HANDBOOK OF SPACE ASTRONOMY AND ASTROPHYSICS

HANDBOOK OF SPACE ASTRONOMY AND ASTROPHYSICS

Third Edition

Fully updated and including data from space-based observations, this Third Edition is a comprehensive compilation of the facts and figures relevant to astronomy and astrophysics. As well as a vast number of tables, graphs, diagrams, and formulae, it also includes a comprehensive index and bibliography, allowing readers to easily find the information they require. The book covers a diverse range of topics in addition to astronomy and astrophysics, including atomic physics, nuclear physics, relativity, plasma physics, electromagnetism, mathematics, probability and statis- tics, and geophysics.

This handbook contains the most frequently used information in modern as- trophysics, and is an essential reference for graduate students, researchers and professionals working in astronomy and the space sciences. A website containing extensive supplementary information and databases, maintained by the author, can be found at www.cambridge.org/9780521782425.

M A R T I N ZOMBECK was a senior scientist at the High Energy Astrophysics

Division of the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts. He is co-editor of High Resolution X-ray Spectroscopy of Cosmic Plasmas (Cambridge University Press, 1990).

HANDBOOK OF SPACE ASTRONOMY AND ASTROPHYSICS

Third Edition

MARTIN V. ZOMBECK

Smithsonian Astrophysical Observatory, Cambridge, USA

CAMBRIDGE

UNIVERSITY PRESS

Cambridge University Press

The Edinburgh Building, Cambridge CB2 8RU, UK

First published in print format

ISBN-13 978-0-521-78242-5 ISBN-13 978-0-511-34872-3

© Cambridge University Press 2007

2006

Information on this title: www.cambridge.org/9780521782425

This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

Published in the United States of America by Cambridge University Press, New York www.cambridge.org

eBook (EBL) hardback

Contents

Some weeks later the Einsteins were taken to the Mt. Wilson Observatory in California. Mrs. Einstein was particularly impressed by the giant telescope.

'What on Earth do they use it for?, she asked. Her host explained that one of its chief purposes was to find out the shape of the Universe. "Oh", said Mrs. Einstein, "my husband does that on the back of an envelope. - Bennett Cerf in "Try and Stop Me".

Foreword Preface

1 General data 1 2 Astronomy and astrophysics 35 3 Radio astronomy 185 4 Infrared and submillimeter astronomy 211 5 Ultraviolet astronomy 233 6 X-ray astronomy 253 7 Gamma-ray astronomy 293 8 Cosmic rays 309 9 Earth's atmosphere and environment 323 10 Relativity and cosmology 347 11 Atomic physics 367 12 Electromagnetic radiation 385 13 Plasma physics 405 14 Experimental astronomy and astrophysics 413 15 Astronautics 535 16 Mathematics 551 17 Probability and statistics 579 18 Radiation safety 597 19 Astronomical catalogs 611 20 Computer science 623 21 Glossary of abbreviations and symbols 651 Appendices 659 Index 753

Foreword

Modern astrophysics requires the use of observations over the broadest range of wavelengths to fully understand the physical nature of the objects and processes we wish to study in the universe.

Data are obtained from ground-based and space-based observations operating in radio, infrared, visible, ultraviolet, x-rays and gamma rays. The design and operation of the instrumentation used to gather this information, the telescopes and detectors themselves, depend on the interaction between matter and radioactivity at the different wavelengths and requires in-depth knowledge of the findings of molecular, atomic, nuclear, and particle physics.

The observer needs to have the data at hand to understand the properties and the limitations of the instrumentation and their relevance to data reduction, analysis, and interpretation.

The theorist who is seeking new models to interpret the findings from the most sensitive and sophisticated observatories that ever existed needs, from time to time, a reality check with what is known.

The Handbook of Space Astronomy and Astrophysics gathers in one place the most frequently-used information in modern astrophysics and presents it in the most useful fashion to the non-specialist in a particular field.

I always loved the chapter on relativistic astrophysics and I am glad it has been retained and improved. I am also glad for the new chapters on experimental subjects that bring the Handbook up-to-date.

I am certain that some young person will find here, as I did, useful food for thought and inspiration that he or she will need to design the next generation of telescopes.

Washington, DC Riccardo Giacconi May, 2005 Nobel laureate, 2002

Physics

Preface

I have compiled the tables, graphs, diagrams, and formulae in this book in order to provide a ready reference and working tool for the practicing space astronomer and astrophysicist. Ground-based astronomers, students, and advanced amateur astronomers will find much here of interest, too. The material represents a diversified selection based upon the circumstance that the space astronomer and astrophysicist must draw upon knowledge of atomic physics, nuclear physics, relativity, plasma physics, electromagnetism, mathematics, probability and statistics, geophysics, experimental physics, et cetera, in addition to the classical branches of astronomy. My hope is that this book will replace hunting through many separate works or a trip to the reference library or to the World Wide Web. In that spirit, I welcome suggestions of material for inclusion in a later edition and, of course, corrections or criticism.

There are 21 chapters in the book. The first chapter contains physical, astronomical, and numerical constants, and unit conversions. Chapters 2-8 cover general astronomy and astrophysics, radio, infrared, ultraviolet, X-ray, and gamma-ray astronomy, and cosmic rays. Chapter 9 contains information on the Earth's atmosphere and environment relevant to space science. Chapter 10 covers special and general relativity and chapter 11 provides relevant information in atomic physics. Electromagnetic radiation and plasma physics are the subjects of chapters 12 and 13. The remaining chapters deal with the tools of the trade, viz., information on radiation and particle interactions, detectors, astronautics, useful mathematical relations, probability and statistics formulae, laboratory radiation safety, a comprehensive list of astronomical catalogs, and computer science. Each chapter ends with a bibliography for further reading on the subject of the chapter and for more extensive reference material. The last chapter contains a glossary of abbreviations and symbols. 11 Appendices contain material that is of a tutorial nature, not suitable for inclusion in the main text, and material suggested recently by reviewers. The book has a complete index.

The question of units is always a problem in a book of this type;

sticking to one consistent set (SI, for example) is not very useful to the practitioner; distance to a galaxy in meters, the energy of an X-ray

most scientists frustrated. I have tried to use the unit systems common to the particular field. Thus I have used SI (International System of Units), c.g.s., and Gaussian (e.s.u. c.g.s. units); whatever is customary.

What is being used is usually noted and whenever the units are not noted, any consistent system will do. If in doubt, perform a numerical check. Besides a complete set of fundamental constants in SI units, I have also provided a subset in c.g.s. units, which are commonly used in the formulae in this book, and unit conversion tables.

I have established and will maintain a Web site at http://www.astrohandbook.com, where I will provide links to supplementary information for each chapter and a list of errata, if any. The links will provide extensive data bases, complete online texts and scientific journal articles, tutorials, online interactive programs for converting units, calculating astronomical coordinates, plotting X-ray absorption and reflectivity, symbolic mathematics, and much more. I have avoided, with a few exceptions, listing the URLs (uniform resource locator) of online source material since locations and file names often change.

I wish to acknowledge colleagues for their useful suggestions and encouragement, especially Gerald Austin, Daniel Fabricant, George Field, who suggested that I first publish the handbook as a Smithsonian Astrophysical Observatory Special Report, Jonathan Grindlay, Paul Gorenstein, F. Rick Harnden, Almus Renter, Ralph Kraft, Jeffrey McClintock, Gary Meehan, Stephen Murray, who first suggested that I publish my set of notes in handbook form, and Daniel Schwartz of the Harvard-Smithsonian Center for Astrophysics, Joachim Truemper of the Max-Planck-Institut fiir Extraterrestrische Physik (MPE), and Rashid Sunyaev of the Max-Plank-Institut fiir Astrophysik.

The typesetting in Latex was initially done by Instill Technologies, BE 277 Salt Lake, Kolkata 700064, India. The partners for this company, Sutanu Ghosh and Pijush K. Maiti did a superior job in typesetting the extensive tables and complex formulae of the handbook. The majority of the typesetting and the completion of the project was accomplished by Gautami Maiti and Pijush K. Maiti of Anin, BC 97 Salt Lake, Kolkata 700064, India. I thank Himel Ghosh, formerly of the Harvard- Smithsonian Center for Astrophysics, for suggesting that I work with Drs. Ghosh and Maiti. The fact that they are physicists helped matters considerably.

My son, Richard, provided substantial technical assistance in the last minute preparations of the book for submission to the publisher.

Now that the book is in electronic format, updated versions will be more easily prepared. A searchable, online version of the book is in the works.

Many of the quotations are from "Physically Speaking, a Dictionary of

Quotations on Physics and Astronomy", Carl C. Gaither and Alma E.

Cavazos-Gaither, Institute of Physics Publishing, 1997.

Please cite the original source, if you are referencing any of the material in the Handbook in research publications.

I have made every effort to cite the sources for the material presented in this book and to obtain permissions, wherever necessary. If I have omitted a citation, please bring it to my attention.

Naples, Florida Martin V. Zombeck March, 2006 mvz@alum.mit.edu

Chapter 1

General data

Facts themselves are meaningless. It's only the interpretation we give those facts which counts. - Earl Stanley Gardner

International system of units (SI) 2 Fundamental physical constants (SI) 3 Fundamental physical constants (c.g.s.) 14 Sun-Earth system constants 15 Cosmological data 16 Unit conversions 17 Conversion tables 18 Energy unit conversion 23 Conversion factors for natural units 23 Flux density conversion 24 Numerical constants 25 Mathematical formulae 26 Elementary particles (short list) 27 Elementary particles 28 Energy conversions 29 Prefixes and symbols 30 Periodic table of the elements 31 Greek alphabet 33 Bibliography 33

International system of units (SI)

Physical quantity Name of unit

Base units length

mass

timeelectric current

thermodynamic temperature amount of substance

luminous intensity

meter kilogram second ampere kelvin molecandela Derived units with special names plane angle

solid angle frequency energy force pressure power

electric charge electric potential electric resistance electric conductance electric capacitance magnetic flux inductance

magnetic flux density luminous flux

illuminance

Celsius temperature

activity (of a radioactive source) absorbed dose (of ionizing radiation) dose equivalent

radian steradian hertz joule

newton pascal wattcoulomb volt ohm Siemens farad weber henry tesla lumen lux

degree Celsius becquerel gray sievert

Symbol

m kg s A K mol

cd

rad sr Hz

J N Pa W C V

n s

F Wb

H T lm

lx

°C Bq GySv

Fundamental physical constants (SI) (1986 recommended values of the fundamental physical constants. The digits in parentheses are the one-standard-deviation uncertainty in the last digits of the given value. For the latest recommended values see: http://physics.nist.gov/constants.) QuantitySymbolValueUnitsRelative uncertainty (ppm)

a, B GENERAL CONSTANTS UNIVERSAL CONSTANTS speed of light in vacuum permeability of vacuum permittivity of vacuum Newtonian constant of gravitation Planck constant in electron volts, h/{e} h/2ir in electron volts, h/{e} Planck mass, (hc/G)z Planck length, h/mPc = (fi.G/c3 )i Planck time, lP/c = (hG/c5 )^

c Mo eo G h h nip h tP

299 792458 4TT x 10"7 = 12.566 370 614... 1/MoC2 = 8.854187817... 6.672 59(85) 6.626 075 5(40) 4.135 6692(12) 1.054572 66(63) 6.582122 0(20) 2.176 71(14) 1.61605(10) 5.390 56(34) ms i NA"2 10-7 NA-2 10"i2 Fm-i 10"n m3 kg"1 s"2 lO-34 jg 10-15 eVs lO-34 Js 10"i6 eVs 10-8 kg 10"35 m lO-44 s

(exact) (exact) (exact) 128 0.60 0.30 0.60 0.30 64 64 64 cons ^{B CO "t/}

Fundamental physical constants (SI) (cont) Quantity ELECTROMAGNETIC CONSTANTS elementary charge magnetic flux quantum, h/2e Josephson frequency-voltage ratio quantized Hall conductance quantized Hall resistance, h/e2 = \\iocja Bohr magneton, eh/2me in electron volts, /xs/je} in hertz, ns/h in wavenumbers, fis/hc in kelvins, fis/k nuclear magneton, eh/2mp in electron volts, /xjv/{e} in hertz, HN /h in wavenumbers, /IN/he in kelvins, fi^/k

Symbol e e/h 2e/h e2 /h RH IJ-N

Value 1.60217733(49) 2.417988 36(72) 2.06783461(61) 4.835 976 7(14) 3.87404614(17) 25812.8056(12) 9.2740154(31) 5.788 382 63(52) 1.399 62418(42) 46.686437(14) 0.671709 9(57) 5.050 786 6(17) 3.15245166(28) 7.622 5914(23) 2.542 622 81(77) 3.658 246(31) Units 10"19 C 1014 AJ"1 10"15 Wb 1014 HzV-1 10-5 s

n

10-24 JT-1 10"5 eVT"1 1010 HzT-1 KT-1 10-27 JT-1 10"8 eVT"1 MHzT"1 lO"2 m^T"1 10-4 KT-1

Relative uncertainty (ppm) 0.30 0.30 0.30 0.30 0.045 0.045 0.34 0.089 0.30 0.30 8.5 0.34 0.089 0.30 0.30 8.5

Fundamental physical constants (SI) (cont) Quantity ATOMIC CONSTANTS ATOM fine structure constant, |/ioce2 //i inverse fine-structure constant Rydberg constant, \meca2 /h in hertz, Ro^c in joules, Roohc in electron volts, R^hc/{e} Bohr radius, a/47ri?O0 Hartree energy, e2 /47reofto = 'ZRoohc in electron volts, Eh/{e} quantum of circulation ELECTRON electron mass in electron volts, mec2 1 \e\

Symbol a a-1 ROD a0 Eh h/2me h/me me

Value 7.297353 08(33) 137.0359895(61) 10 973 731.534(13) 3.289 8419499(39) 2.1798741(13) 13.605 6981(40) 0.529177 249(24) 4.359 748 2(26) 27.2113961(81) 3.636 948 07(33) 7.273 89614(65) 9.109 389 7(54) 5.485 799 03(13) 0.510 999 06(15) Units 10"3 m-i 10" Hz io-i8 J eV 10~ m lu J eV 10-4 m2 s-i 10"4 m2 s-i 10-3 i kg 10-4 u MeV Relative uncertainty (ppm) 0.045 0.045 0.0012 0.0012 0.60 0.30 0.045 0.60 0.30 0.089 0.089 0.59 0.023 0.30

dai B- o' B tanCO ^CO

(is:

₅

Fundamental physical constants (SI) (cont) QuantitySymbolValueUnitsRelative uncertainty (ppm) electron-muon mass ratio electron-proton mass ratio electron-deuteron mass ratio electron-a-particle mass ratio electron specific charge electron molar mass Compton wavelength, h/mec Xc/2n = acio = a2 /inR^ classical electron radius, a2 a0 Thomson cross-section, (87r/3)r2 electron magnetic moment in Bohr magnetons in nuclear magnetons electron magnetic moment anomaly, fJ-e/flB ~ 1 electron g-factor, 2(1 + ae) electron-muon magnetic moment ratio electron-proton magnetic moment ratio

mg/m^ me/mp me/md me/ma —e/me M(e),Me Ac Ac re 0"e fie fi-e/fi-B fle/flN ae 9e Ve/Vv fie/ftp

4.836 33218(71) 5.44617013(11) 2.72443707(6) 1.370 933 54(3) -1.75881962(53) 5.485 799 03(13) 2.426 310 58(22) 3.861593 23(35) 2.817940 92(38) 0.665 24616(18) 928.47701(31) 1.001159 652193(10) 1838.282000(37) 1.159 652193(10) 2.002 319 304386(20) 206.766967(30) 658.2106881(66) lO-3 10"4 10"4 10~4 10n Ckg-1 10~7 kgmor1 10-12 m lO-" m IO-15 m lO-28 m

2 10-26 JT-1 lO-3

0.15 0.020 0.020 0.021 0.30 0.023 0.089 0.089 0.13 0.27 0.34 1 x 10"5 0.020 0.0086 1 x 10~5 0.15 0.010

Fundamental physical constants (SI) (cont) QuantitySymbolValue 1.883 5327(11) 0.113428913(17) 105.658389(34) 206.768 262(30) 1.13428913(17) 4.4904514(15) 4.841970 97(71) 8.890 5981(13) 1.165 923 0(84) 2.002 331846(17) 3.183 345 47(47) 1.672 6231(10) 1.007276470(12) 938.27231(28) 1836.152 701(37) Units 10"28 kg u MeV 10-4 kgmol-1 lO-26 JT-1 10"3

io-

3 lo-27 kg u MeV Relative uncertainty (ppm) 0.61 0.15 0.32 0.15 0.15 0.33 0.15 0.15 7.2 0.0084 0.15 0.59 0.012 0.30 0.020 dai. ^{to- co o"} 8 COB nts

MUON muon mass in electron volts, niyC2 /{e} muon-electron mass ratio muon molar mass muon magnetic moment in Bohr magnetons in nuclear magnetons muon magnetic moment anomaly, muon g-factor, 2(1 + aM) muon-proton magnetic moment ratio PROTON proton mass in electron volts, mpc2 /{e} proton-electron mass ratio

m,, mv mp/me

Fundamental physical constants (SI) (cont) QuantitySymbolValueUnitsRelative uncertainty (ppm) proton-muon mass ratio proton specific charge proton molar mass proton Compton wavelength, h/mpc Ac,p/27r proton magnetic moment in Bohr magnetons in nuclear magnetons diamagnetic shielding correction for protons in pure water, spherical sample, 25°C, 1 — fJ,'p/nP shielded proton moment (H2O, sph., 25°C) in Bohr magnetons in nuclear magnetons proton gyromagnetic ratio uncorrected (H2O, sph., 25°C)

TOp/mM e/mp M(p),Mp XG,p *C,p Pp flp/flB ,pl,N O"H2O P-'p Hp/HB fl'p/flN lp 7P/2TT

i

P

i

P

l^

8.880 2444(13) 9.578 830 9(29) 1.007276470(12) 1.32141002(12) 2.103 089 37(19) 1.41060761(47) 1.521032 202(15) 2.792 847386(63) 25.689(15) 1.410 57138(47) 1.520 993129(17) 2.792 775 642(64) 26 752.2128(81) 42.577469(13) 26 751.5255(81) 42.576 375(13) 107 Ckg-1 10"3 kgmol"1 10"15 m 10^16 m 10~26 JT"1 10"3

io-

6 10_26 JT-i 10"3

io

4

s^r

1 MHzT"1 IO4 s-1 ']?-1 MHzT"1

0.15 0.30 0.012 0.089 0.089 0.34 0.010 0.023 - 0.34 0.011 0.023 0.30 0.30 0.30 0.30

Fundamental physical constants (SI) (cont) Quantity NEUTRON neutron mass in electron volts, mnc2 /{e} neutron-electron mass ratio neutron-proton mass ratio neutron molar mass neutron Compton wavelength, h/mnc Ac,r1/27T neutron magnetic moment'"' in Bohr magnetons in nuclear magnetons neutron-electron magnetic moment ratio neutron-proton magnetic moment ratio DEUTERON deuteron mass in electron volts, mdc2 /{e} deuteron-electron mass ratio Symbol mn mn/me mn/mp M{n),Mn Ac>

A~ o

fin fln/flB fln/flN fln/fle fin 1 flp md md/me

Value 1.674928 6(10) 1.008 664904(14) 939.56563(28) 1838.683662(40) 1.001378 404(9) 1.008 664904(14) 1.31959110(12) 2.10019445(19) 0.966 23707(40) 1.041875 63(25) 1.913 042 75(45) 1.040 668 82(25) 0.684979 34(16) 3.343 586 0(20) 2.013 553 214(24) 1875.61339(57) 3670.483014(75) Units 10"27 kg u MeV 10"3 kgrnol"1 10~15 m 10-16 m 10_26 JT-i

io-

3 10~3 10"27 kg u MeV Relative uncertainty (ppm) 0.59 0.014 0.30 0.022 0.009 0.014 0.089 0.089 0.41 0.24 0.24 0.24 0.24 0.59 0.012 0.30 0.020 dai. ^{to- co}

n

^CO] CO B CO -—. (IS.

Fundamental physical constants (SI) (cont) QuantitySymbolValueUnitsRelative uncertainty (ppm) deuteron-proton mass ratio deuteron molar mass deuteron magnetic moment^ in Bohr magnetons in nuclear magnetons deuteron-electron magnetic moment ratio deuteron-proton magnetic moment ratio PHYSICO-CHEMICAL CONSTANTS Avogadro constant atomic mass constant, mu = j^-m(12 C) in electron volts, muc2 /{e} Faraday constant molar Planck constant molar gas constant ^ 'The scalar magnitude of the deuteron moment is corresponds to the dipole associated with a spinning

md/mp M(d),Md fid fld/flB fJ-d/fJ-N fid/fie fid/fip NA,L mu F NAh NAhc R 1.999 007496(6) 2.013 553 214(24) 0.433 073 75(15) 0.466 975 4479(91) 0.857438 230(24) 0.466434 5460(91) 0.3070122035(51) 6.022136 7(36) 1.660 540 2(10) 931.49432(28) 96485.309(29) 3.990 313 23(36) 0.119626 58(11) 8.314510(70) 10~3 kgmol"1 10_26 JT-i 10~3 io-3 1023 mor1 io-27 kg MeV Cmol"1 10~10 Jsmol"1 Jmrnol"1 Jmol"^"1

0.003 0.012 0.34 0.019 0.028 0.019 0.017 0.59 0.59 0.30 0.30 0.089 0.089 8.4 listed here. The neutron magnetic dipole is directed oppositely to that of the proton, and negative charge distribution. The vector sum, fj,d = fip + fJ-n, is approximately satisfied.

Fundamental physical constants (SI) (cont) QuantitySymbolValueUnitsRelative uncertainty (ppm)

a, ts Boltzmann constant in electron volts, k/{e} in hertz, k/h in wavenumbers, k/hc molar volume (ideal gas), RT/p T = 273.15 K, p = 101 325 Pa Loschmidt constant, A^/Fm T = 273.15 K, p = 100 kPa Sackur-Tetrode constant (absolute entropy constant)/6 ) § + ln{(27rmufcTi//i2 )tA;Ti/j5o} Ti = 1 K, p0 = 100 kPa po = 101 325 Pa Stefan-Boltzmann constant, (ir2 /60)k4 /h3 c2 first radiation constant, 2nhc2 second radiation constant, hc/k Wien displacement law constant, b = AmaxT = c2/4.965 114 23 ... *• ' The entropy of an ideal monoatomic gas of relative atomic weight Ar S = So + |i?lnAr - R\n(p/P0)

n0 So/R 02

1.380 658(12) 8.617385(73) 2.083 674(18) 69.503 87(59) 22.41410(19) 2.686 763(23) 22.71108(19) -1.151693(21) -1.164856(21) 5.67051(19) 3.7417749(22) 0.01438769(12) 2.897 756(24) r is given by

10"23 JK-i 10-5 eVK-i lO" HzK"1 m^K-1 Lmol-i 1025 m-3 Lmol-i 10-8 Wm-2 K-Z IO-1

6 Wm

2 mK

8.5 8.4 8.4 8.4 8.4 8.5 8.4 18 18 1 34 0.60 8.4 10-3 mK8.4

8

a CO

Fundamental physical constants (SI) (cont) MAINTAINED UNITS AND STANDARD VALUES A summary of 'maintained' units and 'standard' values and their relationship to SI units, based on a least-squares adjustment with 17 degrees of freedom. The digits in parentheses are the one-standard-deviation uncertainty in the last digits of the given value. Quantity electron volt, (e/C) J = {e} J (unified) atomic mass unit, 1 u = mu = Y2m(12 C) standard atmosphere standard acceleration of gravity 'AS-MAINTAINED' ELECTRICAL UNITS BIPM(a ) maintained ohm, f^g-ei HBI85 = ^69-BI (1 Ja 1985) drift rate of 069-BI BIPM maintained volt, U76_BI = 483 594 GHz(/i/2e) Symbol eV u atm 9n ^BI85 dfle9-Bl dt V76-BI Value 1.60217733(49) 1.660 540 2(10) 101325 9.806 65 1 - 1.563(50) x 10~6 = 0.999 998 437(50) 0.0566(15) 1 - 7.59(30) x 10"6 = 0.999 992 41(30) Units 10-19 J 10~27 kg Pa ms

n n

V V

Relative uncertainty (ppm) 0.30 0.59 (exact) (exact) 0.050 0.30

Fundamental physical constants (SI) (cont) QuantitySymbolValueUnitsRelative uncertainty (ppm)

a, fcs BIPM maintained ampere, X-RAY STANDARDS Cu x-unit: A(CuKai) = 1537.400 xu Mo x-unit: A(MoKai) = 707.831 xu A*:A(WKai) = 0.209 100 A* lattice spacing of Si (in vacuum, 22.5°C)<6 ) (feo = a/y/8 molar volume of Si, M(Si)/p(Si) = NAa3 /8

1-6.03(30) x 10-6 = 0.999 993 97(30) xu(CuKai) 1.00207789(70) xu(MoKai) 1.002 099 38(45) A* 1.00001481(92) ft 0.54310196(11) d22o 0.192 015 540(40) Vm(Si) 12.0588179(89) A A 10-13 m 10-13 m lo-io m nm nm cm3

0.30 0.70 0.45 0.92 0.21 0.21 0.74

8

B CO : Bureau International des Poids et Mesures. ^ -^The lattice spacing of single-crystal Si can vary by parts in 10 depending on the preparation process. Measurements at Physikalisch-Technische Bundesanstalt (FRG) indicate also the possibility of distortions from exact cubic symmetry of the order of 0.2 ppm. (Reprinted with permission from CODATA Bulletin, Number 63, Cohen, E. Richard & Taylor, Barry N., The 1986 Adjustment of the Fundamental Physical Constants, Copyright 1987, Pergamon Press, Ltd.)

A short list of fundamental physical constants (c.g.s.) Speed of light in vacuum

Gravitational constant Planck's constant Electron charge Mass of electron Mass of proton Mass of neutron Atomic mass unit (amu) Proton-electron mass ratio Fine structure constant Classical electron radius Bohr radius

Electron Compton wavelength Rydberg constant Boltzmann constant Stcfan-Boltzmann constant

Thomson cross-section Bohr magneton Permeability of vacuum Permittivity of vacuum Magnetic flux quantum h/2e Quantized Hall conductance e2/h Avogadro constant

Faraday constant JV^e Molar gas constant Electron volt

(unified) atomic mass unit

c = 2.997924 58 x 1010 cms"1

G = 6.672 59 x 10"8 dyn cm2 g"2

h = 6.626 075 5 x 1(T27 ergs e = 4.803 2068 x 10"10 esu me =9.109 389 7 x 10~28 g mp = 1.672 6231 x 10"24 g mn = 1.674 928 6 x 10"24 g mu = 1.660 540 2 x 10~24 g mp/me = 1836.152 701 hc/2ne2 = I/a = 137.035 989 5

e'2/mec2 = re = 2.817940 92 x 10"13 cm

/i2/47r2mf ie2 — a()

= 0.529 177 249 x 10"8 cm h/mec =\c = 2.426310 58 x lO"10 cm 2x2mee4/ch3 = Roc = 109 737.315 34 cm"1

k = 1.380 658 x lO"16 ergK"1

a = 27r5A:4/15/i3c2

= 5.670 51 x 10"

87rr2/3 = ea = 0.665 246 16 x 10~24 cm2

eh/4irme = \IB

- 9.274 015 4 x 10"21 gauss c Mo = 1

£0 = 1

$o = 2.067834 61 x 10"7 M (maxwell) Go =3.482 76748 x 107 statS NA, L = 6.022 136 7 x 1023 m o r1

F = 2.892 556 8 x 1014 esu mol"1

R = 8.314 510 x 107 erg m o r1 K"1

eV = 1.60217733 x 10"12 erg 1 u = mu = m(12C)/12

= 1.660 540 2 x 10"24 g erg cm 2K 4 s 1

3

(Based on constants recommended by the 1986 CODATA Committee in previous table.)

Sun-Earth system constants 15 Sun-Earth system constants

Sun (Best Estimate) Radius

Semidiameter at mean distance Mass

Mean density Surface gravity

6.96 X 108 m 15'59".63 = 959".63 1.9891 X 1030 kg 1.41 X 103 kgm~3

Motion relative to nearby stars Period of synodic rotation

((f> = latitude) Period of sidereal rotation Earth (IAU System) Equatorial radius for Earth Dynamical form-factor for Earth Flattening of Earth

Polar radius Mass of the Earth Mean density Normal gravity (g)

(</> = latitude)

Rotation period with respect to fixed stars

in mean sidereal time in mean solar time Rate of rotation

Annual rate of precession (T in centuries from J2000.0)

general precession in longitude Constant of nutation (J2000.0) Solar parallax

Constant of Aberration (J2000.0) Light-time for 1 AU

1 AU

Mean eccentricity of orbit Obliquity of the ecliptic (T in centuries from J2000.0) Mean Earth-Sun distance Mean orbital speed Sun/Earth mass ratio Moon/Earth mass ratio Mean lunar distance Time

1.94 X 104 m s "1

26.90 + 5.2 sin2 <j> days 25.38 days

o = 6378140 m J2 = 0.001082 63 1// = 298.257 b = 6356755 m M = 5.9742 x 1024 kg 5.52 X 103 kgin^3

9.80621 -0.025 93 cos 20 + 0.000 03 cos 4<^> m s ^2

24h00m00s.008 4 23h56m04s.098 9

15".041067178 66910 s^1

50".290 966 + 0".022 222 6T N = 9".202 5

8".794 148 20".495 52 499.004 782 s 1.495 787 0 X 1011 m 0.016 708 617

23O26'21".448-46".815T 1.000 001017 8 AU 29.785 9 X 103 m s "1

332946.0 0.012 300 2 3.844 X 108 m 1 day = 24 hours = 1440 minutes = 86400 seconds

1 Julian year = 365.25 days = 8766 hours = 525960 minutes

= 31557600 seconds

Tropical year (J2000.0) 365.242 days (equinox to equinox)

The Earth-Sun Lagrange points are discussed in Chapter 15.

(From Seidelmann, P.K., Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, CA, 1990)

Additional data can be found in Chapters 2 and 9.

Cosmological data Hubble constant Hubble time Hubble distance Critical density Volume

Smoothed density of galactic material throughout universe (Allen 1973)

Space density of galaxies

Luminous emission from galaxies Mean sky brightness from galaxies Cosmic background

thermodynamic temperature Energy density of cosmic

background radiation (CBR) Number density of CBR

Energy density of relativistic particles

Weak coupling constant

Ho = 70±

(1999, HST Key Project Team)

= (2.3 ±0.2) x 10~18 s"1

1/HO = (4.3 ±0.4) x 1017 s

= (14 ± 1) x 109 years R = c/H0 = (4.3 ± 0.4) x 103 Mpc

= (1.3 ±0.1) x 1026 m

pc =3H$/8TTG

= (9.5 ± 1) x 10"27 kgm"3

4 7 ^ / 3 = (3.3 ± 0.3) x 1011 Mpc3

= (9.2 ±0.9) x 1078 m3

2 x 10~31 gem"3

= 2 x 10~28 kgm"3

1 x 10~7 atomem"3

= 1 x 10"1 atom m~3

3 x 109 MQ Mpc"3

0.02 Mpc"3

3 x 108 LQ Mpc"3

1.4 (mv = 10) deg"2

2.728 ±0.002 K (COBE) 0.261 53(T/2.728)4eV cm"3

4.190 17 x 10"14(T/2.728)4

joule m~3

411.87 cm-3 = 4.118 7 x 108 m~3

0.439 72 eV cm"3

= 7.045 09 x 10~14 joule m"3

gwk = 1.435 x 10~49 erg cm3

= 1.435 x 10~62 joule m3

(See Chapter 10 and http://pdg.lbl.gov/2002/astrorpp.pdffor additional data.)

Unit conversions 17 Unit conversions

1 keV: hc/E = 12.398 54 x 1(T⁸ cm 1 keV = 1.602177 x 1(T⁹ erg

= 1.602 177 x lO"¹⁶ joule 1 keV: E/h = 2.417965 x 10¹⁷ Hz 1 joule = 10⁷ erg

1 keV: E/k = 11.6048 x 10⁶ K 1 calorie = 4.184 joule 1.0 EHz: hv = 4.135 71 keV

1 parsec = 3.261633 light years = 3.085 678 x 10¹⁸ cm

= 3.085 678 x 10¹⁶ m

1 light year = 9.460 530 x 10¹⁷ cm = 9.460 530 x 10¹⁵ m 1 XU = 1.002 09 x 10"^{1 1} cm = 1.002 09 x 10"¹³ m 1 Angstrom = 1 x 10~⁸ cm = 1 x 10~¹⁰ m

1 amu: Me2 = 1.492 41 x 10"³ erg = 931.494 MeV

= 1.492 41 x 10~¹⁰ joule

760 torr = 1.013 x 10⁶ dyncm~² = 1 atmos. = 1.013 bars

= 1.013 x 105 pascals

1 Rayleigh = ^{(1/4TT) X} 10⁶ photons cm"²s~¹sr~¹ 1 Uhuru ct s"¹ = 1.7 x 10"¹¹ erg cm"² s"¹ ( 2 - 6 keV)

= 2.4 x 1 0 ~ⁿ erg cm"² s"¹ (2 - 10 keV) X-ray source intensity in millicrabs =

103 I 2 E{dN/dE)dE/ I ^ E(dN/dE)GrabdE

JEX JE1

dN/dE and (dN/dE)cra\3 are the source and Crab Nebula photon spectral flux density, respectively.

For E2 = 10 keV and Ex = 2 keV,

/ E{dNIdE)^G^bdE = 2.3 x 10~⁸ erg cm~² s"¹

JECrab spectrum is from Chapter 6.

1 flux unit = 10~²⁶ watt m~²Hz~¹ = 1 Jansky 1.0 /xJy = 10"11 erg cm"2 s"1 EHz"1

= 0.242 x 10"1 1 erg cm"2 s"1 keV"1

= 1.509 x 10~3 keVcm"2 s"1 keV"1

1 curie: amount of material undergoing 3.7 x 1010 disintegrations s^1

1 nautical mile = 1852 m 1 statute mile = 1609.344 m intensity (ergcm~2 s^1 Hz^1)

= 3.33 x 10-¹⁹A² (A) intensity (erg cm"² s"¹ A"¹) 1 barn = 10"²⁴ cm² = 10"²⁸ m²

1 tesla = 10⁴ gauss 0°C = 273.15 K

Conversion tables (A given amount of a physical quantity, expressed in the units of one system, is expressed as an equivalent number of units in another system.) Quantity LENGTH VOLUME

AmountUnit AmountUnit 1 1 1 1 ^I—1 1 1 1 ^I—1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

meter (SI) = 1.000 00E + light year = 9.460 53E + parscc = 3.085 68E + Angstrom = 1.000 01E - Angstrom = 1.000 01E - micron = 1.000 00E - nanometer = 1.000 00E - XU = 1.002 09E - fermi = 1.000 00E - nautical mile = 1.852 00E + statute mile = "1.609 34E + astron. unit (AU) = 1.495 98E + solar radius = 6.959 90E + centimeter (cgs) = 3.240 78E - centimeter (cgs) = 6.684 56E — meter (SI) = 3.240 78E - meter (SI) = 6.684 54E - inch (Eng) = 2.540 00E - fluid ounce (US) = 2.957 353E - ft3 = 2.831 685E - in3 = 1.638 706E - gallon (US) = 3.785 412E - gallon (US) = 3.785 412E00

02 15 16 10 08 06 09 13 15 03 03 11 08 19 14 17 12 02 • 05 • 02 05 • 03

centimeter (cgs) meter (SI) meter (SI) meter (SI) centimeter (cgs) meter (SI) meter (SI) meter (SI) meter (SI) meter (SI) meter (ST) meter (SI) meter (ST) parsec astron. unit (AU) parsec astron. unit (AU) meter (SI) meter3 (SI) meter3 (SI) meter3 (SI) meter3 (SI) liter

Conversion tables (cont.) QuantityAmountUnit AmountUnit MASS ENERGY

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

gallon (US) = 4.000 quart = 2.000 liter = 1.000 000E - 03 barrel = 1.589 873E - 01 cup = 2.366E + 02 yd3 = 7.645 549E - 01 kilogram (SI) = 1.000 00E + 03 at. mass unit (amu) = 1.660 54E — 24 at. mass unit (amu) = 1.660 54E — 27 solar mass = 1.989 10E + 33 solar mass = 1.989 10E + 30 gram (cgs) = 6.02214E + 23 gram (cgs) = 5.027 40E - 34 kilogram (SI) = 6.022 14E + 26 kilogram (SI) = 5.027 40E - 31 kilogram (SI) = 2.204 62E + 00 kilogram (SI) = 3.527 40E + 01 pound (avdp.) = 4.535 92E - 01 pound (avdp.) = 1.600 00E + 01 ounce (avdp.) = 2.834 95E + 01 gram (cgs) = 3.527 40E - 02 ounce (troy) = 3.110 35E + 01 gram (cgs) = 3.215 07E - 02 joule (SI) = 1.000 00E + 07 joule (SI) = 6.241 51E + 18 quart pint meter3 (SI) meter3 (SI) mL meter3 (ST) gram (cgs) gram (cgs) kilogram (SI) gram (cgs) kilogram (SI) at. mass unit (amu) solar mass at. mass unit (amu) solar mass pound (avdp.) ounce (avdp.) kilogram (SI) ounce (avdp.) gram (cgs) ounce (avdp.) gram (cgs) ounce (troy) erg (cgs) electron volt (eV) 5' a

Conversion tables (cord.) QuantityAmountUnit AmountUnit FORCE PRESSURE POWER

erg (cgs) = 1.000 00E - 07 erg (cgs) = 6.241 51E + 11 electron volt = 1.602 18E - 12 amu x c2 = 9.314 95E + 08 gm (cgs) x c2 = 5.609 59E + 32 calorie = 4.184 00E + 00 newton (SI) = 1.000 00E + 05 dyne (cgs) = 1.000 00E - 05 pound force = 4.448 22E + 00 newton (SI) = 2.248 09E - 01 pascal (SI) = 1.000 00E + 00 bar = 1.000 00E + 06 bar = 9.869 23E - 01 torr = 1.333 22E - 03 psi = 6.894 76E + 03 pascal = 1.450 38E - 04 psi = 6.894 76E - 02 psi = 5.171 49E + 01 watt (SI) = 1.000 00E + 07 horsepower = 7.457 00E + 02 Btu s"1 (Eng) = 1.055 80E + 03 joule (SI) electron volt erg (cgs) electron volt electron volt joule (SI) dyne (cgs) newton (SI) newton (SI) pound force !-2 -2newton m ^ (SI) dyne cm z (cgs) atmosphere bar pascal (SI) psi bar torr ergs"1 (cgs) watt (SI) watt (SI)

Conversion tables (cont.J Quantity TIME TEMPERATURE Energy equivalence Temperature equivalence ELECTRICITY AND MAGNETISM Charge Charge density Current Current density Electric field Potential Amount 1 1 1 1 1 1 1 1 1 T T T T T T 1 1 1 1 1 1 1 1

Unit Amount second (SI) = 1 minute = 6.000 00E + 01 hour = 3.600 00E + 03 day = 8.640 00E + 04 tropical year = 3.155 69E + 07 tropical year = 3.652 42E + 02 second = 3.168 88E - 08 sidereal second = 9.972 70E - 01 sidereal year = 3.652 56E + 02 kelvin = T - 273.15 kelvin = (9/5) x (T - 273.15) + 32 celsius = T + 273.15 fahrenheit = (5/9) x (T - 32) + 273.15 celsius = (9/5) x T + 32 fahrenheit = (5/9) x (T - 32) electron volt : 1.160 48E + 04 kelvin : 8.617 12E - 05 coulomb = 2.997 92E + 09 coulomb m"3 = 2.997 92E + 03 ampere (couls"1 ) = 2.997 92E + 09 ampere m~2 = 2.997 92E + 05 voltm"1 = 3.335 65E - 05 volt = 3.335 65E - 03 Unit second (cgs) second second second second day tropical year second (SI) day celsius fahrenheit kelvin kelvin fahrenheit celsius kelvin electron volt statcoulomb statcoul cm~ statampere statamp cm~ statvolt cm" st at volt

Conversion ^{So" cr CO 1—i}