 0.1 or 0.2 keY, the energy conversion factors in Table 9.4
can be an order of magnitude too large.
9.5.2 Types of Sources
Tables 9.5-9.10 give characteristics of sources in several broad categories, and are by no means
complete. They include some of the brightest sources and others chosen to illustrate the variety of
objects in each category [26].
Thble 9.5. Brightest X-ray emitting supernova remnants [1].
Galactic
coordinates
184.6-5.8
74.3-8.5
263.5-2.7
260.4-3.4
111.7-2.1
120.1+1.4
Flux density
Name
Flux density
O.2-4keV
(millicrab)
Crab Nebula
Cygnus Loop
VelaXYZ
PuppisA
Cassiopeia A
TychoSNR
1000
965
760
365
89
32
1000
Note
4LY = light year = 0.31 parsec ~ 1 x 1016 m.
Reference
1. Seward, F.D. 1990, ApJS, 73, 781
1.5-1OkeV
(millicrab)
10
39
26
80
20
LX
(Ly4)
X-ray
diameter
(arcmin)
O.2-4keV
(ergs-I)
6500
2500
1500
6500
8000
8000
2
160
420
50
4
8
3x
2x
3x
6 x
1x
3 x
Distance
1037
1036
1035
1036
1037
1036
X-ray Pulsar
and Be S....
Biliary
X Per
Remnant
suc:,O:va
Cyg X-3
Binary X-ray
and l-ray Source
~-~
Virgo
Cluster
of Galaxies
Slack Hole Candidale
Burster
Figure 9.8. The HEAO-l X-ray sky [20]_
PKS 2155-304
Bl lacerlae
Object
Active Galaxy
GX 339-4
NGC 6624
I- 1 l,L*=-'I', ,=r=-=:-Y' .I" ."I", ! ~ ...~.....: -.;t
NGC 4151
lMC
large MageilanlC Cloud
Acerellng BlIlanes in
Vela X-I
Binary X-ray Pulsar
MXB 1659-29
Bursler
EX Hya
Cataclysmic
Vanable (U Gem)
\0
\0
\0
-
....
CIl
trl
~
("}
c:::
CI.l
~
o
~
I
><:
("}
&:::
.....
oCIl
(')
VI
200 I
9
X-RAY ASTRONOMY
Table 9.6. Selected X-ray emitting stars.
Name
Capella (a Aur)
HZ 43
Algol (fJ Per)
Wolf 630
24UMa
ProxCen
YYGem
EEri
EQPeg
('Ori
aCen
E
Ori
aTri
Sirius (a CMa B)
Flux density
0.2-4 keY [1]
(millicrab)
type
6.1
2.2
1.8
1.1
0.70
0.70
0.67
0.63
0.60
0.58
0.58
0.44
0.35
0.34
G8V+FV
WD
B8V
M4V+MSV
GlV
MSV
MY
K2V
MY
09.51
KSV+G2V
BOI
F2V
WD
Stellar
LX [2]
O.2-4keV
(erg s-1)
Distance
(LyQ)
2.0
4 x
5x
2.0
1.0
2.5
4 x
2.0
6 x
3.5
3.2
2.0
3.2
6x
44
210
100
20
80
4.3
50
10.8
20
1600
4.4
1500
60
8.6
x
UpO
1031
1030
x 1029
x 1030
x 1027
1029
x 1028
1028
x 1032
x 1027
x 1032
x 1029
1028
Note
QLY = light year = 0.31 parsec ~ 1 x 1016 m.
References
1. Harris, D.E. et aI. 1990, The Einstein Observatory Catalog of fPC X-Ray
Sources, NASA TM 108401, Vol. I, 24
2. Vaiana, G.S. et aI. 1981, ApJ, 245, 163
Table 9.7. Selected X-ray emitting normal galaxies [1, 2].
Galaxy
Type
NGC507
NGC720
NGC4382
NGC4472
M31
NGC253
M81
M82
SO
E
SO
FJSO
Sb
Sc
Sb
Irr
Flux density
0.2-4 keY [1]
(millicrab)
DistanceQ
(MLyb)
O.2-4keV
(ergs-1)
0.46
0.10
0.032
0.73
2.3
0.31
0.35
0.88
320
105
90
90
2.2
10
11
11
1.1
2.2
5.2
1.1
3.6
7.4
1.3
3.5
LX
x
x
x
x
x
x
x
x
1043
1(1'1
1040
1042
1039
1039
1040
1040
Notes
Q HO = 50 kIn s-1 Mpc-1 , qO = 0.5. bMLY = one million light years
=0.31 x 106 pc ~ 1 x 1022 m.
References
1. Fabbiano, G., Kim, D.-W., & Trinchieri, G. 1992, ApJS, BO, 531
2. Harris, D.E. et aI. 1990, The Einstein Observatory Catalog of fPC
X-Ray Sources, NASA TM 108401, Vol. I, p. 24
SSCyg
CygX-2
CygX-3
CygX-I
SgrX-4
Her X-I
GX339-4
Rapid Bur
GX5-1
Vela X-I
CenX-3
CenX-4
CirX-1
ScoX-1
LMCX-3
Name
VI341 Cyg
SS433
VI357Cyg
V404Cyg
VI521 Cyg
AC211
V1727Cyg
AM Her
HZ Her
V821 Ara
V616Mon
UYVol
UGem
GPVel
V779Cen
V822Cen
BRCir
V818Sco
KZTrA
V801 Ara
V725Tau
=
73.2
79.9
65.0
91.6
90.6
87.3
11.3
181.4
273.6
210.0
280.0
199.2
263.1
292.1
332.2
322.1
359.1
321.8
332.9
345.0
58.2
338.9
354.8
5.1
77.9
2.8
39.7
-2.6
-32.1
-6.5
-19.3
23.4
3.9
0.3
23.9
0.0
23.8
-13.1
-4.8
2.5
37.5
-4.3
-0.2
-.0
25.9
-7.9
-2.2
3.1
-2.2
0.7
-27.3
-3.0
-7.1
-11.3
b
Galactic coordinates
250 [5]
300[4]
20000 [6]
850[4]
17000[5]
20[7]
310[4)
1200[1)
160[7]
350[5]
250 [5]
1300[4]
3 [8]
320 [5]
10[4]
1175 [5)
20000 [9]
380 [5]
6 [1)
20[5)
4[8)
750 [7]
2700 [4]
25 [5]
125000 [4]
30[1]
Max Fl. Den.
2-lOkeV
(millicrab)
3.09h
O.l9h
13.1 d
5.60d
6.47d
4.79h
17.1 h
5.24h
6.50h
9.84d
11.3
15.8
16.4
8.2
14.7
14.2
8.9
12.7
12.2
18.5
17.5
14.4
13.0
15.5
III d
1.70d
7.75 h
3.82h
4.22h
8.96d
2.09d
15.1 h
16.6d
18.9h
0.69h
3.80h
2.61d
1.70d
14.8h
POrb
8.9
16.7
11.2
16.9
9.0
6.9
13.3
12.8
(mag)
V
Max.
=
=
9
1.24
7.7
25
283
4.84
104
(s)
Pspin
HMXB
HMXB
LMXB
LMXB
CV
HMXB
HMXB
LMXB
LMXB
LMXB
LMXB
LMXB
LMXB
LMXB
LMXB
LMXB
LMXB
CV
LMXB
HMXB
HMXB
LMXB
HMXB
LMXB
LMXB
CV
LMXB
[3]
Type
=
Bright at 0.25 keY; WD+M5V
In GC NGC 6624; Bur
BH ?;jets
BH+09.7Iab
Tr; BH+(KOIIl-V)
NS+Helium star
In GC MI5;Bur
Tr; ADC; Bur; Triple?
Bright 0.25 keY; DN; WD+K5V
NS+(ASIIl to FlIII)
Bur
Tr; BH+F1V; Eel; jets
Eel; NS+(BOV to roV)
BH?
In GC Liller I, type II Bur
Tr; NS+09.7Ile
In LMC; BH+B3Ve
Tr;BH+K5V
Eel; ADC; Bur
Bright 0.25 keY; DN; WD+M5V
Eel; NS+BO.51b
NS+06.5Il-IIl; Eel
Tr; Bur; NS+K5V
Tr; Bur
Comment
=
=
=
=
=
=
=
=
1. van Paradijs, I. 1995, in X-Ray Binaries, edited by W. Lewin, I. van Paradijs, and E.P.I. van den Heuvel, (Cambridge University Press, Cambridge) p. 536
2. Ritter, H. 1987,A&AS, 70, 335
3. Bradt, H., & McClintock, I. 1983, ARA&A, 21, 3
4. Warwick, R.W. et aI. 1981, MNRAS, 197, 865
5. Forman, W. et aI. 1978, ApI, 38, 357
6. Conner, I.P., Evans, W.O., & Belian, R.O. 1969, ApI, 157, Ll57
7. McHardy, 1M. et aI. 1981, MNRAS, 197, 893
8. Wood, K.S. et aI' 1984, ApIS, 56, 507
9. Makino, F. 1989, IAU Circular No. 4786
References
=
Note
aHMXB high-mass X-ray binary; LMXB
low-mass X-ray binary; CV
cataclysmic variable; ON
dwarf nova; Bur
Burster; GC
globular cluster;
Tr transient; NS
neutron star; LMC Large Magellanic Cloud; BH black hole; Eel eclipse; ADC accretion disk corona; WD white dwarf.
3A0535+26
4U0538-64
3A0620-00
EXOO748-676
H0752+22
4U09OO-40
4U1II8-60
1455-31
4U1516-56
4U1617-15
4UI626-67
4U1636-53
GROJl655-40
4U1656+35
4U1658-48
1730-335
4U1758-25
4U1814+49
4U1820-30
3AI909+048
4U1956+35
GS2023+338
4U2030+40
4U2129+12
4U2129+47
IH2140+433
4U2142+38
Source
Optical
counterpart
Thble 9.8. Selected X-ray emitting accretion-powered binaries [I, 2].a
0
tv
-
......
tI.I
ttl
(")
::0
c:::
0
C/.l
~
I
:;;c
(")
....3:
><
tI.I
0
(')
VI
10
202 / 9
X-RAY ASTRONOMY
Table 9.9. The brightest X-ray emitting clusters of galaxies [1].
Flux density
2-lOkeV
(millicrab)
Cluster
Source
A426 (Perseus)
Ophiuchus Cluster
M87 (Virgo)
A1656 (Coma)
Centaurus Cluster
A2199
A496
A85
4U0316+41
4U 1708-23
4U 1228+12
4U 1257+28
4U 1246-41
4U 1627+39
4U0431-12
4UOO37-1O
47 c
Redshift
z
0.0183
0.028
0.0037
0.0235
0.0107
0.0305
0.0316
0.0518
30
22d
15
5
4
3
3
Distancea
Lx
(MLyb)
2-lOkeV
(ergs-I)
360
550
73
460
210
600
620
1000
1.4
2.5
3
9
6
3
3
8
x
x
x
x
x
x
x
x
l(f5
1045
1043
1044
1043
1044
1044
1044
Notes
a HO = 50kms- 1 Mpc-I, qo = 0.5.
bMLY = one million light years 0.31 x 106 pc R: 1 x 1022 m.
cIncludes the nucleus of the galaxy NGC1275 and diffuse emission from the Cluster.
dIncludes the active nucleus and diffuse emission from M87, and emission from the
surrounding Vugo Cluster.
=
Reference
1. Forman, W. et aI. 1978, ApJS, 38, 357
Table 9.10. Sekcted X·ray emitting active galDxies.
Flux den.
2-10keV
Name
(millicrab)
2E 189
IH0244+OO1
2E 1007
4U0432+05
2E2195
4U 1206+39
IH 1226+022
IH 1226+128
2E2900
4U 1322-42
4U 1414+25
2E4066
lH 1937-106
lH 2156-304
MRK348
NGC 1068
Q0420-388
3C120
M81
NGC4151
3C273
M87
3C279
CenA
NGC5548
E1821+643
NGC6814
PKS 2155-304
1.3 [I)
0.8[2)
0.02 [3]
2.3 [3)
0.16 [1]
4.3 [3)
3.1 [2)
22.4e [3)
0.23 [I)
8.4[3)
1.7 [3)
0.80[1)
1.9 [2)
8.4[2)
Redshift
z
0.014
0.0037
3.12
0.033
0.0006
0.0033
0.158
0.0037
0.538
0.0008
0.0017
0.297
0.005
0.17
Disla
(MLyb)
270
73
80000
650
11.7
65
3200
73
11000
15.6
33
6200
98
3500
LX
2-lOkeV
(ergs-I)
Ix
9x
2x
2x
5x
4x
6x
3x
6x
5x
4x
7x
4x
2x
'JYpe
1043
S~ert2.hl~yobKUred
1041
1046
1044
1039
1042
104S
1043
104S
104 1
104 1
104S
1042
1046
Seyfert 2. Compton thick
High redshift quasar
Superlum VLBI radio galc
Low luminosity AGNd
S~ert 1.5
Radio loud quasar
Radio galaxy
OVV (Blazar)/ y-rays
Radio galaxy
~ertl
Radio quiet quasar
~ett 1. hl~yvariable
BLLac
Notes
aHO 50kms- 1 Mpc-l,qO =0.5.
bMLY one million light years = 0.31 x 106 pc R: 1 x 1022 m.
cVLBI = very long baseline interferometry.
d AGN
active galactic nucleus.
eIncludes diffuse emission from M87 and from Vugo cluster.
f OVV = optically violent variable.
=
=
=
References
1. Harris, D.E. et aI. 1990, The Einstein Obs. Catalog of [PC X-Ray Sources, NASA TM 108401, Vol. 1.
p.24
2. Wood, K.S. et aI. 1984, ApJS, 56, 507
3. Forman, W. et aI. 1978. ApJS, 38. 357
9.6 DIFFUSE BACKGROUND / 203
3
-........
III
::
I
1
.IIC
I
III
I
-S
CI
......
~
.IIC
......
.3
III
.,
CI
c::
l
fit
.1
f....
+
CI
III
Q.
III
.03
HEAO-l A2
HEAO-l A.4
3
10
30
10Q
Photon Energy [keVJ
300
1000
Figure 9.9. The diffuse background spectrum above 3 keV [28].
9.6 DIFFUSE BACKGROUND
Above 3 keY, surface brightness fluctuations of the high-latitude extragalactic diffuse background,
measured in 5° x 5° blocks, are less than 2% above those expected from an extrapolation of the
observed distribution of sources [27]. The spectrum from the HEAO-IA2 detectors is one of the best
measured in astrophysics and, in the range 3-50 keY, is given by
I(E) = 7.8E-0.2ge-EI40 keY cm-2 s-l sCI keV- l [28].
Figure 9.9 shows the HEAO-l A2 and A4 data. Statistical error for the A2 instrument is less than
the width of the heavy solid line. The lighter curve is an empirical fit to all the data and is
I (E) =
{
7.877E-O.2ge-EI41.13, E < 6OkeV,
1652E-2 + 1.75E-0.7, E > 60 keY [29].
In the range 2-60 keY there is an additional component of 2%-10% associated with the galactic
plane. Intensity is concentrated in the plane and is strongest in the direction of the center [30]. Below 2
keV there is structure in the background at all latitudes, which changes appreciably with energy. Both
absorption and local emission contribute to this structure. Figure 9.10 shows the background at 0.25
keV. Similar maps are available from 0.13 to 2.2 keY [31,32].
!
Figure 9.10. The diffuse background at keV measured by ROSAT [32]. Two bright sources, the Cygnus Loop (74, -8) and the Vela supernova remnant (263, -3)
are also clearly visible. Color bar values are 10-6 counts s-1 arcrnin- 2 .
100
300
600
900
1200
1500
-<
a-::
0
z
0
~
til
"":l
>
~
~
I
><
1.0
........
~
9.7 X-RAY ASTRONOMY MISSIONS /
9.7
205
X-RAY ASTRONOMY MISSIONS
Characteristics of some prominent X-ray satellites are given in Tables 9.11 and 9.12.
Table 9.11. Some X-ray astronomy satellites [I, 2).
Energy range b
(keV)
Satellite
Country
Launch
Last data
Typea
Vela 5A,B
Uhuru
OSO-7
Copernicus
ANS
Ariel-V
SAS-3
HEAO-I
Einstein
Hakucho
Tenma
EXOSAT
Spartan 101
Ginga
KVANT
Granat
ROSAT
Astro-I
OXS
ASCA
Alexis
RXTE
lXAE
8eppoSAX
Chandra
USA
USA
USA
USAlUK
Netherlands
UK
USA
USA
USA
Japan
Japan
ESA
USA
Japan
USSR
USSR
Germany
USA
USA
Japan
USA
USA
India
Italy
USA
May 69
Dec. 70
Sep.71
Aug. 72
Aug. 74
Oct. 74
May 75
Aug. 77
Nov. 78
Feb. 79
Feb. 83
May 83
June 85
Feb. 87
June 87
Dec. 89
June 90
Dec. 90
Jan. 93
Feb. 93
Apr. 93
Dec. 95
Mar. 96
Apr. 96
Jul. 99
June 79
Jan. 75
May 73
Dec. 80
July 76
Mar. 80
Apr. 80
Jan. 79
Apr. 81
Apr. 85
Nov. 85
Apr. 86
June 85
Oct. 91
Scanning, small SC
Scanning, large PC
Scanning, PC
Pointed, small concentrator
Pointed, PC, Bragg crystal
Scanning, pointed, ASM, large PC
Scanning, RMC, large PC
Scanning, very large PC, SC
Pointed, telescope, PC, HRI, Si detector
Scanning, RMC, large PC
Scanning, GSPC, ASM
Pointed, small telescope, large PC
PC
Pointed, large PC
Pointed, GSPC, SC, coded mask
Pointed, Coded masks, ASM
Scanning, pointed, telescope, PC, HRI
Pointed, BBXRT collector, Si detector,
Spectrometer to study background
Pointed, telescope, CCO, GSPC
Scanning, small multilayer telescopes
Pointed, large PC, large SC, ASM
Pointed, large PC, ASM
Pointed, GSPC, SC, WFC (3)
Pointed, telescope, CCO, HRI, gratings
Dec. 90
Jan. 93
3-12
2-10
1-40
0.2-10, 0.2-{).6
2-40
2-10
1.5-10
1-20
0.2-4
0.1-2,2-20
2-10
0.05-2.0, 1.5-10
2-10
1.5-30
2-30
40-100,0-1300
0.1-2.5
0.3-12
0.15-{).28
0.4-12
0.06-{).1O
2-50, 15-200
2-18
0.1-300
Notes
a ASM = all-sky monitor; BBXRT = broad-band X-ray telescope; CCD = charged coupled detector;
GSPC = gas scintillation proportional counter; HRI = high resolution, channel plate detector; PC =
proportional counter; RMC = rotating modulation collimator; SC = scintillation counter; WFC = wide
field camera.
bThese data apply to the main survey instrument(s). Since most satellites carried several detectors, data
were usually collected over a broader energy range than that specified here. The range for a given detector also
depends on source strength. Since the background obscures the higher-energy photons from weaker sources,
this range is larger for strong sources than for weaker sources.
References
1. Bradt, H., Ohashi, T., & Pounds, K.A. 1992, ARA&A, 30, 391
2. Charles, P.A., & Seward, F.D. 1995, Exploring the X-Ray Universe (Cambridge University Press,
Cambridge)
3. Boella, G. et al. 1997, A&AS, 122, 299
fible 9.12. Characteristics of X-ray telescope mirrors.
Mission
Aperture
diameter
(cm)
Einstein
EXOSAT
ROSAT
ACSA
(4 mod.)
Chandra
58
28
83
34
(1 mod.)
123
Mirrors
Geometric
area
(cm2)
Field
(arcmin
diam.)
Reflection
angles
(arcmin)
Focal
length
(m)
Mirror
coating
Highest
energy
(keV)
On-axis
resolution
(arcsec)
4 nested
2 nested
4 nested
120 nested
(1 mod.)
4 nested
350
80
1140
1300
(4 mod.)
1145
60
120
120
40
<ID-70
9(}...11O
83-135
14-42
3.45
1.09
2.4
3.5
Ni
Au
Au
Au
4.5
2
2.4
12
4
18
3
180
30
27-52
Ir
10
10.0
0.5
206 / 9
X-RAY ASTRONOMY
ACKNOWLEDGMENTS
Information and advice for this section was kindly supplied by M. Elvis, G. Fabbiano, ER. Harnden Jr.,
J.P. Hughes (Fig. 9.6), C. Jones, J. McClintock, J. McDowell, J. Raymond (Figs. 9.1-9.4), W. Tucker,
D. Worrall, and M. Zombeck at the Harvard-Smithsonian Center for Astrophysics, E. Boldt and S.
Snowden (Fig. 9.10) at the Goddard Space Flight Center, D. Gruber of the University of California,
San Diego (Fig. 9.9), D. Cox and D. McCammon of the University of Wisconsin (Figs. 9.5 and 9.10),
H. Bradt at MIT, and K. Wood of the Naval Research Laboratory (Fig. 9.8).
REFERENCES
1. Karzas, W., & Latter, R. 1961, ApJS, 6, 157
2. Chodil, G. et al. 1968, ApJ, 154, 645
3. Blumenthal, G., & Tucker, W., 1974, in X-Ray Astronomy, edited by R. Giacconi and H. Gursky (Reidel, Dordrecht), p. 99
4. Schwartz, D.A, & Tucker, W.H. 1988, ApJ, 332, 157
5. Holt, S.S., & McCray, R. 1982, ARA&A, 20, 323
6. Allen, C.W. 1973, Astrophysical Quantities (Athlone
Press, London), p. 30
7. Raymond, J.e. 1992, current version of code described
by Raymond, J.C., & Smith, B.W. 1977, ApJS, 35, 419
8. Hamilton, A.J.S., Sarazin, C.L., & Chevalier, R.A.
1983, ApJS, 51, 115
9. Toor, A., & Seward, F.D. 1974, AJ, 79, 995
10. Brown, R.L., & Gould, R. 1970, Phys. Rev., Dl, 2252
II. Morrison, R., & McCammon, D. 1983, ApJ, 270, 119
12. Henke, B.L. et al. 1982, Atomic Data Nucl. Data, 27, I
13. Gorenstein, P. 1975, ApJ, 198, 95 (corrected to MM absorption)
14. Ryter, C., Cezarsky, C., & Andouze, J. 1975, ApJ, 198,
103 (corrected to MM absorption)
15. Bohlin, R., Savage, B., & Drake, J. 1978, ApJ, 224,132
16. Predehl, P., & Schmitt, J.H.M.M. 1995, A&A, 293, 889
17. Forman, W. et al. 1978, ApJS, 38, 357
18. Warwick, R.w. et al. 1981, MNRAS, 197, 865
19. McHardy, I.M. et al. 1981, MNRAS, 197,893
20. Wood, K.S. et al. 1984, ApJS, 56, 507
21. Elvis, M.S., et al. 1992, ApJS, SO, 257
22. Voges, W. 1992, Proceedings of Satellite Symposium 3:
Space Sciences with Panicular Emphasis on High Energy Astrophysics, from the "International Space Year"
conference, Munich, Germany, March 1992 (ESA, ISY3), p. 9
23. Nugent,J.J.etal.1983,ApJS,51,1
24. Levine, AM. et al. 1984, ApJS, 54, 581
25. Priedhorsky, W.C., Terrell, J., and Holt, S.S, 1983, ApJ,
270,233
26. Charles, P.A & Seward, F.D. 1995, Exploring the
X-Ray Universe (Cambridge University Press, Cambridge)
27. Fabian, A.C., & Shafer, R.A. 1983, in Early Evolution
of the Universe, edited by G. Abell and G. Chincarini
(Reidel, Dordrecht), p. 333
28. Boldt, E. 1992, in Proceedings of the International
Workshop on the X-Ray Background, edited by X. Barcons and A. Fabian (Cambridge University Press, Cambridge), p. 1I5
29. Gruber, D. 1992, in Proceedings of the International
Workshop on the X-Ray Background, edited by X. Barcons and A Fabian (Cambridge University Press, Cambridge), p. 44
30. Iwan, D. et al. 1982, ApJ, 260, III
31. McCammon, D. et al. 1983, ApJ, 269, 107
32. Snowden, S. L. et al. 1997, ApJ, 485, 125
Chapter
10
y-Ray and Neutrino Astronomy
R.E. Lingenfelter and R.E. Rothschild
10.1
10.1
Continuum Emission Processes . . . . . . . . . . . ..
207
10.2
Line Emission Processes . . . ..
208
10.3
Scattering and Absorption Processes
.....
...
213
10.4
Astrophysical y-Ray Observations . . . . . ..
...
216
10.5
Neutrinos in Astrophysics .. . . . . . . . . . . . . ..
235
10.6
Current Neutrino Observatories
..........
.......
..
237
CONTINUUM EMISSION PROCESSES
Important processes for continuum emission at y-ray energies are bremsstrahlung, magnetobremsstrahlung, and Compton scattering of blackbody radiation by energetic electrons and
positrons [1-6].
10.1.1
Bremsstrahlung
The bremsstrahlung luminosity spectrum of an optically thin thermal plasma of temperature T in a
volume V is [3]
where the index of refraction is assumed to be unity, m is the electron mass, Z is the mean atomic
charge, ne and nj are the electron and ion densities, and the Gaunt factor g(v, T) ~ (3kT j1rhv)I/2 for
hv > kT and T > 3.6 x lOSZ 2 K, or
L(V)brem ~
6.8 x 1O-38 Z 2n enjVg(v, T)T- 1/ 2 exp(-hvjkT) ergs- l Hz-I.
207
208 /
10
y-RAY AND NEUTRINO ASTRONOMY
10.1.2 Magnetobremsstrahlung
The synchrotron luminosity spectrum of an isotropic, optically thin nonthermal distribution of
relativistic electrons with a power-law spectrum, N(y) = NoY-S, interacting with a homogeneous
magnetic field of strength, H, is [5]
08 (3
3
L(v)s ch ~ ~
yn
3mc2
or
__
e_
)(S-I)/2
4rrmc
V NoH(S+I)/2 v (1-S)/2
L(V)synch ~ 3.60 x 10- 23 V NoH(S+1)/2(4.2 x 106 /v)(S-I)/2 ergs-I Hz-I.
10.1.3
Compton-Scattered Blackbody Radiation
The Compton-scattering (cs) luminosity spectrum of an optically thin, isotropic nonthermal distribution
of relativistic electrons with a power-law spectrum, N(y) = NOY-S, interacting with blackbody
photons having a temperature T is [5]
L(v)
cs
~
4e4
-3m2c3
(
h ) (3-S)/2
-V MOWbbT(S-3)/2v(I-S)/2
3.6k
or
where
Wbb
is the energy density of the blackbody radiation.
10.2 LINE EMISSION PROCESSES
Important processes for line emission at y-ray energies are electron-positron annihilation, nuclear
deexcitation, decay of radio nuclei, and radiative capture (see Tables 10.1-10.3).
10.2.1
Electron-Positron Annihilation Radiation
Positron annihilation can occur either via a direct interaction with a free electron or via positronium
formed by charge exchange with a bound electron or by radiative combination with a free electron
(e.g., [7-12]). See Figure 10.1.
Direct annihilation (da) leads to line emission, e+ e- ~ 2y, at a mean energy,
Te« 107 K,
107 < Te < 1010 K,
Te> 1010 K,
where m e c 2 =510.9991 keVand Te is the temperature of the annihilating electrons and positrons.
The direct-annihilation line spectrum can be approximated by a Gaussian with a linewidth [12]
r da ~ 0.87(Te/104 K)o.so keY, for Te « 109 K, and at higher temperatures the width [10] r da ~ kTe,
for Te » 109 K.
The cross section for direct annihilation of a positron of energy ymec2 with an electron at rest [1] is
+
+
_
30T
(y2 4y
1
u(Y)da - 8(y + 1)
y2 _ 1
In(y
c:;:-:
+ V y- -
1) -
y +3 )
JY2=1
'
where the Thomson cross section, O'f = 8rr e4 / (3m 2c 4 ) = 0.6652 barn (b).
10.2 LINE EMISSION PROCESSES / 209
10.10
'j
U
1&1
...::E
II)
U
10. 11
>t:
II)
Z
1&1
10. ,2
Q
~
1&1
c:I
a: 10.,1
~
~
.....
II)
1&1
~
~
a:
10"'14
10.15
102
10'5
10·
10'
10'
lOT
10'
T(K)
Figure 10.1. Positron-annihilation rates in a thennal medium per unit density as a function of temperature,
for annihilation directly with free electrons (Rda/ne) or with bound electrons (Rda/nH), and via positronium
fonnation by radiative combination with free electrons (Rrc/ne) or by charge exchange with neutral hydrogen
(Rce/nH), from [8].
Annihilation via positronium formation leads to line emission only from the singlet parapositronium, para-Ps ~ 2y, which forms 25% of the time. The mean energy of the positronium line,
hvps
= m ec 2 -
(R/4n2),
where the Rydberg R = 0.0136 keY, and n is 1 for the ground state.
The parapositronium annihilation line spectrum can be approximated by a Gaussian with a
linewidth r rc ~ 0.80(T /104 K)O.44 keY for radiative combination (re), valid at least from 8000 to
106 K, and a Gaussian linewidth r ce ~ 6.4 keV for charge exchange (ee), since the parapositronium
mean life of'" 10- 10 s is much less than the energy loss time [12].
The total number of 511 keV line photons emitted per positron annihilation,
Y511/e+
=2-
1.5/ps ,
where Ips is the fraction of positrons that annihilate via positronium.
Annihilation via positronium formation leads to three-photon continuum emission from the triplet
orthopositronium, ort ho- P s ~ 3y, which forms 75% of the time. The spectrum [7] of this emission is
P(hvh y
= (1T 2 _
2
9)mec2
(17(1 -17)
(2 _ 17)2
+
2(1 -17)
2(1 - 17)2
172
In(1 - 17) - (2 _ 17)3 In(1 - 17)
where 17 = h v / mc2 is the photon energy, and the spectrum is normalized to unity.
2 - 17)
+ -17-
,
210 I
10
y-RAY AND NEUTRINO ASTRONOMY
Thble 10.1. Nucleardeexcitation y-ray lines.a,b
Energy
(MeV)
Emission
mechanism
Excitation
processes
Mean life
(s)
0.4291
0.4776
7Be..o· 429 ~ g.s.
7Li*0.478 ~ g.s.
0.7183
lOB*o.718 ~ g.s.
0.8468
56Fe*O.847 ~ g.s.
1.2383
56Fe*2.085
1.2745
22Ne*1.275 ~ g.s.
1.3685
24Mg*1.369 ~ g.s.
1.4083
55Fe*I.408 ~ g.s.
1.4084
1.4341
54Fe*I.408 ~ g.s.
52Cr*1.434 ~ g.s.
1.6336
2oNe*1.634 ~ g.s.
1.6352
14N*3.948 .... 14N*2.313
1.7790
28Si*I.779 ~ g.s.
1.8086
26Mg*l.809 ~ g.s.
2.2302
32S*2.230 ~ g.s.
2.3126
14N*2.313
4He(a, n)7Be*
4He(a, p)7Li*
4He(a, n)7Be(€)7Li*(1O%)
12C(p, x)lOB*
160(p, x)lOB*
12C(p, x)lOC(e+)lOB*
160(p, x)lOC(e+)lOB*
56Fe(p, p,) 56 Fe*
56Fe(p, n) 56 Co(e+; €) 56 Fe*
56Fe(p, p,) 56 Fe*
56Fe(p, n)56Co(e+; €)56Fe*(67%)
22Ne(p, p')22Ne*
22Ne(a, a')22Ne*
22Ne(p, n)22Na(e+; €)22Ne*
24Mg(p, x)22Na(e+; €)22Ne*
2SMg(p, x)22Na(e+; €)22Ne*
28Si(p, x)22Na(e+; €)22Ne*
24Mg(p, p,) 24 Mg*
24Mg(a, a,) 24 Mg*
28Si(p, x) 24 Mg*
56Fe(p, pn)55Fe*
56Fe(p, 2n)55Co(e+; €)55Fe*(18%)
56Fe(p, x)54Fe*
56Fe(p, x)52Cr*
56Fe(p, x) 52 Mn*(e+; €)5 2Cr*
56Fe(p, x)52Mn(e+; €)52Cr*
20Ne(p, p') 2O Ne*
2ONe(a, a')2oNe*
20Ne(p, n)20Na(e+)20Ne*(80%)
24Mg(p, x)20Ne*
28Si(p, x) 2oNe*
14N(p, p') 14 N*
14N(a, a') 14 N*
160(p, x)14N*
28Si(p, p,) 28 Si*
28Si(a, a,) 28 Si*
32S(p, x)28Si*
26Mg(p, p,) 26 Mg*
26Mg(a, a,) 26 Mg*
26Mg(p, n) 26 A1(e+; €) 26 Mg*
27 A1(p, pn)26Al(e+; €) 26 Mg*
28Si(p, x)26 A1(e+; €) 26 Mg*
32S(p, p,) 32 S*
32S(a, a,)32S*
14N(p, p')14N*
14N(a, a') 14 N*
14N(p, n) 14 O(e+)14N*
160(p, x)14N*
160(p, x) 14 O(e+)14N*
1.9 x 10- 13
1.1 x 10- 13
6.6 x 106
1.0 x 10-9
1.0 x 10-9
27.78
27.78
9.1 x 10- 12
9.6 x 106
1.0 x 10- 12
9.6 x 106
5.2 x 10- 12
5.2 x 10- 12
1.2 x 108
1.2 x 108
1.2 x 108
1.2 x 108
1.9 x 10- 12
1.9 x 10- 12
1.9 x 10- 12
5.5 x 10- 11
9.1 x 104
1.2 x 10- 12
9.8 x 10- 13
1.8 x 103
7.0 x lOS
1.0 x 10- 12
1.0 x 10- 12
6.4 x 10- 1
1.0 x 10- 12
1.0 x 10- 12
6.9 x 10- 15
6.9 x 10- 15
6.9 x 10- 15
6.8 x 10- 13
6.8 x 10- 13
6.8 x 10- 13
6.9 x 10- 13
6.9 x 10- 13
3.2 x 1013
3.2 x 1013
3.2 x 1013
2.4 x 10- 13
2.4 x 10- 13
9.8 x 10- 14
9.8 x 10- 14
101.9
8.7 x 10- 14
~
~
56Fe*O.847
g.s.
101.9
10.2 LINE EMISSION PROCESSES / 211
Table 10.1. (Continued.)
Energy
(MeV)
Emission
mechanism
Excitation
processes
Mean life
(s)
2.6138
2ONe~.248 -+ 2~e*1.634
2.7412
2.7540
24Mg~·123 -+
3.7365
4Oea*3.737 -+ g.s.
4.4380
12C~·439 -+ g.s.
9.2
9.2
9.2
9.2
1.8
3.5
3.5
6.8
6.8
6.1
6.1
6.1
6.1
6.1
6.1
4.4439
II B ~.445 -+ g.s.
5.1049
14N*5.106 -+ g.s.
6.1291
160*6.130 -+ g.s.
6.8778
28Si*6.879 -+ g.s.
6.9174
16 0*6.919 -+ g.s.
7.1152
160*7.117 -+ g.s.
2ONe(p, p')~e*
~e(a, a')20Ne*
24Mg(p, x)20Ne*
28Si(p, x)20Ne*
160(p, p') 160*
24Mg(p, p') 24Mg*
24Mg(a, a')24Mg*
4OCa(p, p')40Ca*
4Oea(a, a')40Ca*
12C(p, p,)12C*
12C(a, a,) 12C*
14N(p, x) 12C*
14N(a, x) 12C*
160(p, x) 12C*
160(a, x) 12C*
12C(p,2p)lIB*
12C(a,x)IIB*
14N(p, p')14N*
14 N (a, a') 14N*
160(p, x)14N*
160(a, x) 14N*
160(p, p,) 160*
160(a, a') 160*
2ONe(p, x) 160*
28Si(p, p')28Si*
28 Si(a, a,)28 Si*
160(p, p,) 16 0*
160(a, a') 160*
160(p, p,) 160*
160(a, a,) 160*
160*8.872 -+ 160*6.130
24Mg*I.369
1.1
1.1
6.3
6.3
6.3
6.3
2.7
2.7
2.7
2.6
2.6
6.8
6.8
1.2
1.2
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
10- 14
10- 14
10- 14
10- 14
10- 13
10- 14
10- 14
IO-Il
IO-Il
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 15
10- 15
10- 12
10- 12
10- 12
10- 12
10- 11
10- 11
10- 11
10- 12
10- 12
10- 15
10- 15
10- 14
10- 14
Notes
aUpdaled from Ramaty, R., Kozlovsky, B., & Lingenfelter, R.E. 1979, ApJS, 40, 487, with data
from Firestone, R.B. et al. 1996, Table of Isotopes (Wiley, New York).
bBecause of recoil the observed y-ray energy hv' = hV(l-hv/2Mc2), where hv is the transition
energy and M is nuclear mass.
Table 10.2. Nucleosynthetic radioactive decay lines. a
Radioactive
decay
Dominant decay
mean life
Line energy
(MeV)
Branching ratio
(%)
8.80 days
0.1584
0.8119
0.7500
0.2695
0.4805
1.5618
98.8
86.0
49.5
36.5
36.5
14.0
212 /
10
y-RAY AND NEUTRINO ASTRONOMY
Table 10.2. (Continued.)
Dominant decay
mean life
Line energy
(MeV)
Branching ratio
48V(e+; €)48Ti
23.0 days
0.9835
1.3121
0.5110
100.
96.6
50.0n c
56Co(e+; €)5 6 Fe
111.3 days
0.8468
1.2383
0.5110
2.5986
1.7715
1.0379
(3.244)
(2.029)
99.9
68.4
21.7
19.0n c
17.4
15.5
14.1
12.4
11.3
1.1155
0.0080
50.6
34.2
0.1221
0.1365
0.0144
85.5
48.9
10.3
9.5
Radioactive
decay
(O.OO64}b
65Zn(e+; €)6 5Cu
352.4 days
57 Co(€)57Fe
392.1 days
(O.OO64)
(%)
22Na(e+; €)22Ne
3.754yr
1.2745
0.5110
99.9
89.4n c
125Sb(e-) 125Te
3.979yr
(0.0274)
0.4279
0.6006
0.6360
0.4634
62.1
29.4
17.8
11.3
10.5
44Ti(€)44Sc
91 ±4yr
0.0679
0.0783
(0.0041)
1.1570
0.5110
100
99.3
16.7
99.9
94.0n c
44Sc(e+; €)44Ca
(0.236 day)
6OFe(e-)60Co
6OCo(e-)60Ni
2.2 x 106 yr
(7.60 yr)
0.0586
1.3325
1.1732
26 AJ(e+; €) 26 Mg
1.03 x 106 yr
1.8086
0.5110
99.7
82.1n c
4OK(€)40Ar
1.84 x 109 yr
1.4608
10.7
2.0
100
99.9
Notes
aBased on data from Browne E., & Firestone, R.B. 1986, Table of Radioactive
Isotopes (Wiley, New York), Firestone, R.B. 1996, Table of Isotopes (Wiley, New
York), and Norman, E.B. et at. 1997, Nuc. Phys., A621, 92 for the 44Ti mean-life.
bBracketted ( ) line energies are the mean of two or more close lines.
cThe number of 0.5110 MeV photons per positron annihilation, n = 2-1.5/ps,
where fps is the fraction of annihilation occurring via positronium formation.
10.3 SCATTERING AND ABSORPTION PROCESSES /
213
Table 10.3. Radiative capture y-ray lines. a
Radiative
capture
Thermal
cross section (b)
Line energy
Branching ratio
(MeV)
(%)
0.332
2.2233
100
2.6
0.0144
7.6316
7.6456
0.3525
5.9205
6.0185
1.7252
64
30
24
12
9
9
9
iH(n, y)2H
56Fe(n, y)57 Fe
Note
aBased on data Nuclear Data Group, 1973, Nuclear Level Schemes
A = 45 through A = 257 from Nuclear Data Sheets (Academic Press,
New York).
10.3
SCATTERING AND ABSORPTION PROCESSES
y-Ray emission spectra can be modified by several processes: photoelectric absorption, electronpositron pair production, Compton scattering, and Landau-level electron scattering in intense magnetic
fields [1-4, 13-21]. See Figure 10.2.
10.3.1
Photoelectric Absorption
The cross section for photoelectric absorption of a photon by the ejection of a K -shell electron from
an atom of nuclear charge Z is [1]
a(hv)K
=
5 4(mc2)5 (y2 _
30'[Z a
2
hv
1)3/2
1
x{-4+ y(y-2) [ 1In (y+JY2=1)])
3
y+1
2yJY2=1
y_Jy 2-1
'
where the Thomson cross section, 0'[
ejected electron y = 1 + hv/mc2.
10.3.2
=
81re 4 /(3m 2e4 )
=
0.6652 b, and the Lorenz factor of the
Pair Production
The cross section for electron-positron pair production (pp) by a photon in the presence of a nucleus
of charge Z is [14]
3aZ20'[[7 (2hV)
109]
a(hv)pp = 21r
gin mc2 - 54
for no screening when 1 « hv/mc2 « 1/aZ I / 3 , and
a(hv)pp
2
= 3aZ21r 0'[
[7gin (183) 1]
for complete screening when hv/mc2 » 1/aZ I / 3 .
ZI/3
- 54
214 /
10
y-RAY AND NEUTRINO ASTRONOMY
! I
I
10'
~
'Leo,
,
rOo
1 = f}".~
..e
.
-ti
c:
I
'v
~
10··
10·'
10·~
~
'\
::-
~
I
1,/
~~
,+;
1\
"
'
\
'0
,
,
.0. 1
,I
\
Photon
)"
(MeV)
100:').a
.v
1,0'
I
Photon Energy (MeV)
10
I'
1\
r\
I
'\
I
\
10"
II
'~
~
10·'
..
~
'v II.a
~
~,
.v
....
~I
L'
~\
~
~~
..a
".
k"e
,.-ff
JI
Y. I.
Photon E:nergy (MeVl
1
..a
.v
r'
I
Photon Energy (MeV)
I'
Figure 10.2. Macroscopic cross sections for y-ray attenuation by photoelectric absorption, Compton scattering
and pair production in hydrogen, air, NaI, and Ge, as a function of photon energy from [21].
The cross section for electron-positron pair production by the interaction of two photons of energy
hv and hv' when hvhv' > m 2 c4 is [1]
10.3 SCATTERING AND ABSORPTION PROCESSES / 215
The attenuation coefficient for electron-positron pair production by a photon in a strong magnetic
field, in the limit h 2 v 2 /2m 2e 4 B* » 1 with B* = B/4.414 x 1013 G, is [15]
R1y
where X
10.3.3
==
ame
= --B* sine =
2h
( 4)
{
0.377 exp - 3x
06
. X -1/3 ,
,
x«
1,
X» 1,
(hv/2me 2 )B* sin e and the threshold energy is 2me 2 / sin e.
Compton Scattering
The cross section for Compton scattering (cs) of photons by electrons is [13]
+ 2) In(21] + 1) + 2:1 + ~4 ----:;;z-
3O'f [(
21]
a(hv)cs = 81]
1-
2(21]
1]
+ 1)2 '
where 1] = h v / me 2 is the initial photon energy.
The angular distribution of the scattered photons, in terms of the scattering angle 41, is
j(cos41)
=
3O'f [(1
8a(hv)cs
+ 1] + 1]2 -
1] cos (1)(1 + cos 2 (1) - 21]2 cos 41]
3 ·
(l + 1] -1] cos (1)
The energy of the Compton-scattered photon h v' relative to the initial photon energy h v is
r = hv'hv = 1/(1
+ 1] -1] cos (1),
and the energy distribution of the Compton-scattered photons is
j(r)
=
3O'f
[
1
(1Jr + r - 1)2]
r - 1+ - +
2 2
81]a(hv)cs
r
1] r
'
for 1/(21] + 1) ::s r ::s 1, corresponding to scattering angles 0 0 ::s 41 ::s 1800 , and j (r) = 0 for other
values of r.
In a magnetic field, where the electron energies are quantized in Landau states, the total scattering
cross section for unpolarized photons in the Thomson limit is [16]
where e and h v are the angle and energy of the incident photon with respect to the magnetic field in
the electron rest frame, and hVB = eB/me is the cyclotron frequency. When (hv/ hVB)B > 10 12 G,
relativistic effects modify the cross section [17, 18].
10.3.4 Cyclotron Absorption
In a magnetic field, the cross section for absorption of photons by electron scattering from ground state
to higher Landau levels is [19]
a~s(e) =
arr21; 2 e 2
En
e- z Zn-1 (
~(hv - hvn ) (n _ I)!
(1
Z)
+ cos2 e) + ;; sin2 e
,
216 I
10
y-RAY AND NEUTRINO ASTRONOMY
where Z = h 2v 2 sin 2 ()j2me 2B*, En = (m 2e4 + h 2v 2 cos 2 ()
1013 G. The photons are absorbed at the resonant energies
In the nonrelativistic limit, nB*
= nBj4.414 x
+ 2nB*m2e4) 1/2, and B* =
Bj4.414
X
1013 G« I, the absorption cross section is [20]
1 + cos2 ()
(n-I)! '
where photons are absorbed at hannonics h Vn = neB j me.
10.4 ASTROPHYSICAL y-RAY OBSERVATIONS
The v-ray sky is extremely variable. Unlike the sources seen at longer wavelengths, most of the
astrophysical v-ray sources have been seen only in their transient emission. Out of roughly a thousand
v-ray sources less than 10% are relatively steady, persistent sources. The latter include a wide variety
of sources such as the Sun, supernova remnants, the interstellar medium, and the cosmic background
emission, but they are mostly compact objects: radio pulsars, accreting neutron stars, and blackhole
candidates, ranging from stellar mass objects in our own galaxy to s~pennassive, active galactic nuclei.
TOTAL CRAB EMISSION
10-'
10"
+11is _ _ 1981
+
\
1
PerMgsfeid et 111.1979
ling el Ill. 1979
<> Toar and Seward
1974
+ Dolan et at. 1977
I (arpenle, et 01. 1967
+ Gruber and ling. 1977
I Helmken and HoffOllM. 1973
~ P. Mandrou
10-"
10-"
10-u
et al.1977
+ Baker et at. 1973
I Portier et Ill. 1973
+ W,lson et at. 1977
t
Haymes el at. 1966
~Sct01lelder et al. 1975
c::J KllIffen et al.1974
(OS- B Db..,.,alians IpWarI
IBemett et at. 19771
Walraven et at. 1975
+
+
...... totat (rab
ILichti et al.19801
--- White et al.19BO
10-"1O'':.1~-'-'-~1O:':-r-~~~1O':r-'-'-~'''''1O",,4,-'-...........u.u.~10:-'--'-'-'''''''''~'''-'''''''''''~101
-
Ey [keV)
Figure 10.3. Total Crab Nebula and pulsar emission from 10 keY to 2 GeV. The Crab flux is the de facto standard
for the expression of source fluxes, e.g., 10 milliCrabs. This figure is provided to relate Crab fluxes at various
energies to the more useful photonscm- 2 s-1 -lkeV. The plot is from Graser, U., & SchOnfelder, V. 1982, ApJ,
263, 677, and references to observations contained within the plot can be found in that paper.
10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / 217
The vast majority of y-ray sources, however, have been seen only briefly for times as short as a few
milliseconds to as much as 1000 s. These are collectively known as y-ray bursts, but because of their
diverse properties, they may arise from a variety of sources and processes.
General reviews of astrophysical y-ray sources are given in [22-25]. Figure 10.3 displays the
famous Crab Nebula spectrum.
Many y-ray bursts are reviewed in [26-31].
The locations and properties of selected galactic and extragalactic y-ray sources are listed in
Tables 10.4-10.9 and basic data on the major hard X-ray and y-ray instruments are included in
Tables 10.10-10.12.
Table 10.4. Selected galactic sources> 100 keY.
Source
name
1YpeQ
periodb
aC
XPersei
0352+308
XRBe
835 s
58.06
+30.90
0422+328
BHC
Crab (total)
0531+219
Crab (pulsar)
0531+219
0535+262
.s
III d
Dist. e
flux!
163.08
-17.14
0.35
4 x 10- 5
1 x 10-5
64.63
+32.79
165.89
-11.91
2
2 x 10- 2
2 x 10- 3
1 x 10-4
SNRand
Pulsar
82.88
+21.98
184.56
-5.79
2
8
6
5
5
2
6
2
x
x
x
x
x
x
x
Pulsar
0.0332 s
82.88
+21.98
184.56
-5.79
2
1x
1x
2x
6x
5x
2x
2x
1x
3x
XRBe
104 s
84.06
+26.32
181.47
-2.54
1.8
I x 10-2
5 x 10-5
SNh
83.96
-69.30
279.71
-31.94
50
0.87
bII
SN1987A
0536-693
(in LMC)
0620-00
BHC
95.05
-0.32
209.96
-6.54
Geminga
0630+178
Pulsar
0.2371 s
97.75
+17.81
195.14
+4.27
< O.4t
Lum. g
Refs.
30keV
100 keY
8 x 1032
2 x 1033
[l]
30keV
100 keY
300 keY
1 x 1037
1 x 1037
6 x 1036
[2]
[2]
[2]
10- 3
10-4
10-5
10-6
10- 8
10- 11
10- 13
30keV
100 keY
300 keY
1 MeV
10 MeV
100 MeV
lGeV
5
5
3
4
2
5
2
x
x
x
x
x
x
x
1036
1036
1036
1036
1036
1035
1035
[3]
[3]
[3]
[3]
[3]
[3]
[3]
10- 3
10-4
10-5
10-7
10-9
10- 11
10- 13
10- 15
10- 21
30keV
100 keY
300 keY
1 MeV
10 MeV
100 MeV
lGeV
IOGeV
1 TeV
7x
8x
1x
5x
4x
2x
2x
8x
2x
1035
1035
1036
1035
1035
1035
1035
1034
1033
[4]
[3]
[3]
[3]
[3]
[3]
[3]
[5]
[6]
30keV
100 keY
6 x 1036
3 x 1035
[7]
[7]
2 x 10-4
4 x 10-5
7 x 10-6
30keV
100 keY
300 keY
1 x 1038
2 x 1038
3 x 1038
[8]
[8]
[8]
3 x 10-3
2 x 10-4
30keV
100 keY
4 x 1035
3 x 1035
[9]
[9]
3 x 10- 11
6 x 10- 13
100 MeV
1 GeV
<6x1033
< 2 x 1034
[10]
[10]
Energy
[I]
218 /
10
y-RAY AND NEUTRINO ASTRONOMY
Table lOA. (Continued.)
Source
1'ype'I
aC
III d
8
bll
name
perioob
Vela (pulsar)
0833-45
Pulsar
0.0892s
128.40
-45.05
1009-45
BHe
1055-52
Nova Muscae
1124-684
Dist.e
Flux!
263.58
-2.82
0.5
4x
2x
1x
3x
6x
1x
2x
153.37
-45.06
275.85
+9.35
3t
1 x 10-4
7 x 10-6
Pulsar
164.50
-52.45
286.00
6.65
l.53
BHe
17l.08
-68.40
295.31
-7.07
1509-58
Pulsar
0.1502 s
227.50
-58.95
1543-47
BHe
10-1
10-1
10-8
10-9
10- 10
10- 10
10- 12
Energy
Lum.g
1032
1033
1033
1034
1034
1034
1034
[11]
[11]
[11]
[12]
[12]
[12]
[12]
lookeV
300keV
2 x 1036
1 x 1036
[13]
[13]
2 x 10- 12
100 MeV
1 x 1034
[14]
It
4 x 10-3
2 x 10-4
1 x 10-5
30keV
lookeV
300keV
7 x 1035
4 x 1035
2 x 1035
[15]
[15]
[15]
320.33
-1.16
It
3 x 10-5
4 x 10-6
8 x 10-1
30keV
lookeV
300keV
5 x 1033
8 x 1033
1 x 1034
[16]
[16]
[16]
235.96
-47.56
330.92
+5.43
4
8 x 10-3
2 x 10-4
30keV
lookeV
2 x 1031
6 x 1036
[17]
lookeV
300keV
3 MeV
10 MeV
30 MeV
100 MeV
lOeV
2x
1x
5x
2x
3x
5x
8x
Refs.
[17]
1655-40
BHe
253.50
-39.85
344.98
+2.46
3.2
2 x 10-4
1 x 10-5
lookeV
300keV
4 x 1036
2 x 1036
[13]
[13]
Her X-I
1656+354
LMXB
l.24 s
254.01
+35.42
58.15
+37.52
5
1 x 10-3
1 x 10-5
3 x 10-20
30keV
lookeV
1 TeV
4 x 1036
5 x 1035
1 x 1035
[18]
[18]
[6]
OX 339-4
1659-487
BHe
254.76
-48.72
338.94
-4.33
lOt
2 x 10- 3
2 x 10-4
1 x 10-5
30keV
lookeV
300keV
4 x 1031
4 x 1031
2 x 1031
[17]
[17]
HMXB
255.14
-37.78
347.76
+2.17
l.7
1 x 10- 3
3 x 10-5
30keV
lookeV
5 x 1035
2 x 1035
[19]
[19]
BHe
256.29
-25.03
358.59
+9.06
lOt
2 x 10-3
1 x 10-4
30keV
lookeV
3 x 1031
2 x 1031
[20]
[20]
1706-44
Pulsar
O.I024s
256.52
-44.42
343.10
-2.68
l.82
7 x 10- 12
1 x 10- 13
100 MeV
lOeV
3 x 1034
6 x 1034
[5]
[5]
1716-249
BHe
259.94
-24.97
0.20
+6.99
2.4
4 x 10-4
2 x 10-5
lookeV
300keV
5 x 1036
2 x 1036
[13]
[21]
[21]
1700-37
NovaOph '77
1705-250
[17]
[13]
Terzian 2
1724-308
LMXB
26l.08
-30.76
356.32
+2.30
14t
2 x 10-4
3 x 10-5
40keV
lookeV
1 x 1031
1 x 1031
OX 1+4
1728-247
LMXB
114s
262.15
-24.70
l.9O
+4.87
lOt
2 x 10- 3
4 x 10-5
30keV
lookeV
3 x 1031
8 x 1036
[19]
[19]
BHe
264.48
-29.52
358.97
+0.52
lOt
1 x 10-3
4 x 10-4
30keV
lookeV
2 x 1031
8 x 1031
[22]
[22]
1737.9-2952
10.4 ASTROPHYSICAL y-RAY OBSERVATIONS I 219
Table lOA. (Continued.)
aC
Source
~
name
III d
bll
Dist.e
Flux!
Energy
Lum. 8
Refs.
1740.7-2942
BHC
265.18
-29.71
359.12
-0.10
lOt
5 x 10-4
7 x 10-5
1 x 10-5
40 keY
100 keY
300 keY
2 x 1037
1 x 1037
2 x 1037
[23]
[23]
[23]
''Galactic
Center"
1742-294
BHC
266.24
-29.38
359.89
-0.71
lot
3 x 10-3
1 x 10-4
2 x 10-5
30 keY
100 keY
300 keY
5 x 1037
2 x 1037
3 x 1037
[24]
[24]
[25]
1743-322
XRT
265.44
-32.21
357.13
-l.61
lot
6 x 10-4
4 x 10-5
30 keY
100 keY
1 x 1037
8 x 1036
[19]
[19]
GX5-1
1758-250
LMXB
269.51
-25.08
5.08
-l.02
lOt
8 x 10-4
4 x 10-5
30 keY
100 keY
1 x 1037
8 x 1036
[19]
[19]
1758-258
BHC
269.53
-25.74
4.52
-1.36
lOt
4 x 10-4
6 x 10-5
3xlO-6
30 keY
100 keY
300keV
7 x 1036
1 x 1037
5 x 1036
[25]
[25]
[25]
1915+105
BHC
288.80
+10.95
45.37
-0.22
12.5
8 x 10-5
2 x 10-6
100 keY
300 keY
3 x 1037
6 x 1036
[13]
[13]
CygX-l
1956+350
BHC
299.04
+35.05
7l.29
+3.12
2.5
9x
1x
4x
1x
10-3
10- 3
10-5
10-5
30keV
100 keY
300 keY
1 MeV
1x
1x
4x
1x
1037
1037
1036
1037
[26]
[26]
[27]
[27]
2000+25
BHC
300.18
+25.10
63.38
-3.00
2t
2 x 10- 3
2 x 10-4
2 x 10-5
30 keY
100 keY
300keV
1 x 1036
2 x 1036
1 x 1036
[28]
[28]
[28]
2023+338
BHC
305.53
+33.71
73.13
-2.09
2t
1 x 10-2
1 x 10-3
1 x 10-4
30 keY
100 keY
300 keY
7 x 1036
8 x 1036
7 x 1036
[13]
[13]
[13]
CygX-3
2030+407
HMXB
.307.52
+40.76
79.76
+0.77
lOt
1x
2x
5x
2x
30keV
100 keY
1 TeV
1 PeV
2x
4x
1x
4x
[18]
[18]
[6]
[6]
10- 3
10-5
10-20
10-26
1037
1036
1036
1035
Notes
aBHC, black hole candidate; HMXB, high mass X-ray binary; LMXB, low-mass X-ray binary system; SN,
su~ova; SNR, supernova remnant; XRBe denotes Be star plus collapsed object binary system; XRT, X-ray transient.
Pulsar periods in seconds are from Taylor, J.H., Manchester, R.N., & Lyne, A.G. 1993, ApJS, 88, 529, and an update
to be found at pulsar.princeton.edu. Binary pulse periods are from Nagase, F. 1989, PAS!, 41, l.
cCelestial coordinates in degrees from Wood, K.S. et al. 1984, ApJS, 56, 507, except for SNl987A (West, R. 1987,
ESO Workshop on the SN1987A, 5); A0620-00 (Boley, F.I. et aI. 1976, ApJ, 203, Ll3); Geminga (Bignami, G.F. et
al. 1983, ApI, 272, L9); Vela Pulsar (Forman, W.R. et al. 1978, ApJS, 38,357); Nova Muscae (West, R. 1991, IAU
Cire. No. 5165); GRSI227+0229 (Jourdain, E. et al. 1991,lnt. Cosmic Ray Corif., 1, 173); PSRI509-58 (Princeton
Pulsar List, 1992); AI524-62(Murdin,P.etaI. 1977,MNRAS, 178, 27);4UI700-37 (Forman, W.R.etal. 1978,ApIS,
38,357); PSRI706-44 (Princeton Pulsar List, 1992); Terzian 2 (Hertz, P.L., & Grindlay, J.E. 1983, ApJ, 275, 105);
1740.7-2942 (Hertz, P.L., & Grindlay, J.E. 1984,ApJ, 278,137); GRSI758-258 (Sunyaev, R. et al. 1991, Sov. Astron.
Lett., 17, 50); Briggs Source (Briggs, M.S. et aI. 1995, ApJ, 442, 638); GS2QOO+25 (Tsunemi, H. et aI. 1989, ApI, 337,
LSI); GS2023+338 (Wagner, R.M. et al. 1989, IAU Cire. No. 4783).
d Galactic coordinates in degrees.
e All distances in kiloparsecs. Those marked with a dagger (t) are assumptions, some of which are based on optical
limitations and some of which are unknown in which case the value of 10 kpc is used. Known distance references
are Crab (Trimble, V. 1968, AI, 73, 535); X Persei (Brucato, RJ., & Kristian, J. 1972, ApI, 173, L105); A0535+26
(Giangrande, A. et al. 1980, A&AS, 40, 289); SNl987A (Arnett, W.D. et al. 1989, ARA&A, 27, 629); A0620-00 (Oke,
220 I
10
y-RAY AND NEUTRINO ASTRONOMY
J.B. 1977,ApJ,lI7,181); Vela (Grenier, IA etal. 1988,A&A, 204,117); A1524-62 (Murdin, P. etal. 1977,MNRAS,
178,27); Her X-I (Bahcall, NA 1973, Sixth Texas Symp., 224,178); 4U1700-37 (Bradt, H.V., & McClintock, J.E.
1983, ARA&A, 21, 13); Terzian 2 (Malkan, M.A. et al. 1980, ApJ, 237, 432); OX 1+4 (Davidsen, A.E et al. 1977, ApJ,
211,866); Cyg X-I (Margon, B.H. et al. 1973, ApJ, 185, L117); Cyg X-3 (Breas, L.L.E. et al. 1973, NaturePS, 242,
66).
f Observed flux in photonslcm2 s keY.
gInferred luminosity per logarithmic interval assuming isotropic emission, E2 x (Flux) = E2 (keV2) x
Distance2 (kpc2) x Flux (photJcm2 s keY) x 2 x 1035 erg/s In E.
hpeak flux from supernova explosion in the Large Magellanic Cloud (LMC).
References
1. Worrall, D.M. et al. 1981, ApJ, 247, L31
2. Paciesas, W.S. et al. 1992, IAU Cire. No. 5580; Harmon, B.A. et al. 1992, IAU Cire. No. 5584; McCrosky, R.E.
1992, IAU Cire. No. 5597
3. Graser, U., & Schonfelder, V. 1982,ApJ, 263, 677
4. Knight, EK. 1982, ApJ, 260, 538
5. Kniffen, D.A. et al. 1992, ApJ, 383, L49
6. Weekes, T.C. 1988, Phys. Rep., 160, 1; Weekes, T.C. 1992, Space Sci. Rev., 59, 315
7. Ricker, O.R. et al. 1976, ApJ, 204, L73
8. Sunyaev, R. et al. 1988, Sov. Astron. Lett., 14, 247
9. Cae, M.J. et al. 1976, Nature,lS9, 544
10. Hermsen, W. 1980, Ph.D. thesis, Leiden University; Bertsch, D.L. et al. 1992, Nature, 357, 306
11. Strickman, M.S. et al. 1996, ApJ, 4(iO, 735
12. Hermsen, W. et al. 1992, AlP Con/. Proc., 280, 204
13. Grove, J.E. et al. 1997, AlP Con/. Proc., 410, 122
14. Thompson, D.J. et al. 1995, ApJS, 101,259
15. Sunyaev, R. et al. 1992, ApJ, 389, L75
16. Ulmer, M.P. et al. 1992, ApJ, 417, 738; Matz, S.M. et al. 1994, ApJ, 434, 288; Marsden, D.C. et al. 1996, ApJ, 491,
L39
17. Harmon, BA et al. 1992, AlP Conj. Proc., 280, 314, 350
18. Trumper, J. et al. 1978, ApJ,l19, L105
19. Levine, A.M. et al. 1984, ApJS, 54, 581
20. Wilson, C.S., & Rothschild, R.E. 1983, ApJ, 274, 717
21. Barret, P.E. et al. 1991, ApJ, 379, L21
22. Orindlay, J.E. et al. 1992, A&AS, 97, 155
23. Cook, M.C. et al. 1991, ApJ, 372, L75; Sunyaev, R. et al. 1992, ApJ, 383, L49
24. Slassi, S. et al. 1991, 22nd International Cosmic Ray Conference, 1,003.2.8
25. Sunyaev, R. et al. 1991, Sov. Astron. Lett., 17, 50
26. Nolan, P.L., & Matteson, J.L. 1983, ApJ, 265, 389
27. Ling, J.C. et al. 1987, ApJ, 321, L1l7
28. Sunyaev, R. et al. 1988, Sov. Astron. Lett., 14, 327
Table 10.5. Brightest annihilation and nuclear line sources.
Process
LineE
(MeV)
FWHM
(keV)
Redshifted
Redshifted
Redshifted
Redshifted
Redshifted
Blueshifted
Backscattered
Backscattered
0.511
0.511
0.511
0.430
0.480
0.481
0.404
0.413
0.500-2.0
0.170
0.19
2
3
< IOC
100
240
60
3
15
Line
source
Max. flux
(phJcm2 s)
Lum.
(ergls)
1.5 x 1O-3a
2 x 10-3
2 x 10- 2
100
1 x 10-2
6 x 10- 3
7 x 10- 3
7 x 10-3
2 x 10-2
7 x 10-4
2 x 10-3
7
I
5
2
6
6
2
6
2
2
7
Refs.
e± Annihilation Radiation
12
40
Interstellar gas
BH? near ocb
Solar flares
OBS0526-66
IE 1740.7-2942
Nova Muscae
CrabPulsar transient
IOJune74 transient
Cygnus X-I
BH?nearOCb
Nova Muscae
x
x
x
x
x
x
x
x
x
x
x
1036
1037
1019
1043
1037
1035d
1036
1035d
1037
1034
lO34d
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[6]
10.4 ASTROPHYSICAL y-RAY OBSERVATIONS /
Table 10.5. (Continued.)
LineE
(MeV)
FWHM
(keV)
~9
44SC(EY, ,8+y)44Ca
26Al(,8+y)26Mg
0.847
1.238
2.598
3.244
0.122
0.068
0.078
l.l57
1.809
5.4
4He(a, n)7Be*
4He(a, p)7Li*
56Fe(p, p'y)
12C, 160(p, x)IOB*
56Fe(p, p'y)
24Mg(p, p'y)
20Ne(p, p'y)
28Si(p, p'y)
12C(p, p'y)
160(p, p'y)
0.429
0.478
0.847
1.023
1.238
1.369
1.634
1.779
4.438
6.129
25 c
30C
5c
30C
7c
15c
22c
20c
97 c
114c
IH(n, y)2H
2.223
2.223
1.790
5.947
< O.lc
Process
Line
source
Max. flux
(phJcm2 s)
Lum.
(erg/s)
I x 10- 3
Ix 10-3
3xlO-4
2xlO-4
4x 10-5
4xlO- 5
4xlO- 5
4xlO- 5
4
6
4
3
3
4
5
8
8
x
x
x
x
x
x
x
x
x
1038
1038
1038
1038
1036
103 3
1033
1034
1036
[II]
[II]
[12]
[12]
[l3]
[14]
[l4]
[15]
[16]
6
7
4
2
6
I
3
4
I
I
x
x
x
x
x
x
x
x
x
x
1019
10 19
10 19
10 19
10 19
1020
1020
1020
1021
1021
[17]
[17]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
[2]
I
6
I
2
x
x
x
x
1022
1036d
1037d
1037d
[2, 18]
[8]
[8]
[8]
Refs.
Radioactive Decay
56Co(EY, ,8+y) 56 Fe
57Co(Ey)57Fe
44Ti(EY)44Sc
Supernova 1987A
Supernova 1987A
Supernova 1987A
Supernova 1987A
Supernova 1987A
SN Remnant CasA
SN Remnant CasA
SN Remnant CasA
Interstellar medium
~Il
~26c
~32c
~
~
~
IC
2c
2c
~3OC
4.5 x 1O-4a
Nuclear Excitation
Solar flares
Solar flares
Solar flares
Solar flares
Solar flares
Solar flares
Solar flares
Solar flares
Solar flares
Solar flares
3
3
I
5
I
2
4
5
5
4
x
x
x
x
x
x
x
x
x
x
10- 2
10-2
10- 2
10- 3
10- 2
10- 2
10- 2
10- 2
10-2
10-2
Neutron Capture
Redshifted
56Fe(n, y)57 Fe
Redshifted
70
95
25
Solar flares
IOJune74 transient
IOJune74 transient
IOJune74 transient
~I
1.5 x 10- 2
3 x 10- 2
1.5 x 10- 2
Notes
aper radian of longitude in the Galactic Plane.
bBlack hole? Near Galactic Center.
cTheoreticai widths for unresolved lines.
dFor a nominal distance of I kpc.
References
I. Haymes, R.C. et aI. 1975, ApJ, WI, 593; Leventhal, M. et aI. 1978, ApJ, 225, LII; Riegler, G.R. et aI. 1981,
ApJ, 248, LI3; Share, G.H. et aI. 1988, ApJ, 326, 717; Wallyn, P. et aI. 1993, ApJ, 403, 621; Leventhal, M. et aI.
1993, ApJ, 405, L25; Purcell, W.R. et aI. 1997, ApJ, 491, 725; Harris, M.J. et aI. 1998, ApJ, SOl, L55
2. Riegler, G.R. et aI. 1981,ApJ, 248, LI3; Leventhal, M. et aI. 1982,ApJ, 260, LI; Leventhal, M. et aI. 1986, ApJ,
302,459
3. ChUpp, E.L. et aI. 1973, Nature, 241, 333; Chupp, E.L. 1984, ARA&A, 22, 359; Murphy, R. et aI. 1990, ApJ,
358,298
4. Mazets, E.P. et aI. 1982, Ap&SS, 84, 173
5. Bouchet, F.R. et aI. 1991, ApJ, 383, U5
6. Goldwurm, A. et aI. 1992,ApJ, 389, L79; Sunyaev, R. et aI. 1992,ApJ, 389, L75
7. Leventhal, M. et aI. 1977, ApJ, 216, 491; Ayre, C.A. et aI. 1983, MNRAS, lOS, 285
8. Ling, J.e. et aI. 1982, AlP Con/. Proc., 77, 143
9. Nolan, P.L., & Matteson, J.L. 1983, ApJ, 265,389; Ling, J.e. et aI. 1987, ApJ, 321, LI17; Ling, J.C., & Wheaton,
W.A. 1989, ApJ, 343, L57
10. Leventhal, M., & MacCallum, C.J. 1980, Ann. N.Y. Acad. Sci., 336, 248; Matteson, I. et aI. 1991, AlP Con!
Proc., 232, 45; Lingenfelter, R.E., & Hua, X.M. 1991, ApJ,381, 426; Smith, D. et aI. 1993,ApJ, 414,165
II. Mahoney, W.A. et aI. 1988, ApJ, 334, LSI; Matz, S.M. et aI. 1988, Nature, 331, 416; Sandie, WG. et aI. 1988,
ApJ, 334, L91; Rester, A.C. et aI. 1989, ApJ, 342, L7I; Theiler, J. et aI. 1990, ApJ, 351, Ul
221
222 I 10
y-RAY AND NEUTRINO ASTRONOMY
Tueller, J. et aI. 1990, ApJ, 351, lAl; Leising, M.D., & Share, G.H. 1990, ApJ, 357, 638
Kurfess, J.D. et aI. 1992, ApJ, 399, Ll37
Rothschild, R.E. et aI. 1998, NucPhys B Proc. Suppl. 69,68
Iyudin, A.F. et aI. 1994, A&A, 284, Ll
Mahoney, W.A. et aI. 1984, ApJ, 286,578; Harris, M.J. et aI. 1990, ApJ, 362, 135; Diehl, R. et aI. 1995, A&A.
298,445; Naya, J. et aI. 1991, Nature, 384, 44
17. Murphy, R. etal. 1990, ApJ, 351, 299
18. Hudson, H.S. et al. 1980, ApJ, 236, L91; Prince, T.A. et aI. 1982, ApJ, 255, L81
12.
13.
14.
15.
16.
Table 10.6. Cyclotron line sources.
(deg)
8 (deg)
I (deg)
b (deg)
Centroid
(keV)
FWHM
(keV)
Field
(10 12 G)
Refs.
3.1 ±0.6
4.3 ±0.9
1.0
[I]
28.5 ±0.5
52.6 ± 1.4
11.0 ± 0.9
1O±3
2.5
[2]
184.56
-5.79
73.3 ± 1.000·b
<4.9
6.7
[3]
83.95
+26.29
181.09
-3.24
~55
4.3
[4]
Xray
Binary
135.53
-40.56
263.06
3.93
25.6±0.9
57.9± 1.0
7.2±2.6
24.0± I
2.2
[5]
Cen X-3
1119-603
Xray
Binary
170.31
-60.62
292.09
0.34
28.5 ±0.5
6.3 ± 2.0
2.5
[6]
1538-522
Xray
Binary
235.60
-52.39
327.42
+2.16
20.9 ± 0.2c
5.1 ± 0.3c
1.7
[7]
4Ul626-67
1627-673
Xray
Binary
248.07
-67.46
321.79
-13.09
~7± Ib
~3
[8]
Source
name
Object
type
IX
0115+634
Xray
Binary
19.82
+63.82
126.00
+1.11
12.1 ±0.2
22.6±0.4
0332+530
Xray
Binary
53.75
+53.18
146.05
-2.19
NP0531
0531+219
Pulsar
83.63
+22.01
0535+262
Xray
Pulsar
Vel X-I
0900-403
~11O
~ 18 ± Ib
36.5 ± 1.0
15
7±2.8
34.7 ±0.9c
12.0± 2.OC
2.9
[9]
~
Her X-I
1656+354
Xray
Binary
254.46
+35.34
58.15
+37.52
1907+097
Xray
Binary
287.41
+9.83
43.74
0.48
20.0± 1.0
4.1 ± 2.6
1.7
[10]
CepX-4
2137+579
Xray
Binary
324.88
+57.99
99.68
+4.06
30.5 ±0.4
15.0 ± 1.4
2.6
[II]
GRB870303
y burst
20.4 ± 0.7
40.6±2.6
3.5 ±2.7
12.3 ±6.3
~
1.7
[12]
GRB880205
y burst
19.3 ±0.7
38.6± 1.6
4.1 ± 2.2
14.4±4.6
~
1.7
[12]
GRB890929
y burst
26.3 ± 1.5
46.6± 1.7
75+4·5
. -4.1
~
2.1
[13]
Notes
°Transient line seen between 73 and 79 keY.
bErnission line.
CLine centroid and width are observed to vary with pulse phase.
12.7:t~
10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / 223
References
1. Nagase, F. et al. 1991, ApJ, 375, LA9
2. Makishima, K. et aI. 1990, ApJ, 365, L59
3. Ling, J.C. et aI. 1979, ApJ, 231, 896; Ayre, C.A. et aI. 1983, MNRAS, lOS, 285
4. Grove, J.E. et aI. 1995, ApJ, 438, L25; Maisack, M. et aI. 1997, AM, 325,212
5. Makishima, K., & Mihara, T. 1992, Frontiers ofX-Ray Astronomy (University Academy Press, Tokyo)
p. 23; Mihara, T. 1995, Thesis, University of Tokyo; Kretschmar, P. et aI. 1997, AM, 325, 623; DaI
Fiume, D. et aI. 1998, Nuc Phys B Proc. Suppl., 69, 145
6. DaI Fiume, D. et aI. 1998, Nuc Phys B Proc. Suppl., 69, 145
7. Clark, G.W. et aI. 1990, ApJ, 353,274
8. Pravdo, S.H. et aI. 1979,ApJ, 231, 912; Orlandini, M. 1998, ApJ, 500, L163
9. Mihara, T. et aI. 1990, Nature, 346,250
10. Makishima, K., & Mihara, T. 1992, Frontiers of X-Ray Astronomy (University Academy Press, Tokyo)
p. 23; Mihara, T. 1995, Thesis, University of Tokyo
11. Mihara, T. et aI. 1991, ApJ, 379, L61
12. Murakami, T. et aI. 1988, Nature, 335, 234
13. Yoshida, A. et aI. 1991, PASJ, 43, L69
Table 10.7. y-Ray burst source positions < 100 arcmin 2.a ,b
Burst
source
Date
(yrmo day)
Time
(s)
GBSoolO-16O
GBS0026-630
GBS0117-289
GBS0502+118
GBS0526-661
GBS0615-461
GBS0625-346
GBS0653+ 793
GBS0702+388
GBS0723-271
GBS0813-326
GBS0836-189
GBS0847-361
GBS0912-51O
GBS 1028+459
GBSl104-229
GBS1156+652
GBS1205+239
GBS1257+592
GBS1327+375
GBS1330-164
GBSI4OO-468
GBS1407+353
GBS1412+789
GBS1450-693
GBS 1528+ 196
GBS1625-583
GBS 1630-765
GBS 1703+006
GBS1730+491
GBS1756-261
GBS1806-207
7911 16
98010ge
78 11 19
970228d
790305bc
790313
791014
970508d
9803 2~
91 11 09
920501
980326d
9203 11
910522
790329
91 11 18
971214d
781124
971227d
920720
920517
790307
91 11 04
790613
970402e
9701 lie
910717
7901 13
78 11 21a
960720
910421
790107c
51400
4341
34021
10681
57125
62636
40412
78106
13478
12458
76695
76733
08423
44036
80512
68252
84041
14130
30187
11524
11875
80330
54282
50755
80352
35040
16378
27360
05736
41813
33246
20155
F>30keV
(erglcm2 )
10-4
10-6
10-4
10-5
10- 3
10-5
10- 5
10- 6
10- 5
10- 6
10-5
10-6
10-4
10-5
10-5
10- 5
10- 5
10- 5
10- 7
10-5
10-5
10-4
10-5
10-7
~ 10- 5
~ 10- 5
7 x 10-6
I x 10-4
9 x 10- 5
3 x 10- 6
4 x 10- 6
1 x 10- 6
2x
4x
3x
1x
1x
6x
1x
4x
5x
7x
4x
1x
1x
3x
7x
5x
I x
4x
7x
2x
4x
2x
1x
4x
ex
(deg)
8
(deg)
(deg)
b
(deg)
Error box
(arcmin2)
3.20
6.48
19.72
75.43
81.51
94.1
96.7
103.37
105.65
110.8
123.34
129.14
131.8
137.9
157.8
166.0
179.13
181.94
194.31
201.8
202.6
210.69
211.8
213.1
222.53
232.06
246.3
249.2
256.4
262.65
268.9
272.17
-15.69
-63.02
-28.64
+11.78
-66.08
-46.1
-34.6
+79.29
+38.84
-27.1
-32.59
-18.86
-36.1
-51.0
+45.6
-22.9
+65.20
+23.65
+59.40
+37.5
-16.4
-46.99
+35.3
+78.9
-69.33
+19.60
-58.3
-76.6
+0.5
+49.10
26.1
-20.41
82.85
307.50
228.50
188.91
276.09
253.8
242.6
134.94
178.12
240.6
250.80
242.37
257.8
271.9
169.9
272.9
132.02
229.93
121.55
89.2
316.3
315.37
64.4
118.0
313.11
29.63
328.1
314.7
20.7
75.76
51.5
10.0
-75.46
-53.86
-83.75
-17.95
-33.24
-25.0
-19.7
+26.71
+18.65
-5.6
+0.96
+13.03
+4.5
-1.9
+56.6
+33.6
+50.95
+79.54
+57.71
+77.2
+45.5
+14.15
+71.9
+37.7
-8.84
+53.39
-6.3
-19.2
+23.6
+33.09
+23.2
-0.24
4
50
8
2
0.05
24
82
28
3
6
4
80
4
4
41
20
48
48
7
6
12
10
16
0.8
2
28
10
78
~ 100
28
~ 100
6
224 /
10
y-RAY AND NEUTRINO ASTRONOMY
Table 10.7. (Continued.)
Burst
source
Date
(yrmoday)
Time
(s)
F>30keV
(erglcm2)
GBS1808+593
GBS181O+314
GBSI847+728
GBS 1900+ 145
GBS1912-577
GBS 1926+036
GBS2ooo-427
GBS2006-216
GBS2142-414
GBS2252-025
GBS231 1+319
GBS2311-499
GBS2320+128
970828e
790325b
920711
790324c
920406
790331
920525
7811 O4b
7906 22
7911 05b
790504
790406
920325
63877
49500
58166
58010
09915
76172
12427
58667
02665
48862
31464
42447
62261
_10-5
5 x 10-5
8 x 10-6
1 x 10-6
1 x 10-4
8 x 10-5
1 x 10-4
3 x 10-4
7 x 10-5
1 x 10-5
6 x 10-6
1 x 10-6
3 x 10-5
(deg)
8
(deg)
(deg)
(deg)
Error box
(arcmin2)
272.13
273.0
281.8
286.83
288.0
292.0
300.0
302.2
326.4
343.55
348.4
348.51
349.9
+59.13
+31.4
+72.8
+9.45
-57.7
+3.7
-42.7
-21.5
-41.2
-2.26
+32.1
-49.66
+12.8
87.95
58.2
103.7
43.08
339.0
40.4
357.2
21.1
0.3
69.45
99.9
336.03
90.8
+28.45
+21.6
+26.1
+0.81
-25.3
-6.4
-30.1
-26.2
-49.6
-52.51
-26.3
-60.74
-44.3
0.8
2
100
7
4
20
6
14
- 100
35
58
0.3
7
a
b
Notes
aQuiescent X-ray counterparts have been suggested for the three repeater burst sources GBS0526-661,
GBS1806-207 and GBSI900+145, which are associated with supernova remnants N49, GlO.0-0.3, and G42.8+O.6
(see note c below and Rothschild, R.E., & Lingenfelter, R.E. 1996, High Velocity Neutron Stars and Gamma-Ray Bursts
(AlP, New York». No quiescent counterparts have been identified for the "classical" bursts, but fading afterglow sources
have been seen following several bursts (see note d) and underlying "host" galaxies have been reported.
bLocations (2000 coordinates) for bursts prior to 1990 are based on catalog of Atteia, J.L. et al. 1987, ApJS, 64, 305,
and ftuences from Mazets, E.P. et al. 1981, Ap&SS, SO, I, except as follows: GBS1550+762 data from Hueter, G.J.
1987, Ph.D. Dissertation, University of California, San Diego; GBS1806-207 position from Atteia, J.L. et al. 1987,
ApJ, 320, LlI0, and private communication; GBS 1900+ 145 position also from Mazets, E.P. et al. 1981; GBS0746-672
data from Katoh, T. et al. 1984, in AlP Conf. Proc. 115, 390; locations of bursts after 1990 are from Hurley, K., private
communication on behalf of the 3rd Interplanetary Network; and from BeppoSAX burst detections listed in notes d and
e. Fluences are from Third BATSE Catalog (Meegan, C.A. et al. 1996, ApJS, 106, 65, and the online update of that
catalog.
cRepeaters: 17 bursts have been observed from the source GBS0526-661 (Golenetskii, S.V. et al. 1979, SOy. Astron.
Lett., 13, 166) associated with supernova remnant N49 in LMC and possibly an X-ray source at a 05h26mO.55 s, .5
-66°4'35.56" (Rothschild, R.E., Kulkarni, S.R., & Lingenfelter, R.E. 1994, Nature, 368, 432); > 100 bursts from
GBS1806-204 (Atteia, J.L. et al. 1987, ApJ, 320, Ll05; Laros, J.G. et al. 1987, ApJ, 320, L111) associated with
Galactic supernova remnant GlO.0-0.3 and an X-ray source at a 18h8m4O.34s , 8 -20°24'41.67" (Murakami, T. et
al. 1994, Nature, 368, 127), and six bursts from GBSI900+145 (Mazets, E.P. et al. 1979, SOy. Astron. Lett., 5, 343;
Kouveliotou, C. et al. 1993, Nature, 362,728; Hurley, K. etal. 1994, ApJ, 431, L31) associated with Galactic supernova
remnant G42.8+0.6 and possibly an X-ray source ata Igh7m 17s, 8 +9°19'18" (Vasisht, G. et al. 1994,ApJ, 431, L35).
dFading optical sources have been observed for GRB0502+118 (Costa, E. et al. 1997, IAU Circ. No. 6572) at
V = 21.3 discovered 0.9 days after burst at a 05 hOl m46.61 s, 8 +11°46'53.4" (van Paradijs, I. et al. 1997, Nature,
386,686); GRB0653+793 (Heise, J. et al. 1997, IAU Cire. No. 6654) at V = 20.5 discovered 1.28 days after burst
at a O6h53 m49.43 s, 8 +79°16'19.6" (Bond 1997, IAU Circ. No. 6654) and red-shifted absorption lines observed with
z = 0.835 (Metzger, M.R., et al. 1997, Nature, 387. 878); GBS0702+388 (in't Zand, J. et al. 1998, IAU Circ.
No. 6854) at 250 ILJy at 8.4 GHz discovered 2.9 days after burst at a 07h02m38.0217OS, .5 +38°50'44.0170" (Taylor,
G.B. et al. 1998, GeN. No. 40) and at K = 21.4 after 4 days (Metzger, M.R. et al. 1998, IAU Cire. No. 6874)
GBS0836-189 (Celidonio, G. et al. 1998, IAU Cire. No. 6851) at R = 21.7 discovered 0.5 days after burst at
a 8h36m34.28s, 8 -18°51'23.9" (Groot, P.J. et al. 1998, IAU Cire. No. 6852) GRB1156+652 (Heise, J. et al. 1997,
IAU Circ. No. 6787) at I = 21.2 discovered 0.5 days after burst at a 11 h56m26.4s, .5 +65°12'00.5" (Halpern, J. et
al. 1997, IAU Circ. No. 6788) and red-shifted emission lines observed with z = 3.4 (Kulkarni, S. et al. 1998, Nature,
393, 35) GBS1257+592 (Piro. L. et al. 1997, IAU Cire. No. 6797) at R = 19.5 discovered 0.6 days after burst at
a 12h57m 1O.6s, .5 +59°24'43" (Castro-Trrado, A.J. et al. 1997, IAU Circ. No. 6800)
eNo fading optical sourees were observed for GBS0026-630 (in't Zand, J. et al. 1998, IAU Cire. No. 6805) with
I < 21 (Sahu, K.C., & Sterken, C. 1998,lAU Cire. No. 6808) GBS1450-693 (Piro. L. et al. 1997, IAU Circ. No. 6617)
with V < 22.5 (Pedersen, H. et al. 1997, IAU Circ. No. 6628) GBS1528+196 (in't Zand, J. et al. 1997, IAU Cire.
No. 6569) with R < 22.6 (Castro-Trrado, A.J. et al. 1997, IAU Circ. No. 6598) GBS1808+593 (Murakami, T. et al.
1997, IAU Cire. No. 6732) with R < 24.5 (Odewahn, S.C. et al. 1997, IAU Circ. No. 6735)
10.4 ASTROPHYSICAL y-RAY OBSERVATIONS / 225
Table 10.8. y -Ray burst propenies. a
Property
Observed values
Energy range
~
Comments
References
"Soft" Repeating Bursts
1 keV-l MeV
y-yopacity
constraints
with E 2: 25 keY
Redshifted e- e+
Annihilation radiation
[ 1]
Energy spectra
rf>(hv) ex exp(-hv/E)
Emission features
~
Rise times
Size < 60km
[3]
Durations
As short as 0.2 ms
~ 1O-2_~ 102 s
Periodicity
8.0 s
~23ms
Burst GB790305b
Burst GB790305b
[3,4]
[5]
Source
Off-center in
Supernova remnants
high-velocity
neutron stars?
[6]
Energy range
~
Energy spectra
rf>(hv)
rf>(hv)
430keV
[1]
[2]
[1]
"Classical" Bursts
Eo
1 keV-20 GeV
~
(hv)S
(hv)S
50-1000 keY
~
~
y-yopacity
constraints
with s :5 -1 for (hv)S < Eo
with s :5 -2 for (hv)S > Eo
[7]
[9]
[8]
Absorption features
20-50keV
Cyclotron absorption
~ few 10 12 G fields
Rise times
As short as 0.2 ms
~ 1O-2_~ 104 s
Size < 60km
(V/Vmax )
(cos8)
Galactocentric angle 8
0.33 ±0.01
Spatially nonuniform
[ 11]
-0.01 ±0.02
Isotropic
[11]
Source
Optical transient
and host galaxies?
for several bursts
at z ~ 0.8-3.4
Durations
[10]
[7]
=0
[12]
[12]
Note
aFor general reviews, see also Higdon, J.c., & Lingenfelter, R.E. 1990, ARA&A, 28, 401;
Harding, A.K. 1991, Phys. Rep., 206, 327; Fishman, GJ., & Meegan, C.A. 1995, ARA&A, 33, 415;
Rothschild, R.E., & Lingenfelter, R.E. 1995, High Velocity Neutron Star and Gamma-Ray Bursts
(American Institute of Physics, New York) 282 pp.; Kouveliotou, C., Briggs, M.E, & Fishman, GJ.
1996, Gamma-Ray Bursts (American Institute of Physics, New York) 1008 pp.
References
1. Mazets, E.P. et al. 1981, Ap&SS, SO, 1; Mazets, E.P., & Golenetski, S.V. 1981, Ap&SpPhysRev,
1,205; Mazets, E.P. et al. 1982,Ap&SS, 82, 261; Atteia, J.L. et al. 1987,ApJ, 320, Ll05; Laros,
J.G. et al. 1987, ApJ, 320, L111; Murakami, T. et al. 1994, Nature, 368, 127
2. Mazets, E.P. et al. 1982, Ap&SS, 84, 173
3. Cline, T.L. et al. 1980, ApJ, 237, LI
4. Mazets, E.P. et al. 1979, Nature, 282, 587; Barat, C. et al. 1979, A&A, 79, L24
5. Barat, C. et al. 1983, A&A, 126,400
6. Rothschild, R.E., & Lingenfelter, R.E. 1995, High Velocity Neutron Star and Gamma-Ray Bursts
(American Institute of Physics, New York) 282 pp.; and previous Table 10.7
7. Mazets, E.P. et aJ. 1981, Ap&SS, SO, 1; Mazets, E.P., & Golenetski, S.V. 1981, Ap&SpPhysRev,
1,205; Meegan, C.A. et al. 1996, ApJS, 106,65; Hurley, K. et al. 1979, Nature, 372, 652
8. Mazets, E.P. et al. 1981, Ap&SS, SO, 1; Band, D. et al. 1993, ApJ, 413, 281; Higdon, J.c., &
Lingenfelter, R.E. 1986, ApJ, 307, 197
9. Murakami, T. et al. 1988, Nature, 335, 234; Mazets, E.P. et al. 1982, Ap&SS, 82, 261; Hueter,
GJ. 1987, Ph.D. thesis, University of California, San Diego
10. Walker, K.c., & Schaefer, B.E. 1998, "Gamma Ray Bursts," AlP Conf. Proc., 428, edited by C.
226 /
10
y-RAY AND NEUTRINO ASTRONOMY
Meegan. R. Preece. and T. Kashut (AlP. New York) p. 34
11. Meegan. C.A. et aI. 1996. ApJS. 106. 65
12. See previous Table 10.7
Table 10.9. Extragalactic hard X-ray or y-ray sources. a
Source
name
Object
type
NGC253
0045-255
Starburst
galaxy
4C+15.05
0202+149
0208-512
ab
8
Z
de
Fluxd
Energy
Lum. e
11.27
-25.56
0.6
0.0036
2 x 10-3
100keV
5 x 1046
[1]
QSO
blazar
30.53
+15.00
0.833
3.25
3 x 1O- ge
100 MeV
1 x l(f7
[2]
QSO
blazar
32.24
-51.25
1.003
6.0
5x
7x
1x
1x
2x
10-8
10-9
10-9
10- 10
10- 11
30 MeV
100 MeV
300 MeV
lOeV
30eV
3x
5x
6x
7x
1x
1048
[3]
[3]
[3]
[3]
[3]
100 MeV
1 x 1046
[4]
l(f7
l(f7
l(f7
l(f7
Refs.
3C66A
0219+428
BLLac
34.88
+42.81
0.833
3.25
1 x 10-91
4C+28.07
0234+285
BLLac
38.73
+28.59
1.213
3.97
3 x 10-91
100 MeV
3 x 1047
[4]
0235+164
BLLac
38.97
+16.40
0.94
5.6
2x
6x
8x
8x
1x
10- 8
10-9
10- 10
10- 11
10- 11
50 MeV
100 MeV
300 MeV
lOeV
30eV
3
4
4
5
6
1047
1047
1047
1047
1047
[5]
[5]
[5]
[5]
[5]
NGC 1275
0316+413
Seyfert-2
49.12
+41.33
0.0172
0.10
2 x 10- 1
3 x 10- 2
5 x 10- 3
30keV
100 keY
300keV
3 x 1044
6 x 1044
1 x 1045
[6]
[6]
[6]
crA26
0336-019
QSO
blazar
54.25
-1.94
0.852
3.29
1 x 10-81
100 MeV
5 x 1048
[4]
3C 111
0415+379
Seyfert-l
63.75
+37.90
0.0485
0.283
3 x 10-31
lookeV
5 x 1044
[7]
OA 129
0420-014
QSO
blazar
65.18
-1.46
0.915
5.5
4 x 10-91
100 MeV
2 x 1047
[2]
3C 120
0433+052
Seyfert-l
67.63
+5.25
0.0330
0.194
3 x 10-31
l00keV
2 x 1044
[7]
NRA0190
0440-003
QSO
blazar
70.02
-0.39
0.844
3.27
9 x 10-91
100 MeV
4 x 1047
[4]
0454-463
QSO
73.60
-46.34
0.86
5.2
3 x 10-91
100 MeV
1 x 1047
[2]
4C-02.19
0458-020
QSO
blazar
74.67
-2.06
2.286
4.98
3 x 10-91
100 MeV
1 x 1048
[4]
0521-365
BLLac
81.00
-36.49
0.055
0.32
2 x 10-91
100 MeV
4 x 1044
[4]
x
x
x
x
x
10.4 ASTROPHYSICAL y-RAY OBSERVATIONS /
Table 10.9. (Continued.)
Source
name
Object
type
Olb
8
z
de
0528+134
QSO
blazar
82.03
+31.50
2.06
12.4
0537-441
BLLac
84.34
-44.11
MCG 8-11-11
0551+464
Seyfert-I
87.79
+46.43
0716+714
BLLac
109.05
+71.44
OI 158
0735+178
BLLac
113.81
+17.82
0827+243
QSO
blazar
OJ 49
0829+046
Energy
Lum. e
10-7
10- 8
10-9
10- 11
10- 12
30 MeV
100 MeV
300 MeV
lGeV
3GeV
8x
6x
3x
1x
8x
1048
1048
1048
1047
[8]
[8]
[8]
[8]
[8]
0.894
5.4
2 x 10-9
2 x 10- 10
2 x 10- 11
100 MeV
300 MeV
1 GeV
1 x 1047
1 x 1047
1 x 1047
[9]
[9]
[9]
0.0205
0.12
2
6
2
6
3
30keV
l00keV
300keV
1 MeV
10 MeV
5x
2x
5x
2x
1x
1044
1045
1045
1046
1046
[10]
[10]
[10]
[10]
[10]
F1uxd
3x
2x
1x
4x
3x
x
x
x
x
x
10- 1
10- 2
10- 2
10- 3
10-5
ur8
Refs.
2 x 10-9
100 MeV
0.424
2.04
3 x 1O- 9j
100 MeV
4 x 1046
[4]
127.80
+24.05
2.046
4.83
7 x 1O-9j
100 MeV
2 x 1048
[4]
BLLac
127.30
+4.66
0.18
0.98
2 x 1O- 9j
100 MeV
5 x 1045
[4]
4C+71.07
0836+710
QSO
blazar
129.09
+71.07
2.172
4.92
3 x 1O-9j
100 MeV
1 x 1048
[2]
0917+449
QSO
blazar
139.43
+44.91
2.18
4.51
3 x 1O-9j
100 MeV
1 x 1048
[4]
MCG -5-23-16
0945-307
Seyfert-2
146.37
-30.72
0.0485
0.283
4 x 1O- 3j
lOOkeV
2 x 1043
[7]
4C+55.17
0954+556
QSO
blazar
148.56
+55.62
0.909
3.42
5 x 1O-9j
100 MeV
3 x 1047
[4]
0954+658
BLLac
148.74
+65.80
0.368
1.82
2 x 1O- 9j
100 MeV
I x 1046
[4]
MRK421
1101+384
BLLac
165.42
+38.48
0.0308
0.18
1x
4x
7x
2x
2x
2x
2x
3x
10- 1
10- 2
10-9
10-9
10- 10
10- 11
10- 12
10- 17 j
30keV
lOOkeV
50 MeV
100 MeV
300 MeV
1 GeV
3GeV
500GeV
6x
3x
I x
I x
1x
1x
1x
5x
1044
1045
1044
1044
1044
1044
1044
1043
[11]
[11]
2 x 1O- 8j
100 MeV
7 x 1047
[4]
4C+29.45
1156+295
QSO
blazar
179.24
+29.52
0.729
2.99
[2]
[12]
[12]
[12]
[12]
[12]
[13]
227
228 / 10
y-RAY AND NEUTRINO ASTRONOMY
Table 10.9. (Continued.)
Source
name
Object
type
NGC4151
1208+396
Seyfert-l
WComae
1219+285
ab
Z
de
FJuxd
182.00
+39.68
0.003
0.018
2x
5x
1x
8x
BLLac
184.76
+28.51
0.102
0.58
4C+21.35
1222+216
QSO
blazar
185.60
+21.66
NGC4388
1223+126
Seyfert-2
185.81
+12.94
3C273
1226+023
QSO
1227+023
Energy
Lum. e
30keV
100 keY
300keV
1 MeV
1x
3x
6x
5x
1043
1043
1043
1044
[I 4]
[14]
[14]
[14]
5 x 10-91
100 MeV
4 x 1045
[4]
0.435
2.08
5 x 10-91
100 MeV
7 x 1046
[4]
0.00842
0.051
6 x 10- 31
100 keY
3 x 1043
[7]
186.64
+2.33
0.158
0.95
1x
1x
5x
2x
2x
2x
2x
1x
1x
3x
30keV
l00keV
300keV
1 MeV
3 MeV
10 MeV
30 MeV
100 MeV
300 MeV
lGeV
2
2
8
3
3
3
3
2
2
5
[15]
[I5]
[16]
[17]
[17]
[17]
[17]
[17]
[17]
[17]
QSO
186.83
+2.41
0.57
3.4
3 x 10- 1
2 x 10-2
40keV
l00keV
1 x 1048
5 x 1047
[18, 19]
[18, 19]
4C-02.55
1229-021
QSO
blazar
187.36
-2.13
1.045
3.68
2 x 10-91
100 MeV
1 x 1047
[4]
M87
1228+124
NELG
187.08
+12.67
(0.0042)
0.025
1 x 10- 1
6 x 10- 3
30keV
l00keV
1 x 1043
7 x 1042
[20]
[20]
3C279
1253-055
QSO
193.40
-5.52
0.538
3.2
2x
3x
2x
2x
3x
3x
4x
4x
3 MeV
10 MeV
30 MeV
100 MeV
300 MeV
1 GeV
3GeV
IOGeV
4
6
4
4
5
6
7
8
1047
1047
1047
1047
1047
1047
1047
1047
[17]
[17]
[21]
[21]
[21]
[21]
[21]
[21]
XComae
1257+286
Seyfert-l
194.49
+28.67
0.092
0.55
2 x 10- 1
3 x 10- 2
30keV
l00keV
1 x 1046
2 x 1046
[22]
[22]
1313-333
QSO
blazar
198.33
-33.39
1.21
3.96
2 x 10-91
100 MeV
3 x 1047
[4]
CenA
1322-427
Radio
galaxy
200.74
-42.71
(0.001825)
0.0073
1x
1x
2x
2x
7x
30keV
l00keV
300keV
1 MeV
10 MeV
1x
1x
2x
2x
7x
1043
1043
1043
1043
1043
[23]
[23]
[23]
[24]
[24]
OP 151
1331+170
QSO
blazar
202.79
+17.07
100 MeV
3 x 1047
[4]
8
2.084
4.86
10- 1
10-2
10-2
10- 3
10- 1
10- 2
10- 3
10-4
10-5
10-6
10-7
10- 8
10-9
10- 11
10- 5
10-6
10-7
10-8
10-9
10- 10
10- 11
10- 12
10°
10- 1
10- 2
10- 3
10-5
1 x 10-91
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
1046
1046
1046
1046
1046
1046
1046
1046
1046
1045
Refs.
10.4 ASTROPHYSICAL y-RAY OBSERVATIONS /
Table 10.9. (Continued.)
Source
name
Object
type
MCG -6-30-15
1314-340
Seyfert-l
IC4329A
1346-300
ab
z
de
Fluxd
Energy
Lum. e
203.26
-34.04
0.00775
0.048
5 x 1O- 3j
l00keV
2 x 1(j43
[7]
Seyfert-l
206.62
-30.06
0.01605
0.094
7 x 1O- 3j
l00keV
1 x 1<J"4
[7]
MRK279
1348+700
Seyfert-l
207.97
+69.55
0.0294
0.175
3 x 1O- 3j
l00keV
2 x 1<J"4
[7]
OQ-OIO
1406-076
QSO
blazar
211.58
-7.64
1.494
4.34
1 x 1O-8j
100 MeV
2 x 1048
[4]
NGC5548
1415+255
Seyfert-l
214.50
+25.14
0.0168
0.100
4 x 1O- 3j
100 keY
8 x 1043
[7]
1424-418
QSO
blazar
216.00
+41.80
1.522
4.37
6 x 1O-9j
100 MeV
1 x 1048
[4]
OR-017
1510-089
QSO
blazar
227.54
-8.91
0.361
1.79
5 x 1O-9j
100 MeV
5 x 1046
[4]
4C+15.54
1604+159
BLLac
241.21
+15.99
0.357
1.78
4 x 1O-9j
100 MeV
4 x 1046
[4]
OS 319
1611+343
QSO
blazar
242.95
+34.34
1.401
4.23
7 x 1O- 9j
100 MeV
1 x 1048
[4]
1622-253
QSO
blazar
245.68
-25.35
0.786
3.14
7 x 1O-9j
100 MeV
3 x 1047
[4]
1622-297
QSO
blazar
246.36
-29.92
0.815
3.21
3 x 1O- 8j
100 MeV
1 x 1048
[4]
4C 38.41
1633+382
QSO
248.38
+38.24
1.814
10.9
10- 8
10-9
10- 10
10- 11
10- 11
10- 12
50 MeV
100 MeV
300 MeV
lGeV
3GeV
IOGeV
1x
1x
1x
2x
2x
2x
1048
1048
1048
1048
1048
1048
[25]
[25]
[25]
[25]
[25]
[25]
NRA0530
1730-130
QSO
blazar
262.56
-13.05
0.902
3.40
1 x 1O- 8e
100 MeV
6 x 1047
[4]
4C+51.37
1739+522
QSO
blazar
264.87
+52.22
1.375
4.19
4 x 1O-9j
100 MeV
5 x 1047
[4]
ar-68
1741-038
QSO
blazar
265.34
-3.81
1.054
3.70
4 x 1O-9j
100 MeV
3 x 1047
[4]
3C 390.3
1845+797
Seyfert-I
281.41
+79.75
0.0561
0.326
3 x 1O- 3j
l00keV
7 x 1<J"4
[7]
1933-400
QSO
blazar
293.46
-40.08
0.966
3.53
1 x 1O-8j
100 MeV
7 x 1047
[4]
NGC 6814
1942-102
Seyfert-l
295.67
-10.32
0.00521
0.030
3 x 1O- 3 j
100 keY
6 x 1042
[7]
NRA0629
2022-077
QSO
blazar
305.75
-7.76
1.388
4.21
7 x 1O-9j
100 MeV
9 x 1047
[4]
8
2x
6x
7x
8x
1x
1x
Refs.
229
230 /
10
y-RAY AND NEUTRINO ASTRONOMY
Table 10.9. (Continued.)
Source
name
Object
type
MRK509
2041-107
Seyfert-I
2052-474
ab
z
dC
Fluxd
Energy
Lum. e
310.36
-10.91
0.0344
0.203
4 x 10-31
100 keY
3 x 10«
[7]
QSO
blazar
314.52
-46.96
1.489
4.33
3 x 10-91
100 MeV
5 x Hf7
[4]
2155-304
BLLac
328.99
-30.47
0.116
0.655
3 x 10-91
100 MeV
3 x 1045
[4]
BLLacertae
2200+420
BLLac
330.16
+42.04
0.0686
0.398
4 x 10-91
100 MeV
I x 1045
[4]
2209+236
QSO
blazar
332.51
+23.97
1.489
4.33
I x 10-91
100 MeV
2 x 1047
[4]
CTA 102
2230+114
QSO
337.53
+11.47
1.037
6.2
4 x 10-9
100 MeV
3 x 1047
[2]
3CR454.3
2251+158
QSO
342.87
+15.88
0.859
5.2
8 x 10-9
100 MeV
4 x 1047
[2]
NGC7582
2318-422
Seyfert-2
344.18
-43.23
0.00525
0.033
3 x 10- 31
lOOkeV
6 x 1042
[7]
OZ 193
QSO
blazar
359.05
+19.64
1.066
3.72
3 x 10- 91
100 MeV
2 x 1047
[4]
2356+196
8
Diffuse
background
5
2
I
I
I
2
x
x
x
x
x
x
IO I /sr
lOo/sr
IO- I /sr
1O- 2/sr
1O-4/sr
1O-7/sr
Refs.
[26]
[26]
[26]
[26]
[26]
[26]
30keV
100 keY
300keV
I MeV
10 MeV
100 MeV
Notes
a Source type, position, and redshiftare from Hewitt, A., & Burbidge, G. 1987,ApJS, 63, I; 1989,ApJS, 69, I;
and 1991, ApJS, 75, 297, except for M87 and Cen A from Tully, R. 1988, Nearby Galaxies Catalog (Cambridge
University Press, Cambridge) for which the redshifts are corrected for local motion, and for GRS1227+0229
from Grindlay, I.E. 1993,A&AS, 97,113.
bPositions in degrees.
CDistances in Gpc assume cosmological redshifts with HO = 50 kmls Mpc. d (Gpc)
=6 x
(I+Z)~-1
(l+z) +1
dFlux in photonslcm2 s MeV at the energy denoted.
e Assuming isotropic emission, E2 x (flux) = E2 (keV2) x z2 x [flux (phot./cm)2 sMeV] x 7 x
1045 ergs/sin E.
1 Differential flux determined from integral flux assuming a differential spectrum of the form E- 2 .
References
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6. Rothschild, R.E. et aI. 1981, ApJ, 243, L9
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22.
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25.
26.
Punch, M. et al. 1992, Nature, 358, 477
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Bassani, L. et al. 1991, 22nd Int. Cosmic Ray Can!, 1, 173
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Grindlay, J.E. 1993, A&AS, 97, 113
Lea, S. et al. 1981, Api, 246, 369
Kniffen, D.A. et al. 1993, Api, 411,133
Bazzano, A. et al. 1990, Api, 362, L51
Baity, W.A. et al. 1981, Api, 244, 429
von Ballmoos, P. et al. 1987, Api, 312, 134
Mattox, J.R. et a1. 1993, Api, 410, 609
Rothschild, R.E. et al. 1983, Api, 269, 423
Table 10.10. Hard X-ray and y-ray instruments in space since 1970.
Energy range
tl.E/E
Field of view
resolution
Area
(cm2 )
Date
OSO-7
6-500keV
33% @6OkeV
6.5°
64
1971-73
Peterson
UCSD
[ 1]
Solar X-ray
telescope
OSO-7
10-350keV
18% @6OkeV
90° x 20°
9.6
1971-73
Peterson
UCSD
[2]
y-ray
monitor
OSO-7
0.3-10 MeV
< 8%@662keV
120° x 70°
45
1971-73
Chupp
UNH
[3]
y-ray
telescope
SAS-2
30-200 MeV
30°
~ 2°
115
1972-73
Fichtel
GSFC
[4]
Scintillator
telescope
Ariel-V
26 keV-1.2 MeV
30% @662keV
8°
8
1974--80
Imperial
College
[5]
Celestial
X-ray detector
y-ray
detector
OSO-8
15 keV-3 MeV
50% @6OkeV
50MeV-2GeV
40% @ 100 MeV
5°
28
1975-78
[6]
75
1975-82
Frost
GSFC
Caravane
Collaboration
A-4LED
HEAO-I
15-180keV
25%@6OkeV
1.2° x 20°
206
1977-79
Peterson-Lewin
UCSD-MIT
[8]
A-4MED
HEAO-l
0.1-2 MeV
10% @ 1 MeV
16.5°
160
1977-79
Peterson
UCSD
A-4HED
HEAO-l
0.2-10 MeV
1O%@ 1 MeV
40°
120
1977-79
Peterson
UCSD
C-I germanium
spectrometer
HEAO-3
50 keV-I0 MeV
0.2% @ 1.8 MeV
30°
64
1979-80
Jacobson
JPL
[9]
GRS
SMM
0.3-9 MeV
7%@662keV
180°
310
1979-89
Chupp
UNH
[10]
HXRBS
SMM
20-26OkeV
30% @ 122keV
40°
71
1979-89
Frost
GSFC
[11]
HEXE
MIR
KVANT
15-200keV
30% @6OkeV
1.6° x 1.6°
800
1987-
Trumper
MPI
[12]
Pulsar X-I
KVANT
50-800keV
3° x 3°
1256
1987-
[13]
GSPC
KVANT
3-100 keY
3%@6OkeV
2.3°
~
Sunyaev
IKI
Schnopper
SRL
Instrument
Mission
Cosmic X-ray
telescope
~50%
COS-B
~
~
30°
1°
150
1987-
PI
institution
Refs.
[7]
[l4]
232 /
10
y-RAY AND NEUTRINO ASTRONOMY
Table 10.10. (Continued.)
PI
institution
Energy range
t:.EjE
Field of view
resolution
Area
(cm2)
Date
GRANAT
30 keV-1.3 MeV
8% @511keV
4.7 0 x 4.3 0
0.20
797
1989-
Paul-Mandrou
CESR-Saclay
[15]
WATCH
GRANAT
~180KeV
4 sr
30
1989-
Lund
DSRI
[l6]
ART-P
GRANAT
4-100keV
14% @60keV
1.80 x 1.80
0.10
2520
1989-
Sunyaev
JKI
[17]
ART-S
GRANAT
3-IOOkeV
ll% @60keV
2.10 x 2.10
800
1989-
Sunyaev
IKI
[l7]
BATSE
occultation
CGRO
20 keV-1.8 MeV
30%@88keV
211" sr
10
1800
1991-
Fishman
MSFC
[18]
OSSE
CGRO
50keV-IOMeV
8% @511keV
3.80 x 11.40
2620
1991-
Kurfess
NRL
[19]
COMPTEL
CGRO
0.8-30 MeV
9%@ 1.3 MeV
- I sr
- 1.50
45
1991-
Schonfelder
MPJ
[20]
EGRET
CGRO
20 MeV-30 GeV
- 20% 0.1-5 GeV
_400
1600
1991-
Fichtel
GSFC
[21]
O.lo~.40
1600
1995-
Rothschild
UCSD
[22]
800
199~
Instrument
Mission
SIGMA
HEXTE
RXTE
15 KeV-250 KeV
15%@60keV
PDS
BeppoSAX
15 KeV-300 KeV
- 15%60keV
_ 10
- 1.40
Refs.
[22]
TeSRF1IAS
References
l. Peterson, L.E. 1972, IAU Symp. No. 55,51
2. Harrington, T. et al. 1972, IEEE Trans. NucL Sci., NS-19, 596
3. Higbie, P.R. et al. 1972, IEEE Trans. Nucl. Sci., NS-19, 606
4. Derdeyn, S. et al. 1972, NucL Instrum. Metlwds, 98, 557
5. Engel, A.R., & Coe, MJ. 1977, Space Sci.lnstrum., 3, 407
6. Dennis, B.R. et al. 1977, Space Sci. Instrum., 3, 325
7. Bignami, G.F. et al. 1975, Space Sci. Instrum., 1, 245
8. Jung, G.V. 1989, ApJ, 338, 972; Knight, F.K. 1982, ApJ, 260, 538
9. Mahoney, W.A. et al. 1980, Nucl.lnstrum. Methods,178, 363
10. Forrest, D.J. et al. 1980, Solar Phys., 65, 15
11. Orwig, L. et al. 1980, Solar Phys., 65, 25
12. Reppin, C. et al. 1985, in Nonthermal and Very High Temperature Phenomena in X-ray Astronomy, edited by G.C. Perola
and M. Salvati (Instituto Astronomico, Roma) p. 279
13. Sunyaev, R. et al. 1990, Adv. Space Sci., 10,41
14. Smith, A. 1985, in Nonthermal and Very High Temperature Phenomena in X-ray Astronomy, edited by G.c. Perola and M.
Salvati (lnstituto Astronomico, Roma) p. 271
15. Paul, J.A. et al. 1991, Adv. Space Res., 11, (8) 289
16. Lund, N. 1991, Adv. Space Res., 11, (8) 17
17. Sunyaev, R. et al. 1990, Adv. Space Res., 10, (2) 233
18. Fishman, G.J. et al. 1992, NASA Conj. Publ. 3137,26
19. Kurfess, J.D. et al. 1991, Adv. Space Res., 11, (8) 323
20. Schonfelder, V. 1991, Adv. Space Sci., 11, (8) 313
21. Kanbach, G. et al. 1988, Space Sci.lnstrum., 49, 69
22. Rothschild, R.E. et al. 1998, ApJ, 496, 538
23. Frontera, F. et al. 1997, A&AS, 122,357
10.4
ASTROPHYSICAL y-RAY OBSERVATIONS
/
Table 10.11. y -Ray burst instruments.
Trigger
Satellite
Dates
Orbit"
Detectors
Energy
range
(MeV)
Time
resolution
(s)
Time
(s)
Energy
(MeV)
Refs.
0.2-1
::: 0.016
0.25. 1.5
0.0341.1.5
[I]
Vela 5AlB
Vela6AIB
5/69-3/84
GC
&-10 em3 CsI
Helios-2
In&-I2f79
H
21.5 em3 CsI
> 0.1
::: 0.004
0.004
0.032
0.250
> 0.1
[2]
Solrad-II AlB
4n&-6n7
GC
2-43 em3 CsI
0.2-2
::: 0.0003
0.625
0.2-2
[3]
Signe-3
6n7-3n8
GC
950 em2 CsIb
> 0.06
0.008
0.1-1.6
0.03--6
0.000 5-0.02
::: 0.05
0.32
0.1
~
HEAO-I
8n7-2f79
GC
2000 em2 CsIb
280em2 NaI
3300em2 PC
Prognoz-6
9n7-3n8
G
63 em2 NaI
750 em2 CsIb
16 em3 NaI
0.08-1
> 0.3
0.02-> 0.3
::: 0.002
4
0.25
ICE
8n8-3/87
H
22em2 NaI
0.D2-1.25
::: 0.004
35 em3 Ge
0.2-3
0.001
V
2-36em 3 NaI
0.1-2
::: 0.012
2~3em3 NaI
&-50em2 NaI
0.1-2.5
0.03-2
(ISEE-3)
PVO
5n8-9/92
[4]
0.3
0.13-1.7
[5]
[5]
[6]
0.02
0.0841.4
[7]
[7]
[7]
0.000250.008
0.000 130.001
0.132-1.25
[8]
0.2-3
[9]
0.25, 1,4
0.1-2
[10]
> 0.002
::: 0.016
0.02
0.25, 1.5
0.0841.4
0.0541.15
[11]
[12]
Venera 11/12
(Konus)
9n8-1/80
H
Prognoz-7
Iln8~9
G
63 em2 NaI
750 em2 Cslb
0.1-2.5
> 0.1
::: 0.002
0.002
0.25
0.0841.4
[7]
[7]
Venera 13114
(Konus)
11/81-4183
H
2~3 em2 NaI
&-50em2 NaI
0.05-1
0.03-2
::: 0.002
::: 0.004
0.25
0.25,1.5
0.0841.4
0.0541.15
[11]
Prognoz-9
7/83-2/84
G
2-178 em2 NaI
0.04-8
::: 0.016
0.5,2
0.07341.966
[14]
Ginga
2/87-11/91
GC
6Oem2 NaI
63em2 PC
0.0 I 44l.40
0.0024).030
0.031
0.031
0.25, 1,4
1,4
0.01441.4
0.00241.03
[15]
[15]
GRANAT
-SIGMA
-SIGMA
-WATCH
-Konus-B
-Phebus
12/89-
G
800em2 NaI
8-2400 em2 CsI
4-30 em2 NaI/CsI
&-314 em2 NaI
&-573 em3 BOO
0.03-2
0.1-1
0.00&-0.18
0.Dl-8
0.1-100
::: 0.000008
::: 0.000 I
0.002
::: 0.00003
0.25,2
0.25,2
0.004-32
0.25,1.5
0.008
0.03-2
0.1-1
0.00&-0.18
0.0541.2
0.075-1.6
[16]
[16]
[17]
[18]
[19]
Ulysses
11190-
H
41 em2 CsI
0.0154).150
::: 0.008
0.125-4.0
0.01541.150
[20]
Compton
GRO
BATSE-LAD
BATSE-SD
4/91-
GC
8-2025 em2 NaI
8-127 em2 NaI
0.03-1.9
0.Dl5-11O
::: 0.000002
0.000 128
0.06, 0.25, I
0.0&-0.3
[21]
[21]
BeppoSAX
WFC
4/9&-
2-250em2 Xe
0.0024).028
0.0005
0.00241.028
[22]
12/89-2190
GC
Notes
aG, geocentric; GC, geocentric circular; H, heliocentric; V: venuscentric.
b Anticoincidence shield used as burst detector,
References
I. Kiebesadel, RW, et ai, 1973, ApJ, 182, L85
2. Cline, T.L. et aI. 1979, ApJ, 229, IA7
3. Laros, J.G. et aI. 1977, Nature, 267,131
[13]
233
234 I
4.
5.
6.
7.
8.
9.
10.
II.
12.
13.
14.
10
y-RAY AND NEUTRINO ASTRONOMY
Chambon. G. et al. 1979. X-Ray Astronomy (Pergamon. Oxford). p. 509
Hueter. G.J. 1987. Ph.D. thesis. University of California, San Diego
VVood.~S.etal. 1984.~S.S6.507
Chambon. G. et al. 1979. Space Sci.lnstrum.. 5. 73
Anderson, R.D. et al. 1978. IEEE Trons.• GE-16. 157
Teegarden. B .• & Cline. T.L. 1980. Api. 236. 1.67
Klebesadel. R.VV. et al. 1980. IEEE Trons.• GE-18. 76
Barat. C. et al. 1981. Space Sci. Instrum.. 5. 229
Mazets. E.P. et al. 1981. Ap&:SS. 80. 3
Mazets. E.P. et al. 1983. AlP Conf. Proc. No. 101. 36
Boer. M. et al. 1986. Adv. Space Sci.• 6. 97
15.M~. T.etal. 1989.P~.41.405
16. Guerry. H. et al. 1986. Adv. Space Sci.. 6. 103
17. Brandt. S. et al. 1990. Adv. Space Sci.• 10. 239
18. Golenetskii. S.V. et al. 1991. Adv. Space Sci.• 11. 125
19. Terekhov. o. et al. 1991. Adv. Space Sci.. 11. 129
20. Hurley. K. et al. 1992. A&ASS. 92.401
21. Fishman, G.J. et al. 1989. Proc. Gamma Ray Observatory Sci. Workshop. 2-39
22. Jager. R. et al. 1997. A&AS. 125, 557
Table 10.12. Very-high-energy and ultrahigh-energy y-ray experiments: Atmospheric Cherenkov and particle
arrays.a
Array
Country
Lat.
(deg)
Long.
(deg)
Elev.
(kID)
Themis
Albuquerque
Mt. Hopkins
Narrabri
Haleakala
Pachmarchi
Gulmarg
Potchefstroom
White Cliffs
Crimea
Beijing
Plateau Rosa
Gran Sasso
TIbet
TienShan
Ooty
Mt. Hopkins
La Palma
Mt. Aragats
South Pole
Mt. Norikura
Dugway
Mt. Chacaltaya
Cygnus
Baksan
Kolar
Haverah Park
AkenoRanch
Moscow
Buckland Park
Janzos
France
USA
USA
Australia
USA
India
India
South Africa
Australia
Ukraine
China
Italy
Italy
China
Kirghiz
India
USA
Spain
Armenia
Antarctica
Japan
USA
Bolivia
USA
Kab-Ba1kar
India
UK
Japan
Russia
Australia
New Zealand
43N
35N
32N
31S
21N
23N
35N
27S
32S
45N
40N
46N
42N
30N
42N
11N
32N
29N
40N
90S
36N
40N
16S
36N
43N
13N
54N
35N
56N
35S
41N
IVV
107VV
111W
145E
156W
78E
77E
27E
143E
34E
117E
8E
14E
90E
75E
77E
l11W
18VV
44E
OW
137E
112W
68W
I06VV
43E
78E
lW
138E
37E
138VV
172E
1.5
1.5
2.3
0.21
3.0
Area
(104 rn2)
1.1
2.7
1.4
0.16
0.6
1.0
3.5
2.0
4.2
3.3
2.2
2.3
2.2
3.2
2.5
2.8
1.5
5.2
2.1
1.7
0.9
0
0.9
0
0
0.9
3.5
1
10
2.0
0.5
0.5
-0.5
4
-1
=s1
- 2125
>0.5
>8
0.5
1.66
> 1
-1
1.0
> 0.23
Threshold
(TeV)
0.1
0.2
0.3
0.3
0.5
0.5
1
1
1
1
1
10
10
10
100
100
100
100
100
100
100
100
200
200
300
500
500
1000
1000
1000
1000
a9
(deg)
0.1
1.4
5.5
1
0.8
3
3
1
1
1
1
1
0.5-1
1-3
1
1.5
1.5
1
3
3
2.5
2
Began
1986
1986
1983
1986
1985
1987
1985
1985
1986
1986
1987
1981
1988
1990
1974
1984
1985
1986
1987
1988
1988
1989
1986
1986
1984
1984
1986
1981
1982
1984
1988
Note
aBased on Weekes, T.C. 1988. Phys. Rep.• 160,1; Yodh. G. 1992. private communication; and Stepanian.
A.A. 1992. private communication.
10.5 NEUTRINOS IN ASTROPHYSICS / 235
10.5
NEUTRINOS IN ASTROPHYSICS
by Wick C. Haxton
Perhaps the original motivation for studying astrophysical neutrinos was the prospect of directly
probing the interior of our Sun: neutrinos produced as a byproduct of nuclear fusion pass undistorted
through the outer layers of the Sun, carrying in their flux and spectrum a detailed memory of the nuclear
reactions that produced them. As the competition between the three cycles comprising the pp chain
(the process that dominates solar burning of four protons into 4He) depends sensitively on the solar
core temperature Te , one can deduce Te by measuring the various components of the solar neutrino
flux.
Results from the 37 Cl detector, which has operated for nearly 30 years, and from three more
recent experiments, SAGE and GALLEX (radiochemical detectors containing 71Ga) and Kamioka
IIIIII (an active water Cerenkov detector sensitive to higher energy solar neutrinos), have revealed
some surprises. The results are consistent with a flux of high-energy 8B neutrinos reduced to about 50%
of the standard solar model value and a greatly suppressed flux of neutrinos produced from electron
capture on 7Be. This is a surprising pattern because a reduction in Te tends to suppress the 8B solar
neutrino flux more than the 7Be flux, not less. In fact, detailed fits seem to show that the 7Be neutrinos
must be completely absent to account the experimental results.
One popular explanation for this puzzle is the phenomenon of neutrino oscillations: if neutrinos
have nonzero masses and mix (so that the electron, muon, and tauon neutrinos are not identical to the
mass eigenstates, but linear combinations of these), solar electron neutrinos can oscillate into muon
neutrinos and escape detection. While once it was thought that neutrino oscillations would most likely
produce only a small reduction in the solar electron neutrino flux, it was discovered about a decade
ago that oscillation effects can be greatly enhanced within the Sun. This phenomenon, known as the
Mikheyev-Smimov-Wolfenstein or MSW mechanism, arises because the effective masses of neutrinos
change when the neutrinos pass through matter. The MSW solution that best reproduces the results of
the 37 Cl, SAGEIGALLEX, and KamiokalIlIII experiments is consistent with oscillations of a very light
electron neutrino into a muon neutrino with a mass of about 0.003 electron volts (eV).
Two new detectors, SuperKamiokande and the Sudbury Neutrino Observatory (SNO), should be
able to confirm or rule out neutrino oscillations as a solution to the solar neutrino problem. SuperKamiokande is an enormous (22.5 kiloton fiducial volume) Ultrapure water Cerenkov detector located in a Japanese mine. It began operations in the Spring of 1996. By making a precision measurement of the spectrum of recoil electrons following neutrino--electron scattering, the experimentalists
hope to find subtle distortions characteristic of the MSW mechanism. SNO, which should be fully
operational by the end of 1998, is a Canadian-US-UK detector located deep within a nickel mine in
Sudbury, Ontario. The inner volume of this water Cerenkov detector contains heavy water. Reactions
on the deuterium nuclei provide separate charged and neutral current signals. Thus, in addition to
spectrum distortions, the experimentalists hope to measure directly the neutrinos of a different flavor
that are generated by the MSW mechanism.
SuperKamiokande, SNO, and similar detectors are sensitive to another source of neutrinos, those
produced in the atmosphere by the interactions of cosmic rays impinging on the Earth. For some
years most such detectors have found a puzzling result, an unexpected ratio of muon neutrino to
electron neutrino events given our understanding of cosmic ray neutrino production. Very recently
the SuperKamiokande group, by comparing upward- to downward-going neutrinos, have claimed that
this anomaly is definitive evidence for neutrino oscillations and thus of massive neutrinos.
Another source of neutrinos is associated with one of the most spectacular events in astrophysics,
the sudden collapse of the core of a massive star. This collapse triggers the ejection of the star's mantle,
producing the spectacular display known as a supernova. However 99% of the energy released in such
236 /
10
y-RAY AND NEUTRINO ASTRONOMY
a collapse, an enormous 3 x 1053 ergs, is invisible optically as it is carried by an intense three-second
burst of neutrinos emitted by the cooling protoneutron star forming at the star's center.
We were extremely fortunate to have two large water Cerenkov detectors, Kamioka II and 1MB,
operating at the time of Supernova 1987A. The free protons in water absorb electron antineutrinos,
emitting relativistic positrons that can be detected readily in such detectors. In each detector
approximately 10 events were detected from a star that collapsed in the Large Magellanic Cloud
150000 light years from earth. The characteristics of the detected neutrinos-the number of events,
the spectrum, the duration of the neutrino pulse--were in good accord with supernova theory.
There were no detectors operating that had the necessary characteristics and sensitivities to record
the electron neutrinos or the muon and tauon neutrinos and antineutrinos. This was unfortunate because
supernova electron neutrinos may hold the key to one of the central problems in cosmology, the dark
matter. Studies on a variety of astrophysical scales-galaxies, clusters of galaxies, etc.-indicate that
at least 90% of the mass in the Universe is dark, not emitting or absorbing electromagnetic radiation.
Most estimates of the dark matter lead to a minimum mean density in the Universe of 20% of the closure
density, the density that would keep the Universe from expanding forever. As the standard theory of big
bang nucleosynthesis argues that at least some of this dark matter is nonbaryonic, massive neutrinos
seem a natural explanation for this component. In partiCUlar, a heavy tauon neutrino with a mass of
about 5-10 e V could comprise an important fraction of the dark matter and would also help to explain
how galaxies and other structures in the Universe formed.
Such a mass is quite consistent with a theoretical model for generating neutrino masses known
as the seesaw mechanism. If the solar neutrino problem involves oscillations between the electron
neutrino and a 0.003 eV muon neutrino, then the seesaw mechanism predicts that the tauon neutrino
mass might be in the range required to explain large scale structure.
How can one test the hypothesis of a tauon neutrino mass of a few eV? Just as the densities available
in the Sun enhance oscillations between electron and muon neutrinos, the much larger densities found
near the core of a supernova can enhance oscillations between electron neutrinos and massive tauon
neutrinos. Because the tauon neutrinos emitted by a supernova tend to be substantially more energetic
than supernova electron neutrinos, such oscillations would produce an anomalously energetic electron
neutrino spectrum. Thus the detection of these electron neutrinos could demonstrate that massive tauon
neutrinos make up an important component of the dark matter. As the standard model of electroweak
interactions cannot accommodate massive neutrinos, such a discovery would also have a profound
impact on particle physics.
Neutrinos also play a crucial role in nuclear astrophysics. Arguments based on big-bang
nucleosynthesis provided early evidence that there were only a few (three or four) light neutrino flavors,
a result now beautifully confirmed by measurements of the width of the Zoo Neutrinos govern much
of the nucleosynthesis that occurs in a supernova. For example, the process of rapid neutron capture,
by which about half of the heavy elements and all of the transuranics are synthesized, is now believed
to depend on conditions in the hot bubble that resides just above the surface of the protoneutron star.
The entropy and neutron/proton ratio in this bubble are largely determined by neutrino interactions.
Neutrinos also directly synthesize nuclei like 19F and 11 B by scattering off the neon and carbon in the
mantle of the collapsing star. The subsequent supernova explosion is the mechanism by which these
newly synthesized metals are ejected into the interstellar medium.
Finally, there is an enormous density of very low energy neutrinos-about 300/cm3-throughout
the Universe, a relic of the big bang similar to the background microwave photons. Recent precision
measurements of the microwave background allow us to look backward to the time of recombination,
when electrons condensed on nuclei to form neutral atoms, providing a snapshot of conditions in the
early Universe, 100000 years after the big bang. Were we ever to find a method to detect the relic
neutrinos, this would provide a probe of the Universe at the time the neutrinos decoupled from matter,
early in the first minute in the history of the Universe. Detection of these relic neutrinos is likely to
remain a challenge for many decades.
10.6 CURRENT NEUTRINO OBSERVATORIES / 237
10.6 CURRENT NEUTRINO OBSERVATORIES
by Thomas J. Bowles
Table 10.13 lists the existing neutrino observatories and a description of each one. Some of these are
still under development.
'Illble 10.13. Existing 1II!utrino observatories.
Detector
Main
aims"
target
Depth
(mweY'
Scnsorsc
Detection techniques
Remarks
Antan:tica
Hell
9000m2
1800-2400
Cerenkov
Under development
SN,HEII
"'1000
LS
HEII,NO
330 tons
250m2
140 ton
4000
LS
One of the oldest IJIIdcqround
neutrino observatories
Experiment no longer in operation
SN
100 ton
ND,SN
150 ton
5000
NO,SN
90 ton
5000
NO,SN
912 ton
4850
AMANDA
Baksan, Caucusus
Russia
Homestake Mine
S. Dakota
Artyomovsk
Ukraine
Mt. Blanc, Italy
NUSEX
Mt. Blanc, Italy
LSD
Frejus
France
Gran Sasso, Italy
MACRO
Gran Sasso, Italy
LVD
Greece
NESTOR
Hawaii
DUMAND
Lake Baikal, Siberia
NT·200
Soudan, Minnesota
SOUDAND
Soudan, Minnesota
MINOS
Kolar Gold Fields (2)
India
Kamiokande
''Size'' of
LS
Plastic tubes in limited
streamer mode
LS
Experiment no longer in operation
Flasb chambers,
Experiment no longer in operation
Geiger tubes
Experiment no longer in operation
SN,HEII
3240m2
3800
LS, streamer tubes
SN,HEII
I 800 ton
3800
LS, streamer tubes
HEll
I x 104m2
3700
Cerenkov
Under development
HEll
2 x 104m2
4700
Cerenkov
Under development
HEll
500m2
1000
Cerenkov
"NT' stands for neutrino telescope
NO,HEII
1100 ton
7200
Honeycomb
Iron calorimeter
NO,HEII,LB
drift chamber
10000 ton
7200
Honeycomb
drift chamber
Full operation began in 1996
Iron calorimeter
Under development
Experiment no longer in operation
NO,HEII
140 ton
7200
NO,SN,HEII
4500 ton
2400
Proportional counters,
calorimeter
Cerenkov
NO,SN,
NEII,LB
NO,SN,HEII
50000 ton
2400
Cerenkov
HOOton
1580
Cerenkov
Homcstake Mine,
S. Dakota
Homestake mine
S. Dakota
Baksan, Russia
SAGE
Gran Sasso, Italy
Borexino
sol
615 ton
Radiochemical
sol
100 tons
sol
6OtonsGa
4900
(percbloretbylene)
4900
(Nal solution)
4815
sol
300 tons
3800
LS
\Ix +e- ~ "'x +eDetects 7Be neutrinos
Gran Sasso, Italy
GALLEX
Gran Sasso, Italy
GNO
Gran Sasso, Italy
ICARUS
sol
30tonsGa
3800
Radiochemical
Detects p-p neutrinos
sol
30 tons Ga
3800
Radiochemical
Detects p-p neutrinos
sol,NO,LB
1600 tons
3800
Liquid argon
Operation began in 1998
TIDlC production chamber
Under development
Japan
SuperKamiokande
Japan
IMB,Ohio
Radiochemical
Radiochemical
Detected II. from SN I 987a
Detects 8B neutrinos
Experiment no longer in operation
Detects 8B neutrinos
Operational in 1996
Detected ". from SN I 987a
Experiment no longer in operation
37Cl + ". -+ 37 Ar+.Detects 7Be and 8B neutrinos
1271 + II. -+ 127Xe +.Detects 7 Be and 8B neutrinos
710a+ II. -+ 37 Ar+.Detects p-p neutrinos
Operational in 2001
Experiment completed in 1997
238 I
10
y-RAY AND NEUTRINO ASTRONOMY
Table 10.13. (Continued.)
Main
"Size" of
Depth
SensorsC
Detector
aims"
taIget
(mwe)b
Detection techniques
Remarks
Sudbury, Canada
sol,SN
Cerenkov
v. +d ..... p + P +evx+d ..... n+p+vx
vx+c + e- -+ Vx + ev.+d ..... n+n+e+
Operational in 1998
SNO
Notes
aSN, supernova bursts; ND, nucleon decay; HEv, high-energy neutrinos; sol, solar neutrinos; LB, long baseline experiment
using an accelerator neutrino source.
b mwe, meters water equivalent.
cSensors means detectors of neutrino secondaries, e.g., muons; LS, liquid scintillator; Cerenkov light from charged
secondaries is observed by photomultipliers.
ACKNOWLEDGMENTS
We wish to thank Ed Chupp, Carl Fichtel, Gerry Fishman, Alice Harding, Wick Haxton, Jim Higdon,
Kevin Hurley, John Lams, Chip Meegan, Larry Peterson, Reuven Ramaty, A. Stepanian, and Trevor
Weekes for valuable comments and contributions.
REFERENCES
1. Heitler, W. 1954, The Quantum Theory of Radiation
(Clarendon Press, Oxford)
2. Jauch, J.M., & Rohrlich, F. 1976, The Theory of Photons. and Electrons (Springer-Verlag, Berlin)
3. Rybicki, G.B., & Lightman, A.P. 1979, Radiative
Processes in Astrophysics (Wiley, New York)
4. Lang, K.R. 1980, Astrophysical Formulae (SpringerVerlag, Berlin).
5. Felten, J.E., & Morrison, P. 1966,ApJ, 146,686
6. Blumenthal, G.R., & Gould, RJ. 1970, Rev. Mod. Phys.,
42,237
7. Ore, A., & Powell, J.L. 1949, Phys. Rev. 75,1696
8. Bussard, R.W. et al. 1979, ApJ, 228, 928
9. Zdziarski, A.A. 1980, Acta Astron., 30, 371
10. Rarnaty, R., & Meszaros, P. 1981, ApJ, 250, 384
11. Gould, R.J. 1989, ApJ, 344, 232
12. Guessoum, N. et al. 1991,ApJ, 378,170
13. Klein, 0., & Nishina, Y. 1929, Z Phys. 52, 853
14. Marmier, P., & Sheldon, E. 1969, Physics ofNuclei and
Particles (Academic Press, New York)
15. Erber, T. 1966, Rev. Mod. Phys., 38, 626
16. Canuto, V. et al. 1971, Phys. Rev. D, 3, 2303
17. Bussard, R.W. et al. 1986, Phys. Rev. D, 34, 440
18. Daugherty, J.K., & Harding, A.K. 1986, ApJ, 309, 362
19. Harding, A.K., & Daugherty, J.K. 1991, ApJ. 374, 687
20. Canuto, V., & Ventura, J. 1977, Fund. Cosmic Phys., 2,
203
21. ChUpp, E.L. 1972, Gamma-Ray Astronomy (Reidel,
Dordrecht)
22. Rarnaty, R., & Lingenfelter, R.E. 1982, Ann. Rev. Nucl.
Part. Phys., 32, 235
23. Bignami, G.F., & Hemsen, W. 1983, ARA&A, 21, 67
24. ChUpp, E.L. 1984, ARA&A, 22, 359
25. Rarnaty, R., & Lingenfelter, R.E. 1994, Chapter 3
in High Energy Astrophysics (World Scientific, New
York), p. 32
26. Harding, A.K. 1991, Phys. Rep, 206, 327
27. Higdon, J.C., & Lingenfelter, R.E. 1991, ARA&A, 28,
401
28. Fishman, G.J., & Meegan, C.A. 1995, ARA&A, 33, 415
29. Rothschild, R.E., & Lingenfelter, R.E. 1995, High Velocity Neutron Star and Gamma-Ray Bursts (American
Institute of Physics, New York), 282 pp.
30. Kouveliotou, C., Briggs, M.F., & Fishman, G.J. 1996,
Gamma-Ray Bursts (American Institute of Physics,
New York), 1008 pp.
31. Rees, M.J. 1998, Proc. 18th Texas symposium ReL Astrophys.. edited by A.V. Olinto, J.A. Frieman, and D.N.
Schramm (World Scientific, Singapore) p. 34; Rees,
M.J. 1999, NucPhys B, Proc. SuppL, 69681
Chapter
11
Earth
Gerald Schubert and Richard L. Walterscheid
11.1
Oblate Ellipsoidal Reference Figure . . . . . . . . ..
240
11.2
Mass and Moments oflnertia . . . . . . . . . . . . ..
240
11.3
Gravitational Potential and Relation to
Products oflnertia . . . . . . . . . . . . . . . . . . . .
241
11.4
Topography. . . . . . . . . . . . . . . . . . . . . . ..
243
11.5
Rotation (Spin) and Revolution About the Sun . . ..
244
11.6
Gravity. . . . . . . . . . . . . . . . . . . . . . . . . ..
245
11.7
Geoid. . . . . . . . . . . . . . . . . . . . . . . . . . ..
245
11.8
Coordinates. . . . . . . . . . . . . . . . . . . . . . ..
246
11.9
Solid Body Tides . . . . . . . . . . . . . . . . . . . . .
246
11.1 0
Geological Time Scale . . . . . . . . . . . . . . . . ..
248
11.11
Glaciations.........................
251
11.12
Plate Tectonics
......................
252
11.13
Earth Crust . . . . . . . . . . . . . . . . . . . . . . . ..
252
11.14
Earth Interior
255
11.15
Earth Atmosphere, Dry Air at
Standard Temperature and Pressure (STP)
.......................
......
257
11.16
Composition of the Atmosphere . . . . . . . . . . . .
258
11.17
Water Vapor . . . . . . . . . . . . . . . . . . . . . . . .
259
11.18
Homogeneous Atmosphere, Scale Heights
and Gradients . . . . . . . . . . . . . . . . . . . . . . .
259
Regions of Earth's Atmosphere and
Distribution with Height . . . . . . . . . . . . . . . ..
260
11.19
239
240 /
11.1
11
EARTH
11.20
Atmospheric Refraction and Air Path . . . . . . . . .
262
11.21
Atmospheric Scattering and Continuum Absorption.
265
11.22
Absorption by Atmospheric Gases at Visible
and Infrared Wavelengths . . . . . . . . . . . . . . . .
268
11.23
Thermal Emission by the Atmosphere . . . . . . . ..
270
11.24
Ionosphere.........................
271
11.25
Night Sky and Aurora . . . . . . . . . . . . . . . . . .
279
11.26
Geomagnetism
......................
282
11.27
Meteorites and Craters . . . . . . . . . . . . . . . . ..
285
OBLATE ELLIPSOIDAL REFERENCE FIGURE [1,2]
Equatorial radius a = 6.378136 x 106 m.
Polar radius e = 6.356753 x 106 m.
Mean radius Re = (a 2 e)I/3 = 6.371000 x 106 m.
Length of equatorial quadrant = 1.001875 x 107 m.
Length of meridional quadrant = 9.985164 x 106 m.
Ellipticity or Flattening (a - e)/a = 1/298.257 = 0.0033528.
Eccentricity e = (a 2 - e 2)1/2/a = 0.081818.
Surface Area = 21l' {a 2 + e
2(1 _e2/a 2) -1/2 In [ale + (a 2le2 _ 1) 1/2]}
= 5.100657 X 1014 m2 .
Volume
=
11.2
MASS AND MOMENTS OF INERTIA [1-3]
~1l'a2e
=
1.083207 x 1021 m3 .
Earth mass Me = 5.9737 x 1024 kg.
Moon-Earth mass ratio MMoonlMe = 0.012300034.
Sun-Earth mass ratio M01 Me = 332946.038.
Earth mass multiplied by the gravitational constant:
GMe = 3.98600441 x 10 14 m3 s-2,
(GMe)I/2 = 1.996498 x 107 m3/ 2 S-I.
Earth mean density Pe = 5514.8 kg m- 3 .
Moments of inertia (see below):
about rotation axis C = 8.035 8 x 1037 kg m2 ,
average about equatorial axis (A + B)/2 = 8.009 5 x 1037 kg m2 ,
dynamical ellipticity or flattening {C - (A + B) 12} IC = 0.0032729,
11.3 GRAVITATIONAL POTENTIAL AND PRODUCTS OF INERTIA /
lz = {C - (A
+ B) 12} IMea2 =
C I Mea2 = 0.33078,
Me a2 = 2.43014 x 1038 kg m 2 .
241
1.082626 x 10-3 ,
11.3 GRAVITATIONAL POTENTIAL AND RELATION TO
PRODUCTS OF INERTIA [1-3]
The gravitational potential is
u=
G~e 11 + ~ (;y
to
Pi (sin</» [Ci cosmA + Si sinmA]},
= radial distance from Earth center of mass,
Pi = fully normalized associated Legendre polynomials,
r
i.e., the mean square value of
Pi (sin </»(cos mA, sinmA) over a spherical surface is unity,
Pi = {(2-8 m .o)(21+ 1)[(l-m)!/(I+m)!]}lj2 pr, where pr is the ordinary associated Legendre
polynomial,
= degree and order of normalized spherical harmonic Pi (sin </>)(cos mA, sinmA),
</> = latitude,
A = longitude,
Ci, Si = coefficients in spherical harmonic expansion of Earth's gravitational potential using fully
t, m
normalized functions.
C? ct
st
=
=
= O. Table 11.1 gives the
With coordinate system origin at the center of mass
values of the zonal coefficients
in a spherical harmonic expansion of the gravitational potential
using fully normalized functions.
C?
Table 11.1. Zonal coefficients
C?
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
-484.165
0.53952
-0.14951
0.048883
0.054065
0.035629
-0.021555
-0.0061891
0.0085246
0.019924
C? in units of 10-6.
3.
5.
7.
9.
II.
13.
15.
17.
19.
C?
0.95720
0.068343
0.091301
0.026862
-0.049464
0.040 112
0.0032275
0.017427
-0.0021551
Table 11.2 gives values of the coefficients Ci, Si in a spherical harmonic expansion of the
gravitational potential using fully normalized functions. Note that C~ = 0 and S~ = O.
242 /
11
EARTH
I, m
cIm'
2,2
2.439,
3, 1
2.0277,
4,1
4,4
Table 11.2. Coefficients Cj, 8j in units of 10-6.
I, m
cI'm
0.2492
3,2
0.9045,
-0.5362,
-0.1888,
-0.4734
0.3094
4,2
5,1
5,4
-0.0583,
-0.2956,
-0.0961
0.0497
6, 1
6,4
-0.0769,
-0.0868,
7,1
7,4
7, 7
8r
I, m
cr,
8Im
-0.6194
3,3
0.7203,
1.4139
0.3502,
0.6630
4,3
0.9909,
-0.2009
5,2
5,5
0.6527,
0.1738,
-0.3239
-0.6689
5,3
-0.4523,
-0.2153
0.0270
-0.4713
6,2
6,5
0.0487,
-0.2673,
-0.3740
-0.5368
6,3
6,6
0.0572,
0.0097,
0.0094
-0.2371
0.2749,
-0.2756,
0.0010,
0.0975
-0.1238
0.0241
7,2
7,5
0.3278,
0.0013,
0.0932
0.0186
7,3
7,6
0.2512,
-0.3588,
-0.2153
0.1517
8,1
8,4
8, 7
0.0236,
-0.2463,
0.0675,
0.0588
0.0702
0.0751
8,2
8,5
8,8
0.0776,
-0.0250,
-0.1242,
0.0660
0.0895
0.1202
8,3
8,6
-0.0178,
-0.0649,
-0.0863
0.3091
9,1
9,4
9, 7
0.1461,
-0.0101,
-0.1190,
0.0200
0.0190
-0.0970
9,2
9,5
9,8
0.0225,
-0.0171,
0.1871,
-0.0336
-0.0538
-0.0024
9,3
9,6
9,9
-0.1613,
0.0639,
-0.0481,
-0.0760
0.2226
0.0987
10,1
10,4
10, 7
10,10
0.0815,
-0.0853,
0.0076,
0.0998,
-0.1303
-0.0787
-0.0034
-0.0225
10,2
10,5
10,8
-0.0913,
-0.0510,
0.0401,
-0.0511
-0.0511
-0.0917
10,3
10,6
10,9
-0.0086,
-0.0371,
0.1243,
-0.1550
-0.0784
-0.0380
8Im
-1.4001
A simplified expression for the gravitational potential is
GM$
U ~ - { 1-
r
L (a)1
-r 11 PI (sin</»
00
1=2
I
,
where PI is the Legendre polynomial of degree I. Values of the zonal coefficients 11, defined by
1 ~ 2,
are given in Table 11.3.
Table 11.3. Zonal coefficients II, in units of
10- 6.
II
2.
4.
6.
8.
10.
1082.626
-1.6186
0.5391
-0.2015
-0.2478
II
3.
5.
7.
9.
11.
-2.533
-0.2267
-0.3536
-0.1171
0.2372
11.4 TOPOGRAPHY
/
243
1Rble 11.3. (Continued.)
J,
J,
-0.1781
0.1161
0.003555
-0.0051853
-0.12758
12.
14.
16.
18.
20.
-0.2084
-0.01797
-0.10310
0.013459
13.
15.
17.
19.
The relation of the second degree coefficients in a spherical harmonic expansion of the gravitational
potential to products of inertia Iij is
~-o
-'V 5
C2 = h
= Me1a2
{
133 -
III
+2 h2} '
The principal products of inertia 111,122,133 are often denoted A, B, C with C > B > A or
133 > 122 > Ill,
III = A = 8.0094 x
1037 kg m 2 ,
122 = B = 8.0096 x 1037 kg m2,
133
= C = 8.0358 x
1037 kgm2 .
11.4 TOPOGRAPHY [2,4,5]
The topography of solid Earth, T, is:
T (in 103 m)
1
LL
00
=
Pi(sincp) [CTi cosmA + STi sinmA].
1=0 m=O
Pi (sin cp), cp, A are defined in the expression for the gravitational potential in Section 11.3. The
coefficients are given in Table 11.4.
1Rble 11.4. Values o/the coejJicients CTj and STj (in units 0/103 m).
l.m
CTj.
0.0
-2.3890.
STj
l.m
CTj.
STj
l.m
CTj.
STj
1.0
0.6605.
1. 1
0.6072.
0.4062
2.0
0.5644.
2.1
0.3333.
0.3173
2.2
0.4208.
0.0839
3.0
3.3
-0.1683.
0.1299.
3.1
-0.1518.
0.1244
3.2
0.4477.
0.4589
0.5733
244 /
11
EARTH
Table 11.4. (Continued.)
I,m
CTi,
-0.2563
0.4703
4,2
-0.3928,
0.0716
-0.0406,
0.5254,
-0.0770
-0.0654
5,2
5,5
-0.0216,
-0.0549,
-0.1577
0.2276
0.0013,
0.1960,
-0.0171
-0.1737
6,2
6,5
0.0247,
-0.1076,
-0.1323
-0.2075
I,m
CTi,
STi
I,m
CTi,
4,0
4,3
0.3162,
0.3761,
-0.1291
4,1
4,4
-0.2241,
-0.6387,
5,0
5,3
-0.5514,
0.1232,
0.0386
5,1
5,4
6,0
6,3
6,6
0.2567,
0.0601,
0.0354,
0.1865
0.0282
6,1
6,4
STi
STi
Area = 5.100657 x 10 14 m2 .
Land area = 1.48 x 1014 m2 .
Water area = 3.62 x 10 14 m 2 .
Continental area including margins = 2.0 x 1014 m2 .
Mean land elevation = 825 m.
Mean ocean depth = 3770 m.
11.5
ROTATION (SPIN) AND REVOLUTION ABOUT THE SUN [1,2,6,7]
Rotational period with respect to fixed stars
= 24hoomoos.0084 mean sidereal time,
= 23h56m 04s.098 9 mean solar time.
Mean angular velocity = 7.292115 x 10-5 rad s-l, 15.041067 arcsec s-l.
Equatorial rotational velocity = 465.10 m s-l.
Centrifugal acceleration at equator = 3.39157 x 10-2 m s-2.
Angular momentum = wC = 5.8598 x 1033 m2 kg s-l.
Rotational energy = iCw2 = 2.1365 x 1029 J.
The general precession in longitude per Julian century for J2ooo.0 is p = 5 029'~096 6, where p is
the long period motion of the mean pole of the equator about the pole of the ecliptic with a period of
about 26,000 years. The general precession is due to the gravitational torques of the Sun, Moon, and
planets on the Earth's dynamical figure.
Nutations are the motions of the Earth's rotation axis with respect to inertially fixed axes. Nutation
includes the general precession and shorter period motions. A nutation induced by the Moon has a
period of 18.6 years and an amplitude of about 9 arcsec. The gravitation of the Sun causes the lunar
orbit to precess with respect to the plane of the ecliptic with a period of 18.6 years. Smaller nutations
have periods of a solar year and a lunar month and harmonics thereof.
Length of Day (LOD) variations comprise an overall linear increase from tidal dissipation (of about
1 to 2 ms per century). There are large irregular fluctuations with amplitudes of milliseconds and time
scales of decades, and smaller oscillations with shorter time scales. LOD variations with periods of
a year and less are generally attributable to exchange of angular momentum between the solid Earth
and the atmosphere-ocean system and to effects of solid Earth and ocean tides. LOD fluctuations with
decade time scales may be due to angular momentum exchange between the solid Earth and the liquid
outer core.
Polar motion or wobble is the motion of the solid Earth with respect to the spin axis of the Earth.
Polar motion is dominated by nearly circular oscillations at periods of one year, the annual wobble
with an amplitude of about 100 milliarcseconds, and at about 434 days, the Chandler wobble with an
amplitude of about 200 milliarcseconds. The Chandler wobble is a free oscillation of the Earth; its
11.6 GRAVITY
/
245
excitation mechanism is uncertain. Other components of polar motion occur over a wide range of time
scales from weeks to thousands of years. Loading of the solid Earth by the redistribution of mass in
the atmosphere, oceans, groundwater, and ice caps contributes to polar motion.
Mean orbital speed = 2.97848 x 104 m s-l.
Mean centripetal acceleration = 5.9301 x 10-3 m s-2.
Mean distance from Sun = 1.000 001057 AU = 1.49598029 x 1011 m.
Mean eccentricity of orbit about the Sun = 0.016708617.
Obliquity of the ecliptic at J2000.0 = 23°26'21".4119.
1 AU = 1.495978706 6 x 1011 m.
Light time for 1 AU = 499.004 78353 s.
11.6 GRAVITY [5, 7]
Gravity includes the gravitational attraction of the Earth's mass and the centrifugal acceleration of the
Earth's rotation.
Surface gravity on reference ellipsoid g(m s-2) = 9.806 21 - 0.02593 cos 2</> + 0.000 03 cos 4</>
= 9.78031 + 0.05186sin2 </> - 0.00006sin2 2</>.
</> is the geodetic latitude of point p, i.e., the angle between the equator of the reference ellipsoid and
the normal from p to the ellipsoid. Gravity anomalies are actual values of g minus the reference g
given above. A practical unit for the measurement of gravity anomalies is the mgal = 10-5 m s-2.
Reference equatorial gravity = 9.78031 m s-2.
Reference polar gravity = 9.832 17 m s-2.
Reference gravity at </> = 45° = 9.806 18 m s-2.
Gravitation at the equator = GMe/a2 = 9.79829 m s-2.
Centrifugal acceleration at equator/gravitation at equator = 3.46139 x 10-3 .
Variation of g with altitude at the Earth's surface = 0.3086 x 10-5 s-2
= 3.086 mm s-2 km- 1
= 0.3086 mgal m- 1.
g decreases by 3.086 mm s-2 per kilometer of elevation at the Earth's surface.
Gravity anomalies corrected for altitude, i.e., evaluated on the reference ellipsoid, are known as free-air
gravity anomalies.
11.7 GEOID [2,5,7]
The gravity potential is the sum of the gravitational potential U (see above) and the centrifugal potential
2 r2 cos2 </>, where
is the mean angular velocity.
The geoid is the equipotential of gravity that coincides with mean sea level in the oceans. The
geoid lies generally below the topography.
The height of the geoid N is given with respect to a reference ellipsoid with the observed flattening
of the Earth 1/298.257 and with the Earth's equatorial radius 6378.136 km.
The equation of the reference ellipsoid is r = a{1 + [(2/ - /2)/{1 - f)2] sin2 </>}-1/2, where /
is the flattening. With / = 1/298.257
!w
w
r = a { 1 + 0.67395 sin2 </>
~a
{ 1 - 0.33698 sin2 </>
r
1/2
+ 0.17033 sio4 </>} .
246 /
11.8
11
EARTH
COORDINATES [7]
= 692".74 sin 2rjJ -
Geodetic latitude (rjJ) - geocentric latitude (rjJ')
1".16 sin 4rjJ.
Geocentric latitude of a point p is the angle between the equator of the reference ellipsoid and a
line from p to the center of the ellipsoid. Geodetic latitude is defined above.
10 oflatitude = 110.575 + 1.110 sin2 rjJ, 103 m.
10 oflongitude = (111.320 + 0.373 sin2 rjJ) cos rjJ, 103 m.
tan rjJ
,
=
(l-e 2 )Nt/>+h
Nt/> +h
tan rjJ .
e is the eccentricity of the reference ellipsoid
f is the flattening of the ellipsoid.
Nt/> is the ellipsoidal radius of curvature in the meridian
Nt/>
= (1 -
a
e
2 ' 2,/,.)1/2'
SIn
'Y'
h is the height of a point p above the reference ellipsoid.
With f = 1/298.257, e 2 = 6.694385 x 10-3 , e 2 « 1, Nt/> ~ a,
tan rjJ'
~ tan rjJ
(1 -
e2
+ e2 ~ )
~ tan rjJ (0.993306 + 1.049583 x
1O- 9 h(m)) .
11.9 SOLID BODY TIDES [7,8]
The tidal potential due to the gravitation of the Sun and the Moon UT is the gravitational potential of
these bodies expressed in the coordinate system of the Earth's gravitational potential, but without the
I = 1 spherical harmonic terms. These I = 1 terms determine the orbital motion of the Earth. The
tidal potential is a differential gravitational potential. Each spherical harmonic component of the tidal
potential has contributions with different periods and amplitudes. Table 11.5 lists contributions to the
I = 2 tidal potential, the dominant tidal component.
Table U.5. Periods and amplitudes for the l = 2 tidal potential.
m
Tidal contribution
Period
Long Period
m=O
Lunar nodal tides
Sa
Ssa
Mm
Mf
18.613 years
365.26d
182.62 d
27.555 d
13.661 d
(Amplitude) g-I, 10- 2 m
2.79
0.49
3.10
3.52
6.66
11.9 SOLID BODY TIDES
/
247
Table 11.5. (Continued.)
m
m
Tidal contribution
0,
P,
S,
Diurnal
m =I
23.934 h
23.869 h
23.804 h
26.22
12.20
0.29
36.88
0.29
0.52
12.658 h
12.421 h
12. h
11.967 h
12.10
63.19
29.40
8.00
25.819 h
24.066 h
24.h
K,
IV,
4>,
Semi-Diurnal
m=2
(Amplitude) g-', 10- 2 m
Period
N2
M2
S2
K2
The perturbation in the Earth's second degree gravitational potential at the surface of the Earth due
to tidal deformation of the Earth's interior is the product of the second degree tidal potential evaluated
at the Earth's surface with the second degree potential Love number k.
The product of the second degree body tide displacement Love number h with the second degree
component of UT / g evaluated at the Earth's surface gives the tidally induced radial displacement of
the surface.
Southward and eastward displacements of the tidally deformed surface of the Earth are given in
terms of the body tide displacement Love number I by
-I aUT
--g ae
and
aUT
g sine ~'
respectively, where e is colatitude, A is eastward longitude, and g, UT and its derivatives are evaluated
at the Earth's surface. Second degree contributions are understood here.
Second degree tidal effects on surface gravity and surface tilt are represented by the gravimetric
factor
Ii
= 1- ~k+ h
1}
= 1+k -
and the tilt factor
h,
respectively, similar to the above. Table 11.6 gives these Love numbers for a model of the Earth.
Table 11.6. Second degree Love numbers for a spherical. rotating. ellipsoidal.
elastic. oceanless Earth.
m
Tidal contributions
k
h
0
Any long period tide
0.299
0.606
0,
P,
S,
0.298
0.287
0.280
0.256
0.603
0.581
0.568
0.520
K,
B
1/
0.0840
1.155
0.689
0.0841
0.0849
0.0853
0.0868
1.152
1.147
1.l44
1.132
0.689
0.700
0.707
0.730
248 I
11
EARTH
Table 11.6. (Continued.)
Tidal contributions
m
2
k
h
8
1/
0.523
0.660
0.692
"'I
ell I
0.466
0.328
0.937
0.662
0.0736
0.0823
1.235
1.167
Any semi-diurnal tide
0.302
0.609
0.0852
1.160
Values of the Love numbers for the real Earth are strongly modified by ocean tides and slightly
modified by anelasticity in the solid Earth.
11.10 GEOLOGICAL TIME SCALE [9]
Age of Earth = 4.5 - 4.7 Ga
Oldest Geological Dates:
Rocks at Isua in southern West Greenland have yielded dates of metamorphic events at about
3750Ma.
Sand River gneisses in the Limpopo belt of Southern Africa have been dated at about 3800 Ma.
Detrital zircons from Western Australia have yielded dates of about 4200 Ma, indicative of preexisting crust.
Table 11.7 gives dates of various geologic eras in the Phanerozoic eon, and Table 11.8 gives dates in
the Precambrian eon. Table 11.9 lists the major geological and biological events in the Earth's history.
Table 11.7. The Phanerozoic Eon (Present-570 Million Years Ago).
Period
Duration
Cenozoic Era
Quaternary Sub-Era
Holocene Epoch
Pleistocene Epoch
Tertiary Sub-Era
Neogene Period
Pliocene Epoch
Miocene Epoch
Paleogene Period
Oligocene Epoch
Eocene Epoch
Paleocene Epoch
Mesozoic Era
Cretaceous Period
Senonian Epoch
Gallic Epoch
Neocomian Epoch
K2 Gulf Epoch
KI
Jurassic Period
J3, Maim Epoch
J2, Dogger Epoch
]I, Lias Epoch
Triassic Period
Tr3Epoch
Tr2Epoch
Trl, Scythian Epoch
Present-65 Ma
Present-1.64 Ma
Present-O.01 Ma
0.01-1.64 Ma
1.64-65Ma
1.64-23.3 Ma
1.64-5.2Ma
5.2-23.3Ma
23.3-65Ma
23.3-35.4 Ma
35.4-56.5 Ma
56.5-65Ma
65-245Ma
65-145.6Ma
65-88.5Ma
88.5-131.8 Ma
131.8-145.6 Ma
65-97Ma,
97-145.6 Ma)
145.6-208 Ma
145.6-157.1 Ma
157.1-178 Ma
178-208Ma
208-245Ma
208-235Ma
235-241.1 Ma
241.1-245 Ma
11.10 GEOLOGICAL
TIME SCALE
Table 11.7. (Continued.)
Period
Duration
Paleozoic Era
Permian Period
Zechstein Epoch
Rotliegendes Epoch
Carboniferous Period
Pennsylvanian Subperiod
Gzelian, Kasimovian, Moscovian, Bashkirian Epochs
Mississippian Subperiod
Serpukhovian, Visean, Tounaisian Epochs
Devonian Period
D3 Epoch
D2 Epoch
D,Epoch
Silurian Period
Pridoli, Ludlow, Wenlock, Llandovery Epochs
Ordovician Period
Bala Subperiod
Ashgill, Caradoc Epochs
Dyfed Subperiod
Llandeilo, Llanvirn Epochs
Canadian Subperiod
Arenig, Tremadoc Epochs
Cambrian Period
Merioneth Epoch
St. David's Epoch
Caerfai Epoch
245-570Ma
245-290Ma
245-256Ma
256--290Ma
290-362.5 Ma
290-323 Ma
323-362.5 Ma
362.5-408.5 Ma
362.5-377.5 Ma
377.5-386 Ma
386--408.5 Ma
408.5-439 Ma
439-51OMa
439-464Ma
464-476 Ma
476--51OMa
510-570 Ma
510-517 Ma
517-536 Ma
536--570Ma
Table 11.8. The Precambrian Eon (570-4550-4570 Ma)a.
Period
Duration
Sinian Era
Vendian Period
Sturtian Period
Riphean Era
Karatau Period
Yurmatin Period
Burzyan Period
Animikean Era
Gunflint Period
Huronian Era
Cobalt, Qurke Lake, Hough Lake, Eliot Lake Periods
Randian Era
Ventersdorp, Central Rand, Dominion Periods
SwazianEra
Pongola, Moodies, Figtree, Onverwacht Periods
Isuan Era
HadeanEra
Imbrian (pars) Period
Nectarian Period
Pre-Nectarian Period
Cryptic Division
570-800Ma
570-6IOMa
610-800Ma
800-1650Ma
800-1050Ma
1050-1350 Ma
1350-1650 Ma
1650-2200 Ma
1650-2200 Ma
2200-2400-2500 Ma
2400-2500-2800 Ma
2800-3500 Ma
3500-3800 Ma
3800-4550-4570 Ma
3800-3850 Ma
3850-3950 Ma
3950-4150 Ma
4150-4550-4570 Ma
Note
aThe Precambrian is also divided as follows: Proterozoic Eon (570-2500 Ma);
Pt3 (570-900 Ma), Pt2 (900-1600 Ma), Pt, (1600-2500 Ma) Subeons; Archean Eon
(2500-4000 Ma); Ar3 (2500-3000 Ma), Ar2 (3000-3500 Ma), Ar, (3500-4000 Ma)
Subeons; Priscoan Eon (4000-4550-4570 Mal.
/
249
250 I
11
EARTH
Table 11.9. Major "events" in Earth history.
Event
Homo sapiens, Neanderthal man, Homo erectus, Australopithecus africanus, worldwide
glaciations
Approximate age
(Ma, million years ago)
0-3 Ma
Gulf of California opens, Calabria collides Italy-Sicily
3-5 Ma
Mediterranean desiccation, Panama collides NW Columbia, Red Sea Opens
5-10 Ma
FA (First Appearance) Hipparion (horse), FA hominids, Sivapithecus, Kenyapithecus,
Khabylies collides Africa
10-15 Ma
Andaman Sea opens, South China Sea spreading ceases, Calabria rifts SE from Sardinia,
Corsica-Sardinia collide Apulia, Main Himalayan Orogeny
15-20 Ma
Okinawa trough opens, Japanese Sea opens, Corsica-Sardinia parts France, East African
and Red Sea rifting begins, BalearicslKhabalirs rift from Iberia
20-25 Ma
Norwegian Sea opens east of Jan Mayen,
Main Alpine Orogeny
South China Sea opens, Scotia Sea opens
Drake Passage opens, Caribbean Plate moves east
25-30 Ma
30-35 Ma
Late Eocene extinction, FA proboscideans (mastodons, elephants), early anthropoids,
Labrador SeaJBaffin Bay cease spreading, Jan Mayen Ridge rifts from Greenland
35-45 Ma
FA rodents, Cuba collides Bahama Bank, India Eurasia collision begins, Indian-Australian
plates united, Eurasia Basin opens, Norwegian Sea opens, Tasman Sea opens
45-55 Ma
FA horses, FA grasses, mammals diversify, FA primates
55-60 Ma
North Atlantic lavas, Indian Ocean spreads northwest of Seychelles, Yucatan Basin opens
as Cuba moves north, Laramide Orogeny
60-65 Ma
Terminal Cretaceous extinction, Deccan lavas
65-70 Ma
FA early grasses, LA (last appearance) pteridosperms (seed ferns)
70-75 Ma
Cretaceous anoxic event, Labrador Sea opens, India-Madagascar separate, Australia parts
Antarctica
85-95 Ma
FA diatoms (one-cell marine organisms), equatorial Atlantic opens, Bay of Biscay opens,
Iberia parts Grand Banks
105-120 Ma
FA angiosperms (flowering plants), South Atlantic opens, East Indian Ocean opens, India
parts from Australia-Antarctica, FA placental mammals
125-135 Ma
FA birds, Paleo Tethys closed
145-155 Ma
India-Madagascar Antarctica separate, Gulf of Mexico opens, Neo-Tethys opens, central
Atlantic opens, East Gondwana (India, Australia, Antarctica) parts West Gondwana
(Africa, South America)
155-170 Ma
Karoo volcanism
185-195 Ma
Early mammals, terminal Triassic extinction, Rifting between Gondwana and Laurasia
205-215 Ma
Iran, Crete, 1\Jrkey part from Gondwana, FA dinosaurs, Siberian lavas
235-250 Ma
Gondwana Laurasia collide, Appalachian Ocean finally closed
265-280 Ma
Iran, Tibet rift from Gondwana, FA conifers
280-300 Ma
FA winged insects, FA pelycosaurs (early mammal-like reptile)
300-320 Ma
South China rifts from Gondwana, FA sharks
350-380 Ma
FA wingless insects, tims, Iapetus Ocean finally closed
380-400 Ma
FA lungfish, land plants, jawed fish, North China rifts from Gondwana
400-430 Ma
11.11 GLACIATIONS
I 251
Table 11.9. (Continued.)
Approximate age
(Ma, million years ago)
Event
Ediacaran metazoans (soft body multicell animals), Skilogalee microbiota, Grenvilian
Orogeny
570-1000 Ma
Keweenawan, Mackenzie Volcanics, Duluth Muskox intrusives, Oldest megascopic algae
(Iarge-celled algae), algal coals
1100-1400 Ma
Hudsonian and Penokean Orogenies, FA common red beds, Sudbury intrusion, Banded
iron fonnations, Oxygen buildup in atmosphere
1700-2000 Ma
Bushveld intrusion, Gunflint microbial structures in chert, Hammersley & Fortescue biota,
Kenoran Orogeny
2000-2500 Ma
FA red beds, Ventersdorp biota, Stilwater volcanics and intrusives
2500-2800 Ma
Kaap Valley Granite, Fig Tree Group with bacteria and blue green algae, Barberton
Gneisses
3200-3300 Ma
FA stromatolites (bacterial algal mats) in Onverwacht Group and Australia
"" 3400 Ma
Amitsoq & Kaapvaal gneisses, evidence life well established (carbon isotopic ratios)
"" 3800 Ma
Basin formation on the Moon
3800-4200 Ma
Zircons from early crust
4200-4300 Ma
Lunar melting and differentiation of anorthositic crust
"" 4500 Ma
Accretion of Earth and Moon
11.11
4500-4600 Ma
GLACIATIONS [9-11]
The geological record contains evidence of major glaciations as listed in Table 11.10.
Table 11.10. Ages and locations of major glaciations.
Age(Ma)
Locations
0-15, Holocene, Pleistocene
250-380, Pennian, Carboniferous, Devonian
430-450, Silurian, Ordovician
600, Vendian
650,Sturtian
800, Sturtian
900, Karatau
2300-2400, Huronian
2800, Randian, Swazian
Antarctica, North America, Eurasia
Gondwana
Gondwana
China, North Europe, North and South America
Eurasia, South Africa, Australia
Australia, North America, South Africa
Africa
Notth America, South Africa
South Africa
Some glaciations may be related to plate tectonics, e.g., Gondwana moved over the South Pole in
the Paleozoic.
The Quaternary glaciations (most geologically recent glaciations) may be related to cyclical
changes in the Earth's orbital motion about the Sun and in the motion of the Earth's rotation axis
(Milankovitch or astronomical theory of ice ages). The tilt of the Earth's equator to the ecliptic varies
from 21.5 0 to 24.5 0 with a period of about 41,000 years. The eccentricity of the Earth's orbit varies
with periods of about 100,000 years and 400,000 years and the Earth's axis of rotation wobbles with a
period of about 22,000 years. Pleistocene glaciations have occurred cyclically with a period of about
252 I 11
EARTH
lOS years. 'JYpically there has been a relatively slow glaciation phase lasting about 9 x 104 years and a
relatively fast deglaciation phase lasting about 104 years. The last deglaciation event of the current ice
age began about 18,000 years ago and ended about 7000 years ago.
11.12 PLATE TECTONICS [5, 12]
Earth's outer shell is divided into units known as tectonic plates that behave essentially rigidly on
geological time scales. Plates move with respect to each other and the underlying mantle which
defonns like a very viscous fluid on geological time scales. Tectonic plates comprise the lithosphere
or rbeologically stiff outer shell of the Earth. Plates are separated by four types of boundaries:
(1) midocean ridges or sites of seafloor spreading and generation of new oceanic crust; (2) subduction
zones or sites of plate submergence into the mantle; (3) transfonn faults or sites of fault-parallel relative
horizontal motion or sliding; and (4) collisional zones or sites of horizontal convergence characterized
by strong defonnation and mountain building. Nonrigid defonnation of the lithosphere occurs mainly
at plate boundaries.
Major tectonic plates include Eurasia, Pacific, Antarctic, North America, South America, Africa,
Australia, Philippine, Arabia, Nazca, Cocos, Caribbean, and Juan de Fuca.
Plate motions are well described by rigid body rotations of the plates about axes through the center
of the Earth and intersecting the surface at poles of rotation generally located remotely from the plates
(Euler'S theorem). The angular velocity vector of plate rotation is known as the Euler vector. Each
plate rotates counterclockwise relative to the fixed Pacific plate (PA). These main plates are given in
Table 11.11.
Table 11.11. NUVEL-l Euler vectors ofplate rotJJtion.
Latitude of
rotation pole
Plate
Africa,AF
Antarctica, AN
Arabia,AR
Australia, AU
Caribbean, CA
Cocos, CO
Eurasia,EU
India, IN
Nazca,NZ
North America, NA
South America, SA
Juan de Fucao
Philippine"
ON
59.16
64.315
59.658
60.080
54.195
36.823
61.066
60.494
55.578
48.709
54.999
35.0
O.
Longitude of
rotation pole
°E
-73.174
-83.984
-33.193
+1.742
-80.802
-108.629
-85.819
-30.403
-90.096
-78.167
-85.752
+26.0
-47.
Magnitude of
rotation rate
w(deg. Myr-l)
0.9695
0.9093
1.1616
1.1236
0.8534
2.0890
0.8985
1.1539
1.4222
0.7829
0.6657
0.53
1.0
Note
°Listed Euler vectors are not part of the NUVEL-l model.
11.13 EARm CRUST [5, 11]
The crust is the outennost layer of the Earth. The rocks of the crust are chemically and physically
distinct from underlying mantle rocks; the major distinction between crust and mantle is compositional.
Crustal rocks are less dense than mantle rocks and contain greater concentrations of heat-producing
radiogenic elements. The base of the crust is defined by a discontinuity in the depth profiles of seismic
velocities known as the Mohorovici~ discontinuity or Moho.
11.13
EARTH CRUST
/
253
There are two major subdivisions of the crust-the oceanic crust and the continental crust. Both
types of crust generally consist of a sediment layer, an upper layer, and a lower layer. The average
properties of these crustal layers are given in Table 11.12.
Table 11.12. Average properties of oceanic and continental crust.
Property
Sediment layer thickness (km)
Upper layer thickness (km)
Lower layer thickness (km)
Total thickness (km)
AreaJ abundance (%)
Volume abundance (%)
Heat flow (mW m- 2)
Bouguer anomaly (mgal)Q
up. upper layer (km s-l)b
up. lower layer (Ian s-l)b
Oceanic
Continental
0-1
1.5(0.7-2)
5(3-7)
7(5-15)
59
21
78
250
5.1
6.6
17(1()""20)
21(15-25)
36(3()""80)
41
79
56.5
-100
6.1
6.8
()""5
Notes
QBouguer anomaly = free air gravity anomaly (see above) -2rrGpch
(a correction for the gravitational attraction of topography with elevation
h and density Pc. G is the universal gravitational constant).
b up = velocity of seismic P or compressional waves; 1 mgal =
10- 2 mm s-2. Seismic shear velocities of crustal rocks Us are about
3.7 km s-1
The average composition of the oceanic crust is primarily that of a tholeiitic basalt (Table 11.13).
Oceanic tholeiitic basalt is extruded and intruded at mid-ocean ridges as a consequence of pressurerelease melting of upper mantle material that rises beneath the ridges. Oceanic basalts undergo varying
degrees of alteration by reactions with seawater and hydrothermal fluids especially at and near midocean ridges.
The average composition of the upper layer of the continental crust is similar to that of granodiorite.
The lower layer of the continental crust may be largely similar to mafic granulites in composition
though a more felsic composition is possible. Whereas the oceanic crust is produced in a one stage
melting of the upper mantle, continental crustal rocks involve mUltiple melting events.
Table 11.13. Estimated average composition of the oceanic and continental crust
(excluding sediments).
Continental crust
Upper
Lower. mafic
Lower, felsic
Oceanic crust
Oxides (in weight %)
Si02
Ti02
AI203
FeOT
MgO
CaO
Na20
K20
MnO
P20 5
65.5
0.5
15.0
4.3
2.2
4.2
3.6
3.3
0.1
0.2
49.2
1.5
15.0
13.0
7.8
10.4
2.2
0.5
0.2
0.2
61.0
0.5
15.6
5.3
3.4
5.6
4.4
1.0
0.1
0.2
49.6
1.5
16.8
8.8
7.2
ll.8
2.7
0.2
0.2
0.2
254 /
11
EARTH
Table 11.13. (Continued.)
Continental crust
Upper
Lower, mafic
Lower, felsic
Oceanic crust
Trace Elements (in ppm)
Rb
Ba
Sr
La
Yb
Zr
Nb
U
Th
Cr
Ni
llO.
BOO.
325.
30.
2.0
220.
25.
2.5
II.
35.
20.
2.
50.
500.
10.
1.0
30.
3.
0.1
0.3
200.
150.
4.
60.
IBO.
3.5
2.7
100.
5.
0.2
0.6
230.
BO.
10.
7BO.
570.
20.
1.2
200.
5.
0.1
0.5
90.
60.
Properties of the main crustal rocks are given in Table 11.14.
Table 11.14. Properties of crustal rocks. ab
Rock
Density
(kg m- 3)
Young's modulus
(10 11 Pa)
Shear modulus
(10 11 Pa)
Poisson's ratio
Thermal
conductivity
Wm- I K- 1
Thermal
expansivity
10-5 K- 1
Sedimentary
Shale
Sandstone
Limestone
Dolomite
Marble
2100-2700
2200-2700
2200-2800
2200-2BOO
2200-2BOO
0.1~.3
0.14
0.1~.6
0.~.3
O.~.B
0.2~.3
Gneiss
Amphibole
2700
3000
0.~.7
Basalt
Granite
Diabase
Gabbro
Diorite
Anorthosite
Granodiorite
2950
2650
2900
2950
2Boo
2750
2700
O.~.B
0.3
0.~.7
0.2~.3
0.8-1.1
0.6-1.0
0.3~.45
O.~.B
0.3~.35
0.B3
0.35
0.5~.9
0.3~.5
0.~.9
0.2-0.35
0.2-0.3
0.25-0.3
0.1-0.4
1.2-3
1.5-4.2
2-3.4
3.2-5
2.5-3
3.
2.4
Metamorphic
0.1~.35
0.~.15
0.5 - 1.0
0.4
2.1-4.2
2.5-3.B
Igneous
0.2~.35
0.25
0.1-0.25
0.25
0.15-0.2
0.25
1.3-2.9
2.4-3.B
1.7-2.5
1.9-2.3
2.8-3.6
1.7-2.1
2.6-3.5
Notes
aThe specific heats of crustal rocks are all approximately I kJ kg-I K- 1 .
bMean density of the continental crust = 2750 kg m- 3. Mean density of the oceanic crust = 2900 kg m- 3 .
The radioactive heat sources in the Earth's interior are listed in Table 11.15.
2.4
1.6
11.14 EARTH INTERIOR
/
255
Table 11.1S. Radiogenic heat production rates per unit mass H and
half-lives '1"1/2 of the important radioactive isotopes in the Earth's
interior. a
Isotope or
element
238U
235U
U
232Th
40K
K
~antleconcentration
H (Wkg- I )
9.37
5.69
9.71
2.69
2.79
3.58
x
x
x
x
x
x
10-5
10-4
10-5
10-5
10-5
10-9
'1"1/2 (Gyr)
(kg kg-I)
4.47
0.704
25.5 x 10-9
1.85 x 10- 10
25.7 x 10-9
1.03 x 10-7
3.29 x 10-8
2.57 x 10-4
14.0
1.25
Note
aU is 99.27% by weight 238U and 0.72% 235U. Th is 100% 232Th.
K is 0.0128% 4OK. Assumes kg K/kg U = 104, kg Th/kg U = 4, and
H = 6.18 x 10- 12 W kg-I in present mantle. [I]
Reference
1. Turcotte D.L., & Schubert, G. 1982, Geodynamics (Wiley, New
York)
The abundances of uranium, thorium and potassium in the Earth and meteorite rocks is given in
Table 11.16.
Table 11.16. Representative concentrations (by weight) ofheatproducing elements in several rocks and chondritic meteorites. a
Concentrations
Rock
Depleted Peridotites
Tholeiitic Basalt
Granite
Chondritic ~eteorites
U (ppm)
0.012
0.1
4.
0.013
Th(ppm)
K(%)
0.035
0.35
17.
0.04
0.004
0.2
3.2
0.078
Note
aRadiogenic elements are highly concentrated in the continental crust.
11.14 EARTH INTERIOR [13]
The structure of the Earth's interior has been detennined mainly from seismology. Table 11.17
summarizes the values of the physical properties of a spherically symmetric model of the Earth as
a function of radius from the center of the Earth based on seismological data. The major divisions of
the solid Earth model are the core (radius r = 0 to 3480 km), the mantle (r = 3480 to 6346.6 km), and
the crust (r = 6346.6 to 6368 km). The model core is divided into a solid inner core (r = 0 to 1221.5
km) and a liquid outer core. The model mantle is divided into the lower mantle (r = 3480 to 5701
km) and upper mantle (5701 to 6368 km). Subregions of the model mantle are the D"-layer at the base
of the mantle (r = 3480 to 3630 km), the transition zone in the mid-mantle (r = 5701 to 5971), the
seismic low velocity zone (r = 6151 to 6291 km) and the lithosphere or lid (r = 6291 to 6346.6 km).
Similar tenns are used to describe regions of the real Earth whose radial thicknesses are not so readily
defined. The real Earth is, of course, laterally heterogeneous.
256 I
11
EARTH
Table 11.17. Physical properties of the Earth's interior according to PREM (Preliminary Earth Reference Model). a
(ms- I )
P
(kg m- 3)
Ks
(m s-I)
/L
(GPa)
(GPa)
v
P
(GPa)
g
(m s-2)
200.
400.
600.
800.
1000.
1200.
1221.5
11266.20
11255.93
11237.12
11205.76
11161.86
11105.42
11036.43
11028.27
3667.80
3663.42
3650.27
3628.35
3597.67
3558.23
3510.02
3504.32
13088.48
13079.77
13053.64
13010.09
12949.12
12870.73
12774.93
12763.60
1425.3
1423.1
1416.4
1405.3
1389.8
1370.1
1346.2
1343.4
176.1
175.5
173.9
171.3
167.6
163.0
157.4
156.7
0.4407
0.4408
0.4410
0.4414
0.4420
0.4428
0.4437
0.4438
363.85
362.90
360.03
355.28
348.67
340.24
330.05
328.85
0
0.7311
1.4604
2.1862
2.9068
3.6203
4.3251
4.4002
Outer core
1221.5
1400.
1600.
1800.
2000.
2200.
2400.
2600.
2800.
3000.
3200.
3400.
3480.
10355.68
10249.59
10122.91
9985.54
9834.96
9668.65
9484.09
9278.76
9050.15
8795.73
8512.98
8199.39
8064.82
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
12166.34
12069.24
11946.82
11809.00
11654.78
11483.11
11292.98
11083.35
10853.21
10601.52
10327.26
10029.40
9903.49
1304.7
1267.9
1224.2
1177.5
1127.3
1073.5
1015.8
954.2
888.9
820.2
748.4
674.3
644.1
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
328.85
318.75
306.15
292.22
277.04
260.68
243.25
224.85
205.60
185.64
165.12
144.19
135.75
4.4002
4.9413
5.5548
6.1669
6.7715
7.3645
7.9425
8.5023
9.0414
9.5570
10.0464
10.5065
10.6823
D"
3480.
3600.
3630.
13716.60
13687.53
13680.41
7264.66
7265.75
7265.97
5566.45
5506.42
5491.45
655.6
644.0
641.2
293.8
290.7
289.9
0.3051
0.3038
0.3035
135.75
128.71
126.97
10.6823
10.5204
10.4844
Lower
mantle
3630.
3800.
4000.
4200.
4400.
4600.
4800.
5000.
5200.
5400.
5600.
13680.41
13447.42
13245.32
13015.79
12783.89
12544.66
12293.16
12024.45
11733.57
11415.60
11065.57
7265.97
7188.92
7099.74
7010.53
6919.57
6825.12
6725.48
6618.91
6563.70
6378.13
6240.46
5491.45
5406.81
5307.24
5207.13
5105.90
5002.99
4897.83
4789.83
4678.44
4563.07
4443.17
641.2
609.5
574.4
540.9
508.5
476.6
444.8
412.8
380.3
347.1
313.3
289.9
279.4
267.5
255.9
244.5
233.1
221.5
209.8
197.9
185.6
173.0
0.3035
0.3012
0.2984
0.2957
0.2928
0.2898
0.2864
0.2826
0.2783
0.2731
0.2668
126.97
117.35
106.39
95.76
85.43
75.36
65.52
55.90
46.49
37.29
28.29
10.4844
10.3095
10.1580
10.0535
9.9859
9.9474
9.9314
9.9326
9.9467
9.9698
9.9985
5600.
5701.
11065.57
10751.31
6240.46
5945.08
4443.17
4380.71
313.3
299.9
173.0
154.8
0.2668
0.2798
28.29
23.83
9.9985
10.0143
5701.
5771.
10266.22
10157.82
5570.20
5516.01
3992.14
3975.84
255.6
248.9
123.9
121.0
0.2914
0.2909
28.83
21.04
10.0143
10.0038
5771.
5871.
5971.
10157.82
9645.88
9133.97
5516.01
5224.28
4932.59
3975.84
3849.80
3723.78
248.9
218.1
189.9
121.0
105.1
90.6
0.2909
0.2924
0.2942
21.04
17.13
13.35
10.0038
9.9883
9.9686
5971.
6061.
6151.
8905.22
8732.09
8558.96
4769.89
4706.90
4643.91
3543.25
3489.51
3435.78
173.5
163.0
152.9
80.6
77.3
74.1
0.2988
0.2952
0.2914
13.35
10.20
7.11
9.9686
9.9361
9.9048
Lowvelocity
zone
6151.
6221.
6291.
7989.70
8033.70
8076.88
4418.85
4443.61
4469.53
3359.50
3367.10
3374.71
127.0
128.7
130.3
65.6
66.5
67.4
0.2796
0.2796
0.2793
7.11
4.78
2.45
9.9048
9.8783
9.8553
Lid
6291.
8076.88
4469.53
3374.71
130.3
67.4
0.2793
2.45
9.8553
Region
Inner core
Transition
zone
Radius
(kIn)
O.
vp
Vs
11.15
EARTH ATMOSPHERE, DRY AIR AT
STP / 257
Table 11.17. (Continued.)
Region
Crust
Ocean
Radius
(Ian)
(ms- I )
(ms- I )
P
(kgm- 3)
Ks
/.L
(GPa)
(GPa)
v
6346.6
8110.61
4490.94
3380.76
131.5
68.2
0.2789
0.604
9.8394
6346.6
6356.
6800.00
6800.00
3900.00
3900.00
2900.00
2900.00
75.3
75.3
44.1
44.1
0.2549
0.2549
0.604
0.337
9.8394
9.8332
6356.
6368.
5800.00
5800.00
3200.00
3200.00
2600.00
2600.00
52.0
52.0
26.6
26.6
0.2812
0.2812
0.337
0.300
9.8332
9.8222
6368.
6371.
1450.00
1450.00
O.
O.
1020.00
1020.00
2.1
2.1
O.
O.
0.5
0.5
0.300
9.8222
9.8156
vp
Vs
P
(GPa)
O.
g
(m s-2)
Note
a Ks is the bulk modulus, /.L is the shear modulus, and v is Poisson's ratio.
11.15 EARTH ATMOSPHERE, DRY AIR AT
STANDARD TEMPERATURE AND PRESSURE (STP) [14, 15]
Standard temperature To = 273.15 K.
Standard pressure po = 1013.250 x 102 Pa = 1013.25 mbar.
Standard gravity gO = 9.806 65 m s-2.
Mass density of air PO = 1.2928 kg m- 3.
Molecular weight Mo
28.964 x 10-3 kg mole-I.
Mean molecular mass mo
4.810 x 10-26 kg.
Molecular root-mean-square velocity (3RTo/ MO)I/2 = 4.850 x 102 m s-I.
Speed of sound (ypo/ PO)I/2 = (y RTo/ MO)I/2 = 3.313 x 102 m s-I.
Specific heat at constant pressure C p
1005 J kg-I K- 1.
Specific heat at constant volume C v = 717.6 J kg-I K- I .
Ratio of specific heats y
cp/c v
1.400.
Number density of air No = 2.688 x 1025 m- 3.
Molecular diameter a = 3.65 x 10- 10 m.
Mean free path L = 1/(2 1/ 21r N( 2 ) = 6.285 x 10-8 m.
Coefficient of viscosity = 1.72 x 10-5 Pa s.
Thermal conductivity = 2.41 x 10-2 W m- I K- 1.
Refractive index n
=
=
=
=
(n -1) xl
06
=
288.15 (64.328 + 29498.1 x 10-6
146 x 10-6 -a 2
= -27-3-.1-5
a = 1/)..(m).
Rayleigh scattering (molecular) volume attenuation coefficient
k
=
321r 3
1.06--4 (n 3N)"
1)2.
255.4 x 10-6 )
+ -:-4-1-x-1O---;;6"---a~2
.
258 I
11.16
11
EARTH
COMPOSITION OF THE ATMOSPHERE [14, 16-21]
Table 11.18 gives the composition of the atmospheric gases.
'Dlble 11.18. Gases in the well-mixed atmosphere.
Gas
Nl
~c
H2 0def
ArB
C~c
NeB
He'
CM4 h
KrB
code
s~de
H2i
N2 0i
03 dek
Xe8
N02d
HN03d
Node
CFCl3'
CF2Cl2'
Notes
Molecular
weight
28.013
31.999
18.015
39.948
44.010
20.183
4.003
16.043
83.80
28.010
64.06
2.016
44.012
47.998
131.30
46.006
63.02
30.006
137.37
120.91
=
Fraction of dry air at surface
volume percent
78.08
20.95
2 x 10-6 - 3 x 10-2
9.34 x 10-3
3.45 x 10-4
18.2 x 10-6
5.24 x 10-6
1.72 x 10-6
1.14 x 10-6
1.5 x 10-7
3 x 10- 10
5.0 x 10-7
3.1 x 10-7
3.0-6.5 x 10-8
8.7 x 10-8
2.3 x 10- 11
5 x 10- 11
3 x 10- 10
2.8 x 10- 10
4.8 x 10- 10
weight percent
Column amount
(atm-cm)a
75.52
23.14
3 x 10-6 - 5 x 10-2
12.9 x 10-3
5.24 x 10-4
12.7 x 10-6
0.724 x 10-6
0.95 x 10-6
3.30 x 10-6
1.5 x 10-7
7 x 10- 10
0.35 x 10-7
4.7 x 10-7
5.0-11 x 10-8
39.4 x 10-8
3.9 x 10- 11
11 x 10- 11
3 x 10- 10
13 x 10- 10
20 x 10- 10
6.24 x loS
1.67 x loS
1760
7470
276
14.6
4.2
1.3
0.91
0.089
1.1 x 10-4
0.4
0.25
0.343
0.07
2.0 x 10-4
3.6 x 10-4
3.1 x 10-4
2.2 x 10-4
3.8 x 10-4
=
a 1 ann-cm
thickness of gas column when reduced to STP
2.687 x 1023 molecules m- 2 .
Gases are well mixed (constant fractional amount with altitude) in the troposphere unless otherwise
noted. Column amounts are nominal mid-latitude values [1, 2, 3]. Values for fractional amounts are
from [I, 2, 3, 4, 5].
bPbotochemical dissociation in the thermosphere (see Table 11.20 for definition of thermosphere). Well mixed at lower levels [4].
cPhotochemical dissociation above 95 kIn. Well mixed at lower levels [4].
d Considerable tropospheric vertical variation in the fractional amount. Very dry above the
tropopause [1, 2]. See Table 11.20 for definitions of troposphere and tropopause.
eFactor of 102 or more local variability related to local sources such as anthropogenic pollution
and geothermal activity [I, 2,4,5, 6].
fFractional amounts are 1% extremes [1].
'Well mixed up to...., 110 kIn (turbopause). Diffusive separation at higher levels [4].
hDissociated in the mesosphere (see Table 11.20 for definition of mesosphere). Well mixed at
lower levels [4, 7].
iIncrease with altitude in the mesosphere because of dissociation of H20. Minimum value in the
stratosphere (see Table 11.20 for definition ofstratosphere) [1,7].
iDissociated in the stratosphere and mesosphere [4].
kRange in fractional amount refers to monthly averages [5].
'Dissociated in the stratosphere [4].
References
1. COESA, U.S. Standard Atmosphere 1976, (Government Printing Office, Washington DC)
2. Anderson, G.P. et al. 1986, AFGL-TR-86-0110, Atmospheric Constituent Profiles 10-120 kIn,
Air Force Geophysics Laboratory (now Air Force Research Laboratory).
3. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London)
4. Goody R.M., & Yung, Y.L. 1989, Atmospheric Radiation: Theoretical Basis, 2nd ed. (Oxford
11.18 HOMOGENEOUS ATMOSPHERE, SCALE HEIGHTS AND GRADIENTS
/
259
University Press, New York)
5. Watson, R.F. et al. 1990, Greenhouse gases and aerosols, in Climate Change: The [PCC Scientific
Assessment edited by J.T. Houghton, G.H. Henkins, and J.H. Ephraums (Cambridge University
Press, New York)
6. Logan, J.A. et al. 1981, J. Geophys. Res., 86, 7210
7. Allen, M., Lunine, J.I., & Yung, Y.L. 1984, J. Geophys. Res. 89,4841
11.17 WATER VAPOR [22,23]
The water vapor pressure in saturated air is given in Table 11.19.
Table 11.19. Water vapor pressure e in saturated air.
Over pure water
T(°C)
e (Pa)
-30
50.88
-20
125.4
-10
286.3
0
610.8
10
1227
20
2337
30
4243
40
7378
Over ice
T(°C)
e (Pa)
-30
37.98
-20
103.2
-10
259.7
0
610.7
Water vapor density (perfect gas law) = (2.167 x 1O-3 eff) kg m- 3 with T in K and e the water vapor
pressure in Pa.
1 cm precipitable water = 1245 cm STP water vapor.
Density of moist air (perfect gas law) = 3.484 x lO-\p - 0.378e)/T (kg m- 3 ) with P the total
pressure, p the water vapor pressure, e in Pa, and T in K.
Mean change of water vapor pressure with height h
log(eh/eo) = -h/2,
h ::s 7.2 km
7.2 km::s h ::s 13.6 km.
= -(h - 2.16)/1.4,
h
eh
eo
= height above surface (km).
= water vapor pressure at height h.
= water vapor pressure at surface.
11.18 HOMOGENEOUS ATMOSPHERE, SCALE HEIGHTS
AND GRADIENTS [17]
The scale height of the atmosphere (height for e-fold change of pressure in an isothermal atmosphere)
RT/g = R*T/MWg = 2.93 x 1O- 2 T (km),
where R is the gas constant of dry air = 287.05 J kg- 1 K- 1 , R* is the universal gas constant =
8.314 kJ K- 1 kmole- 1, MW is the molecular weight of dry air = 28.964 kg kmole- 1, g is the
acceleration of gravity = 9.8 m s-2, and T is in K.
Height of homogeneous atmosphere. (An idealized abnosphere of finite height, constant temperature
equal to the surface temperature, and constant density equal to the surface density.) = H =
R*T/MWg.
260 /
11
Surface Air T
Hkm
EARTH
eC)
-30
7.11
-15
7.55
o
7.99
15
8.43
30
8.87
Mass of atmosphere per m2 = 1.035 x 104 kg.
Total mass of Earth's atmosphere = 5.136 x 10 18 kg.
Moment of inertia of the Earth's atmosphere = 1.413 x 1032 kg m2 .
Magnitude of the dry adiabatic temperature gradient g / c p (c p is the specific heat at constant pressure =
1005 J kg-I K- I for dry air) = 9.75 K km-I.
Mean temperature gradient in troposphere = -6.5 K km-I.
Mass per unit area of 1 atm-cm of gas of molecular weight MW = 4.462 x 1O-4 MW(kg m- 2 ) where
MW is in kg kmole- I .
11.19 REGIONS OF EARTH'S ATMOSPHERE AND
DISTRIBUTION WITH HEIGHT [14, 17,24]
The Earth's atmospheric layers are detailed in Table 11.20.
Table 11.20. Atmospheric layers and transition levels.
Height, h
Layer
(km)
Characteristics
Troposphere
Tropopause
Stratosphere
Stratopause
Mesosphere
Mesopause
Thermosphere
Exobase
Exosphere
Ozonosphere
Ionosphere
Homosphere
Heterosphere
0-11
11
Weather, T decreases with h, radiative-convective equilibrium
Temperature minimum, limit of upward mixing of heat
T increases with h due to absorption of solar UV by 03, dry
Maximum heating due to absorption of solar UV by 03
T decreases with h
Coldest part of atmosphere, noctilucent clouds
T increases with h, solar cycle and geomagnetic variations
11-48
48
48-85
85
85-exobase
500-1000km
> exobase
15-35 km
> 70km
< 85km
> 85km
Region of Rayleigh-Jeans escape
Ozone layer (full width at e- 1 of maximum)
Ionized layers
Major constituents well-mixed
Constituents diffusively separate
Radiation belts
Inner belt
Outer belt
r / R(B at magnetic equator
Magnetosphere
In direction of Sun
Bow shock in direction of Sun
In direction normal to ecliptic
r / R(B at magnetic equator
,..., 1.3-2.4
,..., 3.5-11
10
12
18
Profiles of physical quantities in the atmosphere are given in Table 11.21.
11.19 REGIONS OF EARTH'S ATMOSPHERE / 261
Table 11.21. Altitude profiles of mean physical conditions at latitude 45 0 [1].
Altitude
(km)
logP
(Pa)
T
(K)
logp
(kgm- 3 )
logN
(m- 3 )
Ha
(km)
loglb
(m)
0
1
2
3
4
5
6
8
10
15
20
30
40
50
60
70
80
90
100
110
120
150
220
250
300
+5.006
+4.95
+4.90
+4.85
+4.79
+4.73
+4.67
+4.55
+4.42
+4.08
+3.74
+3.08
+2.46
+1.90
+1.34
+0.72
+0.022
-0.74
-1.49
-2.15
-2.60
-3.34
-4.07
-4.61
-5.06
-5.84
-6.52
-7.50
-8.12
288
282
275
269
262
256
249
236
223
217
217
227
250
271
247
220
199
187
195
240
360
634
855
941
976
996
999
1000
1000
+0.0881
+0.0460
+0.00286
-0.0413
-0.087
-0.133
-0.180
-0.279
-0.384
-0.71
-1.05
-1.73
-2.40
-2.99
-3.51
-4.08
-4.73
-5.47
-6.25
-7.01
-7.65
-8.68
-9.59
-10.22
-10.72
-11.55
-12.28
-13.51
-14.45
25.41
25.36
25.32
25.28
25.23
25.19
25.14
25.04
24.93
24.61
24.27
23.58
22.92
22.33
21.81
21.24
20.58
19.85
19.08
18.33
17.71
16.71
15.86
15.28
14.81
14.02
13.34
12.36
11.74
8.4
8.3
8.1
7.9
7.7
7.5
7.3
6.9
6.6
6.4
6.4
6.7
7.4
8.0
7.4
6.6
6.0
5.6
6.0
7.7
12.1
23.
36.
45.
51.
60.
69.
131.
288.
-7.2
-7.1
-7.1
-7.0
-7.0
-7.0
-6.9
-6.8
-6.7
-6.4
-6.0
-5.4
-4.7
-4.1
-3.6
-3.0
-2.4
-1.6
-0.85
-0.10
+0.52
+1.52
+2.38
+2.95
+3.41
+3.80
+4.89
+5.86
+6.49
400
500
700
1000
Notes
a H = pressure scale height (km).
bl = mean free path (m).
Reference
1. COESA, u.s. Standard Atmosphere 1976, (Government Printing Office,
Washington DC)
Variations in physical quantities during the day and during the solar cycle are given in Table 11.22.
Table 11.22. Diurnal and solar cycle variations from mean values [1]. ab
Altitude
(km)
200
500
1000
Diurnal
±~p
6.0
46.
43.
Solar
Diurnal
(%)
33
84
71
Solar
HN(%)
6.2
44.
25.
32
80
51
Diurnal
±~p
12.3
52.
35.
Solar
Diurnal
(%)
Solar
±~T(K)
45
87
64
59
121
122
145
207
207
Diurnal
Solar
HMW (kg kmol)-l
0.041
0.49
0.99
0.32
1.62
1.40
Notes
a ~ is the maximum departure in absolute value from mean values.
bValues obtained from the Mass Spectrometer Incoherent Scatter (MSIS) model for the following conditions. Diurnal:
Solar Activity Index FIO.7 = 150, geomagnetic activity index Ap = 10, day of year = 91, latitude = 45°N ; Solar:
Maximum FIO.7 = 200, minimum FIO.7 = 75, Ap = lO,dayofyear = 91, latitude = 45°N, local time of day = O9OOh.
Reference
I. Hedin, A.E. 1983, J. Geophys. Res. A, 88, 170
262 I
11
EARTH
Composition and other atmosphere profile data are given in Table 11.23.
Table 11.23. Mean molecular weight. composition and molecular collision frequency \I [1, 2]. a
Altitude
(kIn)
100
150
200
300
400
500
700
1000
Composition (% by volume)
AI
0
He
MW
(kgkmol- i )
N2
02
28.44
24.18
21.55
18.11
16.42
15.23
10.63
4.48
77.
61.
42.
17.
6.0
1.9
0.1
<0.05
19.
5.6
3.0
0.8
0.2
< 0.05
< 0.05
< 0.05
3.4
34.
55.
81.
91.
90.
55.
5.7
<0.05
< 0.05
.01
0.8
2.7
8.2
43.
88.
0.8
0.1
< 0.05
<0.05
<0.05
<0.05
<0.05
<0.05
H
< 0.05
<0.05
<0.05
< 0.05
<0.05
0.2
1.6
6.7
log(\I)
\I ins- i
3.42
1.36
0.59
-0.377
-1.143
-1.796
-2.66
-3.12
Note
aQuantities obtained from the MSIS model for the following conditions: Solar activity index FIO.7 =
ISO, geomagnetic index Ap = 10, day of year = 91, latitude = 45°N, and local time of day = 0900 h.
References
1. COESA, U.S. Standard Atmosphere 1976, (Government Printing Office, Washington DC)
2. Hedin, A.B. 1983, J. Geophys. Res. A, 88, 170
11.20
ATMOSPHERIC REFRACTION AND AIR PATH
The refractive index n of dry air at pressure Ps = 1 0l3.25 x 102 Pa and temperature Ts
is given by
(ns _ 1) x 106 = 64.328 + 29498.1 x 10-6 + 255.4 x 10-6 ,
146 x 10-6 - u 2
41 x 10-6 - u 2
= 288.15 K
where u = A-I and A is the vacuum wavelength in nm [15]. For other temperatures and pressures the
refractive index is found from
n - 1 = (pTslpsT)(ns - 1).
Water vapor reduces the refractive index by
where Pw is the partial pressure of water vapor [15].
Refractive index of air for radio waves [25]
(n - 1) x 106 = 0.776: - 0.056
P; + 3.75 x 103 ~~ .
Atmospheric refraction R is defined by
R
== Zt
- Za,
where Zt is true zenith distance and Za is apparent zenith distance.
The constant of refraction Ro is
n5 -
1
Ro = - - 2 2no
where no refers to n evaluated at PO
= 0.000 292 6 = 60.35" ,
= 10l3.25 x
102 Pa and To
= 273.15 K.
11.20 ATMOSPHERIC REFRACTION AND AIR PATH / 263
For n
= no refraction is [26]
Rno ~ Ro tan Zt,
Rno
~
=
Ro
Zt
;S 80°,
(2.06
0.0589 + (rr/2 _
Z') - 3.71
),
For other temperature and pressure conditions
Table 11.24 presents refraction data for the atmosphere.
Table 11.24. Refractive index n and refraction R versus wavelength A. a
A(nm)
200
220
240
260
280
300
320
340
360
380
400
450
500
550
600
650
700
800
900
1000
1200
1400
1600
1800
2000
3000
4000
5000
7000
10000
(nd - 1)
X
341.9
329.4
321.2
315.3
310.9
307.6
304.9
302.7
301.0
299.5
298.3
295.9
294.3
293.1
292.2
291.5
290.9
290.1
289.6
289.2
288.7
288.4
288.2
288.1
288.0
287.7
287.7
287.6
287.6
287.6
106
-(nw - 1)
0.19
0.20
0.20
0.21
0.21
0.22
0.22
0.22
0.22
0.22
0.22
0.23
0.23
0.23
0.23
0.23
0.23
0.23
0.23
0.23
0.23
0.24
0.24
0.24
0.24
0.24
0.24
0.24
0.24
0.24
X
106
(n - 1)
X
341.7
329.2
321.0
315.1
310.7
307.2
304.7
302.5
300.8
299.3
298.1
295.7
294.1
292.9
292.0
291.3
290.7
289.9
289.4
289.0
288.5
288.2
288.0
287.9
287.8
287.5
287.5
287.4
287.4
287.4
106
R (arcsec)
70.44
67.87
66.18
64.96
64.06
63.34
62.82
62.37
62.02
61.71
61.46
60.97
60.64
60.39
60.20
60.06
59.94
59.77
59.67
59.58
59.48
59.42
59.38
59.36
59.34
59.28
59.28
59.26
59.26
59.26
Note
aRefractive index nd is for dry air at To = 273.15 K and Po = 1 013.25 X 102 Pa
and the correction nw for water vapor is for Pw = 550 Pa. For other temperatures
and pressures multiply nd - 1 by PTo£ POT and for other vapor pressures multiply
nw - 1 by Pw/PO' Refraction R = (n - 1)/(2n 2 ) ;::;: n - 1 in arc seconds.
For radio waves and dry air with Po = 1013.25 x 102 Pa, To = 273.15 K, nd is (nd -1) x 106
The correction nw for water vapor with Pw = 550 Pa is (nw - 1) x 106 = 30.2.
The refractive index n is (n - 1) x 106 = 318.2.
= 288.0.
264 /
11
EARTH
Transmission data for atmosphere components are in Table 11.25.
Table 11.25. Atmosphere transmission-;;zbsoroerlscatterer [I, 2, 3, 4, 5, 6, 7, 8, 9, 10].
}.. (I-£m)
H2O
C~
03
H2O
continuum
Molecular
scattering
AerosolsD
Other
Total
10.00
7.50
5.00
4.00
3.00
2.00
1.00
0.90
0.80
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.38
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.971
0.126
0.415
0.994
0.462
0.828
0.990
0.790
0.967
0.943
0.981
0.990
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.995
0.723
0.994
0.970
0.980
0.565
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.525
0.0014
0.0000
0.0000
0.851
1.000
0.999
1.000
1.000
1.000
1.000
1.000
1.000
0.993
0.978
0.959
0.972
0.990
0.999
1.000
1.000
1.000
0.986
0.765
0.037
0.0000
0.0000
0.0000
0.0000
0.055
0.946
0.280
0.728
0.983
0.859
0.982
1.000
0.990
1.000
0.999
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.991
0.987
0.979
0.964
0.952
0.934
0.908
0.867
0.802
0.698
0.641
0.572
0.492
0.399
0.298
0.196
0.105
0.040
0.0083
0.0005
0.977
0.983
0.979
0.975
0.966
0.961
0.862
0.836
0.811
0.787
0.765
0.744
0.723
0.689
0.657
0.627
0.615
0.604
0.592
0.578
0.564
0.551
0.538
0.526
0.514
0.502
0.999"
0.993cd
1.000
O.906e
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.759
0.025
0.294
0.837
0.376
0.441
0.846
0.645
0.767
0.709
0.699
0.659
0.637
0.591
0.527
0.438
0.394
0.345
0.287
0.177
0.0062
0.0000
0.0000
0.0000
0.0000
0.0000
Notes
DLowtran rural aerosol model.
bTrace gasses.
cTrace gasses (0.999).
dHN03 (0.934).
eN2 continuum.
References
1. Anderson, G.P. et at. 1986, AFGL-TR-86-0110, Atmospheric Constituent Profiles 10-120 km, Air Force
Geophysics Laboratory (now Air Force Research Laboratory).
2. Kneizys, F.X. et at. 1983, AFGL-TR-0187, Atmospheric TransmittancelRadiance: Computer Code
LOWTRAN6, Air Force Geophysics Laboratory (now Air Force Research Laboratory)
3. McClatchey, R.A. et at. 1973, AFCRL-TR-73-0096, Atmospheric Absorption Line Parameters Compilation, Air Force Cambridge Research Laboratory (now Air Force Research Laboratory)
4. Rothman, L.S. & McClatchey, R.A. 1976, Appl. Optics, IS, 2616
5. Rothman, L.S. 1978, Appl. Optics, 17,507
6. Rothman, L.S. 1978,Appl. Optics, 17, 3517
7. Rothman, L.S. 1981,Appl. Optics, 20, 791
8. Rothman, L.S. 1981,Appl. Optics, 20, 1323
9. Rothman, L.S. 1983,Appl. Optics, 22, 1616
10. Rothman, L.S. 1985, Appl. Optics, 22, 2247
11.21
ATMOSPHERIC SCATTERING AND CONTINUUM ABSORPTION
/
265
11.21 ATMOSPHERIC SCATTERING AND CONTINUUM ABSORPTION
by David Crisp
At wavelengths shorter than about 300 nm, scattering and continuum absorption by gases and airborne
particles (aerosols) renders the Earth's atmosphere virtually opaque to incoming radiation. The depth
of penetration of ultraviolet radiation is shown in Figure 11.1. For cloud-free conditions, Rayleigh
scattering by the atmosphere's principal molecular constituents, N2 and 02, accounts for the majority
of the scattering, while continuum absorption is produced primarily by 02 and 03.
The extinction (scattering and absorption) at these wavelengths obeys the Beer-Bougher-Lambert
law, which states that the intensity 1 at wavelength A and altitude z is given by
I(z, e, A)
= 1(00, e, A) exp{-M(e)r(z)},
1(00, e, A) is the intensity at the top of the atmosphere at zenith angle e, M(e) is the air-mass factor
(M(e) ~ sec
for for < 800 ) , and r(z) is the vertical extinction optical depth
e
e
r(z)
roo
= L Jo
m
i=l
N(i, z)O'(i, z) dz,
0
N(i, z) is the altitude-dependent number density (particles m- 3 ) and O'(i, z) is the effective extinction
cross section of a particle (molecule or aerosol m2 ).
200
+--N2"0_
°2
150
NO·
+
=
w
E
...°2--.
•
100
N·2
0
::;)
~
S
t
< SO
LYMAN <1
a
so
100
150
200
2SO
300
WAVELENGTH (nm)
Figure 11.1. Depth of penetration of solar radiation as a function of wavelength. Altitudes correspond to an
attenuation of 1/e. The principal absorbers and ionization limits are indicated.
266 I
11.21.1
11
EARTH
Rayleigh Scattering
The Rayleigh scattering cross section per molecule O"R()..) is given by
8 is the depolarization factor and ng is the wavelength-dependent refractive index of air. The Rayleigh
scattering optical depth for air can be approximated by
O"R().. )
~ 0.(08569)..-4 (1 + 0.(0113)" -2 + 0.000 13)..-4) pI PO,
P is the pressure (mbar) at altitude z, and PO = 1013.25 mbar is the sea-level pressure. The slight
difference from the).. -4 dependence is introduced by the wavelength dependence of ng [27].
11.21.2 Aerosol Extinction
The continuum absorption and scattering by aerosols cannot be specified uniquely because the aerosol
abundance, composition, and size distribution can vary dramatically with location and time. However,
representative global-annual-average values of the wavelength-dependent aerosol extinction optical
depths have been derived for climate modeling studies. Tropospheric aerosols considered in these
models include sea salt, sulfates, natural dust, hydrocarbons, and other more minor constituents. The
stratospheric aerosols include sulfuric acid and silicates from volcanic eruptions, ammonium sulfates
and persulfates and ammonium hydrates.
The integrated aerosol optical depths above sea-level (0 kID), 3 kID, and 12 kID from one such
modeling study [28] are shown in Figure 11.2. For hazy conditions, actual values of optical depth
can be more than an order of magnitude larger. The wavelength dependence of the optical depths
results from the particle size distribution (particles usually produce the most extinction at wavelengths
1Ir'
1
10
100
W...wIongIh (jAm)
Figure 11.2. The calculated aerosol optical depth of the atmosphere.
11.21 ATMOSPHERIC SCATTERING AND CONTINUUM ABSORPTION / 267
comparable to their radius) as well as wavelength-dependent variations in the complex refractive
indices of these materials.
11.21.3
Continuum Absorption by Gases at UV and Visible Wavelengths
Molecular oxygen 02 and ozone 03 are the principal continuum absorbers at ultraviolet and visible
wavelengths. The principal 02 features include the ionization continuum at}.. < 120 nm, the
Schumann-Runge continuum at 140 < }.. < 180 nm, the Schumann-Runge bands at 180 < }.. <
200 nm, and the Herzberg continuum at}.. > 200 nm [29]. Several other gases, such as H20, C02,
N20, and N02 also contribute absotption at these wavelengths.
The wavelength-dependent absotption optical depths for these gases can be derived from their cross
sections once their number densities are known. If we neglect the temperature dependence of the gas
continuum cross sections, the column-integrated optical depths can be simplified further and expressed
as the product of the mean cross section, and the gas column abundance X which can be derived from
the pressure-dependent gas mixing ratios, r(p),
X =
tx) N(z)dz =
Ao
/-Lag
10
{P r(p')dp',
10
Ao is Avogadro's number (6.02 x 1023 molecules mol-I), /-La is the molecular weight of air (~
29 kg kmol- I ), g is the gravitational acceleration, and p is pressure. The wavelength-dependent,
column-integrated optical depth is then given by
r(}..)
= a(}..)X.
Global-annual average gas mIxmg ratio profiles for the gases mentioned above are shown in
Figure 11.3. Column abundances derived from these profiles are included in Table 11.26.
Global-Annual-Avera
0.000 1 r-r----.:==r--.:.::..:.:.;.::::.=--.:..r:.=~:...-:::~....:.::.:.::.::,::.::L.:~::..:::..:::........,-___,
,,
,,
,
\
0.0010
\
,
\
,
\
I
~
!
~
Q.
0.0100
I
,:03
,,.
CO 2
10
Volume Mixing Ratio
Figure 11.3. Global annual average gas mixing ratios.
268 I 11
EARTH
Table 11.26.
Column abundances of atmospheric gases.
Gas
02
03
H20
C02
N20
N02
11.22
X (molecules cm- 2)
4.47
7.97
8.12
7.04
6.36
1.27
x 1024
x 1018
x 1022
x
102 1
x 1018
x 1016
ABSORPTION BY ATMOSPHERIC GASES AT VISIBLE AND
INFRARED WAVELENGTHS
by David Crisp
At wavelengths longer than 500 run, the principal sources of abnospheric extinction are the vibrationrotation bands of gases. Unlike the slowly-varying ultraviolet gas absorption features described in
the previous section, these bands consist of large numbers of narrow, overlapping absorption lines.
Because the cores of these lines can become completely opaque while their wings remain much
more transparent, the absorption within these bands does not strictly obey the Beer-Bougher-Lambert
absorption law, except in spectral regions that are sufficiently narrow to completely resolve the
individual line profiles « 0.1 cm-1). The absorption coefficients within vibration-rotation bands
also vary much more strongly with pressure and temperature than those at ultraviolet wavelengths.
The absorption by these gases has therefore been characterized by an effective vertical optical depth.
Figures 11.4-11.6 show the vertical optical depth above sea level (top, thick line) and above a
high-altitude site, e.g., Mauna Kea Observatory in Hawaii (z = 4 km, p = 600 mbar, lower thin
line). These synthetic spectra were generated with an abnospheric line-by-line model. This model
employs a spectral resolution adequate to completely resolve the individual absorption lines (0.1 to
10-4 cm -I), but the spectra shown here were then smoothed with a rectangular slit function with a
full-width of 10 cm- I (Figure 11.4) or 5 cm- I (Figures 11.5 and 11.6). These figures therefore do
not resolve individual absorption lines. Absorption line parameters for all gases are from the HITRAN
database [30].
Vertical Optical Depth
10.000 ".-~-,-~~~----,--'-~~.!.,--,--~~~----,
H,O
0,
H,O
H,O
H,O H,O
"~
0
g
0.100
=E,.
0
0.010
0.001
0.4
0.6
Wavelength (1=)
0.8
Figure 11.4. Vertical optical depth versus wavelength.
1.0
11.22 ABSORPTION BY ATMOSPHERIC GASES I 269
H
K
L
3
2
Wavelength
L'
4
(/UI1)
6
5
Figure U.5. Vertical optical depth for near-infrared wavelengths.
co,
H,O
H,O
1.0
5
10
15
Wavelength
(/UI1)
20
25
Figure 11.6. Vertical optical depth at long wavelengths.
Figure 11.4 confirms that Rayleigh scattering and 03 continuum absotption dominate the extinction
optical depth at wavelengths less than 0.5 ILm. At longer wavelengths, water vapor is the principal
absorber with its strongest features near 0.7, 0.82, and 0.94 ILm. 02 also has four significant bands
between 0.65 and 1 ILm. This figure also illustrates the advantage of working at a high-altitude site,
where the atmospheric pressure and scattering optical depth are only 60% of their sea level values.
Much less of an advantage is seen within the strong gas absotption bands, which are opaque even at
the high-altitude site.
Figure 11.5 shows that water is also the principal absorber at near-infrared wavelengths between 1
and 6 1LDl, with very strong bands centered near 1.1, 1.38, 1.88, 2.7, and beyond 6 ILm. C02 is the next
most important absorber at these wavelengths, with strong bands near 2.0, 2.7, and 4.3 ILm, and much
weaker absotption near 1.22, 1.4, 1.6, 4.0, 4.8, and 5.2 ILm. Other trace gases including CF4 (2.4 and
3.3lLm),03 (3.3,3.57, and 4.7 ILm), and N20 (2.1, 2.2, 2.47,2.6,2.9, and 4.7 ILm) also produce some
extinction at these wavelengths.
Water vapor absotption continues to dominate the spectrum at wavelengths beyond 5 ILm
(Figure 11.6). The most prominent water vapor bands at thermal wavelengths are the V2 fundamental
centered near 6.3 ILm and the rotation band beyond 20 JLm, but this gas contributes significant
270 /
11
EARTH
absorption throughout this wavelength region. For example, the far wings of water vapor lines in
the V2 and rotation bands provide much of the absorption in the atmospheric window regions near
8.5 and 12 /Lm. Within these windows, the high-altitude site (thin solid line) has up to a factor of
5 less absorption than the sea-level site (thick solid line), because the H20 absorption coefficients
at these wavelengths are very strong functions of pressure (proportional to density-squared), and the
high-altitude site is above the majority of the water vapor. C02 and 03 are the next most important
absorbers at thermal wavelengths, with strong features near 15 and 9.6 /Lm, respectively. Cf4, N20,
and N02 also have strong absorption bands at these wavelengths, but their bands are largely obscured
by the stronger water vapor bands.
11.23
THERMAL EMISSION BY THE ATMOSPHERE
by David Crisp
The atmosphere emits as well as absorbs thermal radiation. This emission can enhance the sky
brightness significantly at some wavelengths and reduce the detectability of faint astronomical sources.
The intensities of the downwelling thermal radiance at a zenith angle of 21 0 are shown for a sea-level
site (solid line), and a high-altitude site, e.g., Mauna Kea, Hawaii (z = 4 km, p = 600 mbar, dotted
line) in Figures 11.7 and 11.8. At wavelengths within strong absorption bands, the atmosphere emits
almost like a black body. Within the atmospheric window regions centered near 3.5 and 10 /Lm, the
atmosphere emits much less radiation. The downward thermal radiation above a high-altitude site is
substantially less than over the sea-level site because the overlying atmosphere is both cooler and less
opaque.
Downward Thermal Radiance
2
3
4
Wavelength (JLm)
5
6
Figure 11.7. Downward thermal radiance in the near-infrared part of the spectrum.
11.24 IONOSPHERE
/
271
Downward Thermal Radiance
10.0
,....
E
::l..
"...
>-E"'
1.0
"~
'-'
Gl
0
~
!\
c:
0
'i5
0
0::
0.1
II
!
5
10
15
Wavelength
(J.Lm)
25
20
Figure 11.S. Downward thennal radiance at long wavelengths.
11.24 IONOSPHERE [17,31]
The Earth's ionosphere is the partially ionized part of its atmosphere. It is divided into layers or regions,
the main ones being the D, E, F1, and F2 regions, based principally on the altitude (z) profile of the
electron density ne (the number of electrons per unit volume). Ionospheric structure, ne(z), varies
strongly with time of day and month, latitude and solar activity. At night, the D and F1 regions vanish,
the E region weakens considerably, and the F2 region tends to persist at reduced intensity. Table 11.27
summarizes the characteristics of the ionospheric layers. The quantities are explained in the text below
the table.
Table 11.27. Propenies of daytime ionospheric /ayers at middle and low latitudes.
Quantity
R
Approx. altitude range (lan)
Approx. height of max. ne (lan)
Range of max. ne (m- 3)
fo (MHz), X = 0,
Max. ne (m- 3), X
= 0,
q(m- 3 s- I )
Layer thickness (lan)
jqdz (m- 2 s-I)
Ionizing emission at Sun
Surface (photons m -2 s-I)
0
100
0
100
0
100
0
100
0
100
D
E
F1
60--95
At top
108_10 10
0.2
0.28
5.0 x 108
109
2 x loS
105-160
105-110
1011
3.3
3.82
1.35 x 10 11
l.81 x 10 11
5 x 108
109
25
4 x 1013
2.5 x 1013
160--180
170
1011 _10 12
4.25
5.34
2.24 x 10 11
3.54 x 10 11
7 x 108
l.5 x 109
60
3 x 1013
9 x 1013
> 180
200-400
10 12
6.9
1l.95
5.91 x lOll
l.77 x 10 12
108
3 x 108
300
5 x 1017
12 x 1017
18 x 10 17
40 x 10 17
14 x 1013
40 x 1013
15
l.2 x 1013
F2
9 x 1013
272 /
11
EARTH
Table 11.27. (Continued.)
R
Quantity
D
4 x 1020
E
F2
1018
2 x 10 16
1015
10- 12
300
a-Chapman
layer
10- 14_10- 13
900
Chapman
layer
4 x 10- 14
1100
Anomalous.
strongly variable
10- 15
3
7 x loS
10- 3
400
3 x 103
Neutral density at height
of maximum ne (m- 3 )
T at height of max. ne (K)
Behavior
180
Regular
Recombination coefficient
a (m3 s-l)
Attachment (3 (s-I). day
Vej (s-l)
Ven (s-l)
FI
10- 3
200
250
3 x 10-4
400
10
fo = critical frequency = maximum plasma frequency of an ionospheric layer =
(e 2(maximum ne)/41r2€Ome)I/2, me = electron mass, e = electron charge, 100 = permittivity of
free space, ne = electron number density.
(fo (Hz»2
= 80.5 (maximum ne (m- 3».
R = Wolf sunspot number = k(f + 10 g) , f = total number of spots seen, g = number of disturbed
regions (either single spots or groups of spots), k = a constant for a particular observatory.
q = ionization rate = rate of production of ion-electron pairs per unit volume (derived, e.g., from the
Sun's spectrum and ionospheric absorption coefficients).
= recombination coefficient, rate of electron loss by recombination = anjn e (nj = number density
of ions) = an; (normally, nj = ne). Electron loss rate an; has units of number per unit volume per
unit time.
a
a-Chapman layer = idealized model of an ionospheric layer, single species neutral atmosphere
with constant scale height H, solar radiation absorption ()( neutral gas number density, absorption coefficient is constant, q = qmoexp(1 - ZI - (secx)e- Z'), z' = (z - zmo)/H, Z is altitude,
Zmo is the height of maximum production rate when the Sun is overhead (X = 0), qmo is the
production rate at Zmo (when X = 0), X = solar zenith angle, production = loss, q = an;,
ne = ne (Zmo) exp (1 - ZI - e- z' sec X), qm is the maximum production rate = qmo cos X, Zm is the
height of maximum production = Zmo + H In (sec X), ne(Zm) = ne(Zmo) cosl/2 X.
!
{3 = attachment coefficient, rate of electron loss by attachment to neutral particles to form negative
ions = {3ne (neutral species number density» ne). {3 has units of inverse time.
{3-Chapman layer = similar to a- Chapman layer except for electron loss which occurs by attachment,
q = {3ne, ne = ne(Zmo) exp(1 - ZI - e-z' sec X), ne(Zm) = ne(Zmo) cos X.
dne/dt
=q
- an; - {3ne, usually either a or {3.
11.24 IONOSPHERE
Vei, Ven
= collision frequency of mean electron with ions, and neutral particles.
Ven (S-I) = (6.93 x lOSn(N2)
number densities in m- 3 .
WB
(rad s-I)
+ 4.37 x
lOSn(02)) u, u is electron energy in J, n(N2) and n(02) are
= gyrofrequency = QB/m,
Q
(T), m = charged particle mass (kg).
= charge on particle (C), B = magnetic flux density
(rads- I )/21l'.
fB
(Hz) =
WB
(rad s-I) for an electron = 1.759 x 1011 B (T).
!B
1 273
WB
(Hz) for an electron
= 2.799 x
1010 B (T).
WN (rad s-I) plasma frequency = (nee2/Eome) 1/2, e = charge on an electron.
l/1 = Faraday rotation
ionosphere
=
rotation of the polarization angle of a radio wave propagating through the
is the speed of light, B is a unit vector in the direction of B, dl is a path increment along the wave
propagation direction, integration is along the path of the radio wave, cu is the circular frequency of the
wave, f is the frequency of the wave in Hz, /LO is the permeability of fn-.e space, H is the magnetic
field strength (A m- I ), all units are SI, it is assumed that cu » CUB, the formula is approximate for
cross-field propagation but accurate to within a few degrees of the normal to B, the rotation follows
the right-hand rule.
Photon efficiency of ionization,., is the ratio of the rate of production of ion-electron pairs (number
m- 3 s-I) to the total number of photons absorbed per unit volume and per unit time. Ionization of
atomic species yields one ion-election pair for every 5.45 x 10- 18 J absorbed. Accordingly,
C
n
"'
=
1
8
5.45 x 10- 1 J/(hc/A)
= 36.5/A (nm),
2 < A < lOOnm,
h is Planck's constant and A is the wavelength of the radiation. For A < 2 nm,,., is approximately 20.
274 I
11.24.1
11
EARTH
Ionosphere as a Whole
The total electron content of the ionosphere is
I
==
forx ne dz,
where z is altitude. More generally, I can be defined as a line integral along an arbitrary path. Typically,
I is about 10 17 electrons m- 2 .
The equivalent thickness or slab thickness t' of the ionosphere is
t'
I
== ---.
maxne
This is the thickness of a hypothetical layer with uniform electron density equal to the maximum value
of ne and total electron content equal to I. Typically, t' is about 250 Ian.
11.24.2 Effects of Earth Curvature
The factor sec X in the formulas for ionization and absorption should be replaced by Ch(x, X) to
account for Earth curvature, where x = (a + z) I H, H = scale height, a = Earth radius, z = altitude,
and X is the zenith angle.
Curvature effects of the atmosphere are listed in Table 11.28.
Table 11.28. Thefunction Ch(x. x).a
Q
x=
sec X =
50
100
200
400
800
1000
Note
a Q =: (a
30°
1.155
45°
1.414
Ch(x. X)
60°
75°
2.000
3.864
80°
5.76
85°
11.47
90°
1.148
1.151
1.153
1.154
1.154
1.155
1.389
1.401
1.407
l.4ll
1.412
1.413
1.901
1.946
1.972
1.985
1.993
1.994
4.19
4.70
5.10
5.38
5.55
5.59
5.82
7.07
8.28
9.33
10.15
10.35
8.93
12.58
17.76
25.09
35.46
39.65
3.228
3.473
3.646
3.742
3.800
3.812
95°
00
16
30
68
220
1476
+ zo)/ H. zo = altitude of maximum ionization rate.
11.24.3 International Reference Ionosphere (IRI)
IRI is an empirical reference model of ionospheric electron density, electron and ion temperatures, and
ion composition recommended by COSPAR (Committee on Space Research) and URSI (International
Union of Radio Science). It is updated bi-yearly; the 1990 model is used below. IRI is distributed
by the National Space Science Data Center and World Data Center A for Rockets and Satellites
(NSSDCIWDC-A-R&S) in Greenbelt, Md. IRI is available online on SPAN (Space Physics Analysis
Network) now called NSI-DECNET (NASA Science Internet) and can be accessed interactively on
NSSDC's Online Data Information Service (NOmS) account. Tables 11.29 to 11.36 give data about
this IRI ionosphere model.
11.24 IONOSPHERE
Thble 11.29. IRI-90 electron density. a
Noon
z (km)
ne (m- 3)
65
70
75
80
85
90
95
100
8.3
2.1
3.7
5.1
1.1
1.2
5.2
1.1
x
x
x
x
x
x
x
x
ne/ne F2(max)
3
7
1.3
1.8
3.7
4.0
1.8
3.7
107
108
108
108
109
1010
1010
1011
Midnight
x
x
x
x
x
x
x
x
ne (m- 3)
ne/ne F2(max)
0
0
0
0
x
x
x
x
0
0
0
0
x
x
x
x
10-4
10-4
10-3
10-3
10-3
10-2
10- 1
10- 1
2.6
4.8
1.6
1.6
108
108
109
109
Note
aLatitude = 45°, Longitude = 260o E, R = 0, Day
X = 21.6° (Noon), 111.6° (Midnight).
2.3
4.2
1.4
1.4
=
10-3
10- 3
10- 2
10-2
6/22, F10.7
=
63.8,
Thble 11.30. IRI-90 electron density. a
Midnight
Noon
z (kIn)
ne (m- 3)
2.7
6.7
1.2
1.6
3.4
3.3
1.1
1.8
65
70
75
80
85
90
95
100
x
x
x
x
x
x
x
x
108
108
109
109
109
10 10
1011
1011
ne/ne F2(max)
4x
1x
1.7 x
2.4 x
5.0 x
4.8 x
1.6 x
2.6 x
10-4
10-3
10-3
10-3
10-3
10-2
10- 1
10- 1
ne (m- 3)
ne/ne F2(max)
0
0
0
0
x
x
x
x
0
0
0
0
x
x
x
x
2.6
4.8
2.8
3.9
Note
X
6
1.1
6.2
8.8
108
108
109
109
aLatitude = 45°, Longitude = 260o E, R = 150, Day
21.6° (Noon), 111.6° (Midnight).
=
=
10-4
10-3
10-3
10- 3
6/22, FlO.7
=
Thble 11.31. IRI-90 electron tknsity.a
6122
3121
9123
12122
R=O
ne
ne
ne
ne
(70km)
(SOkm)
(9Okm)
(1ookm)
1.9 x
4.5 x
1.0 x
9.5 x
108
108
1010
1010
ne
ne
ne
ne
(70km)
(SOkm)
(9Okm)
(lookm)
5.9 x
1.4 x
2.9 x
1.6 x
108
109
1010
1011
2.1
5.1
1.2
1.1
6.7
1.6
3.3
1.8
x
x
x
x
108
108
1010
1011
1.8 x
4.4 x
1.0 x
9.5 x
108
108
1010
1010
1.5
3.8
8.0
7.0
x
x
x
x
108
108
109
1010
x
x
x
x
108
109
1010
1011
1.6
4.1
9.0
1.0
x
x
x
x
108
108
109
1011
R = 150
Note
x
x
x
x
108
109
1010
1011
5.8
1.0
2.9
1.6
=
aTune = Noon, Latitude = 45°, Longitude = 260o E, FlO.7
63.8
(R
0), 193 (R
150), X
44.5°(3121), 21.6°(6122), 45.4°(9123),
68.5°(12122), units of ne are number m- 3.
=
=
=
193,
/
275
276 /
11
EARTH
Table 11.32. IRI-90 electron density. a
45
60
90
75
R=O
ne
ne
ne
ne
(70km)
(80km)
(90km)
(lOOkm)
1.5
3.8
8.0
7.0
ne
ne
ne
ne
(70km)
(80km)
(90km)
(lOOkm)
1.6
4.1
9.0
1.0
X
X
X
X
108
108
109
1010
1.2
3.7
6.0
3.8
R
X
X
X
X
108
108
109
1011
X
X
X
X
108
108
109
1010
o
o
4.7
4.4
X
X
108
109
= 150
1.2
3.7
6.3
5.4
X
X
X
X
108
108
109
1010
o
o
4.7
6.3
X
X
108
109
1.6
3.8
3.4
4.0
X
X
X
X
108
108
109
109
Note
aTime = Noon, Longitude = 260o E, FlO.7 = 63.8 (R = 0), 193
(R = 150), X = 68.5°(45°N), 83.5°(600 N), 98.5°(75°N), 113.5°(900 N),
Day = 12/22, units of ne are number m- 3.
Table 11.33. IRJ-90 model ionosphere. a
100
200
300
400
500
600
700
800
900
1000
1.08
2.74
2.40
1.11
4.63
2.41
1.61
1.28
1.14
1.07
X
X
X
X
X
X
X
X
X
X
1011
1011
1011
1011
1010
1010
1010
1010
1010
1010
Tn (K)
Tj (K)
Te (K)
0+
786
821
822
822
822
822
822
822
822
786
1011
1237
1513
1813
2113
2413
2712
3012
1419
2689
2831
2835
2846
2936
3042
3148
3254
23
99
100
96
88
80
69
59
50
o
H+
He+
0
0
0
0
4
10
18
28
37
45
0
0
0
0
0
1
2
3
4
5
48
21
52
56
o
o
o
0
0
0
0
o
o
o
o
o
1
0
0
0
Note
aLatitude = 45°, Longitude = 260o E, R = 0, Day = 6/22, FlO.7 = 63.8, X = 21.6°,
Time = Noon, Tn = neutral temperature, Tj = ion temperature, Te = electron temperature, ion
composition is given in percent.
Table 11.34. IRJ-90 model ionosphere. a
100
200
300
400
500
600
700
800
900
1000
1.79
3.92
6.85
6.25
4.63
3.29
2.51
2.10
1.89
1. 77
X
X
X
X
X
X
X
X
X
X
1011
lOll
lOll
lOll
lOll
1011
lOll
1011
lOll
lOll
Tn (K)
11 (K)
Te (K)
0+
1187
1361
1385
1389
1390
1390
1390
1390
1390
1187
1361
1385
1513
1813
2113
2413
2712
3012
1421
2689
2831
2835
2846
2936
3042
3148
3254
59
100
100
96
88
80
69
59
50
o
H+
He+
0
0
0
0
4
10
18
28
37
45
0
0
0
0
0
58
6
o
o
o
1
o
2
3
4
5
o
o
o
o
42
35
0
0
0
0
0
0
0
0
Note
aLatitude = 45°, Longitude = 260o E, R = 150, Day = 6/22, FlO.7 = 193, X = 21.6°,
Time = Noon, Tn = neutral temperature, Tj = ion temperature, Te = electron temperature, ion
composition is given in percent.
11.24 IONOSPHERE
Table 11.35. IRl-90 model i01Wsphere. a
Noon
ne (m- 3)
Til (K)
Tj (K)
Te (K)
%0+
%H+
%He+
Midnight
Noon
R=O
2.87 x lOll
9.07 x 1010
815
692
817
899
2076
1010
53b
42c
0
0
0
0
Midnight
R= 150
5.94 x 1011
3.70 x 1010
1090
1314
1090
1314
2076
1090
99
99
0
0
0
0
Note
aLatitude
45°, Longitude
260o E, Day
6/22, FlO.7
63.8
(R
0), 193 (R
150), Til
neutral temperature, Tj
ion temperature,
Te electron temperature, Altitude 250 kin, X 21.6° (Noon), 111.6°
(Midnight).
bThe other ions in this case are 46% NO+ and 1%
cThe other ions in this case are 57% NO+ and 1%
=
=
=
=
=
=
=
=
=
=
=
ot.
ot.
Table 11.36. IRI-90 model ionosphere. a
Date
3nI
6122
9123
12122
3.27 x 1011
773
864
1882
76
0
0
0
23
4.27 x lOll
687
802
1780
95
0
0
0
5
8.60 x lOll
1219
1219
1882
95
0
0
0
5
1.63 x 1012
1089
1089
1782
95
0
0
0
5
R=O
ne (m- 3)
Til (K)
Tj (K)
Te (K)
%0+
%H+
%He+
%ot
%NO+
3.07 x 1011
777
867
1882
76
0
0
0
23
2.87 x lOll
815
899
2076
53
0
0
1.15 x 1012
1221
1221
1882
95
0
0
0
5
5.94 x 1011
1314
1314
2076
99
0
0
0
0
46
R
ne (m- 3)
Til (K)
Tj (K)
Te (K)
%0+
%H+
%He+
%ot
%NO+
= 150
Note
a Latitude
45°, Longitude
260°, FlO.7
63.8 (R
0), 193
(R
150), Til
neutral temperature, Tj
ion temperature, Te
electron
temperature, Altitude 250 kID, X 44.5°(3121), 21.6°(6122), 45.4°(9123),
68.5°(12122).
=
=
=
=
=
=
=
=
=
/ 277
278 I
11.24.4
11
EARTH
Irregularities of Ionospheric Behavior [31]
Storm
Magnetic Storm
F-Region Ionospheric Storm
11.24.5
A severe departure from normal behavior lasting from one to
several days.
A magnetic storm consists of three phases: (1) an increase of
magnetic field lasting a few hours; (2) a large decrease in the
horizontal component of magnetic field building up to a maximum
in about a day; (3) a recovery to normal over a few days. The initial
phase (1) is caused by the compression of the magnet sphere by a
burst of solar plasma. The main phase (2) is due to the ring current
in the magnetosphere which flows around the Earth from east to
west.
This storm is characterized by an initial positive phase of increasing electron density lasting a few hours followed by a main or
negative phase of decreasing ne. The ionosphere gradually returns
to normal over one to several days during the recovery phase.
Sq Current System
The Sq current system is an ionospheric current system due to neutral winds blowing ions across
magnetic field lines. The Sq winds and currents are driven by solar (S) tides under quiet (q)
geomagnetic conditions. The winds have speeds of tens of meters per second and associated electric
fields are a few millivolts per meter. The Sq currents produce daily magnetic field variations at the
Earth's surface.
Node of EW currents is at latitude 38°.
Current between node and either pole or equator (at equinox and zero sunspots) = 5.9 x 104 A.
11.24.6 Magnetic Indices [31]
K p is based on the range of variation within 3 hour periods of the day observed in the records from
about a dozen selected magnetic observatories. The K p value for each 3 hour interval of the day is
reported on a scale from 0 (very quiet) to 9 (very disturbed). Integer values are subdivided into thirds
by use of the symbols + and -. The K p scale is quasi-logarithmic.
ap-similar to K p , but a linear scale of geomagnetic activity. The value of a p is approximately
half the range of variation of the most disturbed magnetic component measured in n T.
The relation between Kp and Ap is shown in Table 11.37.
Table 11.37. Relation between K p and ap.
Kp
ap
0
0
1
3
2
7
3
15
4
27
5
48
6
80
7
140
8
240
9
400
Ap is a daily index, the average of a p over a day.
AE is a geomagnetic index measuring the activity level of the auroral zone, particularly valuable
as an indicator of magnetic substorms.
L Kp is the sum of the eight Kp values over a UT day.
11.25 NIGHT
11.25
SKY AND AURORA
/
279
NIGHT SKY AND AURORA [17,32-36]
The units for expressing the night sky brightness of spectroscopic features (lines or bands of restricted
extent in wavelength) are:
1 Rayleigh
=
R
=
=
106 photons emitted in 41r sr per cm2 vertical column per sec
1.58 x 1O-7 A-I J m- 2 sr- I s-I at zenith (A in nm)
= 1.95 x 10-7 nit for A = 555 nm.
I Photon = 1.986 x 1O- 16 A-I J (A in nm)
I mv = 10 star deg- 2 near 550 nm through clear atmosphere
= 3.6 x 10-2 R nm- I
= 7.1
x 10-7 nit (for a bandwidth of 100 nm).
Components of the night sky brightness are given in Table 11.38.
Table 11.38. Night sky brightness.
Source
(near zenith)
Airglow
Atomic lines
Bands and continuum
Zodiacal light (away from zodiac)
Faint stars, m > 6 (galactic pole)
(mean sky)
(gal. equator)
Diffuse galactic light
Total brightness (zenith, mean sky)
(15° lat, mean sky)
Photographic
10th mag stars
30
60
16
48
140
10
145
190
Visual
deg -2
Photometry
10-5 nit
40
50
100
30
95
320
20
290
380
3
4
6
2
7
23
I
21
28
Color index of night sky C ~ 0.7 (C = B - V - 0.11, where B is the apparent magnitude at 555
nm and V is the apparent magnitude at 435 nm).
Airglow variation with latitude: Generally brighter at middle and high latitudes than at low
latitudes, a factor of ~ 2 increases with latitude for some emissions [35].
Airglow variation with solar cycle activity: Good correlation with sunspot activity for 01 red line
(630 nm), ambiguous evidence for variation in green line (557.7 nm) [35].
Van Rijin function: Off-zenith path length through a spherically symmetric airglow layer is
increased relative to the zenith viewing by a factor
where r is the Earth's radius, h is the height of the emitting layer above the Earth's surface, and z is the
zenith angle.
The full moon brightness is 1100 tenth magnitude stars per square degree in the photographic
spectral region and 100 in the visual band. For other phases of the Moon multiply by cfJ(a), where a is
the phase angle, the angle between the Sun and Earth seen from the Moon, and cfJ(a) is the phase law
or the change of the Moon's brightness with a(cfJ(O) = 1) [17].
The sky brightness during twilight is given in Table 11.39.
280 I 11
EARTH
Table 11.39. Variation ofsky brightness throughout twilight
relmive to 0° solar depression angle [1].
Solar depression angle
0°
6°
12°
18°
Log relative brightness
0
-2.7
-4.7
-5.8
Reference
1. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed.
(Athlone Press, London)
Table 11.40 lists the night sky emissions from various components.
Table 11.40. Spectral emissions in the night sky [1, 2, 3, 4, 5]. a
Intensity
Emitter
OI
OI
OI
OI
OI
OI
NI
NI
NI
NIl
Nal
In
In
Call
Lil
N2
N2
N2
N2
N2
~2
Oz
Oz
Oz
Oz
0+
2
OR
OR
OR
OR
NOz
NOy
ReI
A,etc.
Night
Twilight
Aurora
run
R
R
kR
557.7
630.0-636.4
297.2
130.4-135.6
777.4
844.6
1040
346.6
519.9
VIS.andFUV
589.0-589.6
summer
winter
656.3
121.6
393.3-396.7
670.8
IR
250
100
180
1000
100
2-100
6
30±2O
10
12
6
1
0.1-2
45
150
13
10
BUV
NUV,VIS.
630-890
300-400
864.5
1270
1580
VIS.,IR
1580
VIS.
8342
Total
500-650
MUV
1083
< 100 R to > 500 R night to night variation
Sporadic enhancements in tropical nightglow
ICBmAurora
Observed from satellites, ICB m Aurora
ICBmAurora
ICBmAurora
ICBmAurora
NaD, Strong seasonal variation
30
200
15
2500
1
1
10
100
1000
5000
Ha
La
150
30
880
110
200-400
55
2000
UV
FUV
Blue
Remarks
100
1000
1500
500
6000
20000
150
630
60
1200
2500
26
150000
130
2000
4.5 x 106
250
20-60
1st positive, ICB m Aurora
2nd positive, ICB m Aurora
LBR bands, ICB m Aurora
VK bands, ICB m Aurora
BR, WK, ICB m Aurora, rough value
deduced from photometer data
1st negative, ICB m Aurora
M, ICB m Aurora
Hertzberg hands
Atm. (0-1), ICB m Aurora
Atm. (0-0), not seen at ground, ICB m Aurora
IR Atm, ICB m Aurora
1st negative, ICB m Aurora
(4-2) Strongest bands are in NIR
(5-0)(7-1) (8-2) (9-3) bands
(6,2)band
Nightglow continuum
ICBmAurora
1000
Note
aLBR = Lyman-Birge-Ropfield, M = Meinel, VK
Ropfield,lCB m = 01(557.7) = 100 kR [1,2,3,4].
= Vegard-Kaplan, WK = Watson-Koontz. BR = Birg~
11.25 NIGHT SKY AND AURORA
I
281
References
1. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London)
2. Vallance Jones, A. 1974, Aurora (Reidel, Boston)
3. Roach, F.E., & Gordon, J.L. 1973, The Light o/the Night Sky, (Reidel, Boston)
4. Krassovsky, V.I. et al. 1962, Planet. Space Sci., 9, 883
5. Chamberlain, J.W. 1961, Physics o/the Aurora and Airglow, (Academic Press, New York)
Zone of maximum auroral activity = 60-75 0 geomagnetic latitude [32].
Seasonal variation: Minima in auroral frequency at solstices, maxima at equinoxes (approximately
a factor of 2 increase from minima to maxima as seen from Yerkes Observatory) [36].
Table 11.41 gives details of the types of aurorae.
Thble 11.41. Auroral heights [1, 2].
Aurora
Height
Lower border strong aurora
Lower border weak aurora
Average value
Average height of maximum emission
Vertical extents
Upper extremity
95km
114km
105-108km
IlOkm
20-40km
frequently> 200 km
Type c (normal aurora)
Sunlit upper extremity
700 km (1000 km in extreme cases)
Type b: red lower border
Type d (red overall) lower border
250km
8~I00km
References
I. Allen, C. W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London)
2. Meinel, A.B. et al. 1954, J. Geophys. Res., 59, 407
The proton input needed to produce auroral Ha is given in Table 11.42.
Table 11.42. Flux o/monoenergetic protons required to produce 10 kR o/Ha in the zenith [l].
Initial energy
keV
Minimum
penetration height
km
130
27
8.5
100
110
120
photons
Proton fiux
cm- 2 s-I
Total incident
energy fiux
eVcm- 2 s-I
60
27
7
1.6 x 108
5 x 108
14 x 108
2.1 x 1013
1.4 x 1013
1.2 x 1013
Ha
Reference
1. Chamberlain, J.W. 1961, Physics o/the Aurora and Airglow (Academic Press, New York)
Auroral International Coefficients of Brightness:
I.C.B.
I
II
III
IV
557.7 brightness
557.7 brightness
557.7 brightness
557.7 brightness
=
=
=
=
1 kR ~ 10-4 nit,
10 kR ~ 10-3 nit,
100 kR ~ 10-2 nit,
1000 kR ~ 10- 1 nit.
282 /
11
EARTH
11.26 GEOMAGNETISM [37-39]
The geomagnetic field arises from sources both interior and exterior to the solid Earth, including
electric currents in the liquid outer core and the ionosphere and the magnetization of crustal rocks.
Models of the global magnetic field are intended to describe the field originating in the core (the main
field). The description of the main field is based on a spherical harmonic description of the potential
V(r,
rp, t) for magnetic induction B(r, 8, rp, t)
e,
B = -VV,
where r, 8, rp are spherical polar coordinates and t is time. The spherical harmonic expansion of V is
V(r,
e, rp, t) =
a 1+1
aLL C:·)
L
1
_
{gi(t) cosmrp + hi(t) sinmrp} pr(cos8),
1=1 m=O
where a is the mean radius of the Earth (a = 6371.2 km), L is the truncation level of the expansion,
and the pr (cos e) are Schmidt quasi-normalized associated Legendre functions, i.e., the integral of
pr squared over all solid angles is 41f/(21 + 1). The quantities gi(t) and hi(t) are known as Gauss
geomagnetic coefficients; they vary with time over a broad range of time scales from less than a year
to hundreds of millions of years. The core dynamo responsible for generating the main magnetic field
is fundamentally time dependent in its behavior. If the small electrical conductivity of the mantle is
neglected, then the above representation of the main geomagnetic field can be used to extrapolate the
surface field down to the core-mantle boundary.
The components of the magnetic field are given by
Br
av
L
= -a; = L
a 1+2
L(l + 1) (;-)
1
{gi(t)cosmrp
_
+ hi(t) sinmrp} pr(cos8),
1=1 m=O
1 aV
a
Be=-;:-ae=-LLC:-)
L
1
1+2
1=1 m=O
1
BtfJ = - - .-8
r SID
av
!l..l.
u."
=
{gi(t)cosmrp+hi(t)sinmrp}
LL -r
L
1 (a)/+2
1=1 m=O
d pm
d~
{gi(t)sinmrp -hi(t)cosmrp}
(cos 8),
mpm(cos8)
I.
sm 8
.
Magnetic field observations are generally described in terms of the quantities:
X
Y
= - Be = north magnetic field component,
= BtfJ = east magnetic field component,
= - Br = vertically downward magnetic field component,
H = (X 2 + y2)1/2 = horizontal magnetic field intensity,
F = (X 2 + y2 + Z2)1/2 = total magnetic field intensity,
1= arctan(Z/ H) = magnetic inclination,
D = arctan(Y / X) = magnetic declination.
Z
Historically, there has been much discussion of the westward drift of the main field or components
thereof, particularly the nondipole part of the field (see below). While some features of the field may
participate in a westward drift, the secular variation of the main field is more complex than a simple
westward drift.
11.26 GEOMAGNETISM
11.26.1
/
283
Geomagnetic Dipole
The contributions to V of the I = 1 terms in the spherical harmonic representation of V are from
magnetic dipoles situated at r = 0 and oriented along the coordinate axes.
a 3 cosO 0
r2
a 3 cos f/> sin 0
gl
is the potential of a magnetic dipole in the +z-direction
(along the Earth's rotation axis),
gl
is the potential of a magnetic dipole in the +x-direction
(along the Greenwich meridian),
a 3 sin f/> sin 0 1
hI
r2
is the potential of a magnetic dipole in the +y-direction.
r2
1
The total dipole potential Vdipo1e is the sum of the above terms.
The total dipole magnetic field Bdipole = - V Vdipole has components
B~pole = ~3 (g? cosO + sin8(g} cosf/> + hI sinf/») ,
B:pole
dipole
BI/>
=
~: (g? sinO - cosO(g} cosf/> + hI sinf/») •
a 3 1·
I
= 3(gl smf/> - hi cosf/».
r
The magnetic dipole moment m has magnitude
The magnetic dipole moment pierces the surface of the Earth at colatitude 8m and longitude f/>m,
given by
lim
~ aICtan { «(g1)2 +gtl>2)1/2},
~ ~ aICtan
(;1).
Table 11.43 lists the values of m/47ra 3 • 8m• and f/>m for the years 1945-1990.
The orientation and magnitude of the centered. tilted. magnetic dipole from the I = 1 terms in the
spherical harmonic representation of the main field is given in Table 11.43.
1Bble 11.43. Orientation and magnitude o/the centered. tilted. magnetic dipole.
(m/4na 3 ). l04nT
Colatitude of
Geomagnetic Pole
(8m• degrees)
Longitude of
Geomagnetic Pole
(I/>m. degrees)"
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
3.122
3.118
3.113
3.104
3.095
3.083
3.070
3.057
3.043
3.032
11.53
11.53
11.54
11.49
11.47
11.41
11.31
11.19
11.03
10.87
291.5
291.2
290.8
290.5
290.1
289.8
289.5
289.2
289.1
288.9
Note
aEast from the Greenwich meridian.
284 /
11
EARTH
The time rate of change of the magnetic dipole is obtained by differentiating the above expressions
for m, em, and <Pm with respect to time.
11.26.2
Eccentric Dipole
The Cartesian coordinates (xo, YO, zo) of the eccentric dipole that best represents the main field are
given by
a(LJ - gfT)
xo----...:"..."..
- 3(m/4rra 3 )2'
YO
=
a(L2 - h~ T)
3(m/4rra 3 )2'
zo
=
a(Lo - g?T)
3(m/4rra 3 )2'
where
11.26.3
Dipole Coordinate System
A coordinate system with its z-axis along the direction of the centered, tilted dipole is the dipole
coordinate system or the geomagnetic coordinate system. The pole of this coordinate system is located
at em, <Pm, given above. This is the geomagnetic pole or dipole pole. If &J is a vector in the dipole
coordinate system and:!. is a vector in the standard coordinate system, then
where R is the rotation matrix with elements
R
-
=[
em cos <Pm
-sin <Pm
sin em cos <Pm
COS
cos em sin <Pm
cos <Pm
sin em sin <Pm
-sin em]
o
cos em
.
11.26.4 Magnetic Dip-Poles
A magnetic dip-pole is a location at which the horizontal magnetic field is zero. At the north and south
dip-poles the magnetic potential has its maximum and minimum values, respectively. Table 11.44 gives
the coordinates of the dip-poles at different times.
11.27 METEORITES
AND CRATERS
/
285
1Bble 11.44. Coordinotes oj the magnetic dip-poles.
Year
Latitude (N)
Longitude (W)
North Dip-Pole
1831.4
1904.5
1948.0
1962.5
1973.5
70"05'
70"30'
73°00'
75°06'
76°00'
96°46'
95°30'
100"00'
100"48'
100"36'
South Dip-Pole
1841.0
1899.8
1909.0
1912.0
1931.0
1952.0
1962.1
11.26.5
75°05'
72°40'
72°55'
71°10'
70"20'
68°42'
67°30'
154°08'
152°30'
155°16'
150°45'
149°00'
143°00'
140"00'
Centered, TOted Dipole Field [39]
Vertical magnetic field at geomagnetic poles, at r = a,
= 2 (4:a 3 ) = 6.064 x
104 nT.
Horizontal magnetic field at geomagnetic equator, at r = a,
= 41ra
~3 = 3.032 x
l04nT.
In the dipole coordinate system
m
V = 41rr2 cos9mag
_ a 3 cos 9mag
-
r2
(~)
41ra 3 '
V(r = a) = (4':3)acOS9mag,
where 9mag is the magnetic colatitude. Numerical values are for the IGRF (1991 Revision).
11.27 METEORITES AND CRATERS [17,40--44]
Classes of meteorites (natural objects of extraterrestrial origin that survive passage through the
atmosphere) and statistics on falls and finds are given in Table 11.45. Falls refer to meteorites that were
seen to fall; they are usually recovered soon after fall. Finds refer to meteorites that were not seen to fall
but were found and recognized subsequently. Meteorites are broadly classified into stones, irons (pure
metal, essentially nickel-iron alloy), and stony-irons. Additional classifications are required because
of the great diversity of objects in these broad classes. Stony meteorites are divided into chondrites
(meteorites containing distinctive features known as chondrules with compositions very similar to
that of the solar photosphere for all but the most volatile elements) and achondrites (differentiated
meteorites with compositions considerably different from the Sun).
286 I
11
EARTH
Table 11.45. Meteorite classes and statistics on/ails andfinds [1].
Findsa
Fall frequency
Class
Chondrites
CI
CM
CO
CV
H
L
LL
EH
EL
Other
Anchondrites
Eucrites
Howardites
Diogenites
Ureilites
Aubrites
Shergottites
Nakhlites
Chassignites
Anorthositic
breccias
Stony-irons
Mesosiderites
Pal1asites
Irons
lAB
IC
IIAB
IIC
lID
lIE
IIF
IIIAB
mCD
IIIE
IIIF
IVA
IVB
Other irons
Non-Antarctic
Antarcticc
0.60
2.2
0.60
0.84
33.2
38.3
7.9
0.84
0.72
0.36
0
5
2
4
347
286
21
3
4
3
0
34
6
5
671
224
42
6
1
3
3.0
2.2
1.1
0.48
1.1
0.24
0.12
0.12
8
3
0
6
1
0
2
0
13
4
9
9
17
2
0
0
0
0
0
6
3
0.72
0.36
22
34
2
6
0
5
0
3
1
1
8
2
0
0
3
0
13
0.73
0.08
0.45
0.05
0.09
97
11
60
7
12
13
4
189
19
13
6
52
12
175
4
0
6
0
0
0
0
0
0
0
0
1
0
0
Falls
(%)h
5
18
5
7
276
319
66
7
6
3
25
18
9
4
9
2
1
1
O.lO
0.03
1.42
0.14
0.10
0.05
0.39
0.09
1.32
Notes
aData for finds are given to provide an indication of available material. The
unusual conditions in the Antarctic favor the recovery of large numbers of
meteorites without the selection biases of non-Antarctic regions (e.g., in nonAntarctic regions, stony meteorites, especially anchondrites are more easily
confused with terrestrial rocks than iron meteorites). The statistics for Antarctic
finds, therefore, more closely resemble those of falls than non-Antarctic finds.
In fact, several rarer classes are overrepresented in the Antarctic collections.
biron-meteorite fall statistics calculated from finds, scaled to percentage of
total iron-meteorite falls.
cus finds in the Antarctic. In addition, > 6000 meteorites have been
recovered from the Antarctic by Japanese teams.
Reference
1. Sears, D.W.G., & Dodd, R.T. 1988, in Meteorites and the Early Solar System,
edited by J.F. Kerridge and M.S. Matthews (University of Arizona Press,
TUcson, Arizona),pp. 3-31
11.27 METEORITES AND CRATERS
11.27.1
/
287
Meteorite Infall Rates
Fall of meteorites large enough to be seen and found, ~ 2 meteorites per day over the whole Earth.
The cumulative flux of meteoroids F in the vicinity of the Earth-Moon system is given by
F (
= 7.9(m (kg))-1.16,
#
)
1()6 km2 yr
10- 10 < m < 105 kg,
where F is the number of meteoroids with mass greater than m per 106 km2 per year. Accordingly,
meteoroids with masses greater than about 6 kg will arrive in the vicinity of the Earth-Moon system at
a rate of about one per 106 km2 per year.
11.27.2
Meteorite Masses
The most probable size of found meteorites for iron is 15 kg and for stones 3 kg. Meteoroid masses
before entry to the Earth's atmosphere are ~ 100 kg. The mass of the greatest known meteorite (Hoba,
an iron meteorite) is 6 x 104 kg.
11.27.3
Cratering Efficiency
Mass displaced from crater/mass of impactor
= cratering efficiency
= 0.2 (1.612g L)-0.65 ,
Vi
g
= gravity(m s-2),
L = projectile diameter (m),
Vi
11.27.4
= impact velocity (m s-I).
Crater Diameter Scaling Relations for Terrestrial Craters [42]
D
= 0.0133W 1/ 3.4 + 1.51p;!2 p~I/2 L,
D
=
1.8p~l1p~I/3g-0.2Lo.13WO.22,
D -- 0 .2Pp1/6 PT-1/2 W O. 28 '
D
> 1 km •
rv
All units in the above formulas are SI.
D = diameter of a transient impact crater,
pp
PT
W
= impactor density,
= target density,
= impactor energy,
L = impactor diameter.
Formulas valid for vertical impacts.
Energy of 1 kiloton of TNT
= 4.2 x
10 12 J.
288 /
11.27.5
11
EARTH
Crater Dimensions
Rim height hR above original ground surface of many fresh (unrelaxed) lunar, terrestrial, explosion,
and laboratory impact craters with diameter (rim to rim), D ;S 15 km,
hR (m)
= 0.036(D (m»1.014.
For craters with D > 15 km on the Moon (collapsed craters)
hR (m) = 0.236(D (m))0.399.
Crater depth H (rim to floor) of fresh lunar craters with diameter D ;S 11 km
H (m) = 0.196(D (m»l.01.
Crater depth of collapsed lunar craters
H (m)
= l.044(D (m))0.301
11 km < D < 400 km.
Crater depth of simple" (relatively young) terrestrial impact craters (e.g., Meteor Crater, Arizona)
H (m)
= 0.14(D (m))1.02.
Crater depth of collapsed or complex terrestrial impact craters
H (m)
= 0.27(D (m))0.16.
Estimated cratering rate from relatively young « 120 Myr) large craters on the North American and
European cratons
(5.4 ± 2.7) x 10- 15 km- 2 yr- 1
for D ~ 20km.
Estimated cratering rate from smaller craters on a nonglaciated area in the U.S.
(2.2 ± 1.1) x 10- 14 km- 2 yr- 1
for
D
~
lOkm.
Important impact craters are listed in Table 11.46.
Table 11.46. Terrestrial impact structures [1].
Diameter
Age
(Ian)
(Myr)
Name
Latitude
Longitude
Amguid, Algeria
Aouelloul, Mauritaniaa
Araguainha Dome, Brazil
Azuara, Spain
Barringer, Arizona, USAa
Bee Bluff, Texas, USA
Beyenchime-Salaatin, Russia
Bigatch,}(azakhstan
Boltysh, Ukraine
Bosumtwi, Ghana
Boxhole, Northern Territory,
Australiaa
B.P. Structure, Libya
Brent, Ontario, Canadaa
26°05'N
20° 15'N
16°46'S
41°01'N
35°02'N
29°02'N
71°50'N
48°30'N
48°45'N
06°32'N
004°23'E
012°41'W
052°59'W
()()()055'W
1l100l'W
099°51'W
123°30'E
082°00'E
032°lO'E
001°25'W
0.45
0.37
40.
30.
1.2
2.4
8.
7.
25.
10.5
< 0.1
3.1 ±0.3
< 250
< 13O
0.025
<40
< 65
6±3
l00±5
1.3 ± 0.2
22°37'S
135°12'E
024°20'E
078°29'W
0.18
2.8
3.8
< 120
450±30
25° 19'N
46°05'N
11.27 METEORITES AND CRATERS
Table 11.46. (Continued.)
Name
Campo del Cielo.
Argentina (20)"b
Carswell. Saskatchewan. Canada
Charlevoix. Quebec, Canada
Clearwater Lake East, Quebec,
Canada
Clearwater Lake West, Quebec,
Canada
Connolly Basin, Western
Australia, AustraliaQ
Crooked Creek, Missouri. USA
Dalgaranga, Western
Australia, AustraiiaQ
Decaturville, Missouri, USA
Deep Bay. Saskatchewan,
Canada
Dellen, Sweden
Eagle Butte, Alberta, Canada
E1' gygytgyn, Russia
Flynn Creek. Tennessee, USA
Glover Bluff. Wisconsin. USA
Goat Paddock. Western
Australia, Australia
Gosses Bluff. Northern
Territory, Australia
Gow Lake, Saskatchewan,
Canada
Gusev. Russia
Haughton. Northwest
Territories, Canada
Haviland, Kansas, USAQ
Henbury, Northern Territory,
Australia (14)"b
Holleford, Ontario, Canada
De Rouleau, Quebec, Canada
Dintsy, Ukraine
Dumetsy, Estonia
Janisjlirvi, Russia
Kaalijlirvi, Estonia (7)"b
Kaluga, Russia
Kamensk, Russia
Kara, RussiaQ
Karla, Russia
Kelly West, Northern
Territory, Australia
Kentland, Indiana, USA
Kjardla, Estonia
Kursk, Russia
Lac Couture, Quebec, Canada
Lac La Moinerie. Quebec,
Canada
Lappajlirvi, FiniandQ
Liverpool, Northern Territory,
Australia
Logancha, Russia
Logoisk, Byelorussia
Lonar, India
Diameter
Age
Latitude
Longitude
(Jan)
(Myr)
27°3S'S
5s027'N
47°32'N
061°42'W
109°30'W
0700 lS'W
0.09
37.
46.
117±S
36O±25
56°05'N
074°07'W
22.
290±20
56°13'N
074°30'W
32.
290±20
23°32'S
37°50'N
124°45'E
091°23'W
9.
5.6
<60
320±SO
27°43'S
37°54'N
117°05'E
092°43'W
0.21
6.
<300
56°24'N
61°55'N
49°42'N
67°3O'N
36°17'N
43°5S'N
102°59'W
016°32'E
lI0030'W
172°05'E
OS5°4O'W
OS9°32'W
12.
15.
10.
23.
3.S
6.
100 ± 50
109.6± I
< 65
3.5 ±0.5
36O±20
< 500
I So 20'S
I 26°4O'E
5.
< 50
23°50'S
132° 19'E
22.
142.5±0.5
56°27'N
""54°N
I04°29'W
""22°E
5.
3.
< 250
65
75°22'N
37°35'N
OS9°4O'W
099°10'W
20.
0.011
24°34'S
44°2S'N
S0041'N
49°06'N
57°5S'N
61°5S'N
5so24'N
54°30'N
4S°2O'N
69°10'N
57°54'N
133°10'E
076°3S'W
073°53'W
029° 12'E
025°25'E
030°55'E
022°4O'E
036° 15'E
040° 15'E
065°00'E
04S°00'E
0.15
2.
4.
4.5
O.OS
14.
0.11
15.
25.
60.
10.
550± 100
<300
395±5
0.002
69S±22
0.004
3S0± 10
65
57±9
10
19°30'S
40045'N
57°00'N
51°4O'N
600OS'N
132°50'E
OS7°24'W
022°42'E
036°00'E
075°2O'W
2.5
13.
4.
5.
S.
< 550
<300
51O±30
250±SO
425±25
57°26'N
63°09'N
066°36'W
023°42'E
S.
14.
4OO±50
77±4
12°24'S
65°30'N
54°12'N
134°03'E
095°5O'E
027°4S'E
076°31'E
1.6
20.
17.
1.83
150± 70
50±20
40±5
0.05
I~SS'N
21.5 ± 1.2
/ 289
290 /
11
EARTH
Table 11.46. (Continued.)
Diameter
Age
(Myr)
Name
Latitude
Longitude
Machi, Russia (5)b
Manicouagan, Quebec, Canada
Manson, Iowa, USA
Middlesboro, Kentucky, USA
Mien, Swedena
Misarai, Lithuania
Mishina Gora, Russia
Mistastin, Newfoundland, and
Labrador, Canada
Monturaqui, Chilea
Morasko, Poland (7)ab
New Quebec, Quebec, Canada
Nicholson Lake, Northwest
Territories, Canadaa
Oasis, Libya
Obolon', Ukraine
Odessa, Texas, USA (3~b
Ouarkziz, Algeria
Piccaninny, Western Australia,
Australia
Pilot Lake, Northwest
Territories, Canada
Popigai, Russia
Puchezh-Katunki, Russia
Red Wing Creek, North Dakota,
USA
Riacho Ring, Brazil
Ries, Germanya
Rochechouart, Francea
Rogozinskaja, Russia
Rotmistrovka, Ukraine
Siiliksjiirvi, Finlanda
Saint Martin, Manitoba, Canada
Serpent Mound, Ohio, USA
Serra da Canghala, Brazil
57°30'N
51°23'N
42°35'N
36°37'N
56°25'N
54°00'N
58°4O'N
116°00'E
068°42'W
Q94°31'W
083°44'W
014°52'E
023°54'E
028°00'E
55°53'N
23°56'S
52°29'N
61° 17'N
063°18'W
Q68°17'W
016°54'E
073°4O'W
28.
0.46
0.1
3.2
38±4
1
0.01
<5
62°4O'N
24°35'N
49°30'N
31°45'N
29°00'N
102°41'W
024°24'E
032°55'E
1Q2°29'W
007°33'W
12.5
11.5
15.
0.168
3.5
<400
17°32'S
128°25'E
7.
60°17'N
71°30'N
57°Q6'N
111°Q1'W
l11°00'E
043°35'E
6.
100.
80.
47°36'N
07°43'S
48°53'N
45°30'N
58° 18'N
49°00'N
61°23'N
51°47'N
39°Q2'N
08°05'S
42°42'N
3Q036'N
46°07'N
61°Q2'N
48°40'N
46°18'N
63°Q2'N
103°33'W
046°39'W
010037'E
OOO056'E
Q62°00'E
032°00'E
022°25'E
098°32'W
083°24'W
046°52'W
072°42'E
102°55'W
134°4O'E
014°52'E
087°OO'W
138°52'E
Q21°35'E
9.
4.
24.
23.
8.
2.5
5.
23.
6.4
12.
2.5
16°30'S
59°31'N
48°41'N
126°00'E
117°38'W
OlOo 04'E
5.
25.
3.4
95±7
14.8±0.7
15°12'S
46°36'N
44°Q6'N
33°19'N
133°35'E
081°11'W
109°36'E
Q04°Q2'E
24.
140.
1.3
1.75
<472
1850± 150
<30
<3
25°50'S
22°55'N
48°Q1'N
27°36'N
69°18'N
120055'E
010024'W
033°05'E
005°07'E
065° 18'E
28.
1.9
8.
6.
25.
1685 ±5
2.5 ±0.5
330±30
<70
57±9
Shunak,~tan
Sierra Madera, Texas, USA
Sikhote Alin, Russia (122)ab
Siljan, Sweden
Slate Island, Ontario, Canada
Sobolev, Russiaa
Soderfjiirden, Finland
Spider, Western Australia,
Australia
Steen River, Alberta, Canada
Steinheim, Germany
Strangways, Northern
Territory, Australiaa
Sudbury, Ontario, Canada
Thbun-Khara-Obo, Mongoliaa
Thlernzane,Algeria
Teague, Western Australia,
Australia
Tenoumer, Mauritania
Ternovka, Ukraine
Tm Bider, Algeria
Ust-Kara, Russia
(kIn)
0.3
100.
32.
6.
5.
5.
2.5
13.
0.0265
52.
30.
0.05
5.5
< 1
210±4
61 ±9
<300
118±3
395 ± 145
<360
215 ±25
< 70
<360
440±2
39±9
183±5
200
14.8±0.7
160±5
55±5
14O±20
< 330
225 ±40
< 320
<300
12
100
368± 1
< 350
<600
11.27
METEORITES AND CRATERS
I
291
Table 11.46. (Continued.)
Diameter
(km)
Age
(Myr)
Name
Latitude
Longitude
Upheaval Dome, Utah, USA
Veevers. Western Australia,
Australiaa
Vepriaj. Lithuania
Vredefort, South Africa
Wabar. Saudi Arabia (2~b
Wanapitei Lake. Ontario.
Canadaa
Wells Creek, Tennessee. USA
West Hawk Lake. Manitoba,
Canada
Wolf Creek. Western Australia,
Australiaa
Zeleny Gai. Ukraine
Zhamanshin. Kazakhstan
38°26'N
1()9°54'W
22°58'S
55°06'N
27°OO'S
21°30'N
125°22'E
024°36'E
027°30'E
Oso028'E
0.08
8.
140.
0.097
<450
160±30
1970± 100
46°44'N
36°23'N
osoo44'W
087°4O'W
8.5
14.
37±2
200± 100
49°46'N
095°11'W
2.7
l00±SO
19°IO'S
48°42'N
48°24'N
127°47'E
035°54'E
O6Oo48'E
0.85
1.4
10.
120±2O
0.75±0.06
5.
Notes
a Structures with meteoritic fragments or geochemical anomalies considered to have a
meteoritic source.
bSites with multiple craters, with (n) indicating number of craters. Diameter given
corresponds to largest crater.
Reference
1. Grieve. R.A.P. 1987. Ann. Rev. Earth Planet. Sci.• IS. 245
There is increasing acceptance of the importance of impacts in the evolution of the Earth and
planets. Examples of possible impact-related events in the Earth's history include the fonnation of the
Moon by a Mars-sized impactor early in the Earth's evolution and the Cretaceous-Tertiary extinctions
(about 65 Ma) by the effects of an impactor of mass about 1015 kg, energy about 1023 J, and diameter
about 100 km.
REFERENCES
1. Lerch. F.J. et aI. 1992. NASA Technical Memorandum
10455S Geopotential Models of Earth from Satellite
Tracking and Altimeter and Surface Gravity Observations GEM-TI and GEM-TIS
2. Cazenave. A. 1994. American Geophysical Union
Handbook of Physical Constants (American Geophysical Union, Washington. DC)
3. International Earth Rotation Service Standards. Central
Bureau of IERS (Observatoire de Paris)
4. ETOPO 5 Data Base (distributed by NOAA), 1986. (National Geophysical Data Center. Boulder. CO)
5. Thrcotte DL.• & Schubert, G. 1982. Geodynamics (Wiley. New York)
6. Dickey, J.O. 1994. American Geophysical Union Handbook of Physical Constants (American Geophysical
Union. Washington. DC)
7. ExplmuJtory Suppkment to the Astronomical Almanac.
edited by P.K. Seidelmann 1992. (University Science
Books. Mill Valley. CA)
8. Wahr. J. 1994. ArMrican Geophysical Union Handbook
of Physical
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Constants (American Geopbysical Union,
Washington. DC)
Harland, W.B. et al. 1990. A Geologic 7irMscale 1989
(Cambridge University Press, Cambridge)
Imbrie. J. 1985, J. GeoL Lond.. 142. 417
Condie. K.C. 1989. Plate Tectonics and Crustal Evolution (Pergamon Press. Oxford)
DeMets. C. et al. 1990. Geophys. J. Int.• 101.425
Dziewonski. A.M. & Anderson. D.L. 1981. Phys. Earth
Planet. Int.• 15. 297
COESA, U.S. Stmu.llJrdAtmosphere 1976. (Government
Printing Office. Washington, DC)
EdI6n. B. 1953. J. Opt. Soc. ArM!:, 43, 339
Anderson. G.P. et aI. 1986. AFGL-TR-86-0110. Atmospheric Constituent Profiles 10-120 km, Air Forr:e
Geophysics Laboratory (now Air Force Research Lab0ratory).
Allen. C.W. 1973. Astrophysical Quantities, 3rd ed.
(Athlone Press. London)
Goody R.M .• & Yung, Y.L. 1989, Atmospheric Radi-
292 I 11
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
EARTH
ation: Theoretical Basis, 2nd ed. (Oxford University
Press, New York)
Watson, R.P. et al. 1990, Greenhouse gases and
aerosols, in Climate Change: The IPCC Scientific
Assessment, edited by J.T. Houghton, G.H. Henkins,
and J.H. Ephraums (Cambridge University Press, New
York)
Logan, J.A. et al. 1981, J. Geophys. Res., 86, 7210
Allen, M., Lunine, 1.1., & Yung, Y.L. 1984, J. Geophys.
Res., 89, 4841
Smithsonian Meteorological Tables, 5th rev. 1949,
(Smithsonian Institution Press, Washington, DC)
Walterscheid, R.L., DeVore J.G., & Venkateswaran,
S.V. 1980, J. Atmos. Sci., 37, 455
Champion, K.S.W., Cole, A.E., & Kantor, A.J. 1985,
Standard and reference atmospheres, in Handbook of
Geophysics and the Space Environment, edited by A.S.
Jursa (Air Force Geophysics Laboratory, Available from
National Technical Information Service, ADA 167_
1985).
Smith E.K. Jr., & Wientraub, S. 1953, Institute ofRadio
Engineers Proc., 41, No.8, 1035
Berman, A.L., & Rockwell, S.T. 1992, New Optical
and Radio Frequency Angular Troposphere Refraction
Models for Deep Space Applications, NASA TR-321601
Hansen, J.E., & Travis, L.D. 1974, Space Sci. Rev. 16
Toan, O.B., & Pollack, J.B. 1976, J. Appl. Met. 15
Brasseur, G., & Solomon, S. 1986, Aeronomy of the
Middle Atmosphere: Chemistry and Physics of the
Stratosphere and Mesosphere, 2nd ed. (Kluwer Academic, Amsterdam)
Rothman, L.S. et al. 1992, JQSRT, 48, 469
31. Hargreaves, J.K. 1992, The Solar-Terrestrial Environment (Cambridge University Press, Cambridge)
32. Vallance Jones, A. 1974, Aurora (Reidel, Boston).
33. Roach, F.E., & Gordon, J.L. 1973, The Light of the
Night Sky (Reidel, Boston)
34. KrassovskY, V.I. et al. 1962, Planet. Space Sci., 9, 883
35. Chamberlain, J.W. 1961, Physics of the Aurora andAirglow (Academic Press, New York)
36. Meine1, A.B. et al. 1954, J. Geophys. Res., 59, 407
37. Bloxham, J. 1995, Global Earth Physics: A Handbook
of Physical Constants. T.J. Ahrens, Editor, AGU Reference Shelf 1. American Geophysical Union, Washington,DC)
38. Langel, R.A. 1987, in Geomagnetism, edited by J.A. Jacobs (Academic Press, Orlando), Vol. I, p. 249
39. 1992 IAGA Division V, Working Group 8, IGRF, 1991
Revision, EOS Trans. American Geophys. Union, 73,
182
40. Sears, D.W.G., & Dodd, R.T. 1988, in Meteorites and
the Early Solar System, edited by J.P. Kerridge and M.S.
Matthews, (University of Arizona Press, Tucson, AZ),
pp.3-31
41. Wasson, J.T. 1985, Meteorites-Their Record of Early
Solar System History (W.H. Freeman, New York)
42. Me1osh, H.J. 1989, Impact Cratering-A Geologic
Process, (Oxford University Press, New York)
43. Pesonen, L.J., Terho, M, & Kukkonen, T.T. 1993, Physical properties of 368 meteorites: Implications for meteorite magnetism and planetary geophysics, Proc. NIPR
Symp. Antarct. Meteorites, 6, 401
44. Grieve, R.A.F. 1987, Ann. Rev. Earth Planet. Sci., IS,
245
Chapter
12
Planets and Satellites
David J. Tholen, Victor G. Tejfel, and Arthur N. Cox
12.1
Planetary System . . . . . . . . . . . . . . . . . . . . .
293
12.2
Orbits and Physical Characteristics of Planets . . . .
294
12.3
Photometry of Planets and Asteroids. . . . . . . . ..
298
12.4
Physical Conditions on Planets . . . . . . . . . . . ..
300
12.5
Names, Designations, and Discoveries of Satellites
302
12.6
Satellite Orbits and Physical Elements. . . . . . . ..
303
12.7
Moon. . . . . . . . . . . . . . . . . . . . . . . . . . ..
308
12.8
Planetary Rings . . . . . . . . . . . . . . . . . . . . . .
311
12.1 PLANETARY SYSTEM
Total mass of planets [I]
Total mass of satellites [2]
Total mass of asteroids
Total mass of meteoric and cometary matter
Total mass of entire planetary system
Total angular momentum of planetary system
Total translational kinetic energy of planetary system
Total rotational energy of planets
293
446.6M e {M e = 5.9742 x 1027 g)
6.2 x 1026 g = O.I04M e
1.8 x 1024 g = 0.000 301M e
1O-9 M e
2.669 x 103° g = 446.7M e
3.148 x Hfo gcm2 s-1
1.99 x 1042 erg
0.7 x 1042 erg
= 0.00134M 0
294 I
12
PLANETS AND SATELLITES
Invariable (Laplacian) plane of the solar system [1,3]
with respect to the ecliptic and equinox of J2ooo.0
Longitude of ascending node
Inclination
North pole longitude
North pole latitude
with respect to the equator and equinox of 12000.0
(International Celestial Reference Frame)
Longitude of ascending node
Inclination
North pole right ascension
North pole declination
Gaussian period of comet or asteroid
where a is the sernimajor axis of orbit in AU
12.2
107°34' 57~'7
1°34' 43~'3
17°34' 57~'7
88°25' 16~'7
3°51' 09~'4
23°00' 32~'0
273°51' 09~'4
66°59' 28~'0
1.000 040 27a 3 / 2 tropical years
ORBITS AND PHYSICAL CHARACTERISTICS OF PLANETS
The orbital elements in Tables 12.1 and 12.2 are given in [3]. They are given with respect to the mean
ecliptic and equinox of J2ooo.0 at the epoch J2000 (JD 2451545.0). The longitudes of the ascending
node, n, and perihelion, W, are measured from a mean y, the intersection of the ecliptic and equator.
Therefore, W = n + w, where w is the argument of perihelion measured from the ascending node along
the orbit. L, the planet longitude for noon January 1,2000, is also measured the same way from the
mean y. For the Earth, data are given for the Earth-Moon barycenter.
Thble 12.1. Planetary orbit data [l].
Semimajor axis of orbit
Planet
(AU)
(106 km)Q
Mercury l;!
Venus 9
0.38709893
0.72333199
1.000000 II
1.52366231
5.20336301
9.53707032
19.19126393
30.06896348
39.48168677
57.909175
108.20893
149.59789
227.93664
778.41202
1426.7254
2870.9722
4498.2529
5906.3762
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
6
<1
4
I)
0
W
I?
Period
Sidereal
(Julian years)
Synodic
(days)
0.24084445
0.61518257
0.99997862
1.880711 05
11.85652502
29.42351935
83.74740682
163.7232045
248.0208
115.8775
583.9214
779.9361
398.8840
378.0919
369.6560
367.4867
366.7207
Mean daily
motion
(deg.)
Mean
orbit vel.
(kms-l)
4.09237706
1.60216874
0.98564736
0.52407109
0.08312944
0.03349791
0.01176904
0.006020076
0.003973966
47.8725
35.0214
29.7859
24.1309
13.0697
9.6724
6.8352
5.4778
4.7490
Note
aCalculated using 1 AU = 1.4959787066 x 1011 rn.
Reference
1. Explanatory Supplement to the Astronomical Almanac 1992, edited by P.K. Seidelrnann (University
Science, Mill Valley. CA). pp. 316, 704
12.2 ORBITS AND PHYSICAL CHARACTERISTICS OF PLANETS I 295
Table
Planet
Eccentricity
e
(2000.0)
[1.2]
Inclination
to ecliptic i
(2000.0)
[1.2]
(deg.)
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
0.20563069
0.00677323
0.01671022
0.09341233
0.04839266
0.05415060
0.04716771
0.00858587
0.24880766
7.00487
3.39471
0.00005
1.85061
1.30530
2.48446
0.76986
1.76917
17.14175
12~
Additional planetary orbit data.
Planet L
2000.0
Jan. 1.5
[1,2]
(deg.)
Perihelion
latest date
before
1999
[3]
252.25084
181.97973
100.46435
355.45332
34.40438
49.94432
313.23218
304.88003
238.92881
1998 Dec. 2
1998Sep.7
1998 Jan. 4
1998 Jan. 7
1987 Jul. 10
1974 Jan. 8
1966 May 20
1876Sep.2
1989Sep.5
Mean longitude of
ascending node n
perihelion if>
[1.2]
[1.2]
"Ta
"To
(deg.)
(deg.)
48.33167
76.68069
-11.26064
49.57854
100.55615
113.71504
74.22968
131.72169
110.30347
-446
-997
-18228
-1020
+1217
-1591
+1681
-151
-37
77.45645
131.53298
102.94719
336.04084
14.75385
92.43194
170.96424
44.97135
224.06676
+574
-109
+1198
+1560
+840
-1949
+1312
-844
-132
Note
a T is in centuries.
References
1. Explanatory Supplement to the Astronomical Almanac 1992. edited by P.K. Seidelmann. (University Science. Mill
Valley. CA). p. 316
2. Lang. K.R. 1991. Astrophysical Data: Planets and Satellites (Springer-Verlag. New York). p. 937
3. Astronomical Almanac (USNO. Government Printing Office)
In Table 12.3, the closest approach is at inferior conjunction for Mercury and Venus, at opposition
for the other planets. Note that the total mass of the Earth and Moon is 1.012300034 that of the Earth
alone. For Venus, Uranus, and Pluto the rotation is retrograde with respect to the orbit. Table 12.4
gives additional physical information for the planets.
Table 12.3. Physical characteristics o/planets [I].
Semi-diameter
equator
at
IAU
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
(")
3.37
8.34
8.794
4.69
98.48
83.3
32.7
33.4
1.5
at closest
approach
(")
5.5
30.1
8.95
23.43
9.76
1.95
1.15
0.04
Radius equator
Re
(km)
2439.7
6051.8
6378.14
3397
71492
60268
25559
24764
1195
$=1
0.3825
0.9488
1.000
0.5326
11.209
9.449
4.007
3.883
0.180
Ob1ateness
Re -Rp
Rp
Volume
$=1
[2]
0.0
0.0
0.00335364
0.00647630
0.0648744
0.0979624
0.0229273
0.0171
0
0.054
0.88
1.00
0.149
1316.
755.
52.
44.
0.005
Reciprocal mass
(including satellites)
[3]
1/0= I
Mass 1027 g
(excluding
satellites)
[1]
Mass
(excluding
satellites)
$=1
6023600
408523.71
328900.56
3098708
1047.3486
3497.898
22902.98
19412.24
135000000
0.33022
4.8690
5.9742
0.64191
1898.7
568.51
86.849
102.44
0.013
0.055274
0.81500
1.000000
0.10744
317.82
95.161
14.371
17.147
0.002200
References
1. Explanatory Supplement to the Astronomical Almanac 1992. edited by P.K. Seidelmann (University Science. Mill Valley.
CA)
2. Allen. C.W. 1973. Astrophysical Quantities (Athlone Press. London)
3. Standish. E.M. 1995. Report of the IAU WGAS sub-group on numerical standards. In Highlights of Astronomy. edited
by I. Appenzeller (Kluwer Academic. Dord:recht)
296 /
12
PLANETS AND SATELLITES
Table 12.4. Additional physical characteristics ofplanets [1].
Surface gravity [2]
Density
(gcm- 3 )
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto [9]
5.43
5.24
5.515
3.94
1.33
0.70
1.30
1.76
1.1
(cms- 2 )
equator
attractive
centrifugal
370
887
980
371
2312
896
869
1100
81
-0.0
-0.0
-3.391
-1.706
-224.841
-175.310
-26.195
-29.065
-0.014
Equatorial
escape
velocity [2]
(kIns-l)
4.25
10.36
11.18
5.02
59.54
35.49
21.29
23.71
1.27
Siderealab
rotation period
(equatorial)
[3-8]
(day)
58.6462
-243.0187
0.99726968
1.02595675
0.41354
0.44401
-0.71833
0.67125
-6.38718
Inclination
of equator
to orbit
(deg.)
0.0
177.3
23.45
25.19
3.12
26.73
97.86
29.58
119.61
Moment
of inertia
[2]
(MeR~)
0.4
0.34
0.3335
0.377
0.25
0.22
0.23
0.29
Notes
aEquatorial Jupiter I: gh5om3OS. High latitudes Jupiter IT: gh55m~3. Deep interior Jupiter m: gh55m29'!37. This
deep interior rotation rate is given in the table.
bEquatorial Saturn: I lohl4m. High latitudes Saturn: IT loh38m. Deep interior Saturn:
loJt3gm24s .
m
References
1. Exp1muuory Supplement to the Astronomical Almanac 1992, edited by P.K. Seidelmann (University Science, Mill
Valley, CA), p. 369
Allen, C.W. 1973, Astrophysical QutUltities (Athlone Press, London)
Davies, M.E. et al. 1994, eeL Mech., 63,127
Klassen, K.P. 1976, Mercury's rotation axis and period. Icarus, 28, 469
Shapiro, 1.1., Campben. D.B., & De Campli, W.M. 1979, Nonresonance rotation of Venus? ApJL, 230, L123
Linda!, G.F. et al. 1987, The atmosphere ofUranus-results of radio occultation measurements with Voyager 2. J.
Geophys. Res., 92, 14937
7. Warwick et al. 1986, Voyager 2 radio observations of Uranus. Science, 233, 102
8. Warwick et al. 1989, Voyager planetary radio astronomy at Neptune. Science, 246, 498
9. Tholen, D.J. & Buie, M.W. 1997, The orbit of Charon. I. New Hubble space telescope observations. Icarus, 125,
245
2.
3.
4.
5.
6.
12.2.1
Rotation Axes
Table 12.5 lists the right ascension and declination of the angular momentum vectors at epoch J2000.0
with the equinox J2ooo.0 for the Sun and the nine planets. Also listed are even more recent and accurate
sidereal rotation periods. Those given in Table 12.4 were used for recent Astronomical Almanacs. The
reference frame for the coordinates is the mean equator and equinox of J2ooo.0. The rotation periods
for Jupiter, Saturn, Uranus, and Neptune with no visible markings on a hard surface refer to their
magnetic fields. For information about prime meridians, see [3,4].
Table 12.5. Solar system cartographic dJJta [1].
a
Object
Sun [1,2]
Mercury
Venus
(deg.)
286~13
281~01
272~76
&
(deg.)
+63?87
+61?45
+67?16
Sidereal Period
(days)
25.38
58.646225
-243.01999
12.2 ORBITS AND PHYSICAL CHARACTERISTICS
OF PLANETS
/
297
Table 12.5. (Continued.)
Object
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
a
(deg.)
(deg.)
O?OO
317%81
268?05
40?589
257?311
299?36
313?02
+90?00
+52?886
+64?49
+83?537
-15?175
+43?46
-9?09
Sidereal Period
(days)
8
0.9972696323
1.025 956 754 3
0.413 538 325 8
0.444 009 259 2
-0.7183333333
0.671 2500000
-6.387 24600
References
1. Davies, M.E. et al. 1994, Cel. Mech., 63, 127
2. Carrington. R.C. 1863. Observations of Spots on the Sun
(Williams and Norgate. London)
12.2.2
Gravity Fields
Table 12.6 gives the spherical harmonic terms in the gravitational potential for the Earth and the outer
planets. See Chapter 11 for more details for the Earth.
Table 12.6. Coefficients of potential. a
Planet
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
12
J3
+0.00108263
+0.001964
+0.014736(1)
+0.016298(10)
+0.012
+0.003411(10)
-0.000 002 54
+0.000036
+0.0000014(50)
J4
J6
-0.00000161
-0.000 587(5)
-0.000915(40)
-0.000 026( + 12/-20)
Reference
[1]
+0.000031(20)
+0.000 103(50)
[2]
[3]
[4]
[5]
Note
a Numbers in parentheses are uncertainties in the last digits as given.
References
1. Explanatory Supplement to the Astronomical Almanac. 1992, edited by P.K. Seidelmann. (University Science,
Mill Valley. CAl. p. 697
2. Campbell, J.K .• & S.P. Synnott 1985. Gravity field of the Jovian system from Pioneer and Voyager tracking
data. Astron. J.• 90. 364
3. Campbell. J .K.• & J.D. Anderson 1989. Gravity field of the Saturnian system from Pioneer and Voyager tracking
data. Astron. J., 97. 1485
4. Anderson. J.D .• J.K. Campbell. R.A. Jacobson. D.N. Sweetnam. & A.H. Taylor 1990, Radio science with
Voyager 2 at Uranus: Results on masses and densities of the planet and five principal satellites. J. Geophys.
Res.• 92. 14877
5. 'lYler. G.L.. D.N. Sweetnam. J.D. Anderson. S.E. Borutzki. J.K. Campbell, V.R. Eshleman. D.L. Gresh. E.M.
Gurrola. D.P. Hinson. N. Kawashima. E.R. Kurinski. G.S. Levy. G.F. Linda!. J.R. Lyons. E.A. Marouf, P.A.
Rosen. R.A. Simpson. & G.E. Wood 1989, Voyager radio science observations of Neptune and Triton. Science.
246. 1466
298 I 12
PLANETS AND SATELLITES
12.2.3 Planetary Magnetic Fields
The dipole field strength at the planet surface in units of tesla-mete.-3 are given in Table 12.7.
Quadrupole and octapole strengths are the Schmidt nonnalized coefficients relative to the dipole
moment.
Table 12.7. Planet magnetic,Mlds and angles.
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Dipole
2-6 x 1012
< lOll
7.84 x 1015
< 1012
1.55 x 1020
4.6 x 1018
3.9 x 1017
2.2 x 1017
?
Quadrapole (%)
Octapole (%)
Angle (deg.)
13
10
10.8
23
14
20
7
10
0
59
47
Reference
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
References
1. Connemey, J.E.P., & N.F. Ness 1988, Mercury's magnetic field and interior. In Mercury
edited by Vilas, C.R. Chapman, and M.S. Matthews, (University of Arizona Press, Thcson)
pp.494-513
2. Phillips, J.L., & C.T. Russell 1987, Upper limit on the intrinsic magnetic field of Venus. J.
Geophys. Res., 92, 2253
3. Barton, C.E. 1989, Geomagnetic secular variation: Direction and intensity. In The EncyclopediD of Solid Earth Geophysics, (Van Nostrand Reinhold, New York) pp. 561-577
4. Russell, C.T. 1978, The magnetic field of Mars: Mars 5 evidence re-examined. Geophys. Res.
Len.,S,85
5. Connerney, J.E.P. 1981, The magnetic field of Jupiter: A generalized inverse approach. J.
Geophys. Res., 86, 7679
6. Connerney, J.E.P., M.H. Acuna, & N.F. Ness 1984, The Z3 model of Saturn's magnetic field
and the Pioneer 11 vector helium observations. J. Geophys. Res., 89, 7541
7. Connerney, J.E.P., M.H. Acuna, & N.F. Ness 1987, The magnetic field of Uranus. J. Geophys.
Res., 92, 15379
8. Connemey, J.E.P., M.H. Acuna, & N.F. Ness 1991, The magnetic field of Neptune. J.
Geophys. Res., !J6, 19023
12.3 PHOTOMETRY OF PLANETS AND ASTEROIDS
Table 12.8 gives the photometry data for the planets and some asteroids.
12.3 PHOTOMETRY OF PLANETS AND ASTEROIDS I 299
Table 12.8. Photometry o/the planets and five asteroids [1,2].
Planet or asteroid
Visual
geometric
albedo
Opposition
V
B-V
u-v
[1,3,4]
VO,O) or H
(rnag.)O
Mercury
0.106
0.93
0.41
-0.42
Venus
0.65
0.82
0.50
-4.40
Earth
Mars
Jupiter
Saturn
0.367
0.150
0.52
0.47
0.2
1.36
0.83
1.04
0.58
0.48
0.58
-3.86
-1.52
-9.40
-8.88
Uranus
Neptune
Pluto [5,6]
(1) Ceres [7,8,11,12]
(2) Pallas [7,8,11,12]
(3) Juno [7,8,11,12]
(4) Vesta [7,9,11,12]
(10) Hygiea [10-12]
(243) Ida [10-12]
(253) Mathilde [10-12]
(433) Eros [7,10-12]
(951) Gaspra [10-12]
-2.01
-2.70
+0.67c
0.51
0.41
variabled
+5.52
+7.84
+15.12
0.56
0.41
0.842d
0.28
0.21
0.31
-7.19
-6.87
-0.81
0.113
0.159
0.238
0.423
0.072
0.238
0.044
+6.78
+7.60
+8.57
+5.73
+9.56
+13.57
+13.39
+lO.28
+13.59
0.72
0.67
0.79
0.81
0.69
0.81
0.48
0.28
0.52
0.66
0.39
0.61
0.92
0.87
0.80
0.77
+3.34
+4.13
+5.53
+3.20
+5.43
+9.94
+lO.2
+11.16
+11.46
Variation of V with phase
(a, L in deg.)o.b
+0.038a - 2.73 x lO 4a 2
+2.00 x lO-6a 3
+O.OOO9a + 2.39 x lO- 4a 2
-0.65 x lO-6a 3
+0.0100
+0.005a
+0.0441 - 2.6 sin b
+1.25 sin 2 b
+0.0028a
0.037a
0.12
0.11
0.32
0.32
0.46
Notes
°For the asteroids the V(1.0) is designated as H, and the phase function is given by the slope parameter G [13].
b a is the phase angle between the Sun and Earth as seen from the planet. I is the Saturnicentric longitude difference of the
Sun and Barth and lies between _6° and 6°. b is the Saturnicentric ring latitude of the Earth that lies between -27° and 27°.
c V refers to the Saturn disk only.
dThe Pluto visual geometric albedo is variable by 30%. The Pluto color is the combination of the planet and its satellite
Charon.
References
1. Astronomical Almanac, 1998 (USNO, Government Printing Office)
2. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. Athlone Press, London
3. Irvine, W.M. et al. 1968, AJ, 73, 251, 807
4. Harris, D.L. 1%1, in Planets and Satellites, edited by G. Kuiper and B. Middlehurst (University of Chicago, Chicago),
p.272
5. Tholen D.J. & Tedesco, B.E 1994, Icarus, 108, p. 200
6. Buie, M.W., Tholen, D.J., & Wasserman L.H. 1997, Separate lightcurves of Pluto and Charon, Icarus, 125, 233
7. Haupt, H. 1951, Min. U.S. Wien, 5, 31
8. Watson, EG. 1956, Between the Planets, rev. ed. (Harvard University Press, Boston)
9. Gehrels, T. 1967, AJ, 72, 929
lO. Tedesco, E.E & Veeder, G.J. 1992, in The lRAS Minor Planet Survey edited by E.E Tedesco, G.J. Veeder, J.w. Fowler, and
J.R. Chillemi (Phillips Laboratory, Hanscom Air force Base)
11. Tedesco, E.E, Marsden, B.G., & Williams, G.V. 1990, Minor Planet Circulars 17256-17273 (Smithsonian Astrophysical
Observatory, Cambridge)
12. Bowell, E. Hapke, B, Domingue, D. Lumme, K., Peltoniemi, J., & Harris, A.W. 1989, in Asteroids II edited by R.P. Binzel,
T. Gehrels, and M.S. Matthews (University of Arizona Press, Tucson)
13. Zellner, B., Tholen, D.J., & Tedesco, E.E 1985, Icarus, 61, 355
300 / 12
PLANETS AND SATELLITES
12.4 PHYSICAL CONDITIONS ON PLANETS
by Glenn S. Orton
Planetary atmosphere and surface conditions are given in Table 12.9:
Te = Effective temperature of the planet.
Ta = Atmospheric temperature at the level with pressure 1 bar.
Ts = Mean temperature at the solid surface.
Ps = Atmospheric pressure at the solid surface for the terrestrial planets and
satellites or at visible cloud surface for major planets.
H
Scale heighL
So, Cl = Solid, cloud; for lowest visible surface.
=
Table 12.9. Planetary and selected satellite atmoSpMTf! and swface conditions.
VISible
Planet
surface
Mercury
Venus
Pluto
So
Cl
So,CI
So
Cl
Cl
Cl
CI
So
Moon
So
10
Europe
Ganymede
Callisto
TItan [2]
Triton [3]
So
So
.So
So
CI
So
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
T.
(K)
-230
-255
-212
124.4±0.3
95.0±0.4
59.1±O.3
59.3±O.8
50-70
Ta (lbar)
(K)
Ps
(bar)
H
(Ian)
730
288-293
183-268
90
I
0.007-0.010
-0.3
-0.4
15
8
11
19-25
35-50
22-29
18-22
57.8 [1]
8x 10-5 [1]
Ts
(K)
440
288
165
134
76
73
120-380
99
97
107
117
86
100-140 (300 locd)
1O-6 ?
83
94
38
References
1. Trafton L. & Stern S.A. 1983, Ap. 1., 'Hi7, 872
2. Saturn, 1984, edited by T. Gehrels (University of Arizona Press, 1\icson)
3.Scknce, 1990,250,4979
Compositions of planetary atmospheres are given in Table 12.10.
1.496±O.020
-1.5xl0-5
20-22
10- 5
10- 5
10- 5
10- 9
3 x 10-6
1.5 x 10-4
1.2 x
7x
1x
3x
0.016
2.5 x 10- 6
3 x 10- 7
8 x 10-8
10-9
< 10-6
< 10- 9
10-8
10- 10
10-8
10-6
10-9
(0.7-1.7) x 10-8
:'S 4.5 x 10- 6
3.4 x 10- 7
2 x 10- 9
:'S 1 x 10- 7
:'S 5 x 10- 6
< 10- 9
< 10-6
:'S 1 x 10-4
(0.2-2) x 10- 7
0.94
0.06
(1-3) x 10- 9
(1-4) x 10- 3
:'S 3 x 10- 10
Saturn [2,5,6]
:'S 10- 7
~
2x
6x
:'S 3 x
:'S 3 x
< 1x
~ 1.1 x 10-5
:'S 6 x 10-6
1 x 10- 10
(2.4 ± 0.5) x 10- 3
:'S 7 x 10-4
:'S 6.5 ± 2.9 x 10- 5
0.863 ± 0.007
0.156 ± 0.006
(1.0 ± 0.4) x 10- 5
(2.3 ± 0.25) x 10- 5
< (8.5 ± 4) x 10-9
< (5 ± 2.5) x 10-9
(1-8) x 10-5
Jupiter [2-4]
:'S4xlO- 7
~ 2 x 10- 6
(6-10) x 10- 5
< 3 x 10- 10
< 5 x 10- 7
:'S 0.02
< 10-4
:'S (0.5-1.2) x 10-8
0.85
0.15
Uranus [2,4,5]
<1x
~ 1x
0.85
0.15
10-8
10-6
< (1.5-3.5) x 10- 9
:'S 0.02-0.04
~6x 10- 7
:'S 5 x 10- 10
Neptune [2,5,7]
:'S 2
:'S 2
:'S 2
:'S 4
:'S 4
:'S (0.1-1)
:'S (0.1-1)
:'S (0.1-1)
x
x
x
x
x
x
x
x
(0--0.25)
10- 6
10- 5
10- 7
10-6
10-7
10-7
10-7
10- 7
:'S (0.4-1.4) x 10-9
2 x 10- 3
1.5 x 10- 9
(0.6-1.5) x 10-4
:'S 0.02-0.10
0.73-0.99
Titan [8]
I. Lewis, lS. 1995, Physics and Chemistry of the Solar System (Academic Press, San Diego)
2. Encrenaz, T. & Bibring l-P. 1990, The Solar System (Springer-Verlag, Berlin), 330 pp.
3. Niemann H.B. et al. 1996, Science, 272, 846; Niemann H.B. 1998, JGR, 103, 22831; Folkner, W.M., Woo, R., & Nandi, S. 1998, JGR, 103, 22847; Encrenaz, T. et al. 1996, A&A, 315,
L347; Bezard, B. et al. 1998, A&A, 334, L41
4. Encrenaz, T. et al. 1998, A&A, 338, L48
5. Feutchtgruber, H. et al. 1997, Nature 232, 139
6. Griffin, M. et al. 1996, A&A, 315, L389; Davis, G. et al. 1996, A&A, 313, L393; de Graauw, T. et al. 1997, A&A, 321, L43
7. Orton, G.S. 1992, Icarus, 100, 541
8. Science, 1989,246, N4936; Saturn, 1984, edited by T. Gehrels (University of Arizona Press, Tucson); Science, 1990,250, N 4979
References
HCN
C3 H8
C2f4
HC3N
C2N2
CH3NH2
C2~
PH3
CH3D
Gef4
C2 H2
HD
Xe
H2S
S02
Kr
Ne
Ar
2 x 10- 5
3 x 10-4
0.027
1.3 x 10- 3
0.953
2.7 x 10- 3
0.78084
0.20948
3.33 x 10-4
2 x 10- 7
2.0 x 10-6
4 x 10-9
~ 10- 6
5 x 10- 7
5.24 x 10-6
9.34 x 10- 3
1.818 x 10- 5
1.14 x 10-6
8.7 x 10-8
2 x 10-8
1 x 10-9
0.035
N2
02
CO2
CO
Cf4
NH3
H2O
H2
He
0.965
3 x 10- 7
Mars [2]
Earth [2]
Venus [2]
Gas
Table 12.10. Selected gas components of planetary atmospheres [1].
o
w
-
........
....,
en
>
ztr1
r
Z
'"C
o
en
Z
(3
....,
o
z
o......
n
......
n
>
r
-<
en
:::c
'"C
~
tv
-
302 /
12.5
12
PLANETS AND SATELLITES
NAMES, DESIGNATIONS, AND DISCOVERIES OF SATELLITES
byDanPascu
Table 12.11 lists the names, designations, and discoveries of the planetary satellites.
Table 12.11. Names, designations, and discoveries [I, 2, 3].
Satellite Name
Discovery
date
Discoverer
Earth
Moon
Mars
I
II
Jupiter
I
II
1II
IV
V
VI
VII
VlII
IX
X
Xl
XII
XlII
XIV
XV
XVI
Saturn
I
II
1II
IV
V
VI
VII
Vlll
IX
X
Xl
XII
XIII
XIV
Phobos
Deimos
1877
1877
10
Europa
Ganymede
Callisto
Amalthea
Himalia
Elara
Pasiphae
Sinope
Lysithea
Carme
Ananke
Leda
Thebe
Adrastea
1610
1610
1610
1610
1892
1904
1905
1908
1914
1938
1938
1951
1974
1980
1979
Metis
1980
Mimas
Enceladus
Tethys
Dione
Rhea
Titan
Hyperion
Iapetus
Phoebe
Janus
Epimetheus
Helene
Telesto
Calypso
1789
1789
1684
1684
1672
1655
1848
1671
1898
1966
196611978
1980
1980
1980
A.Hall
A. Hall
Galileo
Galileo
Galilco
Ga1ileo
E.E.Bamard
C. Perrine
C. Perrine
P. Melotte
S. Nicholson
S. Nicholson
S. Nicholson
S. Nicholson
C. Kowal
S.SynnoUfVoyagerI
D. Jewitt,
E. DanielsonIVoyager 2
S. SynnoUfVoyager 2
Satellite Name
Discovery
Discoverer
date
XV
XVI
Atlas
Prometheus
1980
1980
XVII
Pandora
1980
XVIII
Pan
1990
Ariel
Umbriel
Titania
Oberon
Miranda
Cordelia
Ophelia
Bianca
Cressida
Desdemona
Juliet
Portia
Rosalind
Belinda
Puck
Calibana
1851
1851
1787
1787
1948
1986
1986
1986
1986
1986
1986
1986
1986
1986
1986
1997
Sycoraxa
1997
Triton
Nereid
Naiad
Thalassa
Despina
Galatea
Larissa
1846
1949
1989
1989
1989
1989
1982
Proteus
1989
W. Lassen
G. Kuiper
Voyager 2
R. TerrileIVoyager 2
S. SynnoUfVoyager 2
S. SynnoUfVoyager 2
H. Reitsema, W. Hubbard,
L. Lebofsky. D. Tholen
S.SynnoUfVoyager2
Charon
1978
J. Christy
Uranus
I
II
1II
IV
V
VI
VII
VlII
IX
X
XI
XII
XIII
XIV
XV
XVI
XVII
W. Herschel
W. Herschel
Neptune
G.D. Cassini
I
G.D. Cassini
II
G.D. Cassini
III
C. Huygens
IV
W. & G. BondIW. Lassen
V
G.D. Cassini
VI
W. Pickering
VII
A. Dollfus
R.WalkedJ.Fountain.S.Larson VlII
P. Laques, J. Lecacheux
Pluto
B. Smith. H. Reitsema,
I
S. Larson. J. Fountain
D. Pascu. P.K. Seidelmann,
W. Bawn, D. Currie
R. TerrilelVoyager 1
S.A. Collins.
D. CarlsonIVoyager 1
S.A. Collins.
D. CarlsonIVoyager 1
M. ShowaiterlVoyager 2
W. Lassell
W. Lassen
W. Herschel
W.Herschel
G. Kuiper
R.TerrileIVoyager2
R. TerrileIVoyager 2
Voyager 2
S.SynnoUfVoyager2
S. SynnoUfVoyager 2
S. SynnoUfVoyager 2
S. SynnoUfVoyager 2
S. SynnoUfVoyager 2
S. SynnoUfVoyager 2
S. SynnoUfVoyager 2
B.J. Gladman. P.O. Nicholson.
J.A. Burns, JJ. Kavelaars
P.O. Nicholson, BJ. Gladman,
J .A. Burns, J.J. Kavelaars
Note
aThe two distant satellites of Uranus. Caliban and Sycorax still have provisional names. They will be accepted or changed
at the IAU General Assembly in 2000.
References
1. Burns, J.A. 1986, Satellites, edited by J.A. Burns and M.S. Matthews (University of Arizona Press, Tucson)
2. Pasachoff, J. 1998, From the Earth to the Universe, 5th ed. (Saunders College Pub., Fort Worth)
3. Veverka, J.M. 1998, Observers Handbook, edited by R.L. Bishop (University of Toronto Press, Toronto)
12.6 SATELLITE ORBITS AND PHYSICAL ELEMENTS / 303
12.6
SATELLITE ORBITS AND PHYSICAL ELEMENTS
byDanPascu
The main orbital and physical elements for the planetary satellites are given in Tables 12.12 and 12.13.
For comparison with observations, several factors are related to terrestrial opposition, labeled Op.
Synodic periods are relative to the main planet.
The inclinations of satellite orbits are complicated by precession around the "proper plane," which
is normally close to the planet's equator. Inclinations are measured from the planet's equator and values
greater than 90° indicate that the motion is retrograde. The inclination of the Moon to the ecliptic is
only 5? 145396. Reciprocal mass of satellite totals:
Jupiter
Saturn
Uranus
Neptune
Pluto
4831 (Jupiter)-l,
4050 (Saturn)-l,
9571 (Uranus)-l,
4780 (Neptune-I,
8.3 (Pluto)-l,
Total mass of all satellites 7.34 x 1026 g.
The following commensurabilities exist among the mean motions
Jupiter
Saturn
Uranus
nI
-
ni
of planetary satellites [5-7]:
+ 2n3 = 0,
+ 4n4 = 0,
3n I + 2n2 = 0,
n2 - 2n3 + n4 = O.
3n2
5nl - 10n2 + n3
ns nI -
Table 12.12. Planetary satellite orbits [1, 2, 3].
Semimajor axis
(10- 3) AU
(10 3 Ian)
Satellite
Max elong.
at mean
opposition
'"
Sidereal
perioda •b
(days)
Earth
Moon
Mars
I
II
Jupiter
I
II
ill
IV
V
VI
VII
vm
IX
X
Phobos
Deimos
10
Europa
Ganymede
Callisto
Amalthea
Himalia
Elara
Pasiphae
Sinope
Lysithea
384.400
2.5696
9.378
23.459
0.0627
0.1568
025
102
2.8209
4.4854
7.1525
12.5871
1.2099
76.7391
78.4570
157.0878
158.4247
78.3434
218
340
551
10 18
059
6246
6410
12826
12931
6404
422.
671.
1070.
1883.
181.
11480.
11737.
23500.
23700.
11720.
27.321661
0.31891023
1.2624407
1.769137786
3.551181041
7.15455296
16.6890184
0.49817905
250.5662
259.6528
R735.
R758.
259.22
304 /
12
PLANETS AND SATELLITES
Table 12.12. (Continued)
Semimajor axis
(10- 3) AU
(103 kIn)
Satellite
Jupiter (Cont.)
XI
Canne
XII
Ananke
xm
Leda
XN
Thebe
XV
Adrastea
XVI
Metis
Saturn
I
II
m
IV
V
VI
VII
vm
IX
X
XI
XII
xm
XN
XV
XVI
XVII
XVIII
Uranus
I
II
m
IV
V
VI
VII
vm
IX
X
XI
XII
xm
XN
XV
XVI
XVII
Neptune
I
II
m
IV
V
VI
VII
vm
22600.
21200.
11094.
222.
129.
128.
Maxelong.
at mean
opposition
1/1
151.0717
141.713 2
74.1588
1.4840
0.8623
0.8556
12331
11552
6039
1 13
042
042
Mimas
Enceladus
Tethys
Dione
Rhea
Titan
Hyperion
Iapetus
Phoebe
Janus
Epimetheus
Helene
Telesto
Calypso
Atlas
Prometheus
Pandora
Pan
185.52
238.02
294.66
377.40
527.04
1221.83
1481.1
3561.3
12952.
151.472
151.422
377.40
294.66
294.66
137.670
139.353
141.700
133.583
1.240 1
1.5910
1.9697
2.5228
3.5230
8.1674
9.9005
23.8053
86.5788
1.0125
1.0122
2.5228
1.9697
1.9697
0.9203
0.9315
0.9472
0.8929
030
038
048
101
125
317
359
935
3451
024
024
101
048
048
022
023
023
021
Ariel
Umbriel
Titania
Oberon
Miranda
Cordelia
Ophelia
Bianca
Cressida
Desdemona
Juliet
Portia
Rosalind
Belinda
Puck
Calibanc
Sycoraxc
191.02
266.30
435.91
583.52
129.39
49.77
53.79
59.17
61.78
62.68
64.35
66.09
69.94
75.26
86.01
7169.
12214.
1.2769
1.7801
2.9139
3.9006
0.8649
0.3327
0.3596
0.3955
0.4130
0.4190
0.4302
0.4418
0.4675
0.5031
0.5749
47.29
81.64
014
020
033
044
010
004
004
004
005
005
005
005
005
006
007
856
1526
Triton
Nereid
Naiad
Thalassa
Despina
Galatea
Larissa
Proteus
354.76
5513.4
48.23
50.07
52.53
61.95
73.55
117.65
2.3714
36.8548
0.3224
0.3347
0.3511
0.4141
0.4917
0.7864
017
421
002
002
002
003
003
006
Sidereal
perioda,b
(days)
R692.
R631.
238.72
0.6745
0.29826
0.294780
0.942421813
1.370217855
1.887 802 160
2.736914742
4.517500436
15.94542068
21.2766088
79.3301825
R550.48
0.6945
0.6942
2.7369
1.8878
1.8878
0.6019
0.6130
0.6285
0.5750
2.52037935
4.1441772
8.7058717
13.4632389
1.41347925
0.3350338
0.376400
0.43457899
0.46356960
0.47364960
0.49306549
0.51319592
0.55845953
0.62352747
0.76183287
R579.
R1289.
R5.8768541
360.13619
0.294396
0.311485
0.334655
0.428745
0.554654
1.122315
12.6 SATELLITE ORBITS AND PHYSICAL ELEMENTS / 305
Table 12.12. (Continued.)
Semimajor axis
(10- 3) AU
(10 3 Ian)
Satellite
Pluto
I
Charon
19.6
0.1310
Max elong.
at mean
opposition
'"
<001
Sidereal
perioda,b
(days)
6.38725
Notes
a R before the period indicates a retrograde orbit.
bTropical periods are given for the Saturn satellites I to VIII.
cProvisional names.
References
1. 1998 Astronomical Almanac (USNO, Government Printing Office)
2. Jacobson, R.A. 1998, AJ, 115, 1195
3. Owen, W.M., Vaughn, R.M., & Synnott, S. 1991,AJ,101, 1511
Table 12.13. Additional satellite data [I, 2, 3,4].
Orbit
Satellite
Inclination
(deg)
Eccentricity
Radius
(Ian)
Mass
(1IPIanet)
Mass
(g)
18.28-28.58
0.05490049
1737.4
0.012300034
7.3483 x 1025
1.654 x lO- S
3.71 x 10- 9
1.063 x 1019
2.38 x 10 1S
Earth
Moon
Mars
II
Jupiter
I
II
ill
IV
V
VI
VII
Vill
IX
X
XI
XII
xm
XIV
XV
XVI
Saturn
I
II
ill
IV
V
VI
VII
VIII
Phobos
Deimos
1.0
0.9-2.7
0.015
0.0005
13.4 x 11.2 x 9.2
7.5 x 6.1 x 5.2
10
Europa
Ganymede
Callisto
Amalthea
Himalia
Elara
Pasiphae
Sinope
Lysithea
Carme
Ananke
Leda
Thebe
Adrastea
Metis
0.04
0.47
0.21
0.51
0.40
27.63
24.77
145
153
29.02
164
147
26.07
0.8
0.004
0.009
0.002
0.007
0.003
0.15798
0.20719
0.378
0.275
0.107
0.20678
0.16870
0.14762
0.015
1830.0 x 1818.7 x 1815.3
1565
2634
2403
131.0 x 73.0 x 67.0
85
40
18
14
12
15
10
5
55 x 45
13 x 10 x 8
20 x 20
4.7041 x 10- 5
2.528 Ox 10-5
7.8046x 10- 5
5.6667xlO-5
3.8xlO- 9
5.0xlO-9
4xlO- 1O
lxl0- 10
4x 10- 11
4xl0- 11
5x 10- 11
2x 10- 11
3x 10- 12
4xlO- 1O
1 x 10- 11
5x 10- 11
8.9316x 1025
4.799 82x 1025
1.481 86x 1026
1.07593 x 1026
7.2x 102 1
9.5 x 102 1
8.x102O
2.x102O
8.x 10 19
8.x10 19
9.x10 19
4.x10 19
6.x 10 1S
8.x102O
2.x10 19
9.x 10 19
Mimas
Enceladus
Tethys
Dione
Rhea
Titan
Hyperion
Iapetus
1.53
0.00
1.86
0.02
0.35
0.33
0.43
14.72
0.0202
0.00452
0.00000
0.002230
0.00 1 00
0.029192
0.104
0.02828
209.1 x 196.2 x 191.4
256.3 x 247.3 x 244.6
535.6 x 528.2 x 525.8
560
764
2575
180 x 140 x 112.5
718
6.60xlO- S
Lx 10-7
1.l0x 10-6
1.95 x 10-6
4.06 x 10-6
2.366 7 x 10-4
4xlO- S
2.8x 10-6
3.75x1022
7.x1022
6.27xl023
1.l0xl024
2.31 x 1024
1.345 5 x 1026
2.x1022
1.6 x 1024
306 I
12
PLANETS AND SATELLITES
'nlble 12.13. (Continued.)
Orbit
Inclination
(deg)
Satellite
Satum(eont.)
IX
Phoebe
X
Janus
XI
Epimetheus
XII
Helene
xm
Telesto
XIV
Calypso
XV
Atlas
XVI
Prometheus
xvn Pandora
xvm Pan
U1'Q1IIU
I
II
m
IV
V
VI
VII
vm
IX
X
XI
XII
xm
XIV
XV
XVI
xvn
Neptune
I
II
m
IV
V
VI
VII
vm
Pluto
I
Ariel
Umbriel
Titania
Oberon
Miranda
Cordelia
Ophelia
Bianca
Cressida
Ina
Radius
(Ian)
Eccentricity
0.14
0.34
0.0
0.16326
0.007
0.009
0.005
0.3
0.0
0.0
0.000
0.003
0.004
110
97.0 x 95.0 x 77.0
69 x 55 x 55
18 x 16 x 15
15 x 12.5 x 7.5
15.0 x 8.0 x 8.0
18.5 x 17.2 x 13.5
74.0 x 50.0 x 34.0
55.0 x 44.0 x 31.0
0.0034
0.0050
0.0022
0.0008
0.0027
0.00026
0.0099
0.0009
0.0004
0.00013
0.00066
0.0000
0.0001
0.00007
0.00012
0.082
0.509
581.1 x 577.9 x 577.7
584.7
788.9
761.4
240.4 x 234.2 x 232.9
13
15
21
31
27
42
54
27
33
77
30
Triton
Nereid
Naiad
Thalassa
Despina
Galatea
Larissa
Proteus
157.345
0.000016
0.7512
0.000
0.000
0.000
0.000
0.00139
0.0004
1352.6
170
29:
40:
74
79
104 x 89
218 x 208 x 201
Charon
96.16c
Juliet
Portia
Rosalind
Belinda
Puck
Calibanb
Sycoraxb
Mass
(g)
7xlO- 1O
3.38xlO-9
9.5xlO- 1O
4.x1020
1.92 x loll
5.4x1020
1.55xlO-S
1.35x10-S
4.06x10-S
3.47x10-S
7.6xlO-7
1.35 x 1024
1.17 x 1024
3.53x1024
3.01 x 1024
6.6x1022
2.089 x 10-4
2xlO-7
2.x1022
0.125
1.62 x 1024
10
0.3
0.36
0.14
0.10
4.2
0.08
0.10
0.19
O.ol
0.11
0.07
0.06
0.28
0.03
0.32
139.:za
152.7"
Desdemona
Mass
(lJPlanet)
27.6c
4.74
0.21
0.07
0.05
0.20
0.55
60
593
Notes
"Relative to the ecliptic plane.
bProvisional names.
cRefeIred to the Earth equator of 1950.0 (Nereid) and of J2000 (Charon).
References
1. 1998 Astronomical Almanac (USNO, Government Printing Office)
2. Davies, M.E. et al. 1995, CeL Meeh., 63, 127
3. Jacobson,R.A.1998,AI,l1!,1195
4. Owen, W.M., Vaughn, R.M., & Synnott, S. 1991, AI, 101, 1511
2.140x102S
12.6 SATELLITE ORBITS AND PHYSICAL ELEMENTS I 307
Rotation and photometric data for many of the planetary satellites are given in Table 12.14.
Table 12.14. Satellite rotation and photometric datil [1. 2. 3].
Sidereal
period of
rotation (d)"
Geometric
albedo
(V)b
V(l.O)C
v.0d
B-V
U-B
Moon
S
0.12
0.21
-12.74
0.92
0.46
Phobos
Deimos
S
S
0.07
0.08
11.8
12.89
11.3
12.40
0.6
0.65
0.18
10
Europa
S
S
S
S
S
0.4
0.5
0.63
0.67
0.44
0.20
0.07
0.03
0.03
0.10
0.05
0.06
0.06
0.06
0.07
0.04
0.05
0.05
-1.68
-1.41
-2.09
-1.05
7.4
8.14
10.07
10.33
11.6
11.7
11.3
12.2
13.5
9.0
12.4
10.8
5.02
5.29
4.61
14.1
14.84
16.77
17.03
18.3
18.4
18.0
18.9
20.2
15.7
19.1
17.5
1.17
0.87
0.83
0.86
1.50
0.67
0.69
0.63
0.7
0.7
0.7
0.7
0.7
1.3
0.5
1.0
0.9
0.7
0.7
0.22
0.3
0.2"
0.06
0.9:
0.8:
0.7:
1.0:
1.0:
0.8:
0.5:
0.7:
0.5:
3.3
2.1
0.6
0.8
0.1
-1.28
4.63
1.5
6.89
4.4:
5.4:
8.4:
8.9:
9.1:
8.4:
6.4:
6.4:
12.9
11.7
10.2
10.4
9.7
8.28
14.19
11.1
16.45
14.:
15.:
18.:
18.5:
18.7:
18.:
16.:
16.:
0.35
0.19
0.28
0.25
0.27
0.07:
0.07:
1.45
2.10
1.02
1.23
3.6
11.4
11.1
14.16
14.81
13.73
13.94
16.3
24.1
23.8
Satellite
Earth
Mars
I
n
Jupiter
I
n
m
IV
V
VI
vn
vm
IX
X
XI
XU
xm
XIV
XV
XVI
Saturn
I
n
m
IV
V
VI
vn
vm
IX
X
XI
XU
xm
XIV
XV
XVI
xvn
xvm
UrtUJIIS
I
n
m
IV
V
VI
vn
Ganymede
Callisto
Ama1thea
HimaIia
Elara
Pasipbae
Sinope
Lysithea
Carme
Ananke
Leda
Thebe
Adrastea
Metis
Mimas
Enceladus
Tethys
Dione
Rhea
TItan
Hyperion
Iapetus
Phoebe
Janus
Epimetheus
Helene
Telesto
Calypso
Atlas
Prometheus
Pandora
S
S
S
S
S
S
S
S
0.4
S
S
Pan
Ariel
Umbriel
TItania
Oberon
Miranda
Cordelia
Ophelia
S
S
S
S
S
5.6S
1.30
0.52
0.50
0.55
0.30
0.28
0.34
0.70
0.73
0.71
0.78
1.28
0.78
0.72
0.70
0.28
0.30
0.31
0.38
0.75
0.33
0.30
0.34
0.65
0.68
0.70
0.68
0.28
0.20
308 I
12
PLANETS AND SATELLITES
Table 12.14. (Continued.)
Sidereal
period of
rotation (d)il
Satellite
Uranus (cont.)
Bianca
vm
IX
Cressida
X
Desdemona
Juliet
XI
Portia
xn
Rosalind
Belinda
XN
Puck
XV
Calibanf
XVI
Sycoraxf
XVII
xm
Neptune
I
II
m
IV
V
VI
VII
vm
Geometric
albedo
(V)b
v.0d
0.07:
0.07:
0.07:
0.07:
0.07:
0.07:
0.07:
0.075
0.07:
0.07:
10.3
9.5
9.8
8.8
8.3
9.8
9.4
7.5
23.0
22.2
22.5
21.5
21.0
22.5
22.1
20.2
22.4
20.9
-1.24
4.0
10.0:
9.1:
7.9
7.6:
7.3
5.6
13.47
18.7
24.7
23.8
22.6
22.3
22.0
20.3
0.9
16.8
Triton
Nereid
Naiad
Thalassa
Despina
Galatea
Larissa
Proteus
S
0.77
0.4
0.06:
0.06:
0.06:
0.06:
0.06
0.06
Charon
S
0.5
Pluto
I
V(1,O)C
B-V
U-B
0.72
0.65
0.29
Notes
a S means the rotation is synchronous with the orbit period.
bThe solar V used is -26.75.
cThe apparent V magnitude with the planet 1 AU from both Sun and Earth at zero phase angle.
dThe apparent mean opposition V magnitude.
eBright side 0.5, faint side 0.05.
f Provisional names.
References
I. 1998 Astronomical Almanac (USNO, Government Printing Office)
2. Bums, J.A. 1986, Satellites, edited by J.A. Bums and M.S. Matthews (University of Arizona Press,
"lUcson)
3. Veverka, J.M. 1998, Observers Handbook, edited by R.L. Bishop (University of Toronto Press,
Toronto)
12.7 MOON
Mean distance from Earth [8]
Extreme range
Mean equatorial horizontal parallax
Eccentricity of orbit
Inclination of orbit to ecliptic
oscillating ±9' with period of 173 d
Sidereal period (fixed stars)
Mean orbital speed [9]
Synodical month
(new moon to new moon)
384401 ± 1 krn
356400-406 700 krn
3422%08
0.05490
5° 8' 43~'42
27.321661
1.023 krns- 1
29.530588
12.7 MOON / 309
Tropical month
(equinox to equinox)
Anomalistic month
(perigee to perigee)
Nodical month (node to node)
Period of Moon's node (nutation period,
retrograde)
Period of rotation Moon's perigee (direct) [3]
Moon's sidereal mean daily motion
27.321582
27.554550
27.212220 days
18.61 Julian years
8.849 Julian years
47434~'889
13?176358
Mean transit interval
Main periodic terms in the motion [10]
Principle elliptic term in longitude
Principle elliptic term in latitude
Evection
Variation
Annual inequality
Parallactic inequality
where g = Moon's mean anomaly
g' = Sun's mean anomaly
D = Moon's age
u = distance of mean Moon
from ascending node
Physicallibration [11]
Displacement (selenocentric)
Period
Opticallibration [11]
Displacement (selenocentric)
Period
Surface area of Moon at some time
visible from earth
Inclination of lunar equator [11]
To ecliptic
To orbit
Moon radii: a toward Earth,
b along orbit, c toward pole.
Mean Moon radius (b + c)/2 [8]
Moon mass [12]
Moon semi-diameter at mean distance
geocentric
topocentric, zenith
Mean volume
Moon mean density
24h50~47
22 639" sin g
18461" sin u
4586" sin(2D - g)
2370" sin 2D
-669" sin g'
-125" sin D
longitude
±66"
1 yr
latitude
±105'' [9]
6yr
approximately sidereal lunar
59%
1° 32'
6° 41'
32~'7
1738.2 km
0.272 52 Earth equatorial radius
a - c = l.09km
a - b = 0.31 km
b -c =0.78km
M~/81.301 = 7.353 x 1025 g
15' 32%
15' 48~'3
2.200 x lQ25 cm3
3.341 gcm- 3
310 /
12
PLANETS AND SATELLITES
Surface gravity
Surface escape velocity
Moment of inertia (about rotation axis) [13]
Moment of inertia differences [13-15]
(a + y = fJ)
162.2 cms-2
2.38 kms- 1
0.396Meb2
a
= (C -
y
=
B)/ A
A)/ B
(B - A)/C
fJ = (C -
= 0.000400
= 0.000628
= 0.000228
A-axis toward Earth, B along orbit, C toward pole.
Gravitational potential term [13]
Jz = 2.05 X 10-4
Mascons [16]
Number of strong mascons
on the near side of the Moon
4 exceeding 80 milligals
Mean surface temperature [12]
+107 C (day), 153 C (night)
Temperature extremes [12]
-233 C(?), +123 C
29mWm- 2
Flow of heat through Moon's surface [12]
Moon's atmospheric density [12]
'" 104 molecules cm- 3 (day)
2 x 105 molecules cm- 3 (night)
Number of maria and craters on lunar surface
with diameters greater than d [8, 17-19]
This rule extends from the largest maria (d ~ 1000 km) to the smallest holes (d
Lunar surface and photometric data are given in Tables 12.9 and 12.14.
Table 12.15 gives the integral phase function for the Moon.
Table 12.15. Lunar integral phase function [1].
Phase
angle
(deg.)
Before
full
Moon
After
full
Moon
0
1.000
0.787
0.603
0.466
0.356
0.275
0.211
0.161
1.000
0.759
0.586
0.453
0.350
0.273
0.211
0.156
10
20
30
40
50
60
70
Phase
angle
(deg.)
Before
full
Moon
After
full
Moon
80
0.120
0.0824
0.0560
0.0377
0.0249
0.0151
0.111
0.0780
0.0581
0.0405
0.0261
0.0158
0.0093
0.0046
90
100
110
120
130
140
150
Reference
1. Hapke B. 1974, Optical properties of lunar surface. In
Physics and Astronomy of the Moon, edited by Zd. Kopal
(Academic Press, New York)
~
I cm).
12.8 PLANETARY RINGS / 311
12.8 PLANETARY RINGS
12.8.1
Rings of Jupiter
The four rings of Jupiter are described in Table 12.16.
Table 12.16. Rings of Jupiter [1].
Distance
Ring
Halo ring
Main ring
Gossamer ring (inner)
Gossamer ring (outer)
Optical
depth
(krn)
(Rj)
100 000--122 ()()()
122000--129 ()()()
129200-182 ()()()
182000--224900
1.40-1.71
I. 71-1.81
1.81-2.55
2.55-3.15
Albedo
3 x 10-6
5 x 10-6
~0.015
1.0 x 10-7
Reference
1. http://nssdc.gsfc.nasa.gov/planetary/factsheetljupringfact.htrnl, and private communication from G.S. Orton
12.8.2
Rings of Saturn
Table 12.17 lists the details of the rings of Saturn.
Table 12.17. Rings of Satum a [1,2].
Radius
Zone
O-ring inner edge
C-ring inner edgeb
Titan ringlet
Maxwell ringlet
B-ring inner edge
B-ring outer edge
Cassini division
A-ring inner edgeC
Encke gap center
A-ring outer edge
F-ring center
G-ring center
E-ring inner edge
E-ring outer edge
(krn)
Distance
Rj RS aturn
>66900
74658
77871
87491
91975
117507
l.ll
1.239
1.292
1.452
1.526
1.950
122340
133589
136775
140374
170 ()()()
2.030
2.216
2.269
2.329
2.82
3
8
~180()()()
~480()()()
Optical
depth
Albedo
0.05-0.35
0.12-0.30
0.4-2.5
0.4-0.6
0.05-.015
0.4-1.0
0.2-0.4
0.4-0.6
0.1
1.0 x 10-6
1.5 x 10- 5
0.6
Notes
aTotai mass of rings 6 x 10- 8 MS aturn = 3.4 x 1022 g.
bThickness of C-ring no more than 10 m.
cThickness of A-ring about 50 m.
References
I. Zebker, H.A. & lYler, G.L. 1984, Science, 223, 396
2. http://nssdc.gsfc.nasa.gov/planetary/factsheetlsatringfact.htrnl
312 I
12
12.8.3
Rings of Uranus
PLANETS AND SATELLITES
Table 12.18 lists the details of the rings of Uranus.
Table 12.18. Rings of Uranus [I, 2, 3].
Radius
Zone
6
5
4
ex
f3
1/
y
8
A
€
(kIn)
Distance
RJRUranus
Optical
depth
41837
42235
42571
44718
45661
47176
47626
48303
50024
51149
1.637
1.652
1.666
1.750
1.786
1.834
1.863
1.900
1.957
2.006
~0.3
~0.5
~0.3
~0.4
~.3
~0.4-
~1.5+
~0.5
~O.I
0.5-2.3
Albedo
~15
~15
~15
~15
~15
~15
~15
~15
~15
~18
x
x
x
x
x
x
x
x
x
x
10- 3
10- 3
10- 3
10- 3
10- 3
10- 3
10- 3
10- 3
10- 3
10-3
References
1. Stone, E.C. & Miner, E.D. 1986, Science, 233,39
2. AstronomicalAlmanac, 1996 (USNO, Government Printing Office)
3. http://nssdc.gsfc.nasa.gov/planetary/factsheetluranringfact.htrnl
12.8.4
Rings of Neptune
Table 12.19 lists the details of the rings of Neptune.
Table 12.19. Rings of Neptune [I, 2].
Radius
Zone
Galle (1989 N3R)
LeVerrier (1989 N2R)
Lassell (1989 N4R)a
Arago (1989 N4R)a
Unnamed (indistinct)
Adams (1989 NIR)b
(kIn)
~41900
~532oo
~532oo
~572oo
61950
62933
Distance
RJ RNeptune
1.692
2.148
2.148
2.310
2.501
2.541
Optical
depth
Albedo
~0.OOO08
~0.002
~O.OOO
15
~0.0045
~15 x 10- 3
~15 x 10- 3
~15 x 10- 3
~15 x 10-3
Notes
aLeVerrier and Lassell were originally identified as one ring, designated 1989N4R.
b Arcs in the Adams Ring with optical depths of 0.12 and albedos of about 0.04 are:
Courage, Liberte, Egalite I, Egalit6 2, and Fraternite.
References
1. Lang, K.R. 1991, Astrophysical Data: Planets and Satellites, (Springer-Verlag,
New York), p. 937
2. http://nssdc.gsfc.nasa.gov/planetary/factsheetlnepringfact.htrnl
12.8 PLANETARY RINGS I 313
REFERENCES
1. Myles Standish. DE 4OS. private communication
2. Robert Jacobson. private communication
3. Exp/QnQtory Suppkment to tIu! Astronomical Almonac
1992. edited by P.K. Seidelmann (University Science.
Mill Valley. CA)
4. Davies. M.E. et al. 1994. eeL Meeh.. 63. 127
S. Handbook of the British Astronomy Association (Annual)
Roy. A.E. &; Ovenden. M.W. 1954. MNRAS. 114.232
Roy. A.E. &; Ovenden. M.W. 19S5. MNRAS. 115.296
Astrophysical QlIIJIItities. I. Sec. 86; 2. Sec. 69
Lang. K.R. 1991. Astrophysical Data: Pionets and
Satellites. (Springer-Verlag. New York) p. 937
10. Landolt-Bomstein Tabks. 1962 (Springer-Verlag. New
6.
7.
8.
9.
York). pp. 3. 83
11. Astronomical Almanacs (USNO. Government Printing
Office)
12. LwuJr Source Book. 1991. edited by G. Heiken. D. Vaniman. and B.M. French (Cambridge University Press.
Cambridge)
13. Cook, A.H. 1970. MNRAS. ISO. 187
14. Goudas. C.L. 1967. AI. 72. 9SS
IS. Koziel, K. 1967. Proc. R. Soc. London.. 296. 248
16. Mutch, T.A. 1970. Geology of the Moon (Princeton University Press. Princeton. NJ). pp. SO. 217. 26S
17. Jaffe. L.D. 1969. SSRv. 9. SOS
18. Cross. C.A. 1966. MNRAS. 134.24S
19. Marcus. A. 1966. MNRAS.I34. 269
Chapter
13
Solar System Small Bodies
Richard P. Binzel, Martha S. Hanner, and Duncan I. Steel
13.1
13.1.1
13.1
Asteroids or Minor Planets. . . . . . . . . . . . . . ..
315
13.2
Comets. . . . . . . . . . . . . . . . . . . . . . . . . ..
321
13.3
Zodiacal Light . . . . . . . . . . . . . . . . . . . . . ..
328
13.4
Infrared Zodiacal Emission . . . . . . . . . . . . . . .
331
13.5
Meteoroids and Interplanetary Dust. . . . . . . . . ..
333
ASTEROIDS OR MINOR PLANETS
Populations and Locations [1-3]
Number of minor planets having well-determined orbits, cataloged by permanent designations
(numbers) as of 1998, January 1: 8125.
Number of known minor planets having less well-determined orbits, cataloged by provisional
designations: > 25, 000.
Most are located in the Main-belt, between Mars and Jupiter.
Semimajor axis, range 2.06 to 3.28 AU, mean a
Mean orbital eccentricity: e = 0.142.
Mean orbital inclination: i = 7.92 deg.
Mean orbital period: 4.40 yr.
= 2.68.
Number of main-belt asteroids larger than 100 kIn in diameter: 188,50 kIn: 475.
Estimated population of main-belt asteroids larger than diameter D (in kIn):
315
316 /
13
SOLAR SYSTEM SMALL BODIES
Near-Earth Asteroids (NEAs) are those approaching within 0.3 AU of the Earth's orbit.
Atens: a < 1.0 AU, aphelion Q > 0.983 AU.
Number known as of 1998, January 1 = 27.
Apollos: a ~ 1.0 AU, perihelion q ::s 1.017 AU.
Number known as of 1998, January 1 = 213.
Amors: a > 1.0 AU, 1.017 < q ::s 1.3 AU.
Number known as of 1998, January 1 = 207.
Aten and Apollo asteroids have orbits which cross the Earth's orbit.
Orbits of many Amor asteroids can evolve to become Earth-crossing.
Estimated population of Earth-crossing asteroids having diameter:
> 1 kIn: 2100.
> 100 m: 320,000. (A size likely to survive passage through the terrestrial atmosphere.)
'JYpical collisional frequency (per object) with Earth, for an NEA having an Earth-crossing orbit:
Pj = 2.2 per 109 yr.
Mean collision velocity with Earth: Vc = 22.5 kmls.
Trojan asteroidsare located in the vicinities of the L4 and L5 Lagrange points of Jupiter.
Mean semimajor axis: a = 5.20 AU.
Mean eccentricity: e = 0.080.
Mean inclination: i = 15.9 deg.
Number known as of 1998, January 1: 413.
13.1.2 Magnitudes [4]
An asteroid's absolute magnitude, H, is defined as its mean V magnitude (neglecting rotational and
aspect variations), if it were observed at a distance r = 1 AU from the Sun, ll. = 1 AU from the Earth,
and a phase angle (Earth-object-Sun angle) a = O. For other locations, an asteroid's mean apparent
V magnitude can be expressed by
V = H(a)+5Iogrll.,
where
H(a) = H - 2.5Iog[(1 - G)4>1 (a)
+ G4>2(a)].
G is called the slope parameter which accounts for an asteroid's nonlinear change in brightness as
a function of phase angle only. 4>1 and 4>2 are described by
4>j
= exp{-Aj[tan(a/2)]Bi};
Al = 3.33,
BI = 0.63,
i = 1,2,
A2 = 1.87,
B2 = 1.22.
An asteroid's diameter D (in kIn) can be estimated by
logD = 3.129 - 0.5logp - 0.2H,
where p is its geometric albedo in the V passband.
An asteroid's Bond albedo, A, is related to the geometric albedo by the phase integral, q, where
A=pq,
q = 0.290 + 0.684G;
o ::s G ::s 1.
13.1 ASTEROIDS OR MINOR PLANETS I 317
13.1.3 Physical Properties [5]
Estimated total mass of the asteroids = 1.8 x 1()24 g.
Estimated densities for most asteroids, 1.0 - 3.5 g cm- 3.
Possible compositions, typical albedos, slope parameters, and color indices for selected taxonomic
types of asteroids.
C-types: Carbonaceous chondrite, p = 0.05, G = 0.15, B - V = 0.70, U - B = 0.35.
S-types: Stony-Iron? Ordinary chondrite?, p = 0.19, G = 0.25, B - V = 0.85, U - B = 0.44.
M-types: Metal-rich?, p = 0.10, G = 0.20, B - V = 0.70, U - B = 0.25.
Typical rotation period, P '" 9 h. Observed range: 2 to > 1000 h.
Typical rotation light curve amplitude variation, l:!.M '" 0.2 mag. Observed range: 0 to > 1 mag.
Typical shape, modeled by a triaxial ellipsoid with axes a, b, c, where a> b > c:
a:b:c=2:..fi: 1.
Lowest energy rotation state occurs about the c-axis.
13.1.4 Data Tables
Tables 13.1 and 13.2 give the 100 largest and 147 of the nearest asteroids.
Table 13.1. The 100 largest asteroids [1].
No.
Name
1
2
4
10
511
704
52
15
87
16
24
31
65
3
324
107
624
532
451
48
19
29
121
423
13
45
Ceres
Pallas
Vesta
Hygica
Davida
Interamnia
Europa
Eunomia
Sylvia
Psyche
94
88
7
702
Themis
Euphrosyne
Cybcle
Juno
Bamberga
Camilla
Hektor
Herculina
Patientia
Doris
Fortuna
Amphitrite
Hermione
Diotima
Egeria
Eugenia
Aurora
Thisbc
Iris
Alauda
Year of
Discovery
D
(km)
1SOl
1802
1807
1849
1903
1910
1858
1851
1866
1852
1853
1854
1861
1804
1892
1868
1907
1904
1899
1857
1852
1854
1872
1896
1850
1857
1867
1866
1847
1910
913
523
501
429
337
333
312
272
271
264
249
248
245
244
242
237
233
231
230
225
221
219
217
217
215
214
212
210
203
202
a
e
2.77
2.77
2.36
3.14
3.18
3.06
3.10
2.64
3.49
2.92
3.13
3.14
3.44
2.67
2.68
3.48
5.18
2.77
3.06
3.11
2.44
2.55
3.44
3.08
2.58
2.72
3.16
2.77
2.39
3.19
0.078
0.234
0.091
0.120
0.178
0.148
0.100
0.185
0.083
0.134
0.134
0.228
0.104
0.258
0.341
0.084
0.024
0.176
0.071
0.069
0.158
0.072
0.143
0.034
0.086
0.083
0.082
0.164
0.230
0.029
P
(h)
10.6
34.8
7.1
3.8
15.9
17.3
7.4
11.8
10.9
3.1
0.8
26.3
3.5
13.0
11.1
9.9
18.2
16.4
15.2
6.5
1.6
6.1
7.6
11.2
16.5
6.6
8.0
5.2
5.5
20.6
9.075
7.811
5.342
18.4
5.13
8.727
5.631
6.083
5.183
4.196
8.38
5.531
6.07
7.21
29.43
4.84
6.921
9.405
9.727
11.89
7.445
5.39
6.1
4.622
7.045
5.699
7.22
6.042
7.139
8.36
l!.M
(mag)
0.04
0.0~.16
0.12
0.09-{).18
0.06-0.25
0.0~.11
0.09-{).1O
0.4-0.56
0.30-0.62
0.0~.42
0.10-0.14
0.09-{).13
0.04-0.12
0.14-0.22
0.07
0.32-{).52
0.1-1.1
0.08-0.18
0.05-0.10
0.35
0.22-{).35
0.01~.15
0.03
0.06-0.18
0.12
0.08-0.41
0.12
0.08-0.21
0.04-0.29
0.07~.1O
'JYpe
P
H
G
U-B
B-V
G
B
0.10
0.14
0.38
0.07
0.05
0.06
0.05
0.19
0.04
0.10
3.32
4.13
3.16
5.27
6.17
6.00
6.25
5.22
6.95
5.99
7.07
6.53
6.79
5.31
6.82
6.SO
7.47
5.78
6.65
6.83
7.09
5.84
7.39
7.48
6.47
7.27
7.55
7.05
5.76
7.23
0.11
0.15
0.34
-0.04
0.02
0.02
0.00
0.20
0.28
0.22
0.10
0.15
0.15
0.30
0.10
-0.17
0.15
0.25
0.20
-0.05
0.10
0.21
0.15
0.68
-0.02
0.15
0.09
0.17
0.51
0.13
0.43
0.29
0.50
0.35
0.36
0.26
0.33
0.46
0.25
0.25
0.35
0.32
0.27
0.41
0.30
0.30
0.24
0.41
0.33
0.43
0.39
0.42
0.39
0.30
0.46
0.27
0.30
0.29
0.48
0.32
0.72
0.66
O.SO
0.69
0.72
0.64
0.66
0.84
0.70
0.70
0.68
0.67
0.67
0.81
0.70
0.70
0.79
0.85
0.65
0.72
0.75
0.83
0.72
0.67
0.75
0.66
0.66
0.66
0.85
0.66
V
C
C
F
CF
S
P
M
C
C
P
S
CP
C
D
S
CU
CG
G
S
C
C
G
FC
CP
CF
S
C
0.07
0.05
0.22
0.05
0.06
0.16
0.07
0.06
0.16
0.04
0.03
0.09
0.04
0.03
0.21
0.05
318 /
13
SOLAR SYSTEM SMALL BODIES
Table 13.1. (Continued).
No.
375
372
128
6
154
76
130
22
259
776
41
2060
9
120
747
790
566
911
96
194
59
386
54
1437
334
444
241
409
185
11
139
354
804
165
39
89
173
488
536
85
150
238
145
49
117
168
14
51
106
20
1172
137
283
209
361
617
18
211
308
508
895
93
144
196
420
Name
Ursula
Palma
Nemesis
Hebe
Bertha
Freia
Elektra
Kalliope
Aletheia
Berbericia
Daphne
Chirona
Metis
Lachesis
Wmchester
Pretoria
Stereoskopia
Agamemnon
Aegle
Prokne
Elpis
Siegena
Alexandra
Diomedes
Chicago
Gyptis
Germania
Aspasia
Eunike
Parthenope
Juewa
Eleonora
Hispania
Loreley
Laetitia
Julia
Ino
Kreusa
Merapi
10
Nuwa
Hypatia
Adeona
Pales
Lomia
Sibylla
Irene
Nemausa
Dione
Massalia
Aneas
Meliboea
Emma
Dido
Bononia
Patroclus
Melpomene
Isolda
Polyxo
Princetonia
Helio
Minerva
Vibilia
Philomela
Bertholda
Year of
Discovery
D
(kin)
a
e
1893
1893
1872
1847
1875
1862
1873
1852
1886
1914
1856
1977
1848
1872
1913
1912
1905
1919
1868
1879
1860
1894
1858
1937
1892
1899
1884
1895
1878
1850
1874
1893
1915
1876
1856
1866
1877
1902
1904
1865
1875
1884
1875
1857
1871
1876
1851
1858
1868
1852
1930
1874
1889
1879
1893
1906
1852
1879
1891
1903
1918
1867
1875
1879
1896
200
195
194
192
192
190
189
187
185
183
182
180
179
178
178
176
175
175
174
174
173
173
171
171
170
170
169
168
165
162
162
162
161
160
159
159
159
158
158
157
157
156
155
154
154
154
153
153
152
151
151
150
150
149
149
149
148
148
148
147
147
146
146
146
146
3.13
3.14
2.75
2.43
3.18
3.42
3.11
2.91
3.15
2.93
2.76
13.68
2.39
3.12
3.00
3.41
3.39
5.21
3.05
2.62
2.71
2.90
2.71
5.11
3.87
2.77
3.05
2.58
2.74
2.45
2.78
2.80
2.84
3.13
2.77
2.55
2.74
3.14
3.50
2.65
2.98
2.91
2.67
3.08
2.99
3.38
2.59
2.37
3.16
2.41
5.16
3.11
3.04
3.14
3.95
5.23
2.30
3.05
2.75
3.16
3.20
2.75
2.66
3.11
3.41
0.102
0.264
0.126
0.202
0.095
0.169
0.219
0.098
0.112
0.166
0.273
0.380
0.122
0.064
0.343
0.154
0.093
0.068
0.140
0.238
0.117
0.169
0.196
0.046
0.041
0.173
0.103
0.070
0.127
0.100
0.177
0.116
0.138
0.070
0.115
0.181
0.209
0.179
0.090
0.194
0.125
0.089
0.146
0.236
0.023
0.049
0.166
0.065
0.182
0.144
0.104
0.224
0.151
0.067
0.216
0.139
0.218
0.155
0.038
0.023
0.149
0.142
0.233
0.027
0.047
15.9
23.9
6.2
14.8
21.1
2.1
22.9
13.7
10.7
18.2
15.8
6.9
5.6
7.0
18.2
20.6
4.9
21.8
16.0
18.5
8.6
20.3
11.8
20.6
4.7
10.3
5.5
11.2
23.2
4.6
10.9
18.4
15.3
11.2
10.4
16.1
14.2
11.5
19.4
12.0
2.2
12.4
12.6
3.2
14.9
4.6
9.1
10.0
4.6
0.7
16.7
13.4
8.0
7.2
12.7
22.0
10.1
3.9
4.4
13.3
26.1
8.6
4.8
7.3
6.7
P
(h)
11M
(mag)
16.83
6.58
39
7.274
0.0~.17
0.0~.20
9.98
5.225
4.147
0.15-0.2
0.19-0.58
0.04-0.30
7.672
5.988
0.13-0.23
0.16-0.38
5.078
0.04-0.36
9.4
10.37
7
0.12
0.10
0.13
0.16
0.2-0.4
Type
C
BFC
C
S
P
G
M
CP
C
C
B
S
C
PC
P
C
D
T
15.67
13.69
9.763
7.04
18
0.27
0.1
0.11
0.12
0.3~.42
6.214
0.15
9.03
10.83
7.83
41.8
4.277
7.42
7.6
5.138
11.39
5.93
0.10-0.14
6.875
8.14
8.9
8.1
10.42
0.15
0.09
0.12
0.08
0.1~.20
9.35
7.785
0.04-0.1
0.14-0.25
0.07-0.12
0.18
0.12-0.30
0.19
0.12
0.08-0.53
0.10-0.25
0.04-0.11
8.098
0.17-0.27
6.888
8
0.31
0.20
11.57
0.22-0.35
12.03
0.20
5.97
13.81
8.333
0.10
0.13
0.07-0.33
C
CP
C
C
DP
C
C
CP
ex
C
S
CP
S
PC
CD
S
S
C
C
X
FC
CX
C
C
CG
XC
C
S
CU
G
S
D
C
X
C
DP
P
S
C
T
C
FCB
CU
C
S
P
p
0.05
0.04
0.25
0.07
0.02
0.08
0.12
0.03
0.07
0.04
0.04
0.03
0.03
0.04
0.03
0.05
0.04
0.06
0.05
0.02
0.06
0.04
0.06
0.05
0.05
0.15
0.05
0.19
0.04
0.06
0.29
0.16
0.05
0.05
0.04
0.06
0.03
0.03
0.04
0.05
0.04
0.05
0.08
0.08
0.19
0.03
0.04
0.02
0.04
0.03
0.04
0.22
0.05
0.04
0.03
0.02
0.08
0.05
0.18
0.03
H
G
U-B
B-V
7.43
7.33
7.55
5.70
7.09
8.08
6.86
6.50
7.86
7.68
7.16
6.62
6.32
7.73
7.68
8.05
8.15
7.88
7.97
7.66
7.72
7.42
7.70
8.30
7.46
7.85
7.50
7.60
7.73
6.62
7.79
6.32
7.87
7.49
5.94
6.57
7.79
7.83
8.08
7.56
8.32
8.38
8.05
7.91
8.18
7.93
6.27
7.36
7.42
6.52
8.26
8.04
8.73
8.15
8.27
8.17
6.41
7.84
8.18
8.30
8.64
7.47
7.87
6.64
8.35
0.23
0.25
0.15
0.24
0.15
0.44
-0.04
0.22
0.15
0.34
-0.06
0.25
0.29
0.17
0.15
0.15
0.43
0.15
0.15
0.15
0.34
0.68
0.36
0.38
0.68
0.83
0.29
0.47
0.25
0.28
0.39
0.37
0.28
0.51
0.38
0.32
0.30
0.30
0.22
0.34
0.35
0.29
0.40
0.36
0.24
0.36
0.30
0.29
0.34
0.33
0.42
0.29
0.54
0.38
0.31
0.50
0.48
0.32
0.36
0.28
0.28
0.27
0.38
0.36
0.39
0.30
0.38
0.39
0.47
0.47
0.42
0.26
0.33
0.30
0.29
0.19
0.21
0.39
0.36
0.37
0.33
0.70
0.75
0.69
0.67
0.70
0.73
0.70
0.86
0.70
0.71
0.70
0.70
0.77
0.77
0.73
0.67
0.74
0.70
0.70
0.72
0.68
0.69
0.72
0.68
0.85
0.70
0.95
0.71
0.74
0.89
0.88
0.70
0.70
0.69
0.66
0.71
0.73
0.69
0.75
0.68
0.75
0.84
0.77
0.74
0.81
0.73
0.70
0.71
0.69
0.75
0.70
0.85
0.72
0.79
0.73
0.25
0.39
0.46
0.23
0.73
0.72
0.86
0.69
om
0.23
0.15
0.15
-0.06
0.23
0.04
0.28
0.27
0.27
0.15
0.32
0.22
0.15
-0.03
0.14
0.12
0.15
0.15
0.05
0.15
0.51
om
0.39
0.48
0.16
0.09
0.06
0.17
0.26
0.15
0.10
0.15
-0.09
0.15
0.15
0.18
0.03
0.28
0.15
0.15
-0.11
0.08
0.48
0.04
13.1 ASTEROIDS OR MINOR PLANETS / 319
Table 13.1. (Continued).
No.
95
489
69
349
762
Name
Year of
Discovery
Arethusa
Cornacina
Hesperia
Dernbowska
Pulcova
1867
1902
1861
1892
1913
D
(Ian)
145
144
143
143
142
a
3.07
3.16
2.98
2.92
3.16
P
(h)
e
0.144
0.032
0.169
0.091
0.092
12.9
12.9
8.6
8.3
13.0
AM
(mag)
1Ype
8.688
0.24
5.655
4.701
0.20
0.08"'{).47
C
C
M
R
F
p
H
0.06
0.03
0.12
0.34
0.03
7.84
8.36
7.10
5.98
8.58
G
U-8
8-V
0.37
0.36
0.23
0.54
0.31
0.71
0.69
0.70
0.93
0.65
0.08
0.15
0.15
0.33
0.50
Note
a Object 2060 Chiron is known to exhibit cometary activity, e.g., IAUC 4770, and is catalogued as comet 95p.
Reference
I. Binzel, R.P., Gehrels, T., & Matthews, M.S., editors, 1989, Asteroids II Database, in Asteroids II (University of Arizona
Press, Tucson), pp. 997-1190
Table 13.2. Near-eanh asteroids having permanent designations [l_3].a
No.
433
719
887
1036
1221
1566
1580
1620
1627
1685
1862
1863
1864
1865
1866
1915
1916
1917
1943
1980
1981
2059
2061
2062
2063
2100
2101
2102
2135
2201
2202
2212
2329
2340
2368
2608
3102
3103
3122
3199
3200
3271
3288
3352
3360
Name
Eros
Albert
Alinda
Ganyrned
Arnor
Icarus
Betu1ia
Geographos
Ivar
Toro
Apollo
Antinous
Daedalus
Cerberus
Sisyphus
Quetzalcoatl
Boreas
Cuyo
Anteros
Tezcatlipoca
Midas
Baboquivari
Anza
Aten
Bacchus
Ra-Shalorn
Adonis
Tantalus
Aristaeus
01jato
Pele
Hephaistos
Orthos
Hathor
Beltrovata
Seneca
Krok
Eger
Florence
Nefertiti
Phaethon
UI
Seleucus
McAuliffe
Provisional
designation
q
(AU)
a
e
1898 DQ
1911 MT
1918 DB
1924TD
1932 EAl
1949MA
1950KA
1951 RA
1929 SH
19480A
1932 HA
1948 EA
1971 FA
1971 UA
1972XA
1953 EA
1953 RA
1968AA
1973 EC
1950 LA
1973 EA
1963 UA
1960UA
1976AA
1977 HB
1978 RA
1936CA
1975 YA
1977 HA
1947 XC
1972 RA
1978 SB
1976 WA
1976 UA
1977RA
1978DA
1981 QA
1982 BB
1981 ET3
1982RA
1983 TB
1982 RB
1982DV
1981 CW
1981 VA
1.133
1.189
1.087
1.226
1.083
0.187
1.119
0.828
1.124
0.771
0.647
0.891
0.563
0.576
0.873
1.081
1.250
1.066
1.064
1.085
0.622
1.256
1.048
0.790
0.701
0.469
0.441
0.905
0.794
0.626
1.119
0.362
0.820
0.464
1.234
1.044
1.188
0.907
1.021
1.128
0.140
1.271
1.102
1.186
0.633
1.458
2.584
2.486
2.658
1.919
1.078
2.195
1.245
1.863
1.367
1.471
2.260
1.461
1.080
1.893
2.537
2.272
2.150
1.430
1.710
1.776
2.651
2.265
0.967
1.078
0.832
1.874
1.290
1.599
2.174
2.292
2.168
2.402
0.844
2.105
2.491
2.152
1.406
1.769
1.574
1.271
2.102
2.032
1.879
2.465
0.223
0.540
0.563
0.539
0.436
0.827
0.490
0.335
0.397
0.436
0.560
0.606
0.615
0.467
0.539
0.574
0.450
0.504
0.256
0.365
0.650
0.526
0.537
0.183
0.349
0.437
0.765
0.299
0.503
0.712
0.512
0.833
0.659
0.450
0.414
0.581
0.448
0.355
0.423
0.284
0.890
0.395
0.458
0.369
0.743
10.8
10.8
9.3
26.6
11.9
22.9
52.1
13.3
8.4
9.4
6.4
18.4
22.2
16.1
41.2
20.4
12.8
23.9
8.7
26.9
39.8
11.0
3.8
18.9
9.4
15.8
1.4
64.0
23.0
2.5
8.8
11.8
24.4
5.8
5.3
15.3
8.4
20.9
22.2
33.0
22.1
25.0
5.9
4.8
21.7
H
1Ype
11.2
16.0
13.8
9.5
17.7
16.9
14.5
15.6
13.2
14.2
16.3
15.5
14.9
16.8
13.0
19.0
14.9
13.9
15.8
13.9
15.5
15.8
16.6
16.8
17.1
16.1
18.7
16.2
17.9
15.3
17.6
13.9
14.9
19.2
15.2
17.5
15.6
15.4
14.2
14.8
14.6
16.7
15.3
15.8
16.3
S
S
S
S
C
S
S
S
Q
S
SQ
S
S
S
S
S
S
S
TCG
S
C
S?
SG
CSU
SQ
S
QRS
E
S
F
S
D
(Ian)
17
2
5
41
1
2
8
2
7
12
1
2
3
I
10
0.5
3
6
2
13
3
3
3
I
I
4
I
2
I
2
I
5
4
I
3
1
2
3
6
3
5
2
3
3
2
Pi
(109 yr)
Vc
(km/s)
1.5
1.8
0.5
3.8
1.8
4.0
2.8
1.3
1.0
2.5
15.4
30.6
30.6
16.7
14.0
17.2
20.3
19.9
26.0
20.9
1.3
3.5
17.8
13.4
3.8
30.7
1.3
7.1
6.5
6.3
2.8
2.5
2.0
2.3
0.1
0.4
1.8
14.0
14.2
16.0
15.8
17.9
25.4
34.8
21.0
26.4
14.8
34.6
23.3
16.3
3.9
2.1
17.3
17.0
1.4
35.0
1.4
21.0
0.7
26.6
Category
Arnor
Arnor
Arnor
Arnor
Arnor
Apollo
Arnor
Apollo
Arnor
Apollo
Apollo
Apollo
Apollo
Apollo
Apollo
Arnor
Arnor
Arnor
Arnor
Arnor
Apollo
Arnor
Arnor
Aten
, Apollo
Aten
Apollo
Apollo
Apollo
Apollo
Arnor
Apollo
Apollo
Aten
Arnor
Arnor
Arnor
Apollo
Arnor
Arnor
Apollo
Arnor
Arnor
Arnor
Apollo
320 /
13
SOLAR SYSTEM SMALL BODIES
1Bble 13.2. (Continued.)
No.
3361
3362
3551
3552
3553
3554
3671
3691
3752
3753
3757
3838
3908
3988
4015 b
4034
4055
4179
4183
4197
4257
4341
4401
4450
4486
4487
4503
4544
4581
4596
4660
4688
4769
4947
4953
4954
4957
5011
5131
5143
5189
5324
5332
5370
5381
5496
5587
5590
5604
5620
5626
5645
5646
5653
5660
5693
5731
5751
5786
5797
5828
5836
5863
5869
5879
6037
6047
Name
Orpheus
Khufu
Verenia
Don Quixote
Mera
Amun
Dionysus
Camillo
Epona
WilsonHarrington
Magellan
Toutatis
Cuno
Ubasti
Poseidon
Aditi
Pan
Mithra
Pocahontas
Cleobulus
Xanthus
Asclepius
Nereus
Castalia
Ninkasi
Eric
Brucemurray
Ptah
Heracles
Lyapunov
Taranis
Sekhmet
Zeus
Zao
Talos
Bivoj
Tara
Tanith
Provisional
designation
(AU)
a
e
1982HR
1984QA
1983RD
1983 SA
1985 JA
1986EB
1984KD
1982Fr
1985 PA
19861'0
1982XB
1986WA
1980PA
1986 LA
1979 VA
0.819
0.526
1.073
1.209
1.117
0.701
1.003
1.270
0.986
0.484
1.017
0.449
1.043
1.055
1.000
1.209
0.989
2.092
4.233
1.645
0.974
2.196
1.774
1.414
0.998
1.835
1.505
1.926
1.545
2.644
0.323
0.469
0.487
0.714
0.321
0.280
0.543
0.284
0.302
0.515
0.446
0.702
0.459
0.317
0.622
1986PA
1985002
1989AC
1959LM
1982 TA
1987QA
1987KF
1985 TB
1987 SY
1987 SB
1987UA
1989WM
1989 FB
1989 FC
1981 QB
1982 DB
1980WF
1989 PB
1988 TJI
1990MU
1990SQ
1990XJ
6743 P-L
1990BG
1991 VL
1990UQ
1987 SL
1990DA
1986RA
1991IY
1973 NA
1990 SB
1990 VA
1992 FE
19900A
1991 FE
1990SP
1990TR
1992 WD5
1974MA
1993 EA
1988 VP4
1992AC
1991 RC
1980AA
1991 AM
1993 MF
1983 RB
1988 VN4
1992 CHI
1988EG
1991 TBI
0.589
1.226
0.920
0.718
0.523
0.876
0.588
1.117
0.596
0.743
1.217
1.279
0.781
0.657
1.077
0.953
1.081
0.549
1.139
0.555
1.104
1.223
0.818
0.639
0.419
0.810
1.136
1.176
1.228
0.667
0.881
1.080
0.710
0.551
1.247
1.201
0.830
1.205
1.248
0.424
0.527
0.786
1.215
0.187
1.053
0.517
1.143
1.097
1.231
1.154
0.636
0.942
1.060
1.820
2.512
1.980
2.298
1.647
1.835
2.578
1.442
2.200
1.731
2.703
1.042
1.022
2.239
1.490
2.232
1.063
1.370
1.621
2.001
1.565
1.635
1.486
1.835
1.551
2.958
2.163
3.344
0.947
2.433
2.392
0.985
0.927
2.159
2.196
1.355
2.143
1.794
1.786
1.272
2.267
2.104
1.081
1.893
1.698
2.443
2.222
1.812
1.625
1.269
1.454
0.444
0.326
0.634
0.638
0.773
0.468
0.679
0.567
0.586
0.663
0.297
0.527
0.250
0.357
0.519
0.360
0.516
0.483
0.168
0.658
0.448
0.219
0.500
0.570
0.771
0.478
0.616
0.456
0.633
0.296
0.638
0.548
0.279
0.405
0.422
0.453
0.387
0.438
0.304
0.763
0.585
0.653
0.423
0.827
0.444
0.696
0.532
0.506
0.321
0.289
0.499
0.352
q
H
Type
2.7
9.9
9.5
30.8
36.8
23.4
13.6
20.4
55.6
19.8
3.9
29.3
2.2
10.8
2.8
19.0
18.3
16.8
13.0
16.5
15.8
16.3
14.9
15.5
15.1
19.0
15.5
17.4
18.2
16.0
V
11.2
23.2
0.5
6.8
12.2
40.7
11.9
26.7
5.5
3.0
16.4
2.5
14.1
4.9
37.1
1.4
6.4
8.9
15.6
24.4
17.5
35.0
7.4
36.4
9.2
3.6
19.5
25.4
19.0
49.0
68.0
18.1
14.2
4.8
7.8
3.9
13.5
7.9
6.9
38.0
5.1
11.5
16.1
23.3
4.2
30.0
8.0
19.4
17.9
21.6
3.5
23.5
18.1
14.8
15.3
14.4
14.6
16.2
15.5
15.8
17.2
15.6
17.1
15.6
17.1
20.4
16.0
18.2
19.0
16.9
18.7
14.1
12.6
15.1
17.1
14.1
14.0
17.3
15.2
13.9
15.7
16.5
15.3
13.6
19.7
16.4
17.0
14.7
17.0
14.3
15.4
15.7
17.0
15.8
14.8
17.0
19.1
16.3
13.9
15.5
17.0
17.9
18.7
17.0
V
D
M
S
V
CF
V
SQ
S
S
C
S
S
D
(km)
1
1
1
18
2
3
2
4
3
4
0.5
3
1
1
4
1
3
3
5
5
2
3
3
1
3
1
3
1
0.5
2
I
0.5
2
1
6
12
4
I
6
6
1
3
6
5
2
3
7
0.5
2
2
4
2
5
3
3
2
3
4
2
1
2
6
3
2
I
I
2
Pi
(109 yr)
Vc
(kmIs)
21.0
5.3
14.0
19.8
5.4
1.5
17.4
16.0
1.0
3.0
5.1
1.0
4.0
27.0
22.0
13.4
29.0
14.7
0.8
15.5
1.3
1.0
21.3
27.0
1.5
23.3
6.4
5.5
22.2
18.5
6.6
13.3
0.8
22.5
1.1
4.2
15.5
15.4
21.8
13.1
20.9
18.9
0.6
26.5
3.8
0.6
16.7
26.3
5.8
17.2
2.9
0.5
26.7
40.5
5.4
16.5
1.6
4.0
16.4
17.0
0.9
32.0
1.0
20.1
0.3
0.5
13.2
28.0
8.8
18.3
Category
Apollo
Aten
Amor
Amor
Amor
Aten
Amor
Amor
Apollo
Aten
Amor
Apollo
Amor
Amor
Amor
Apollo
Amor
Apollo
Apollo
Apollo
Apollo
Apollo
Amor
Apollo
Apollo
Amor
Amor
Apollo
Apollo
Amor
Apollo
Amor
Apollo
Amor
Apollo
Amor
Amor
Apollo
Apollo
Apollo
Apollo
Amor
Amor
Amor
Aten
Apollo
Amor
Aten
Aten
Amor
Amor
Apollo
Amor
Amor
Apollo
Apollo
Apollo
Amor
Apollo
Amor
Apollo
Amor
Amor
Amor
Amor
Apollo
Apollo
13.2 COMETS / 321
Table 13.2. (Continued.)
No.
6050
6053
6063
6178
6239
6455
6456
6489
6491
6569
6611
7025
7088
7092
7236
7335
7336
7341
7350
7358
7474
7480
7482
7753
7822
7839
7888
7889
7977
8013
8014
8034
8035
8037
Name
Jason
Minos
Golornbek
Golevka
Ishtar
Cadmus
Norwan
Hermesc
Provisional
designation
q
(AU)
a
e
1992AE
1993 BW3
1984KB
1986DA
1989QF
1992 HE
1992 OM
1991 JX
19910A
1993MO
1993 VW
1993 QA
1992AA
1992 LC
1987 PA
1989 JA
1989 RSI
1991 VK
1993 VA
1995 YA3
1992TC
1994 PC
1994 PCl
1988 XB
1991 CS
1994ND
1993 UC
1994 LX
1977 QQ5
I990KA
1990MF
1992LR
1992TB
1993 HOI
1937 UB
1.240
1.010
0.522
1.174
0.676
0.959
1.298
1.011
1.036
1.267
0.873
LOll
1.208
0.744
1.185
0.913
1.195
0.909
0.825
1.095
1.108
1.071
0.905
0.761
0.938
1.047
0.819
0.825
1.189
1.246
0.950
1.082
0.721
1.159
0.618
2.202
2.146
2.216
2.817
1.151
2.241
2.194
2.517
2.508
1.626
1.695
1.476
1.981
2.522
2.717
1.771
2.305
1.842
1.356
2.198
1.566
1.568
1.346
1.468
1.123
2.166
2.436
1.262
2.226
2.198
1.746
1.830
1.342
1.987
1.644
0.437
0.529
0.764
0.583
0.413
0.572
0.409
0.598
0.587
0.221
0.485
0.315
0.390
0.705
0.564
0.484
0.481
0.507
0.391
0.502
0.292
0.317
0.328
0.482
0.165
0.517
0.664
0.346
0.466
0.433
0.456
0.409
0.462
0.417
0.624
H
6.4
21.6
4.8
4.3
3.9
37.4
8.2
2.3
5.5
22.6
8.7
12.6
8.3
17.8
16.4
15.2
7.2
5.4
7.3
4.7
7.1
9.5
33.5
3.1
37.1
27.2
26.0
36.9
25.2
7.6
1.9
2.0
28.3
5.9
6.1
15.4
15.1
15.3
15.1
17.9
13.8
15.9
19.2
18.5
16.5
16.5
18.3
16.7
15.4
18.4
17.0
18.7
16.7
17.3
14.4
18.0
17.2
16.8
18.6
17.4
17.9
15.3
15.3
15.4
16.6
18.7
17.9
17.3
16.6
18.0
Type
S
M
D
(Ian)
3
4
3
4
I
7
3
I
I
2
2
I
2
3
I
2
I
2
I
5
I
I
2
I
1
I
3
3
3
1
0.5
I
I
I
I
Pi
(109 yr)
Vc
(km/s)
1.1
28.8
6.4
17.9
2.8
17.5
6.2
5.0
17.0
22.0
16.6
14.1
2.2
21.7
Category
Arnor
Arnor
Apollo
Arnor
Apollo
Apollo
Arnor
Arnor
Arnor
Arnor
Apollo
Arnor
Arnor
Apollo
Arnor
Apollo
Arnor
Apollo
Apollo
Arnor
Arnor
Arnor
Apollo
Apollo
Apollo
Arnor
Apollo
Apollo
Arnor
Arnor
Apollo
Arnor
Apollo
Arnor
Apollo
Notes
aCollision probabilities are available only for objects discovered prior to mid-1991. These values are presented only
for objects which can evolve into an Earth-intersecting orbit.
bObject 4015 Wilson-Harrington is also catalogued as comet 107P.
CObject Hermes received a permanent name upon discovery, but is currently lost.
References
I. IAU Minor Planet Center web page as of 1998 January 1. hnp:/Icfa.www.harvard.edu/cfa/ps/mpc.html
2. The Spaceguard Survey, Report of the NASA International Near-Earth Object Detection Workshop (1992)
3. T. Oehrels, editor, 1994, Hazards Due to Comets and Asteroids, (University of Arizona Press, Tucson)
13.2
13.2.1
COMETS
Locations and Populations [6,7,2]
The source region for long-period and high-inclination, short-period comets is the Oort cloud.
Estimated distance: 103 to 105 AD.
Estimated number of comets: 1011_1013.
Estimated total mass: 1025 _1027 kg.
The primary source for low-inclination, short-period comets is the Kuiper belt.
Estimated distance: 30 to 1000 AU.
Estimated number of comets: 108_10 12 .
322 /
13
SOLAR SYSTEM SMALL BODIES
Estimated total mass: 1022 _1026 kg.
Total number known as of 1998, January 1: 60.
Short-period comets, defined as orbital period P < 200 yr.
Total number known as of 1998, January 1: 193.
Average number of apparitions per year: 17.
Typical discovery rate per year for new comets: 6.
Mean semimajor axis: a = 5.8 AU.
Mean orbital eccentricity: e = 0.6.
Mean inclination: i = 19 deg.
Long-period comets. defined as orbital period P > 200 yr.
Total number known as of 1998, January 1: 756.
Typical discovery rate per year for new comets: 6.
Estimated semimajor axes: 102-105 AU.
Typical orbital eccentricity: e '" 1.
Inclinations are isotropic.
13.2.2
Magnitudes [6]
A comet's absolute magnitude, Ho. is defined as its integrated V magnitude if it were observed at a
distance r = 1 AU from the Sun, ~ = 1 AU from the Earth. and zero phase angle. At other distances,
a comet's integrated V magnitude can be estimated by
v = Ho + 2.5n log r + 5 log ~.
Typical range for n: 2 to 8.
Average value: n '" 4.
For a body with no coma, tail, or emission: n
= 2.
13.2.3 Physical Properties [6-8]
Nucleus:
Diameter range: 1.0-40 km (Halley = 16 x 8 x 7 km).
Mass range: 10 14_10 19 g (Halley = 10 17_10 18 g).
Density range: 0.1-1.1 g cm-3 (Halley estimates: 0.2 to 1.1 g cm- 3).
Estimated albedo range: 0.01-0.05 (Halley = 0.035).
Typical rotation period: 12 h (Halley = 2.2 and 7.4 days).
Typical dust production rate at 1 AU: 104-106 gls.
Typical gas production rate at 1 AU: 1028 _1030 molecules/so
Gas/dust expansion rate at 1 AU: 0.5 to 1.0 kmls.
Typical dust/gas ratio (by mass): 1.0 to 2.0.
Typical mass loss per apparition: 0.05 to 1.0 percent of total mass.
Estimated composition of ices: H20 (80%), CO (3-7%), C02 (3%), CH30H (1-6%), plus CH3CN,
(H2CO)n, HCN.
Estimated composition of grains: Mg-rich silicates. refractory organics.
13.2 COMETS / 323
Coma:
Typical radius: 104 _105 kIn.
Typical composition: H20, CO, C02, OH, H2CO, CH30H, CH3CN, CN, C2, C3.
Hydrogen cloud:
TYpical radius: 107 kIn.
"TYPical production rate at 1 AU: 1028 _1030 H atoms/so
Ion Tail (TYpe I):
Typical length: 106 _108 kIn.
Direction: anti solar.
Principal species: CO+, H20+,
cot, OH+, H30+.
Dust Tail (Type II):
Typical length: 106 _107 kIn.
Direction: Initially anti solar, becoming curved as dust particles follow independent orbits.
Particle size range: 0.1 to 100 microns.
Typical particle composition: silicates and refractory organics.
13.2.4 Comet Data Tables
Table 13.3 lists short-period comets with more than one apparition, while Table 13.4 lists those with
only one appearance. Table 13.5 gives selected long-period comets. Table 13.6 lists probable cometary
nature objects.
1Bble 13.3. Shorr period comets having more than one blown apparition [1].
Comet Name
2P
107pa
26P
79P
96P
45P
73P
25D
5D
41P
lOP
9P
46P
71P
88P
lID
lOOP
83P
37P
116P
103P
54P
81P
7P
6P
57P
I04P
31P
76P
Enclee
Wilson-Harrington
Grigg-Skjellerup
du Toit-Hartley
Macbho1z
Honda-Mrkos-Pajdusakova
Schwassmann-Wachmann 3
Neujmin2
Brorsen
Tuttle-Giacobini-Kresak
Tempe12
Tempel I
Wntanen
Clark
Howell
Tempel-Swift
Hartley I
Russell I
Forbes
WJ.ld4
Hartley 2
de Vico-Swift
Wild 2
Pons-Wmnecke
d'Arrest
du Toit-Neujmin-Delporte
Kowal 2
Schwassmann-Wachmann 2
West-Kohoutek-lkemura
Perihelion Orbital
Longitude
Orbital
Apehelion
date
period Perihelion
Orbital
Longitude
(Year)
(AU)
(AU)
(yrs)
eccentricity of perihelion ofasc. node inclination
1994.1
1992.6
1992.6
1987.4
1991.6
1990.7
1990.4
1927.0
1879.2
1990.1
1994.2
1994.5
1991.7
1989.9
1993.2
1908.8
1991.4
1985.5
1993.2
1996.7
1991.7
1965.3
1991.0
1989.6
1989.1
1989.8
1991.8
1994.1
1994.0
3.28
4.29
5.10
5.21
5.24
5.30
5.35
5.43
5.46
5.46
5.48
5.50
5.50
5.51
5.58
5.68
6.02
6.10
6.13
6.16
6.26
6.31
6.37
6.38
6.39
6.39
6.39
6.39
6.41
0.33
1.00
1.00
1.20
0.13
0.54
0.94
1.34
0.59
1.07
1.48
1.49
1.08
1.56
1.41
1.15
1.82
1.61
1.45
1.99
0.95
1.62
1.58
1.26
1.29
1.72
1.50
2.07
1.58
0.850
0.623
0.664
MOl
0.958
0.822
0.694
0.567
0.810
0.656
0.522
0.520
0.652
0.501
0.552
0.638
0.451
0.517
0.568
0.408
0.719
0.524
0.541
0.634
0.625
0.502
0.564
0.399
0.543
186.3
90.9
359.3
251.6
14.5
325.8
198.8
193.7
14.9
61.6
194.9
178.9
356.2
209.0
234.8
113.4
178.8
0.4
310.5
170.8
174.9
325.4
41.6
172.3
177.1
115.3
189.5
358.2
360.0
334.7
271.1
213.3
309.3
94.5
89.3
69.9
328.7
103.0
141.6
118.2
69.0
82.3
59.7
57.7
291.8
38.9
230.8
334.5
22.1
226.8
25.1
136.2
93.4
139.5
189.1
247.8
126.2
84.2
11.9
2.8
21.1
2.9
60.1
4.2
11.4
10.6
29.4
9.2
12.0
10.6
11.7
9.5
4.4
5.4
25.7
22.7
7.2
3.7
9.3
3.6
3.2
22.3
19.4
2.8
15.8
3.8
30.5
4.09
4.29
4.93
4.81
5.91
5.54
5.18
4.84
5.61
5.14
4.73
4.73
5.15
4.68
4.88
5.22
4.80
5.06
5.25
4.73
5.84
5.21
5.30
5.62
5.59
5.17
5.38
4.82
5.33
324 /
13
SOLAR SYSTEM SMALL BODIES
Table 13.3. (Continued.)
Comet Name
105P
22P
43P
87P
114P
94P
67P
21P
3D
44P
112P
75P
62P
18P
51P
49P
60P
65P
1I0P
19P
16P
86P
15P
84P
48P
69P
77P
33P
17P
113P
98P
108P
100P
102P
30P
4P
89P
47P
61P
91P
52P
97P
70P
39P
78P
50P
83P
80P
II1P
24P
14P
58P
36P
74P
115P
32P
59P
72P
93P
64P
42P
40P
68P
34P
85P
56P
53P
Singer Brewster
Kopff
Wolf-Harrington
Bus
Wiseman-Skiff
Russell 4
Churyumov-Gerasimenko
Giacobini-Zinner
Biela
Reinmuth2
Urata-Niijima
Kohoutek
Tsuchinshan 1
Perrin~Mrkos
Harrington
Arend-Rigaux
Tsuchlnshan 2
Gunn
Hartley 3
Borrelly
Brooks 2
Wild 3
Finlay
Giclas
Johnson
Taylor
Longmore
Daniel
Holmes
Spitaler
Takamizawa
Ciffreo
Schuster
Shoemaker 1
Reinmuth 1
Faye
Russell 2
Ashbrook-Jackson
Shajn-Schaldach
Russell 3
Harrington-Abell
Metcalf-Brewington
Kojima
Oterma
Gehrels 2
Arend
Gehrels 3
Peters-Hartley
Helin-Roman-Crockett
Schaumasse
Wolf
Jackson-Neujmin
Whipple
Smimova-Chemykh
Maury
Comas Sola
Keams-Kwee
Denning-Fujikawa
Lovas 1
Swift-Gehrels
Neujmin 3
Vaisala 1
Klemola
Gale
Boethin
Slaughter-Burnham
Van Biesbroeck
Perihelion Orbital
Orbital
Apehelion
Longitude
date
period Perihelion
Orbital
Longitude
(AU)
(AU)
(yrs)
eccentricity of perihelion ofasc. node inclination
(Year)
1992.8
1990.1
1991.3
1994.5
1993.4
1990.5
1989.5
1992.3
1852.7
1994.5
1993.5
1987.8
1991.7
1968.8
1994.6
1991.8
1992.4
1989.7
1994.4
1988.0
1994.7
1994.6
1988.4
1992.7
1990.9
1991.0
1988.8
1992.7
1993.3
1994.1
1991.6
1993.1
1992.7
1992.0
1988.4
1991.9
1994.8
1993.5
1993.9
1990.4
1991.5
1991.0
1994.1
1958.4
1989.8
1991.4
1993.6
1990.5
1996.8
1993.2
1992.7
1987.4
1995.0
1992.6
1994.2
1987.6
1990.9
1978.8
1989.8
1991.2
1993.9
1993.3
1987.6
1938.5
1986.0
1993.5
1991.3
6.43
6.46
6.51
6.52
6.53
6.57
6.59
6.61
6.62
6.64
6.64
6.65
6.65
6.72
6.78
6.82
6.82
6.84
6.84
6.86
6.89
6.91
6.95
6.96
6.97
6.97
7.00
7.06
7.09
7.10
7.22
7.23
7.26
7.26
7.29
7.34
7.38
7.49
7.49
7.50
7.59
7.76
7.85
7.88
7.94
7.99
8.11
8.13
8.16
8.22
8.25
8.42
8.53
8.57
8.74
8.78
8.96
9.01
9.09
9.21
10.6
10.8
10.9
11.0
11.2
11.6
12.4
2.03
1.59
1.61
2.18
1.51
2.22
1.30
1.03
0.86
1.89
1.46
1.78
1.50
1.27
1.57
1.44
1.78
2.47
2.46
1.36
1.84
2.30
1.09
1.85
2.31
1.95
2.41
1.65
2.18
2.13
1.59
1.71
1.54
1.99
1.87
1.59
2.28
2.32
2.35
2.52
1.77
1.59
2.40
3.39
2.35
1.85
3.43
1.63
3.49
1.20
2.43
1.44
3.09
3.57
2.03
1.83
2.22
0.78
1.68
1.36
2.00
1.78
1.77
1.18
1.11
2.54
2.40
0.414
0.543
0.539
0.375
0.568
0.366
0.630
0.706
0.756
0.464
0.588
0.498
0.576
0.643
0.561
0.600
0.504
0.314
0.317
0.624
0.491
0.366
0.699
0.493
0.366
0.466
0.341
0.552
0.410
0.422
0.575
0.543
0.590
0.470
0.503
0.578
Q.400
0.395
0.388
0.343
0.540
0.594
0.393
0.144
0.410
0.537
0.151
0.598
0.139
0.705
0.406
0.653
0.259
0.147
0.522
0.570
0.487
0.820
0.614
0.692
0.586
0.635
0.640
0.761
0.778
0.504
0.553
46.6
162.9
187.0
24.4
171.9
93.0
11.4
172.5
223.2
45.9
21.5
175.7
22.8
166.0
233.5
329.1
203.1
197.0
168.4
353.3
198.0
179.3
322.3
276.5
208.3
355.6
195.7
11.0
23.2
50.2
147.7
358.0
355.7
18.8
13.1
203.9
249.2
348.7
216.6
353.2
138.7
208.0
348.5
354.9
183.5
47.1
231.6
338.3
10.2
57.5
162.3
196.6
201.9
89.0
119.8
45.5
131.8
334.1
73.6
84.8
147.0
47.4
154.5
209.2
11.7
44.1
134.2
192.6
120.9
254.9
182.2
271.7
71.0
51.0
195.4
248.0
296.2
31.9
269.7
96.8
240.9
119.3
122.1
288.3
68.5
287.9
75.4
176.9
72.6
42.4
112.5
117.3
108.9
15.7
69.1
328.0
14.5
124.9
53.7
50.6
340.0
119.8
199.6
42.5
2.7
166.9
248.7
337.3
187.8
154.8
155.8
216.3
356.2
243.3
260.1
92.0
81.1
204.1
163.8
182.5
77.5
176.8
61.1
315.8
41.6
342.4
314.4
150.4
135.1
176.5
67.9
26.5
346.4
149.1
9.2
4.7
18.5
2.6
18.2
6.2
7.1
31.8
12.5
7.0
24.2
5.9
10.5
17.8
8.7
17.9
6.7
10.4
11.7
30.3
5.5
15.5
3.7
7.3
13.7
20.6
24.4
20.1
19.2
5.8
9.5
13.1
20.1
26.2
8.1
9.1
12.0
12.5
6.1
14.1
10.2
13.0
0.9
4.0
6.7
19.9
1.1
29.8
4.2
11.8
27.5
14.1
9.9
6.6
11.7
13.0
9.0
8.7
12.2
9.3
4.0
11.6
10.9
11.7
5.8
8.2
6.6
4.89
5.35
5.37
4.80
5.47
4.79
5.73
6.01
6.19
5.17
5.61
5.30
5.57
5.85
5.59
5.75
5.41
4.74
4.75
5.86
5.40
4.96
6.19
5.44
4.98
5.35
4.91
5.71
5.21
5.25
5.88
5.77
5.96
5.51
5.65
5.96
5.31
5.34
5.31
5.15
5.95
6.25
5.50
4.53
5.61
6.14
4.64
6.46
4.61
6.94
5.74
6.84
5.25
4.81
6.46
6.68
6.42
7.88
7.03
7.43
7.67
7.98
8.09
8.70
8.91
7.70
8.33
13.2 COMETS I 325
Table 13.3. (Continued.)
Perihelion Orbital
Orbital
date
period Perihelion
Longimde
LongibJde
Apebelion
Orbital
(AU)
(Year)
(yn)
(AU)
eccentricity ofperibelion ofasc. node inclination
Comet Name
92P
63P
8P
IOIP
29P
66P
99P
90P
28P
27P
55P
38P
95pb
20D
13P
23P
121P
IP
100P
35P
Sanguin
Wild I
Thttle
Cbemykh
Schwassmann-Wachmann I
du Toit
Kowall
Gehrels 1
Ncujmin 1
Crommelin
Tempel-Thttle
Stephan-Oterma
Chiron
Westphal
Olbers
Brorsen-Metcalf
Pons-Brooks
Halley
Swift-Thttle
Herscbel-Rigollet
1990.2
1973.5
1994.5
1992.1
1989.8
1974.2
1992.2
1987.6
1984.8
1984.1
1965.3
1980.9
1996.1
1913.9
1956.5
1989.7
1954.4
1986.1
1993.0
1939.6
12.5
13.3
13.5
14.0
14.9
15.0
15.0
15.1
18.2
27.4
32.9
37.7
50.7
61.9
69.6
70.5
70.9
76.0
135.
155.
1.81
1.98
1.00
2.36
5.77
1.29
4.67
2.99
1.55
0.74
0.98
1.57
8.45
1.25
U8
0.48
0.77
0.59
0.96
0.75
0.663
0.647
0.824
0.594
0.045
0.787
0.233
0.510
0.776
0.919
0.904
0.860
0.383
0.920
0.930
0.972
0.955
0.967
0.964
0.974
162.8
167.9
206.7
263.2
49.9
257.2
174.5
28.5
346.8
195.8
172.6
358.2
339.6
57.1
64.6
129.6
199.0
1l1.9
153.0
29.3
182.5
358.9
270.5
130.4
312.8
22.8
28.8
13.6
347.0
250.9
235.1
79.2
209.4
348.0
86.1
311.6
255.9
58.9
139.4
356.0
18.7
19.9
54.7
5.1
9.4
18.7
4.4
9.6
14.2
29.1
162.7
18.0
6.9
40.9
44.6
19.3
74.2
162.2
113.4
64.2
8.96
9.24
10.3
9.24
6.31
10.9
7.50
9.21
12.3
17.4
19.6
20.9
19.0
30.0
32.6
33.7
33.5
35.3
51.7
56.9
Notes
aObject 107P, Wilson-Harrington is also catalogued as minor planet 4015.
bObject 95P, Chiron is also catalogued as minor planet 2060.
Reference
1. Marsden, B.G., & Williams, G.V. 1995, Catalogue of Cometary Orbits, 10th ed., IAU Central Bureau for Astronomical
Telegrams and Minor Planet Center
Table 13.4. Short-period comets hoving one known apparition [l].
Comet
Name
D/1766Gl
D/1819 WI
P/I994 PI
D/1884 OJ
D/1886 Kl
P/I991 R2
DlI770Ll
PIl991 Fl
D/1783 WI
D/1978 Rl
P/I990R2
D/1978 C2
D/1952 Bl
P/I991 C2
Helfenzrieder
Blanpain
Machho1z2
Barnard 1
Brooks 1
Spacewatch
Lexell
Mrkos
Pigott
Haneda-Campos
DlI892Tl
P/I990Rl
D/1896R2
D/1918Wl
P/I991 SI
P/I991 V2
PIl986 WI
D/1895 Ql
PIl991 CI
Dl1984 HI
P/I994 Al
P/I993 Xl
D/1894Fl
PIl992 G2
DlI977 CI
PIl991 VI
Holt~lmstead
Tritton
Harrington-Wilson
Shoemaker-Levy 4
Barnard 3
Mueller 2
Giacobini
Schorr
McNaught-Hughes
Shoemaker-Levy 7
Lovas 2
Swift
Shoemaker-Levy 3
Kowal-Mriros
Kushida
Kushida-Muramatsu
Denning
Shoemaker-Levy 8
SldlJ-Kosai
Shoemaker-Levy 6
Peribelion
date
(Year)
Orbital
period
(yrs)
1766.3
1819.9
1994.7
1884.6
1886.4
1991.0
1770.6
1991.2
1783.9
1978.8
1990.8
1971.8
1951.8
1990.5
1892.9
1990.9
1896.8
1918.8
1991.4
1991.8
1986.7
1895.6
1990.9
1984.4
1994.0
1993.9
1894.1
1992.5
1976.6
1991.8
4.35
5.10
5.23
5.38
5.44
5.59
5.60
5.64
5.89
5.97
6.16
6.35
6.36
6.51
6.52
6.56
6.65
6.67
6.70
6.72
6.7S
7.20
7.25
7.32
7.36
7.40
7.42
7.47
7.54
7.57
Perihelion
(AU)
Orbital
eccentricity
0.41
0.89
0.75
1.28
1.33
1.54
0.67
1.41
1.46
UO
2.04
1.44
1.66
2.02
1.43
2.08
1.46
1.88
2.12
1.63
1.46
1.30
2.81
1.95
1.37
2.75
U5
2.71
2.85
U3
0.848
0.699
0.750
0.583
0.571
0.511
0.786
0.555
0.552
0.665
0.392
0.580
0.515
0.421
0.590
0.406
0.588
0.469
0.404
0.542
0.592
0.652
0.250
0.483
0.639
0.277
0.698
0.291
0.259
0.706
LongibJde
of perihelion
178.7
350.3
149.3
30U
176.9
87.1
225.0
18G.4
354.7
240.5
2.6
147.7
343.0
302.2
170.0
171.0
140.5
279.3
223.2
91.7
71.3
167.8
181.7
338.0
214.5
348.3
46.4
22.4
26.6
333.1
LongibJde
ofasc. node
76.3
79.8
246.2
6.8
55.1
153.4
134.5
1.7
58.7
132.2
15.3
300.8
128.5
152.1
208.0
218.9
194.9
119.0
90.2
313.0
283.8
171.8
303.8
249.3
245.9
93.7
85.7
213.4
80.8
37.9
Orbital
inclination
7.9
9.1
12.8
5.5
12.7
10.0
1.6
31.5
45.1
5.9
14.9
7.0
16.3
8.5
31.3
7.1
1l.4
5.6
7.3
10.3
1.5
3.0
5.0
3.0
4.2
2.4
5.5
6.1
3.2
16.9
Aphelion
(AU)
4.92
5.03
5.27
4.86
4.86
4.76
5.63
4.92
5.06
5.48
4.68
5.42
5.20
4.95
5.55
4.93
5.62
5.21
4.99
5.49
5.69
6.16
4.68
5.59
6.20
4.85
6.46
4.93
4.84
6.58
326 /
13
SOLAR SYSTEM SMALL BODIES
Table 13.4. (Continued.)
Comet
Name
P/1989 E3
West-Hartley
Shoemaker 2
Shoemaker-Holt 2
Helin-Roman-Alu 2
Mueller I
Mueller 3
Shoemaker-Levy 5
Parker-Hartley
Mueller 4
Shoemaker-Levy 2
Helin-Lawrence
Helin-Roman-Alu 1
Shoemaker-Holt I
Brewington
Ge-Wang
IRAS
Mueller 5
Helin
Shoemaker 4
van Houlen
Bowell-Skiff
Kowal-Vavrova
Shoemaker 3
Shoemaker-Levy 1
Shoemaker-Levy 9
McNaught-Russell
McNaught-Hartley
Hartley-IRAS
Levy
Pons-Gambart
Dubiago
de Vico
Bradfield 2
Vaisala 2
Bamard2
Mellish
Bradfield I
Wilk
0/1984 WI
P/1989 E2
PI1989 Ul
P/1987 U2
P/1990 SI
P/I991 Tl
P/1989 EI
P/I992 G3
P/1990 UL3
P/I993 K2
P/1989 T2
P/1987 Ul
P/1992 QI
PI1988 VI
P/1983 M1
P/I993 WI
P/1987 G3
P/I99413
0/1960 SI
P/1983 C1
P/198313
PI1986 Al
P/I990 VI
0/1993 F2
PI1994 Xl
P/I994N2
PI1983 VI
P/1991 L3
0/1827 M1
0/1921 HI
0/1846 Dl
0/1989 A3
0/1942EA
0/1889 MI
0/1917FI
0/1984 Al
0/193701
Perihelion Orbital
Orbital
Longitude
date
period Perihelion
Orbital
Longitude
(yrs)
(AU)
(Year)
eccentricity of perihelion ofasc. node inclination
1988.8
1984.7
1988.6
1989.8
1987.9
1990.6
1991.9
1987.6
1992.1
1990.7
1993.5
1987.8
1988.4
1992.4
1988.4
1983.6
1994.7
1987.6
1994.8
1961.3
1983.2
1983.2
1986.0
1990.7
1994.2
1994.7
1994.9
1984.0
1991.5
1827.4
1921.3
1846.2
1988.9
1942.1
1889.5
1917.3
1984.0
1937.1
7.59
7.84
8.01
8.19
8.45
8.65
8.66
8.85
8.97
9.28
9.45
9.50
9.55
10.7
11.3
13.2
13.8
14.5
14.6
15.6
15.7
15.9
16.9
17.3
17.7
18.4
20.8
21.5
51.3
57.5
62.3
76.3
81.9
85.4
145.
145.
151.
187.
2.13
1.32
2.65
1.93
2.75
3.00
1.98
3.03
2.64
1.84
3.09
3.71
3.05
1.60
2.52
1.70
4.25
2.57
2.94
3.96
1.95
2.61
1.79
1.52
5.38
1.28
2.49
1.28
0.98
0.81
1.12
0.66
0.42
1.29
1.11
0.19
1.36
0.62
0.449
0.666
0.339
0.525
0.338
0.288
0.529
0.292
0.389
0.582
0.309
0.174
0.322
0.671
0.501
0.696
0.261
0.567
0.507
0.367
0.689
0.588
0.728
0.772
0.207
0.817
0.671
0.834
0.929
0.946
0.929
0.963
0.978
0.934
0.960
0.993
0.952
0.981
46.8
55.5
99.8
203.0
4.6
138.0
29.7
244.3
145.4
236.0
92.0
73.5
214.6
343.7
180.5
357.9
100.7
143.7
92.9
23.6
346.3
202.6
97.3
52.0
220.9
218.0
36.0
1.5
329.4
320.0
67.2
79.7
28.4
172.3
272.6
88.7
356.9
58.3
102.7
317.6
5.9
200.7
30.3
226.0
6.0
181.3
43.6
140.1
163.7
216.3
210.4
47.8
176.1
356.9
30.0
216.3
192.2
14.4
169.0
19.5
14.9
310.6
355.0
171.1
312.2
47.1
41.5
19.2
97.4
12.9
194.7
335.2
60.2
121.3
219.2
31.5
15.4
21.6
17.7
7.4
8.8
9.4
ll.8
5.2
29.8
4.6
9.9
9.8
4.4
18.1
11.7
46.2
16.5
4.7
24.8
6.7
3.8
4.3
6.4
24.3
5.8
29.1
17.6
95.7
19.2
136.5
22.3
85.1
83.1
38.0
31.2
32.7
51.8
26.0
Aphelion
(AU)
5.59
6.57
5.36
6.19
5.55
5.43
6.45
5.53
6.00
6.99
5.85
5.27
5.95
8.12
7.58
9.45
7.24
9.30
8.99
8.54
10.6
10.1
11.4
ll.8
8.20
12.70
12.60
14.2
26.6
29.0
30.3
35.3
37.3
37.5
54.2
55.1
55.5
64.9
Reference
1. Marsden, B.G., & Williams, G.V. 1995, Catalogue of Cometary Orbits, 10th ed., IAU Central Bureau for Astronomical
Telegrams and Minor Planet Center
Table 13.5. Selected long-period comets [1, 2].
Comet
Name
Designation
Discovery date
(Year)
Perihelion
(AU)
Orbital
eccentricity
Orbital
inclination
C/1843 Dl
C/1858 Ll
C/1882 RI
C/1908 Rl
C/1956 Rl
C/1965 SI
C/1969 Yl
C/1973 El
Great March Comet of 1843
Donati
Great September Comet of 1882
Morehouse
Arend-Roland
Ikeya-Seki
Bennett
Kohoutek
West
Bowell
lRAS-Araki-Alcock
Levy
1843 I
1858 VI
1882ll
1908m
1957m
1965vm
1970ll
1973 xn
1976 VI
1982 I
1983 Vll
1987 XXX
1843
1858
1882
1908
1956
1965
1970
1973
1976
1980
1983
1988
0.005
0.58
0.008
0.95
0.32
0.008
0.54
0.14
0.20
3.36
0.99
1.17
1.000
0.996
1.000
1.001
1.000
1.000
0.996
1.000
1.000
1.057
0.990
0.998
144.3
117.0
142.0
140.2
119.9
141.9
90.0
14.3
43.1
1.7
73.3
62.8
CI1975 VI
C/1980 El
C/1983 HI
C/1988 Fl
13.2 COMETS / 327
Table 13.5. (ContinuetL)
Discovery date
Comet
Cl198811
C/1990 Kl
ClI991 C3
C/I992J2
ClI995 01
ClI996B2
Name
Designation
Shoemaker-Holt
1988m
1990 XX
1990 XIX
1992 XIII
Levy
McNaught-Russell
Bradfield
Hale-Bopp
Hyakutake
(Year)
Perihelion
(AU)
Orbital
eccentricity
Orbital
inclination
1988
1990
1991
1992
1995
1996
1.17
0.94
4.78
0.59
0.91
0.23
0.998
1.000
1.002
1.000
0.996
1.0
62.8
131.6
113.4
158.6
89.4
124.9
References
1. Marsden. B.G .• & Williams. G.V. 1995. Catalogue of Cometary Orbits. 10th ed .• lAU Central Bureau for Astronomical
Telegrams and Minor Planets
2. Beatty. 1.K.. & Chaikin. A.• editors. 1990. in The New Solar System (Sky Publishing. Cambridge). p. 292
Table 13.6. Outer solar system objects of probable cometary nature. a,b,c
Provisional
designation
Perihelion
(AU)
Aphelion
(AU)
a
e
1977 VB
1992 AD
1993 HA2
1994TA
19950W2
1995 GO
1997CU26
8.45
8.67
1l.8
11.7
18.9
6.84
13.1
18.8
31.8
37.4
22.0
31.0
29.3
18.4
13.648
20.226
24.594
16.843
24.916
18.069
15.712
0.381
0.571
0.519
0.304
0.243
0.622
0.169
6.9
24.7
15.7
5.4
4.2
17.6
23.4
6.5
7.0
9.6
11.5
9.0
9.0
6.0
180
150
75
25
100
100
300
Trans-Neptunian Objects
1992 QBI
1993FW
1993RO
1993 RP
1993 SB
1993 SC
1994 ES2
1994EV3
1994GV9
1994JQl
1994JRl
1994JS
1994N
1994TB
1994TG
1994TG2
1994TH
1994 VK8
19950A2
19950B2
1995DC2
1995 FB21
1995GA7
1995 GJ
1995 GY7
1995 HM5
1995 KII
1995 KKI
40.9
41.5
31.5
34.9
26.9
32.3
40.3
40.8
41.0
41.8
34.8
33.0
35.3
27.1
42.3
42.4
40.9
41.7
33.7
40.1
40.8
42.4
34.8
39.0
41.3
29.5
43.5
32.0
47.7
45.5
47.7
43.8
52.4
47.5
50.8
44.7
46.0
46.1
44.1
51.6
35.3
52.6
42.3
42.4
40.9
44.0
38.7
52.5
46.9
42.4
44.2
46.8
41.3
49.3
43.5
47.0
44.298
43.522
39.608
39.329
39.633
39.880
45.530
42.763
43.495
43.959
39.434
42.289
35.251
39.845
42.254
42.448
40.940
42.830
36.181
46.290
43.850
42.426
39.455
42.907
41.347
39.369
43.468
39.475
0.077
0.045
0.205
0.1l4
0.321
0.191
0.1l5
0.046
0.058
0.049
0.1l9
0.219
0
0.321
0
0
0
0.027
0.069
0.134
0.070
0
0.1l9
0.091
0
0.251
0
0.190
2.2
7.8
3.7
2.6
1.9
5.1
1.1
1.7
0.6
3.8
3.8
14.1
18.1
12.1
6.8
2.2
16.1
1.5
6.6
4.1
2.3
0.7
3.5
22.9
0.9
4.8
2.7
9.3
7.0
7.0
8.0
9.0
8.0
7.0
7.5
7.0
7.0
7.0
7.5
8.0
7.0
7.0
7.0
7.0
7.0
6.5
8.0
7.5
7.0
7.5
7.5
7.0
7.5
8.0
6.5
8.5
250
250
150
100
150
250
200
250
250
250
200
150
250
250
250
250
250
300
150
200
250
200
200
250
200
150
300
125
Number
Centaurs
2060
5145
7066
Name
Chiron
Pholus
Nessus
H
D
(kIn)
328 I
13
SOLAR SYSTEM SMALL BODIES
Table 13.6. (ContinuetL)
Number
Name
Provisional
designation
Perihelion
(AU)
Aphelion
(AU)
a
e
1995QY9
1995 QZ9
1995WY2
1995 YY3
1996KVl
1996 KWl
1996KXl
1996KYl
1996RQ20
1996RR20
1996 SZ4
1996TK66
1996TL66
1996T066
1996TP66
1996TQ66
1996TR66
1996TS66
1997CQ29
1997CR29
1997CS29
1997CT29
1997CU29
1997CV29
1997CW29
1997QH4
1997 QJ4
1997 RT5
1997RX9
1997RY6
1997 SZ10
1997TX8
29.2
33.7
40.6
30.7
41.2
46.6
35.7
35.7
39.2
32.8
29.6
42.9
35.1
38.1
26.4
34.6
33.2
38.5
41.2
42.0
43.4
42.3
41.9
40.0
36.3
41.3
34.8
42.2
42.1
41.4
31.6
32.0
51.0
45.8
52.3
48.1
44.7
46.6
43.4
43.3
49.4
47.1
50.1
43.2
134.0
49.3
53.0
44.7
52.1
49.7
47.7
42.0
44.0
44.9
44.8
48.5
42.5
47.4
44.3
42.2
42.1
41.4
47.6
46.6
40.115
39.769
46.432
39.389
42.966
46.602
39.543
39.517
44.291
39.936
39.817
43.035
84.457
43.700
39.703
39.667
42.636
44.100
44.412
41.996
43.703
43.580
43.331
44.227
39.375
44.359
39.568
42.239
42.135
41.360
39.584
39.312
0.271
0.153
0.126
0.221
0.041
0
0.097
0.096
0.115
0.180
0.257
0.004
0.585
0.128
0.335
0.127
0.222
0.126
0.073
0
0.006
0.030
0.034
0.096
0.079
0.070
0.121
0
0
0
0.201
0.186
D
H
4.8
19.5
1.7
0.4
8.4
5.5
1.5
30.9
31.6
5.3
4.7
3.3
24.0
27.3
5.7
14.6
12.3
7.4
2.9
20.2
2.3
1.0
1.5
7.8
19.0
12.8
16.0
12.6
29.8
12.4
12.7
9.0
7.5
7.5
7.0
8.5
7.0
7.0
8.5
8.0
7.0
7.0
8.0
7.0
5.0
4.5
6.5
6.5
7.5
6.0
6.5
6.5
5.0
5.0
6.5
7.0
6.5
7.0
7.5
7.0
8.0
7.5
8.5
8.5
(kIn)
200
200
250
125
250
250
125
150
250
250
150
250
600
750
300
300
200
400
300
300
600
600
300
250
300
250
200
250
150
200
125
125
Notes
alAU Minor Planet Center web page as of 1998, January 1. URL http://cfa.www.harvard.edU/cfaJpsfmpc.html.
bPor explanation of symbols, see section on Minor Planets.
CObject 2060 Chiron is known to exhibit cometary activity, e.g., IAUC 4770 and is catalogued as comet 95P.
13.3
ZODIACAL LIGHT
The zodiacal light is due to sunlight scattered by the interplanetary dust cloud. Zodiacal light brightness
is a function of viewing direction, wavelength, heliocentric distance (r) and position of the observer
relative to the dust symmetry plane. The brightness does not vary with the solar cycle [9,10]. A
comprehensive review is given in [11].
Table 13.7 presents the surface brightness (radiance) and degree of linear polarization of the
zodiacal light at ),,5000 A for an observer at r = 1 AU in the dust symmetry plane as a function of
helioecliptic longitude ()., - ).,0) and latitude (fJ) [11-15].
13.3 ZODIACAL
LIGHT
Table 13.7. Zodiacal light brightness and polarization.
IW)
15
20
25
30
45
60
75
0
2450
.08
1260
.10
770
.11
500
.12
215
.16
117
.19
78
.20
5
2300
.09
1200
.10
740
.11
490
.12
212
.16
117
.19
78
.20
3700
.11
1930
.11
1070
.12
675
.13
460
.14
206
.17
116
.19
78
.20
).. - )..0(°)
0
5
10
15
10
.13
5300
.13
2690
.13
1450
.13
870
.13
590
.14
410
.15
196
.17
114
.19
78
.20
20
5000
.14
3500
.14
1880
.14
1100
.15
710
.15
495
.15
355
.15
185
.17
110
.19
77
.20
25
3000
.15
2210
.15
1350
.16
860
.16
585
.16
425
.16
320
.16
174
.18
106
.19
76
.20
30
1940
.16
1460
.16
955
.16
660
.16
480
.16
365
.17
285
.17
162
.18
102
.19
74
.20
35
1290
.17
990
710
.17
530
.17
400
.17
.17
310
.17
250
.17
151
.18
98
.20
73
.20
925
.17
735
.17
545
.17
415
.17
325
.18
264
.18
220
.18
140
.19
94
.20
.20
45
710
.18
570
.18
435
.18
345
.18
278
.18
228
.18
195
.18
130
.19
91
.20
70
.20
60
395
.19
345
.19
275
.19
228
.19
190
.19
163
.20
143
.20
105
.20
81
.20
67
.20
75
264
.18
248
.18
210
.18
177
.18
153
.18
134
.19
118
.19
91
.19
73
.19
64
.19
90
202
.16
196
.16
176
.16
151
.16
130
.16
115
.16
103
.17
81
.18
67
.18
62
.19
105
166
.12
164
.12
154
.12
133
.12
117
.13
104
.13
93
.14
75
.15
64
.17
60
.19
120
147
.08
145
.08
138
.09
120
.09
108
.09
98
.10
88
.11
70
.13
60
.15
58
.18
135
140
.05
139
.05
130
.05
115
.06
105
.06
95
.07
86
.08
70
.11
60
.14
57
.17
150
140
.02
139
.02
129
.02
116
.03
107
.03
99
.04
91
.05
75
.08
62
.12
56
.16
165
153
-.02
150
-.02
140
-.01
129
-.01
118
0
110
.02
102
.03
81
.07
64
.11
56
.16
180
180
0
166
-.02
152
-.03
139
-.02
127
-.01
116
0
105
.02
82
.06
65
.11
56
.16
40
9000
72
I 329
330 I 13
SOLAR SYSTEM SMALL BODIES
The brightness is given in SIO (V), the equivalent number of tenth visual magnitude solar-type stars
per square degree. One SIO (V) = 1.26 x 10-8 W m- 2 sr- 1 Jl,m- 1 at 5000 A. The uncertainty in
brightness and polarization is 10% in the bright regions, to 20% in the faint regions. Negative values
mean that the direction of polarization lies in the scattering plane. The brightness at the ecliptic pole
({3 = 90°) is 60 SIO (V) and the degree of linear polarization is 0.19 [11, 12].
The component of the solar corona due to scattering by interplanetary dust is known as the F corona.
The brightness of the solar F corona in SIO (V) is given in Table 13.8 as a function of elongation
(E) [16, 17], for the line of sight in the ecliptic plane (i = 0°) and line of sight in a plane perpendicular
to the ecliptic plane (i = 90°).
Table 13.8. Brightness a/the solar F corona.
5
3.9 x 106
8.6 x loS
1.2 x loS
10
2.4 x 104
2.6 x 106
4.3 x loS
4.8 x 104
8300
UBV colors of the zodiacal light are given by [15]
Iv
IB
= 1.14 -
4
5.5 x 10-
E,
18
-
lu
= 1.11-5.0 x 10
-4
E,
where E ~ solar elongation in degrees. An intensity ratio of 1.0 corresponds to solar color.
The dependence of intensity on heliocentric distance for an observer at r AU (0.3 ::: r ::: 1.0) as
measured from the Helios probe is [15]
I(r)
_ -2.3
1(1 AU) - r
.
The dependence of polarization on heliocentric distance [15] can be approximated by
P(r)
P(1 AU)
= r+O.3.
For 1 < r < 3.3 AU, the I (r) is given by
I(r)
-2.5±O.5
1(1 AU) = r
,
as measured from Pioneer 10 [18].
The plane of symmetry of the zodiacal light deviates from the ecliptic by a few degrees, causing
annual variations of 10%-20% (peak to peak) in the zodiacal light brightness as viewed from Earth.
The symmetry plane differs in the inner and outer solar system; at r > 1 AU it is close to the invariant
plane
where i
for r < 1 AU,
i = 3°.0 ± 0°.3,
g = 87° ± 4°,
[19],
for r 2: 1 AU,
i = 1°.5 ± 0°.4,
g = 96° ± 15°,
[9],
= inclination to the ecliptic and g = ecliptic longitude of the ascending node.
13.4 INFRARED ZODIACAL EMISSION I 331
-
I 0-'
10-'
10- 10
10- 10
~
L
0
~
~
E
"
,
N
E
0
~
.-<
lL
10-11
10-11
),~20.9I'm
30
60
90
1 0
1 0
1 0
SOLAR ELONGATION
Figure 13.1. Zodiacal emission (radiance) as a function of solar elongation in the ecliptic plane [20]. 0: 1O.9/.LID;
6: 20.9/.LID.
13.4 INFRARED ZODIACAL EMISSION
At A ~ 3 J.Lm, thennal emission from the interplanetary dust (zodiacal emission, or ZE) dominates
over scattered light. The zodiacal emission at 1 AU has been measured from rockets [20], from the
Infrared Astronomical Satellite (IRAS) [21,22], and from the Diffuse Infrared Background Experiment
(DIRBE) on the Cosmic Background Explorer (COBE) satellite [23).
The observed variation in the 10.9 J.Lm and 20.9 J.Lm radiance along the ecliptic plane is presented in
Figure 13.1 [20). Absolute calibration accuracy is approximately 20%. Model fits for assumed radial
dust distribution <X r-1. 3 and r-l. O are shown by the dashed and solid lines.
Figure 13.2 shows the variation of zodiacal emission with ecliptic latitude at or near E = 90° (Le.,
in a plane perpendicular to the Earth-Sun line) as determined from survey observations of the IRAS
satellite between February and November 1983 [21,24]. Only the smooth component of the ZE is
shown, represented by the following slowly-varying empirical function [25]. To remove zodiacal dust
bands [22], point sources, and the diffuse emission of the Galaxy, the function was fitted in a lower
envelope sense to IRAS scans that extended nearly from one ecliptic pole to the other:
1 (fJ) = 10 - c5J (l - 8fJ I cosec(fJ)
I [1 - exp( - fJ 18fJ
- (fJ I 8fJ)2 13)]),
where
1 (fJ)
= brightness at ecliptic latitude fJ,
fJ = geocentric ecliptic latitude,
10 = peak brightness,
81 = parameter with units of brightness, and
8fJ
= angle parameter characterizing the width of the brightness distribution.
The parameter values shown in Table 13.9 represent an annual average of the ZE at E = 90°.
The position of peak emission deviates sinusoidally from the ecliptic plane by about two degrees on
332 I
13
SOLAR SYSTEM SMALL BODIES
80
,,
,,
...
,
60
' ....
.,
<Il
~
,~
40
., ,
,,
.s~
---I
251l1l\
--------
20
-........ .............. _- .......... -..... _--._-_ ... .
o
~~
__
~
o
__- L__
~
__
~
__
~~
__
~
__
~
90
60
30
Ecliptic latitude I ~ I (degrees)
Figure 13.2. Intensity of the smooth component of the zodiacal emission as a function of the ecliptic latitude at
solar elongation 90 0: annual average from IRAS data [25].
a yearly cycle owing to the Earth's orbital motion in a plane inclined with respect to the approximate
symmetry plane of the interplanetary dust; the peak brightness of the ZE near the ecliptic plane, la, and
the ecliptic pole brightness, given by 10 - 81 (1- 8{J), similarly vary modestly on an annual cycle [25].
1Bble 13.9. Empirical function parameters for the ZE at E
= 90°.
Wavelength
Fitted parameter
12ILm
2SlLm
60ILm
10 (MJy sr- I )
81 (MJysr- l )
8fJ (degrees)
37
34
15.6
77
70
14.0
31
29
12.0
At 12 and 25 /Lm the diffuse infrared emission of the sky is dominated by zodiacal emission; at
60 /Lm, the ZE becomes less prominent, and by 100 /Lm emission from the galactic plane dominates
the appearance of the sky, and the ZE is too weak compared with emission from the Galaxy to permit
reliable separation by this method.
A linear transfonnation converts the IRAS values in Table 13.9 and Figure 13.2 to the somewhat
different DIRBE calibration to an nns accuracy of several percent [26]. (Unlike IRAS, DIRBE has an
instrumentally established zero point, an ability to measure electrical and radiative offsets, and superior
stray light rejection.) The transformation is given as
(DIRBE value) = Gain x (IRAS value)
+ Offset,
where, at 12, 25, and 60 /Lm, respectively, Gain = 1.06, 1.01, and 0.87, and Offset
and 0.13 MJy sr- 1•
= -0.48, -1.32,
13.5 METEOROIDS AND INTERPLANETARY DUST / 333
13.5
METEOROIDS AND INTERPLANETARY DUST
This section deals with the characteristics of meteoroids and interplanetary dust as determined from
studies of their ablation or collection in the Earth's atmosphere, and from detections of impacts on
spacecraft. The remote sensing of the space dust population through observations of the zodiacal light,
or infrared studies such as from IRAS, COBE, ISO, etc., are covered in the preceding section.
Solid particles in space smaller than about 10 m in size are termed meteoroids, larger bodies being
asteroids. Meteoroids produce meteors (synonym shooting star) when they enter the atmosphere.
The term "meteor" encompasses the atmospheric phenomena resulting (optical emission, train of
ionization, etc.). Dependent upon composition, entry angle, speed, and density, particles smaller than
about 100 JLm in size do not ablate, but remain intact and gradually settle to the Earth's surface. These
particles are termed interplanetary dust. Such a size limit is also convenient because the majority of
the zodiacal light is the result of scattering by particles in the 10-100 JLm range.
The absolute visual magnitude of a meteor (M) is the observed magnitude corrected to a standard
height of 100 kIn at the observer's zenith. Meteor activity (i.e., detection rate) is normally expressed
in terms of the zenithal hourly rate. Sporadic (nonshower) activity is of the order of 5-10 per hour
to M = 6.5, although there is a seasonal variation which depends upon the solar longitude and the
observer's latitude. Meteor shower activity may be detectable at rates as low as a few per hour, although
most well-known showers have zenithal rates of order 20-50 per hour. The prominent meteor showers,
occurring when the Earth passes through a meteoroid stream, are listed in Tables 13.10 and 13.11.
Every so often an exceptional shower will occur, with rates up to many thousands per hour being seen.
At the time of writing the next such events, termed meteor storms, are anticipated in 1998 and/or 1999
November when the Leonid storm is due. For a more extensive discussion of all of the above, see [27].
Table 13.10. Principal meteor showers. a
Radiant
Diurnal drift
Shower nameb
Activity period
Solar long.C
RA
Dec
RA
Dec
Local time
of transit
Vgd
re
Peak
ZHR
Number
density!
Quadrantids
Lyridsg
~ Aquarids
Arietids h
~ Perseids h
P Tauridsh
a Capricomids
S ~ Aquarids
Perseids i
K Cygnids
S Taurids
N Taurids
Orionids
Draconids j
Leonidsk
Geminids
Ursidsl
JanOI-{)5
Apr 16-25
Apr 19-May 28
May 29-Jun 19
JunOI-17
Jun 07-Jul 07
Jul03-Aug 19
Jul15-Aug 28
Ju117-Aug24
Aug 03-31
Sep 15-Nov 25
Sep 15-Nov 25
Oct02-Nov07
Oct 06-10
Nov 14-21
Dec 07-17
Dec 17-26
283.3
32.1
43.1
230
271
336
+49
+34
-02
+23
+23
+19
-10
-16
+58
+59
+14
+23
+16
+54
+22
+33
+75
+0.4
+1.1
+0.9
+0.7
+1.1
+0.8
+0.9
+0.7
+1.3
+0.3
+0.8
+0.9
+0.7
+0.4
+0.7
+1.0
0
-0.2
0.0
+0.4
+0.6
+0.4
+0.4
+0.3
+0.2
+0.1
+0.1
+0.2
+0.2
+0.1
0
-0.4
-0.1
0
08.5
04.0
07.6
09.9
11.0
11.2
00.0
02.2
05.7
21.3
00.5
00.5
04.3
16.1
06.4
01.9
08.4
39
48
65
35
25
28
20
39
58
22
25
27
65
17
70
33
31
2.2
2.9
2.7
120
20
50
80
8-10
4-5
2.5
3.2
2.6
3.0
2.3
2.3
2.9
2.6
2.5
2.6
3.0
10
20
100
5
10
8
25
150
20-25
10-20
125
50
30
2
25
110
20
1-2
290
80
77
77
97
127
126
139.9
146
221
231
208
197.0
235.2
262.0
270.9
44
62
86
307
339
46
286
50
60
95
262
152
112
217
Notes
aCourtesy I. Rendtel, M. Gyssens, P. Roggemans, and P. Brown, International Meteor Organization. All angles are in
der.ees, and referred to the 1950.0 equinox.
See Table 13.11 for parent comet identifications.
cThe solar longitude is that at the time of peak shower activity.
d Vg is the geocentric velocity of the meteoroid; the velocity at the top of the atmosphere after acceleration by the Earth is
given by V 2 = Vi + 125 (in kmIs).
eThe mass index s is related to the population index r by s = 1+ 2.3 log 10 r (see [1] for details).
f The number density gives the number of particles of m > 10- 3 g per 109 lan3 [2].
334 I 13
SOLAR SYSTEM SMALL BODIES
gZHR to 90.
hDaytime showers.
i ZHR > 200 in 1992-94 near parent comet return.
j Also known as the Giacobinids; periodic shower with ZHR > 200 occurring near alternate parent comet returns.
kMeteor storms anticipated in 1998 and 1999 near parent comet return with ZHR > 1000.
'ZHR to 50.
References
1. Hughes. D.W. 1978. in Cosmic Dust. edited by J.A.M. McDonnell (W"lley. New York). p. 123
2. Hughes. D.W. 1987. A&A. 187.879
Table 13.11. Orbits o/meteoroid streams [1].
ne
(AU)
e"
qC
(AU)
of1
Shower name
(0)
(D)
(0)
Quadrantids
Lyrids
3.08
28
13
1.6
1.6
2.2
2.53
2.86
28
3.09
1.93
2.59
15
3.51
11.5
1.36
5.70
0.683
0.968
0.958
0.94
0.79
0.85
0.77
0.976
0.965
0.68
0.806
0.861
0.962
0.717
0.915
0.896
0.85
0.977
0.919
0.560
0.09
0.34
0.34
0.59
0.069
0.953
0.99
0.375
0.359
0.571
0.996
0.985
0.142
0.939
170
214
95
29
59
283.3
32.1
43.1
77
77
277
127
306
139.9
146
41
231
28
197.0
235.2
262.0
270.9
72.5
79
163.5
21
0
6
7
27.2
113.8
38
5.2
2.4
163.9
30.7
162.6
23.6
53.6
aa
" Aquarids
Arietids
~ Perseids
fJ Taurids
a Capricomids
S 8 Aquarids
Perseids
K Cygnids
S Taurids
NTaurids
Orionids
Draconids
Leonids
Geminids
Ursids
246
269
153
152
194
113
292
83
172
173
324
206
if
Parent objects
96PlMachholz 1 & 149111
ClI'hatcher (1861 G 1)
IPlHalley
96PlMachholz 1 & 149111
2PlEncke & various asteroids
96PlMachholz 1 & 149111
I09P/Swift-Thttle
2PlEncke & various asteroids
IPlHalley
21P/Giacobini-Zinner
55Plrempel-Thttle
(3200) Phaethon
8PIThttle
Notes
aa is the semimajor axis.
be is the orbital eccentricity.
Cq is the perihelion distance. q a(l - e).
d (i) is the argument of perihelion.
is the longitude of the ascending node (equinox 1950.0).
f i is the inclination to the ecliptic.
=
en
Reference
1. Cook. A.F. 1973. in Evolutionary and Physical Properties 0/ Meteoroids. NASA SP-319. edited by C.L.
Hemenway and A.F. Cook (NASA. Washington. DC)
The above discussion pertains to visual meteors. mostly produced by meteoroids larger than '" 1 cm
in size. Fainter meteors may be detected through HFNHF radio wave scattering from their trains of
ionization [27,28]. Such meteors are due to smaller meteoroids, typically 100 #LIn-I mm in size.
The limiting magnitude is about +15 (corresponding to the micrometeor limit at '" 100 #Lm); radars
sensitive to such magnitudes may detect meteors at rates of one per few seconds, and especially
powerful radars covering large areas at rates exceeding one per second [29]. It was thought for some
years (see [27]) that the deficit of meteors detected in the radar regime (masses 10-6-10-2 g) was due
to the reduced ionizing efficiency of low-speed meteoroids (that efficiency varies as '" V 3.5- 4.O, V
being the top-of-the-atmosphere velocity), but it is now known that the finite "echo ceiling" [28] of
HFNHF radars has led to only those ablating lower than...., 105 km being detected, meaning that the
majority ablating higher have been missed, but are detectable using MF radars [29,30].
13.5 METEOROIDS AND INTERPLANETARY DUST / 335
The magnitude of a meteor is given in [27,28]:
M
= 40 -
2.5 log 10 (xz,
where {xz is the zenithal electron line density (per meter) in the train.
There have been many determinations of the relationship between (xz, V, and the initial meteoroid
mass m [27,31], both from theory and from observations. The form of the expression is generally
given as
where the normalizing constant Cl has values typically in the range 2-8 x 10- 10 , x = 0.9-1.1, and
y = 3.2-4.0. Dependent upon the velocity, one finds [27]:
where C2 = 16-17. This implies that a meteor of zenithal magnitude zero (M = 0) has a mass of
,....,O.I-lg.
The above assumed that the mean sporadic meteoroid speed is ,...., 30-40 kmls; in fact the initial
analysis of the Harvard Radar Meteor Project results [32] implied that the mean speed, at least for
faint radar meteors, is < 20 kmls, but apparently an error was made such that the real mean speed is
somewhat higher than 20krn s-I[33]. Particles arriving from heliocentric elliptical orbits may impact
the Earth at speeds between 11 and 73 kmls.
The composition of meteoroids and dust is still a matter of uncertainty. Spectroscopic observations
of meteors indicate highly differentiated material similar to various meteorite classes, whilst dust
collection in the stratosphere also indicates compositions similar to meteorite classes although volatile
components may have been lost through heating in atmospheric entry; hypervelocity spacecraft impacts
are unlikely to leave traces of any but the most refractory components. A variety of recent papers
on these topics, and other features of meteoroids and interplanetary dust, may be found in [34-39].
The present state of knowledge indicates that the particles under consideration are largely comprised
of meteoritic-type materials (silicates, nickel-iron) but with a significant fraction of heavy organics
(kerogens) that are thermodynamically stable over periods of""" 104 yr after release from their parent
bodies, but which are destroyed on atmospheric entry.
The origin of at least some meteoroids is indicated by the association of various meteor showers
with specific comets through orbit similarity [40]. The orbits of meteoroids determined in various
surveys are reviewed and cataloged in [41], where evidence linking showers with various Earthcrossing asteroids (see Table 13 .11) is also discussed. Larger meteoroids in the 5-10 m size range
may also be cometary fragments [42]. While many meteoroids appear to be of low density (p <
1 glcm3 ), there is also a high-density component with p = 3-8 glcm3 [43], [44]. The evolution of
meteoroid streams is reviewed in [45]. The origin of sporadic meteors appears to be gravitational
stirring of streams, in particular by Jupiter; small meteoroids and dust are also subject to orbital
circularlzationlinspiralling toward the Sun under the influence of the Poynting-Robertson drag force,
with various other effects also being significant.
Meteoroids tend to end their lives through impacts upon smaller dust particles, their comminution
maintaining the interplanetary dust supply (although it is not clear whether the present complex is in
balance [46]), which in tum is depleted through collisions, in spiralling, and eventual ejection from the
solar system by radiationlsolar wind pressure.
The terrestrial mass accretion rate of small meteoroids and dust has been established from impact
data collected with the Long Duration Exposure Facility [47] and other satellites [48], the small particle
influx being 40 ± 20 x 106 kg per year (see Figure 13.3), in accord with the influx determined by radar
336 I
13
SOLAR SYSTEM SMALL BODIES
FIgure 13.3. The logarithmic incremental mass influx to the Earth, in units of loti kg per year per logarithmic
mass interval. For these small particles (meteoroids and dust) the peak influx is at "" 10-5 g, and the integral under
this curve is "" 40, 000 tonneslyear [47], although larger particles (asteroids and comets) dominate the long-term
averaged mass influx [50]. From [47], Figure 4.
meteor techniques [29]. The small particle influx can also be measured from ice cores [49]. The influx
over the whole mass spectrum (from dust through to large asteroids and comets) is reviewed in [50].
Whilst the interplanetary complex of meteoroids and dust is significant in a number of ways (such as
its effect upon atmospheric chemistry and the light it scatters producing a diffuse background), its total
mass is only equivalent to an asteroid or comet a few tens of kilometers in diameter.
REFERENCES
1. Through Minor Planet Circular 31044. 1997. December
14
2. Marsden.
B.G..
&
Williams.
G.V..
and
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K. Schaifers and H.H. Voigt (Springer-Verlag. Berlin).
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17. Blackwell. D.E.• Dewhirst, D.W.• & Ingham. M.P.
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20.
21.
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31.
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Chapter
14
Sun
William C. Livingston
14.1
Basic Data . . . . . . . . . . . . . . . . . . . . . . . . .
340
14.2
Interior Model . . . . . . . . . . . . . . . . . . . . . ..
341
14.3
Solar Oscillations .. . . . . . . . . . . . . . . . . . ..
342
14.4
Photospheric-Chromospheric Model . . . . . . . . ..
348
14.5
Spectral Lines . . . . . . . . . . . . . . . . . . . . . ..
351
14.6
Spectral Distribution . . . . . . . . . . . . . . . . . . .
353
14.7
Limb Darkening . . . . . . . . . . . . . . . . . . . . ..
355
14.8
Corona. . . . . . . . . . . . . . . . . . . . . . . . . . ..
357
14.9
Solar Rotation . . . . . . . . . . . . . . . . . . . . . ..
362
14.10
Granulation.........................
364
14.11
Surface Magnetism and its Tracers. . . . . . . . . ..
364
14.12
Sunspots...........................
367
14.13
Sunspot Statistics ..... . . . . . . . . . . . . . . ..
370
14.14
Flares and Coronal Mass Ejections. . . . . . . . . ..
373
14.15
Solar Radio Emission. . . . . . . . . . . . . . . . . ..
375
339
340 I
14.1
14.1.1
14
SUN
BASIC DATA
Global
Solar radius
Volume
Surface area
Solar mass
Mean density
Gravity at surface
Moment of inertia
Angular rotation velocity at equator
Angular momentum (based on surface rotation)
Work required to dissipate solar matter to infinity
Sun's total internal radiant energy
Escape velocity at solar surface
14.1.2
R0 = 6.95508 ± 0.000 26 x 1010 cm [1]
V0 = 1.4122 x 1033 cm3
6.087 x 1022 cm 2
M0 = 1.989 x 1033 g
P0 = 1.409 g cm- 3
2.740 x 104 cms- 2
5.7 x 1053 gcm2
2.85 x 10-6 rad s-1
1.63 x 1048 gcm2 s- 1
6.6 x 1048 erg
2.8 x 1047 erg
6.177 x 107 cms- 1
Viewed from Earth
Mean equatorial horizontal parallax [2]
Mean distance from Earth
(A = AU = astronomical unit)
Distance at
Perihelion
Aphelion
Semidiameter of Sun
At mean Earth distance
Oblateness: Semidiameter equator-pole difference [3,4]
Solid angle of Sun, mean distance
Surface area of sphere of unit radius
In heliographic coordinates
At mean distance A
14.1.3
8~'79418
= 4.263 54 x 10-5 rad
1 AU = 1.495 979 x 1013 cm
1.4710 x 1013 cm
1.5210 x 1013 cm
959~'63
0.004 652 4 rad
0~'0086
6.8000 x 10-5 sr
AI R0 = 214.94
(AI R0)2 = 46200
(AI R0)1/2 = 14.661
47l' A2 = 2.8123 x 1027 cm2
1°= 12147km
l' of arc = 4.352 x 104 km
I" of arc = 725.3 km
Total Solar Radiation
Solar constant S (total solar irradiance) = flux of total radiation received outside the Earth's
atmosphere per unit area at the mean Sun-Earth distance [5-9]:
Radiation from whole Sun
Radiation per unit mass
S = 1.365-1.369 Wm- 2 = 1.365-1.369 x 106 ergcm- 2 s-1,
L0 = 3.845 x 1026 W = 3.845 x 1033 erg s-1.
L01 M0 = 1.933 X 10- 4 W kg- 1 = 1.933 erg s-1 g-1 .
14.2 INTERIOR MODEL I 341
Radiation emittance
at Sun's surface
Mean radiation intensity
of Sun's disk
F
= FIn = 2.009 x
= 2.009 x
107 Wm- 2 sr-l.
10 10 ergcm- 2 s-l.
14.1.4 SUD as a Star
Magnitudes of the Sun in three wavelength bands and the bolometric magnitude are given in
Table 14.1 [10-13].
Table 14.1. Solar magnitudes.
Visual (mv)
Blue
Ultraviolet
Bolometric
Apparent
Modulus
Absolute
= -26.75
= -26.10
= -25.91
mbol = -26.83
31.57
MV = +4.82
MB = +5.47
Mu = +5.66
mbal = +4.74
V
B
U
Color indices [10-14]:
B
U
U
V
-
V
B
V
R
= +0.650,
= +0.195,
= +0.845,
= +0.54,
V - 1= +0.88,
V - K = +1.49.
Bolometric correction
Spectral type
Effective temperature
Velocity relative to near stars
Solar apex
Age of Sun [15, 16]
Mean magnetic field [17]
Average
Peak
BC
= -0.08.
G2V.
5777 K.
19.7 kms- 1
A = 271°,
D
L n = 57°,
Bn
(4.5-4.7) x 109 yr.
= 30°(1900),
= 22°.
OG,
±1 G.
14.2 INTERIOR MODEL
by Pierre Demarque and David Guenther
The tabulated data in Table 14.2 are for a standard model of the Sun (no rotation, no diffusion), from
Table 3B in [18]. This model was constructed using opacities from [19] and the solar mixture from [20].
Other similar recent models can be found in [21] and [22].
342 /
14
SUN
Central values
Temperature
Density
Pressure
Central hydrogen content by mass
= 15.7 x 106 K.
Pc = 151 gcm- 3 .
Pc = 2.33 X 10 17 dyn cm- 2 .
Xc = 0.355.
Tc
Surface composition parameters
X
Z
= 0.6937,
= 0.0188.
The fraction of the radius at the base of the surface convection (SCZ or surface convection zone) can
be determined by helioseismology [23, 24], which is within 1% of model [18]:
rsczl Ro = 0.71.
Table 14.2. Model of solar interior.
Mr
(Mo)
Lr
(ergs-I)
Lr
(LO)
P
(dynem- 2)
logP
(dynem- 2)
150
146
95.73
0.00003
0.001
0.057
1.01 x 1030
3.97x 1031
1.39 x 1033
0.0002
0.010
0.361
2.33 x 10 17
2.27x 1017
1.50x 1017
17.369
17.355
17.177
8.77
6.42
4.89
28.72
9.77
3.22
0.399
0.656
0.817
3.72xI033
3.85x 1033
3.85x1033
0.966
1.000
1.000
3.35x 1016
5.29x 1015
2.lOx10 15
16.525
15.724
15.324
3.62xlO lO
4.18xlO lO
4.94 x 1010
3.77
3.15
2.23
1.05
0.500
0.177
0.908
0.945
0.977
3.85xl033
3.85x 1033
3.85x 1033
1.000
1.000
1.000
5.28x 1014
2.lOx 1014
5.26x10 13
14.722
14.322
13.721
0.81
0.91
0.96
5.64xlOlO
6.33 x 1010
6.68xlO lO
1.29
0.514
0.208
0.0766
0.0194
4.85xl0- 3
0.992
0.999
0.9999
3.85x 1033
3.85x 1033
3.85x 1033
1.000
1.000
1.000
1.32 x 1013
1.32 x 10 12
1.31 x 1011
13.119
12.119
lLl18
0.99
0.995
0.999
6.89xlO lO
6.93x 1010
6.95 x 1010
0.00441
0.00266
0.00135
2.56xlO-4
4.83xlO- 5
1.29 x 10-6
1.0000
1.0000
1.0000
3.85x 1033
3.85x 1033
3.85x1033
1.000
1.000
1.000
1.31 x 109
1.31 x 108
1.31 x 106
9.118
8.118
6.118
1.000
6.96xlO lO
0.00060
2.18xlO- 7
1.0000
3.85x1033
1.000
8.27x 104
4.918
r
(Ro)
r
(em)
0.007
0.02
0.09
4.87x108
1.39 x 109
6.24x109
15.7
15.6
13.6
0.22
0.32
0.42
1.53 x 1010
2.23xlO lO
2.92xlO lO
0.52
0.60
0.71
14.3
T
(106 K)
p
(gem- 3)
SOLAR OSCILLATIONS
by Frank Hill
= solar radius.
g = gravitational acceleration at solar surface.
Ro
e=
spherical harmonic degree of mode of oscillation.
m = spherical harmonic azimuthal degree of mode.
14.3 SOLAR OSCILLATIONS / 343
n = radial order of mode.
v = frequency of mode.
(J)
kh
Pi
= angular frequency of mode, = 21l' v.
= horizontal wave number of mode, kh = J i(i + 1) /,R0'
(J)
= Legendre polynomial of degree i.
A(v, i) = amplitude of mode.
r(v, i) = full width at half maximum of mode.
Characteristic period of p (pressure) modes
Characteristic photospheric amplitude of p modes
Characteristic lifetime of p modes
Estimated number of excited p modes
14.3.1
5 min.
10 ems-I.
7 days.
107 .
Approximations for Frequencies Vn,t of Zonal (m
= 0) p
Modes
(a) Tassoul first-order asymptotic approximation for low-degree modes with i :::: 3 and 11 :::: n ::::
33 [25]:
v(n, i) =
V()
(n
+~ +
8)
with measured coefficients in Table 14.3 [26] and accuracy of 2.8-4.1 JLHz.
Table 14.3. Fit values.
e
II()
(ILHz)
135.4
135.7
135.4
135.7
0
1
2
3
8
1.43
1.36
1.36
1.24
(b) Tassoul second-order asymptotic approximation for low-degree modes with i :::: 3 and 11 <
n :::: 33 [25]:
v(n, i) =
V()
(n
i
+ 2" + 8 -
i(i
n
+ l)a - f3)
+ i/2 + 8 '
with measured coefficients in Table 14.4 [26] and accuracy of 1.4-2.0 JLHz.
Table 14.4. Second-order fit values.
e
0
1
2
3
II()
(ILHz)
137.0
137.9
137.4
137.0
a
fJ
8
0.20
0.15
0.20
5.6
7.8
7.8
7.4
0.90
0.62
0.70
0.80
344 /
14
SUN
(c) Polynomial approximation for low-degree modes with l
v(n. l)
= t::. Vi + Vi (n + ~ -
no)
+ Yi
~
(n
3 and 11
~ n ~
+ ~ _ no)
2
33 [27]:
•
using no = 22 as a reference order. measured coefficients listed in Table 14.5 in JLHz [26] and accuracy
of 1.0-1.2 JLHz.
Thble 14.5. Polynomialjit values.
i
~Vl
Vi
Ye
0
1
2
3
3169.4
3166.2
3160.5
3150.8
135.31
135.52
135.35
135.52
0.090
0.105
0.085
0.070
The quantities t::. Vi and Vi are linear functions of l(l
+ 1):
+ I)Do.
Vi = vo + l(l + l)do.
t::.Vi
= t::.vo -
l(l
with fitted values [26]
t::.vo
vo
Do
do
= 3169.4 JLHz.
= 135.35 JLHz.
= 1.54 JLHz.
= 0.012 JLHz.
(d) Parabolic fit for intermediate-degree modes with 4
1-10 JLHz [26]:
~
l ~ 100. 3 ~ n ~ 24. and accuracy of
where coefficients aj are fitted to second-order polynomials in n expressed in matrix form as
( ao) = (6438.6
al
a2
-0.025
101.3
2.9
-0.008
0.71) ( 1 )
-0.047
n.
-0.0002
n2
(e) Empirical fit for low- and intermediate-degree modes with 1
5.0 mHz. 'R0 in kIn. and accuracy of 10 JLHz [28]:
v(n. l)
x
~
l < 200. 1.7 mHz
~
v <
= 2354.2(n + 1.57)eO.2053[(lnx-14.523)2+4.1l75f/2 -lnx JLHz.
= (n + 1.57)1l"'R0 [l(l + l)rl/2.
The Duvall dispersion law [29] collapses all p-mode ridges in an kh-(J) diagram to a single ridge via a
transformation of coordinates. This transformation is
(n
+ a)1l" = f
W
(w)
kh
14.3 SOLAR OSCILLATIONS / 345
with fitted value
a = 1.67.
The dependence of v on m for p modes is [30]
v(t, m, n) = v(t, n)
+ Jt(t + 1)
I:
a; (v, t)P; (
j=1
-m
),
Jt(t + 1)
where the splitting coefficients aj depend on v(n, t), in mHz [31]:
aj(v, t) = a7(t)
+ b7(t)[v(n, t) -
2.5].
Some of these coefficients are given in Table 14.6.
Thble 14.6. Selected splitting coefficients [1]. All coefficients in nHz.
l
a*1
11
436.7
438.4
439.5
440.7
441.4
441.5
20
29
38
47
56
b*1
a*2
b*2
-1.0
-0.7
-0.5
0.3
0.1
0.7
-3.5
-0.9
-0.5
-0.1
-0.3
0.2
-1.7
0.2
-0.5
-0.8
-1.0
0.6
a*3
12.0
16.9
19.9
21.3
21.5
22.3
b*3
a*4
b*4
a*5
b*5
-2.1
0.3
-5.1
-2.0
-0.7
-0.5
1.3
0.8
1.2
0.9
0.4
0.4
6.8
1.3
-1.1
1.4
1.9
1.3
1.3
-3.1
-3.4
-2.5
-3.3
-3.5
3.2
2.2
1.0
-0.1
0.5
0.3
Reference
1. Libbrecht, K.G. 1989, ApJ, 336, 1092
The dependence of p-mode frequency change
absolute magnetic field B in Gauss [32] is
~v
~v
of v(t, n) on area-weighted average full-disk
= a(B -7),
with fitted value
a = 0.027 JLHzjG.
The approximate formulas for amplitude A(v, t) of p modes [33,34]
A(v, t) = 1O(b+c)/2 cm/s,
with fitted values
b=
=
c=
=
2.2v - 3.5,
-0.9v + 5.6,
-8.8 x 1O-4 t,
-3.1 x 1O-3 t + 0.75,
v<
v>
t <
t >
2.9 mHz,
2.9 mHz,
340,
340.
The observed estimate of absorption fraction a of p-mode power by sunspots is discussed in [35] and
listed in Table 14.7.
346 I
14
SUN
Table 14.7. Sunspot absorption.
kh (Mrn-l)
a
0.2
0.3
0.4
0.10
0.18
0.34
0.42
~0.5
Approximate formulas for the full width at half maximum (FWHM) r(v, l) of p modes
[33, 36, 37] are
r(v, l) = 1.7 x 1O- 2 (l - 20) + lotI tLHz,
with fitted values
d
= v -2.3,
v <
2.4 mHz ~ v ~
3.1 mHz ~ v ~
4.3mHz <
=0.1,
= v -3.0,
= O.4v - 0.6,
The dispersion relation for
f
2.4 mHz,
3.1 mHz,
4.3 mHz,
v.
(fundamental) mode is
(J)
or equivalently
= ..jgkh,
v = 99.8569[l(l + 1)]1/4 tLHz.
The first-order asymptotic approximation for period P(n, l) of g (gravity) mode with n
P(n, l)
Po
»l
2n+l+4>
= "2 [l(l + 1)]1/2'
Theoretical estimates of period spacing Po and phase 4> from standard solar models [38] are
Po
4>
= 33.9 to 38.0 min,
= -0.42 to -0.25.
Po
4>
= 29.9 to 42.6 min,
= -0.35 to +2.
Observational estimates [38] are
Properties of "160-min" oscillation [38] are
period
amplitude
= 160.010 min,
= 54 cm/s.
Table 14.8 gives zonal p-mode frequencies for selected nand l values.
[25] is
1823.60
2093.50
2362.50
2629.60
2899.30
3168.60
3439.80
3711.50
3984.90
4257.40
4532.30
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
1823.33
2098.45
2371.21
2641.07
2913.54
3186.12
3459.57
3734.52
4009.61
5
1443.40
1737.84
2021.53
2302.80
2578.64
2855.70
3132.88
3410.10
3688.24
3967.99
4247.68
10
1489.44
1847.91
2181.78
2494.35
2797.28
3096.17
3390.93
3684.81
3977.49
4270.76
25
1409.99
1833.33
2296.79
2676.98
3045.59
3402.83
3753.12
4095.93
4428.00
4753.20
50
1655.77
2181.39
2638.73
3067.43
3474.37
3868.91
4252.25
4628.75
4999.33
75
1844.12
2423.47
2928.67
3397.96
3844.40
4271.92
4688.09
100
2148.50
2811.51
3405.04
3954.48
4475.10
150
2395.6
3130.2
3800.2
4425.0
200
References
I. Duvall, Jr., T.L., Harvey, J.W., Libbrecht, K.G., Popp, B.D., & Pomerantz, M.A. 1988, ApJ, 324, 1158
2. Libbrecht, K.G., Woodard, M.P., & Kaufman, I.M. 1990, ApJS, 74, 1129
£=0
n
1743.6
2780.3
3650.1
4458.8
300
1998.0
3089.6
4092.1
4974.2
400
2227.8
3359.1
4475.4
500
Table 14.8. Selected measured zonal p-mode frequencies [1, 2]. All values in fLHz.
2438
3622
4815
600
2632
3877
5124
700
2821
4120
800
2984
4374
900
3140
4601
1000
~
.....J
~
w
........
(I)
oz
~
t=
t'"'
n
(I)
o
>
:;;0
ot'"'
CI'.l
W
.-
348 /
14
SUN
14.4 PHOTOSPHERIC-CHROMOSPHERIC MODEL
by Eugene Avrett
Table 14.9 gives a model of the average quiet solar atmosphere, from [39]. The height h is the distance
above TSOO = 1, where TSOO is the radial optical depth in the continuum at 500 om. Hydrostatic
equilibrium is assumed so that m = Prot! g, where m is the column mass, Prot is the total pressure, and
g is the gravitational acceleration at the solar surface. In the photosphere (-100 < h < 525 kIn) and in
the chromosphere (525 < h < 2100 kIn) the temperature T has been adjusted empirically so that the
computed spectrum is in agreement with the spatially averaged spectrum from quiet areas (away from
sunspots and active regions). The temperature distribution in the transition region above h ~ 2100 kIn
(up to T = lOS K) has been determined theoretically by balancing the downftow of energy from the
corona (due to thermal conduction and diffusion) with the radiative energy losses. The microvelocity
Vt roughly accounts for the Doppler broadening that is observed to exceed the thermal broadening of
lines formed at various heights (see [40,41)). The total pressure Prot is the sum of the gas pressure Pgas
and the turbulent pressure pv; /2, where p is the gas density.
The table also lists the total hydrogen density nH and the proton and electron densities np and ne.
The number densities and other quantities are determined by solving the coupled radiative transfer and
statistical equilibrium equations [without assuming local thermal equilibrium (LTE)], given the T and
Vt distributions. The helium to hydrogen abundance ratio is assumed to be 0.1. The abundances of the
other contributing elements are from [42].
See [43] and [44] for similar empirical models of the photosphere. Models for faint and bright
components of the quiet Sun and for a plage region are given in [39]. See [45] for a theoretical lineblanketed LTE photospheric model, and [46] for theoretical non-LTE line-blanketed chromospheric
models. Bifurcated chromospheric models based on a combination of hot and cool components are
given in [47] and [48]. Papers in [49] and [50] discuss related studies and include references to earlier
work.
Other aspects of the chromosphere, such as infrared and radio data, are referred to in [51-53].
h
2218.20
2216.50
2214.89
2212.77
2210.64
2209.57
2208.48
2207.38
2206.27
2205.72
2205.21
2204.69
2204.17
2203.68
2203.21
2202.75
2202.27
2201.87
2201.60
2201.19
2200.85
2200.10
2199.00
2190.00
2168.00
2140.00
2110.00
2087.00
2075.00
2062.00
2043.00
2017.00
1980.00
1915.00
1860.00
1775.00
1670.00
1580.00
1475.00
1378.00
(km)
0.00 x
7.70 x
1.53 x
2.60 x
3.75 x
4.38 x
5.06 x
5.81 x
6.64 x
7.10 x
7.55 x
8.05 x
8.61 x
9.19 x
9.81 x
1.05 x
1.13 x
1.21 x
1.27 x
1.36 x
1.44 x
1.63 x
1.90 x
4.15 x
9.85 x
1.76 x
2.62 x
3.30 x
3.66 x
4.05 x
4.62 x
5.41 x
6.53 x
8.53 x
1.03 x
1.31 x
1.69 x
2.07 x
2.59 x
3.19 x
10- 10
10- 10
10-9
10-9
10-9
10-9
10-9
10-9
10-9
10-9
10-9
10-9
10-9
10-9
10-9
10- 8
10- 8
10- 8
10- 8
10- 8
10- 8
10- 8
10- 8
10- 8
10- 8
10- 7
10-7
10-7
10- 7
10- 7
10- 7
10- 7
10- 7
10- 7
10- 6
10- 6
10- 6
10-6
10-6
10-6
'500
m
6.777 x
6.779 x
6.781 x
6.785 x
6.788 x
6.790 x
6.792 x
6.794 x
6.797 x
6.798 x
6.800 x
6.801 x
6.803 x
6.805 x
6.807 x
6.809 x
6.812 x
6.815 x
6.817 x
6.820 x
6.823 x
6.830 x
6.840 x
6.936 x
7.203 x
7.588 x
8.063 x
8.483 x
8.724 x
9.005 x
9.453 x
1.014 x
1.128 x
1.387 x
1.676 x
2.298 x
3.510 x
5.186 x
8.435 x
1.363 x
10- 6
10- 6
10-6
10-6
10-6
10-6
10-6
10- 6
10-6
10-6
10-6
10-6
10-6
10-6
10- 6
10-6
10- 6
10-6
10-6
10- 6
10- 6
10- 6
10- 6
10- 6
10- 6
10- 6
10- 6
10- 6
10- 6
10- 6
10- 6
10- 5
10- 5
10- 5
10- 5
10- 5
10- 5
10-5
10-5
10-4
(gcm- 2)
100000
95600
90816
83891
75934
71336
66145
60 170
53284
49385
45416
41178
36594
32145
27972
24056
20416
17925
16500
15000
14250
13500
13000
12000
11150
10550
9900
9450
9200
8950
8700
8400
8050
7650
7450
7250
7050
6900
6720
6560
11.73
11.65
11.56
11.42
11.25
11.14
11.02
10.86
10.67
10.55
10.42
10.27
10.09
9.90
9.70
9.51
9.30
9.13
9.02
8.90
8.83
8.74
8.66
8.48
8.30
8.10
7.87
7.70
7.61
7.52
7.41
7.26
7.06
6.74
6.49
6.12
5.69
5.34
4.93
4.53
VI
(km s-I)
T
(K)
5.575 x
5.838 x
6.151 x
6.668 x
7.381 x
7.864 x
8.488 x
9.334 x
1.053 x
1.135 x
1.233 x
1.356 x
1.521 x
1.724 x
1.971 x
2.276 x
2.658 x
3.008 x
3.255 x
3.570 x
3.762 x
4.013 x
4.244 x
4.854 x
5.500 x
6.252 x
7.314 x
8.287 x
8.882 x
9.569 x
1.055 x
1.203 x
1.446 x
1.971 x
2.547 x
3.788 x
6.292 x
9.900 x
1.726 x
2.970 x
nH
109
109
109
109
109
109
109
109
1010
1010
1010
1010
10 10
1010
1010
1010
1010
1010
1010
10 10
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1011
1011
1011
1011
1011
1011
1011
1011
10 12
10 12
(cm- 3)
5.575 x
5.837 x
6.150 x
6.667 x
7.378 x
7.858 x
8.476 x
9.307 x
1.047 x
1.125 x
1.217 x
1.332 x
1.483 x
1.667 x
1.887 x
2.154 x
2.483 x
2.778 x
2.979 x
3.218 x
3.343 x
3.441 x
3.456 x
3.411 x
3.619 x
3.806 x
3.923 x
3.954 x
3.956 x
3.952 x
3.937 x
3.921 x
3.908 x
3.974 x
4.100 x
4.399 x
4.922 x
5.390 x
6.037 x
6.824 x
np
109
109
109
109
109
109
109
109
1010
1010
1010
1010
1010
1010
1010
1010
10 10
1010
1010
1010
1010
1010
1010
1010
1010
1010
10 10
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
(cm- 3)
Table 14.9. Solar atmospheric model.
6.665
6.947
7.284
7.834
8.576
9.076
9.718
1.059
1.182
1.266
1.365
1.491
1.657
1.858
2.098
2.389
2.743
3.049
3.256
3.498
3.619
3.699
3.695
3.663
3.889
4.095
4.238
4.291
4.305
4.314
4.314
4.313
4.310
4.351
4.423
4.630
5.085
5.535
6.191
7.007
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
ne
109
109
109
109
109
109
109
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
10 10
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
1010
(cm- 3)
1.857 x
1.857 x
1.858 x
1.859 x
1.860 x
1.860 x
1.861 x
1.862 x
1.862 x
1.863 x
1.863 x
1.863 x
1.864 x
1.864 x
1.865 x
1.866 x
1.866 x
1.867 x
1.868 x
1.869 x
1.869 x
1.871 x
1.874 x
1.900 x
1.974 x
2.079 x
2.209 x
2.324 x
2.390 x
2.467 x
2.590 x
2.778 x
3.092 x
3.800 x
4.593 x
6.297 x
9.616 x
1.421 x
2.311 x
3.735 x
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 10
10- 10
10- 10
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
Ptot
(dyncm- 2)
0.952
0.950
0.948
0.945
0.941
0.938
0.935
0.931
0.925
0.921
0.916
0.910
0.903
0.894
0.883
0.871
0.856
0.843
0.834
0.823
0.816
0.808
0.801
0.785
0.775
0.769
0.760
0.753
0.748
0.743
0.738
0.732
0.727
0.724
0.727
0.736
0.752
0.767
0.787
0.809
Pg.. /Ptot
1.31 x
1.37 x
1.44 x
1.56 x
1.73 x
1.84 x
1.99 x
2.19 x
2.47 x
2.66 x
2.89 x
3.18 x
3.56 x
4.04 x
4.62 x
5.33 x
6.23 x
7.05 x
7.63 x
8.36 x
8.81 x
9.40 x
9.94 x
1.14 x
1.29 x
1.46 x
1.71 x
1.94 x
2.08 x
2.24 x
2.47 x
2.82 x
3.39 x
4.62 x
5.97 x
8.87 x
1.47 x
2.32 x
4.05 x
6.96 x
10- 13
10- 13
10- 13
10- 13
10- 13
10- 13
10- 12
10- 12
10- 12
10- 12
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 14
10- 13
10- 13
10- 13
10- 13
10- 13
10- 13
10- 13
P
(gcm- 3)
\0
~
UJ
'-
ttl
t'"'
0
0
~
(")
:;:tj
ttl
......
::t
'"'C
til
0
s::
0
:;:tj
::t
I
()
(")
......
:;:tj
ttl
::t
'"'C
til
0
o-l
0
::t
""C
~
~
-
50.00
35.00
20.00
10.00
0.00
-10.00
-20.00
-30.00
-40.00
-50.00
-60.00
-70.00
-80.00
-90.00
-100.00
600.00
560.00
525.00
490.00
450.00
400.00
350.00
300.00
250.00
200.00
175.00
150.00
125.00
100.00
75.00
1278.00
1180.00
1065.00
980.00
905.00
855.00
805.00
755.00
705.00
650.00
h
(km)
1.00
1.25
1.61
2.14
2.95
4.13
5.86
8.36
1.20
1.70
2.36
X
X
X
10 1
10 1
10 1
4.02 x 10-6
5.19 x 10-6
7.43 x 10-6
1.03 x 10-5
1.44 x 10-5
1.85 x 10-5
2.39 x 10-5
3.09 x 10-5
4.00 x 10-5
5.55 x 10-5
8.53 x 10-5
1.40 x 10-4
2.39 x 10-4
4.29 x 10-4
8.51 x 10-4
1.98 x 10- 3
4.53 x 10- 3
1.01 x 10- 2
2.20 X 10- 2
4.73 x 10-2
6.87 x 10-2
9.92 x 10-2
1.42 X 10- 1
2.02 x 10- 1
2.87 x 10- 1
4.13 x 10- 1
5.22 X 10- 1
6.75 x 10- 1
8.14 x 10- 1
~SOO
x
x
x
x
x
x
x
x
2.538
3.680
5.125
7.149
1.044
1.664
2.626
4.103
6.344
9.705
4.686
4.975
5.269
5.567
5.869
6.174
6.481
6.790
7.102
7.417
3.148
3.496
3.869
4.132
4.404
1.195
1.466
1.790
2.174
2.625
x
x
x
x
x
3.282
4.710
6.868
1.022
1.624
x
X
x
x
x
x
x
2.312
4.022
8.074
1.396
2.314
10-4
10-4
10-4
10-3
10-3
10-3
10-3
10- 3
10-2
10- 2
10-2
10-2
10-2
10-2
10- 1
10- 1
10- 1
10- 1
10- 1
10- 1
(gcm- 2)
m
6720
6980
7280
7590
7900
8220
8540
8860
9140
9400
4550
4430
4400
4410
4460
4560
4660
4770
4880
4990
5060
5150
5270
5410
5580
5790
5980
6180
6340
6520
5650
5490
5280
5030
4750
6390
6230
6040
5900
5755
(K)
T
1.64
1.67
1.70
1.73
1.75
1.77
1.79
1.80
1.82
1.83
1.00
0.89
0.80
0.72
0.65
0.55
0.52
0.55
0.63
0.79
0.90
1.00
1.10
1.20
1.30
1.40
1.46
1.52
1.55
1.60
4.04
3.53
2.94
2.52
2.19
1.99
1.77
1.54
1.38
1.18
(kms-I)
VI
9.895
1.478
2.078
2.898
4.192
6.549
1.012
1.545
2.331
3.476
4.211
5.062
6.024
7.107
8.295
9.558
1.027
1.098
1.142
1.182
1.219
1.246
1.264
1.280
1.295
1.307
1.317
1.325
1.337
1.351
X
X
X
X
X
X
X
x
x
X
x
X
x
x
x
x
x
x
X
x
x
x
x
x
x
x
x
x
x
x
5.393 x
1.002 x
2.164 x
3.931 x
6.806 x
9.931 x
1.481 x
2.268 x
3.560 x
6.033 x
x
x
x
x
x
x
x
x
x
x
x 1011
X 1011
x 1011
x 10 12
x 10 12
10 12
10 13
1013
10 13
10 13
X 10 13
x 10 14
x 10 14
X 10 14
X 10 14
5.368
2.825
2.424
2.618
3.600
6.715
1.267
2.604
5.605
1.253
2.028
3.579
7.119
1.485
3.281
7.614
1.439
2.588
3.926
6.014
9.269
1.536
2.597
4.249
6.668
1.022
1.515
2.180
2.942
3.826
X
X
X
X
X
x
x
x
x
x
lOIS
lOIS
lOIS
lOIS
lOIS
109
109
109
109
109
109
1010
1010
1010
1011
1011
1010
1010
1010
10 10
10 14
lOIS
1015
1015
1015
1015
10 16
10 16
10 16
10 16
10 16
10 16
10 16
10 16
10 16
10 16
10 17
10 17
10 17
10 17
10 17
10 17
10 17
10 17
10 17
1017
10 17
10 17
10 17
10 17
x
x
x
x
x
1.051
9.014
6.493
3.637
1.375
1013
10 14
10 14
10 14
10 14
1010
1010
1010
1011
1011
7.768
8.783
9.992
1.068
1.078
x
x
x
x
x
(cm- 3)
np
10 12
1013
10 13
1013
10 13
(cm- 3)
nH
1Bble 14.9. (Continued.)
7.994 x
9.083 x
1.047 x
1.142 x
1.192 x
1.208 x
1.122 x
9.690 x
8.387 x
9.000 x
1.255 x
1.767 x
2.413 x
3.300 x
4.714 x
7.344 x
1.134 x
1.737 x
2.645 X
4.004 x
4.945 x
6.153 x
7.770 x
1.003 x
1.353 x
1.980 x
2.779 x
4.064 x
5.501 x
7.697 x
1.107 x
1.730 x
2.807 x
4.480 X
6.923 X
1.050 X
1.546 X
2.215 X
2.979 X
3.867 X
lOIS
lOIS
lOIS
lOIS
lOIS
1010
1010
1011
1011
1011
1011
1011
1010
1010
1010
1011
1011
1011
1011
1011
1011
10 12
10 12
10 12
10 12
10 12
10 12
10 12
10 13
10 13
10 13
1013
10 13
1013
10 13
10 14
10 14
10 14
10 14
10 14
(cm- 3)
n.
x
x
x
x
x
104
104
loS
loS
loS
102
103
103
103
103
103
103
104
104
104
104
104
104
104
104
102
102
102
102
1.284 x loS
1.363 x loS
1.444 X loS
1.525 X loS
1.608 X loS
1.691 X loS
1.776 X loS
1.860 X loS
1.946 X loS
2.032 X loS
8.624
9.578
1.060
1.132
1.207
6.954 x
1.008 x
1.404 x
1.959 x
2.860 x
4.558 x
7.194 x
1.124 X
1.738 x
2.659 x
3.274 x
4.017 x
4.905 x
5.957 x
7.192 x
6.335 x
1.102 x
2.212 x
3.824 x
6.341 x
8.993 x
1.290 x
1.882 x
2.799 x
4.451 x
10- 10
101
101
101
101
101
(dyncm- 2)
Ptot
0.983
0.986
0.989
0.991
0.993
0.995
0.996
0.995
0.994
0.990
0.988
0.985
0.983
0.980
0.977
0.975
0.973
0.972
0.971
0.971
0.970
0.970
0.970
0.971
0.971
0.972
0.972
0.973
0.973
0.974
0.837
0.867
0.901
0.924
0.940
0.949
0.958
0.967
0.972
0.978
Pgas/Ptot
x
x
X
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
2.86 x
2.92 x
2.96 X
3.00 X
3.04 X
3.06 X
3.09 X
3.10 X
3.13 X
3.17 X
2.32
3.46
4.87
6.79
9.82
1.53
2.37
3.62
5.46
8.14
9.87
1.19
1.41
1.67
1.94
2.24
2.40
2.57
2.68
2.77
1.26
2.35
5.07
9.21
1.59
2.33
3.47
5.31
8.34
1.41
10-9
10-9
10-9
10-9
10-9
10- 8
10- 8
10- 8
10- 8
10- 8
10- 8
10-7
10-7
10-7
10-7
10-7
10-7
10-7
10-7
10-7
10-7
10-7
10-7
10- 7
10-7
10-7
10-7
10- 7
10-7
10-7
10- 10
10- 10
10-9
IO~IO
10- 11
10- 11
10- 11
10- 11
10- 10
10- 10
(gcm- 3)
p
-Z
c::
en
.J:>.
0
VI
W
14.5 SPECTRAL LINES I 351
14.5 SPECTRAL LINES
by William Livingston and Oran R. White
14.5.1
Absorption Features
Selected Fraunhofer absorption features are given in Table 14.10. Equivalent width refers to disk
center. Cycle variability, where known, refers to solar irradiance, or Sun as a star [54-64].
Table 14.10. AbsorptionJeatures.
Wavelength
(nm)
279.54
280.23
388.36
393.36
396.85
430.79
517.27
518.36
525.02
537.96
538.03
557.61
587.56
589.00
589.59
612.22
630.25
656.28
676.78
769.89
777.42
854.21
868.86
1006.37
1083.03
1281.81
1564.85
1565.29
2231.06
4652.55
4666.24
12318.3
Name
Species
MglI
MglI
(CNband
head)
K
H
Gband
~
h]
D3
D2
D]
C(Ra)
HPaschfJ
HPfundfJ
CN
Call
Call
CH (Fe I, Ti II)
MgI
MgI
Fel
Fel
CI
Fel
Equiv. width
(om)
Cyclevar.
[% (p-to-p)]
2.2
10
UV emission, high chromosphere
0.03 (index)
3
Photosphere, magnetic field tracer
2.0
1.5
0.72
0.075
0.025
0.0070
0.0079
0.0025
15
10
Chromosphere
0.3
0.3
0.0
Photo. magnetic fields (g = 3)
Medium photosphere
Low photosphere
Photo. velocity fields (g = 0)
Chromo., flares, prominences
Upper photo., low chrom., prom.
(same except water blend free)
Photo. magnetic fields (g - 1.5)
Photo. magnetic fields (g = 2.5)
Chromo., prom., flares
Photo. oscillations
Photo. oscillations
High photo. (?) (NLTE?)
Low chromo., prom.
Photo. magnetic fields (g = 1.7)
Umbra! (only) mag. fields (g = 1.22)
High chromosphere
Chromosphere
Photo. magnetic fields (g = 3)
Photo. magnetic fields (g = 1.8)
Umbra! (only) mag. fields (g = 2.5)
Chromo., electric fields
High photo. thermal structure
High photo., magnetic fields (g = 1)
He!
Nal
Nal
Cal
Fel
HI
Nil
KI
0.075
0.056
01
0.0066
0.37
0.014
-I
0.003
0.19
0.0035
0.003
200
Cal
Fel
FeH
Hel
HI
Fe]
Fel
Til
HI
CO
MgI
Comment
0.0083
0.40
6
Magnetic field tracer
Low chromosphere
14.5.2 Emission Features
Table 14.11 gives absolute spectral irradiances at the Earth for the UV and EUY with estimates of solar
cycle variability where known. Irradiances from both individual lines and integration over bands are
given in the table. The irradiance for all entries identified as a "line" in column 3 (bandwidth) is the
integral for the line, and is in units ofmWm-2. In contrast, irradiances for the "bands" are mean fluxes
per nanometer wavelength interval for that band [65,66].
352 /
14
SUN
Table 14.11. Solar spectral irradiances: 0.5-300 nm.
Band
GOESa
4
5
6
7
8
9
10
II
12
14
15
17
18
19
20
21
22
24
25
27
28
29
33
34
35
36
37
Band
center
(nm)
0.50
22.50
25.63
28.42
27.50
30.33
30.38
32.50
36.81
37.50
46.52
47.50
55.44
58.43
57.50
60.98
62.97
62.50
70.33
72.50
77.04
78.94
77.50
97.70
97.50
102.57
103.19
102.50
121.50
150.00
Solar irradiance
Bandwidth
(nm)
Solar max.
Solar min.
0.6
5
1.9 x 10- 2
6.5 x 10- 2
line
line
2.6
2.9
8.6 x 10- 3
1.6
7.4
6.9 x 10- 2
1.2
1.5 x 10- 2
7.1 x 10- 1
3.0 x 10- 3
1.7
3.5 x 10- 1
1.1 x 10- 2
9.8 x 10- 1
1.5 x 10- 1
9.3 x 10- 3
1.2 x 10- 1
3.9 x 10-3
4.1 x 10- 1
5.5 x 10- 1
2.2 x.IO- 3
9.0 x 10- 1
5.4 x 10- 2
1.8
1.7
5.1 x 10- 2
1.0 x 10 1
1.0 x 10- 1
0
1.6
7.7
5.9
3.9
1.6
3.9
1.1
1.1
7.8
1.3
1.5
5.7
1.6
5.5
4.9
5.5
2.9
4.8
2.1
2.0
2.2
1.0
3.6
2.4
6.2
7.0
1.7
5
line
line
5
line
5
line
5
line
line
5
line
line
5
line
5
line
line
5
line
5
line
line
5
x
x
x
x
x
10-2
10-2
10- 1
10-3
10- 1
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
10-2
10- 1
10-3
10- 1
10-3
10- 1
10- 1
10-3
10- 1
10-2
10- 3
10- 2
10-3
10- 1
10- 1
10-3
10- 1
10-2
10- 1
10- 1
10-2
Solar cycle
variability
/max//min
4
34
5
2
10
2
6
10
2
5
2
3
2
2
2
3
3
3
2
2
3
2
2
2
3
2
3
1.5
1.15
Species
Hell, Six
Fe XV
SixI
Hell
Mglx
NeVIl
OIV
Hel
Mgx
Ov
Om
Nevm
OIV
em
HI (LyP)
OVI
HI (Lya)
Note
a Geostationary Operational Environmental Satellite.
14.5.3
Line Widths and Heights
See [67] for a detailed description of curve-of-growth analysis techniques. These yield the following
results [68-74]:
Atomic thermal velocity
Microturbulence (~mi)
Macroturbulence (~ma)
Velocity for line breadth
= (2kT /ma)I/2
= 1.4kms-l.
= 1.1 kms- 1.
= 1.6 kms- 1 (vertical)
= 2.8 kms- 1 (horizontal).
= (~~ + ~~ + ~im) 1/2
= 2.4 km s-1 at center of disk
= 3.3 km s-1 at limb.
14.6 SPECTRAL DISTRIBUTION 1 353
Table 14.12 gives heights offormation of spectral lines [75,76]:
Table 14.12. Spectral line heights ojjol7lUJtion.
Line
(run)
Continuum (388.385)
CN388.33
Continuum (500.0)
FeI537.9
C1538.0
HI 656.0
FeII564.8
Fe I 1564.8 (spot)
Optical depth t'
(FWHM)
Height(km)
3.2 to 0.32
0.003 to 0.000039
2.5 to 0.25
0.35 to 0.0025
1.6 to 0.16
-45 to 60
370 to 740
-35 to 90
60 to 400
-20 to 110
2000 to 3000
-20 to -30
20 to 80
(FWHM)
14.6 SPECTRAL DISTRIBUTION
by Heinz Neckel
F).. = intensity of the mean solar disk per unit wavelength with spectrum irregularities smoothed
(±50 A). Thus F = J F).. d'J....
:F).. = 1r F).. = emittance of the solar surface per unit wavelength range.
fA = :F).. (R0 1A)2 = 6.80 x 10-5 F)..solar flux outside the Earth's atmosphere per unit area and
wavelength range. A = astronomical unit.
F{ same as for F).. but referring to the continuum between the lines. The curve joining the most
intense windows between the lines is regarded as the continuum. This may differ appreciably from the
continuum in the entire absence of absorption lines. F{ does not have any sudden changes (e.g., at the
Balmer limit).
1)..(0) = intensity at the center of the Sun's disk with spectral irregularities smoothed (±50 A).
I{ (0) = intensity of the center of the Sun's disk between spectrum lines. This is obtained by
interpolation from the most intense windows, as for F{.
I)..(O)II{ (0) represents the observed line blanketing for the center of the Sun's disk.
FA! 1)..(0) represents the broadband (loo-A) disk-to-center ratio. It is approximately equal to
F{II{ (0). The solar spectrum is given in Table 14.13.
Table 14.13. Solar spectral distribution, 0.2-5.0 j.tm [1-3].
A
(j.tm)
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
F)..
F')..
h(O)
I~ (0)
(103 Wm- 2 sr- I A-I)
0.01
0.07
0.08
0.19
0.34
0.83
1.12
1.34
1.42
0.014
0.10
0.13
0.27
0.68
1.48
1.97
2.39
2.56
0.014
0.13
0.13
0.37
0.60
1.34
1.67
1.89
1.96
0.02
0.19
0.21
0.53
1.21
2.39
2.94
3.30
3.47
h
(10- 3 Wm- 2 A-I)
h(O)/I~(O)
F)../h(O)
0.65
4.5
5.2
13
23
56
76
91
97
0.7
0.7
0.6
0.7
0.5
0.56
0.57
0.57
0.56
0.7
0.5
0.6
0.5
0.56
0.62
0.67
0.71
0.72
354 /
14
SUN
Table 14.13. (Continued.)
A
(tt m )
F).
F').
h(O)
l{ (0)
(103 Wm- 2 sr- I A-I)
f).
(10- 3 Wm- 2 A-I)
h(O)/I{ (0)
F)./h(O)
0.37
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0.45
1.67
1.58
1.52
2.17
2.50
2.54
2.34
2.71
2.94
2.67
2.99
3.21
3.35
3.42
3.47
3.50
3.49
3.47
2.28
2.16
2.08
2.97
3.38
3.45
3.12
3.61
3.87
3.60
4.14
4.41
4.58
4.63
4.66
4.67
4.62
4.55
113
107
103
148
170
173
159
184
200
0.63
0.52
0.47
0.65
0.73
0.74
0.67
0.78
0.85
0.73
0.73
0.73
0.73
0.74
0.74
0.75
0.75
0.76
0.46
0.48
3.01
2.99
3.41
3.28
3.95
3.84
4.44
4.22
205
203
0.89
0.91
0.76
0.78
0.50
0.55
0.60
0.65
0.70
0.75
2.83
2.76
2.61
2.34
2.08
1.87
3.20
2.93
2.67
2.41
2.13
1.92
3.61
3.43
3.17
2.81
2.46
2.18
4.08
3.63
3.24
2.90
2.52
2.24
192
188
177
159
141
127
0.88
0.94
0.98
0.97
0.975
0.975
0.78
0.80
0.82
0.83
0.85
0.86
0.8
0.9
1.0
l.l
1.2
1.68
1.38
l.ll
0.90
0.76
1.71
1.39
1.12
0.90
0.76
1.94
1.57
1.25
1.01
0.84
1.97
1.58
1.26
1.01
0.84
114
94
75
61
52
0.983
0.993
0.995
1.0
1.0
0.87
0.88
0.89
0.89
0.90
1.4
1.6
1.8
0.51
0.37
0.25
0.56
0.40
0.27
35
25.5
16.9
1.0
1.0
1.0
0.91
0.92
0.92
2.0
2.5
3.0
4.0
5.0
0.17
0.076
0.039
0.0130
0.0055
0.18
0.081
0.041
0.0135
0.0057
11.6
5.2
2.6
0.9
0.4
1.0
1.0
1.0
1.0
1.0
0.93
0.94
0.95
0.96
0.%
References
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd 00. (Athlone Press, London), Sees. 81
&82
2. Labs, D., Neckel, H., Simon, P.C., & Thuiller, G. 1987, Solar Phys., 90, 25
3. Neekel, H., & Labs, D. 1984, Solar Phys., 90, 205
Brightness temperatures for two optical wavelengths are given in Table 14.14, and Table 14.15
gives them for the infrared.
Table 14.14. Brightness temperatures.
4400 A
5500 A
5850K
6125 K
6165 K
6465K
5860K
5940K
6155 K
6240K
14.7 LIMB DARKENING / 355
Mean intensity and brightness temperature in mid- and far-infrared regions with heights from the
Vemazza, Avrett, and Loeser (VAL-C) model [77-79]:
Table 14.15. Infrared brightness temperatures.
14.7
J.. (j.Lm)
h (kIn)
5
10
20
50
100
200
1000= 1 mm
lem
70
160
240
340
410
450
logF.. (:::: h:::: F{:::: I{)
(Wm- 2 sr- 1 /Lm)
Tb (K)
4.77
3.57
2.36
0.76
-0.45
-1.67
-4.31
5730
5140
4820
4500
4340
4200
5920
10-23000
(temp min.)
(transition)
LIMB DARKENING
by Keith Pierce
I{ (0) = intensity of the solar continuum at an angle 0 from the center of the disk; 0 = angle between
the Sun's radius vector and the line of sight.
I{ (0) = continuum intensity at the center of the disk.
The ratio I{ (0)/ I{ (0), which varies with the wavelength A, defines limb darkening. As far as
possible, measurements are made in the continuum between the lines (hence the primes in the notation).
The results may be fitted to the following expressions:
I{(O)/I{(O)
= 1-
I{ (0)/ I{ (0)
= A + B cos 0 + C[1 -
or
where
A
U2 -
V2
+ U2COS 0 + V2 cos2 0,
+ B + (1 -
cos 0 In(1
In 2)C
=
+ sec 0)],
1.
The ratio of the mean to central intensity is
or
F{/I{(O)
= A + C + ~B - 2C(~ In2 = A + 0.667 B + 0.409C.
1)
The ratio of the limb-to-central intensity is
I{(90 0 )/I{(0)
= 1-
U2 -
V2
~ 1-
Ul
=A+C.
Table 14.16 presents limb darkening details, and the fit constants are given in Table 14.17.
356 I
14
SUN
Table 14.16. If (8)/ If (0) [1-16].
A (Jl,m)
0.20
0.22
0.245
0.265
0.28
0.30
0.32
0.35
0.37
0.38
0.40
0.45
0.50
0.55
0.60
0.80
1.0
1.5
2.0
3.0
5.0
10
20
Total
cos 8
sin 8
1.0
0.000
0.8
0.600
0.6
0.800
0.5
0.866
0.4
0.916
0.3
0.954
0.2
0.980
0.1
0.995
0.05
0.9987
[7]
[7]
[7]
[7]
[7]
[7]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[9]
[8]
[8]
[8]
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.85
0.58
0.71
0.68
0.72
0.77
0.809
0.837
0.851
0.83
0.835
0.860
0.877
0.890
0.900
0.924
0.941
0.957
0.966
0.976
0.986
0.992
0.994
0.898
0.74
0.33
0.49
0.42
0.47
0.57
0.623
0.665
0.687
0.66
0.663
0.714
0.744
0.769
0.788
0.843
0.870
0.902
0.922
0.944
0.963
0.981
0.983
0.787
0.69
0.26
0.42
0.32
0.38
0.48
0.532
0.579
0.603
0.58
0.585
0.637
0.675
0.703
0.727
0.793
0.828
0.873
0.896
0.922
0.949
0.973
0.975
0.731
0.65
0.21
0.36
0.24
0.29
0.39
0.438
0.487
0.513
0.48
0.490
0.556
0.599
0.633
0.664
0.744
0.783
0.831
0.865
0.902
0.937
0.964
0.970
0.669
0.61
0.16
0.31
0.19
0.22
0.30
0.347
0.397
0.421
0.39
0.403
0.468
0.513
0.556
0.587
0.681
0.731
0.789
0.826
0.873
0.916
0.956
0.964
0.602
0.58
0.12
0.25
0.14
0.16
0.22
0.262
0.306
0.332
0.30
0.308
0.378
0.425
0.468
0.508
0.615
0.675
0.735
0.780
0.835
0.890
0.937
0.957
0.525
0.14
0.17
0.21
0.23
0.22
0.222
0.278
0.323
0.371
0.412
0.533
0.59
0.65
0.70
0.78
0.84
0.90
0.95
0.448
0.19
0.18
0.18
0.21
0.26
0.31
0.35
0.47
0.54
0.58
0.61
0.67
0.76
0.87
0.93
0.39
References
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Sec. 81
2. Pierce, A.K., McMath, R.R., Goldberg, L., & Mohler, O.C. 1950, ApJ, 112, 289
3. Pierce, A.K., & Waddell, J.H. 1961, MNRAS, 68, 89
4. Gaustad, J.E., & Rogerson, J.R. 1961, ApJ, 134, 323
5. Mouradian, Z. 1965, Ann. d'Astrophys., 28, 805
6. Heintz, J.R.W. 1965, Rech. Astron. Obs. Utrecht, 1712
7. Bonnet, R. 1968, Ann. d'Astrophys., 31, 597
8. Lena, P. 1970, A&AS, 4, 202
9. Pierce, A.K., & Slaughter, C.D. 1977, Solar Phys., 51, 25
10. Neckel, H., & Labs, D. 1987, Solar Phys., 110, 139
11. Neckel, H., & Labs, D. 1994, Solar Phys., 153,91
12. Neckel, H. 1996, Solar Phys., 167,9
13. Neckel, H. 1997, Solar Phys., 171, 257
14. Pierce, AK., Slaughter, C.D., & Weinberger, D. 1977, Solar Phys., 52,179
15. Petro, C.D., Foukal, P.V., Rosen, W.A., Kurucz, R.L., & Pierce, AK. 1984, ApJ, 283, 462
16. Elste, G.H. 1990, Solar Phys., 126,37
Table 14.17. Limb darkening constants.
A
u2
112
A
0.20
0.22
0.245
0.265
0.28
0.30
+0.12
-1.3
-0.1
-0.1
+0.38
+0.74
+0.33
+1.6
+0.85
+0.90
+0.57
+0.20
-0.2
-3.4
-1.9
-1.9
-1.3
-0.4
B
C
0.9
2.9
2.0
2.1
1.8
1.2
+0.9
+5
+3
+2.7
+1.8
+0.5
:F'J,.
If (0)
If (90°)
If (0)
0.79
0.51
0.61
0.540
0.588
0.648
0.54
0.06
0.20
0.08
0.10
0.06
0.02
0.9998
0.14
0.19
0.24
0.28
0.32
14.8 CORONA /
357
Table 14.17. (Continueti)
A
u2
v2
A
B
C
0.32
0.35
0.37
0.38
0.40
0.45
0.50
0.55
0.60
0.80
1.0
1.5
2.0
3.0
5.0
10.0
+0.88
+0.98
+1.03
+0.92
+0.91
+0.99
+0.97
+0.93
+0.88
+0.73
+0.64
+0.57
+0.48
+0.35
+0.22
+0.15
+0.84
+0.03
-0.10
-0.16
-0.05
-0.05
-0.17
-0.22
-0.23
-0.23
-0.22
-0.20
-0.21
-0.18
-0.12
-0.07
-0.07
-0.20
-0.02
+0.25
+0.42
+0.26
+0.20
+0.54
+0.68
+0.74
+0.78
+0.92
+0.97
+1.11
+1.09
+1.04
+1.02
+1.04
+0.72
0.97
0.79
0.68
0.78
0.81
0.60
0.49
0.43
0.39
0.25
0.18
0.08
0.07
0.06
0.05
0.00
+0.42
+0.1
-0.3
-0.4
-0.2
-0.1
-0.44
-0.56
-0.56
-0.57
-0.56
-0.53
-0.61
-0.49
-0.34
-0.18
-0.22
-0.45
Total
14.8
.rr
l{ (0)
l{ (90°)
l{ (0)
0.685
0.705
0.71
0.71
0.718
0.755
0.782
0.803
0.817
0.862
0.886
0.916
0.932
0.948
0.964
0.982
0.82
0.08
0.11
0.13
0.13
0.13
0.11
0.16
0.20
0.24
0.39
0.48
0.56
0.60
0.72
0.81
0.87
0.32
CORONA
by Serge Koutchmy
Optical radiation from the corona contains three components:
K
F
L
= continuous spectrum due to Thomson scattering by electrons of the coronal plasma,
= Fraunhofer spectrum diffracted and/or scattered by interplanetary dust particles [81],
= coronal emission of forbidden lines; L is negligible for coronal photometry (about 1%).
The total coronal light beyond 1.03R0 (for typical lunar disk at eclipse) [82-84] is
at sunspot maximum
= 1.5 x
= 0.6 x
Total F corona = 0.3 x
at sunspot minimum
10-6 solar flux:::::: 0.66 full Moon,
10-6 solar flux:::::: 0.26 full Moon.
10-6 solar flux.
Earthshine on Moon at total eclipse [85] = 2.5 x 10- 10 mean Sun brightness.
The brightness of the sky near the Sun during a total eclipse [82, 84, 86] is
6 x 10- 10 < S < 10-8 x [mean Sun brightness
(80 )],
The spectral distribution of K components is similar to the solar spectrum, with B - V = 0.65. The
F component is slightly redder in the outer corona [87], with B - V :::::: 0.75. The base of corona may
be taken as the transition region at r = 1.0025R0 from the visible limb. Chromospheric extensions
are seen up to r = 1.015R0 .
The coronal ellipticity from isophotes € [83, 88, 89] is
358 / 14
SUN
where Al and PI are equatorial and polar diameters, and for A3,P3 the corresponding diameters are
averaged with those oriented 22.5° on either side.
E
at sunspot max.
~
0.06,
E
at sunspot min.
~
0.26 near r
Values are tabulated against r(R 0 ).
The polarization of coronal light (K
= 2R0 (extrapolated values; the a + b index).
+ F) [82,90,91] is
Ptot = (It - Ir)/(lt
+ Ir ),
where It and Ir are intensities polarized in the tangential and radial direction.
Pmax
= 50%.
Other values tabulated against rl R0 are listed in Tables 14.18 and 14.19.
A most relevant parameter to describe the distribution of electron densities in the plasma corona is
Pk = (It - Ir)/K with K = (It + Ir) - F; see [90].
Density irregularities in the corona may be specified approximately by an irregularity factor
x = N;/(Ne)2, where Ne is the electron density. Then rms Ne = N e x l / 2 . In the striated outer
corona one might write
x
~
1If.f. ,
where f.f. is the filling factor, which could be very small indeed. Only approximate data exist (see
Table 14.18). x varies with r I R0'
Temperature of corona:
Loops
Quiet corona Tmax at r
Coronal condensation
Coronal hole
Table 14.18. Radial variations o/p,
E,
~
2R0
(1.0-3.0) x 106 K.
1.6 x 106 K.
3 x 106 K.
lx106 K.
and x/or homogeneous and minimum cycle corona at 0.55/Lm [1-3].
r/R0
1.0
1.2
1.5
2
3
Polarization in %
Plot at equator
Plot at pole
Ellipticity E, minimum corona
Irregularity x
20
20
0.06
35
25
0.10
41
17
0.16
38
10
0.13
> 2.5
21
3
0.11
4
References
1. Saito, K. 1972, Ann. Tokyo Astron. Obs. XlI, 53, 120
2. Koutchmy, S., Picat, J.P.• & Dantel, M. 1977, A&A, 59, 349
3. Allen, C.W. 1961, Solar Corona IAU Symp.• 16, I
5
10
10
< 1
0.12
8
4
0.18
17
20
25
2.6
0.25
21
25
14.8 CORONA /
359
Table 14.19. Smoothed coronal brightness and electron density in average models [1-5].
log (surface brightness)
K
Max.
F
Min.
Eq.
p = r/R0
Eq.fPole
Max.
Eq.
Pole
Pole
(cm- 3)
10- 10 B0
log(p - 1)
logNe
Min.
9.0
8.8
8.7
8.6
8.4
8.25
-8.20
3.10
9.0
8.8
8.7
8.6
8.4
8.25
3.06
2.5
1.95
1.24
2.90
2.50
2.25
1.9111.82
7.90
7.44
7.05
6.52
7.8
7.35
7.05
6.50
7.10
6.25
5.95
5.0
1.63
1.25
0.7
0.25
1.6611.56
1048/1.33
6.00
5.60
5.95
5.50
4.75
4.50
0.61
0.2
-0.75
-0.35
-0.75
1.23/1.03
1.010.80
0.3110.06
-0.33/-0.72
5.1
4.8
4.10
3.2
5.05
4.75
4.05
4.20
4.0
1.003
1.005
1.01
1.03
1.06
1.10
-2.5
-2.3
-2.0
-1.5
-1.2
-1.0
4.9
4.65
4.45
4.3
4.8
4.6
4.35
4.20
4.25
4.10
3.85
3.60
1.2
104
1.6
2.0
-0.7
-0.4
-0.2
0.0
3.9
3.34
2.92
2.23
3.75
3.26
2.88
2.25
2.5
3.0
+0.2
+0.3
1.63
1.23
4.0
5.0
10.0
20.0
+0.5
+0.6
1.0
1.3
0.70
0.3
-0.5
8.0
7.50
References
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London), Sees. 73,84,
and 85
2. Newkirk, G., Dupree, R.G., & Schmahl, E.J. 1970, Solar Phys., 15, 15
3. Koutchmy, S., Zirker, J.B., Steinolfson, R.S., & Zhugzda, J.D. 1991, in Solar Interior and
Atmosphere, edited by A.N. Cox, W.e. Livingston, and M.S. Matthews (University of Arizona Press,
Tucson)
4. Blackwell, D.E., & Petford, A.D. 1966, MNRAS, 131,383
5. Saito, K. 1972, Ann. Tokyo Astron. Obs. xn,53, 120
14.8.1
Coronal Photometry and Electron Density N e
Assuming spherical symmetry, the distribution of coronal intensity 10 as a function of the projected
radial distance p may be used to determine the distribution of Ne as a function of radial distance r in
Table 14.20. The classical Baumbach expressions [92] are
106/0110
= 0.0532p-2.5 + 1.425p-7 + 2.565p-17,
leading to
The temperature in the inner corona is well described by the approximation of hydrostatic equilibrium [89] with Thyd = 6.08 x 106 [d (log N e)ld(r- 1)r 1 in K, assuming HIHe = 10.
360 /
14
SUN
Table 14.20. Electron densities (log Ne (cm- 3» in
coronal structures.
r/R0
Coronal
streamer
Coronal
hole (Void)
1.0
1.1
1.3
1.5
2.0
2.5
3.0
4.0
5.0
10.0
8.75
8.25
7.90
7.30
7.0
6.75
6.3
6.1
5.45
7.0
6.6
6.2
5.25
4.80
Thread
Loop
10.0
9.5
9.0
8.25
10.0
9.0
Coronal line spectrum quantities are:
Tm = temperature (K) at which spectrum reaches greatest intensity,
f
= energy flux (10- 6 W cm- 2 ) from the coronal line seen outside the Earth's atmosphere,
W = equivalent width of coronal line in terms of K continuum,
A = transition probability (s-I).
Tables 14.21, 14.22, 14.23, and 14.24 give some permitted, forbidden, and infrared coronal lines.
Table 14.21. Selected permitted lines, 1-61 nm [1-4].
A (nm)
0.92
1.21
1.36
1.51
1.69
Ion
Transition
f
logTm
MgXI
Nex, Fe XVII
NeIX
Fe XVII
Fe XVII
Is2_1s2p
6.4
Is 2-1s2p
2p6_2p 53d
2p6_2p 53s
2
1
2
8
9
6.20
6.58
6.58
8
6
6
4
85
6.36
5.9
6.14
6.27
5.85
1.90
2.16
5.06
6.97
17.10
Six
Fe XIV
Fe IX
Is-2p
Is 2-1s2p
2p-3d
3p-4s
3p6_3p 53d
17.48
17.72
18.04
18.83
19.50
Fex
Fex
Fe XI
Fe XI
Fe XII
3p5_3p4 3d
3p5_3p4 3d
3p4-3p 33d
3p4-3p 33d
3p3_3p 23d
90
33
75
40
60
6.00
6.00
6.11
6.11
6.16
20.20
21.13
28.41
30.34
33.54
Fexm
Fe XIV
Fe xv
SiXI
Fe XVI
3p2-3p3d
3p-3d
3s 2-3s3p
2s 2-2s2p
3s-3p
25
15
40
30
20
6.21
6.27
6.31
6.22
6.40
Ovm
o VII
14.8 CORONA /
Table 14.21. (Continued)
A (nrn)
Ion
Transition
f
36.81
49.9
61.0
MgIX
SiXII
Mgx
2s 2-2s2p
2s-2p
2s-2p
15
10
12
logTm
5.97
6.27
6.04
References
1. Batstone, R.M., Evans, K., Parkinson, J.H., & Pounds,
K.A. 1970, Solar Phys., 13, 389
2. Walker, A.B.C., & Rugge, R.H. 1970, A&A, S, 4
3. Jordan, C. 1965, Commun. Univ. London Obs., 68
4. Freeman, F.F., & Jones, B.B. 1970, Solar Phys., IS, 288
Table 14.22. Selectedforbidden lines, 100-300 nrn [1, 2].
Ion
Transition
logTm
124.22
Fe XII
6.16
134.96
Fe XII
144.60
Si VIII
146.70
Fe XI
pHS J-2 P J
1'7
1'7
pHS J-2 p\
1'7
'7
2p3 4 S J-2 D \
1'7
1 '7
212.60
214.95
216.97
NixIII
SiIX
Fe XII
ADm
6.16
5.93
3p43pI_ l So
6.11
3p43~_ID2
2p23~_ID2
3p3p 4 S J-2 D \
1'7
2'7
6.27
6.04
6.16
References
1. Jordan, C. 1971, Eclipse of 1970, COSPAR Symp.
2. Gabriel, A.H. et a1. 1971, ApJ, 434,807
Table 14.23. Selectedforbidden lines, 300-700 Dm [1-3].
A
(nrn)
Ion
Transition
A
(s-I)
W
(10- 10 DmxB0)
3.72
488
0.07
6.19
5.96
3.44
87
193
1.0
0.13
6.19
6.37
2.93
237
0.11
6.17
Upper
E.P. (eV)
logTm
332.9
CaxII
2 p 52p \_2pJ
338.82
360.09
Fe XIII
NixVI
3p2 31'2_1 D2
3p2p\_2p \
423.20
NixII
3p5 2 p \
530.281
Fe XIV
3p2PJ_2 p \
2.34
60
2.0
6.27
569.44
637.45
Caxv
Fex
2p 23J>o_3 PI
3 p 52p \_2p\
2.18
1.94
95
69
0.03
0.5
6.00
670.19
Nixv
3p23J>o_3 PI
1.85
57
0.12
6.32
1'7
'7
'7
1'7
1'7
'7
1'7
1 '7
'7
References
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London),
Sees. 73, 84, and 85
2. Livingston, W., & Harvey, J. 1982, Proc. lnd NatL Sci. Acad., 48, Suppl. 3, 18
3. Jefferies, J.T., Orrall, F.Q., & Zirker, J.B. 1971, Solar Phys., 16, 103
361
362 / 14
SUN
Table 14.24. Near IR lines [I, 2].a
f
(10- 2 Wm- 2 sr- I )
A-
Ion
789.19
1074.617
1079.783
1083.0
1252.0
[Fe XI]
[Fe XIII]
[Fe XIII]
Hel
[SIX]
1.5
3p4 3l'7._3 PI
3 p 23J>o_3PI
3p 23PI_3 P2
2p 3 p_2s 3 S
}s22s 22p4 3 PI_3 P2
1283.0
1431.0
HI
[Six]
3.00
1.55
Paschen (5-3)
}s22s 22p 2 P3 _2 P I
1523.0
1856.0
1876.0
[CrxI]
[CrxI]
HI
0.47
0.4
13.0
1922.0
2167.0
2747.0
3019.0
[SiXI]
HI
[Alx]
[MgvIII]
<0.7
<0.5
< 1
<I
Transition
l
l
3s 23p2 3 P2-3 PI
3s 23 p2 3 PI-3 Po
Paschen (4-3)
}s22s2p 3l'7._3 PI
Brackett (7-4)
Is 22s2p 3l'7._3 PI
}s22s 22p 2 P3 _2 PI
l
l
Note
aKuhn [3] points out that many of the IR lines in this table were not
observed at the eclipse of 3 Nov. 1994 and questions their reality.
References
I. Olsen, K.H., Anderson, C.R., & Stewart, J.N. 1971, Solar Phys., 21, 360
2. Penn, M.J., & Kuhn, J.R. 1994, ApJ, 434,807
3. Kuhn, J. 1995, private communication
14.9 SOLAR ROTATION
by Robert Howard
The inclination of the solar equator to the ecliptic [93-96] is 7°15' .
The longitude of the ascending node is 75°46' +84' T, where T is epoch in centuries from 2000.00.
The sidereal differential rotation coefficients from the formulas
w
= A + B sin2 cp deg/day,
where cp is the latitude, and
w = A
+ B sin2 cp + C sin4 <I> deg/day,
are often used for features that extend to higher latitudes. These are given in Table 14.25. See also [97].
14.9 SOLAR ROTATION I 363
Table 14.25. Empirical rotation coefficients.
B
c
14.522
14.39
14.06
14.37
14.71
-2.84
-2.95
-1.83
-2.30
-2.39
-1.62
-1.78
14.48
13.46
14.42
-2.16
-2.99
-2.00
-2.09
A
From tracers
Individual sunspots [1]
SUDSpot groups [I, 2]
Plages [3]
Magnetic field pattern [4]
Supergranular pattern [5, 6]
(Doppler features)
Filaments, prominences [7]
Coronal features [8, 9]
Small magnetic features [10]
From the Doppler effect in solar lines
Surface plasma [11]
Ha line [12]
14.11
14.1
-1.70
-2.35
References
1. Howard, R., Gilman, P.A., & Gilman, P.I. 1984, ApJ, 283, 373
2. Balthasar, H., Vazquez, M., & Woehl, H. 1986, A&A, 155, 87
3. Howard, R.F. 1990, Solar Phys., 126,299
4. Snodgrass, H.B. 1983, ApJ, 270, 288
5. Duvall, Jr., T.L. 1980, Solar Phys., 66, 213
6. Snodgrass, H.B., & Ulrich, R. 1990, ApJ, 351, 309
7. d' Azambuja, M., & d' Azambuja, L. 1948, Ann. Observ. Paris, 6, 1
8. Dupree, A.K., & Henze, Jr., W. 1972, Solar Phys., 27, 271
9. Henze, Jr., W., & Dupree, A.K. 1973, Solar Phys., 33, 425
10. Komm, R.W., Howard, R.F., & Harvey, I.W. 1993, Solar Phys., 145, 1
11. Snodgrass, H.B., Howard, R., & Webster, L. 1984, Solar Phys., 90, 199
12. Uvingston, W.C. 1969a, Solar Phys., 7,144; 1969b, 9, 448
Rotation of solar plasma as a function of depth from oscillation measurements increases from the
surface rate by about 0.8 deglday at a depth from 0.01R0 to 0.08R0 , then decreases slowly with
depth [98,99].
The period of sidereal rotation adopted for heliographic longitudes is 25.38 days. The corresponding synodic period is 27.2753 days. Conversion factors between different units are given in
Table 14.26.
Table 14.26. Conversion/actors.
To convert from
Multiply by
deglday to p.rads- 1
deglday to ms- 1
degldaytooHz
0.20201
140.596 cos 1/1
32.150
Sidereal-synodic rotation = Earth's orbital motion
= 0.9856 deglday (averaged over a year).
364 I
14.10
14
SUN
GRANULATION
by Richard Muller
The solar surface is covered by a hierarchy of patterns that are convective in origin: granulation,
mesogranulation, and supergranulation [98-109]:
Granules
Diameter of granules
Range about 0~'25 to 3~'5
Intergranular distance
Number of granules on whole photospheric surface
Corresponding area occupied by a cell
Granule intensity contrast
Brighter granule/intergranule
Corresponding temperature difference
Root-mean-square variations
Intensity at 550 nm observed
Corrected
Temperature
Mean lifetime of granules
Upward velocity of brighter granules
14.11
1~'4
=
1000 km
t'o
5 x 106
1.5 x 106 km2
1.3
300K
0.09
0.15
IIOK
10 min
1 km s-1
Mesogranulation
Diameter
Lifetime
Vertical velocity
Proper motion
5000km
3h
0.06 km s-1
0.4kms- 1
Supergranulation
Diameter
Lifetime
Horizontal velocity to edge
32000km
20h
0.4 kms- l
SURFACE MAGNETISM AND ITS TRACERS
by Peter Foukal, Sami Solanki, and Jack Zirker
Buoyancy lofts magnetic fields from the solar interior into the photosphere where they emerge as active
regions to be dispersed laterally under the influence of convection (various scales) and other largescale horizontal flows. White light tracers of magnetism are sunspots and faculae. Monochromatic
tracers (line weakening) are plage, filigree, the network, internetwork, coronal holes, and prominences.
The network and plages are presumed to be composed of aggregates of flux tubes. Prominences are
found along magnetic neutral lines or above active regions. Magnetic field details for various surface
structures are given in Table 14.27.
14.11 SURFACE MAGNETISM AND ITS TRACERS / 365
Table 14.27. Magneticfields. a
Field strength
Sunspot umbrae
Sunspot penumbrae
Pores
Plage or facular magnetic elements B (z
Network magnetic elements B (z = 0)
Internetwork
= 0)
2-4 kG
0.8-2 kG
1.7-2.5 kG
1.4-1.7 kG
1.3-1.5 kG
:::: 600 G (probably)
Aux [1]
3 x 1019 Mx
3 x 1020 Mx
3 x 102 1 Mx
::: 1022 Mx
(20-50) x 1022 Mx
Ephemeral region
Small active region
Moderate active region
Large active region
Giant active region
=
Magnetic elements
Diameter [2, 3]
Lifetime [4]
200-300km
18 min
Global aspects [1]
= (15-20) x 1022 Mx
= (100-120) x 1022 Mx
Total flux at solar min
Total flux at solar max
Note
aThe field strength is strongly height dependent. See Sec. 14.12 on sunspots
for more information on sunspot field gradients. For magnetic elements the field
drops from the tabulated values at z
0 (i.e., the quiet Sun continuum forming
layer) to roughly 200-500 G (in plage) near the temperature minimum (e.g., [6]
and [7]). The magnetic element lifetime [5] is probably only a lower limit, being a
lifetime measurement of the brightness structure that probably lives less long than the
underlying magnetic structure. There is no permanent dipole field but one develops
over solar cycle due to evolution of polar fields; at other times there is a dipole
component to lower-latitude extended active-region fields [8,9]. Mx means maxwell
(Gcm2).
=
References
1. Harvey, K. 1992, in Proceedings of the Workshop on Solar Electromagnetic
Radiation Study for SOLAR CYCLE 22, edited by R.F. Donnelly (Nat!. Info. Tech.
Service, Springfield, VA), p. 113
2. Keller, C.U. 1992, Nature, 359, 307
3. Grossmann-Doerth, U., Knolker, M., Schiissler, M., & Solanki, S.K. 1994, A&A,
285,648
4. Muller, R. 1985, Solar Phys., 100,237
5. Deming D., Boyle, R.J., Jennings D.E., & Wiedemann, G. 1988, ApJ, 333, 978
6. Zirin, H., & Popp, B. 1989, ApJ, 340, 571
7. Sheeley, Jr., N.R., & Boris, J.P. 1985, Solar Phys., 98, 219
8. Wang, Y.M., & Sheeley Jr., N.R. 1989, Solar Phys., 124, 81
14.11.1
Faculae
Faculae are cospatial with photospheric magnetic fields. They become visible in white light near the
limb (i.e., as p, = cos (J .... 0). While fragmented and irregular, they do tend to outline the circular
boundaries of supergranular cells [112, 113].
The center-to-limb dependence of wide-band facular contrast (integrated over the spectral range
0.35-1.0 p,m) can be expressed as
C(p,) - 1 = 0.115(1 - p,),
366 / 14
SUN
where
C(/L)
= Iracula/ [photosphere
[114]. At the highest spatial resolution values of C(/L) increase by a factor of 3-4 [115].
The wavelength dependence of facular contrast is approximately given by
where C5300(/L) is the intensity of the faculae relative to the photosphere at 5300 A [116].
Life of average faculae
Life of large faculae (dominating solar variations)
15 days
2.7 months
The excess temperature of magnetic elements [117, 118] is given in Table 14.28.
Table 14.28. Excess temperatures.
iog1"5000
Piage: TMagel - Tphot (K)
Network: TMagel - Tphot (K)
-5
-4
-3
-2
-1
1400
1400
1500
1500
650
700
500
700
560
770
0
-130
460
14.11.2 Plages
Plages or bright flocculi are readily visible in Hex and in the H and K lines of Ca II. The locations agree
well with faculae but plages are visible over the whole disk. Measurements of area and eye estimates
of intensity (scale 1 ~ 5) are made regularly [119].
Table 14.29 shows the approximate relation between plage area and sunspot area (both in 10-6
hemisphere).
Table 14.29. Plage and sunspot areas.
Piage area
Sunspot area
500
0
1000
30
2000
100
3000
180
4000
280
6000
500
8000
900
10000
2000
Since the duration of the plage is longer than that of the spot, the spot area may be much less than the
value given. Normally sunspots are present when the plage intensity is 2: 3.
The exponential decay time of a plage observed area is 1.6 rotations (43 days). The actual area of
a plage expands continuously but the fainter parts are below measurement threshold.
Values for a typical large active region [115] are:
Sunspot area
Plage area
Plage area at disk center
Plage diameter
600 x 10-6 hemisphere.
6000 x 10-6 hemisphere.
12000 x 10-6 disk.
3.5 arcmin.
14.12 SUNSPOTS /
14.11.3
367
Prominences
Table 14.30 shows the physical conditions in quiescent prominences.
Table 14.30. Quiescent prominences.
log [electron density (cm- 3)]
Temperature (K)
10.48-11.02 [1]
9-10
5000-7000
20000-600000 [2]
References
1. Hirayama, T. 1986, Coronal and Prominence Plasmas, edited
by A.l. Poland (NASA, Washington, DC), p. 2442
2. Orrall, F.Q., & Schmahl, EJ. 1980, ApJ, 240, 908
The temperature varies considerably within a prominence.
The proton-to-hydrogen density ratio is 0.05 < N p / NH < 1 [120].
Sizes
Threads [121]
Height
Length
Thickness
Magnetic field (horizontal)
Velocity
300-1800 km (diameter).
2000 kIn (active),
10000-50000 kIn (quiescent).
50000-200 000 kIn.
3000-5000 km.
2-20 G (quiescent) [122],
10-40 G (active).
15-35 kIn s-1 (threads, apparent) [123],
1-3 kIns- 1 (Doppler, horizontal) [124],
2-10 kIns- 1 (turbulent).
The angle of the field with the axis of the prominence'" 20° [122].
Lifetimes are approximately 1 week to 3 months; the average is 2 months.
14.12
SUNSPOTS
by Sami Solanki
The formula for the center-to-limb variation of umbra! brightness (1 2: f.L > 0.3) is
iu = Iu/1q, where Iq is the quiet Sun brightness, and ip
given in Table 14.31.
=
Ip/lq. Brightness data for sunspots are
14
368 I
SUN
Table 14.31. Center-to-limb variation and A dependence of umbra I and penumbral brightness [1-4].
A (IAom)
iu (lAo
iu (lAo
iu (lAo
= I, A)early
= I, A)middle
= I, A)late
bu (A)
ip (lAo
= l,A)
0.387
0.579
0.669
0.876
1.215
1.54
1.67
1.73
2.09
2.35
0.008
0.022
0.066
0.110
0.061
0.090
0.119
0.191
0.215
0.239
0.327
0.345
0.358
0.451
0.495
0.534
0.507
0.548
0.590
0.543
0.577
0.612
0.567
0.589
0.611
0.565
0.581
0.597
-0.010
0.012
0.009
0.019
0.031
0.087
0.087
0.094
0.090
0.058
0.64
0.768
0.794
0.827
0.876
0.914
0.928
References
1. Albregtsen, F., & Matby, P. 1978, MaJ., 274, 41
2. Albregtsen, F., JorAs, P.B., & Matby, P. 1984, Solar Phys., 90, 17
3. Maltby, P. 1972, Solar Phys., 26, 76
4. Matby, P., Avrett, B.B., Carlsson, M., Kje1dseth-Moe, 0., Kurucz, R.L., & Loeser, R. 1986, ApI, 306, 284
A model for the sunspot umbral core is given in Table 14.32.
Table 14.32. Model of the dark umbral core [1-4].
log
1"
T (K)
log Pg (egs)
log Pe (egs)
z (kIn)
6140
5.78
2.01
-94
0
-1
-2
-3
-4
-5
-6
4040
3540
4.91
-0.28
95
3420
4.28
-0.80
220
3400
3.64
-1.28
380
3450
2.95
-1.75
600
6400
0.99
-1.96
1115
8700
-0.61
-1.04
1850
5.43
0.52
0
References
1. Maltby, P., Avrett, B.A., Carlsson, M., Kje1dseth-Moe, 0., Kuruez, R.L., & Loeser, R.
1986,ApJ,306,284
2. Avrett, E.B. 1981, in The Physics of Sunspots, edited by L.E. Cram and J.B. Thomas
(Sacramento Peak Obs., Sunspot, NM), p.235
3. Van Bal1egooijen 1984,A&A, 91,195
4. Obridko, V.N., & Staude, J. 1988, A&A, 189,232
Magnetic field data for sunspots are given in Tables 14.33 and 14.34.
Table 14.33. Maximum magneticjield BO as afunction ofumbral radius ru [1,2].
ru (kIn)
BO (G)
500
2000
1000
2000
2000
2000
4000
2300
6000
2700
References
1. Brants, J.J., & Zwaan, C. 1982, Solar Phys., 80, 251
2. Kopp, G., & Rabin, D. 1992, Solar Phys., 81, 231
8000
3100
10000
3500
3.8
0.936
14.12SUNSPOTS
/
369
Table 14.34. Relative magnetic field B / BO and its inclination y' relative to the vertical versus
position in spot r Jor a large symmetric sunspot [I-51.
r/rp
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
B/ BO
y' (deg)
1
0
0.99
7
0.96
15
0.92
24
0.84
35
0.74
48
0.62
58
0.50
66
0.41
73
0.35
77
0.30
80
References
1. Solanki, S.K., Riiedi, I., & Livingston, W. 1992, A&A, 263, 339
2. McPherson, M.R., Lin, H., & Kuhn, J.R. 1992, Solar Phys., 139, 255
3. Lites, B.W., & Skumanich, A. 1990, ApJ, 348, 747
4. Kawakami, H. 1983, PASJ, 35, 459
5. Adam, M.G. 1990, Solar Phys., 125,37
The azimuthal angle of the field is ljJ ~ 20° for symmetric sunspots. In the penumbra y' is an
average value, with bright and dark filaments inclined relative to each other by 20°-40° [125-127].
In the outer penumbra the inclination depends on the size of the sunspot, with smaller sunspots having
more vertical fields [128].
Table 14.35 gives structure details of the outer parts of sunspots.
Table 14.35. Superpenumbral canopy: Base height Zc as a function oj
distanceJrom center oJ spot r/rp normalized by the spot radius rp [1,21.
r/rp
1.0
1.2
1.4
1.6
Base height Zc (km)
B/BO
y' (deg)
o
200
0.21
86
300
0.15
89-90
350
0.11
89-90
0.30
80
References
1. Giovanelli, R.G. 1980, Solar Phys., 68, 49
2. Giovanelli, R.G., & Jones, H.P. 1982, Solar Phys., 79, 267
Table 14.36 gives the magnetic field gradients in sunspots.
Table 14.36. Vertical gradient oj the field [1-7].
r/rp
0.0
0.6
1.0
dB/dz in photosphere (GIkm)
dB/dz in photosphere and chromosphere (GIkm)
2
0.5
2
0.4
0.2
1
References
1. Bruls, J.H.M.J., Solanki, S.K., Carlsson, M., & Rutten, R.J. 1993, A&A, 293, 225
2. Abdussamator, HJ. 1971, Solar Phys., 16, 384
3. Henze, N., Jr., Tandberg-Hanssen, E., Hagyard, M.J., Woodgate, B.E., Shine, R.A.,
Beckers, J.M., Bruner, M., Gurman, J.B., Hyder, L.L., & West, E.A. 1982, Solar
Phys., 81, 231
4. Lee, J.W., Gary, E.E., & Hurford, GJ. 1993, Solar Phys., 144,45 and 349
5. Riiedi, I., Solanki, S.K., & Livingston, W. 1994, A&A, 293, 252
6. Whittman, A.D. 1974, Solar Phys., 36, 29
7. Pahlke, K.-D. 1988, Ph.D. thesis, University of Gottingen, Gottingen, Germany
370 /
14
SUN
Wilson depression. The apparent depression of '['
and derived from MHS equilibrium [133, 134] is
ZW
= 1 of the umbra seen near the limb [129-132]
= 600 ± 200 kIn.
The relative magnetic flux in umbra and penumbra [135], with <l>t the total magnetic flux of spot,
<l>u the magnetic flux of the umbra, and <I> p the magnetic flux of the penumbra, is
= 1/3 <l>p/<I>t = 1/2 -
1/2,
<l>u/<I>t
2/3.
The variation of the umbral-to-photosphere intensity ratio rp with solar cycle (at A = 1.67 /Lm) is
rp
= 0.44 + 0.15t/to,
where t is the time elapsed from the starting epoch and to is the length of the solar half-cycle [136].
The average East-West inclination of field lines in spots is
all spots
leading
following spots
-3?4,
-2?8,
-3?8.
The negative angle indicates that the field lines trail the rotation [137].
Sunspot axial tilt angles (individual sunspots) are the angles between the line joining the leading
and following spots of a group and the local parallel of latitude. The leading spots on average are closer
to the equator than the following spots as a function of latitude with the value of about 2° at the equator
to about 12° at ±35° latitude [138-141].
The area distribution of individual sunspots can be described as a two-parameter log-normal
distribution [142]:
In
= _ (In
+ In
dA
2lnua
dA max
(dN)
A-In{A})2
(dN)
in terms of sunspot umbral area A (in units of 1O-6 2rr R~). Values of the three other quantities in the
above equation (Table 14.37) depend somewhat on the range ofumbral areas used to derive them:
Table 14.37. Sunspot area distribution.
Range
(A)
1.5-141
5.5-116
0.62
0.34
(dN/dA)max
3.8
4.8
9.2
16.4
14.13 SUNSPOT STATISTICS
by Karen Harvey and Robert M. Wilson
The sunspot number is defined as
R
= k(10g + s),
where k is an observatory reduction constant of order unity, g is the number of sunspot groups, and s is
the total number of individual spots [143-145]. Prior to January 1981, R was referred to as the Zurich
sunspot number. From January 1981 on, R has been referred to as the International sunspot number.
14.13 SUNSPOT STATISTICS / 371
Monthly values of R are combined to yield the 12-month moving average of R (denoted Ro),
which is also known as the smoothed sunspot number [146]. For a cycle, the minimum value of Ro
denotes the sunspot minimum (Rm), while the maximum value denotes the sunspot maximum (RM).
Conventionally, the length of a sunspot cycle is determined from minimum to minimum (m ~ m) and
is comprised of two parts: the ascent interval, the time from minimum to maximum (m ~ M), and
the descent interval, the time from maximum to succeeding cycle minimum (M ~ m). Occasionally,
the time between maxima is also of interest (M ~ M). Each sunspot cycle is numbered with the most
recent sunspot cycle being cycle 22 (Rm occurred in September 1986 and RM occurred in July 1989).
The sunspot record is of uneven quality [144]. The most reliable sunspot data extend from the
present back to about 1850 and 1818 (covering cycles 7-9), while data of poor quality occur for earlier
times (cycles before cycle 7). Some evidence exists suggesting that there was an extensive period of
time when sunspots were few in number [147]. This interval of time (ca. 1645-1715; cycles -9 to
-4) is often referred to as the Maunder minimum.
Other information from the sunspot record follows:
Waldmeier effect. The sunspot amplitude (RM) varies inversely with the ascent duration (m ~ M).
Hale cycle. The magnetic polarity changes in alternate cycles (even-numbered cycles have leading
spots of southern polarity in the northern hemisphere, and vice versa).
Sporer law. The latitude of sunspots progresses equatorward with the phase of the solar cycle
(yielding the so-called butterfly diagram).
Odd-even effect. The odd-following cycle tends to be of larger amplitude than the even-preceding
cycle.
Gleissberg effect. Sunspot cycles vary according to an 8-cycle variation (the so-called 80--100 year
variation).
Tables 14.38 and 14.39 list the sunspot number variations over the solar cycle.
Table 14.38. Variation of the annual sunspot number over the solar cycle (based on the reliable data of cycles [10-21 J). a
Elapsed time (yr) from sunspot minimum occurrence year
Parameter
0
Mean
Standard deviation
High
Low
6.2
5.9
2804
0.0
18.9
16.7
89.2
0.0
2
3
4
5
6
7
8
9
10
60.2
38.6
201.3
9904
50.0
253.8
24.5
107.0
41.1
202.5
39.3
98.5
36.6
21704
17.8
79.1
27.6
153.8
3404
5204
19.7
108.5
14.8
36.5
19.6
8804
0.3
21.2
1304
60.7
1.6
12.0
lOA
lOA
55.8
0.2
Note
aYalues listed are monthly mean values based on cycles 10-21 only.
Table 14.39. Variation of the smoothed sunspot number over the solar cycle (based on the reliable data of cycles [10-21]).a
Elapsed time (month) from Rm
Parameter
0
12
24
36
48
60
72
84
96
108
120
132
Mean
Standard deviation
High
Low
5.1
3.2
12.2
1.5
18.6
6.1
26.3
9.3
61.6
23.9
118.7
35.5
98.0
41.2
181.0
52.5
109.2
41.3
196.8
54.5
99.3
33.9
169.2
56.9
79.9
25.9
119.6
48.0
5204
14.9
70.5
31.2
34.7
13.9
60.6
13.8
2004
9.8
41.3
11.5
11.7
8.3
30.3
3.2
11.7
704
1504
2.6
Note
aYalues listed are smoothed sunspot number values based on cycles 10-21 only.
Characteristics of all the known sunspot cycles are listed in Table 14.40. Mean values are listed in
Table 14.41.
372 I
14
SUN
1Bble 14.40. Characteristics of sunspot cycles [1]. a
Data
quality
p
MaximumM
epoch RM
Cycle
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
1615.5
1626.0
1639.5
1649.0
1660.0
1675.0
1685.0
1693.0
1705.5
1718.2
1727.5
1738.7
1750.3
1761.5
1769.8
1778.4
1788.2
1805.2
1816.3
F
7
8
9
R
10
11
12
13
14
15
16
17
18
19
20
21
22
Minimumm
epochRM
Intervals (yr)
m_m
m_M
M_m
4.7
7.0
5.5
4.0
5.0
9.0
5.5
3.5
7.5
6.2
4.0
4.7
5.3
6.2
3.3
2.9
3.4
6.8
5.6
3.5
8.0
5.5
6.0
6.0
4.5
4.5
5.0
6.5
5.3
6.5
6.3
4.9
5.0
5.7
6.4
10.2
5.5
7.1
M_M
92.6
86.5
115.8
158.5
141.2
49.2
48.7
1610.8
1619.0
1634.0
1645.0
1655.0
1666.0
1679.5
1689.5
1698.0
1712.0
1723.5
1734.0
1745.0
1755.3
1766.5
1775.5
1784.8
1798.4
1810.7
8.4
11.2
7.2
9.5
3.2
0.0
8.2
15.0
11.0
10.0
11.0
13.5
10.0
8.5
14.0
11.5
10.5
11.0
10.3
11.2
9.0
9.3
13.6
12.3
12.7
1829.9
1837.3
1848.2
71.7
146.9
131.6
1823.4
1833.9
1843.6
0.1
7.3
10.5
10.5
9.7
12.4
6.5
3.4
4.6
4.0
6.3
7.8
13.6
7.4
10.9
1860.2
1870.7
1840.0
1894.1
1906.2
1917.7
1928.3
1937.3
1947.4
1958.3
1968.9
1980.0
1989.6
97.9
140.5
74.6
87.9
64.2
105.4
78.1
119.2
151.8
201.3
110.6
164.5
158.5
1856.0
1867.3
1879.0
1990.3
1902.1
1913.7
1923.7
1933.8
1944.2
1954.3
1964.8
1976.5
1986.8
3.2
5.2
2.2
5.0
2.6
1.5
5.6
3.4
7.7
3.4
9.6
12.2
12.3
11.3
11.7
10.7
11.8
11.6
10.0
10.1
10.4
10.1
10.5
11.7
10.3
4.2
3.4
5.0
3.8
4.1
4.0
4.6
3.5
3.2
4.0
4.1
3.5
2.8
7.1
8.3
6.3
8.0
7.5
6.0
5.5
6.9
6.9
6.5
7.6
6.8
12.0
10.5
13.3
10.1
12.1
11.5
10.6
9.0
10.1
10.9
10.6
10.5
13.5
9.5
11.0
15.0
10.0
8.0
12.5
12.7
9.3
11.2
11.6
ILl
8.3
8.6
9.8
17.0
ILl
ILl
9.6
Note
aR denotes a "reliable" data interval, F denotes a ''fair'' interval, and P denotes a "poor" interval.
Reference
1. Allen, C.W., editor, 1973, Astrophysical Quantities, 3rd cd. (Athlone Press, London), Sec. 87
1Bble 14Al. Mean values for selected sunspot cycle parameters.
Mean value
Parameter
R
R+F
All (R+F+ P)
m _
M _
m _
M _
RM
Rm
10.9
10.9
3.9
7.0
119.6
5.7
10.9
10.8
4.0
6.8
119.0
5.7
11.0
11.0
4.7
6.3
112.9
6.0
m period (yr)
M period (yr)
M ascent interval (yr)
m descent interval (yr)
14.14 FLARES AND CORONAL MASS EJECTIONS /
373
Table 14.42 shows how certain solar activity characteristics vary throughout the sunspot cycle.
Table 14.42. Solar activity.
0
Year
Minimum
1
2
3
5
4
Maximum
6
7
8
9
10
11
Sunspot regions
R new cycle
R old cycle
Spot latitude
68
9
24
237
7
22
488
3
19
547
561
510
360
269
168
99
38
13
17
14
13
12
10
9
8
7
6
Low
To high
16
42
7
39
3
1
42
0
33
0
28
0
24
0
20
1
16
1
9
Latitude range
40
0
38
0
37
Characteristics of an average size sunspot group:
Sunspot number
Number of individual spots
Spot area (umbra + penumbra)
= 12.
10.
200 millionths of hemisphere,
260 millionths of disk.
Spot radius (if a single spot)
Ca II plage area
O.020R 0 ·
R
1800 millionths of hemisphere.
14.14 FLARES AND CORONAL MASS EJECTIONS
by Steve Kahler
14.14.1
Flares
Chromospheric (Cool) Component of Flares [148, 149]
The Hex line importance classes are detailed in Table 14.43.
Table 14.43. Classes of optical importance in the Ha line.
Ha importance
Area (10- 6 hemisphere)
Mean duration
S
1
2
A < 200
200 < A < 500
500 < A < 1200
1200 < A < 2400
A> 2400
few minutes
25 min
55 min
2hr
2hr
3
4
Ha brilliance: f
= faint. n = nonnal. b = bright
Temperature - 15000 K
Density - 3 x 1013 cm- 3
374 /
14
SUN
Frequency of observed importance ~ 1 flares:
Frequency near solar maximum
Frequency near solar minimum
1000-2000 flares per year.
20--60 flares per year.
White-light flares [150, 151]:
Frequency near solar maximum
Luminosity
'" 15 per year.
1027 _1028 erg s-1 .
Coronal (Hot) Component [152]
Classes of soft X-ray (1-8 A) peak fluxes measured at 1 AU:
Bn
Mn
=n x
=
10-7 Wm- 2 ,
n x 10-5 Wm- 2 ,
en
Xn
=n x
=
10-6 Wm- 2 ,
n x 10-4 Wm- 2 •
Frequency of 1-8 A flares [153]:
Frequency of ~ Ml flares near solar maximum
Frequency of ~ Ml flares near solar minimum
Peak temperatures
Peak emission measures (n;V)
Density
'" 500 per year.
'" 15 per year.
(8-22) x 106 K.
1048-1050 cm- 3 .
1010_10 12 cm- 3 .
Impulsive Component
The duration is from < 1 min to > 30 min; the median duration'" 100 s. The y-ray fluence [154]
from < 10 to 104 y cm- 2 at > 300 keY; from < 0.3 to 3 x 102 y cm-2 for 4-8 MeV lines. For hard
X-rays [155, 156]:
Peak flux at E > 20 keY from < 10-6 to > 10-3 ergcm- 2 s-l.
Spectra: 3 < y < 9, where N(E) = AE-Y photons cm- 2 s-l keV- 1•
Thermal fits yield T ~ 108 K.
For EUV (10--1030 A) [157]:
Peak fluxes from < 3 x 10-2 to 10 ergcm- 2 S-l.
Temporal profiles match those of E > 10 keY X-rays.
For microwaves (1000-35000 MHz) [156]:
Peak fluxes from < 10 to ~ 104 solar flux units (s.f.u.) (10- 22 W m- 2 Hz-I).
Temporal profiles match those of E > 20 keY X-rays, and flux (E > 20 keY) (ergcm- 2 s- 1)
'" 10-7 x flux (3 cm) (s.f.u.).
14.14.2
Coronal Mass Ejections
Most coronal mass ejection (CME) quantities range over about two orders of magnitude. Average
values follow [158-161]:
Mass
Kinetic energy
3 x 1015 g.
2 x 1030 erg.
14.15 SOLAR RADIO EMISSION / 375
Speeds (of leading edges)
at solar maximum
at solar minimum
Angular width (plane of sky, subtended to solar disk)
Frequency [162]
at solar maximum
at solar minimum
450 kms- I .
160kms- l .
47°.
2-3 CMEs per day.
0.1--0.3 CMEs per day.
14.15 SOLAR RADIO EMISSION
by Timothy Bastian
Solar radio emission is expressed quantitatively in terms of the flux density Sv, usually in solar flux
units (s.f.u.), where 1 s.f.u. = 10- 22 W m- 2 Hz-I. For observations that spatially resolve the source of
radio emission, the intensity of the radiation is often expressed in terms of its brightness temperature
TB, where Sv = 7.22 x 1O- 51 TBV 2 Wm- 2 arcsec- 2 Hz-I. Tc refers to the brightness temperature
at the center of the solar disk. The degree of polarization, Pc, is defined by the ratio of the Stokes
polarization parameters V and I. Expressed in terms of brightness temperature in the orthogonal
(right- and left-hand) senses of circular polarization, Pc = (TRCP - hcp)/(TRCP + hcp), where the
RCP sense corresponds to a counterclockwise rotation for radiation propagating toward the observer.
14.15.1
Properties of Radio Emission from the Quiet Sun
The brightness temperature of the quiet Sun at disk center may be calculated approximately from the
following expressions for millimeter and centimeter wavelengths (Tc in K, U = loglo A, A in cm):
log Tc = 3.9609 + 0.1856u
+ 0.0523u 2 + 0.13415u 3 + 0.0834u 4 ,
valid between 0.1 and 20 cm;
log Tc
= 0.7392 + 4.3185u -
0.9049u 2 ,
valid for A = 20--2000 cm. The fits are based on [163-165].
14.15.2
Properties of Radio Emission from Solar Active Regions
Meter and Decameter Wavelengths
Storm continua and type I bursts (see below and [166]) are often associated with solar active regions.
Type I storm durations range from hours to days and are distinguished by high values of pc, bandwidths
of a few times 10 MHz, and apparent brightness temperatures < 10 10 K.
Decimeter and Centimeter Wavelengths
Decimetric and microwave emission associated with active regions is characterized by [167,168] a
diffuse morphology for A i2: 10 cm and a low to moderate degree of circular polarization PC ;S 15%.
Its brightness is typical of coronal temperatures [TB '" (1-2) x 106 K]. For A ;S 10 cm, the
diffuse morphology gives way to one or more compact components associated with sunspot umbrae
376 I 14
SUN
and penumbrae that possess a degree of polarization that ranges from low (pc "" few %) to high
(pc ;::: 90%) values. The brightness of compact components is again near coronal values. Radio
emission associated with solar active regions typically possesses a spectral maximum in flux density
between 8 and 10 em [169].
14.15.3
Properties of Solar Radio Bursts (Flares)
Meter Wavelengths
(i) 'JYpe I [166, 170]:
Frequency· range
Bandwidth
Duration
Brightness
Polarization
Fine structure
(ii) 'JYpe IT [171]:
Frequency range
Bandwidth
Frequency drift rate
Duration
Brightness
Polarization
Fine structures
(iii) 'JYpe m [172]:
Frequency range
Frequency drift rate
Duration
Brightness
Polarization
Variants
(iv) 'JYpe IV [173, 174]:
Frequency range
Bandwidth
Duration
Brightness
Polarization
Variants
150-350 MHz.
2.5-7 MHz (...... 0.025v MHz; v in MHz).
0.2-0.7 s (...... 80/v s).
As high as 107_10 10 K.
Up to 100% circularly polarized.
Chains, periodic variations.
< 20-150 MHz; harmonic structure in 60%.
...... IOOMHz.
...... 1 MHzs- l .
5-15 min.
107_10 13 K.
Unpolarized or weakly circularly polarized;
herringbone structure sometimes displays
...... 50% circular polarization.
Band splitting, multiple lanes, herringbone
structure.
Full range; harmonic structure common,
1-100 MHz.
-O.Olvl.84 MHzs- l .
...... 220v- 1 s.
108_10 12 K.
Pc ;S 15% (harmonic); Pc ;S 50%
(fundamental).
'JYpe J and type U bursts.
20-200 MHz.
Broadband continuum.
3-45 min.
< 108_10 10 K.
Pc ;S 20% (early), often increasing to high
values for events with durations longer than
20 min.
Moving type IV, slow-drift continuum,
type IT-associated, pulsations.
14.15 SOLAR RADIO EMISSION / 377
(v) Type V [172]:
Frequency range
Bandwidth
Duration
Brightness
Polarization
< 10-120 MHz.
Broadband continuum.
'" 500v- I / 2 s.
107 _10 12 K.
Pc ;S 10%, decreasing from disk center-tolimb, sense of polarization usually opposite
to that of preceding type III bursts.
Decimeter Wavelengths [175]
(i) Type III-like or fast-drift bursts:
Bandwidth
Variable.
Duration
0.5-1.0 s.
Drift rate
> 100 MHz s-I.
Variants
Classical type III and type U bursts, dm
extensions to type 111m bursts, narrowband
type III bursts (blips), long duration type III
bursts.
(ii) Pulsations:
Bandwidth
Few x 100 MHz.
Periods
Pulses recur periodically or quasiperiodically
with separations of 0.1-1.0 s.
Duration
Groups of pulses (10-100 s) last from seconds
to minutes.
Quasiperiodic pulsations (regular, long period),
Variants
dm pulsations (irregular, short period).
(iii) Diffuse continua or type IV-like bursts:
Bandwidth
Duration
Variants
(iv) Spikes:
Bandwidth
Duration
Variants
Few x 100 MHz.
10 s of seconds to minutes.
Smooth continua, modulated continua, ridges.
Few MHz.
< 0.1 s individually, with groups (10-104 )
occurring in broadband clusters during some
seconds to minutes.
Type III-associated spikes, type IV-associated
spikes.
Centimeter and Millimeter Wavelengths
Solar bursts at centimeter and millimeter wavelengths tend to be broadband continua, moderately
polarized, with a brightness of a few x 106 K to a few x 109 K. The spectral peak is generally
near 8 GHz [176]; roughly 80% of solar radio burst display more than one spectral component [177].
378 I
14
SUN
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(Cambridge University Press, Cambridge), p. 443
Zirin, H., Baumert, B.M., & Hurford, G.J. 1991, ApJ,
370, 779
Elgarl1ly, E.O. 1977, in Solar Noise Storms (Pergamon,
Oxford), p. 366
Kundu, M.R. 1985, Solar Phys., 100,491
Marsh, K.A., & Hurford, G.J. 1982, ARA&A, 20, 497
Kundu, M.R 1965, in Solar Radio Astronomy (Wiley,
New York), p. 660
Kai, K., Melrose, D.B., & Suzuki, S. 1985, in Solar Radiophysics, edited by J.J. McClean and N.R.
Labrum (Cambridge University Press, Cambridge),
p.415
Nelson, G., & Melrose, D.B. 1985, in Solar Radiophysics, edited by J.J. McClean and N.R. Labrum
(Cambridge University Press, Cambridge), p. 333
Suzuki, S., & Dulk, G. 1985, in Solar Radiophysics,
edited by J.J. McClean and N.R. Labrum (Cambridge
University Press, Cambridge), p. 289
Robinson, R.D. 1985, in Solar Radiophysics, edited
by J.J. McClean and N.R. Labrum (Cambridge University Press, Cambridge), p. 385
Stewart, R.T. 1985, in Solar Radiophysics, edited by
J.J. McClean and N.R. Labrum (Cambridge University Press, Cambridge), p. 361
Giidel, M., & Benz, A.D. 1988,A&AS, 75, 243
Guidice, D.A., & Castelli, J.P. 1975, Solar Phys., 44,
155
Stiihli, M., Gary, D.E., & Hurford, G.l. 1989, Solar
Phys., 120,351
Chapter
15
Normal Stars
John S. Drilling and Arlo U. Landolt
15.1
Stellar Quantities and Interrelations. . . . . . . . . . .
381
15.2
Spectral Classification
383
15.3
Photometric Systems
..................
...................
15.4
Stellar Atmospheres . . . . . . . . . . . . . . . . . . . .
393
15.5
Stellar Structure
......................
395
385
IS. 1 STELLAR QUANTITIES AND INTERRELATIONS
M =
R=
L =
p=
Sp =
m=
U, B, V =
M =
B - V =
BC =
A=
mass (M0 = Sun's mass).
radius (R0 =Sun's radius).
luminosity (L0 Sun's luminosity) total outflow of radiation (ergs s-I).
mean density = MI(~;n' R 3 ).
spectral classification, which may be combined with a luminosity class.
apparent magnitude = -2.5 log apparent brightness. '!ypical subscripts: V = visual,
B = blue, U = ultraviolet, pg = photographic, pv = photovisual, bol = bolometric (total
radiation); in general, mA. = apparent magnitude of spectral region A.
mu, mB, mv = apparent magnitudes in the UBV system.
absolute magnitude = apparent magnitude standardized to 10 pc without interstellar
absorption.
color index; (B - V)o = intrinsic color index (i.e., no interstellar absorption); or, in
general a color index is the difference in the apparent magnitude as measured at two
different wavelengths.
bolometric correction = mbol - V (always negative).
space absorption in magnitudes (usually visual).
=
=
381
382 I 15
mo
EB- V
m- M
mo - M
NORMAL STARS
= magnitude corrected for absorption = m = color excess = (B - V) - (B - V)o.
= distance modulus = Slog d - S + A.
A.
= distance modulus corrected for absorption = Slog d -
S, where d is distance in
parsecs (pc).
F = total radiant flux at stellar surface.
f = radiant flux for a star outside the Earth's atmosphere.
Teff = stellar effective temperature (from F = (7 Te where (7 is Stefan's constant.
Vrot = equatorial rotational velocity.
g = surface gravity (cm s-2).
d = distance, usually in parsecs (pc).
7r = parallax in seconds of arc (") = lid, with d in pc.
1r),
All the logarithms in this chapter are common logs with a base of 10.
15.1.1
Numerical Relations
= m + S + Slog 7r - A = m +
MhoJ = -2.5 log LI L0 + 4.74,
M
S - Slog d - A,
where L0 = 3.84S x 1033 ergs s-J, and +4.74 is the absolute bolometric magnitude of the Sun. The
bolometric correction is the difference between the absolute visual and absolute bolometric magnitude:
Be
= MboJ- Mv.
Bolometric luminosities, radii, and effective temperatures are related by
MhoJ = 42.36 - Slog RI R0 - 10 log Teff,
where solar values of MhoJ0
= 4.74 and Teff0 = S777 K have been adopted.
= -3.147 + 2 log R + 4 log Teff,
(mhoJ =
== 2.48 x 10-5 erg cm- 2 s-l outside the Earth's atmosphere,
(MboJ = 0) star == 2.97 x 1028 watts emitted radiation,
(Mv = 0) star == 2.4S x 1029 candela.
log L
0) star
The zero age main sequence (ZAMS) is represented by [1]
logRIR0 = 0.640 log M/M0 +0.011
log R/ R0 = 0.917 log M/ M0 - 0.020
(0.12 < logM/M0 < 1.3),
(-1.0 < logM/M0 < 0.12).
The mass-luminosity relation may be written [2,3]:
logM/M0
= 0.48 -
O.1OSMboJ
for
-8::; MhoJ < 1O.S,
or
logL/L0 = 3.81ogM/M 0 + 0.08
for
M > 0.2M0.
15.2 SPECTRAL CLASSIFICATION / 383
Another representation is [4]
logM/M0
logM/M0
= 0.46 = 0.75 -
O.lOMboJ.
Mbol < 7.5,
0.145Mbol,
Mbol > 7.5.
The most reliable stellar masses are summarized in [5] and [6]; also, see the discussion in [2].
15.2 SPECTRAL CLASSIFICATION
We define normal stars to be those which can be classified on the MK system (specifically, [7,8], and
more generally [9]), or which are classified as white dwarfs according to the system described in [10].
Table 15.1 gives these classes.
Table 15.1. MK spectral classes.
MK spectral class
o
B
A
F
G
K
M
Class characteristics
Hot stars with He II absorption
He I absorption; H developing later
Very strong H, decreasing later; Ca II increasing
Ca II stronger; H weaker; metals developing
Ca II strong; Fe and other metals strong; H weaker
Strong metallic lines; CH and CN bands developing
Very red; no bands developing strongly
The spectral classes are further subdivided into decimal subclasses (e.g., BO, Bl, B2, etc.), although
not all subdivisions are used, and some classes are further subdivided (e.g., 09.5). Table 15.2 lists the
MK luminosity classes.
Table 15.2. MK luminosity classes.
MK luminosity class
Examples
I supergiants
II bright giants
mgiants
IV subgiants
V dwarfs (main sequence)
BOI
B5 II
GOm
G5IV
GOV
The luminosity classes are further subdivided (e.g., la, lab, Ib, etc.).
The MK classification is based on the appearance of pairs of spectral lines in the blue spectral
region at a spectral resolution of approximately 2 A, as compared to standard stars [7,8]. The main
line pairs are as shown in Table 15.3 and are illustrated in [11], [12], and [13].
Table 15.3. Line pairs for spectral classes and luminosity.
Class
Line pairs for class
Class
Line pairs for luminosity
05<:>09
BO<:>BI
B2<:>B8
4471 He I14541 He II
4552 Si nIl4089 Si IV
4128-30 Si 1114121 He I
09~B3
4116-21 (Si IV, He 1)/4144 He I
3995 N III4009 He II
Balmer line wings
BO~B3
Bl
~A5
384 I
15
NORMAL STARS
Table 15.3. (Continued.)
Class
Line pairs for class
Class
Line pairs for luminosity
B8~A2
4471 He 114481 Mg II
4026 He 113934 Ca II
4030-34 Mn I14l28-32
4300 CHl4385
4300 (G band)/4340 Hy
4045 Fe 114101 H8
4226 Ca I14340 Hy
4144 Fe 114101 H8
4226 Ca I14325
429014300
A3~FO
4416/4481 Mg II
FO~F8
417214226 Ca I
F2~K5
4045-63 Fe 114077 Sr II
4226 Ca I14077 Sr II
Discontinuity near 4215
421514260, Ca I increasing
A2~F5
F2~K
F5~G5
G5~KO
KO~K5
G5~M
K3~M
Other characteristics sometimes included with MK types:
e
f
p
n
s
k
m
= emission lines, e.g., Be;
= certain 0 type emission line stars;
= peculiar spectrum;
= broad lines;
= sharp lines;
= interstellar lines present;
= metallic line star.
Additional classes [2] are shown in Table 15.4.
Table 15A. Additional spectral classes
Spectral class
S
R(orC)
N (orC)
IS.2.1
Class characteristics
Strong bands of ZrO and YO, LaO, TiO
Strong bands of CN and CO instead of TiO in class M
Swan bands of C2, Na I (D), Ca I 4227, for the rest
similartoR
White Dwarf Spectral Classification
The following information on white dwarf spectral classification was provided by J. Liebert and
E. Sion ([10] and illustrated examples in [14]). The system consists of: (1) first symbol: an uppercase
D for a degenerate star spectrum; (2) second symbol: an uppercase letter designating the primary or
dominant ion or type of element in the optical spectrum; (3) third and possible subsequent symbols:
(optional) uppercase letters designating any secondary ions or types of elements appearing in the
optical spectrum, usually due to species with trace abundances (special secondary symbols are also
provided for spectra showing polarized light and magnetic fields, and others with peculiar spectra);
and (4) a temperature index defined by l08eff, which is equal to 50400ITeff. Originally, this index was
specified to be a single digit from 0 to 9. This index can be estimated only from at least a rough analysis
of spectrophotometric data, using colors, an energy distribution or the strengths of absorption features.
In this way, the system differs from traditional, purely spectroscopic methodology. If such information
is unavailable or ambiguous, the temperature subtype is omitted.
15.3
PHOTOMETRIC SYSTEMS
I 385
Definition of Primary Symbols
DA
DB
DO
DZ
DQ
DX, DXP
Hydrogen Balmer lines dominate optical spectrum.
Neutral helium (He I) lines dominate.
Ionized helium lines strongest, He I and/or H may be visible.
Metal lines dominate, usually with Ca II strongest.
Carbon features, either molecular or atomic, in any part of the electromagnetic
spectrum (often strongest in the ultraviolet).
Star with unidentified features, presumably due to a strong magnetic field. If light
polarized, the secondary symbol "P" is also appropriate.
Secondary Symbols: All of the Above. Plus ...
P
H
V
PEC
Star showing polarized light.
Star known to be magnetic from optical Zeeman features, but not known to be
polarized.
Star known to be photometrically variable (optional).
Star with spectral peculiarities.
Examples
DAI
DAOI
DOZI
DBAQ4
DXP5
DZA7
DC9
A white dwarf showing only hydrogen lines with 37 500 < Teff < 100000 K.
Star in same temperature range showing hydrogen and weak He II.
A star showing strong He II, weak He I, H, and N v features at Teff = 70000 K.
A star showing He I, H, and C features in that order of decreasing strengths, near
Teff = 12000 K.
A polarized, magnetic white dwarf with unidentified spectral features,
Teff '" 10 000 K.
A metallic line white dwarf also showing weak hydrogen lines, Teff = 8500 K.
A featureless, continuous spectrum with an estimated Teff = 5500 K.
15.3 PHOTOMETRIC SYSTEMS
Various photometric systems are used to supplement or replace the spectral classifications referred to
in the last section. Optical filters are used to isolate specific spectral features or wavelength ranges, and
the fluxes received through these filters are usually expressed in magnitudes,
m =
-2.5 log(f/fo) ,
where f is the measured flux (corrected for atmospheric effects), and fo is the corresponding flux for
a star with m = O. The system is defined by the magnitudes and color indices (magnitude differences)
for a set of standard stars, which have been detennined using a particular instrumental setup. The
standard stars are used to transform measurements made with other instrumental setups to the standard
system. Also important for theoretical studies are the sensitivity functions (response of the original
instrumental setup to a source that emits the same flux at all wavelengths) for the various filters as a
function of wavelength. The effective wavelengths (peak sensitivity) and widths at half maximum of
the sensitivity functions for selected photometric systems in common use at the present time are given
in Table 15.5. References containing lists of standard stars, sensitivity functions, and calibrations, are
indicatd in the last column.
386 /
15
NORMAL STARS
Thble 15.5. Modem photometric systems.
System
Stromgren four-color system
Geneva seven-color system
Vilnius seven-color system
Walraven system
Washington system
DDO five-color system
RGV
UBVRI and (RI)KC
Characteristic wavelength passbands
(effective wavelengths and half-widths) (A)
3500 (380), 4100 (200), 4700 (200), 5550
(200), plus HfJ (150/30)
UBV system plus 4020 (170), 4480 (165),
5400 (200), 5810 (210)
3450 (400), 3740 (260), 4050 (220), 4660
(260),5160 (210), 5440 (260), 6550 (200)
5400 (710), 4300 (540), 3820 (430), 3620
(230),3250 (140)
3910 (1100), 5085 (1050), 6330 (800), 8050
(1500)
4886 (186), 4517 (76),4257 (73), 4166 (83),
additional: 3815 (330),3460 (383)
3593 (530), 4658 (495), 6407 (430)
3600 (700), 4400 (1000), 5500 (900), 7000
(2200),8800 (2400), 6400 (1750), 7900
(1400)
Designations
References
uvbyfJ
[1-6]
UBVBIB2VIG
[1,7-9]
[10--13]
[I, 14-16]
UPXfZVS
VBLUW
CMTIT2
C(41--42)
C(42--45)
C(45--48)
RGU
UBVRI
[1,7,17,18]
[19,20]
[21-26]
[1,7,27,28]
[1,7,9,29-33]
[1,34-38]
References
1. Schmidt-Kaler, Th. 1982, Landolt-Bomstein: Numerical Data and Functional Relationships in Science and
Technology, edited by K. Schaifers and H.H. Voigt (Springer-Verlag, Berlin), VIl2b
2. Crawford, D.L. 1975, AJ, 80, 955
3. Crawford, D.L. 1978, Ai, 83, 48
4. Crawford, D.L. 1979, AJ, 84, 1858
5. Olson, E.C. 1974, PASP, 86, 80
6. Stromgren, B. 1966, ARA&A, 4, 433
7. Golay, M. 1974,lntroduction to Astronomical Photometry (Reidel, Dordrecht)
8. Rufener, E, & Maeder, A. 1971, A&AS, 4, 43
9. Philip, A.G.D., editor, 1979, Problems of Calibration of Multicolor Photometric Systems (Davis, Schenectady)
10. Hauck, B. 1985, in Calibration of Fundamental Stellar Quantities, edited by D.S. Hayes, L.E. Pasinetti, and A.G.D.
Philip (Kluwer Academic), p. 271
11. North, P., & Nicolet, B. 199O,A&A, 228, 78
12. Rufener, E, & Nicolet, B. 1988, A&A, 206, 357
13. Meynet, G., & Hauck, B. 1985, A&A, ISO, 163
14. Straizys, V., & Zdanavicius, K. 1970, Bull. Vilnius Astron. Obs. No. 29, 15
15. Straizys, V., 1977, Multicolor Stellar Photometry, Photometric Systems and Methods (Mokslos, Vilnius)
16. Straizys, V., & Jodinskiene, E. 1981, Bull. Vilnius Astron. Obs. No. 56
17. Lub, J., & Pel, J.W. 1977,A&A, 54,137
18. Pel, J.W. 1976, A&AS, 24, 413
19. De Ruiter, H.R., & Lub, J. 1986, A&AS, 63,59
20. Brand, J., & Wouterloot, J.G.A. 1988, A&AS, 75, 117
21. Cantema, R. 1976, Ai, 81, 228
22. Cantema, R., & Harris, H.C. 1979, Dudley Obs. Rep. No. 14; op. cit. [9], p. 199
23. Harris, H.C., & Cantema, R. 1979, Ai, 84,1750
24. Geisler, D. 1984, PASP, 96, 723
25. Geisler, D. 1990, PASP, 102, 344
26. Geisler, D., Claria, 1.1., & Minniti, D. 1991, Ai, 102, 1836
27. McClure, R.D. 1976, AJ, 81, 182
28. McClure, R.D., & van den Bergh, S. 1968, Ai, 73, 313
29. Steinlin, V.W. 1968, Z Astrophys., 69, 276
30. Smith, L.L., & Steinlin, V.w. 1964, Z Astrophys., 58, 253
31. Bell, R.A. 1972, MNRAS, 159, 34; 1972, A&A, 62, 411
32. Buser, R. 1978, A&A, 62, 411
33. Buser, R. 1978, A&A, 62, 425
34. Cousins, A.W.J. 1976, MemRAS, 81, 25
35. Landolt, A.V. 1992, AJ, 104, 340
36. Bessell, M.S. 1979, PASP, 91, 589
15.3 PHOTOMETRIC SYSTEMS /
387
37. Bessell, M.S. 1976, PASP, 88, 557
38. Menzies, l.W. et aI. 1991, MNRAS, 248, 642
Absolute calibration of a star of the spectral type AO V with the magnitude V
system is shown in Table 15.6.
= 0 [2] on the Johnson
Table 15.6. Flux calibration for an AO V star.
Symbol
Flux(ergcm- 2 s- 1 A-I)
U
4.22
6.40
3.75
1.75
8.4
B
V
R
I
x 10- 9
x 10-9
x 10-9
x 10-9
x 10- 10
AO(/Lm)
0.36
0.44
0.55
0.71
0.97
Useful relations for the UBV system [2]:
= 0.08 + 3.85(B - V)o unreddened main sequence, (B - V)o < 0 and (U
Q = (U - B) - O.72(B - V) independent of reddening for early-type stars,
EU-B = {0.65 - 0.05(U - B)o + 0.05EB-V,
(U - B)o < 0,
EB-V
0.64 + 0.26(B - V)o + 0.05EB-V,
(B - V)o > 0,
(U - B)o
Av
- - = 3.30 + 0.28(B EB-V
V)o
- B)o < 0,
+ O.D4EB-v,
where EU-B = (U - B) - (U - B)o, Av = V - Vo, EB-V = (B - V) - (B - V)o; and Vo, (B - V)o,
and (U - B)o are the magnitude and color indices stars would have if space were transparent.
Useful relations for the uvbyf3 system [15-20]:
CI
ml
f3
= (u = (v -
v) - (v - b),
b) - (b - y),
= 2.510g(W / N),
where W and N are the fluxes measured through interference filters centered on Hf3 with half-widths
of about 150 and 30 A, respectively.
E(Cl)
E(ml)
E(u - b)
= 0.20E(b - y), }
= -0.32E(b - y),
= 1.50E(b -
color excesses according to standard reddening law,
y),
[cd = Cl - 0.20(b - y),
}
[md = ml + 0.32(b - y),
reddening independent quantities,
[u - b] = (u - b) - 1.50(b - y),
388 / 15
NORMAL STARS
(b - y)o = -0.116
+ 0.097C! for an unreddened main-sequence B star,
(b - y)o = 2.946 - 1.0,8 - O.lekl (-0.2Sc5ml if ml < 0) for A stars with
2.870 > ,8 > 2.720 and c5C! < 0.28,
(b - y)o
= 0.222 + 1.11t::..{J + 2.7(t::..{J)2 -
O.OSc5C! - (0.1 + 3.6t::..,8)c5ml for F stars
with 2.630 < ,8 < 2.720 and c5C! < 0.28, or 2.S90 < ,8 < 2.630 and
c5Cl < 0.20,
where t::..,8
= 2.720 -,8,
IS.3.1
Calibration of MK Spectral Types [2,21,22]
c5C!
= C! -
Cstd, c5ml
= mstd -
ml;
See Section lS.3.2 for Cstd and mstd·
Table lS.7 presents the absolute magnitude, color, effective surface temperature, and bolometric
correction calibrations for the MK spectral classes. Table lS.8 gives the calibrated physical parameters
for stars of the various spectral classes.
Table 15.7. Calibration of MK spectral types.
Sp
M(V)
B-V
U-B
V-R
R-J
TeIJ
BC
MAIN SEQUENCE, V
-5.7
-0.33
05
-4.5
-0.31
09
-4.0
-0.30
BO
-2.45
B2
-0.24
-1.2
B5
-0.17
-0.25
-0.11
B8
AO
+0.65
-0.02
+0.05
A2
+1.3
AS
+1.95
+0.15
FO
+2.7
+0.30
F2
+3.6
+0.35
+0.44
F5
+3.5
F8
+4.0
+0.52
GO
+4.4
+0.58
02
+4.7
+0.63
05
+5.1
+0.68
+0.74
08
+5.5
+0.81
KO
+5.9
+0.91
K2
+6.4
K5
+7.35
+1.15
MO
+8.8
+1.40
M2
+1.49
+9.9
M5
+12.3
+1.64
-1.19
-1.12
-1.08
-0.84
-0.58
-0.34
-0.02
+0.05
+0.10
+0.03
0.00
-0.02
+0.02
+0.06
+0.12
+0.20
+0.30
+0.45
+0.64
+1.08
+1.22
+1.18
+1.24
-0.15
-0.15
-0.13
-0.10
-0.06
-0.02
0.02
0.08
0.16
0.30
0.35
0.40
0.47
0.50
0.53
0.54
0.58
0.64
0.74
0.99
1.28
1.50
1.80
-0.32
-0.32
-0.29
-0.22
-0.16
-0.10
-0.02
0.Ql
0.06
0.17
0.20
0.24
0.29
0.31
0.33
0.35
0.38
0.42
0.48
0.63
0.91
1.19
1.67
42000
34000
30000
20900
15200
11400
9790
9000
8180
7300
7000
6650
6250
5940
5790
5560
5310
5150
4830
4410
3840
3520
3170
-4.40
-3.33
-3.16
-2.35
-1.46
-0.80
-0.30
-0.20
-0.15
-0.09
-0.11
-0.14
-0.16
-0.18
-0.20
-0.21
-0.40
-0.31
-0.42
-0.72
-1.38
-1.89
-2.73
OIANTS,m
05
+0.9
08
+0.8
KO
+0.7
K2
+0.5
-0.2
K5
MO
-0.4
M2
-0.6
M5
-0.3
+0.56
+0.70
+0.84
+1.16
+1.81
+1.87
+1.89
+1.58
0.69
0.70
0.77
0.84
1.20
1.23
1.34
2.18
0.48
0.48
0.53
0.58
0.90
0.94
1.10
1.96
5050
4800
4660
4390
4050
3690
3540
3380
-0.34
-0.42
-0.50
-0.61
-1.02
-1.25
-1.62
-2.48
+0.86
+0.94
+1.00
+1.16
+1.50
+1.56
+1.60
+1.63
15.3 PHOTOMETRIC SYSTEMS I 389
Table 15.7. (Continued.)
Sp
B-V
M(V)
SUPERGIANTS, I
09
-6.5
-0.27
-0.17
B2
-6.4
B5
-6.2
-0.10
-6.2
-0.03
B8
-6.3
-0.01
AO
-6.5
A2
+0.03
-6.6
A5
+0.09
-6.6
FO
+0.17
-6.6
F2
+0.23
-6.6
F5
+0.32
-6.5
F8
+0.56
-6.4
GO
+0.76
-6.3
G2
+0.87
-6.2
G5
+1.02
-6.1
G8
+1.14
-6.0
KO
+1.25
-5.9
K2
+1.36
-5.S
K5
+1.60
-5.6
MO
+1.67
M2
-5.6
+1.71
-5.6
M5
+1.80
U-B
V-R
R-J
Teff
BC
-1.13
-0.93
-0.72
-0.55
-0.38
-0.25
-0.08
+0.15
+0.18
+0.27
+0.41
+0.52
+0.63
+0.83
+1.07
+1.17
+1.32
+1.80
+1.90
+1.95
+1.60:
-0.15
-0.05
0.02
0.02
0.03
0.07
0.12
0.21
0.26
0.35
0.45
0.51
0.58
0.67
0.69
0.76
0.85
1.20
1.23
1.34
2.18
-0.32
-0.15
-0.07
0.00
0.05
0.07
0.13
0.20
0.21
0.23
0.27
0.33
0.40
0.44
0.46
0.48
0.55
0.90
0.94
1.10
1.96
32000
17600
13600
11100
9980
9380
8610
7460
7030
6370
5750
5370
5190
4930
4700
4550
4310
3990
3620
3370
2880
-3.18
-1.58
-0.95
-0.66
-0.41
-0.28
-0.13
-0.01
-0.00
-0.03
-0.09
-0.15
-0.21
-0.33
-0.42
-0.50
-0.61
-1.01
-1.29
-1.62
-3.47
Table 15.8. Calibration of MK spectral types. a
Sp
M/M0
R/R0
MAIN SEQUENCE, V
03
120
15
05
12
60
37
06
10
08
23
8.5
BO
17.5
7.4
7.6
B3
4.8
B5
5.9
3.9
BS
3.8
3.0
AO
2.9
2.4
A5
2.0
1.7
1.6
FO
1.5
F5
1.4
1.3
1.05
GO
1.1
G5
0.92
0.92
KO
0.79
0.85
K5
0.67
0.72
MO 0.51
0.60
M2
0.40
0.50
M5
0.21
0.27
MS
0.06
0.10
]og(g/g0)
log (PI P0)
-0.3
-0.4
-0.45
-0.5
-0.5
-0.5
-0.4
-0.4
-0.3
-0.15
-0.1
-0.1
-0.05
+0.05
+0.05
+0.1
+0.15
+0.2
+0.5
+0.5
-1.5
-1.5
-1.45
-1.4
-1.4
-1.15
-1.00
-0.85
-0.7
-0.4
-0.3
-0.2
-0.1
-0.1
+0.1
+0.25
+0.35
+0.8
+1.0
+1.2
Vrot
(kms-l)
200
170
190
240
220
180
170
100
30
10
<10
<10
<10
390 / 15
NORMAL STARS
Table 15.8. (Continueti)
R/R0
log(g/g0)
log(P/P0)
Vrot
GIANTS. ill
20
BO
B5
7
AO
4
1.0
GO
1.1
G5
KO
1.1
1.2
K5
MO
1.2
15
8
5
6
10
15
25
40
-1.1
-0.95
-1.5
-1.9
-2.3
-2.7
-3.1
-2.2
-1.8
-1.5
-2.4
-3.0
-3.5
-4.1
-4.7
120
130
100
30
<20
<20
<20
SUPERGIANTS. I
70
05
06
40
08
28
BO
25
B5
20
AO
16
AS
13
FO
12
F5
10
10
GO
G5
12
KO
13
K5
13
13
MO
M2
19
30:
25:
20
30
50
60
60
80
100
120
150
200
400
500
800
-1.1
-1.2
-1.2
-1.6
-2.0
-2.3
-2.4
-2.7
-3.0
-3.1
-3.3
-3.5
-4.1
-4.3
-4.5
-2.6
-2.6
-2.5
-3.0
-3.8
-4.1
-4.2
-4.6
-5.0
-5.2
-5.3
-5.8
-6.7
-7.0
-7.4
Sp
M/M0
(kms- 1)
125
102
40
40
38
30
<25
<25
< 25
< 25
< 25
Note
a A colon indicates an uncertain value.
Also see [23]. An independent absolute magnitude calibration is given in graphical form in [8]. Plots
of (B - V) and (U - V) versus Mv for the various white dwarf subclasses are in [24]. Intrinsic colors
and absolute magnitudes of the zero-age main sequence (ZAMS) (locus of young stars just starting
hydrogen burning) follow [2]. See [25] for an alternative, and plots in Chapter 20. Table 15.9 gives the
zero-age main sequence colors and absolute magnitudes.
Table 15.9. Zero-age main sequence.
(B - V)o
(U - B)o
-0!'l33
-0.305
-0.30
-0.28
-0.25
-0.22
-0.20
-0.15
-0.10
-0.05
0.00
+0.05
+0.10
-1!'l20
-1.10
-1.08
-1.00
-0.90
-0.80
-0.69
-0.50
-0.30
-0.10
+0.01
+0.05
+0.08
Mv
-5!'l2
-3.6
-3.25
-2.6
-2.1
-1.5
-1.1
-0.2
+0.6
+1.1
+1.5
+1.7
+1.9
(B - V)o
(U - B)o
+0.40
+0.50
+0.60
+0.70
+0.80
+0.90
+1.00
+1.10
+1.20
+1.30
+1.40
+1.50
+1.60
-0.01
0.00
+0.08
+0.23
+0.42
+0.63
+0.86
+1.03
+1.13
+1.20
+1.22
+1.17
+1.20
Mv
+ 3.4
+ 4.1
+ 4.7
+ 5.2
+ 5.8
+ 6.3
+ 6.7
+ 7.1
+ 7.5
+ 8.0
+ 8.8
+10.3
+12.0
15.3 PHOTOMETRIC SYSTEMS / 391
Table 15.9. (Continued)
15.3.2
(8 - V)o
(U - 8)0
+0.15
+0.20
+0.25
+0.30
+0.35
+0.09
+0.10
+0.07
+0.03
0.00
Mv
+2.1
+2.4
+2.55
+2.8
+3.1
(B - V)o
(U - 8)0
+1.70
+1.80
+1.90
+2.00
+1.32
+1.43
+1.53
+1.64
Mv
+13.2
+14.2
+15.5
+16.7
uvbyfJ Standard Relations
For the early-type stars, Table 15.10 gives the standard relation between the fJ index, colors, and the
absolute magnitudes.
Table 15.10. uvbyfJ standard relations.
fJ
b-y
m,
2.590
2.600
2.620
2.640
2.660
2.680
2.700
2.720
2.740
2.760
2.780
2.800
2.820
2.840
2.860
2.880
2.900
2.910
-0.134
-0.126
-0.118
-0.109
-0.100
-0.091
-0.080
-0.070
-0.061
-0.050
-0.044
-0.041
-0.039
-0.037
-0.034
-0.029
-0.023
-0.020
0.045
0.055
0.075
0.080
0.085
0.093
0.100
0.100
0.109
0.110
0.116
0.120
0.120
0.123
0.128
0.132
0.138
0.140
2.880
2.870
2.860
2.850
2.840
2.830
2.820
2.810
2.800
2.790
2.780
2.710
2.760
2.750
2.740
2.730
2.720
0.066
0.076
0.086
0.096
0.106
0.116
0.126
0.136
0.146
0.156
0.166
0.176
0.186
0.196
0.206
0.216
0.226
0.200
0.202
0.205
0.206
0.208
0.207
0.206
0.204
0.203
0.200
0.196
0.192
0.188
0.185
0.182
O.ISO
0.177
q
MV
[mil
[q]
-4.65
-4.12
-3.17
-2.36
-1.69
-1.12
-0.65
-0.27
0.04
0.30
0.51
0.68
0.83
0.97
1.10
1.24
1.39
1.46
0.005
0.017
0.040
0.047
0.055
0.066
0.076
0.079
0.091
0.095
0.103
0.108
0.108
0.112
0.118
0.123
0.131
0.134
-0.223
-0.103
-0.001
0.087
0.170
0.253
0.337
0.418
0.503
0.588
0.665
0.732
0.793
0.840
0.885
0.931
0.980
1.004
2.30
2.40
2.50
2.57
2.64
2.67
2.70
2.73
2.76
2.79
2.82
2.85
2.88
2.92
2.96
3.03
3.10
0.220
0.225
0.231
0.235
0.240
0.242
0.244
0.245
0.247
0.247
0.246
0.245
0.244
0.244
0.244
0.245
0.245
0.917
0.895
0.873
0.851
0.829
0.812
0.795
0.713
0.751
0.729
0.707
0.685
0.663
0.641
0.619
0.587
0.555
B Stars
-0.250
-0.128
-0.025
0.065
0.150
0.235
0.321
0.404
0.491
0.578
0.656
0.724
0.785
0.833
0.878
0.925
0.975
1.000
A Stars
0.930
0.910
0.890
0.870
0.850
0.835
0.820
0.800
0.7SO
0.760
0.740
0.720
0.700
0.680
0.660
0.630
0.600
392 I
15
NORMAL STARS
Table 1S.10. (Continued.)
b-y
{3
ml
Cl
Mv
[mil
[cil
0.244
0.244
0.246
0.248
0.251
0.256
0.263
0.272
0.281
0.292
0.304
0.317
0.332
0.350
0.536
0.513
0.481
0.443
0.411
0.383
0.355
0.327
0.304
0.281
0.258
0.235
0.211
0.188
FStars
2.720
2.710
2.700
2.690
2.680
2.670
2.660
2.650
2.640
2.630
2.620
2.610
2.600
2.590
0.222
0.233
0.245
0.258
0.271
0.284
0.298
0.313
0.328
0.344
0.360
0.377
0.394
0.412
0.177
0.174
0.172
0.171
0.170
0.171
0.174
0.178
0.183
0.189
0.196
0.204
0.214
0.226
0.580
0.560
0.530
0.495
0.465
0.440
0.415
0.390
0.370
0.350
0.330
0.310
0.290
0.270
3.14
3.21
3.29
3.38
3.48
3.60
3.74
3.88
4.04
4.20
4.36
4.52
4.70
4.90
See [15-17] and [26]. See also [27] and [28] for grids for determining effective temperatures and
surface gravities. Other calibrations may be found in [29-38].
15.3.3 Empirical U BV(RI)KC Calibrations [39]
The colors and spectral classes are given as a function of the surface effective temperature for dwarf
and giant stars in Table 15.11.
Table 1S.11. Empirical U BV(RI)KC calibrations.
TetT
b-y
B-V
13000
12000
11000
10000
9500
9000
8500
8000
7500
7000
6500
6000
5500
5000
4500
4000
3500
3000
2750
-0.054
-0.041
-0.027
-0.010
+0.007
+0.035
+0.072
+0.118
+0.165
+0.220
+0.286
+0.360
+0.445
+0.535
+0.60
+0.80
+1.01
+1.22
+1.37
-0.14
-0.10
-0.065
-0.025
+0.005
+0.055
+0.14
+0.22
+0.275
+0.35
+0.45
+0.57
+0.70
+0.88
+1.02
+1.32
+1.53
+1.74
+2.0
(V - R)KC
(R - I)KC
(V - I)KC
-0.070
-0.050
-0.032
-0.012
+0.008
+0.040
+0.084
+0.132
+0.168
+0.207
+0.250
+0.303
+0.364
+0.43
+0.51
+0.74
+1.18
+1.77
+2.18
-0.120
-0.085
-0.055
-0.020
+0.015
+0.072
+0.155
+0.250
+0.330
+0.415
+0.515
+0.625
+0.760
+0.93
+1.11
+1.53
+2.19
+3.03
+3.58
MK
Dwarfs (V)
-0.050
-0.035
-0.023
-0.008
+0.007
+0.032
+0.071
+0.118
+0.162
+0.208
+0.265
+0.322
+0.396
+0.50
+0.60
+0.79
+1.01
+1.26
+1.40
B7
B8
B9
AO
Al
A2
AS
A7
PO
F2
F5
GO
G6
K2
K4
K7
M2
M4.5
M6
15.4 STELLAR ATMOSPHERES I
393
Table 15.11. (Continued.)
Teff
b-y
5 ()()()
4750
4500
4250
4 ()()()
3750
3500
3250
+0.55
+0.60
+0.68
+0.80
+0.90
+1.00
8-V
(V - R)KC
(R - I)KC
(V - I)KC
MK
Giants (ill)
15.4
+0.89
+0.98
+1.11
+1.26
+1.43
+1.62
+0.497
+0.539
+0.60
+0.68
+0.795
+0.945
+1.19
+0.433
+0.461
+0.510
+0.600
+0.735
+1.025
+1.57
+0.93
+1.00
+1.11
+1.28
+1.53
+1.97
+2.76
+3.80
G7
KO
K2
K3
K5
M2
M4.5
M6
STELLAR ATMOSPHERES
15.4.1
Model Atmospheres for Normal Stars (Solar Composition) [40]
Table 15.12 lists stellar atmosphere parameters depending on the surface effective temperature and
gravity of a star.
Table 15.12. Model atmospheres Jar normal stars.
Teff
Feonv
logg
log 'fa
5500
4
-3.0
-2.0
-1.0
0.0
1.0
5500
log x
F
T
logP
logne
logna
logp
log Pr
6.79
7.65
7.92
8.08
8.14
4282
4487
4846
6130
8176
3.23
3.84
4.41
4.92
5.10
11.35
11.91
12.49
13.50
14.94
15.47
16.05
16.59
16.99
17.04
-8.19
-7.61
-7.07
-6.66
-6.62
0.09
0.10
0.17
0.54
1.05
0.00
0.00
0.00
0.01
0.85
-3.0
-2.0
-1.0
0.0
1.0
10.65
10.98
11.14
11.22
11.24
4104
4444
4846
6145
8431
1.28
2.09
2.73
3.13
3.18
9.53
10.35
11.08
12.55
14.06
13.52
14.30
14.91
15.20
15.07
-10.13
-9.36
-8.75
-8.46
-8.58
0.09
0.10
0.17
0.56
1.10
0.00
0.00
0.00
0.00
0.91
6 ()()()
4
-3.0
-2.0
-1.0
0.0
1.0
7.60
7.90
8.08
8.18
8.22
4667
4891
5293
6789
8709
3.29
3.87
4.42
4.82
4.95
11.48
12.04
12.62
13.94
15.12
15.49
16.04
16.55
16.85
16.86
-8.17
-7.61
-7.10
-6.81
-6.79
0.24
0.25
0.32
0.70
1.16
0.00
0.00
0.00
0.05
0.88
6000
1
-3.0
-2.0
-1.0
0.0
1.0
10.75
11.03
11.17
11.24
11.25
4489
4869
5318
6861
8981
1.26
2.02
2.59
2.89
2.92
9.72
10.62
11.44
13.01
14.11
13.47
14.19
14.72
14.90
14.73
-10.19
-9.47
-8.94
-8.75
-8.93
0.24
0.25
0.33
0.75
1.21
0.00
0.00
0.00
0.00
0.91
7000
4
-3.0
-2.0
-1.0
0.0
1.0
7.63
7.95
8.12
8.20
8.24
5458
5726
6190
8217
9911
3.10
3.67
4.17
4.45
4.55
11.87
12.45
13.13
14.63
15.37
15.22
15.77
16.23
16.39
16.37
-8.44
-7.89
-7.42
-7.26
-7.28
0.51
0.52
0.60
1.02
1.38
0.00
0.00
0.00
0.20
0.92
I
394 /
15
NORMAL STARS
Table 15.12. (Continued.)
Teff
logP
logne
logna
logp
logPr
Fconv
F
7586
8030
8982
11655
16287
1.71
2.36
2.86
3.17
3.75
12.84
13.42
14.08
14.62
15.08
13.63
14.26
14.67
14.71
15.12
-10.03
-9.40
-8.99
-8.95
-8.54
1.13
1.15
1.28
1.68
2.25
0.00
0.00
0.00
0.00
0.00
8.70
8.90
9.02
9.15
9.28
13060
14067
15560
19521
27451
1.38
2.09
2.71
3.33
4.03
12.81
13.49
14.07
14.60
15.15
12.84
13.52
14.08
14.60
15.15
-10.82
-10.14
-9.57
-9.05
-8.50
2.34
2.35
2.40
2.63
3.15
0.00
0.00
0.00
0.00
0.00
9.48
9.66
9.77
9.87
9.97
28059
31336
34855
40920
53682
1.19
2.16
2.93
3.55
4.21
12.31
13.24
13.96
14.52
15.06
12.29
13.21
13.93
14.48
15.02
-11.37
-10.45
-9.72
-9.18
-8.64
3.54
3.55
3.62
3.85
4.32
0.00
0.00
0.00
0.00
0.00
logg
IOgT a
10 000
4
-3.0
-2.0
-1.0
0.0
1.0
8.34
8.48
8.58
8.65
8.83
20000
4
-3.0
-2.0
-1.0
0.0
1.0
40000
4
-3.0
-2.0
-1.0
0.0
1.0
log x
T
Note
aT = continuum optical depth (5000 A); x = geometric depth; T = temperature (K); P = pressure; ne = electron
number density; na = atom number density; p = mass density; Pr = radiation pressure; Fconv / F = fraction of flux
carried by convection. All units are cgs.
Model atmospheres for metal-deficient stars are given in [40] and [41].
15.4.2
Theoretical Physical Continuum Fluxes [40]
Logarithms of theoretical physical continuum fluxes (ergs cm- 2 s-1 A-I) for normal stars (solar
composition) with logg
4 [40] are given in Table 15.13.
=
Table 15.13. Continuum fluxes for normal stars.
A. (A)
506
890
920
1482
2012
2506
3012
3636
3661
4012
4512
5025
5525
6025
7075
8152
8252
10050
14594
= 5500
6000
7000
-00
-00
-00
-00
-00
-00
-5.80
0.05
4.14
5.91
6.80
6.86
6.94
6.94
6.92
6.89
6.86
6.81
6.72
6.62
6.61
6.45
6.13
-4.49
1.63
5.41
6.55
7.00
7.04
7.16
7.15
7.12
7.08
7.03
6.97
6.86
6.75
6.74
6.56
6.19
-2.07
3.83
6.88
7.19
7.29
7.27
7.56
7.52
7.46
7.38
7.31
7.24
7.09
6.95
6.95
6.74
6.29
Teff (K)
10000
-6.26
1.11
3.73
8.28
8.12
7.98
7.89
7.79
8.33
8.21
8.06
7.92
7.79
7.68
7.46
7.26
7.33
7.03
6.47
20000
40000
4.81
7.34
10.28
9.84
9.48
9.22
8.99
8.76
8.93
8.80
8.63
8.46
8.32
8.19
7.94
7.71
7.73
7.41
6.80
11.19
10.93
11.28
10.75
10.35
10.05
9.78
9.49
9.49
9.35
9.17
8.99
8.84
8.70
8.44
8.20
8.19
7.86
7.23
15.5 STELLAR STRUCTURE / 395
Table 15.13. (Continued.)
A (A)
Teff (K)
27000
50000
100000
200000
5.22
4.20
3.03
1.83
= 5500
6000
7000
10000
5.27
4.24
3.06
1.87
5.34
4.31
3.13
1.94
5.48
4.45
3.27
2.07
20000
40000
5.77
4.72
3.52
2.32
6.17
5.10
3.89
2.67
15.5 STELLAR STRUCTURE
Age-zero models for X = 0.70, Z = 0.02, l/Hp = 1.7 [1]. I = mixing length; Pc = central pressure
(dyn cm- 2 ); Tc = central temperature (K); Pc = central density (g cm- 3 ); Hp = pressure scale
height; qcc = fraction of stellar mass within convective core; qce = fraction of stellar mass at bottom
of convective envelope are given in Table 15.14.
Table 15.14. Age-zero models [I].
M/M0
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.8
logL/L0
3.7600
3.6118
3.4433
3.2480
3.0184
2.7381
2.3815
1.9087
1.6002
1.2157
1.0298
0.8186
0.5562
0.2325
-0.1523
-0.5742
log Teff
logg
R/R0
log Pc
logTc
log Pc
qcc
qce
4.4096
4.3855
4.3576
4.3251
4.2865
4.2380
4.1766
4.0928
4.0376
3.9658
3.9297
3.8855
3.8355
3.7964
3.7514
3.7016
4.269
4.275
4.280
4.287
4.296
4.303
4.317
4.330
4.338
4.339
4.334
4.317
4.322
4.422
4.548
4.674
3.8434
3.6213
3.3916
3.1472
2.8860
2.6122
2.2992
1.9620
1.7737
1.5858
1.5120
1.4532
1.3526
1.1157
0.8813
0.6820
16.6331
16.6688
16.7116
16.7617
16.8243
16.8995
16.9982
17.1280
17.2085
17.2943
17.3260
17.3476
17.3274
17.2645
17.1851
17.0651
7.5051
7.4959
7.4853
7.4729
7.4583
7.4400
7.4163
7.3844
7.3631
7.3333
7.3151
7.2913
7.2500
7.1936
7.1306
7.0603
0.974
1.024
1.081
1.148
1.229
1.326
1.450
1.614
1.716
1.834
1.883
1.930
1.948
1.941
1.924
1.882
0.3193
0.3088
0.2877
0.2772
0.2666
0.2455
0.2350
0.1928
0.1717
0.1401
0.1190
0.0874
0.0386
0.0129
0.0073
0.0875
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
;:: 0.9999
0.9965
0.9720
0.8725
Reference
1. SchOnbemer, D., BlOCker, T., Herwig, F., & Driebe, T. 1996, private communication.
REFERENCES
I. Lacy, C.H. 1977, ApiS, 34, 479
2. Schmidt-Kaler, Th. 1982, Landolt-Bornstein: Numerical Data and Functional Relationships in Science and
Technology, edited by K. Schaifers and H.H. Voigt
(Springer-Verlag, Berlin), VII2b
3. McCluskey, G.E., Jr., & Kondo, Y. 1972,A&SS, 17,134
4. Harris, D.L., ill, Strand, K.Aa., & Worley, C.E. 1963,
in Stars and Stellar Systems, ill (University of Chicago
Press, Chicago), p. 273.
5. Popper,D.M. 1980, ARA&A, 18, 115
6. Andersen, J. 1991, A&AR, 3, 91
7. Morgan, W.w., & Keenan, P.C. 1973,ARA&A,l1, 29
8. Keenan, P.C. 1985, in Calibration of Fundamental Stellar Quantities, edited by D.S. Hayes, L.E. Pasinetti and
A.G.D. Philip (Kluwer Academic), p. 121
9. Garrison, R.F., editor, 1984, The MK Process and Stellar Classification (David Dunlap Observatory, Toronto)
10. Sion, E.M., Greenstein, J.L., Landstreet, J.D., Liebert,
J., Shipman, H.L., & Wegner, G.A. 1983, Api, 269, 253
II. Morgan, w.w., Abt, H.A., & Tapscott, J.w. 1978, Revised MK Spectral Atlas for Stars Earlier than the Sun
(Yerkes Observatory)
12. Keenan, P.e., & McNeil, R.e. 1976, An Atlas of the
Spectra of the Cooler Stars: Types G, K, M, S, & C
(Ohio State University Press, Columbus)
13. Yamashita, Y., Nariai, K., & Morimoto, Y. 1977, An
Atlas of Representative Stellar Spectra (University of
Tokyo Press, Tokyo)
396 I
15
NORMAL STARS
14. Wesemael, F., Greenstein, J.L., Liebert, J., Lamontagne,
R., Fontaine, G., Bergeron, P., & Glaspey, J.W. 1993,
PASP, lOS, 761
15. Crawford, D.L. 1975, AJ, 80, 955
16. Crawford,D.L.I978,AJ,83,48
17. Crawford, D.L. 1979,AJ, 84,1858
18. Stromgren, B. 1966, ARA&A, 4, 433
19. Crawford, D.L., Glaspey, J.W., & Perry, C.L. 1970,AJ,
75,822
20. Crawford, D.L. 1975, PASP, 87, 481
21. Johnson,H.L. 1966,ARA&A,4,193
22. De Jager, C., & Nieuwenhuijzen, H. 1987, A&A, 177,
217
23. Habets, G.M.H.J., & Heintze, J.R.W. 1981, A&AS, 46,
193
24. Greenstein, J.L. 1988, PASP, 100, 82
25. VandenBerg, D.A., & Poll, H.E. 1989,AJ, 98,1451
26. Perry, C.L., Olsen, E.H., & Crawford, DL. 1987, PASP,
99,1184
27. Moon, T.T., & Dworetsky, M.M. 1985, MNRAS, 217,
305
28. Napiwotzki, R., SchOnbemer, D., & Wenslte, V. 1992,
in The Atmospheres of Early-Type Stars, edited by U.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
Heber and C.S. Jeffery (Springer-Verlag, Berlin and
New York), p. 18
Philip, A.G.D., & Egret, D. 1980, A&AS, 40, 199
Balona, L.A. 1984, MNRAS, 211, 973
Crawford, D.L. 1984, in The MK Process and Stellar
Classification, edited by R.F. Garrison (David Dunlap
Observatory, Toronto), p. 191
Balona, L.A., & Shobbrook, R.R. 1984, MNRAS, 211,
375
Kilkenny, D., &. Whittet, D.C.B. 1985, MNRAS, 21(;,
127
Greenstein, J.L. 1984, PASP, 96,62
Olsen, E.H. 1988, A&A, 189, 173
McNamara, D.H., & Powell,J.M. 1985,PASP,97, 1101
Olsen, E.H. 1984, A&AS, 57, 443.
Hayes, D.S., Passinetti, L.E., & Philip, A.G.D. 1985, in
Calibration of FundDmental Stellar Quantities, edited
by D.S. Hayes, L.E. Pasinetti, and A.G.D. Philip (Reidel, Dordrecht)
Bessell, M.S. 1979, PASP, 91, 589
Kurucz, Robert L. 1979, ApJS, 40, 1
Bell, R.A., Eriksson, K., Gustafsson, B., & Nordlund,
A. 1976, A&AS, 23, 37
Chapter
16
Stars with Special Characteristics
J. Donald Fernie
16.1
Variable Stars..
16.2
Cepheid and Cepheid-Like Variables.
16.3
Variable White Dwarf Tables
400
16.4
Long-Period Variables ...
406
16.5
Other Variables
........
...
. . . .
406
16.6
Rotating Variables. . . . . . ..
...
. . . . .
407
16.7
T Tauri Stars ..
....
...
408
16.8
Flare Stars . . . . . . . . . . . . . . .
16.9
Wolf-Rayet and Luminous Blue Variable Stars.
410
16.10
Be Stars. . . . . . . . . . . . . . . .
413
16.11
Characteristics of Carbon-Rich Stars . . . ..
16.12
Barium, CH, and Subgiant CH Stars
16.13
Hydrogen-Deficient Carbon Stars . . . . . . . . .
417
16.14
Blue Stragglers.
418
16.15
Peculiar A and Magnetic Stars
16.16
Pulsars.........................
420
16.17
Galactic Black Hole Candidate X-Ray Binaries
422
16.18
Double Stars
397
........
........
...
......
. .
399
. . .
409
..
415
. . . . .
416
............
. . . . . . . . . . .
398
. .
. .
..
. . .
. .
419
424
398 I
16.1
16
STARS WITH SPECIAL CHARACTERISTICS
VARIABLE STARS
by Douglas S. Hall
All types of variables are collected in the General Catalogue of Variable Stars [1]. Except for the
eclipsing variables, all are considered intrinsic variables, with the physical mechanism responsible for
the variability being of four main classes. The approximate numbers of the principal types, as of 1990,
are given in the following:
Abbreviation
Description
Number
Pulsating (periodic, multiperiodic, quasiperiodic, or nonperiodic)
DCEP/CEP
CW
RR
DSCT
SXPHE
BCEP
ZZ
RV
SR
L
M
RCB
Classical Cepheids + those of uncertain type
W Vrrginis stars + BL Herculis stars
RR Lyrae stars
8 Scuti stars (some called dwarf Cepheids)
SX Phe variables, pop. II 8 Sct variables
f3 Cephei stars = f3 Canis Majoris stars
ZZ Ceti variables
RV Tauri stars
Semiregular (sometimes called LPV) variables
Slow irregular (sometimes called LPV) variables
Mira stars (sometimes called LPV)
R Coronae Borealis stars
638
172
6180
100
15
89
28
120
3377
2389
5827
37
Rotating (periodic or quasiperiodic)
ELL
ACV
SXARI
PSR
BY
RS
FKCOM
INT
Ellipsoidal variables
a 2 Canum Venaticorum variables
SX Ari variables
Optically variable pulsars
BY Draconis variables
RS Canum Venaticorum binaries
FK Comae Berenices stars
Orion variables of the T Tauri type
45
163
15
2
34
67
4
59
16.2 CEPHEID AND CEPHEID-LIKE VARIABLES / 399
Eruptive (all nonperiodic)
Orion variables, including T Tauri stars
and RW Aurigae stars
FU Orionis variables
y Cassiopeiae variables
R Coronae Borealis variables
UV Ceti variables or flare stars
S Doradus variables or P Cygni stars
IN
FU
GCAS
RCB
UV
SDOR
898
3
108
37
746
15
Explosive or Cataclysmic (quasiperiodic or nonperiodic)
N
NL
NR
SN
UG
ZAND
Novae
Novalike variables
Recurrent novae
Supernovae
U Geminorum variables or dwarf novae
Symbiotic variables of the Z Andromedae type
Eclipsing (periodic) all types
16.2
61
30
8
7
182
46
5074
CEPHEID AND CEPHEID-LIKE VARIABLES
Descriptions of Cepheid families are given below [2-13]:
IAU designation
Name
DCEP
CW
RR
DSCT
BCEP
Classical Cepheids
W Vir + BL Her stars
RR Lyrae stars
8 Scuti
fJ Cephei stars
Population
I
II
II
I
I
Period
(days)
1.5-60
1-50
0.4-1
0.04--0.2
0.15--0.25
Cepheid mean characteristics as a function of period P are given below. The period is that of the
fundamental mode. In the K band MK = -2.97 log P - 1.08. The Cepheid ratio of radial velocity
amplitude to V -light amplitude is 50 ± 5 lans- I mag. -I.
16
400 /
logP
STARS WITH SPECIAL CHARACTERISTICS
Mv
B-V
logL/L0
logR/R0
logg
Qa
0.54
0.61
0.68
0.75
0.82
0.89
0.97
1.04
2.2
1.9
1.7
1.5
1.3
1.0
0.8
0.6
0.036
0.037
0.039
0.040
0.041
0.042
0.044
0.045
0.21
0.25
0.31
4.5
3.9
3.6
0.039
0.037
0.037
-0.22
-0.22
-0.22
-0.22
2.5
2.1
1.5
1.2
0.049
0.059
0.076
0.080
3.86
3.82
3.78
-0.26
-0.26
-0.26
3.1
2.8
2.7
0.036
0.037
0.043
4.34
4.38
4.42
1.02
1.15
1.22
3.8
3.7
3.6
0.020
0.030
0.037
log Teff
logM/M0
Classical Cepbeids
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
-2.4
-2.9
-3.5
-4.1
-4.7
-5.3
-5.8
-6.4
0.49
0.57
0.66
0.75
0.84
0.93
1.01
1.10
2.81
3.05
3.30
3.55
3.80
4.06
4.32
4.58
1.41
1.55
1.70
1.85
2.00
2.15
2.29
2.44
3.76
3.75
3.74
3.72
3.71
3.70
3.70
3.69
8 SctlDwarf Cepbeidsb
-1.4
-1.0
-0.7
+2.7
+1.7
+0.8
0.1
0.5
1.0
1.3
-0.1
-0.9
-1.8
-2.4
0.20
0.25
0.29
0.90
1.22
1.58
0.07
0.37
0.59
3.91
3.88
3.86
Population II Cepbeids
0.30
0.44
0.60
0.70
1.95
2.27
2.63
2.87
0.86
1.08
1.34
1.52
3.82
3.79
3.75
3.72
RR Lyrae starsc
-0.5
-0.3
-0.1
0.7
0.7
0.7
0.20
0.25
0.38
1.47
1.57
1.59
0.54
0.67
0.76
f3 Cepbei stars
-1.0
-0.8
-0.6
-2.5
-3.1
-3.8
-0.23
-0.25
-0.27
3.99
4.33
4.69
0.84
0.93
1.03
Notes
a Q == P(p/ P0)O.S is the pulsation constant expressed in days.
bMany of these stars show higher-order and/or nonradial modes as well.
C Mv depends on metallicity: Mv = 0.20[FeIH] + 1.0.
16.3 VARIABLE WHITE DWARF TABLES
by Paul A. Bradley
Tables 16.1, 16.2, and 16.3 give data for the DAV, DBV, and DOV variable white dwarfs, respectively.
BPM 30551 [1.2]
R548 [3-5]
BPM 31594 [6--8]
HL Thu 76 [9-11]
G 38-29 [12]
G 191-16 [13, 14]
HS0507+0434B [15]
GD 66 [16,17]
KUV 08368+4026 [18]
GD99 [19]
G117-B15A [~22]
KUV 11370+4222 [18]
G255-2 [23]
BPM 37093 [24]
GD 154 [25, 26]
G 238-53 [27]
EC 14012-1446 [28]
GD 165 [29-31]
L 19-2 [32-34]
R 808 [19]
G 226-29 [35, 36]
BPM 24754 [37]
G 207-9 [38]
G 185-32 [13]
GD 385 [7,39]
PG 2303+242 [40,41]
G 29-38 [12,42-44]
EC 23487-2424 [45]
0104 -464
0133 -116
0341 -459
0416 +272
0417 +361
0455 +553
0507 +0435
0517 +307
0837 +403
0858 +363
0921 +354
1137 +422
1159 +803
1236 -495
1307 +354
1350+656
1401 -1454
1422 +095
1425 -811
1559 +369
1647 +591
1714 -547
1855 +338
1935 +276
1950 +250
2303 +242
2326 +049
2349 -244
z:z
V470Lyr
PYVul
PTVul
KRPeg
Psc
HWAqr
BTCam
V886Cen
BGCVn
DUDra
IUVir
CXBoo
MYAps
TYCrB
DNDra
VWLyn
RYLMi
V361 Aur
VYHor
V411 Tau
V468 Per
BRCam
AXPhe
z:z Cet
Variable star
name
010656
013610
034325
04 1859
042018
045928
051013
052038
084008
090149
09 2417
11 3941
120148
123848
13 09 58
135212
140357
142440
143218
1601 21
164826
17 1854
185730
1937 13
195228
230616
232849
235122
a (2000.0)
1.
2.
3.
4.
5.
(2000.0)
-4610.2
-1120.7
-4548.7
+2718.4
+3616.6
+5525.3
+0438.6
+3048.5
+4015.1
+3607.2
+3516.9
+4205.3
+8005.0
-4949.0
+3509.5
+6524.9
-1501.1
+0917.3
-8120.1
+3647.0
+5903.5
-5447.1
+3357.2
+2743.3
+2509.3
+2432.0
+0515.0
-2408.2
~
12.0 [46, 49]
12.1 [46.48-51]
11.2 [46, 48]
12.5 [46--51]
12.9
12.0 [46--48, 51]
12.1 [46--48,50, 51]
11.7 [46, 47]
11.5 [46, 47]
11.8 [46--50]
11.4 [46,47]
11.7 [46.48,50,51]
11.2 [46,48-51]
11.9 [46, 49]
11.8 [46--49,51]
11.6 [46--51]
11.3 [46,47]
12.0 [46--50]
11.5 [46,47]
11.4 [46,47]
11.2 [46,47]
11.4 [46, 47]
11.8
12.0 [46, 49, 50]
Teff
(103 K)
Hesser,I.E., Lasker, B.M., & Neupert, H.E. 1976, ApJ, 209, 853
McGraw,I.T. 1977, ApJ, 214, LI23
Lasker, B.M., & Hesser, I.E. 1971, ApJ, 163, L89
Stover, R.I., Hesser,I.E., Lasker, B.M., Nather, R.E., & Robinson, E.L. 1980, ApJ, 240, 865
Kepler, S.D. et aJ. 1995, Baltic Astr., 4,238
References
bPhotographic (blue) magnitude.
Notes
aC means combination of frequencies and H means harmonics.
Name
WDNo.
15.26
14.16
15.03
15.20
15.59
15.98
15.36
15.56
15.55
14.55
15.50
16.56
16.04
13.96
15.33
15.51
15.67
14.32
13.75
14.36
12.24
15.60
14.62
12.97
15.12
15.50
13.03
15.33
(mag.)
V
14.14
15.51
15.7
15.50
14.46
14.00
14.53
12.40
15.87
14.81
13.15
15.32
15.58b
13.17
15.52
15.43
14.33
15.24
15.40
15.79
16.1
15.6
15.78
15.77
14.74
15.72
16.78
(mag.)
B
Table 16.1. Names. positions. and magnitudes of the ZZ eeti (DAV) stars.
0.22
0.012
0.28
0.28
0.22
0.3
0.2
0.02
0.03
0.07
0.05
0.006
0.04
0.004
0.10
0.02
0.30
0.10
0.03
0.15
0.006
0.07
0.06
0.02
0.05
0.2
0.27
0.24
Amp.
(mag.)
610, 724 + others
114, 120 192,250, C
113, 118, 143, 192,350
833, complex, C, H
109
~ 1100
259,292,557,739,C
141,215, C, H
256,C
394,483,54O,611,936,C,H
284,615, 820, C, H
~ 800-1000, complex
~206
403, 1089, 1186, C, H
~6OO
823 + others
213,274
402,618, C, Ha
393, 625, 746, C, H
~ lOOO,C,H
510,6OO,710893,C,H
355,445, 560, CH
197,272,302,819,C,H
495,618
350,481,592
215,271,304, C, H
257 + others
685,830 + others
Periods
(seconds)
0
~
-
.......
til
t""'
ttl
t;x:j
~
'"I1
~:;g
0
>-l
ttl
::I:
~
-
t""'
trJ
>
t:I:1
:;g
-
~
0'1
UJ
-
6. McGraw,I.T. 1976,ApJ, 210, L35
7.0'Donoghue,D. 1986,AlN~S,220, 19P
8. O'Donoghue, D., Warner, B., & Cropper, M. 1992, AlN~S,158, 415
9.Page,C.G. 1972,AlN~S,159,25P
10. Fitch, W.S. 1973,ApJ, 181, L95
11. Dolez, N., & Kleinman, SJ. 1997 in White Dwarfs, edited by I.lsern, M. Hemanz, and E. Garcia-Berro (Kluwer Academic, Dordrecht), p. 437
12. McGraw,I.T., & Robinson, E.L. 1975, ApJ, 200, L89
13. McGraw,I.T., Fontaine, G., Dearborn, D.S.P., Gustafson,I., Lacombe, P., & Starrfield, S.G. 1981, ApJ, 250, 349
14. Vauclair,G.etal.I991,A&A,215,Ll7
15. Iordan, S., Koester, D., Vauclair, G., Dolez, N., Heber, U., Hager, H.I., Reimers, D., Chevreton, M., & Dreizler, S. 1998, A&A, 330, 277
16. Dolez, N., Vauclair, G., & Chevreton, M. 1983, A&A, 121, L23
17. Fontaine, G., Wesemael, F., Bergeron. P., Lacombe, P., Lamontagne, R., & Saumon. D. 1985,ApJ, 294, 339
18. Vauclair, G. et al. 1996, A&A, 322, 155
19. McGraw,I.T., & Robinson, E.L. 1976, ApJ, 205, Ll55
20. Kepler, S.O., Robinson. E.L., Nather, R.E., & McGraw,I.T. 1982, ApJ, 254, 676
21. Kepler, s.o. et al. 1991, ApJ, 378, L45
22. Kepler, S.O. et al. 1995, Baltic Astr., 4, 221
23. Vauclair, G., Dolez, N., & Chevreton, M. 1983, A&A, 103, Ll7
24. Kanaan, A.N. et al. 1992, ApJ, 390, L89
25. Robinson, E.L., Stover, R.I., Nather, R.E., & McGraw,I.T. 1978, ApJ, 220, 614
26. Pfeiffer, B. et al. 1996, A&A, 314, 182
27. Fontaine, G., & Wesemael, F. 1984,AJ, 89,1728
28. Stobie, R.S. et al. 1995, AlN~, 272, L21
29. Becldin, E.E., & Zuckerman, B. 1988, Nature, 336, 656
30. Bergeron, P., & McGraw,I.T. 1990, ApJ, 352, L45
31. Bergeron, P. et al. 1993, AJ, 106, 1987
32. O'Donoghue, D., & Warner, B. 1982, AlN~S, 200, 573
33. O'Donoghue, D., & Warner, B. 1987, AlN~S, 228, 949
34. Sullivan, DJ. 1995, Baltic Astr., 4, 261
35. Kepler, S.O., Robinson, E.R., & Nather, R.E. 1983, ApJ, 271, 744
36. Kepler, S.O. et al. 1995, ApJ, 447, 874
37. Giovannini, O. et al. 1998, A&A, 329, Ll3
38. Robinson, E.L., & McGraw,I.T. 1976, ApJ, 207, L37
39. Kepler, s.o. 1984, ApJ, 278, 754
40. Vauc1air, G., Chevreton, M., & Dolez, N. 1987, A&A, 175, Ll3
41. Vauclair, G. et al. 1992, A&A, 264, 547
42. Winget, D.E. et al. 1990, ApJ, 357, 630
43. Patterson,I.etal. 1991,ApJ,374,330
44. Kleinman, S.I. 1997 in White Dwarfs, edited by 1. !sern, M. Hemanz, and E. Garcia-Berro (Kluwer Academic, Dordrecht), p. 437
45. Stobie, R.S., Chen, A., O'Donoghue, D., & Kilkenny, D. 1993, AlN~S, 263, L13
46. Bergeron, P. Wesemael, F., Lamontagne, R. Fontaine, G., Saffer, R.A. & Allard, N.F. 1995, ApJ, 449, 258
47. Weidemann, V., & Koester, D. 1984, A&A, 132, 195
()
CIl
CIl
o-j
tt1
iiIC
o-j
--
n
::z::
>
iiIC
>
()
t""'
()
tt1
~
->
til
::z::
o-j
~
CIl
-
iiIC
~
til
0'1
s
--
48.
49.
50.
51.
VI063 Tau
SWLMi
DTLeo
EMUMa
CWBoo
V777 Her
V824 Her
QUTel
KUV 0513+2605 [1]
CBS 114 [2]
PG 1115+ 158 [3,4]
PG 1351+489 [5]
PG 1456+ 103 [6]
GD 358 [7-10]
PG 1654+160 [11]
EC 20058-5234 [11]
0513 +261
0954 +342
1115 +158
1351 +489
1456 +103
1645 +325
1654 +160
2006 -523
(2000.0)
051628
09 57 50
111823
13 5310
145833
1647 19
165658
200940
IX
(2000.0)
+2608.6
+3359.7
+1533.5
+4840.4
+1008.3
+3228.5
+1556.4
-5225.4
~
T:ff
22.5: [13, 14]
22.0: [13, 14]
22.5: [13, 14]
25.3 ± 0.3 [13, 14]
21.5: [13, 14]
(103 K)
15.54
13.65
16.3
V
(mag.)
17b
16.12b
16.38b
15.8gb
13.54
16.15b
B
(mag.)
0.10
0.30
0.06
0.05
0.10
0.10
0.10
0.07
Amp.
(mag.)
400, complex
650, complex
1000, complex
489+harmonics
420-860, complex
700, -complex
150-850, complex
134,195,204,257,281
Period
(seconds)
References
1. Grauer, A.D., Wegner, G., & Liebert, J. 1989, Ai, 98, 2221
2. Winget, D.E., & Claver, C.F. 1989, in White Dwarfs, edited by G. Wegner (Springer-Verlag, Berlin), IAU Colloq. 114, p. 290
3. Winget, D.E., Nather, R.E., & Hill, J.A. 1987, Api, 316, 305
4. Clemens, J.C., et aI. 1993, in White Dwarfs: Advances in Observation and Theory, edited by M.A. Barstow (Kluwer Academic, Dordrecht), p. 515
5. Grauer, A.D., Bond, H.E., Green R.F., & Liebert, J. 1988,AJ, 95, 879
6. Winget, D.E., Robinson, E.R., Nather, R.E., & Fontaine, G. 1982, Api, 262, Lli
7. Winget, D.E. et aI. 1994, Api, 430, 839
8. Bradley, P.A., & Winget, D.E. 1994, Api, 430,850
9. Provencal, J.L. et aI. 1996, Api, 466, lOll
10. Winget, D.E., Robinson, E.L., Nather, R.E., & Balachandran, S. 1984, Api, 279, Ll5
II. O'Donoghue D. 1995, 9th European Workshop on White Dwarf Stars, edited by D. Koester & K. Werner (Springer-Verlag, Berlin), p. 297
12. Liebert, J. et al. 1986,Api, 309,241
13. Thejll, P., Vennes, S., & Shipman, H.L. 1991, Api, 370, 355
Notes
aUncertain temperatures are marked by a colon.
bPhotographic (blue) magnitude.
Variable star
name
Name
WDNo.
Table 16.2. Names, positions, and magnitudes of the DBV sUlrs.
Kepler. S.O., & Nelan, E.P. 1993, AJ, lOS, 608
Daou, D., Wesemael, F., Bergeron, P., Fontaine, G., & Holberg, J.B. 1990, Api, 364, 242
Wesemael, F., Lamontagne, R., & Fontaine, G. 1986, Ai, 91, 1376
Koester, D., Allard, N., & Vauc1air, G. 1994,A&A, 291, L9
W
~
......
CI.l
tr1
r
I:I:l
;;2
'Tl
~~
o
tr1
~
::z::
.....
~
tr1
r
I:I:l
:;
~
~
W
0\
-
RXJ 0122.9-7521
0123 -754
0130 -196
0444+045
0704 +615
VV47
1144 +005
1151 -029
1424 +535
1504 +652
1517 +740
1520+525
NGC246
NGC 1501 [6]
NGC 2371-2 [7]
NGC2S67
Lo-4 [S]
NGC51S9
Sanduleak 3 [15]
K 1-16
NGC6905
2117 +341
PG 0122+200 [1-3]
PG 1159-035 [4, 5,]
PG 1707+427 [6-8]
PG 2131+066 [6, 9]
HS 2324+3944 [10-12]
0122 +200
1159 -035
1707 +427
2131 +066
2324 +3944
V2027Cyg
DSDra
LV Vel
KNMus
IS9+19°1 [13, 15]
27S-5° 1 [13]
274+9°1 [16, 17]
307-3°1 [13]
94+27°1 [IS, 19]
61-9°1 [13, 15]
RXJ 2117+3412 [20-22]
CHCam
8 (2000.0)
+2017.S
-0345.6
+4241.0
+0650.9
+4001.4
012255
013240
044704
0709 32
075750
114636
11 54 15
142555
1502 OS
15 1646
152147
-7521.2
-1921.7
+04 5S.7
+614S.3
+5325.0
+00 12.5
-03 12.1
+5315.4
+6612.5
+7352.1
+5222.0
Nonpulsating PG 1159 stars
0125 22
120146
17 OS 4S
2134 OS
232716
Pulsating PG 1159 (DOV) stars
a (2000.0)
ISO
95
100
65
130
150
140
100
170
95
150
75
140
100
SO
130
(103 K)
Teff
004703
040659
072535
09 2125
100545
133333
1603 OS
IS 2152
202223
211707
-1152.3
+6055.2
+2929.4
-5S IS.7
-4421.5
-655S.4
-3537.3
+6421.9
+2006.3
+3412.4
150
ND
ND
ND
120
ND
130
-140
ND
170
Pulsating planetary nebula nuclei (PNNVs)
BBPsc
GWVir
VS17 Her
IRPeg
144+6°1 [13, 14]
lIS-74° 1 [13]
PG 1144+005
PG 1151-029
PG 1424+535
H 1504+65
HS 1517+7403
PG 1520+525
164+31°1
HS 0444+0453
HS 0704+6153
MeT 0130-1937
Name
WDNo.
Variable star
name
15.0S
15.7
13.16
16.6
11.96
14.20
14.S5
15.52
16.2
16.24
16.S3
15.45
15.84
14.S4
16.69
16.63
14.S
V
(mag.)
14.66
14.gb
13b
16.45
16.62b
14.91
15.9
15.56
15.12
15.55
15.9
16.S
16.53
15.04
16.07
15.S6
16.13
14.21
16.0S
16.24
B
(mag.)
Table 16.3. Names, positions, and magnitudes of the PG 1159 and PNNV stars.
-0.002
-0.15
-0.01
-0.02
-0.06
-0.003
-0.01
-0.05
- 0.01
0.05
0.10
0.10
0.10
0.10
0.02
Amp.
(mag.)
-1500
- 1500, complex
- 1000, complex
-770
IS00-2000, complex
-690
-1000
1500-1700, complex
710, S75, + others
- SOO, complex
- 500, complex
- 450, complex
400--600, complex
- 2100
400--600, complex
Period
(seconds)
til
n
.....
til
~
:;c
.....
trl
~
>
:;c
>
n
::z::
t'"'
(')
>
n
.....
trl
'tI
en
::z::
~
~
.....
til
~
:;c
en
0'\
-
.....
§
p.491
16. Longmore, AJ., 1977, MNRAS,I7B, 251
17. Bond, H.E., &; Meakes, M.G. 1990,AJ, 100, 788
18. Grauer, A.D., & Bond, H.E. 1984, ApI, 277, 211
19. Grauer, A.D., Bond, H.E., Green, R.F., &; Liebert, J. 1987, in The Second Conference on Faint Blue Stars, edited by A.G.D. Philip, D.S. Hayes, and J.W. Liebert
(Davis, Schenectady), IAU Colloq. 95, p. 231
20. Watson, T.K. 1992, IAU Cire. 5603
21. Vauclair, G. et aI. 1993, A&A, 267, L35
22. Motch, C., Werner, K., & Pakull, M.W. 1993, A&A, 268, 561
References
I. Bond, H.E., &; Grauer, A.D. 1987, ApI, 321, LI23
2. Vauclair, G. et aI. 1995, A&A, m, 707
3. O'Brien, M.S. et aI. 1996, ApI, 467, 397
4. Wmget, D.E. et aI. 1991, ApI, 378, 326
5. Kawaler, S.D., & Bradley, P.A. 1994,ApJ, 427, 415
6. Bond, H.E., Grauer, A.D., Green, R.F., & Liebert, J. 1984, Api, 279,751
7. Fontaine, G. et aI. 1991, ApI, 378, L49
8. Grauer, A.D., Green, R.F., &; Liebert, J. 1992, ApJ, 399, 686
9. Kawaler, S.D. et aI. 1995, ApI, 450, 350
10. Silvotti, R. 1996, A&A, 309, L23
11. Dreizler, S. et aI. 1996, A&A, 309, 820
12. Handler, G. et aI. 1997,A&A,326, 692
13. Ciardullo, R., & Bond, H.E. 1996, AJ, 111, 2332
14. Bond, H.E. et aI. 1996,AJ,I12, 2699
15. Bond, H.E., & Ciardullo, R. 1993, in The 8th European Workshop on White Dwarf Stars, edited by M.A. Barstow (Kluwer Academic, Dordrecht), NATO ASI Ser.,
Notes
aThmperatures for the DOV stars taken from Sion, E.M., & Downes, R.A. 1992, ApJ, 3%, L79; Werner, K., 1992, A&A,lSl, 147; Werner, K., & Heber, U. 1991,
A&A,147, 476; Werner, K., Heber, U., & Hunger K. 1991, A&A,144, 437; and estimated by me from comparisons of optical and UV spectra given in Wesemael, F.,
Green, R.F., &; Liebert, J. 1985, ApIS, 58, 379.
bPhotographic (blue) magnitude.
~
CIl
t11
-
=
t'""
~
"!1
~:;g
o
t11
~
:z:
~
-
t'""
t11
:;g
->=
~
w
0'1
-
406 /
16
STARS WITH SPECIAL CHARACTERISTICS
16.4 LONG-PERIOD VARIABLES [14-19]
Long-period variables (LPVs) including Mira stars are mostly M-type giant and supergiant stars,
usually with emission lines in their spectra. Many carbon stars (C-type) and zirconium (S-type) stars
also show this type of variability. OHIIR stars are probably dust-enshrouded Miras having periods
~ 600 to 2000 days and are not visible optically.
16.4.1
Properties of Mira Variables
The visual magnitude variation range is 2.5-10 mag.
The galactic scale height is 240 pc.
The mass is '" 1 M0
log Teff
~
4.255 - 0.35 log P
(100 < P < 500).
Luminosity: Mv at maximum light ~ O.OO4OP - 2.6 (200 < P < 500).
= -3,47 log P + 1.0,
(Mbol) = - 2.34 log P + 1.3.
(MK)
1Ypes of variables are given below:
Designation
Type
Pop
P (days)
Sp
Mv
AV
(gal. lat.)
Periodicity
M
SR
a, b,c,d
Mira, oxygen-rich;
Long period,
serniregular
I&n
I&n
200-600
100-500
M,e,S
F-M,e,S
in text
-1
in text
::: 2.5
in text
22°
regular
serniregular
L
Slow irregular
I&n
100-500
M,e,S
-1
::: 2.5
22°
not regular
16.5
OTHER VARIABLES [19-22]
Details of the classes and subclasses are given in [20].
Types of other kinds of variables are given below:
Designation
1Ype and features
Pop
P
RV
RV Tau. Alternating
depth of minimum
R CrB. Deep fades
+ pulsation
n
40--150
days
'" years
40--70 days
40--70 days
RCB
UUHer
UUHer
I?
I&n
~v
G-K
Mv
-2
Average
galactic
latitude
1.3
23°
F-G
-4
5
0.2
14°
FI
?
0.3
20°
Sp
16.6 ROTATING VARIABLES I 407
16.6
ROTATING VARIABLES
by Douglas S. Hall
These stars vary in brightness periodically as the star rotates about its axis. Except for the ellipsoidal
variables, the star is essentially spherical, and it is a longitudinally asymmetric distribution of surface
brightness that causes the variability.
Four basic mechanisms apply here:
1. The ellipticity effect results when one or both stars in a binary is ellipsoidal in shape.
2. The reflection effect in a close binary causes the facing hemisphere of one star to be brighter
than its opposite hemisphere.
3. The oblique rotator model explains the ACV, SXARI, and PSR variables, where a strong dipolar
magnetic field is not parallel to the rotation axis.
4. Starspots explain the BY, RS, and FKCOM variables and one component of the variability
in some INT variables. The spots are magnetic in origin, like sunspots and sunspot groups, but a
hundredfold larger in area. The temperature difference, photosphere minus spot, is 1000--2000 K [23].
Variability is periodic with the star's rotation but periods differ by a few percent due to solar-type
differential rotation [24]. Physical mechanism for the large spots is strong dynamo action due to rapid
rotation and deep convection [24]. Size of spots can be predicted by rotation period, B - V, and
luminosity class [24]. Full amplitude can be up to 0.5 magnitude [24].
16.6.1
Types of Rotating Variables
ELL. No formal prototype, though b Persei is often considered so. Tidal forces in a close binary make
one or both stars ellipsoidal (prolate) in shape. The difference in projected surface area between end-on
and broad-side views causes the brightness to vary, with gravity darkening enhancing the effect [25].
There are two maxima and two minima per rotation, but limb-darkening effects can make the two
minima unequal in depth [26]. Full amplitude, maximum to deeper minimum, can be up to 0.35
magnitude in V.
Reflection variables. These are not defined formally in the GCVS. There is no formal prototype.
The sole source of the variability is the reflection effect. Only a few cases are known. Examples are
BH Canum Venaticorum [27] and HZ Herculis [28].
ACV. The prototype is a 2 Canum Venaticorum. Signatures of a strong (several kilogauss) magnetic
field and an anomalous strengthening of absorption lines of certain elements both vary, along with the
brightness, with the star's rotation period. These include the so-called Ap or peculiar A stars. The full
amplitude can be up to around 0.1 magnitude in V [28].
SXARI. The prototype is SX Arietis. These are high-temperature, spectral type B, analogs of the
ACV variables and are sometimes called the helium variables. The full amplitude is up to around 0.1
magnitude in V [28].
PSR. There is no formal prototype. These are optically variable pulsars like CM Tauri, the
supernova remnant in the Crab Nebula: rapidly rotating neutron stars with very strong (several
megagauss) magnetic fields emitting narrow beams of radiation in the radio, optical, and X-ray bands.
The rotation periods are between milliseconds and seconds. The amplitude of light pulses can be up to
about 1 magnitude in V [28]. More details can be found in Section 16.16.
BY. The prototype is BY Draconis. These are defined by [29] and are K Ve or M Ve stars, where
e means Ha emission. These can be single or binary. Rapid rotation is a consequence of the star's
youth, i.e., recent arrival upon the main sequence, or by tidally enforced synchronism in a binary of
short orbital period. There is considerable overlap with the UV variables, i.e., flare stars.
408 /
16
STARS WITH SPECIAL CHARACTERISTICS
RS. The prototype is RS Canum Venaticorum. These are defined by [24, 30] and are G or K
stars, always in binaries, by definition. Rapid rotation is caused by tidally enforced synchronism in
a relatively short-period binary orbit, where "short" means days, weeks, or months for luminosity class
V, IV, or III [24]. A spotted star typically is post-main-sequence but before Roche lobe overflow.
FKCOM. The prototype is FK Comae Berenices. These stars are defined by [31] and are single,
rapidly rotating G or K giants. They may be coalesced W UMa-type binaries [31] or A-type mainsequence stars after evolution into the Hertzsprung gap [32].
INT. Starspots cause one component of the complex variability in some T Tauri stars, Le., INT
variables of spectral type G, K, M. Variability is periodic with the star's rotation [33].
16.7
T TAURI STARS [34-37]
by Gibor Basri
The T Tauri stars are systems containing solar-type pre-main sequence stars. As such, they provide
the opportunity to learn something about our own early solar system. Indeed, many of them are now
thought to contain circumstellar disks analogous to the solar nebula. Signs of youth include their
position in the HR diagram, association with molecular clouds, and undepleted lithium in their spectra.
They fall into two basic categories: the so-called "classical" TIS, and the weak-lined TIS. These are
roughly distinguished observationally by the strength of their Ha emission. Physically, the distinction
is probably between systems containing an active accretion disk or disk extending almost to the stellar
surface (the CTIS), and those that have no disk or only an outer disk (the WITS).
The eTIS show many phenomena associated with accretion disks and (apparently related) strong
mass loss, including infrared excesses (from 2 to 100 JLm), strong Balmer line (and continuum)
emission, other emission lines (including forbidden-line emission in many systems), and an optical and
ultraviolet excess thought to be generated by the accretion onto the star. When the accretion is strong,
the photospheric absorption lines can be "veiled" by dilution from the accretion-related continuum. In
extreme cases the light from the accretion disk can completely mask the stellar light (FU Ori systems).
The WITS show none of these effects, displaying only the effects of very strong magnetic activity
(chromospheres, coronae, starspots). Their properties generally lie along the activity sequence that
extends down to old main-sequence stars, but they are among the most active examples known. The
underlying stars in the eTIS are probably very similar. The eTIS and WITS are commingled both
spatially and on the HR diagram, except that CTIS much older than 10 Myr are not found. There
are generally more WITS than CTTS in well-surveyed clouds (and the WITS are more likely to be
incompletely sampled).
See Table 16.4 for characteristics of T Tauri stars.
Table 16.4. TTauri Star Characteristics.
Namea
V (V range)b
EW(Ha)(A)C
v sinje
f
L star
HBC No.; Sp.T.
Av
Veiling (5500 A)d
P:"t
L~ystem
Remarks
TTau
35; KOIV,V
9.9 (9.3-13.5)
1.3
50-70
0-0.2
20
2.8
12:
18.9+4.4
Prototype, but somewhat
atypical; IR companion
BPTau
32;K7V
12.1 (10.7-13.6)
0.5
30-50
0.5-1
<10
7.6
0.9
1.6
A fairly typical case,
bright spots seen
DFTau
36; MO,I V
11.5 (11.5-15)
0.45
30-90
1-1.5
22
8.5
2.0
5.1
Also typical; speckle binary
16.8 FLARE STARS
/
409
Table 16.4. (Continued.)
f
Namei'
V (V range)b
EW(HaXA)C
v sini e
HBCNo.; Sp.T.
AV
Yeiling (5500 A)d
pe
rot
L:
Remarks
DR Tau
74;c(M0)
11.2 (10.5-16)
17
40-90
3-8
< 10
137
0.9
5.3
Extremely variable,
many emission lines
RWAur
80; c(KS)
10.1 (9.6-13.6)
1.2
70-90
0.5-3
15
5.47
2.5
4.4
Very broad lines, variable veiling
DGTau
37;c(K7MO)
12.0 (10.5-14.5)
17
70-100
3-5
20
7
0.9
10.1
Optical jet source,
many emission lines
FUOri
186; G: I,ll
9.6: (9.2-16.5)
1.85
27
Yerybigh
110:
7
47
490
Prototype of extreme outburst
sources; light is declining
slowly; pure disk spectrum
Y410Tau
29;K3Y
10.8 (10.8-12.4)
0.03
3
0
73
1.88
2
2
Large spots, 1 solar mass,
1 Myrold
Y830Tau
405;K7-MOY
12.2 (12.1-12.4)
0.4
3
0
29
2.75
1.2
1.2
Typical "weak" or "naked"
T Tauri star
Lsw:
ystem
Notes
aHerbig and Bell catalog: compendium of 742 pre-main-sequence stars. For spectral types, c indicates a heavily veiled or
"continuum" star.
bYisuai magnitude and range; extinction is not very accurate, somewhat model-dependent (in classical T Tauri stars).
cEstimated range of Ha equivalent width (A) (Iow-dispersion spectra).
dExcess continuum veiling at 5500 A (in units of photospheric continuum).
eProjected rotation velocity in kmls; period (from photometric modulation) in days.
f Stellar luminosity (bolometric, in solar luminosities); estimated from flux near 1 ILm; not very accurate due to extinction
and accretion disk effects, except on weak-lined stars.
gSystemic bolometric luminosity (in solar luminosities, from 0.3-100 ILm); dominated by IR excess when well above
stellar value.
16.8 FLARE STARS [38-42]
by Douglas S. Hall
Flares are observed on K Ve and M Ve (classical UV Cet stars), on spectral classes G and K, with
luminosity classes V and IV (RS CVn, W UMa, and Algol binaries, FK Com stars). Flare amplitudes
are up to :::::: 5 mag. in U. The energy output of any flare in the spectral windows are
Ex :::::: Eeuv :::::: E opt » Eradio,
Ebol :::::: 6Eopt;
Eopt :::::: 4Eu,
Eu : EB : Ev = 1.8: 1.5 : 1.0.
The largest flare yet observed is represented by
Eu
= 1037 erg,
Ebol = 2 x 1038 erg.
The time-averaged bolometric luminosity of flares on a given star is
(Lflare) = 0.OO3Lstar for active stars at saturation level,
(Lflare) < 0.OO3Lstar for less active stars.
410 /
16
STARS WITH SPECIAL CHARACTERISTICS
The flare duration (rise time and half-life of decay time) in sis
log trise
log t1/2
= 0.25 log Eu = 0.30 log Eu -
6.0,
7.5.
Flare colors and temperatures are
(B - V)
T
= +0.34 ± 0.44,
=
(U - B)
= -0.88 ± 0.31,
{3 X 107 K for dMe stars,
108 K for RS CVn stars.
The flaring frequency, for a given star, depends on flare energy:
vex E-f3,
For UV Cet itself, v
16.9
=
1 flare/day at EB
0.4 < {J < 1.4.
= 1031 erg.
WOLF-RAYET AND LUMINOUS BLUE VARIABLE STARS
by Kenneth R. Brownsberger and Peter S. Conti
Wolf-Rayet (WR) stars are highly evolved descendants of massive stars, stars whose initial masses
are larger than about 40M 0 . WR stars are characterized by strong, broad emission lines in their
spectra, due to their intense stellar winds. The strengths of the emission lines serve as the basis for
the classification of these stars. There are two main WR spectra types, WN and WC, and a third, less
numerous type, WOo The WN types have spectra dominated by helium and nitrogen emission lines
(see Table 16.5); in WC types, the predominant lines are from helium, carbon, and oxygen. The WO
types have very strong oxygen lines (see Table 16.6).
Because the underlying stars are shrouded behind their dense stellar winds, the intrinsic stellar
parameters of WR stars are difficult to ascertain. Furthermore, comparisons with non-LTE (local
thermodynamic equilibrium) wind models yield a spread of values of the stellar parameters for different
stars of the same spectral subtype: Radii of WR stars range from 2 to 20 R0, temperatures from
30000 to 70000 K, wind velocities from 1000 to 3000 kms- I , and mass loss rates from 10-5 to
10-4 M0 yr- 1 [43,44]. (See Tables 16.7-16.11.)
Luminous blue variables (LBVs) are hot, massive stars that show strong photometric and
spectroscopic variations. LBVs include Hubble-Sandage variables, P Cygni stars, and S Doradus stars
and can vary by 1 to 2 magnitudes on time scales of a few decades. Occasionally, they can erupt and
increase their brightness by more than 3 mag. During their quiescent phases of minimum brightness,
LBVs appear to be blue, B-type supergiants. During periods of maximum brightness they resemble
late-type (A-F) supergiants [45,46]. (See Table 16.12.)
Table 16.5. Classification criteria/or WN spectra [I, 2].
WN SUbtypes
Nitrogen ions
Other criteria
WN2
WN2.5
WN3
N v weak or absent
N v present, N IV absent
N IV « N v. N II weak or absent
Hell strong
16.9 WOLF-RAYET AND LUMINOUS BLUE VARIABLE STARS I 411
Table 16.5. (Continued.)
WNsubtypes
Nitrogen ions
Other criteria
WN4
WN4.5
WN5
WN6
WN7
WN8
WN9
N IV ~ N V, N III weak or absent
N IV > N v, N III weak or absent
Nm ~NlV ~Nv
N m ~ N IV, N V present but weak
N m > N IV, N III A4640 < He II A4686
N III » N IV, N m A4640 ~ He II A4686
N III present, N IV weak or absent
He I weak P Cyg
He I strong P Cyg
He I, lower Balmer series P Cyg
References
l. van der Hucht, K.A., Conti, P.S., Lundstrom, I., & Stenholm, B. 1981, SSRv, 28, 227
2. Conti, P.S., Massey, P., & Vreux, I.M. 1990, ApJ, 354, 359
Table 16.6. Classification criteria/or WC, WO spectra [1, 2, 3].
SUbtypes
Carbon ions
Other criteria
WC4
WC5
WC6
WC7
WC8
WC9
C IV strong, C III weak or absent
Cm« CIV
Cm« CIV
Cm < CIV
Cm > CIV
Cm > CIV
OVmoderate
Cm<Ov
Cm>Ov
Cm»Ov
C II absent, 0 V weak or absent
C II present, 0 V weak or absent
Subtypes
Oxygen ions
Other criteria
WOl
OVI strong
OVI strong
OV<CIV
W02
OV~CIV
References
1. van der Huchl, K.A., Conti, P.S., Lundstrom, I., & Stenholm, B. 1981, SSRv, 28, 227
2. Conti, P.S .• Massey, P., & Vreux, I.M. 1990, ApJ. 354,359
3. Barlow, 1.1., & Hummer, O.G. 1982, in Wolf-Rayet Stars: Observations, Physics,
Evolution (Reidel, Dordrecht), IAU Symp. 99, p. 387
Table 16.7. Observed numbers o/Wolf-Rayet subtypes [1-7].
Galaxy
LMC
SMC
WNE
(WN2-WN5)
WNL
(WN&-WN9)
WCE
(WC4-WC7)
WCL
(WC8-WC9)
30
61
5
50
25
2
40
19
27
WNIWC
WO
7
1
2
1
1
References
1. van der Huchl, K.A., Conti, P.S., Lundstrom, I., & Stenholm, B. 1981. SSRv, 28, 227
2. Breysacher,I. 1981, A&A, 43,203
3. Azzopardi, M., & Breysacher, 1. 1979,A&A, 75,120
4. Lundstrom, 1., & Stenholm, B. 1984, A&A, 58, 163
5. Vacca, W.O., & Torres-Dodgen, A.V. 1990, ApJS, 73, 685
6. Conti, P.S., & Vacca, W.O. 1990, AJ, 100(2),431
7. Morris, P.W., Brownsberger, K.R., Conti, P.S., Massey, P., & Vacca, W.O. 1993, ApJ, 412, 324
412 /
16
STARS WITH SPECIAL CHARACTERISTICS
Table 16.8. Observed numbers of single Wolf-Rayet stars and those with
companions and/or absorption lines [1-7].
Galaxy
LMC
SMC
WN
WN+abs
WC
WC+abs
WO
64
64
1
22
16
51
15
12
2
6
7
WO+abs
1
References
1. van der Hucht, K.A., Conti, P.S. Lundstrom, I., & Stenholm, B. 1981,
SSRv,28,227
2. Breysacher, J. 1981, A&A, 43, 203
3. Azzopardi, M., & Breysacher, J. 1979, A&A, 75, 120
4. Lundstrom, I., & Stenholm, B. 1984, A&A, 58, 163
5. Vacca, W.O., & Torres-Dodgen, A.V. 199O,ApJS, 73, 685
6. Conti, P.S., & Vacca, W.O. 1990, AJ, 100(2), 431
7. Morris, P.W., Brownsberger, K.R., Conti, P.S., Massey, P., & Vacca,
W.O. 1993, ApJ, 412, 324
Table 16.9. Average intrinsic colors and absolute magnitudes [1-3].
Mv
(b - v)o
WNE
WNL
WCE
WCL
-3.8
-0.2
-5.5
-0.2
-4.5
-0.3
-4.8
-0.3
References
1. Vacca, W.O., & Torres-Dodgen, A.V. 1990, ApJS, 73, 685
2. Conti, P.S., & Vacca, W.O. 199O,AJ,I00(2), 431
3. Morris, P.W., Brownsberger, K.R., Conti, P.S., Massey, P., &
Vacca, W.O. 1993, ApJ, 412, 324
Table 16.10. Selected Wolf-Rayet stars [1-4].
ID
Star
Other
AB5
Br08
Br26
WROO6
WR011
WR048
WR 111
WR 136
HD5980
HD32257
HD36063
HD50896
HD68273
HD 113904
HD 165763
HD 192163
AzV229
Sk-69°42
Sk-71°21
EZCMa
y2 Vel
(J Mus
MR84
MR 102
III
bll
302.07
280.81
282.64
234.76
262.80
304.67
9.24
75.48
-44.95
-35.29
-32.63
-10.08
-7.69
-2.49
-0.61
+2.43
Sp. Class
v
WN4+07I:
WC4
WN7
WN5+(cc?)
WC8+09I
WC6+09.5I
WC5
WN6(SBl)
11.88
14.89
12.68
7.26
1.74
5.58
8.25
7.79
E(b - v)
[5,6]
(m-M)
0.05
0.08
0.07
0.05
0.03
0.17
0.32
0.45
19.2
18.5
18.5
11.3
8.3
11.9
11.0
11.6
References
1. van der Hucht, K.A., Conti, P.S., Lundstrom, I., & Stenholm, B. 1981, SSRv, 28, 227
2. Breysacher, J. 1981, A&AS, 43, 203
3. Azzopardi, M., & Breysacher, J. 1979,A&A, 75,120
4. Conti, P.S., & Vacca, W.O. 1990, AJ, 100(2),431
5. Vacca, W.O., & Torres-Dodgen, A.V. 1990, ApJS, 73, 685
6. Morris, P.W., Brownsberger, K.R., Conti, P.S., Massey, P., & Vacca, W.O. 1993,ApJ, 412, 324
7. Lundstrom, I., & Stenholm, B. 1984, A&AS, 58, 163
[7]
16.10 BE STARS / 413
Thble 16.11. Representative UV·NIR (0.1-1.1 JLm) emission lines in Wolf-Rayet stars. WN stars
contain He. N. and C; WC stars contain He. C. and O.
Ion
IF (eV)
A (A)
Ion
IF (eV)
Hel
Hell
24.6
54.4
Nm
NIV
47.4
77.4
1751.4634.4641
1486.3480.4058.6383.
7115
CII
24.4
Nv
97.9
1240.1718.4604.4620
Cm
47.9
om
54.9
3265.3708.3760.3962
CIV
64.5
5876.6678.7065.10830
1640.2511.2734.3203.
4686.4860.5412.6560.
6683.6891.8237.10124
1335.4267.7236.9234.
9891
1176. 1247. 19091.2297.
4650.5696.6742.8500.
8665.9711
1549.2405.2530.4441.
4787.5017.5470.5805.
7061.7726.8859
OIV
77.4
3411.3730
Ov
OVI
113.9
138.1
A (A)
2788.3140.4933.5592
3811.3834
Thble 16.12. Observed properties of luminous blue variables (LEV) [1. 21.
LBV
Star
Galaxy
1/Car
AGCar
HRCar [31
WRA 751 [41
PCyg
T (K)
Minimum brightness
Maximum brightness
27000:
25000:
14000:
< 30000:
19000
9000
Mbol
Mass loss
yr- I )
(M0
-11.3
-10.1
-9.4
-9.5
-9.9
10- 3 to 10- 1
3 x 10-5
2 x 10-6
2 x 10-6
2 x 10-5
LMC
SOor
R 71
R 127
R 143 [51
20000--25 000
13600
30000
19000
8000
9000
8500
6500
-9.8
-8.8
-10.5
-10.0
5 x 10-5
5 x 10-5
6 x 10- 5
M33
VarC
VarA
20000--25 000
35000
7500-8000
8000
-9.8
-9.5
4 x 10- 5
2 x 10-4
References
1. Humphreys. R.M. 1989. in Physics of Luminous Blue Variables (Kluwer Academic. Oordrecht). IAU
Symp. 157. p. 3
2. Conti. P.S. 1984. in Observational Tests of Stellar Evolution Theory (Reidel. Dordrecht). IAU
Symp. 157. p. 233
3. Hutsemekers. D .• & van Drom. E. 1991. A&A. 248. 141
4. van Genderen. A.M .• The. P.S .• & de Winter. D. 1992. A&A. 258. 316
5. Parker. I.W.. Clayton. G.C .• Winge. C.• & Conti. P.S. 1993. ApJ. 409. 770
16.10 Be STARS
by Arne Slettebakt and Myron Smith
Be stars may be defined as nonsupergiant B-type stars whose spectra have or had at one time Balmer
lines in emission; the "Be phenomenon" is the episodic occurrence of rapid mass loss in these stars,
resulting in Balmer emission. As a group, Be stars are characterized by rapid rotation, v sin i up to
400 km/s, but below the critical velocity.
tDeceased.
414 /
16
STARS WITH SPECIAL CHARACTERISTICS
Statistical studies show that Be stars are not exotic objects. They comprise nearly 20% of the BOB7 stars in a volume-limited sample of field stars, with a maximum incidence at B2 and considerably
lower frequencies among late B-types.
Studies of Be stars in clusters show that Be stars may exist anywhere from the main sequence to
giant regions in the H-R Diagram, with an average of to 1 magnitudes above the ZAMS. These
positions are consistent with core hydrogen-burning rapid rotators.
Balmer (and occasionally He I) emission lines arise from equatorially confined disks of (typically)
5-20 stellar radii, 10000 K temperature, and 1010_1013 cm- 3 electron density. These disks are
expelled from the star on a timescale from days to years.
Be stars are variable on a continuum of timescales from several decades to minutes. Periodic
variations in radial velocities and/or flux are often observed. The optical spectra of some Be stars
can exhibit continual low-level absorptions and/or emission components which alter the line profile.
Disks are fonned, sometimes quasi-periodically, on a variety of timescales from days to years and
their dispersal from weeks to decades; the fractional amount returning to the star is unknown. It is
generally assumed that the disk material is in Keplerian orbit. Departures from axisymmetry and/or
inhomogeneous density particle distributions can cause cyclic variations in the Violet and Red emission
components in the Balmer lines.
Ultraviolet studies show that another side of the Be phenomenon is the appearance of strong, highvelocity absorption components in the UV resonance lines of C IV, Si IV (and occasionally Al III,
N V, 0 VI) which can be attributed to the acceleration of a radiatively driven wind. The strengthening
features are well, but imperfectly, correlated with Balmer emission episodes. Mass loss rates from the
UV data are 10- 11 _10- 9 M0 ye 1; these are typically 10-50x lower than rates estimated from the
slow expansion of the equatorial disks from infrared and radio data.
1\vo hypotheses are current explanations of the Be phenomenon: surface magnetic activity and
nonlinearities in nonradial pulsations. Historically, rapid rotation, stellar winds, nonlinear pulsations,
magnetic fields, and binary interactions, singly and in combination, have been invoked to explain this
activity. Because there are a few subclasses of Be stars, various combinations of different mechanisms
could be responsible in particular cases.
Be-star catalogs (see [47]) list thousands of these objects. We list in Table 16.13 several of the
brightest, recently well-studied stars which are not in interacting binaries (significant numbers are also
Algol-type).
!
Table 16.13. Best-known Be stars [1-8].
Be star name
lID"
Sp. type
v sini
(km/s)
y Casb
5394
22192
23862
24534
33328
37202
45542
45725
56139
58715
105435
109387
120324
138749
142926
BO.5 IVe
B5ille
B8Ve
09.5ille
B2ille
Bl IVe
B6IVe
B4Ve
B2.5 Ve
B8Ve
B2IVe
B5ille
B2IV-Ve
B6ille
B7IVe
230
280
320
200
220
220
170
300
80
245
220
200
155
320
300
'" Pet'
28 Taub
X Per
A Eri
~ Taub
v Gem
fJMonAb
wCMa
fJ CMi
8 Cen
K Ora
Jl,Cen
OCrB
4 Her
16.11 CHARACTERISTICS OF CARBON-RICH STARS / 415
Table 16.13. (Continued.)
Be star name
lID"
Sp. type
v sini
(km/s)
48 Lilf'
X Oph
660ph
59 Cyg>
1C Aqr
EWLacb
142983
148184
164284
200120
212571
217050
217 891
B3Ne
B1.5 Ve
B2N-Ve
Bl Ve
Blm-Ne
B3Ne
B5Ve
400
140
240
260
300
300
100
fJPsc
Notes
"Henry Draper Catalogue number.
bIn addition to the Balmer emission and rotationally broadened lines of neutral
helium, these stars' spectra may show hydrogen lines with sharp absorption cores
as well as narrow absorption lines of ionized metals during the stars' shell phases.
References
1. Doazan, V. 1982, in B Stars with and without Emission Lines, edited by A.
Underhill and V. Doazan, Monograph Series on Nonthermal Phenomena in
Stellar Atmospheres, NASA-CNRS, NASA SP-456, p. 277
2. Physics of Be Stars, 1987, IAU Colloq. 92, edited by A. Slettebak and T.P. Snow
(Cambridge University Press, Cambridge)
3. Landolt-Bomstein, Vol. 2,1982, Part I, Peculiar Stars; 5.2.1.4,
4. Slettebak, A. 1988, PASP, 100,770
5. Slettebak, A. 1992, in The Astronomy and Astrophysics Encyclopedia, edited by
S.P. Maran (Van Nostrand Reinhold, New York), p. 710
6. Balona, L.A., Henrichs, H.F., & Lecontel, 1.M. 1994, Pulsation, Rotation,
and Mass Loss in Early-Type Stars, IAU Symp. No. 162 (Kluwer Academic,
Dordrecht)
7.1aschek, M., & Egret, D. 1981, A Catalogue of Be Stars, Centre de Donnees
Stellaires (CDS) Microfiche #3067
8. 1aschek, M. & Egret, D. 1982, Catalogue of Special Groups, Part 1: The Earlier
Groups, CDS Pub. Spec. No.4
16.11
CHARACTERISTICS OF CARBON-RICH STARS
by Cecilia Bambaum
Carbon-rich stars (defined as having atmospheric C/O> 1 and C/O = 1 for C and S stars, respectively)
make up an odd assortment of peculiar abundance stars. Atmospheric enhancement of carbon is caused
either by internal dredge-up of processed material during the late stages of stellar evolution, or by
environmental interactions such as mass transfer from an evolved, close companion. Carbon stars (C
designation, also classified as spectral types R, N, or J [48,49]) on the asymptotic giant branch (AGB)
have acquired their enriched carbon and s(slow)-process elements through convective dredge-up of the
interior processed layers due to thermal pulsing [50]. s-Process elements result from slow neutron
capture (and subsequent fJ decay) due to the low neutron flux in the stellar interior; the s-process
produces different elements than the rapid (r-process) neutron capture that takes place in high neutron
flux environments, such as in supernova events. An evolutionary sequence M-S-C is possible, but
not verified [51]. Some stars with carbon-rich atmospheres have been shown to be the result of mass
transfer in a binary system, e.g., the CH and Ba II stars [52,53], and a number of C and S stars that
lack the s-process element 99Tc, a signature of the ABG phase [54]. A few C stars have a great overabundance of l3C; these are known as the J types. For most carbon stars, 12C1l3C is '" 30-50, whereas
for J types it is '" 3 [55]. Most of these I-type stars are not enriched in s-process elements, although
there are a few exceptions (e.g., WX Cyg). Finally, there are the dwarf C stars [56]. These faint
416 I
16
STARS WITH SPECIAL CHARACTERISTICS
carbon-rich stars have a large proper motion, indicating that they are nearby and are therefore underluminous for the AGB (asymptotic giant branch). They are thought to be main sequence stars that have
acquired their carbon-richness by mass transfer from a giant companion that has since evolved into a
white dwarf. Table 16.14 gives characteristics of C-rich stars.
Thble 16.14. Characteristics of carbon-rich stars.
Type
Evol.
Pop.
Chemistry
Variability
Lum.
Special characte,o
References
C (Nand
late R)
AGB
I. II
C/O > I; CN. C2.
s-pr. enhanced.
often Tc
LPV:
Lb.M.SR
6 x 1037 x 10".c0
CSE: CO. dust;
.oM - 10-7
to 10- 5 M0/yr
[1-3]
C (J and
early R)
? preAGB
I. II
C/O> I; CN. C2. I3c
isotopic species.
not s-pr. enhanced
Lb.M.SR
< 103.c0
CSE: CO. dust;
.oM - 10-7 M0/yr
[4]
S
AGB+?
I. II
C/O I; ZrO; CN; s-pr.
enhanced. often Tc
Lb.M.SR
10" .c0
CSE: CO. dust;
.oM 6 x 10- 8
[5-7]
Ball
Giant
s-process enhanced.
esp. Ba, Sr; no Tc
Var.
My <
Oto-3
Binaries.
C-rich by
mass transfer
[8.9]
CH
Giant
II
Stronger eN. CH than
Ba II stars; s-pr.
enhanced but weaker
metals than Ba II stars
Var.
My Oto-3
Binaries.
C-rich by
mass
transfer
[9.10]
sgCH
Subgiant
I. II
CN. CH. s-pr. enhanced
esp. Sr and Ba
Var.
Fainter than
CH stars
Progenitors
ofCH stars?
[9. II]
dC
Main
Sequence?
11
CN; some I3C enhanced
My -10
Binaries?
Mass transfer?
[3.12]
Note
a CSE
=
= circumstellar envelope.
References
1. Claussen, M.J. et al. 1987, ApJS, 65, 385
2. Dean, C.A. 1976,AJ, 81, 364
3. Kastner, J.H. et al. 1993, A&A, 275, 163
4. Lambert, D.L. et al. 1986, ApJS, 62, 373
5. Jura, M. 1988, ApJS, 66, 33
6. Smith, V.V., & Lambert, D.L. 1988, ApJ, 333, 219
7. Johnson, H.R., Ake, T.B., & Ameen, M.M. 1993, ApJ, 402, 667
8. Jorrison A., & Mayor M. 1988, A&A, 198, 187
9. McClure, R.D. 1989, in Evolution ofPeculiar Red Giant Stars, edited by H.R. Johnson and B. Zuckerman (Cambridge
University Press, Cambridge), p. 196
10. McClure, R.D. 1984, ApJ, 280, L31
II. Luck, R.E., & Bond, H.E. 1982, ApJ, 259, 792
12. Green, P.J., Margon, B., & MacConnell, D.J. 1991, ApJ, 380, L31
16.12 BARIUM, CD, AND SUB GIANT CD STARS
by William Dean Pesnell
Barium stars show absorption at Ball A4554, Srll A4077 and A4215, and bands of CH, CN, and C2.
The enrichment of material is due to mass exchange from an evolved companion [57]. The subgiant
16.13
HYDROGEN-DEFICIENT CARBON STARS
/
417
CH stars may be the main-sequence progenitors of the barium stars. CH stars have strong bands of
CH, CN, and C2, but less metal enrichment than the Ba stars. See Tables 16.15 and 16.16.
Table 16.15. The brighter barium stars [1, 2].
HR
ex (2000.0)
8 (2000.0)
my
Sp.
774
2392
3123
3842
4474
4862
5058
5802
8204
24747.6
63246.9
75905.6
93801.4
113752.9
124944.9
13 2607.7
153629.5
21 2639.9
+812655
-11 09 59
-231838
-431127
+503704
-715911
-394519
+10 00 36
-222441
5.9
6.3
5.1
5.5
6.1
5.5
5.1
5.3
3.7
G8p
KOm
K2
G8II
KOp
G8Ib-II
KO.5m
KOm
G4lb
References
1. McClure, R.D. 1989, in Evolution of Peculiar Red
Giant Stars, edited by H.R. lohnson and B. Zuckerman
(Cambridge University Press, Cambridge), p. 196
2. MacConnell, D.l., Frye, R.L., & Upgren, A.R. 1972,
AJ,77,384
Table 16.16. Subgiant CH stars [1, 2].
No.
ex (2000.0)
8 (2000.0)
HD89948
BD +17°2537
HD 123585
HD 127392
BD -10°4311
CPD -62°6195
HD207585
HD224621
102221.9
124722.8
140935.9
143153.5
162413.2
210602.8
215034.8
235917.3
-293321.1
+164935.0
-442201.7
-311201.1
-1113 07.5
-613345.3
-2411 11.4
-360237.0
my
Sp.
7.50
8.82
9.28
9.89
10.1
10.1
10.0
9.59
G8m
GO
F7Vwp
Gp
GO
G5
Gwp
GOIIIIIV
References
1. Hipparcos Input Catalogue (ESA), 1990
2. Luck, R.E., & Bond, H.E. 1991, ApJS, 77, 515
16.13
HYDROGEN-DEFICIENT CARBON STARS
by Warrick Lawson
Hydrogen-deficient carbon stars are luminous, probable born-again post-AGB stars consisting of the
cool R Coronae Borealis (RCB) and hydrogen-deficient Carbon (HdC) stars (Teff :=:::; 5000 to 7000
K [58]) and extreme helium (eHe) stars (Teff :=:::; 8400 to 55000 K [59]). Three hot RCB-like stars may
be unrelated [60]. Typically CIH > HP although at least two stars are relatively H-rich [61]. RCBIHdC
and cooler eHe stars are unstable to radial pulsations [58-62], whereas higher-temperature eHe stars
are nonradial pulsators. RCB stars have pulsation-related declines in light of up to 8 magnitudes due
to dust formation [63,64] and have bright IR excesses [65,66]. See Table 16.17.
418 /
16
STARS WITH SPECIAL CHARACTERISTICS
Table 16.17. Selected hydrogen-dejicient carbon stars.
V
Star
Type
a
(2000.0)
(2000.0)
HV5637
WMen
HV 12842
SUTau
xx Cam
HdC?
RCB
RCB
RCB
RCB
040839
051132
052624
054503
054906
+532139
-675600
-711118
-642424
+190400
7.3
14.8
13.9
13.7
9.7
BO+371977
UWCen
OYCen
HD 124448
V854Cen
eHe
RCB
RCB?
eHe
RCB
092424
124317
132534
141459
143448
+364254
-543141
-541447
-461719
-393319
RCrB
BO-94395
HD 148839
V20760ph
PVTeI
RCB
eHe
HdC
eHe
eHe
154834
162835
163546
174150
182315
V348Sgr
MVSgr
LS IV -14109
RYSgr
UAqr
RCB?
RCB?
eHe
RCB
RCB
184020
184432
185939
191633
220320
&
B-V
-
Teff
(K)
Notes
0.87
1.23
0.42
0.51
1.10
7000
5000
7000
7000
7000
LMC
LMC
LMC
10.2
9.1
12.5
10.0
7.1
0.67
0.35
-0.10
0.50
55000
6800
14000
15500
7000
+280924
-091934
-670737
-175408
-563743
5.8
10.5
8.3
9.8
9.3
0.59
0.06
0.93
0.14
0.00
7000
28000
6500
31900
12400
-225429
-205716
-142611
-333118
-163740
11.8
12.7
11.1
6.2
11.2
0.30
0.26
0.33
0.62
1.00
20000
15400
8400
7000
5500
(at maximum)
sdO?
Nonvariable?
Balmer lines present
Nonradial pulsator?
C/H-0.05
Nonradial pulsator
Sr-. V-rich
16.14 BLUE STRAGGLERS
by Peter J. T. Leonard
Blue stragglers are main-sequence or slightly evolved stars in a stellar system that are apparently much
younger than the majority of the stars in the system. Consequently, these stars pose a problem for
standard stellar evolutionary theory. Blue stragglers have been discovered everywhere that they could
have possibly been discovered, which includes OB associations, open clusters of all ages, globular
clusters, the population II field, and dwarf spheroidal galaxies. Theories for these objects include
stellar mergers due to physical stellar collisions, stellar mergers due to the slow coalescence of contact
binaries, mass transfer in close binary systems, extended main-sequence lifetimes due to internal
mixing (which may be induced by rapid rotation, strong magnetic fields, or pulsation), recent star
formation, and several others. Table 16.18 provides a sample of blue stragglers found in various stellar
systems.
Table 16.18. Selected blue stragglers.
Name
Type of the parent stellar system
HD93843 [1]
HD 152233 [1]
HD60855 [2]
HD 162586 [2]
HD27962 [3]
HD73666 [3]
F 81 [4]
F 184 [4]
S I. IT, 21 [5]
Car OBI. OB association
Sco OB 1. OB association
NGC 2422. young open cluster
NGC 6475. young open cluster
Hyades. intermediate-age open cluster
Praesepe. intermediate-age open cluster
M67. old open cluster
M67. old open cluster
M3. globular cluster
Characteristics
= -9.5. 05m(f)var. v sini = 90 kms- l
= -9.7. 06m:(f)p. vsini = 140kms- l
Mv = -2.86. B2IVe. vsini = 320lmlS- l
Mv = -1.08. B6V. vsini < 4Okms- l
Am(KJHIM=A2JA3:/AS). v sini = 18 kms- l
AIVP(Si). v sini = 40 kms- l
V = 10.04. B8V
V = 12.22. FO. vsini = 80kms- l
mpv = 17.39. Cl = 0.06
MOOl
MOOl
16.15 PECULIAR A AND MAGNETIC STARS
/
419
Thble 16.18. (Continued.)
Name
Type of the parent stellar system
Characteristics
E 39 [6]
NC 6 [7]
AOL I [8]
NH 19 [9]
HST-I [10]
BD +25°1981
BD -12°2669
MA 308 [12]
D 227 [13]
SI267 [14]
BSS-19 [15]
w Cen, globular cluster
NGC 5053, globular cluster
NGC 6397, globular cluster
NGC 5466, globular cluster
47 Tuc, globular cluster
Population 11 field
Population 11 field
Carina dwarf spheroidal galaxy
Sculptor dwarf spheroidal galaxy
M67, old open cluster
47 Tuc, globular cluster
0.056-day dwarf cepheid, V = 17.03, B - V = 0.31
g = 18.33, g - r = -0.47
V = 14.42, B - V = 0.16
0.34-day contact binary, V = 18.54, B - V = 0.15
m220 = 16.0, ml40 = 16.7
V = 9.29, B - V = 0.30, v sini = 9 krns- I
V = 10.22, B - V = 0.30, v sini = 31 kms- I
V = 20.54, B - V = -0.07
V = 21.67, B - V = 0.14
Porb = 846 days, eorb = 0.475 ± 0.125
M = 1.7 ± 0.4M0' v sini = 155 ± 55 km s-I
[11]
[11]
References
I. Mathys, G. 1987, A&AS, 71, 201
2. Mermilliod, I.-C. 1982,A&A, 109, 37
3. Abt, H.A. 1985, ApJ, 294, LI03
4. Mathys, G. 1991, A&A, 245, 467
5. Sandage, A.R 1953, AJ, 58, 61
6. IlIIrgensen, H.E., & Hansen, L. 1984, A&A, 133, 165
7. Nemec, I.M., & Cohen, I.G. 1989, ApJ, 336, 780
8. Auriere, M., Ortolani, S., & Lauzeral, C. 1990, Nature, 344, 638
9. Mateo, M., Harris, H.C., Nemec, I., & Olszewski, E.W. 1990, AJ, 100,469
10. Paresce, F. et al. 1991, Nature, 352, 297
11. Carney, B.w., & Peterson, RC. 1981, ApJ, 251, 190
12. Mould, I., & Aaronson, M. 1983, ApJ, 273, 530
13. Da Costa, G.S. 1984, ApJ, 285, 483
14. Latham, D.W., & Milone, A.R.R 1996, ASP ConfSer., 90, 385
15. Shara, M.M., Saffer, R.A., & Livia, M. 1997, ApJ, 489, L59
16.15 PECULIAR A AND MAGNETIC STARS [67-70]
The peculiar A stars comprise the following:
1. Ap stars, which extend into B and earlier F types as well. The hotter (but not hottest) ones have
unusually strong lines of Mn, Si, and Hg; the cooler ones have similarly strong lines of Si, Cr, Sr, and
Eu, and other rare earth elements.
2. Am stars, for which the spectral type varies with the criterion used: the type based on the K-line
is earlier than that from the Balmer lines and that, in tum, is earlier than the type from metallic lines.
Differences are ~ 5 subclasses.
Table 16.19 lists some other properties.
Thble 16.19. Other properties.
Ap(Mn,Hg)
Temperature:
Luminosity and mass:
v sin i (krn/s):
Magnetic field (gauss):
Close binary frequency
Ap (Sr, Eu)
Am
10000-15000 K
8000-12000 K
7000-9000 K
At or near main sequence values
30
30
40
o orlow
103 -104
Oorlow
Normal
Low
High
420 /
16
STARS WITH SPECIAL CHARACTERISTICS
Ap stars show spectrum, light, and magnetic variability due to rotational modulation on time scales
of days to years. Magnetic Ap stars can also show rapid oscillations (roAp stars) on time-scales of 4 to
15 minutes due to high-overtone, low-degree, nonradial p modes [69].
16.16 PULSARS
by Kaiyou Chen and John Middleditch
Pulsars are believed to be strongly magnetized rotating neutron stars. The radiated spectrum of a pulsar
can extend over many decades in wavelength. So far, more than 500 radio pulsars have been discovered.
Among these are about 50 so-called millisecond pulsars, the majority of which have spin periods less
than 10 ms, and all of which are thought to have fields significantly weaker than the so-called pulsars
with a canonical magnetic field strength near 1011 _1012 G, typical of the vast majority of known radio
pulsars.
A disproportionately large number of millisecond pulsars have been found to belong to the Galactic
globular cluster population (about 30 so far). The suggestion that. the millisecond pulsar population is
the result of recycling of old (radio-dead) neutron stars through accretion from an orbital companion
in a low-mass X-ray binary phase has gained a wide acceptance. However, alternative production
mechanisms have also been proposed, some of which do not suffer from the vast overpopUlation of the
millisecond pulsars with respect to that of the low mass X-ray binaries.
There are only about a few dozen accretion-powered X-ray pulsars known to date, with all of these
thought to be strongly magnetized. Only two (Her X-I and 4UI626-67) are known to produce optical
pulsations through reprocessing of the pulsed X-ray flux.
There is only one rotation-powered pulsar (Geminga) with strong y-ray emission, which is not
yet known as a radio source. The existence of non-(or slowly)-varying high-energy y-ray sources
discovered by EGRET on the Compton Gamma-Ray Observatory satellite may indicate a larger
population of y-ray pulsars yet undiscovered.
So far there are three neutron star-neutron star binary systems known, two of which belong to the
galactic disk population and one in the globular cluster MIS. Such binaries provide the best-known
tests of general relativity theory in addition to the accurate measurement of the mass of the component
neutron stars.
At least one millisecond pulsar (1257+12) is thought to have at least two (few Earth mass)
planetary companions in orbits apparently synchronized with a 2:3 period ratio. Further study of such
systems may eventually be able to exclude pulsar precession as an alternative explanation to the timing
irregularities.
Neutron stars are thought to be the compact remnants of supernova explosions. The pulsar in the
Crab nebula is almost certainly such a remnant. The most rapidly spinning pulsar associated with a
supernova remnant, the 16 ms pulsar in N157B, may have had an initial spin period of only seven
milliseconds. The detection of neutrinos from SN1987A indicated that a neutron star was indeed
formed in the original core collapse. However, no evidence for a strong pulsar has yet been detected in
this remnant.
See Table 16.20 for characteristics of a few important pulsars and Figure 16.1 for a radio pulsar
diagram.
16.16PULSARS /
421
-12.
.:0.
~
'(i)'
0 :.:
>
.......
~
>
.......
-14.
"Cl
"Cl
-16.
~
Q.)
~. -: •• °
•
0
......
~
Q.)
&
.'
-18.
~
0
......
. ..
.........
~
-20.
~
'.
-3.
-2.
-1.
o.
log [Period (s)]
Figure 16.1. The "RR diagram" of 645 pulsars showing the period and the period derivative (seconds per second).
Thble 16.20. Some important pulsars.
Period (s)
Comments
0021-72c
0.0058
Nine more pulsars with P < 6 ms in the
same globular cluster, 47 Thc
[I]
0531+21
(Crab pulsar)
0.033
Pulsed emission from radio to y-ray;
obvious supernova association
[2]
0538-69
(N157B pulsar)
0.016
In the Large Magellanic Cloud (LMC);
fastest known pulsar associated with a
supernova remnant
0540-69
(LMC pulsar)
0.050
Also in the LMC and supernova association;
pulsed radio, optical, and X-ray emission
[5]
Geminga
(lE0630+ 17)
0.237
Strong y-ray pulsar; no radio detection
[6]
0833-45
(Vela pulsar)
0.089
Supernova association; strong y-ray source
[7]
1257+12
0.0062
Having two companion planets
[8]
1534+12
0.0379
Having a companion neutron star
[9]
Her X-I
1.24
Accretion-powered X-ray pulsar
[10]
1821-24
0.003
First (millisecond) pulsar discovered; in a
globular cluster, M28
[11]
1845-19
4.3082
Slowest known pulsar
[12]
Name
Reference
[3,4]
422 /
16
STARS WITH SPECIAL CHARACTERISTICS
Table 16.20. (Continued.)
Name
Period (s)
Comments
0.059
First binary pulsar discovered; evidence of
gravitational radiation
[13]
1919+21
1.337
First pulsar discovered;
[14]
1937+21
0.0015
First millisecond pulsar discovered; fastest
known pulsar
[15]
1957+20
0.0016
Eclipsed by the evaporating companion
every 9.2 hours
[16]
1913+16
(Hulse-Taylor pulsar)
Reference
References
1. Manchester, R.N. et aI. 1991, Nature, 352, 219
2. Staelin, D.H., & Reifenstein, E.C. 1968, Science, 162, 1481
3. Marshall, F.E. et aI. 1998, IAU Circ. No 6810
4. Wang, D.Q., & Gotthelf, E.V. 1998,ApJ, 494, 623
5. Seward, F.D. et aI. 1984, ApJ, 287, Ll9
6. Halpern, J.P., & Holt, S.S. 1992, Nature, 357, 222
7. Large, M.I. et aI. 1968, Nature, 220, 340
8. Wolszczan, A., & Frail, D.A. 1992, Nature, 355,145
9. Wolszczan,A.I991,Nature,350,688
10. Tananbaum, H. et aI. 1972, ApI, 174, Ll43
11. Lyne, A.G. et aI. 1987, Nature, 328, 399
12. Newton, L.M. et aI. MNRAS, 194, 841
13. Hulse, R.A., & Taylor, J.H. 1975, ApI, 195, L51
14. Hewish, A. et aI. 1968, Nature, 217, 709
15. Backer, D.C. et aI. 1982, Nature, 300, 615
16. Fruchter, A.S. et aI. 1988, Nature, 333, 237
16.17
GALACTIC BLACK HOLE CANDIDATE X-RAY BINARIES
by Jonathan E. Grindlay
Black hole candidates in the Galaxy are best defined as X-ray binaries in which the accreting compact
object has a probable mass Mx ;::: 3M 0 , or above the limit for neutron stars, as determined
from spectroscopic measurements of the semiamplitude velocity, K, of the companion star with
mass Me. Together with the orbital period P, this defines the mass function of the system:
f(Mx) = P K3 /2rrG = M~ sin3 i/(Mx + Me)2. The mass function thus gives a firm lower limit
for M x, although with additional constraints on system inclination, sin i, and spectral type and thus
mass Me, the black hole candidate mass Mx can be measured [71,72]. The measurement [73]
of Mx = 7.02 ± 0.22M0 obtained for the galactic "micro-quasar" source, with relativistic jets,
GR0J1655-40 = Nova Sco 94 provides the currently (1998) most accurate determination of the mass
of a probable black hole in the Galaxy.
Secondary indicators for galactic black hole candidates are their similar hard X-ray spectra,
with power law form typically extending out beyond 100 keY and containing a significant fraction
of the total luminosity [74] and (in high luminosity states) accompanying ultra-soft X-ray spectral
components [75]. The black hole binaries are most often found as transient X-ray sources which are
often particularly luminous in their soft X-ray emission at their peak and are thus frequently called soft
X-ray transients (despite their nearly universal accompanying hard X-ray emission which dominates
the emission during the decay phase). In comparison with transients known to contain neutron stars
from their X-ray bursts, the black hole transients show significantly larger increase from their quiescent
low states to outburst, consistent with their having an event horizon and advection-dominated accretion
flow at the low accretion rates found in quiescence [76].
16.17
GALACTIC BLACK HOLE CANDIDATE X-RAY BINARIES
/
423
The most reliable black hole candidates are the eight systems listed in Table 16.21 with lower mass
companions for which radial velocities and mass functions were derived when these transient type
X-ray sources faded to quiescent optical levels. The 7-8 mag. optical brightening of some of these
recurrent (~ 50 year) transients resemble novae leading to the tenn X-ray novae for these systems.
The three high mass (;G lOM 0 ) companion systems included in Table 16.22 are less well determined
(with LMC X-I particularly questionable), although the prototype system Cyg X-I is most secure [72].
A general summary of the properties of X-ray transients of all types provides constraints on the galactic
population of black holes in binary systems [77], and a statistical analysis of the quiescent transients
suggests [78] the black hole masses may be clustered near 7 M0 for all but V404 Cyg.
Table 16.21. Galactic black hole candidates with low mass companions [1-5].
Object
Opt. ID
GROI0422+32
Nova Per 92
A0620-00
NovaMon 75
GS1124-68
Nova Mus 91
4U1543-47
ILLup
GROJl655-40
Nova Sco 94
H1705-25
NovaOph 77
OS2000+25
Nova Vu188
OS2023+33
V404Cyg
ex (2000.0)
13 (2000.0)
04 2146.9
325436
06 2244.5
-00 2045
11 2626.7
-684033
154708.6
-474009
165400.2
-395045
17 0814.2
-250532
200249.6
25 1411
202403.8
335204
mv
Sp. Type
22
MOV
18
f(Mx/Mo}
Mx/Mo
5.1
1.21 ± 0.06
3.5-14
K5V
7.8
2.91 ± 0.08
2.8-25
20
K5V
10.4
3.01 ±0.15
4.5-6.2
17
AOV
27.0
0.22±0.02
2.7-7.5
21
F4IV
62.9
3.24±0.09
6.5-7.8
21
K3V
12.5
4.86±0.13
4.7-8.0
21
K5V
8.3
4.97 ±0.1O
5.8-18
19
G9V
155.3
6.08 ± 0.06
10.3-14
P (hours)
References
1. McClintock, I.E. 1998, in Accretion Processes in Astrophysical Systems, AlP Conf. Proc., p. 431.
2. Van Paradijs, I., & McClintock, I.E. 1995, in X-ray Binaries, edited by W.H.G. Lewin, I. van Paradijs, and E.P.I.
van den Heuval (Cambridge University Press, Cambridge), p. 58.
3. Orosz, I.A., & Bailyn, C.D. 1997, ApJ, 477, 876.
4. Tanaka, Y., & Shibazaki, N. 1996, ARA&A, 34, 607.
5. Bailyn, C.D., lain, R.K., Coppi, P., & Orosz, I.A. 1998, ApJ, 499,367.
Table 16.22. Galactic black hole candidates with high mass companions [1, 2].
Object
Opt. ID
LMCX-l
star R148
LMCX-3
starWP
Cyg X-I
HDE226868
ex (2000.0)
13 (2000.0)
053938.7
-694436
053856.4
-64 05 01
195821.7
35 1206
mv
Sp. Type
P (hours)
f(Mx/Mo}
14
OB
4.2
0.14 ± 0.05
17
B3V
1.7
2.3 ±0.3
>7
9
09.71ab
5.6
0.24± 0.01
>7
Mx/Mo
References
1. Van Paradijs, I., & McClintock. I.E. 1995, in X-ray Binaries, edited by W.H.G. Lewin, I. van Paradijs and
E.P.I. van den Heuval, (Cambridge University Press, Cambridge), p. 58.
2. Tanaka, Y., & Shibazaki, N. 1996, ARA&A, 34, 607.
424 /
16
STARS WITH SPECIAL CHARACTERISTICS
16.18 DOUBLE STARS
Indications are that some 40%-60% of all stars are members of double or multiple systems [79], with
some estimates running as high as 85% [80]. As far as selection effects allow, there seems no significant
dependence on stellar type. Such effects preclude any reliable determination of the percentage of
duplicity as a function of semimajor axis size.
The eccentricity of binary orbits and the orbital period are given below:
log P (P in days)
Mean eccentricity
o
0.03
1
2
0.17
0.31
345
0.42 0.47 0.45
6
7
0.64
0.8
For further statistics of binary stars, see [79-82].
16.18.1
Visual binaries
Dawes's rule is the limit of resolution = 11.6/ D arcsec (D is objective diameter in centimeters).
The limit of largest refractors under best conditions""" 0.1 arcsec.
The angular separation beyond which it is unlikely that pairs are physical binaries
log p
= 2.8 -
0.2V,
where p is in arcsec and V is the combined magnitude. Reference [83] suggests that a pair is likely not
physical if the projected linear separation exceeds 0.01 pc.
A catalogue of orbital elements for""" 850 visual binaries is given in [84]. See Table 16.23.
Table 16.23. Selected visual binaries.
a"
Name
Component
T
w (deg)
e
Sirius
A
B
A
B
A
B
A
B
A
B
50.1
1894.1
40.4
1967.9
79.9
1955.6
88.1
1984.0
44.6
1925.6
7.50
0.59
4.50
0.36
17.52
0.52
4.54
0.50
2.41
0.41
Procyon
ct
Cen
700ph
Kriiger60
i (deg)
Q (deg)
P (yr)
Equinox
147.3
44.6
268.8
284.8
231.6
204.9
13.2
301.7
217.8
161.1
136.5
1950
31.9
2000
79.2
2000
121.2
2000
164.5
2000
nil
0.379
0.290
0.760
0.199
0.253
Sp.
Mho)
M/M0
AIV
DA
F5IV-V
WD
G2V
KOV
KOV
K4V
dM4
dM6
0.8
11.2
2.6
12.6
4.4
5.6
5.6
6.8
9.6
10.6
2.28
0.98
1.69
0.60
1.08
0.88
0.90
0.65
0.27
0.16
16.18.2 Spectroscopic Binaries
The formula relating the observed radial velocity maximum and period to the eccentricity, semimajor
axis, and orbital inclination is
for al in units of 106 km, K I in km s-l , and P in days, similarly for a2 and K2.
16.18 DOUBLE STARS / 425
If only one velocity curve is available, the mass function is
If both velocity curves are available, then
MI
sin3 i
=
1.036 x 1O-7(KI
+ K2)2 K2P (1
- e 2 )1.5,
and similarly for M2 and K I. The mass is expressed in solar masses.
The catalogue of orbital elements for'" 1470 spectroscopic binaries is given in [85].
Table 16.24.
See
Table 16.24. Selected spectroscopic binaries.
Name
w
(deg)
e
(days)
T
(2400000+)
Phea
1.6698
41643.689
0.0
f3 Aur
3.9600
31075.759
.0
a Vir
4.0145
40284.78
142
0.18
f3 Lyr
31 Cyg
12.9349
3784.3
42260.922
37169.73
201.1
0.0
0.22
~
16.18.3
P
K
(kms- l )
131.5
202.6
111.5
107.5
120
189
184
14.0
20.8
Vy
(kms- l )
f(M)
(M0)
17.2
11.6
-17.1
0
-2
-17.8
-7.7
-12.3
M sin3 i
(M0)
a sini
006 km)
Sp.
3.9
2.5
2.1
2.2
7.2
4.5
3.02
4.65
6.07
5.85
6.52
10.3
32.7
711
1060
B6V
B8V
A2IY
A21V
BIV
B3V
B8pe
K41b
B4V
8.4
9.2
6.2
Eclipsing binaries
Classification schemes are as follows:
1. By ellipticity:
EA
EB
EW
Algol type
f3 Lyr type
W UMa type
near spherical.
P> 1 day
P < 1 day
ellipsoidal, unequal brightness.
ellipsoidal, equal brightness.
2. By stability within critical equipotential surfaces (Roche lobes). Mass loss occurs when Roche
lobes are filled:
o
SO
C
OC
Detached
Semidetached
Contact
Overcontact
Both components are well within Roche lobes.
One component reaches Roche lobes.
Both components reach Roche lobes.
Both components overfill Roche lobes.
The inter-relations
EA.= 0, SO,
EB.= SD(D),
EW.= C.
No comprehensive catalogue of reliable elements for eclipsing binaries is presently available, but
see [86] for a selection of 323 eclipsing systems. See Table 16.25.
426 I
16
STARS WITH SPECIAL CHARACTERISTICS
Table 16.25. Selected eclipsing binaries (from [1 J).
Name
P
(days)
aa
(RO)
EROri
0.423
RYAqr
e
(deg)
2.12
0.00
80.9
1.967
7.61
0.00
82.1
RWMon
1.906
9.97
0.00
88.0
V889Aql
11.121
34.3
0.37
88.4
AIPhe
24.592
47.75
0.19
88.5
(r)b
(unit = a)
(K)
qC
0.31
0.43
0.17
0.27
0.20
0.32
0.054
0.053
0.037
0.061
5800
5650
7605
4520
10650
5055
10200
10500
6310
5160
1.99
T
0.20
0.37
1.0
1.03
Fd
1.00
1.00
1.00
1.00
4.99
1.00
2.34
2.34
1.49
1.49
Sp.
F8V
A3
B9V
B9
FlV
KOIV
Notes
aa (= at + a2) is the semimajor axis of the relative orbit.
b (r) is the approximate mean stellar radius.
Cq is the mass ratio of secondary to primary.
d F is the ratio of spin angular speed to mean orbital angular speed.
Reference
1. Terrell, D., Mukherjee, J.D., & Wilson, R.E. 1992, Binary Stars: A Pictorial Atlas (Krieger, Florida)
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Chapter
17
Cataclysmic and Symbiotic Variables
W.M. Sparks, S.G. Starrfield,
B.M. Sion, S.N. Shore,
G. Chanmugamt , and R.F. Webbink
17.1
Types of Cataclysmic Variables . . . . . . . . . . . ..
429
17.2
Types of Symbiotic Variables . . . . . . . . . . . . ..
447
17.1 TYPES OF CATACLYSMIC VARIABLES
A cataclysmic variable (CV) [1,2] is a binary star system in which a white dwarf primary accretes
hydrogen-rich material usually through an accretion disk from a Roche lobe filling secondary that is on
or near the main sequence. The CVs consist of several classes such as classical novae, recurrent novae,
nova-likes, dwarf novae, helium CVs, and magnetic CVs. The distributions of their orbital periods are
shown in Figure 17.1. Catalogues ofCVs are found in [3,4]. Proceedings ofCV conferences [5-9] are
bountiful sources of information.
A classical nova [10-12] is a CV that has undergone an outburst (9-15 mag. increase) which
ejects a shell of gas at high velocity. Tables 17.1 and 17.2 contain the brightest and best-observed
classical novae in our Galaxy. More extensive lists are found in [13] and [3]. Table 17.3 lists the
brightest novae from 1991 to 1995. Well-observed novae in the Large Magellanic Cloud are given in
Table 17.4. Classical novae are commonly assumed to be caused by a thermonuclear runaway in the
accreted material on the white dwarf. The classical novae are also designated as CNO and ONeMg
novae according to the composition of the ejecta (see Table 17.5). It is inferred that these novae occur
on CO and ONeMg white dwarfs, respectively, and their ejecta include white dwarf material. As their
name implies, recurrent novae have been observed to undergo more than one outburst. Although there
are currently only nine members listed in this class (see Tables 17.6 and 17.7), it may be necessary
to subdivide them according to their type of outburst or their type of secondary when they are better
understood. In some systems the outbursts are probably caused by thermonuclear runaways, but in
tDeceased.
429
430 I
17
CATACLYSMIC AND SYMBIOTIC VARIABLES
CJ AM Her
~ SUUMa
~UGern
30
El Zearn
li3 VV Sci
J:!) UX UMa
~ Recurrent Novae
ImJ Novae
25
~ 20
g
z
15
10
-1.2 -1.0 -O.B -0.6 -0.4
-0.2
0.0
log P (d)
0.2
0.4
0.6
O.B
1.0
Figure 17.1. The orbital period distributions of the cataclysmic variables.
other systems the outburst may result from an episodic mass transfer accompanied by the release of
gravitational energy onto the primary which could be a white dwarf or a main-sequence star [14, 15].
In addition, for some recurrent novae, the secondary is a late-type giant.
The dwarf novae (Table 17.8) [16] undergo a periodic brightening (2-5 mag.) on a time scale of
weeks to years with little or no mass ejection aside from the wind outflow during the outburst in most of
the systems. Most dwarf novae change from having an emission line spectrum to having an absorption
line spectrum during outburst. This phenomenon is normally assumed to be caused by an instability in
the accretion disk surrounding the white dwarf. The SU UMa stars are a subclass of dwarf novae that
also show semiperiodic outbursts of unusually large amplitude (superoutburst), distinguished by the
appearance at outburst maximum of periodic modulations (superhumps) in the light curve with periods
a few percent larger than the orbital period. Dwarf novae that show occasional standstills (episodes of
intermediate brightness lasting days to years) during decline from maximum are termed Z Cam stars.
The remainder of the dwarf novae are called U Gem systems after the original prototype.
The nova-likes [16] are CVs that have the appearance of quiescent classical novae, i.e., they are
probably classical novae that have not had a recorded outburst. Table 17.9 contains the best observed
nova-likes. Additional listings are found in Ritter [3]. There are two subclasses of nova-likes: UX UMa
and VY ScI. The UX UMa systems look like dwarf novae in a permanent outburst state while the
VY Scl systems (or antidwarf novae) are normally in a high state but have slow, short excursions to a
low state. These variations of luminosity are probably due to changes in the accretion rate. The helium
CVs (or AM CVn systems) are transferring helium-rich material instead of hydrogen-rich material.
Otherwise they appear to be nova-likes.
The white dwarf in a magnetic CV has a sufficiently strong magnetic field to channel the flow of
accreting material at least near the white dwarf's surface [17]. The magnetic CVs may be divided into
two subclasses depending on whether the white dwarf is rotating synchronously (Table 17.10) with
its binary companion, as in the AM Her binaries or polars, or asynchronously (Table 17.11) as in the
DQ Her binaries or intermediate polars. In the AM Her binaries, the magnetic field is sufficiently strong
so that the accretion flows via an accretion column and no accretion disk is formed. In the DQ Her
17.1 TYPES OF CATACLYSMIC VARIABLES / 431
binaries, the magnetic field is probably weaker and an accretion disk may form but is disrupted close
to the white dwarf's surface.
Being a member of one class of CVs does not prevent a system from being a member of another.
For example, OK Per, an old classical nova, also shows dwarf nova outbursts. Nova V1500 Cyg is also
an AM Her system. The space density of CVs, Pcv, is a subject of much controversy. Assuming that
the novae, dwarf novae, and nova-likes found in a galactic plane survey [18] represent all the CVs, their
space density, Pcv, is (5.3-8.2) x 10-7 pc-3. However, if novae fade considerably between outbursts,
then a higher space density like that of Pcv 2:: 3 x 10-5 pc-3 found in a deep but narrow survey [19]
may be more realistic.
Many of the following tables make use of the SIMBAD database, operated at CDS (Centre de
Donnees Stellaires), Strasbourg, France. Uncertain numbers are followed by a colon.
Table 17.1. Selected list of classical novae.
Name
(alternate name)
aD (2000)
aD (2000)
hrminsec
degmin sec
GKPer
(N Per 1901)
TAur
(N Aur 1891)
RRPic
(N Pic 1925)
CPPup
(NPup 1942)
GQMus
(NMus 1983)
DQHer
(NHer 1934)
FHSer
(N Ser 1970)
V693CrA
(NCrA 1981)
V603Aql
(N Aq11918)
V1370Aql
(N Aq11982)
PWVul
(NVulI984No.l)
HRDeI
(NDell967)
VlSOOCyg
(N Cyg 1975)
VI668Cyg
(NCyg 1978)
OS And
(N And 1986)
0331 11.82
435416.8
150.55
-10.60
053159.06
302645.2
176.79
-2.30
06 35 36.05
-623823.4
272.30
-25.71
08 1145.96
-352105.7
252.59
-1.08
115202.35
-671220.2
296.92
-4.78
180730.17
455131.9
73.09
26.68
183046.92
023651.5
32.59
6.33
184157.63
-373113.1
357.51
1848 54.50
003502.9
32.82
1.37
192321.10
022926.1
38.43
-5.43
192605.03
272158.3
60.80
5.55
204220.18
190940.3
62.96
-13.64
2111 36.61
480901.9
89.48
-0.00
214235.22
440154.9
90.42
-6.70
231205.76
472819.7
105.69
-11.97
eb (deg) Ii' (deg)
-13.79
mC
max
mC.
t 3d
(days)
Light
curve
Refs.
Secondary
spectral
typee
0.2v
13.Ov
4.1B
14.9B
1.2v
12.3v
0.2v
15.Ov
7.2v
17.5v
1.3v
14.7v
4.4v
16.1v
6.5v
> 19v
-1.4v
11.6v
7.5p
20.Op
6.4v
17.Ov
3.3v
12.1v
2.0B
16.3B
6.Ov
20:
6.2v
17.8v
13
[1]
K2IV-V
[2]
100
[3]
150
[4,5]
8
[4,6]
45
[8]
94
[4,9]
62
[11]
12
[12]
8
[4,13]
13:
[14, 15]
97
[16]
230
[17]
3.6
[19,20]
23
[21,22]
22
[23]
mm
>M6
[7]
M3V
[10]
K8
[18]
Notes
°Adapted from Duerbeck [24] and precessed to equinox 2000.
bGalactic coordinates.
cMaximum and minimum magnitudes from Warner [25]. and the light curve references B, v, and p are the blue, visual, and
photographic magnitudes.
dThe time for the visual light curve to fall three magnitudes after maximum, t3, was taken from Duerbeck [24].
eThe secondary spectral types are from spectroscopic or infrared photometric observations and do not include estimates
from mass determinations.
432 /
17
CATACLYSMIC AND SYMBIOTIC VARIABLES
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'IlIble 17.2. Data for selected classical novae.
Nebular
Distancec
(PC)
Max.
abs.
Periodd
Rapid optical
oscillation
period' (s)
Expansion Outvelocity
burst
spectra!
(kmIs)
mag.
(days)
490n
-9.20 1.996 803 [3]
-8.4n 0.204 378 29 [11]
-7.3n 0.1450255 [18]
-9.7n 0.06143 [24]
0.068 34 [25]
-7.4 0.0594 [29]
-350QPO[4]
[12]
20-40 QPO [19]
1200 [5]
655 [13]
475 [13]
710 [13]
[6,7]
[14]
[20,21]
[26,27)
800 [28]
[28,30]
5600
-7.8n 0.1936206
[33,34,35]
71.074514
[36,37]
384 [38]
[39,40]
[41]
[43]
Name
E(B - V)"
shell
studiesi'
GKPer
TAur
RRPic
CPPup
0.3 [1]
0.6 [9]
0.07 [16]
0.08 [23]
[2)
[9,10]
[17)
[23]
GQMus
0.45 [28]
DQHer
0.11 [31]
FHSer
0.4[42]
850n
-6.5n
560 [13]
[43]
V693CrA
0.56 [44]
5030
-8.8
2200 [44]
[44,45]
V603Aql
0.07 [16]
370n
1700 [5]
[50]
V1370Aql
0.6[52]
-9.5n 0.138 15 [47]
0.144854 [48, 49]
2800 [53]
[52,53)
BOOn
460n
835n
4280
[10,32]
[10,46)
Quiescent
spectra.!
[8]
[15]
[22)
[24]
Descrip-
tiong
VF
MF
S
VF
MF
[51]
CNO
no dust
MF
CNO
dust
MF
Cdust
VF
ONeMg
VF
VF
ONeMg
C,SiC,
Si~
PWVul
0.45 [54]
HRDel
0.29 [58]
V1500Cyg
0.5 [66]
2050
-6.6
[59,60]
850n
[67]
I080n
-7.3n 0.214165 [61]
0.1775 [62]
-9.8n 0.139613 [68,69]
0.2137 [55]
[12]
dust
MF
285 [56]
[57]
520 [13)
[58,63]
[64,65]
1180 [13]
[70,71]
[68]
Solar
Cdust
VS
VF
CNO
17.1 TYPES OF CATACLYSMIC VARIABLES / 433
Thble 17.2. (Continued.)
Name
E(B - V)a
VI66S Cyg 0.4 (72)
OS And
0.25 (76)
Nebular
shell
studiesb
Distancec
(pc)
Max.
abs.
mag.
Periood
(days)
3660
-S.I
0.1384 (73)
7200
-S.2
Rapid optical
oscillation
period' (s)
Expansion
velocity
(kmIs)
Outburst
spectra.!
700 (72)
[74.75)
1000 (77)
[7S)
Quiescent
spectra.!
Descrip-
tion'
F
CNO
Cdust
F
CNO
Notes
aThe color excess. E(B - V). is assumed to be related to the visual interstellar extinction. Av. by Av = 3.2E(B - V).
bIn addition to these nebular shell studies. a short spectroscopic description of the nova remnant is given by Duerbeck and
Seitter [79].
cThe distances and absolute maximum magnitudes that are followed by an "n" have been determined by the nebular
expansion parallax method. The angular shell sizes are from Cohen and Rosenthal [13]. except for V1500 Cyg [80]. DQ
Her [38]. and FH Ser [42]. The other distances and absolute magnitudes are found from the maximum magnitude -t2
relationship derived by Cohen [80] and assuming t2 - t3/2 [81]. The time for the visual light curve to fall after maximum by
n magnitudes is denoted by tn.
d The spectroscopic period is the first entry while the photometric period is the second if it is different. Orbital parameters
can usually be found in the reference for the spectroscopic period.
elf only a reference is given in this column. it means an unsuccessful search.
f Only optical references are given. Surveys or catalogues of novae exist in the radio [82. 83]. infrared [84-86]. visual [87.
88]. ultraviolet [89. 90]. and X-ray [91-93] spectral regions. References of observations for individual novae can be found in
Payne-Gaposchkin [94]. Ritter [95-97]. Duerbeck [98]. and Bode et al. [99]. Finding charts can be found in these last two
references and in Williams [87].
gThe speed class is defined by Payne-Gaposchkin [94] as
Speed class
Rate of decline
(mag.lday)
Very fast (VF)
Fast (F)
Moderately fast (MF)
Slow (S)
Very slow (VS)
> 0.20
0.18 to 0.08
0.07 to 0.025
0.024 to 0.013
0.013 to 0.008
The type of nova is defined by the strong enhancement above solar values of the chemical composition of the ejecta (CNO
or ONeMg) and often implies the composition of the white dwarf. The types of dust fonned. if any. is quoted from Gehrz [56].
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7. Stratton, EI.M. 1936, Ann. Solar Phys. Obs. Cambridge, 4, part 2
8. Bianchini, A., Sabbadin, E. & Harnzaoglu, E. 1982, A&A, 106, 176
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10. Mustel, E.R., & Boyarchuk, A.A. 1970, Ap&SS, 6, 183
11. Beuennann, K., & Pakull, M.W. 1984, A&A. 136, 250
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13. Cohen, I.G., & Rosenthal. A.I. 1983. ApI, 268, 689
14. Mclaughlin. D.B. 1941, PASP, 53, 102
15. Bianchini, A. 1980, MNRAS, 192. 127
16. Gallagher, I.S., & Holm, A.V. 1974, ApI, 189, LI23
17. Williams, R.E., & Gallagher, I.S. 1979, ApI, 228, 482
18. Haefner, R., & Metz, K. 1982.A&A,l09, 171
19. Schoembs, R., & Stolz, B. 1981,1nf. Bull. Var. Stars, No. 1986
434 I
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
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40.
41.
42.
43.
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Krautter, J. et al. 1984,A&A,137, 307
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Williams, R.E., Woolf, N.J., Hege, E.K., Moore, R.L., & Kopriva, D.A. 1978, ApI, 224,171
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Rosino, L., Ciatti, F., & Della Valle, M. 1986, A&A, ISS, 34
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76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
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91.
92.
93.
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99.
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Bode, M.F., & Evans, A. 1989, in Classical Novae, edited by M.F. Bode and A. Evans (Wiley, New York), p. 163
Harrison, T.E., & Gehrz, R.D. 1988, AJ, 96, 1001
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Williams, G. 1983, ApJS, 53, 523
Bruch, A. 1984, A &AS, 56, 441
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Table 17.3. Recent novae.
Name
(alternate
name)
(2000)
hrmin sec
IX
8 (2000)
deg min sec
Date of
discovery
IAU
Cire.
No.
mmax
t3 Q
(days)
E(B - V)b
FWHMc
emission vel.
(kmls)
V351 Pup
(N Pup 91)
8 1138.38
-350730.4
27 Dec 1991
5422
6.4v
3000
V4160 Sgr
(N Sgr 91)
V838 Her
(NHer91)
18 14 13.83
-321228.5
29 July 1991
5313
7v
8000
184631.48
+121401.8
24 Mar 1991
5222
5.3v
2.8
0.6
6000
VI974Cyg
(NCyg 92)
203031.66
+523750.8
20 Feb 1992
5454
4.9B
43
0.35 ±0.05
2000
V705 Cas
(NCas 93)
V1425 Aql
(N Aq195)
234147.25
+573059.7
7 Dec 1993
5902
5.3v
190526.64
-014203.3
7 Feb 1995
6133
6.2:v
22:
2: 0.56
1600
Notes
QThe time for the visual light curve to fall three magnitudes after maximum.
bThe color excess.
cThe full width half maximum velocity of the emission lines in IUE spectra measured by S. Shore.
dThe description is the same as in Table 17.2 for classical novae.
Desc.d
ONeMg
no dust
VF
ONeMg
ONeMg
Dust
VF
ONeMg
No dust
MF
CO
Dust
ONeMg
Dust
F
436 /
17
CATACLYSMIC AND SYMBIOTIC VARIABLES
'Dlble 17.4. Recent novae in the Large Magellanic Cloud [1, 2].
a (2000)
Nova
hrminsec
~ (2000)
deg min sec
IAU Cire. No.
LMCV3479
LMCV1161
LMCV2361
LMCV1341
LMCV0850
LMCI992
LMCI995
53529.33
50801.10
52321.82
50958.40
50344.99
51919.84
52650.33
-702129.4
-683737.7
-692948.5
-713951.6
-701813.7
-685435.1
-700123.8
4569
4663
4946
4964
5244
5651
6143
Outburst
Vmax
1YPe
Remarks
21 Mar 1988
12 Oct 1988
16 Jan 1990
15 Feb 1990
18 Apr 1991
11 Nov 1992
2 Mar 1995
11.0
10.4
10.6
11.9
8.9
10.2
11.3
Dust,CNO
ONeMg
ONeMg
Recurrent
CNO?
CNO
CNO
a
b
c
d
e
/
Notes
aUV versus optical analysis: Austin, S., Starrfield, S., Saizar, P., Shore, S.N., & Sonneborn, G. 1990, in Evolution in
Astrophysics: lUE in the Era o/New Space Missions, edited by E. Rolfs (ESA SP 310), p. 367. Possible dust-forming
nova.
buy description: IAU Cire. No. 4669. First extragalactic ONeMg nova.
C t3(optical)
5.8 days. Sonneborn, G., Shore, S.N., & Starrfield, S.G. 1990, in Evolution in Astrophysics: lUE in
the Era 0/ New Space Missions, edited by E. Rolfs (ESA SP 310), p. 439; see also, Starrfield, S., Shore, S.N., Sparks,
W.M., Sonneborn, G., Truran, J.W., & Politano, M. 1992, ApJ, 391, L71.
dRecurrence of Nova LMC 1968. Dynamics, abundances: Shore, S.N., Starrfield, S., Sonneborn, G., Williams,
R.E., Haumy, M., Cassatella, A., & Drechsel, H. 1991, ApJ, 370,193. First spectroscopically confirmed, extragalactic
recurrent nova; U Sco analog (low mass companion, helium rich).
e FUV.max
1.64 x 10-£0 erg s-1 cm- 2 ; t3(UV)
140 days; delay: optical versus UV peak Rl 10 days. This was
the intrinsically brightest nova yet observed in the Local Group. Probable CNO nova.
I Star is a match to the Galactic nova OS And 1986.
=
=
=
References
1. General reference for LMC novae: van den Bergh, S. 1988, PASP, 100, 1486.
2. General reference for M31 novae: Tomaney, A.B. & Shafter, A.W. 1992, ApJS, 81,683
3. General reference for extragalactic novae: Artiukhina, N.M. et al. 1995, General Catalogue o/Variable Stars, Vol. V.
Extragalactic Variable Stars (Kosmosinform, Moscow)
'Dlble 175. Element abundances in novae (mass fraction).
Object
Year
X
Y
TAur
RRPic
DQHer
DQHer
HRDeI
V1500Cyg
V1500Cyg
V1668 Cyg
V693CrA
V693CrA
V1370Aql
GQMus
PWVul
PWVul
QUVul
QUVul
V842Cen
V827 Her
QVVul
V22140ph
V977 Sco
V433 Sct
LMC 1990 No.1
V351 Pup
1891
1925
1934
1934
1967
1975
1975
1978
1981
1981
1982
1983
1984
1984
1984
1984
1986
1987
1987
1988
1989
1989
1990
1991
0.47
0.53
0.34
0.27
0.45
0.49
0.57
0.45
0.29
0.40
0.053
0.37
0.69
0.62
0.30
0.36
0.41
0.36
0.68
0.34
0.51
0.49
0.53
0.37
0.40
0.43
0.095
0.16
0.48
0.21
0.27
0.23
0.32
0.21
0.088
0.39
0.25
0.25
0.60
0.19
0.23
0.29
0.27
0.26
0.39
0.45
0.21
0.25
C
0.0039
0.045
0.058
0.070
0.058
0.047
0.046
0.0040
0.035
0.0080
0.0033
0.Q18
0.0013
0.12
0.087
0.014
0.0056
N
0
0.079
0.022
0.23
0.29
0.027
0.075
0.041
0.14
0.080
0.069
0.14
0.125
0.049
0.068
0.Q18
0.071
0.21
0.24
0.010
0.31
0.042
0.053
0.069
0.064
0.051
0.0058
0.29
0.22
0.047
0.13
0.050
0.13
0.12
0.067
0.051
0.095
0.014
0.044
0.039
0.19
0.030
0.016
0.041
0.060
0.030
0.0070
0.10
0.19
Ne
0.Q11
0.0030
0.023
0.0099
0.0068
0.17
0.23
0.52
0.0023
0.00066
0.00014
0.040
0.18
0.00090
0.00066
0.00099
0.017
0.026
0.00014
0.049
0.11
Z
Ref.
0.13
0.043
0.57
0.57
0.077
0.30
0.16
0.32
0.39
0.39
0.86
0.24
0.067
0.13
0.10
0.44
0.36
0.35
0.053
0.40
0.10
0.062
0.26
0.38
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[17]
[17]
[17]
[17]
[17]
[18]
[19]
17.1 TYPES OF CATACLYSMIC VARIABLES / 437
Table 17.5. (ContinuetL)
Object
Year
X
Y
C
N
0
V838 Her
V838 Her
V1974Cyg
V1974Cyg
Solar
1991
1991
1992
1992
0.80
0.60
0.30
0.19
0.705
0.093
0.31
0.52
0.32
0.275
0.018
0.010
0.015
0.019
0.012
0.023
0.085
0.001
0.0032
0.0021
0.10
0.29
0.010
0.003
Ne
0.068
0.056
0.037
0.11
0.002
Z
Ref.
0.11
0.09
0.18
0.49
0.020
[20]
[10]
[21]
[16]
[22]
References
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6. Ferland, G.J., & Shields, G.A. 1978,ApJ, 226,172
7. Lance, C.M., McCall, M.L., & Uomoto, A.K. 1988, ApJS, 66, 151
8. Stickland, D.J. et al. 1981, MNRAS, 197, 107
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11. Snijders, M.AJ. et al. 1987, MNRAS, 228, 329
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Table 17.6. RecuTTf!nt novae. a
ab
/jb
(2000)
(2000)
Name
hr
min
sec
LMC 1990#2
TPyx
TCrB
USco
RSOph
V745 Sea
V394CrA
V3890Sgr
V1017 Sgr
05
09
15
16
17
17
18
18
18
09
04
59
22
50
55
00
30
32
58.40
41.47
30.09
30.68
13.08
22.13
25.97
43.32
04.30
min sec
-71
39
22
55
52
42
14
00
01
23
-32
+25
-17
-06
-33
-39
-24
-29
(deg)
bC
(deg)
Years of
recorded outbursts
283.04
256.76
42.43
357.29
19.48
357.02
352.50
8.85
4.15
-33.49
+9.51
+48.66
+22.47
+10.96
-3.40
-7.13
-5.84
-8.50
1968,1990
1890, 1902, 1920, 1944, 1966
1866,1946
1863, 1906, 1936, 1979, 1987
1898, 1933, 1958, 1967, 1985
1937, 1989
1949, 1987
1962, 1990
1901, 1919, 1973
IC
deg
51.6
47.0
11.4
42.1
28.4
58.3
35.1
08.6
12.8
Notes
aThree possible recurrent novae have been found in M31. 1\vo are recorded by Rosino, L. 1973, A&AS, 9, 347, and
all three (M31 V0609, M31 V0665, and M31 V(979) by Artiukhina, N.M. et al. 1995, General Catalogue o/Variable
Stars, Vol. V. Extragalactic Variable Stars (Kosmosinfonn, Moscow).
b Adapted from Duerbeck, H.W., 1987, Sp. Sci. Rev., 45, I, and precessed to equinox 2000.
cGalactic coordinates.
438 /
17
CATACLYSMIC AND SYMBIOTIC VARIABLES
Table 17.7. Recurrent novae data.
Name
t3a
(days)
Vrnax
Vrnin
Av
(mag.)
LMC 1990#2
TPyx
TCrB
USco
RSOph
V745 Sco
V394CrA
V3890 Sgr
VI017 Sgr
<7
88
6.8
5
9.5
14.9
5.0
17
130
11.7
7.0
2.0
8.9
4.6
9.6
7.0
8.2
7.0
> 20
~
15.2
10.2
17.9
1l.5
19.0
18.0
17.0
13.6
~
0.45
1.0
~0.35
0.6
2.3
~3
~3
1.5
1.2
Distance
(kpc)
Spectral type
secondary
55
?
?
M4.1 ±0.1 ill
G3
K5.7 ± 0.4 I-ill
M4/5ill
K
M5ill
G5ill
> 1
1
15:
<1.3
4.6
> 10:
~
~5
2
Periodb
(days)
~0.1
227.5
1.23
460
?
0.7577
?
5.7
Refs.
[1.2]
[3-6]
[3,5,7-9]
[3-5]
[3,5,10--13]
[5, 14, 15]
[4,5,16]
[5, 14, 17]
[3,5,18]
Notes
a The time for the visual light curve to fall three magnitudes after maximum.
bOrbital period.
References
1. Shore, S.N. et a1. 1991, ApJ, 370,193
2. Sekiguchi, K. et a1. 1990, MNRAS. 245, 28P
3. Webbink, R.F. et a1. 1987, ApJ, 314. 653
4. Schaefer, B.E. 1990, ApJ, 355, L39
5. Duerbeck, H.A. 1987, A Reference Catalog and Atlas of Galactic Novae (Reidel, Dordrecht)
6. Schaefer, B.E. et al. 1992, ApJS, 81, 321
7. Kenyon, S.J., & Garcia, M. 1986,AJ. 91,125
8. Selvelli, P.L., Cassatella, A., & Gilmozzi, R. 1992, ApJ, 393. 289
9. Shore, S.N., & Aufdenberg, J.P. 1993, ApJ, 416, 355
10. Bode, M. 1987, RS Oph (1985) and the Recurrent Nova Phenomenon (VNU Science, Utrecht)
11. Garcia, M.R. 1986, AJ, 91, 1400
12. Dobrzycka, D., & Kenyon, S.l. 1994. AJ, 108. 2259
13. Shore, S. et a1. 1996, ApJ, 456,717
14. Harrison, T.E. et a1. 1993. AJ, 105.320
15. Sekiguchi, K. et al. 1990, MNRAS. 246,78
16. Sekiguchi, K. et a1. 1989, MNRAS. 236, 611
17. Gonzalez-Riestra, R. 1992. A&A, 265, 71
18. Sekiguchi, K. 1992, Nature, 358, 563
Table 17.8. Dwaifnovae.
(I)
Name a •b
(aIt. name)
WWCet
RXAnd
HTCas
FOAnd
WXCet
(N Cet 1963)
TYPsc
ARAnd
WXHyi
UVPer
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11) (12) (13)
Coord. c
(2000.0)
ON
POrb
Vrnin
Vmax
tree
Incl.
MWD
XRS
EC
QP
0.85
0.11
1.14
0.33
0.62
0.04
1.62d
1.41'
N
N
N
Y
3.od
N
Y
Y
Y
0.7d
1.64'
N
Y
Y
Y
N
N
N
N
N
450
N
N
N
N
N
12.2 11-35
370
11.0
25
N
N
N
N
N
N
N
N
N
N
O.3od
N
N
N
Y
N
N
N
N
01124.77
-112842.7
10435.55
41 1758.0
I 10 12.98
6004 35.9
I 1532.14
373735.5
1 17 04.17
-17 56 23.0
1 2539.35
322309.7
14503.27
375633.3
20950.65
-631839.9
21008.25
571120.6
Z
0.1765
15.0
9.3
31
Z
0.209893 12.6
10.9
5-20
SU
0.073647 16.4
SU
0.071
17.5
10.8 30-35
430
13.5
0.052:
17.5
SU
0.068:
15.3
U
0.19:
16.9
SU
0.074813 14.7
SU
0.0622:
17.5
9.5
12.5
11.7
14
140
360
54
4
51
9
81
40 0.9
10 0.3
0.82'
N
(14)
WO
SP Wind
(15)
Spect.
type
sec.
17.1 TYPES OF CATACLYSMIC VARIABLES I 439
1Bb1e 17.8. (ContinUild.)
(I)
Name"·b
(all. name)
CPEri
OK Per
(NPer 1901)
AFCam
VWHyi
AHEri
TUMen
AQEri
FSAur
CNOri
SSAur
CWMon
HLCMa
(lE0643-1648)
IRGem
AWGem
BVPup
UGem
ZCha
YZCnc
SUUMa
ZCam
ATCnc
(Ton 323)
SWUMa
EIUMa
(PG0834+488)
BZUMa
CUVel
(2)
(3)
(4)
(6)
(7)
(8)
(9)
(10)
Coord.C
(2000.0)
ON
Porb
31032.76 U 0.01995
-094505.3
33111.82 ON 1.996803
435416.8
33215.59 ON 0.23:
584722.1
4 09 11.34 SU 0.074271
-71 1741.1
42238_10 U
-13 2130.2
44140.71 SU 0.1176
-763646.3
50613.04 SU 0.06094
-040807.0
54748.34 U 0.059:
2835 ILl
55207.77 U 0.163199
-052500.7
61322.44 U 0.1828
474425.7
63654.53 U 0.1762
000216.3
645 17.21 Z 0.2145
-165135.4
647 34.58 SU 0.0684
280622.7
7 22 40.83 SU 0.0762
283016.1
74905.26 U 0.225:
-233400.7
7550S.29
U
0.176906
220005.7
8 07 28.30 SU 0.074499
-763201.3
81056.62 SU 0.0868
280833.6
81228.20 SU 0.07635
623622.6
82513.20 Z 0.289840
730639.4
82836.92 Z 0.238691
252002.6
83642.80 SU 0.056815
532838.2
83821.98 U 0.26810
48 38 01.7
85344.14 ON 0.0679
5748 41.1
85832.87 SU 0.0773
-4147 SO.8
90103.35 Z 0.380
175356.1
92207.48 U? 0.2146
ARCnc
310314.6
94636.67 SU? 0.08597
OVUMa
(US 943)
444645.1
95101.51 U 0.1644
X Leo
11 5231.1
10 06 22.43 SU 0.063121
OYCar
-701404.9
CHUMa
10 07 00.57 U 0.3448:
(PGl0030+678)
673246.5
DO Leo
10 40 51.21
0.234515
(PO 1038+ 155)
IS 11 33.7
SYCnc
(5)
Vrnin
Vrnax
tree
19.7
16.5
10.2
0.2
17.0
13.4
75
13.4
9.5
27
179
18.4
13.5
> 16
11.6
17.7
12.5
16.2
14.4
14.2
11.9
14.5
IO.S 40-75
16.3
11.9
122
13.2
11.7
17
16.3
11.7 22-48
150
13.8
98
410
13.1
19
18.8
15.6
Inc!.
< 73
37
194
40:
8-22
(II) (12) (13)
QP
N
N
WD
Wind
Y
N
N
N
Y
N
N
N
N
N
N
N
Y
Y
N
N
Y
N
N
N
N
N
N
Y
N
N
N
N
N
N
N
N
N
N
< 0.32Ft
N
Y
N
N
M4-5
N
N
N
N
Y
MI-5
N
Y
N
N
N
M3-S
- 1.2od
N
N
N
Y
N
N
N
N
N
N
N
N
N
N
0.55'
N
N
N
N
1.12
0.13
0.84
0.09
- o.lsd
Y
Y
Y
N
M4.5
0.87Ft
1.97F'
Y
Y
Y
N
MS.5
O.24d
0.95e
N
Y
N
Y
N
N
N
N
0.90
0.20
EC
N
60 0.63
65 0.6
10
67
3
38
16
0.74
0.10
1.08
0.40
45: 1.0:
118
15.3
12.4
82
287
14.1
11.9
38 0.82
3 0.05
14.2
12.2
6-16
134
5-33
13.6
IO.S
19-28
Y
N
Y
14
2.1Ft
18.7e
N
N
12.7B
57 0.99
11 0.15
Y
N
N
N
45 0.71
18 0.22
0.32e
Y
Y
N
N
N
N
N
N
10.6
14.9B
69.7
0.7
81.8
0.1
1.5IY
9.1
16.5
160
459
sec.
K0-4
10 0.15
14.0
15.0B
(15)
Spect.
type
SP
MWO
XRS
(14)
0.4IY
O.08e
-3.l d
Ll3'
1.01 e
K7
M5.5
17.8
IO.S
N
N
N
N
N
15.5
10.7
N
N
N
N
N
< O.SlFt
N
Y
N
Y
08-9
N
Y
N
N
N
M4-5
N
N
N
N
N
M4.5
< 0.21Ft
N
Y
N
N
M2
0.11'
Y
N
Y
N
M6
N
N
N
N
N
N
N
N
N
N
13.5
113
386
ILl 22-35
26 0.89
6 0.28
18.7
15.3
18.6
15.4
15.8
12.4
15.3
12.4 25-50 82.6 0.90
300 0.1 0.04
10.7
204 21.0 1.9S
4.0 0.30
15.9
16.0B
8-38
440 I
17
CATACLYSMIC AND SYMBIOTIC VARIABLES
Table 17.8. (Continued.)
(1)
Name",b
(all. name)
CYUMa
V436Cen
V442Cen
RZLco
TLco
DO Ora
(PG1140+719)
lWVll"
ALCorn
BVCen
LYHya
(1329-294)
UZBoo
TTBoo
EKTrA
DMOra
BRLup
SSUMi
(PG1551+719)
AHHer
V20510pb
V4260ph
UZSer
BDPav
AYLyr
EMCyg
ABOra
EYCyg
UUAql
V4140Sgr
(NSV 12615)
RZSge
WZSge
CMDel
V503Cyg
VWVul
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11) (12) (13)
Coonl,C
(2000.0)
DN
Pori>
Vrnin
Vmax
tree
locI.
Mwo
XRS
EC
QP
SU
0.0583
17.0
11.9
N
N
N
N
N
SU
0.062501 15.3
12.4
N
Y
N
N
U
0.46:
N
N
Y
N
N
0.41"
N
N
N
N
65 0.16
19 0.04
42 0.83
N
N
N
N
N
N
N
Y
N
N
M3-S
43 0.91
13 0.25
0.3sd
N
N
N
Y
M2-4
N
N
Y
N
N
N
N
N
N
N
N
N
N
N
105657.05
494118.7
111400.10
-374048.6
112451.92
-355437.7
113722.30
014857.8
113826.96
032208.1
114338.34
714120.4
114521.13
-042605.9
123225.90
142042.5
13 31 19.55
-545833.6
133153.84
-294059.1
144401.30
220056.0
145744.74
404342.2
15 1401.47
-650531.3
153412.13
594831.9
153553.15
-403405.5
1551 22.24
714511.9
164409.99
25 1502.1
170819.09
-254830.8
180751.71
055148.5
18 1124.90
-145533.9
1843 11.90
-573044.2
18 44 26.73
375951.8
193840.10
303028.0
194906.50
77 4423.5
195436.77
322154.7
195718.68
-091920.8
195849.71
-385612.3
20 03 18.49
170252.6
2007 36.40
174215.4
202456.92
17 1754.3
20 2717.44
434123.1
20 57 45.08
253026.0
16.5
22
335
11.9 14-39
19.0
11.5
0.058819 15.2
11.0
SU? 0.0708
SU
U
U
115:
297:
450
0.165
15.6B
1O.6B
0.18267
15.8
12.1 15-44
0.061:
20.8
12.8
225:
0.610116 12.6
10.5
150
65: 0.7:
5 0.1
5 0.18
62 0.83
5 0.10
8.3F!
(14)
WD
SP Wind
0.13695
14.4
0.125:
19.B
1l.5
360:
N
N
N
N
N
SU
0.077:
< 15.6
12.7
45
N
N
Y
N
N
SU
0.0636
> 17
12.1
Y
N
N
N
N
U
0.087:
20.8
15.5
231
487
N
N
N
N
N
SU
0.0793
> 17.5
13.1
N
N
N
N
N
U
0.088:
16.9
12.6 30-48
N
N
N
N
N
Z
0.258116 13.9
11.3
N
Y
N
Y
U?
0.062428 15.0
13.0
O.48F!
2.38"
Y
y
N
N
1.07"
N
N
N
N
N
N
N
N
N
N
Y
N
N
N
N
N
N
N
Y
y
N
N
N
N
N
Y
N
N
N
N
N
N
N
N
N
7-27
Z
0.2853
11.5
17-5S
U
0.1730
15.5
11.9 10-40
U
0.17930
15.4
12.4
SU
0.07340
18.4B
13.2
8-43
205
46 0.95
3 0.10
80.5 0.44
2.0 O.OS
S7 0.9
11 0.15
> 5S
N
Z
0.290909 13.3
12.5
1~
Z
0.15198
14.5
12.3
8-22
U
0.18123:
15.5
1l.4
96
U
0.14049:
16.1
11.0
71
SU? 0.061430 17.5
15.5
N
Y
N
N
N
SU
0.0686
N
N
N
N
N
SU
0.056688 14.9
y
y
N
N
N
N
N
SU
0.07599
13.4
15.3
17.4
-0.30"
0.21"
y
0.162
72 0.8:
2 0.3
73: 0.48
47 O.lS
Y
U
12.8 62-93
266
7.0:
11876
N
N
N
N
N
U?
0.0731
13.6
44 0.24
12 0.06
N
N
N
N
N
16.9
13.4
28
14-29
63 0.S7
10 0.08
1.6"
3.62"
N
(15)
Spect.
type
sec.
OS-8
K2-MO
K2-4
KS
KO
17.1 TYPES OF CATACLYSMIC VARIABLES /
441
Table 17.8. (Continued.)
(I)
Name"·b
(alt. name)
VY Aqr
SSCyg
RUPeg
TYPsA
(PS 74)
GD552
IP Peg
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(II)
(12) (13)
Coord.c
(2000.0)
DN
Porb
Vmin
Vrnax
tree
Incl.
MWO
XRS
EC
QP
SU
0.06312
3.96'
N
N
N
N
86Ft
1.12'
18.2d
7.90'
N
N
Y
Y
Y
K5
N
Y
N
Y
K2-3
N
Y
N
N
21 1209.20
-084936.5
214242.66
433509.5
221402.58
1242 11.4
224939.86
-270654.2
225039.64
632839.3
232308.60
182459.4
17.1
8.0B
U
0.275130 11.4
8.2 24-63
U
0.3746
12.7
9.0 75--85
SU
0.08400
16.0
0.07134
16.5
U
0.158206 14.0
18.5B
12.0
12.B
95
37 1.19
5 0.02
33 1.21
5 0.19
(14)
WD
SP Wind
20:
1.4:
N
N
N
N
N
68
1.15
0.10
N
Y
N
N
N
(15)
Spect.
type
sec.
M4
Key definitions of columns
(I) System name. (2) Right ascension, declination (Equinox 2000.0). (3) Dwarf nova sub-type, U Gem, Z Cam (standstills),
SU UMa (superoutbursts), DN (undetermined subtype). (4) Orbital period in days (spectroscopic period), colon indicates
uncertain value as adapted from [I]. (5) Vrnin: minimum visual brightness in quiescence, B denotes a B magnitude
measurement (adapted from [1, 2]). (6) Maximum visual brightness peak at dwarf nova outburst (adapted from [1, 2]).
(7) Recurrence time of dwarf nova outbursts in days; the second entry is the approximate recurrence time of super outbursts
in the case of SU UMa systems (adapted from [I]). (8) Orbital inclination in degrees; second entry is the ± error estimate in
degrees (adapted from [1]). (9) Mass determination for the white dwarf in solar masses; the second entry is ± error estimate
(adapted from [3] and [1]). (10) X-ray data. If the system is a detected hard-X-ray source (0.1-4 keY) with the Einstein
Observatory (HEAO-B) imaging proportional counter (!PC) [4-7] or has an upper limit detection, then an X-ray luminosity
is given in units of 1031 ergs/s when a distance estimate is available, otherwise a count rate. If the system is a detected X -ray
source with the EXOSAT (2-20 keY) medium energy (ME) experiment [8] or is an upper limit detection, then an X-ray
luminosity is given in units of 1031 ergs/so If the system is a detected Einstein !PC source but with no distance estimate,
then a count rate is given followed by an F. If the entry is N, then the system has not been observed with either Einstein
or EXOSAT, but ROSAT data may exist. (11) Does the system undergo eclipses, yes (Y) or no (N)? (12) Does the system
exhibit quasiperiodic oscillations (QPO), yes or no? (13) Is the underlying white dwarf detected spectroscopically during
dwarf nova quiescence (Le., dominates the light in the far UV, EUV (IUE, HST, HUT, EUVE) andlor in the optical), yes
or no [9-13] and references therein? (14) Does the system exhibit direct spectroscopic evidence of wind outflow (e.g., P
Cygni line structurelshortward-shifted absorption or broad wind emission, during dwarf nova outburst), yes or no [14] and
references therein? (15) Spectral type of the cool, normally main sequence, lower mass, secondary star, if known.
Notes
aFinding charts for dwarf nova systems are given in [2]. Other references to finding charts are in [I] and [15].
bReferences to the key ground-based and space-based spectroscopic studies of dwarf novae are given in [1,2, 15, 16] and
references therein.
cCoordinates for equinox 2000.0 adapted from [1, 2]. Coordinates for 2000.0 measured off the Space Telescope Guide
Star plates are given in [2].
d Einstein !PC X-ray luminosity.
e EXOSAT ME data.
I Einstein IPC observed flux.
Informative and stimulating reviews of virtually all aspects of dwarf novae can be found in [13, 14, 17-22].
References to original spectroscopy can be found in [1, 14-18, 21].
References
1. Ritter, H. 1990, A&AS, 85, 1179
2. Downes, R.A., Webbink, R.F., & Shara, M.M. 1997, PASP, 109,345
3. Webbink. R.E. 1990, in Accretion-Powered Compact Binaries, edited by C. Mauche (Cambridge University Press,
Cambridge), p. 177
4. C6rdova, F.M., & Mason, KO. 1984, MNRAS, 206, 879
5. Eracelous, M., Halpern, J., & Patterson, J., 1991, ApJ, 370, 330
6. Eracelous, M., Halpern, J., & Patterson, J., 1991, ApJ, 382, 290
7. Patterson, J., & Raymond, J. 1985, ApJ, 292, 535
8. Mukai, K, & Shiokawa, K 1993, ApJ, 418,803
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442 /
17
CATACLYSMIC AND SYMBIOTIC VARIABLES
10. Sion, E.M. 1987, in The 2nd Conference on Faint Blue Stars, IAU Coll. No. 95, edited by A.G.D. Philip, D. Hayes, and
J. Liebert (Davis, Schenectady), p. 413
11. Smak, J. 1992, AcA, 42, 323
12. Long, K. et al. 1993, ApJ, 405, 327
13. La Dous, C. 1991, A&AS, 252, 100
14. Pattemon,J. 1984,ApJS,S4,443
15. Williams, G. 1983, ApJS, 53, 523
16. Szkody, P. 1987, ApJS, 63, 685
17. Robinson, E.L. 1980, ARA&A, 14, 119
18. C6rdova, F.M. 1995, X-Ray Binaries, edited by W.H.G. Lewin, J. van Paradijs, and E.P.J. van den Heuvel (Cambridge
Univemity Press, Cambridge)
19. Verbunt, F. 1986, in The Physics ofAccretion onto Compact Objects, edited by M.G. Watson and N.E. White (SpringerVerlag, Berlin), p. 59
20. Wade, R. 1985,Interacting Binaries, edited by P.P. Eggleton and J.E. Pringle (Reidel, Dordrecht)
21. Warner, B. 1995, Cataclysmic Variable Stars (Cambridge Univemity Press, Cambridge)
22. Szkody, P. 1985, in Cataclysmic and Low Mass X-Ray Binaries, edited by D.Q. Lamb and J. Pattemon (Reidel, Dordrecht),
p.385
Table 17.9. Selected listofnova-1Uces.
Name
(alt. names)
IT Ari
(BD+14°341)
RWTri
Coord.a
(2000)
Galactic Vrnax b
coord.
B-V
Vrnin
E(B - V)C
020653.09
+151743.0
02 25 36.14
+28 05 51.4
081518.90
-4913 18.3
10 1956.63
-084156.0
110542.80
-683758.0
147.69
-44.05
146.34
-30.59
264.80
-8.09
251.32
38.28
293.35
-7.79
9.5
16.3
12.6
15.6
9.1
10.0
10.4
10.8
11.1
11.5
-0.04 [I]
0.02 [I]
0.10 [2]
133640.97
+515450.3
MVLyr
190716.30
(MacRAE+43° 1) +440108.4
V3885 Sgr
194740.54
(CD-42°14462) -420025.5
107.67
63.91
74.61
16.08
357.32
-27.14
12.7
14.1
12.1
18.0
9.6
10.3
0.07 [I]
0.0 [2]
-0.13 [I]
-0.35 [I]
0.0 [I]
0.0 [2]
V794Aql
39.38
-20.22
19.84
-71.14
13.7
20.2
12.9
18.5
IX Vel
(CPD-48°1577)
RWSex
(BD-7°3007)
QUCar
(HOE 310376)
(CD-67° 1010)
UXUMa
VYScl
(pS 141)
(SPC Var4)
201733.97
-033951.0
232900.45
-294646.0
Second.
spectral
classd
0.0 [2]
0.15 [I]
0.25 [9]
0.1 [2]
-0.03 [13] 0.03 [13]
K5V
[10]
Period'
(d)
0.137551 [3.4]
0.1329 [5. 6]
0.231 883 297
[11, 12]
0.193929
[14, 15]
0.245 07 [25]
Rapid
oscillation
period (s)
Spec.!
Refs.
1000-1600 [3,8]
QPO [7]
[11]
'JYpe
VY
UX
[16-22]
[14,23] UX
620.1280
QPO [26]
[24.25] UX
28-30
QPO[32]
2800
QPO [36]
29-30
[38,41]
[33,34] UX
0.32 [19] 0.0 [2]
0.19667126
[30,31]
0.1336 [35]
0.1379 [36]
0.206-0.259
[38.39]
0.2163 [40]
0.237 [20]
-0.10 [16] 0.06 [16]
0.1662 [17]
-500
QPO [18]
-0.04 [24] 0.0 [2]
0.0 [2]
0.454 [27]
0.113471 [28]
K8VM6V[29]
M5V
[35]
[27]
[35.37] VY
[39]
UX
[21,42] VY
[17,19] VY
Notes
a Adapted from [43].
bThe range in magnitudes is taken from [44].
cThe color excess, E(B - V), is assumed to be related to the visual intemtellar extinction, Av. by Av = 3.2 E(B - V).
dThe secondary spectral types are from spectroscopic or photometric observations and do not include estimates from mass
determinations.
eThe spectroscopic period is the fimt entry while the photometric period is the second if it is different. Orbital parameters
can usually be found in the reference for the spectroscopic period.
f Only optical references are given. Surveys or catalogues of nova-likes exist in the infrared [45], visual [1, 46, 47],
ultraviolet [2, 48, 49], far ultraviolet [50], and X-ray [51, 52] spectral regions. References of observations for individual
nova-likes can be found in [43, 53, 54] and finding charts in [43, 46].
17.1 TYPES OF CATACLYSMIC VARIABLES / 443
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1.
2.
3.
4.
5.
6.
7.
444 I
17
CATACLYSMIC AND SYMBIOTIC VARIABLES
1Bble 17.10. Synchronously rotating magnetic CVs (AM Her binaries).a
Mag. fieldc •e
Name
(alt. name)
BLHyi
(H0139-68)
WWHor
(EXOO234.5-5232)
EFEri
(2A0311-227)
VYFor
(EXOO32957-2606.9)
UZFor
(EXOO33319-2554.2)
BY Cam
(H0538+608)
VVPup
EKUMa
(lEI048+524l)
ANUMa
STLMi
(CWI103+254)
DPLeo
(lE1114+ 182)
EUUMaf
(REI 149+28)
V834Cen
(lEI405-45l)
MRSer
(PGI550+191)
AMHer8
(3Ul809+50)
EPDra
(HI907+690)
QSTel
(RE 1938-461)
QQVul
(lE2003+225)
V1500Cyg
(Nova Cyg 1975)
CEGru
(Grus VI)
Coord. b
(2000)
14100.25
-675327.7
23611.45
-521913.5
31413.03
-223541.4
33104.58
-255655.5
33528.61
-254422.6
54248.90
60 5131.8
81506.73
-190316.8
105135.23
540436.0
110425.71
450315.0
11 05 39.75
250628.9
11 17 16.00
17 57 41.1
11 4955.70
284507.5
140907.46
-451717.1
155247.23
185627.6
18 16 13.33
495204.2
1907 06.13
690842.4
193835.73
-461256.5
200541.93
223959.1
21 11 36.61
480901.9
21 3756.38
-434213.1
Dist.c
(PC)
pd
om
(min)
mv c .d
128
113.6
14-18.5
500
114.6
19-21
> 89
81.0
13.5-17.5B
228
17.5
250
126.5
18-20.5
200
201.9
14.5->17B
145
100.4
14.5-18
114.5
18-20
> 270
114.8
14.5-19B
128
113.9
15.~17
>380
89.8
17.5-19.5B
16.5B
86
90:
103:
101.5
112
113.6
15-17
75
185.6
12-15.5
600:
104.6
18
140.0
15.5
>400
222.5
14.5-15.5
10001400
201.0
197.5i
108.6
17-18
199.3h
14.~17
18-218
Polarization
BI> B2
Bd
Lsx
Cire.
(MG)
(MG)
(ergs s-l)
(%)
(%)
Refs.
30
I x loJ l
17
12
[1.2]
4 x loJ 3
30
> I x loJ 2
20
33
P
25:
P
Z
15
Z
Lin.
[3]
9
[6]
1~50:
P
53.75:
C
41:
C
31.5.56
C
47:
C
36
C
7 x loJ 3
6
3
5 x loJ 2
30.5.59
C.Z
15
[7.8]
[9-12]
10
18
Z
[4.5]
15
[13-15]
20
[16. 17]
>3xlO32
35
[18-20]
2 x loJ2
20
12
[21-24]
> I x loJ3
35
9
[25.26]
[27]
23
Z.C
24
C
14.28
C
1~50:
P
25-50:
P
20:.20:
P
10
Z
22
Z
1 x 1032
30
10
[28-31]
5 x loJ°
12
5
[32.33]
9 x 1032
10
8
[34-37]
[38]
10
> 4 x 1034
6
10
[39]
8
2
[40]
10
[41]
15
[42.43]
Notes
aThese binaries contain accreting white dwarfs that are strongly magnetized and rotate essentially synchronously, i.e.,
rotation period within 2% of the orbital period Porb [44, 45]. They are more commonly known as AM Herculis binaries, or
polars, and are characterized by the strong optically polarized radiation they emit.
mv: Visual magnitude. B indicates blue magnitude. Nova outburst magnitude not given.
BI, B2 are the dominant and less dominant accretion poles, respectively.
Bd is the polar field if a dipole structure is assumed to model the Zeeman features.
Z: Zeeman features.
c: Cyclotron features.
P: Magnetic field estimated from polarization.
Lsx: Soft X-ray luminosity (see [46, 47] for uncertainties in the estimates).
b Adapted from [44].
C Adapted from [45].
d Adapted from [48].
e Adapted from [49].
f Shows strong He II >..4686 line and strong EUV emission, characteristics of AM Her binaries.
gRadio source.
hRotation period.
• White dwarf presumed to have become asynchronous following nova outburst and is now synchronizing.
17.1 TYPES OF CATACLYSMIC VARIABLES / 445
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Table 17.11. Asynchronously rotating magnetic CVs (DQ Her binaries).a
Name
(alt. name)
XY Arif
(1 H0253+ 193)
Coord. b
(2000)
25608.1
192634.
Dist. c
Prot
Porb
(pc)
(min)
(h)
200
3.42
6.06
Lhx c •e
mud
12-13.5K
(erg s-l)
2 x 1032
Refs.
[1.2]
446 /
17
CATACLYSMIC AND SYMBIOTIC VARIABLES
Table 17.11. (Continued.)
Name
(alt. name)
Coord. b
GKPer8
(Nova Per 1901)
V471 Tau
33111.82
435416.8
35024.79
171447.8
52925.44
-324904.5
53450.67
-580140.9
54320.22
-410155.2
73128.98
95622.6
TV Col
(2A0526-328)
TWPic
(H0534-581)
TXCoI
(1H0542-407)
BGCMih
(3A0729+ 103)
PQGemi
(RE0751+14)
EXHya
V795Herf
(PO 1711+336)
DQHer
(Nova Her 1934)
V533Herf
(Nova Her 1963)
V1223 Sgr
AEAqr8
FOAqr
(82215-086)
AOPsc
(H2252-035)
(2000)
75117.39
144424.6
125224.40
-291456.7
171256.09
333121.4
180730.17
455131.9
181420.34
415121.3
185502.24
-310948.5
204009.02
-05215.5
22 1755.43
-82104.6
225517.97
-31040.4
Dist. c
(PC)
Prot
(min)
(h)
mv d
Lhxc,e
(erg s-l)
Refs.
525
5.86
47.9
10-14.0
7.4 x 1032
[3-5]
49
9.24
12.51
9-10
>500
31.9
5.49
13.5-14
650:
126:
6.5:
14-16
>500
31.9:
5.72
15.5
700-1000
14.1:
15.2:
28.2:
13.9:
3.24
14-14.5
-6:
14.5
76-90
67.0
1.64
10-14
2.60
12.5-13B
300-500
93.8:
106.4:
1.18
4.65
14-17.5
< (1.1-3.0) x 1030
1000:
1.06
5.04
14.5-16
< 2 x 103 1
540-660
12.4
3.37
12-> 17
28-78
0.55:
9.88
10-11.5
200-640
20.9
4.85
13-14
100-750
13.4
3.59
13.5-15
Porn
[6-8]
> 6.1 x 1032
[9.10]
[11]
> 2.8 x 1032
[12. 13]
(0.7-1.4) x 1033
[14-19]
[20.21]
(0.3-1.8) x 1032
[22.23]
[24.25]
[26-28]
[26.27.29]
(0.9-1.3) x 1033
[30-33]
< (0.5-3.6) x 1030
[34-37]
(0.8-8.3) x 1032
[38-41]
(0.02-1.3) x 1033
[33,42-44]
Notes
aThese binaries are believed to contain accreting magnetized white dwarfs that rotate asynchronously with the rotation
period Prot differing by more than 2% from the orbital period Porb. They do not in general emit optically polarized radiation
and probably have magnetic fields strengths that are weaker than those found in the synchronously rotating magnetic CVs.
They are more commonly. but inconsistently, referred to as DQ Herculis binaries and/or intermediate polars. For example,
some authors refer to only those binaries with Prot « 0.1 Porb as DQ Hers and the others as intermediate polars. Prot is
often difficult to identify so that some of the binaries in the table should not actually belong to it. mv: Visual magnitude.
B. K indicate blue. K band magnitudes. Nova outburst magnitude not given. Lhx: Hard-X-ray luminosity. The main
uncertainty is due to that in the distance.
b Adapted from [45].
c Adapted from [46. 47].
d Adapted from [48].
e Adapted from [47.49].
fIdentification as a magnetic CV uncertain. XY Ari lies behind Lynds dark cloud L 1457 and is not visible optically.
gRadio source.
~ Shows weak but significant opticallIR circular polarization implying a magnetic field of roughly 4 MG.
• Shows significant opticallIR linear and circular polarization implying a magnetic field of 8-18 MG.
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