Handbook of Space Astronomy and Astrophysics, 3rd Edition

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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 statistics, and geophysics. This handbook contains the most frequently used information in modern astrophysics, 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. 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). M A R T I N ZOMBECK

HANDBOOK OF SPACE ASTRONOMY AND ASTROPHYSICS Third Edition MARTIN V. ZOMBECK Smithsonian Astrophysical Observatory, Cambridge, USA

CAMBRIDGE UNIVERSITY PRESS

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521782425 © Cambridge University Press 2007 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. First published in print format 2006

ISBN-13

978-0-511-34872-3

eBook (EBL)

ISBN-13

978-0-521-78242-5

hardback

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.

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".

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Foreword Preface General data Astronomy and astrophysics Radio astronomy Infrared and submillimeter astronomy Ultraviolet astronomy X-ray astronomy Gamma-ray astronomy Cosmic rays Earth's atmosphere and environment Relativity and cosmology Atomic physics Electromagnetic radiation Plasma physics Experimental astronomy and astrophysics Astronautics Mathematics Probability and statistics Radiation safety Astronomical catalogs Computer science Glossary of abbreviations and symbols Appendices Index

1 35 185 211 233 253 293 309 323 347 367 385 405 413 535 551 579 597 611 623 651 659 753

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 May, 2005

Riccardo Giacconi 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

photon in joules, or the pressure of a gas in newton m 2 would leave 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 HarvardSmithsonian 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 March, 2006

Martin V. Zombeck [email protected]

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) Fundamental physical constants (SI) Fundamental physical constants (c.g.s.) Sun-Earth system constants Cosmological data Unit conversions Conversion tables Energy unit conversion Conversion factors for natural units Flux density conversion Numerical constants Mathematical formulae Elementary particles (short list) Elementary particles Energy conversions Prefixes and symbols Periodic table of the elements Greek alphabet Bibliography

2 3 14 15 16 17 18 23 23 24 25 26 27 28 29 30 31 33 33

2

General data

International system of units (SI) Physical quantity

Name of unit

Symbol

Base units length mass time electric current thermodynamic temperature amount of substance luminous intensity

meter kilogram second ampere kelvin mole candela

Derived units with special names radian plane angle steradian solid angle hertz frequency joule energy newton force pascal pressure watt power coulomb electric charge volt electric potential ohm electric resistance Siemens electric conductance farad electric capacitance weber magnetic flux henry inductance tesla magnetic flux density luminous flux lumen lux illuminance degree Celsius Celsius temperature activity (of a radioactive source) becquerel absorbed dose (of ionizing radiation) gray dose equivalent sievert

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 Gy Sv

eo G h

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)^ tP

h

nip

h

c Mo

Symbol

UNIVERSAL CONSTANTS speed of light in vacuum permeability of vacuum

GENERAL CONSTANTS

Quantity

1/MoC

1.61605(10) 5.390 56(34)

= 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)

2

299 792458 7 4TT x 1 0 " = 12.566 370 6 1 4 . . .

Value

Fm-i

10" n m3 kg" 1 s"2 lO- 34 j g 10-15 eVs lO- 34 Js 10"i6 eVs 10- 8 kg 10"35 m lO- 44 s

10"i2

ms i NA" 2 10- 7 NA- 2

Units

64

64

64

0.60 0.30 0.60 0.30

128

(exact)

(exact)

(exact)

Relative uncertainty (ppm)

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.) B

a,

"t/

CO

B

cons

in kelvins, fi^/k

in wavenumbers, /IN/he

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

ELECTROMAGNETIC CONSTANTS elementary charge

Quantity

IJ-N

RH

2e/h e2/h

e e/h

Symbol

Fundamental physical constants (SI) (cont)

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)

Value

KT-1 10- 27 J T - 1 10"8 eVT" 1 MHzT" 1 lO"2 m ^ T " 1 10- 4 K T - 1

10- 24 J T - 1 10"5 eVT" 1 1010 HzT- 1

n

10"19 C 1014 AJ" 1 10"15 Wb 1014 HzV- 1 10- 5 s

Units

8.5

0.34 0.089 0.30 0.30

8.5

0.30 0.30 0.30 0.30 0.045 0.045 0.34 0.089 0.30 0.30


Ci B

4 sral data

in electron volts, mec21 \e\

electron mass

ELECTRON

ATOM fine structure constant, |/ioce 2 //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

ATOMIC CONSTANTS

Quantity

me

h/2me h/me

Eh

a0

ROD

a a-1

Symbol

9.109 389 7(54) 5.485 799 03(13) 0.510 999 06(15)

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)

Value

8

m2s-i m2s-i

m J

10- 3 i kg 10- 4 u MeV

10~ lu eV 10- 4 10"4

eV

io-i J

1 0 " Hz

m-i

10"

3

Units

0.59 0.023 0.30

0.045 0.045 0.0012 0.0012 0.60 0.30 0.045 0.60 0.30 0.089 0.089


CO

B

o'

B-

CO

tan

(is:

Fundamental physical constants (SI) (cont) dai

5

electron g-factor, 2(1 + ae) electron-muon magnetic moment ratio electron-proton magnetic moment ratio

fJ-e/flB ~ 1

mg/m^

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, a 2 a 0 Thomson cross-section, (87r/3)r2 electron magnetic moment in Bohr magnetons in nuclear magnetons electron magnetic moment anomaly,

fie/ftp

Ve/Vv

9e

ae

fi-e/fi-B fle/flN

fie

0"e

Ac Ac re

me/mp me/md me/ma —e/me M(e),Me

Symbol

Quantity


1.159 652193(10) 2.002 319 304386(20) 206.766967(30) 658.2106881(66)

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)

Value

0.0086 1 x 10~5 0.15 0.010

lO- 3

m

m

10-26 J T - 1

IO-1 5 m lO- 2 8 m 2

10-12 lO-"

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


lO- 3 10" 4 10" 4 10~4 10 n Ckg- 1 10~7 k g m o r 1

Units

o> B

6 Ida

in electron volts, mpc2/{e} proton-electron mass ratio

proton mass

PROTON

muon g-factor, 2(1 + aM) muon-proton magnetic moment ratio

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 muon mass

Quantity

mp/me

mv

m,,

Symbol


1.672 6231(10) 1.007276470(12) 938.27231(28) 1836.152 701(37)

1.165 923 0(84) 2.002 331846(17) 3.183 345 47(47)

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)

Value

l o - 2 7 kg u MeV

io- 3

10- kgmollO- 2 6 J T - 1 10" 3

4

10" 2 8 kg u MeV

Units

1

0.59 0.012 0.30 0.020

7.2 0.0084 0.15

0.61 0.15 0.32 0.15 0.15 0.33 0.15 0.15


CO B

8

o"

co

to-

dai. nts

uncorrected (H 2 O, sph., 25°C)

TOp/mM

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 (H 2 O, sph., 25°C) in Bohr magnetons in nuclear magnetons proton gyromagnetic ratio G,p

iP iPl^

7P/2TT

lp

Hp/HB fl'p/flN

P-'p

O"H2O

,pl,N

flp/flB

Pp

*C,p

X

e/mp M(p),Mp

Symbol

Quantity


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)

25.689(15)

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)

Value

s^r 1

JT-i

MHzT" 1

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

io4

10"

3

_26

0.34 0.011 0.023 0.30 0.30 0.30 0.30

-

io- 6 10

0.15 0.30 0.012 0.089 0.089 0.34 0.010 0.023

107 C k g - 1 10" 3 kgmol" 1 10" 1 5 m 10^ 16 m 10~ 26 J T " 1 10" 3

Units


si

B

C5

mn/me mn/mp M{n),Mn Ac>

in electron volts, mnc2/{e} neutron-electron mass ratio neutron-proton mass ratio neutron molar mass neutron Compton wavelength, h/mnc

fin 1 flp

md md/me

DEUTERON deuteron mass

in electron volts, mdc2/{e} deuteron-electron mass ratio

fln/fle

fln/flN

fin fln/flB

neutron magnetic moment'"' in Bohr magnetons in nuclear magnetons neutron-electron magnetic moment ratio neutron-proton magnetic moment ratio

A~o

mn

NEUTRON neutron mass

Ac,r 1 /27T

Symbol

Quantity

3.343 586 0(20) 2.013 553 214(24) 1875.61339(57) 3670.483014(75)

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)

Value

JT

10" 27 kg u MeV

10~3

3

_26

io-

1 0

-i

10" 3 kgrnol" 1 10~15 m 10- 16 m

10" 27 kg u MeV

Units

0.59 0.012 0.30 0.020

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


n

co

to-

CO -—.

B

CO

CO]

(IS.

Fundamental physical constants (SI) (cont) dai.

md/mp M(d),Md

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

F NAh

NAhc R

molar gas constant

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)

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)

Value

Cmol" 1 10~10 Jsmol" 1 Jmrnol" 1 Jmol"^"1

JT-i

1023 m o r 1 io- 2 7 kg MeV

io-3

3

_26

10~

1 0

10~3 kgmol" 1

Units

0.59 0.59 0.30 0.30 0.089 0.089 8.4

0.003 0.012 0.34 0.019 0.028 0.019 0.017


^ 'The scalar magnitude of the deuteron moment is listed here. The neutron magnetic dipole is directed oppositely to that of the proton, and corresponds to the dipole associated with a spinning negative charge distribution. The vector sum, fj,d = fip + fJ-n, is approximately satisfied.

mu

NA,L

PHYSICO-CHEMICAL CONSTANTS Avogadro constant atomic mass constant, m u = j^-m(12C) in electron volts, muc2/{e} Faraday constant molar Planck constant

fld/flB fJ-d/fJ-N fid/fie fid/fip

fid

Symbol

Quantity


a.

02

So/R

n0

Symbol

8.4

S = So + | i ? l n A r -

R\n(p/P0)

2

10- 3 m K

W m

2.897 756(24)

IO-1 6

mK

Lmol-i 1025 m- 3 Lmol-i

22.41410(19) 2.686 763(23) 22.71108(19)

10-8 Wm- 2 K- Z1

8.4 8.5 8.4

10"23 JK-i 10-5 eVK-i lO" HzK"1 m^K-1

1.380 658(12) 8.617385(73) 2.083 674(18) 69.503 87(59)

18 18 34 0.60 8.4

8.5 8.4 8.4 8.4

Units

Value

-1.151693(21) -1.164856(21) 5.67051(19) 3.7417749(22) 0.01438769(12)


*• ' The entropy of an ideal monoatomic gas of relative atomic weight Arr is given by

constant)/ 6 ) § + ln{(27rmufcTi//i2)tA;Ti/j5o} Ti = 1 K, p0 = 100 kPa po = 101 325 Pa Stefan-Boltzmann constant, (ir2/60)k4/h3c2 2 first radiation constant, 2nhc second radiation constant, hc/k Wien displacement law constant, b = A max T = c 2 /4.965 114 23 . . .

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 ^ / F m T = 273.15 K, p = 100 kPa Sackur-Tetrode constant (absolute entropy

Quantity


CO

a

8

ts

a,

drift rate of 0 6 9 - B I BIPM maintained volt, U 76 _ BI = 483 594 GHz(/i/2e) V76-BI

dt

dfle9-Bl

^BI85

1 - 7.59(30) x 10" 6 = 0.999 992 41(30)

0.0566(15) V V

n n

1985)

1 - 1.563(50) x 10~6 = 0.999 998 437(50)

HBI85 = ^ 6 9 - B I (1 Ja

9n

10~ 27 kg Pa ms

1.660 540 2(10) 101325 9.806 65

u atm

0.30

0.050

0.59 (exact) (exact)

0.30

J

10- 1 9

1.60217733(49)

eV

electron volt, (e/C) J = {e} J (unified) atomic mass unit, 1 u = mu = Y2m(12C) standard atmosphere standard acceleration of gravity 'AS-MAINTAINED' ELECTRICAL UNITS BIPM(a) maintained ohm, f^g-ei


Units

Symbol

Quantity Value

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.

95"

a.

0.54310196(11) 0.192 015 540(40) 12.0588179(89)

ft d22o V m (Si)

cm3

nm nm

l o -io

m

10- 1 3 m 10- 1 3 m

A A

1-6.03(30) x 10- 6 = 0.999 993 97(30) 1.00207789(70) 1.002 099 38(45) 1.00001481(92)

Units

Value

xu(CuKai) xu(MoKai) A*

Symbol

0.74

0.21 0.21

0.70 0.45 0.92

0.30


: 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.)

(feo = a/y/8 molar volume of Si, M(Si)/p(Si) = NAa3/8

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) = latitude) 26.90 + 5.2 sin2 <j> days Period of sidereal rotation 25.38 days Earth (IAU System) Equatorial radius for Earth o = 6378140 m Dynamical form-factor for Earth J2 = 0.001082 63 Flattening of Earth 1// = 298.257 Polar radius b = 6356755 m Mass of the Earth M = 5.9742 x 1024 kg Mean density 5.52 X 103 kgin^ 3 Normal gravity (g) 9.80621 -0.025 93 cos 20 ( = latitude) + 0.000 03 cos 4 m s ^ 2 Rotation period with respect to fixed stars in mean sidereal time 24h00m00s.008 4 in mean solar time 23h56m04s.098 9 Rate of rotation 15".041067178 66910 s^ 1 Annual rate of precession (T in centuries from J2000.0) general precession in longitude 50".290 966 + 0".022 222 6T Constant of nutation (J2000.0) N = 9".202 5 Solar parallax 8".794 148 Constant of Aberration (J2000.0) 20".495 52 Light-time for 1 AU 499.004 782 s 1 AU 1.495 787 0 X 1011 m Mean eccentricity of orbit 0.016 708 617 Obliquity of the ecliptic (T in centuries from J2000.0) 23 O 26'21".448-46".815T Mean Earth-Sun distance 1.000 001017 8 AU Mean orbital speed 29.785 9 X 103 m s " 1 Sun/Earth mass ratio 332946.0 Moon/Earth mass ratio 0.012 300 2 Mean lunar distance 3.844 X 108 m Time 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.

General data

16

Cosmological data Hubble constant Hubble time Hubble distance Critical density Volume Smoothed density of galactic material throughout universe (Allen 1973)

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 7 1 x 10~ atomem" 3 = 1 x 10"1 atom m~3 9 3 x 10 MQ Mpc"3 0.02 Mpc"3 Space density of galaxies 3 x 108 LQ Mpc"3 Luminous emission from galaxies Mean sky brightness from galaxies 1.4 (mv = 10) deg"2 Cosmic background 2.728 ±0.002 K (COBE) thermodynamic temperature Energy density of cosmic 0.261 53(T/2.728)4eV cm"3 background radiation (CBR) 4.190 17 x 10"14(T/2.728)4 joule m~3 3 411.87 cm- = 4.118 7 x 108 m~3 Number density of CBR Energy density of relativistic 0.439 72 eV cm"3 particles = 7.045 09 x 10~14 joule m" 3 gwk = 1.435 x 10~49 erg cm3 Weak coupling constant = 1.435 x 10~62 joule m3 (See Chapter 10 and http://pdg.lbl.gov/2002/astrorpp.pdffor additional data.)

17

Unit conversions

Unit conversions 1 keV: hc/E = 12.398 54 x 1(T 8 cm

1 keV = 1.602177 x 1(T 9 erg = 1.602 177 x lO" 1 6 joule 1 joule = 107 erg 1 calorie = 4.184 joule

1 keV: E/h = 2.417965 x 1017 Hz 1 keV: E/k = 11.6048 x 106 K 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 10 17 cm = 9.460 530 x 1015 m 1 XU = 1.002 09 x 10" 1 1 cm = 1.002 09 x 10" 1 3 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" 2 s~ 1 sr~ 1 1 Uhuru ct s" 1 = 1.7 x 10" 1 1 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

JEX

2

E{dN/dE)dE/

I ^ E(dN/dE)GrabdE 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, / JE

E{dNIdE)G^bdE

= 2.3 x 10~ 8 erg cm~ 2 s" 1

Crab spectrum is from Chapter 6. 1 flux unit = 10~ 26 watt m~ 2 Hz~ 1 = 1 Jansky 1.0 /xJy = 10" 1 1 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- 19 A 2 (A) intensity (erg cm" 2 s" 1 A" 1 ) 24 2 1 barn = 10" cm = 10" 2 8 m2 1 tesla = 104 gauss 0°C = 273.15 K

1 1 1 1

Amount

1 1 1

1 1

1 1

1

1 1 1 1 1 1 1 1 1

I—1

VOLUME

LENGTH

Quantity

fluid ounce (US) = ft3 = in3 = gallon (US) = gallon (US) =

meter (SI) = light year = parscc = Angstrom = Angstrom = micron = nanometer = XU = fermi = nautical mile = statute mile = astron. unit (AU) = solar radius = centimeter (cgs) = centimeter (cgs) = meter (SI) = meter (SI) = inch (Eng) =

Unit + 02 + 15 + 16 - 10 - 08 - 06 - 09 - 13 - 15 + 03 + 03 + 11 + 08 - 19 —14 - 17 - 12 - 02 2.957 353E -• 0 5 2.831 685E -• 0 2 1.638 706E - 05 3.785 412E -• 0 3 3.785 412E00

1.000 00E 9.460 53E 3.085 68E 1.000 01E 1.000 01E 1.000 00E 1.000 00E 1.002 09E 1.000 00E 1.852 00E "1.609 34E 1.495 98E 6.959 90E 3.240 78E 6.684 56E 3.240 78E 6.684 54E 2.540 00E

Amount

meter3 meter3 meter3 meter3 liter

(SI) (SI) (SI) (SI)

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)

Unit

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.)

I—1

CD

ENERGY

MASS

Quantity

Conversion tables (cont.)

1 1

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

1 1

1 1 1

Amount

= = = = = = = = = = = = = = = = =

= = = = = = 1.000 00E + 03 1.660 54E — 24 1.660 54E — 27 1.989 10E + 33 1.989 10E + 30 6.02214E + 23 5.027 40E - 34 6.022 14E + 26 5.027 40E - 31 2.204 62E + 00 3.527 40E + 01 4.535 92E - 01 1.600 00E + 01 2.834 95E + 01 3.527 40E - 02 3.110 35E + 01 3.215 07E - 02

4.000 2.000 1.000 000E - 03 1.589 873E - 01 2.366E + 02 7.645 549E - 01

Amount

joule (SI) = 1.000 00E + 07 joule (SI) = 6.241 51E + 18

kilogram (SI) at. mass unit (amu) at. mass unit (amu) solar mass solar mass gram (cgs) gram (cgs) kilogram (SI) kilogram (SI) kilogram (SI) kilogram (SI) pound (avdp.) pound (avdp.) ounce (avdp.) gram (cgs) ounce (troy) gram (cgs)

gallon (US) quart liter barrel cup yd3

Unit

erg (cgs) electron volt (eV)

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)

meter3 (ST)

mL

quart pint meter3 (SI) meter3 (SI)

Unit

5' a

POWER

PRESSURE

FORCE

Quantity

Conversion tables (cord.) Amount = = = = = =

1.000 00E 1.000 00E 9.869 23E 1.333 22E 6.894 76E 1.450 38E 6.894 76E 5.171 49E

1.000 00E 1.000 00E 4.448 22E 2.248 09E + + + +

+ + -

1.000 00E 6.241 51E + 1.602 18E 9.314 95E + 5.609 59E + 4.184 00E +

Amount

00 06 01 03 03 04 02 01

05 05 00 01

07 11 12 08 32 00

watt (SI) = 1.000 00E + 07 horsepower = 7.457 00E + 02 Btu s " 1 (Eng) = 1.055 80E + 03

pascal (SI) = bar = bar = torr = psi = pascal = psi = psi =

newton (SI) = dyne (cgs) = pound force = newton (SI) =

erg (cgs) erg (cgs) electron volt amu x c 2 gm (cgs) x c 2 calorie

Unit

e r g s " 1 (cgs) watt (SI) watt (SI)

newton m! - 2^ (SI) dyne cm - 2z (cgs) atmosphere bar pascal (SI) psi bar torr

dyne (cgs) newton (SI) newton (SI) pound force

joule (SI) electron volt erg (cgs) electron volt electron volt joule (SI)

Unit

a.

o

to

Energy equivalence Temperature equivalence ELECTRICITY AND MAGNETISM Charge Charge density Current Current density Electric field Potential

TEMPERATURE

TIME

Quantity

Conversion tables (cont.J

coulomb coulomb m" 3 ampere (couls" 1 ) ampere m~ 2 voltm" 1 volt

1 1 1 1 1 1

1 1

kelvin kelvin celsius fahrenheit celsius fahrenheit electron volt kelvin

1 6.000 00E + 01 3.600 00E + 03 8.640 00E + 04 3.155 69E + 07 3.652 42E + 02 3.168 88E - 08 9.972 70E - 01 3.652 56E + 02

= = = = = =

2.997 92E + 09 2.997 92E + 03 2.997 92E + 09 2.997 92E + 05 3.335 65E - 05 3.335 65E - 03

= T - 273.15 = (9/5) x (T - 273.15) + 32 = T + 273.15 = (5/9) x (T - 32) + 273.15 = (9/5) x T + 32 = (5/9) x (T - 32) : 1.160 48E + 04 : 8.617 12E - 05

second (SI) = minute = hour = day = tropical year = tropical year = second = sidereal second = sidereal year =

Unit Amount

T T T T T T

1 1 1 1 1 1 1 1 1

Amount

statcoulomb statcoul cm~ statampere statamp cm~ statvolt cm" st at volt

celsius fahrenheit kelvin kelvin fahrenheit celsius kelvin electron volt

day

tropical year second (SI)

day

second (cgs) second second second second

Unit

1—i

CO

cr

So"

Conversion

Resistance Resistivity Conductance Conductivity Capacitance Magnetic flux Magnetic flux density Magnetic field Inductance MISCELLANEOUS Radio-activity Intensity Elux density Flux density Elux density Flux density Energy equivalence Energy equivalence Wavelength equivalence Angle Angle Angle Solid angle Solid angle Solid angle

Quantity

Conversion tables (cord.) Amount

curie (SI) rayleigh fu or jansky jansky jansky jansky cV eV Angstrom arcsec arcmin degree arcsec arcmin deg

ohm ohm in Siemens, mho mliom" 1 farad weber tesla ampere-turnm" 1 henrv

1.112 65E 1.112 65E 8.987 52E 8.987 52E 8.987 52E 1.000 00E 1.000 00E 1.256 64E 1.112 65E

- 12 - 10 + 11 + 09 + 11 + 08 + 04 - 02 - 12

= 3.700 00E + 10 = 7.957 75E + 04 = 1.000 00E - 26 = 1.000 00E - 05 = 2.417 97E - 06 = 1.509 00E + 03 : 1.239 85E + 04 : 2.417 97E + 14 : 1.239 85E + 04 = 4.848 14E - 06 = 2.908 88E - 04 = 1.745 33E - 02 = 2.350 40E - 11 = 8.461 70E - 08 = 3.046 20E - 04

= = = = = = = = =

Unit Amount

Angstrom Hz eV radian radian radian steradian steradian steradian

disinteg. s ph cm s sr watt m~ Hz~ erg cm" 2 s" 1 EHz" 1 ergcm~ s~ keV~

cm gauss cm (maxwell) gauss oersted

Unit

CD

to to

~\

1. 99 x 1Q- 8IE

10

1/v 1 /

3.00 x 10 / " 1.24 x 1 0 - 7IE

1.99 x 1 0 - 1 2 / £ 1.99 x 1Q- 1(3 / / -*-Z7

10 /z>

4

10 /u

1.24 x 1 0 - / £

8

3

3.00 x 10 /z/

12A/E

3 .00 x 1 0 1 8

1 7

26

1..51 X 10 E

10

10l £

1

7

1010/A

g

eV amu erg

K

cm

s-l

2 .998 1 .310 1 .519 1 .415 0 .948 0 .852

24

X 10

X 10

X 10 X 1Q48

2V

ib

X 1011

X 10iu

1

s- l

5

10

0 .507 X 10 i4 0. 472 X 10 iv 0. 316 X 10 37 2. 843 X 10

4. 369

0. 334 X 10 1

cm 1

1.160 1.081 0.724 0.651

4

n

x 10 x 10 13 x 10 16 x 10 37

1

0.764 x 1 0 " 0.229

K 15

9

0.931 x:10 0.624 x 10 12 0.561 x 10 33

1

0.658 x :10" 1.973 x 1 0 - 5 4 0.862 x l O -

eV

7

3

0.670 x 10 0.602 x 10 24

1

0.707 x 10~ 2.118 x 1 0 - 1 4 0.962 x IO-1 3 1.074 x 1 0 - 9

24

x W8E

amu

i5.24

1 .24 x 10- z>

1

4 .14 x 10~ u

18

1..24 x 10~ /A

1..24 x 10~ /A

1014/A

3 .00 X: 10 u

2..42 X

3. 00 X

3

12.4/A

S(keV)

1018/A

(Reprinted with permission from Eureka Scientific, Inc., Oakland, CA) Note: 1 A = 0.1 nanometer. Conversion factors for natural units; c = ft, = 1.

£(erg)

~(

1

.E(keV)

i/(Hz)

14

10 8 A

A(cm)

10 A

4

3. 00 X

1

10 4 A

A(/ im )

10" 4 A

10" 4 A

1 3. 00 X

'0Hz)

10" 8 A

i

A(cm)

A (/mi)

A(A)

FROM j

A(A)

Energy unit conversion

n

0.899 X:10 2 1

1 .492 X 10" 1

3

1 .055 X 1 0 " 2 7 17 3 .161 X 1 0 6 1 .381 X 10-1 1 .602 X 10-1 2

<srg

5.03 x 1 0 1 5 £

1

8.07 x 10 E

6

3.34 x 10~ u

I/A

10 4 /A

10 8 /A

.(cm"1)

1.173 0.352 1.537 1.783 1.661 1.113

10 -48

1

X

X

X

10- 24 10-21

10 -33

X 10- 37

X 10- 37

X

g

1

1 .99 x 10- 16 f5

1 .60 x 10- i?

9

27

6 .63 x 10~ z/

1. 99 x 10" 16 /A

1. 99 x 10" 12 /A

1 .99 x 10~ 8 /A

B(erg)

w

to

o

8a

lergy UJ

ph

2°t?nwN)

)

5.03 x 10 7 AF A

1.51 x W26Fu/\

4.06 x 10 6 A 3 F A

1.51 x 10 2 6 F,/£;

fx

3.34 x 10 4 A 2 F A

10

8.07xl0-2E2fE

8.07 x 1 0 " 2 A 2 / A

- 6 3x

fE

1.51 x 103S,,/A

/photons\ V cm2 s A /

"4A/A

6

6.63 x W-4EfE

1.51 x lOZS^/E

SV(Jy)

/A

(Reprinted with permission from Eureka Scientific, Inc., Oakland, CA)

Ciil s xlz /

2 SS 2 T TT T

Vcm

/A ( P h ° 2 t 0 I f ) cm' s A 7

\ cm s ke V /

IE (

FROMj

fE 1 lcm 2 skeV7

S,(Jy)

f photons \

Flux Density Conversion yE in keV; A in A) o

% }

Vcnr s A /

I

3.00 x 1018Fv/X2

FA

1.99 x 1 0 " 8 / A / A

1.29 x 10-10E3fE

3.00 x l O - ^ ^ / A 2

A

10" 2 3 5 v

( ergs \ Vcm2 sRzJ

3.34 x 1 0 " 1 9 A 2 F A

6.63 x 1 0 " 2 7 A / A

6.63 x \Q-27EfE

Fv

CD

Numerical constants

25

Numerical constants 3.141 592 7 e = 2.718 281 8 In 2 = 0.693147 2 log10 2 = 0.301 030 0

rad = 57.295 78 deg = 3.437 747 x 103 arcmin = 2.062 648 x 105 arcsec

TT =

steradian = 32 400/TT 2

In 10 = 2.302 5851 l o g l 0 e = 0.434 294 5 (27T)1/2 =2.506 628 7T2 =9.869 604 2 10 = 1024 e - 1 =0.367879 4

Feigenbaum's constants: 6 = 4.669 2016

a = 2.502 907875 0 Euler-Mascheroni: 0.577215 664 9 Golden mean = 0.618 033988 7...

n 0 1 2 3 4 5 6

7 8 9 10 11 12 13 14 15 20 25 n

Powers of 2: 2n log 2™ 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16 384 32 768 1048 576 33 554432

0.00 0.30 0.60 0.90 1.20 1.51 1.81 2.11 2.41 2.71 3.01 3.31 3.61 3.91 4.21 4.52 6.02 7.53 0.301n

= 3.2828 x 103 deg2 = 1.1818 x 107 arcmin 2 = 4.2545 x 1010 arcsec2 degree = 0.0174533 rad arcmin = 2.908 88 x 10~ 4 rad arcsec = 4.848 137 x 10~ 6 rad deg2 = 3.0462 x 10~ 4 steradian arcmin 2 = 8.4617 x 10~8 steradian arcsec2 = 2.3504 x 1 0 ~ n steradian Fibonacci numbers: Fi = 1 F2=l Fn+2 = F n + Fn+1, n > l

Number system conversions: Decimal Octal Binary Hexadecimal 0 1 2 3 4 5 6

0 1 2 3 4 5 6

7

7

8 9 10 11 12 13 14 15 16

10 11 12 13 14 15 16 17 20

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 10000

0 1 2 3 4 5 6

7 8 9

A B

C D E F

10

26

General data

Mathematical formulae ,„

/

„

„ 1

+ • • • + naxn~x + xn,

where n is any positive integer.

x3

x 2

'

x

n ( n — l ) ( n —2) „ » ,

n(n — 1) „ 9 9

e =l + x + — + — + .... ln(l + x)=x-

— + — ~^-H 2 3 4

X3

_

X5

X7

smx - x - — + — - —H udv = uv —

/

for - 1 < x < 1. _

,

cosx-

vdu + C,

X2

X4

~ ^ [ + ^ J ~ ^ [ + '"'I cos2 nxdx

I siT?nxdx=

J

X6

Jo

Jo IT

f°° Jo

-a2x2

= — for an integer, n / 0. f°° n -ax Jo

1/2/

_

f°°

-2-Kiux

f°°

J — oo

2mux

J — oo

The factorial n\ is defined for a positive integer n as n\ = n(n — l) • • • 2-1. n\ « (27r) 1 / 2 n" + 1 / 2 e- n (for large n). The functional equation of the Gamma Function: r ( x + 1) = xr(x), for x > 0.

T(n + 1) = n\, for integer n > 0.

f f(x)dx = - f f(x)dx,

f f(x)dx = f

a.

J a.

Jh

f(x)dx

J a

+

,-b

d df du — f[u{x) = — — , dx du dx

d du dv —[u{x)v(x)\=v—+u —. dx dx dx

— In y(x) = y'(x)/y(x),

2.30 log10 x = loge x

= v(x)[u'(x)/v(x) - u(x)v'(x)/v(x)2]/\n(W)u(x), where ' denotes — . dx sin(A + B) = sin A cos B + cos A sin B, cos(A + B) = cos A cos i? — sin A sin B, (cos 8 + i sin 0)n = cos n9 + i sin n(9.

sin 2A = 2 sin A cos A cos 2A = cos2 A — sin2 A.

Elementary particles (short list)

27

Elementary particles (short list) Particle Photon vr-meson Neutrino Electron, positron /i-meson Proton Neutron

Mass (amu)

Spin

0

0

+ 1, - 1

0.149 84 0.144 90

1 1

Charge

0 0 - 1 , +1 - 1 , +1

+ 1, - 1

0

< nr 6

0.000 548 6 0.1134 1.007 276 1.008 665

0 1/2 1/2 1/2 1/2 1/2

Magnetic moment

Mean life(Q)

0 0 0 ~0

stable 2.60 x 10~ 8 0.83 x io- 1 6 stable

1.001160 nB{h) 0.004 842 fiB 2.792 85 MB ( C ) -1.913 04 fiN

00

stable 2.20 x 10"6 stable 917 ± 14

(^half-life = mean life x In 2 ( 6 V B = eh/4irmec = 9.274 015 4(31) x 1CT24 J T " 1 (c)MAr =eh/4Trmpc=

5.050 786 6(17) x 10~ 27 J T " 1 .

(Data from 'Reviews of Particle Properties', Rev. Mod. Phys. 52, No. 2, April 1980)

28

General data

Short List of Elementary Particles

(The second column is the isospin t, while the next column is the spin and parity, J . Masses and lifetimes have generally been rounded; see the original reference for error bars and a complete listing of particle properties.) Mass (MeV)

Particle LEPTONS

NONSTRANGE ™ A A

STRANGENESS A

BARYONS

h 2 3 2

h h h k+ \ 3+ 2

= - 1 BARYONS 0

£+

0.511003 105.6594

Mean life (s) Stable 6 2.19714 X 10~ 5 X io-

1784 938.280

Stable

939.573

925

1232

6 X 10-

STRANGENESS

1

1189.36

8.00 X 1 0 "

2

6 x IO-20

+

1314.9

2.9 X

+

1321.3

1.64 X

io- 1 0 io- 1 0

8.2 X

io- 1 1

= - 3 BARYON 3+ 0 1672.5 NONSTRANGE CHARMED BARYON 1+ 0 2282 At NONSTRANGE MESONS 2" 1 7T± 0" 139.567 1 0" 134.963 0 0" 548.8 »?

j / *

T

STRANGENESS K±

K°, R°

CHARMED NONSTRANGE D±

D°. D°

1l~

o~ 1~ 11-

= --1 MESONS

1 2

io- 1 0

1.48 X

STRANGENESS

1 0 0 0 0

11

1197.34 2 1

io- 1 0

2.63 X

= - 2 BARYONS 1 2 1 2

24

1115.60 1192.46

=•0

13

Q-

o-

Q-

CHARMED STRANGE MESON F± 0 0~

2.603 x 10" 8 8.3 x IO-I 7 8 x IO-I 9 4.3 X lO- 2 4 6.6 x 10" 2 3 2.4x10-21

769

782.6 957.6 1019.6 3096.9 9456 493.67 497.7

MESONS

o-

1 x 10-1 3

1.6 X 10"22 1.0 x 10 1.6 x l O - 2 0

Ks KL

1.237 x I O - 8 : 8.92 X 1 0 " 1 1 : 5.18 X I O - 8

1869.4 1864.7

9 X IO-I3

2021

2 x 10 - 1 3

5 X IO-I3

(From Shapiro, S.L. & Teukolsky, S.A., Black Holes , White Dwarfs, and Neutron Stars, John Wiley and Sons, 1983, with permission.) For a complete list of elementary particles see http://pdg.lbl.gov/.

Energy conversions

29

Energy conversions 1 erg 1 joule 1 foot-pound 1 calorie 1 Btu 1 horsepower-hour 1 kilowatt-hour 1 MeV Energy of fission of 1 atom of 236U Energy equivalent of 1 ton of TNT Energy of fission of 1 kilogram of 236U Hydrogen fusion: Energy equivalent of 1 gram of matter High heat value of 1 ton of coal High heat value of 1 cord of red oak High heat value of 100 gallons of fuel oil High heat value of 20 000 cu ft natural gas US energy consumption Earth's daily receipt of solar energy Earth's rotational energy Earth's total heat content 1 D-cell flashlight battery

= = = = = = =

1 dyne-centimeter = 10 joule 1 newton-meter 1.356 joule 4.184 joule 1.055 x 103 joule 2.6845 x 106 joule 3.6 x 106 joule = 3.413 x 103 Btu

= 1.6 x 10~ 1 3 joule = 199 MeV = 3.2 x 1 0 ~ u joule = 4.2 x 109 joule = 20 kilotons of TNT D + T - • 2 He 4 + n + 17.6 MeV = 9 x 10 1 3 joule = 26 x 10 6 Btu = 30 x 10 6 Btu = 15 x 10 6 Btu

= = = = = =

20 x 106 Btu 10 20 joule y r " 1 (proj. 1970-2000) 1.49 x 10 22 joule = 4.2 x 10 12 Mwh 2.2 x 10 29 joule 3 x 10 31 joule 104 watt-s = 104 joule

General data

30

Prefixes and symbols (used with SI units to indicate decimal multiples and submultiples) Submultiples

Multiples Factor 1024 1021

10 i8 10 i 5 1012 9

10 106 103 102 10

Prefix

Symbol

Factor

Prefix

Symbol

yotta zetta exa peta tera giga mega kilo hecto deca

Y Z E P T G M k h da

io-i lO- 2 10"3 10"6 10"9

deci centi milli micro nano pico femto atto zepto yocto

d c m

2

10-i IO-15 10-i g

10- 21

10-24

n n P f a z y

Periodic table of the elements

31

Periodic table of the elements GROUP 1A

|

PERIODIC TABLE OF THE ELEMENTS

1.00797

-252.7 -259.2

I I

o.o7i

n

3 1330 ,80.5 0.53

6939 I I— I

KEY

ZBe

^906

^ ^

^9;t Zn-— S Y M

MELTING — POINT, °C

12

!lNa ;:iMg 20

22

S°T

IS

J\

rL Ca

37

8547

e762

0.86

38

56

" Cs

\J\S

0297

W

•f Ti

2 4 51.996

2 5 54.938

2665

!LMn

» Cr

57

l38 91

-

I-

l226)

m

LANTHANUM

89

87

88

"iFr

To R a

5400

l86 2

75 5425

5900 __

5930

104

58 3468 6.67

140.12 e g

140.907

60

Ce z, Pr

3027

CERIUM

90 LIQUIDS AT THE BOILING POINT. OUTLINE - SYNTHETICALLY PREPARED.

3850

232.038

' 76

(23I)

Th ";::Po

THORIUM

7.00

144.24

PROTACTINIUM

92

3818 1132 19.07

238.03

77

5300 2454 22.5

61 «"> 62

PROMETHIUM

93

(237)

u T»Np

URANIUM

58 71

-

NEPTUNIUM

46

106 4

-

Z Rh ToPd

Nd rPm

PRASEODYMIUM NEODYMIUM

91

2730

3980

iRu

Nb Mo 72

28

2900

45 1

60

Ba Z La -:; Hf T. Ta 7, W•;:: R e 3470

2 7 58.933

Fe r; Co

43

40

I Rb Z Sr

55'

3.0

23 5

1900 1072

l922 j , I I

78 ' 4530

T. Pt

150.35

63

151.96

Sm

826 5.26

Eu Gd

SAMARIUM

94 3235 640

(242)

(243)

Py

PLUT ONIUM

157.25

1312

EUROPIUM

95

64

GADOL INIUM

96

(247)

înn AMEF ICIUM

CUR IUM

32

General data

Periodic table of the elements (cont.)

0.126 I I V HELIUM

5

g

I0.8II

4830 D 3727 9 D 2.26

(2030) 234

14.0067 g

y

12.01115

-195.8

20

/ ^ W

0.81 26 9815

13

-

M

28.086

6

f4 ?o° q j 2.70 r " M

29

906

8 96

69 72

31

—.

-

32

K

:,: Z n 1, Go

2595 0 8

6537

63.54 3 0

2.33

49

^

4Q

47

:: Ag

112.40

765

^

320 9

16

44.2*

119.0 2.07

33

Â

32064

O C5 78.96

17

?

354

35

4.79 O W

51

-

52

39.948

83 80

36

53 '

Te

OD

IQ -185.8

-

Br ™ Kr

Ge L As " S e ll8 69

"

r ci

6

8

!i Sn

8.65 V - / V J

74922

613

5.32 V J C

50

. QJ

I *

.82W

-

o

N "!;:

IK

O l 72 59

15.9994

I3L3

54

4.94

3.06 A 6

I

IODINE

y g 196.967 8 0 '

82

2970

7. AU :;:Hg

303

J l

11.85

Q4

s

1 1

(210)

85

86

560

:::Pb '; Bi

(9.2) I

\J

POLONIUM

65 2800

l58 924

-

.

356 JU 8.27

I »J

66

l62 50

-

2600 - ^

g J 164.930 QQ 167.26 69 l 2600 , . 1461 M

A

8.54 L ^ y 880 n o

JQ

71 3327 ,652

SS? p

9.05 I — I

9.84

174 97

-

I

UU

DYSPROSIUM

97

98

99

(254)

100

101 MENOELEVIUM

°

-108.0

102

103

{257)

33

Greek alphabet

Greek alphabet

r

A E Z H

e

i K A M

a (3 1 S e

c

V 0 i K

A

Alpha Beta Gamma Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu

N

V

[i]

A B

0

n p s

T T $ X

0

7T

P 0~ T V

X

i>

Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Chi Psi Omega

Bibliography BETA Mathematics Handbook, Rade, L. and Westergren, B., CRC Press, Inc. (1990). CODATA recommended values of the fundamental physical constants: 1998, P.J. Mohr and B.N. Taylor, Rev. Mod. Phys., 72, No. 2, 2000. Handbook of Chemistry and Physics, CRC Press, Inc. International Critical Tables of Numerical Data, Physics, Chemistry, and Technology, McGraw-Hill Book Company. Landolt-Bornstein: Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik, und Technik, Springer-Verlag. Reviews of Particle Properties, C. Caso, et al., The European Physical Journal C3 (1998). Standard Mathematical Tables and Formulae, D. Zwillinger, ed., CRC Press, Inc. (1996). Note: Links to WWW resources material in this chapter can be found at:

http://www. astrohandbook.com

which

supplement

the

Chapter 2

Astronomy and astrophysics . . . to observe is not enough. We must use our observations, and to do that we must generalize. - Henri Poincare

The Solar System The Sun Solar eclipses Solar system elemental abundances The planets (physical elements) The planets (mean orbital elements) The planets (additional data) Natural satellites in the solar system (orbital data) Natural satellites in the solar system (physical and photometric data) Selected comets Periodic comets Selected asteroids Asteroid distribution histogram Annual major meteor showers Meteoroid flux density Glossary of meteor astronomy terms Contents of the solar system Extrasolar planets Stars Star charts Constellations The 50 visually brightest stars in the sky (in order of brightness) The 100 visually brightest stars (limiting magnitude, V = 2.59J

38 38 48 50 51 52 53 54 56 58 59 62 63 64 65 66 68 69 71 71 73 75 78

36

Astronomy and astrophysics

Stars within 5 pc Stars of large proper motion Bright white dwarfs Pulsars Globular clusters Prominent OB associations Orbital elements of some binary stars Classification of variable stars Galactic supernova remnants Typical supernova light curves Henry Draper spectral classification Spectral type and luminosity class Hertzsprung-Russell diagram Hertzsprung-Russell diagram with stellar examples Infrared and visible spectral features Calibration of MK spectral types Classification and absolute magnitude of stars Stellar mass, luminosity, radius and density Present-day mass function (PDMF) Star number densities Relative number of stars Integrated star light Mean star density vs visual magnitude Star counts Luminosity functions Parameters of the interstellar gas Proton-proton chain and the CNO cycle Stellar structure equations Galaxies Properties of the Milky Way Galaxy The Local Group Hubble's classification of galaxies Selected brighter galaxies Named galaxies Representative active galactic nuclei Objects with large redshifts (Z > 5.06,1 Prominent clusters of galaxies The Messier catalog

83 86 87 88 93 94 96 97 100 100 101 101 102 103 104 105 107 108 110 112 114 114 115 116 116 117 118 119 120 120 121 122 123 124 125 128 129 130

Contents Universe Mass-radius-density data for astronomical objects Primordial light element abundances The background radiation spectrum of the Universe Redshift survey Astronomical photometry Standard photometric systems Interstellar reddening Absolute magnitude Moon, night sky, sun, and planetary brightness Spherical astronomy Time The celestial sphere Coordinates The Zodiac Astronomical coordinate transformations Approximate reduction of astronomical coordinates Reduction for precession - approximate formulae Major ground-based astronomical telescopes Reflecting telescopes Refracting telescopes Schmidt telescopes Radio telescopes The Hubble Space Telescope Description of the Hubble Space Telescope Glossary of astronomical terms Bibliography

37 133 133 134 135 136 137 139 142 144 144 146 146 151 152 152 153 155 156 157 157 158 159 160 162 163 168 184

38


The Solar System The Sun Global parameters Mass Radius Surface area Volume Moment of inertia Mean density Gravity at surface Escape velocity at surface Magnetic field strengths (typical) Sunspots Polar field Bright, chromospheric network Ephemeral (unipolar) active regions Chromospheric plages Prominences Sidereal rotation (func. of lat.) Sidereal period for helio. long. Sunspot cycle Luminosity Radiation emittance at Sun's surface Mean radiation intensity of Suns's disk Specific mean energy production Standard Model parameters' 3 ' Central density Central temperature Central pressure Central hydrogen content by mass, Xc Density at 1 R© Temperature at 1 R@ Pressure at 1 R@ Photospheric abundances' 4 ' X(H) Y(He) Z(Li-U)

1.989 x 1030 kg 6.955 x 108 m 6.079 x 1018 m2 1.409 x 1027 m 3 5.7 x 1046 kg m2 1.412 x 103 kg m - 3 2.740 x 102 m s~2 6.177 x 105 m s" 1 2000-4000 x 10" 4 tesla 1 x 10-4 25 x 10-4 20 x 10"4 200 x 10"4 10-100 x 10" 4 14°.4-3 o .0sin 2 per dayW 25.38 days ~ 11.4 y 3.842 x 1026 W (var.) A2 and A < Ai. (Data from Lang, K., Astrophysical Formulae, Vol. I, Springer-Verlag, 1999.)


48

Solar eclipses, Date

2001-2010

Eclipse Eclipse1 Central2 Type Magnitude Duration

Geographic R,egion of Eclipse Visibility3

1.050

04m57s

e S. America, Africa

2001 Dec 14 Annular

0.968

03m53s

N. & C. America, nw S. America

2002 Jun 10 Annular

0.996

00m23s

e Asia, Australia, w N. America

2002 Dec 04

1.024

02m04s

s Africa, Antarctica, Indonesia, Australia

2003 May 31 Annular

0.938

03m37s

Europe, Asia, nw N. America

2003 Nov 23

1.038

01m57s

Australia, N. Z., Antarctica, s S. America

0.736 0.927 1.007

00m42s

Antarctica, s Africa ne Asia, Hawaii, Alaska N. Zealand, N. & S. America

2001 Jun 21

Total

[Total: s Atlantic, s Africa, Madagascar] [Annular: c Pacific, Costa Rica] [Annular: n Pacific, w Mexico]

Total

[Total: s Africa, a Indian, s Australia] [Annular: Iceland, Greenland]

Total

[Total: Antarctica]

2004 Apr 19 Partial 2004 Oct 14 Partial 2005 Apr 08 Hybrid4

[Hybrid: a Pacific, Panama, Colombia, Venezuela]

2005 Oct 03 Annular

0.958

04m32s

Europe, Africa, s Asia

2006 Mar 29

1.052

04m07s

Africa, Europe, w Asia

0.935

07m09s

S. America, w Africa, Antarctica

[Annular: Portugal, Spain. Libya. Sudan, Kenya]

Total

[Total: c Africa, Turkey, Russia]

2006 Sep 22 Annular

[Annular: Guyana. Suriname, F. Guiana, s Atlantic]

2007 Mar 19 Partial 2007 Sep 11 Partial 2008 Feb 07 Annular

0.874 0.749 0.965

02ml2s

Asia, Alaska S. America, Antarctica Antarctica, e Australia, N. Zealand

2008 Aug 01

1.039

02m27s

ne N. America, Europe, Asia

[Annular: Antarctica]

Total

[Total: n Canada, Greenland, Siberia, Mongolia, China]

2009 Jan 26 Annular

0.928

07m54s

s Africa, Antarctica, se Asia, Australia

2009 Jul 22

1.080

06m39s

e Asia, Pacific Ocean, Hawaii

2010 Jan 15 Annular

0.919

llmO8s

Africa, Asia

2010 Jul 11

1.058

05m20s

s S. America

[Annular: a Indian, Sumatra, Borneo]

Total

[Total: India, Nepal, China, c Pacific] [Annular: c Africa, India, Malymar, China]

Total

[Total: s Pacific. Easter Is.. Chile. Argentina]

Eclipse magnitude is the fraction of the Sun's diameter obscured by the Moon. For annular eclipses, the eclipse magnitude is always less than 1. For total eclipses, the eclipse magnitude is always greater than or equal to 1. For both annular and total eclipses, the value listed is actually the ratio of diameters between the Moon and the Sun. 2 Central Duration is the duration of a total or annular eclipse at Greatest Eclipse. Greatest Eclipse is the instant when the axis of the Moon's shadow passes closest to Earth's center. 3 Geographic R.egion of Eclipse Visiblity is the portion of Earth's surface where a partial eclipse can be seen. The central path of a total or annular eclipse covers a much smaller region of Earth and is described in brackets [].

Hybrid eclipses are also known as annular/total eclipses. Such an eclipse is both total and annular along different sections of its umbral path. (From F. Espenak, NASA/GSFC, 2001)

49

The Solar System Solar eclipses (cont.) Total Solar Eclipse Paths: 2001-2025

Annular & Hybrid Solar Eclipse Paths: 2001-2025

180° W

150° W

120° W

Annular Eclipses Hybrid Eclipses

90° W

60° W

30° W

0'

30° E

60° E

sunearth,gsfc.nasa,go v/eclipse/eclipse.html

90* E

120° E

150° E

130° E


50

Solar tsystem elemental abundances (log N H = 12.00) Element Photosphere* 1H 2 He 3 Li 4 Be 5B 6C 7N 8O 9F 10 Ne 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo

Meteorites'

12.00 [12.00] [10.99 ±0.035] [10.99] 3.31 ±0.04 1.16±0.1 1.15 ±0.10 1.42 ±0.04 2.88 ±0.04 (2.6 ±0.3) 8.56 ±0.04 [8.56] 8.05 ±0.04 [8.05] 8.93 ±0.035 [8.93] 4.56 ±0.3 4.48 ±0.06 [8.09 ±0.10] [8.09 ±0.10] 6.33 ±0.03 6.31 ±0.03 7.58 ±0.05 7.58 ±0.02 6.47 ±0.07 6.48 ±0.02 7.55 ±0.02 7.55 ±0.05 5.45 ±(0.04) 5.57 ±0.04 7.21 ±0.06 7.27 ±0.05 5.5 ±0.3 5.27 ±0.06 [6.56 ±0.10] [6.56 ±0.10] 5.12 ±0.13 5.13 ±0.03 6.36 ±0.02 6.34 ±0.03 3.10 ±(0.09) 3.09 ±0.04 4.99 ±0.02 4.93 ±0.02 4.00 ±0.02 4.02 ±0.02 5.67 ±0.03 5.68 ±0.03 5.53 ±0.04 5.39 ±0.03 7.67 ±0.03 7.51 ±0.01 4.92 ±0.04 4.91 ±0.03 6.25 ±0.04 6.25 ±0.02 4.21 ±0.04 4.27 ±0.05 4.60 ±0.08 4.65 ±0.02 2.88 ±(0.10) 3.13 ±0.03 3.41 ±0.14 3.63 ±0.04 2.37 ±0.05 3.35 ±0.03 2.63 ±0.08 3.23 ±0.07 2.60 ±(0.15) 2.40 ±0.03 2.90 ±0.06 2.93 ±0.03 2.24 ±0.03 2.22 ±0.02 2.60 ±0.03 2.61 ±0.03 1.42 ±0.06 1.40 ±0.01 1.92 ±0.05 1.96 ±0.02

Element

Photosphere

44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 55 Cs 56 Ba 57 La 58 Ce 59 Pr 60 Nd 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 90 Th 92 U

1.84 ±0.07 1.12 ±0.12 1.69 ±0.04 (0.94 ±0.25) 1.86 ±0.15 (1.66 ±0.15) 2.0 ±(0.3) 1.0 ±(0.3) 2.13 ±0.05 1.22 ±0.09 1.55 ±0.20 0.71 ±0.08 1.50 ±0.06 1.00 ±0.08 0.51 ±0.08 1.12 ±0.04 (-0.1 ±0.3) 1.1 ±0.15 (0.26 ±0.16) 0.93 ±0.06 (0.00 ±0.15) 1.08 ±(0.15) (0.76 ±0.30) 0.88 ±(0.08) (1.11 ±0.15) 1.45 ±0.10 1.35 ±(0.10) 1.8 ±0.3 (1.01 ±0.15) (0.9 ±0.2) 1.85 ±0.05

Meteorites

1.82 ±0.02 1.09 ±0.03 1.70 ±0.03 1.24 ±0.01 1.76 ±0.03 0.82 ±0.03 2.14 ±0.04 1.04 ±0.07 2.24 ±0.04 1.51 ±0.08 2.23 ±0.08 1.12 ±0.02 2.21 ±0.03 1.20 ±0.01 1.61 ±0.01 0.78 ±0.01 1.47 ±0.01 0.97 ±0.01 0.54 ±0.01 1.07 ±0.01 0.33 ±0.01 1.15 ±0.01 0.50 ±0.01 0.95 ±0.01 0.13 ±0.01 0.95 ±0.01 0.12 ±0.01 0.73 ±0.01 0.13 ±0.01 0.68 ±0.02 0.27 ±0.04 1.38 ±0.03 1.37 ±0.03 1.68 ±0.03 0.83 ±0.06 1.09 ±0.05 0.82 ±0.04 2.05 ±0.03 0.71 ±0.03 0.08 ±0.02 0.12 ±(0.06) (

to

The Solar System

53

The planets (additional data) Planet

Perihelion Aphelion Distance Distance (AU) (AU)

Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto

0.31 0.72 0.98 1.38 4.95 9.00 18.27 29.71 29.7

0.47 0.73 1.02 1.67 5.45 10.4 20.06 30.34 49.1

V max

-1.2 -4.28 -3.86 a -2.52 -2.7 -0.6 +5.3 +7.50 +13.8

Magnetic Solar T B B Oblateness Dipole Constant (K) Moment (Wm- 2 ) 3xlO 19 O

c o

o o

-2

-1 Log [Period (s)]

19 19 00 00 17 02 00 00 00 00 19 22 18 18 06 16 00 17 19 17

h

39 59 34 23 01 18 24 24 24 24 08 29 24 07 13 40 24 01 10 01

m

s

03.85 04.65 03.98 52.0 50.89 32.01 21 43.97 16.75 06.70 13 52 13

38.56 36.77 21.83 59.40 13 06.35

a J2000

- 0 5 34 36.6 - 7 2 03 58.8 - 3 0 06 43 +42 32 17.5 - 7 2 04 - 7 2 04 42.8 - 7 2 04 53.7 - 7 2 04 42.3 - 3 7 41 35 +26 43 57.8 - 2 4 52 10.8 - 2 4 59 51 - 0 2 00 47.1 +22 24 09.0 - 7 2 04 06.8 - 3 0 06 43 - 5 9 58 54 - 3 0 06 43

+21 °34'59.1" +20 48 15.1

6 J2000 0.0015578064924327 0.0016074016848063 0.0018771818543796 0.0021006335458588 0.0022950000000000 0.0023230904564000 0.0023520000000000 0.0026235793491669 0.0026433432956678 0.0028304059560080 0.0029471094385460 0.0029778192947192 0.0030543146293258 0.0030594487974000 0.0030618440367440 0.0031633158173403 0.0032103407094388 0.0032340000000000 0.0032661820000000 0.0034180000000000

P(s)

1.90000E-06 1.61845E-03 -7.00000E-04 9.57200E-06 2.90000E-06 1.64000E-06

6.45070E-05 3.03800E-05 -1.20470E-04

7.50000E-05

1.05110E-04 1.68515E-05 5.06000E-06 -9.78420E-06

dP/dt 71.0370 29.1168 13.7630 24.5845 115.6400 61.2500 24.3000 24.3819 24.3000 24.3000 10.3500 23.0190 119.8289 134.0000 38.7792 18.4150 24.3700 115.6400 33.5200 115.6400

DM(pc c m " 3 ) 9.65 1.53 0.98 5.00 4.16 5.85 5.00 5.00 5.00 5.00 0.55 1.43 5.50 3.27 2.19 1.18 5.00 4.16 2.18 4.16

d (kpc)

e2

( 1

1 A

Ne dl where d = distance of the pulsar from the Sun, Ne = electron number density in interstellar space.

s

51000.000000 51000.000000 51779.744510 52055.870432 49440.000000 47953.500000 51734.975100 50315.000000 49360.000000 51000.000000 52247.000000 51745.000000 52247.000000

50100.000000 48196.000000 49550.000000 51000.000000 52247.000000 49150.608600

Epoch (MJD)

The pulse arrival time for two different observing frequencies fi and ]•% differs by: t-2 — t\ = ( -777 z^ I DM. 2-7rmec d = Pulsar distance in most cases estimated using the Taylor & Cordes (1993) model for N e (Data from the Australia National Facility Catalog of 1323 Pulsars, 2002.)

Jo

DM = dispersion measure = /

a, 8 = position of pulsar, P = pulse period, dP/dt = pulse period derivative in unit of 10 Epoch = modified Julian date of the epoch of observation,

J1939+2134 J1959+2048 J0034-0534 J0023-7203J J1701-3006F J0218+4232 J0024-7204W J0024-7204F J0024-7204O J0024-7204S J1908-3741 J2229+2643 J1824-2452 J1807-2459 J0613-0200 J1640+2224 J0024-7204H J1701-3006E J1910-5958 J1701-3006D

Pulsar Name

The 20 fastest radio pulsars (as of February 2002)

00 CO

90


Binary pulsars in the Galaxy Pulsar J0045-7319 1259-63 1820-11 1534+12 1913+16 2303+46 J2145-0750 0655+64 0820+02 J1803-2712 1953+29 J2019+2425 J1713+0747 1855+09 J0437-4715 J1045-4509 J2317+1439 J0034-0534 J0751+18 1718-19 1831-00 1957+20 a

P P~b (ms) (d) ea 926.3 51 0.808 47.8 1237 0.870 279.8 358 0.794 37.9 0.42 0.274 59.0 0.32 0.617 1066.4 12.3 0.658 16.0 6.8 0.000021 195.7 1.03 7 x 10~6 864.8 1232 0.0119 334 407 0.00051 6.1 117 0.00033 3.9 76.5 0.000111 4.6 67.8 0.000075 5.4 12.3 0.000022 5.8 5.7 0.000018 7.5 4.1 0.000019 3.4 2.46 < 0.000002 1.9 1.6 < 0.0001 3.5 0.26 < 0.01 1004 0.26 < 0.005 520.9 1.8 < 0.004 1.6 0.38 < 4 x 10~5

f(M)b (M 0 ) 2.169 1.53 0.068 0.315 0.132 0.246 0.0241 0.071 0.0030 0.0013 0.0024 0.0107 0.0079 0.0056 0.0012 0.00177 0.0022 0.0012 (0.15) 0.00071 0.00012 5xlO~ 6

Mi (M 0 ) ~ 10 ~ 10 (0.8) 1.34 1.39 1.4 (0.51) (0.8) (0.23) (0.17) (0.21) (0.37) (0.33) 0.26 (0.17) (0.19) (0.21) (0.17)

\og(B)d P/(2P) (G) (y) 12.3 3xlO6 11.5 3xlO 5 11.8 3xlO6 10.0 2xlO8 10.4 lxlO 8 11.9 3xlO 7 8xlO 9 10.1 5xlO9 11.5 lxlO 8 10.9 3xlO 8 8.6 3xlO9 8.3 lxlO 1 0 8.3 9xlO9 8.5 5xlO9 8.7 2xlO9 8.6 6xlO9 8.1 lxlO 1 0 8.0 4xlO9

(0.14) 12.2 (0.07) 10.9 0.02 8.1

lxlO 7 6xlO 8 2xlO9

Eccentricity. Mass function, f(M) = (M2 sin i) 3 /(Mi+ M 2 ) 2 , where Mi and M2 are the masses of the pulsar and companion, respectively; i, the orbital inclination, is the angle between the plane of the orbit and the plane of the sky. M 0 represent's the Sun's mass as a unit of measurement. c Mass of pulsar's companion. Values in parentheses are estimated from f(M), assuming a pulsar mass of 1.4 M@ and i = 60°. d Dipole surface field, B = 3.2 x 1019 (PP) 1 / 2 gauss. (Adapted from Phinney, E.S and Kulkarni, S.R., Annu. Rev. Astron. Astrophys, 32: 591, 1994.) b

Stars

91

Binary pulsar PSR

1913+16

A schematic diagram showing the binary pulsar PSR 1913+16. (Longair, M.S., High Energy Astrophysics, Cambridge University Press, 1994, with permission)

Orbital eccentricity e - 0.617

M2

Binary period = 7.751939337 hours Pulsar period = 59 milliseconds Neutron star mass Mi = 1.4411 (7) M o

Neutron star mass M2 = 1.3874(7)

Parameters of PSR 1913+16 Symbol Value (units) Parameter (i) "Physical" parameters a 19 h 15 m 28.00018(15) Right Ascension 8 16°06 / 27 // .4043(3) Declination 59.029997929613(7) Pulsar Period PP (ms) 8.62713(8)xl0~ 18 Derivative of Period Pp (ii) "Keplerian" parameters ap sin i(s) 2.3417592(19) Projected semimajor axis e 0.6171308(4) Eccentricity pb (day) 0.322997462736(7) Orbital Period OJQ(°) 226.57528(6) Longitude of periastron 46443.99588319(3) Julian date of periastron To (MJD) (iii) "Post-Keplerian" parameters3 (Co) (° y r " 1 ) 4.226621(11) Mean rate of periastron advance 4.295(2) Redshift/time dilation 1 (ms) 12 (10~ ) -2.422(6) Orbital period derivative Pb (Will, CM., The Confrontation between General Relativity and Experiment, http://www.livingreviews.org/Articles/Volume4/2001-4will/, 2002.)


92

Pulsars (cont.) Distribution of periods and period derivatives for 353 pulsars. The seven known binary pulsars, indicated by circles around the dots, have unusually small period derivatives and hence relatively weak magnetic fields. (Dewey, R. J. et a/., Nature, 322, 712, 1986, with permission.) 1

1

1

1 ' '

1

i

|

i

-

i

i

i

i -

Crab

#

Vela*. * • -

1

1

•

-

-14

1

.

1509-58 •

-

-12

i

•.

.

-

•

.. V

k•

• •

#

•

*5 -•*

fcj\ / '

-:< ••

'%} 2303+46 _ i

:

•o. - 1 6 - -

3 -

1913+16 c

-18 —

0655+64 0 ,

1855 + 09 § -20 -3

.

i

i

i

// //

1953+29

I . .

1

1 * I

—

1831-00

9

/

- ^1937+21

1

?/ /

0820+02 i

—

1

-2 LOG P (s)

1

_L

Stars

93

A selection of globular clusters Name

Equatorial Coord. a(2000)

NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC

104 = 47 Tuc 362 3201 = Dun 445 4833 = LacI-4 5024= M 53 5139= UJ Cen 5272= M3 5286 = Dun 388 5904= M5 5986= Dun 552 6093= M80 6121= M4 6205= M13 6218= M12 6254= M10 6266= M62 6273= M19 6341= M92 6388 6397 6402 = M 14 6441 6626= M28 6637= M69 6656= M22 6715= M54 6723 = Dun 573 6752= Dun 295 6809= M55 7078 = M 15 7089 = M 2 7099= M30

1

m

0 »24 l 1 03.2 10 17.6 12 59.6 13 12.9 13 26.8 13 42.2 13 46.4 15 18.6 15 46.1 16 17.0 16 23.6 16 41.7 16 47.2 16 57.1 17 01.2 17 02.6 17 17.1 17 36.3 17 40.7 17 37.6 17 50.2 18 24.5 18 31.4 18 36.4 18 55.1 18 59.6 19 10.9 19 40.0 21 30.0 21 33.5 21 40.4

Galactic Coord.

6(2000)

I

-7205' - 7 0 51 - 4 6 25 - 7 0 53 + 18 10 - 4 7 29 +28 23 - 5 1 22 + 2 05 - 3 7 47 - 2 2 59 - 2 6 32 +36 28 - 1 57 - 4 06 - 3 0 07 - 2 6 16 +43 08 - 4 4 44 - 5 3 40 - 3 15 - 3 7 03 - 2 4 52 - 3 2 21 - 2 3 54 - 3 0 29 - 3 6 38 - 5 9 59 - 3 0 58 + 12 10 - 0 49 - 2 3 11

305?9 301.5 277.2 303.6 333.0 309.1 42.2 311.6 3.9 337.0 352.7 351.0 59.0 15.7 15.1 353.6 356.9 68.4 345.5 338.2 21.3 353.5 7.8 1.7 9.9 5.6 0.1 336.5 8.8 65.0 53.4 27.2

V

.D(arcmin)

b -44°9 -46.3 +8.6 -8.0 +79.8 + 15.0 +78.7 + 10.6 +46.8 + 13.3 + 19.5 + 16.0 +40.9 +26.3 +23.1 +7.3 +9.4 +34.9 -6.7 -12.0 + 14.8 -5.0 -5.6 -10.3 -7.6 -14.1 -17.3 -25.6 -23.3 -27.3 -35.8 -46.8

Diameter

4.0 6.6 6.8 7.4 7.7 3.6 6.4 7.6 5.8 7.1 7.2 5.9 5.9 6.6 6.6 6.6 7.2 6.5 6.8 5.6 7.6 7.4 7.0 7.7 5.1 7.7 7.3 5.4 6.9 6.4 6.5 7.5

30 13 18 14 13 36 16 9 17 10 9 26 17 14 15 14 14 11 9 26 12 8 11 7 24 9 11 20 19 12 13 11

V = integrated apparent visual magnitude. (Data from Roth, G.D., ed., Compendium of Practical Astronomy, Vol. 3, Springer-Verlag, 1994.) For a catalog of galactic globular clusters see Harris, W.E. 1996, AJ, 112, 1487 or http://www.physics.mcmaster.ca/Globular.litml

Cas OB4 Cas OB14 Cas OBI Cas OB8 Per OBI Cas OB6 Cam OBI Per OB3 Per OB2 Aur OB2 Aur OBI Gem OBI Ori OBI Mon OBI Mon OB2 CMa OBI Pup OBI Vel OB2 Vel OBI Car OBI Car OB2 Car OB4 Cen OB2 Cen OBI Nor OBI

Name

m

0 28 4 0 28.8 1 00.8 1 46.2 2 14.5 2 43.2 3 31.6 3 27.8 3 42.2 5 28.3 5 21.7 6 09.8 5 31.4 6 33.1 6 37.2 7 07.0 7 54.8 8 11.8 8 49.9 10 46.7 11 06.0 11 08.3 11 35.3 13 04.8 15 58.7

h

a 2000

+62°42' +63 22 +61 30 +61 19 +57 19 +61 23 +58 38 +49 54 +33 26 +34 54 +33 52 +21 35 - 2 41 +8 50 +4 50 -10 28 -27 05 -47 50 -45 00 -59 05 -59 51 -60 31 -62 36 -62 04 -54 30

S 2000

Prominent OB associations

360

360x240 120x66 330x150 114x54 84x48

240x180

240

840x300 360x250

300 960

360x300

480x300

360 480

120

(')

Diameter

5 6 8 2 0

2500 2510 2500

1 5 5 4 9 1 10 4 7

5 0 0 1 9 17 3

O stars

1400 2510 2000

460

1510 1320 2510

460 550

3160 1320 1510

170 400

2880 1110 2510 2880 2290 2190 1000

(PC)

Distance

19 6

11 15 6

3 3 5 13 6 0 7 3 0

12 3 5 10 56 8 9

B stars

+22 +28 +27 +43

-13 -3 +13

-43 -8 -38 -30 -41 -47 -6

(kms- 1 )

RV

2659? 3293;IC 2581? 3572, Tr 18 3590 IC 2944 4755 6031?

1893,IC 410 1912, 60; 1931? 2175? Trapezium 2264 2244 2335, 53; 2343? 2467?

381? 581, 663; 654? h, x Per IC 1805 1444? 1502?

103

Clusters

A Cen X Cru

Vela pulsar?

X2 Ori 0,/3,7,£,e Ori S Mon Plaskett's star

a, S Per C,o,x Per

re Cas

Stars

95

a,

b

95

a oS

3

in

16: 16 39.5 16 53.5 16 14.9 18 07.9 18 14.4 18 20.8 18 18.6 19 44.0 20 04.7 20 17.8 20 23.3 20 32.4 21 13.1 21 02.7 21 47.9 22 24.6 22 41.2 23 00.4 23 58.7 23 59.5

h

a 2000

-25: -46 46 - 4 1 57 -25 55 - 2 1 28 -19 03 -14 35 - 1 1 58 +24 13 +35 50 +37 38 +39 56 +41 17 +37 52 +49 43 +61 04 +55 14 +39 05 +64 03 +60 22 +67 35

6 2000

OB associations

150

480 210 900 X 540

30

420 X 240

300 x 180 500:

570 x 240

270 x 180 96 x 66

Diameter (')

(cont.)

160 1380 1910 160 1580 2400 2190 2000: 2000 2290 1820 1200 1820 1000 830 830 3470 600 870 2510 840

Distance (pc)

18 0 8 1 9 9 5 9 12 7 13

O stars

26 0 3 10 0

10 3 9 6 9 6 7 15 28 7 2

B stars

: denotes approximate value. (adapted from Sky Catalogue 2000.0, Vol. 2, Sky Publishing Corp., 1985.)

Sco-Cen Ara OBI Sco OBI Sco OB2 Sgr OBI Sgr OB4 Ser OBI Ser OB2 Vul OBI Cyg OB3 Cyg OBI Cyg OB9 Cyg OB2 Cyg OB4 Cyg OB7 Cep OB2 Cep OBI Lac OBI Cep OB3 Cas OB5 Cep OB4

Name

Prominent

7160,IC 1396 7380? 7788; 7790?

-21 -46

6514, 30-1 6603 6611 6604? 6823 6871? 6913,IC 4996 6910

IC 2602? 6169, 93 6231

Clusters

-10 -20 -51

-4 +3 -23 +6 +8 0 -7 -20

-18

RV (kms^ 1 )

p Cas

a" Cyg H, v, A Cep 13 Cep 10 Lac

Cyg X - 1

a C M a , a Carm a Eri fi Nor C 1 Sco a, /? , b Sco /uSgr

Sta

to

5 14

- 6 0 50 - 2 6 26

07 39 18

14 39 36 16 29 24 900

79.920

40.65

1200 420.07

1508.6 50.09

480

41.623 171.37

1955.56 1889.0

1927.6

1437 1965.3

1934.008 1836.433 1889.6 2070.6 1894.13

Epoch of periastron, t

pz

Q

231.560 0.0

269.8

57.19 261.43

219.907 252.88 268.59 47.3 147.27

w{°)

periastron,

of

Longitude

17.583 3.21

4.548

6.9753 6.295

0.907 3.746 11.9939 2.728 7.500

79.240 86.3

35.7

63.28 115.94

59.025 146.05 34.76 72.0 136.53

(°)

Inclin. orbit, i

204.868 273.0

284.3

18.38 40.47

23.717 31.78 278.42 155.5 44.57

(°)

Position angle of ascending node, H

1.3 100

3.5

18 14

14 11 5.9 340 2.7

Distance, d(pc)

2), where G is the gravitational constant (Kepler's third law).

0.0

0.516

0.40

0.1100 0.33

0.2763 0.8808 0.497 0.07 0.5923

Eccentricity, e

Semimajor axis of orbit, a (arcsec)

If we express masses in solar masses, periods in years, and distances in astronomical units, we have (M1 + M2)P2 = a 3 (a (AU) = a (arcsec) X d (pc)). e eccentricity, t epoch of the periastron passage (the closest approach of the stars), H position of the ascending node. The nodes are points of intersection of the relative orbit and a plane tangential to the celestial sphere at the position of the bright component, u) longitude of the periastron, the angle between the radius vector to the ascending node and that in the direction of the periastron, measured from the node to the periastron in the direction of the orbital motion, i inclination, the angle between the orbital plane and the plane tangential to the celestial sphere. (Adapted from Duffett-Smith, P., Practical Astronomy With Your Calculator, Cambridge University Press, 1988.)

t-w-

a semi-major axis, P period of revolution, M\7M2 stellar masses, —^- = -

2159 3153

30° 17' - 0 1 27 57 49 - 0 1 56 - 1 6 43

15 h 23 m 21 s 12 41 40 00 49 06 05 40 46 06 45 09

77 O B 7 Vir r\ Cas C Ori a CMa (Sirius) S Gem a Gem (Castor) a CMi (Procyon) a Cen a Sco (Antares)

07 20 07 07 34 36

6 2000

a 2000

Name

Period, P (mean solar years)

The orbital elements of some binary stars

fcr

a.

g

o a o S

CO O5

RV Tauri variables

« 2 CV

SSc

PC

SR SRa SRb SRc SRd RR RRa RRc RV RVa RVb

Red giant variables

RR Lyrae variables

M

Ic

la Ib

I

CW

CS

C

Long-period variables

Cepheids

Main class

Semiregular variables Semiregular variables Semiregular variables Semiregular variables Semiregular variables Cluster variables Cluster variables Cluster variables Variable supergiants Red-giant variables Red-giant variables P Cephei V. P Canis Major V. Scuti variables a Canis Ven. variables

Classical cepheids Classical cepheids Long-period cepheids Irregular variables Irregular variables Irregular variables Irregular variables Mira Ceti stars

Subclass

The classification of variable stars

— — — —

1.0

< 0.25 < 0.1

1-25

30-150 30-150 30-150 0.1-0.3

0.3

0.05-1.2 0.5 and 0.7

— — — —

30-1000

80-1000

1-50 or 70 1-50 or 70 1-50 or 70

(d)

Period

3 3 3 0.1

—

< 1 -2.0 < 1.5

— — —

2.5-5.0 and more 1-2.0 < 2.5

— — — —

0.1-2.0 0.1-2.0 0.1-2.0

Brightness variation (mag) 9.5 4.1 9.9 7.5 7.8 9.6 9.2 2.0

TW CMa S Cep W Vir RX Cep V395 Cyg CO Cyg TZ Cas o Cet

7.4 9.0 3.3

4.9 3.0

S Set a C Vn

12.3 6.94 10.6 10.2

VW UMa Z Aqr AFCyg /J Cep UU Her V756 Oph RR Lyr SX UMa EP Lyr AC Her RSge /3Cep 8.4 9.5 7.4 3.6 8.5

max

Brightness'") (mag)

Typical representative

5.19 p 3.1 p

9.1 p 12.0 p 9.4 p 5.1 v 10.6 p 13.7 p 8.03 p 11.2 p 11.6 p 9.2 p 11.2 p 3.35 p

11.0 p 5.2 p 11.3 p 7.8 v 8.4 v 10.6 v 10.5 v 10.1 v

min

0.194 5.47

0.567 0.307 83.43 75.46 70.594 0.190

— — —

136.9 94.1

125

331.62

— — — —

6.99 5.37 17.29

(d)

Period

Ell

E EA EB EW

UV Z

RW UG

RCB

N Na Nb Nc Nd Ne SN

—

R Coronae Borealis variables RW Aurigae variables U Geminorum varibales (SS Cygni variables) UV Ceti variables Z Camelopardalis variables Eclipsing variables Algol variables /3 Lyrae variables W Ursae Majoris variables Ellipsoid variables

Novae Recurrent novae Nova-like variables Supernovae

Novae Novae Novae

Subclass

— —

—

— —

< 2.0

0.8

1-6 2-5

2-6

1-9

20

—

7-16 7-16 7-16 7-16 7-16

Brightness variation (mag) — — — — — — —

1

— —

0.2-10 000 >1

—

—

10-40

20-600

—

10-100

(d)

Period

5.8 9.6 8.9 7.0 —

RW Aur U Gem UV Cet

2.2 3.4 8.3 4.6 5.5

b Per V389 Cyg

10.2

2.0 3.0 -6

10.6

QX Cas /3 Per /3Lyr W UMa

—

-1.1

V603 Aql RR Pic RT Ser T GrB PCyg CM Tau (SN 1054 Crab Nebula) R CrB 1.2

—

max

Brightness^) (mag)

—

Typical representative

(°) P = photographic, V = visual. (Adapted from Roth, G.D., ed., Handbuch fur Sternfreunde, springer-Verlag, 1967.)

Unclassifiable variables

Eclipsing variables

Main class Eruptive variables

The classification of variable stars (cont.)

4.66 p 5.69 p

10.6 p 3.47 v 4.34 9.03 p

12.9 v —

13.6 p 14.0 v

14.8 v

10.8 p 12.8 p 16 p 10.8 v 6v 15.9 p

—

min

—

1.527

2.867 12.908 0.334

—

— —

— 103

—

— —

29000

(d) — — — —

Period

a

CO

fcr

o

w-

g

S

O

o

oo

CD

99

Stars

Position of various classes of variable stars in the H-R diagram. (Adapted from Roth, G.D., Compendium of Practical Astronomy, SpringerVerlag, 1994.)

RV Tauri stars Semiregular variables \

\

V Long-period \variables \ 1


100

Representative

Name CTA 1 Tycho HB 3 HB 9 OA 184 VRO 42.05.01 S 147 Crab IC 443 Monoceros Puppis Vela MSH 10-53 RCW 86 RCW 89 RCW 103 Kes 45 Kepler W28

3C 400.2 DR4

Cygnus Cas A CTB 1

galactic supernova

remnants

Galactic coordinates ln,bn

OL

1950

8 1950

Radio size

119P53 120.09 132.70 160.39 166.07 166.27 180.33 184.55 189.01 205.62 260.40 263.37 284.17 315.44 320.36 332.43 342.05 004.52 006.46 053.62 078.13 074.27 111.73 116.94

00 h 04 rr 00 22 33 02 14 04 57 05 15 38 05 23 21 05 36 45 05 31 31 06 14 06 06 35 08 20 30 08 32 10 15 40 14 39 08 15 09 30 16 13 54 16 50 11 17 27 41 17 57 36 19 36 30 20 20 38 20 49 30 23 21 10 23 56 45

+72°04(5 +63 51.8 +62 18 +46 36 +41 46 +43 00 +27 44.5 +21 58.9 +22 37.2 +06 30 - 4 2 50 - 4 5 00 - 5 8 40.5 - 6 2 15 - 5 8 46 - 5 0 55.8 - 4 3 30.3 - 2 1 26.6 - 2 3 25 + 17 08 +40 03.4 +30 45 +58 32.4 +62 10

90' 8' 140' 130' 70' 70' 175' 290" 47' 210' 45' 300' 33' 55' 8': 7' 30' 3' 30' 20' < 3' 160' 4' 35':

+9?77 +1.41 +1.30 +2.75 +4.40 +2.53 -1.68 -5.78 +3.02 -0.10 -3.42 -3.01 -1.78 -2.33 -0.97 -0.39 +0.13 +6.82 -0.09 -2.23 +1.81 -8.49 -2.13 +0.18

Optical size 50' X90' 8'

X155' x90' x75' x420" X54' X65'

90' 70' 35' 195 290'

X125' x80' X40' X200' x420" 48' 180' X200' 50' X80' 270'

I'x5' 8' x3l' 450" X580" 5'.7x9'.5 ••• X20' 21" x64"

x50'

30'

4' x6' 2' x3' X240' X45':

160' X210' 4' 32'

denotes approximate value. (Adapted from van den Bergh et ah, Ap. J. Supply 26, 19, 1973.) See http://www.mrao.cam.ac.uk/surveys/ for a complete catalog of SNRs. Typical super novae light curves

V * CD

4

Type I

\

Typell-P

•

E '

Typell-L 50

100

ISO

200

2S0

300

350

400

Days (after minumum light)

(Adapted from Doggett, J. and Branch, D., Astron. J., 90, 2303, 1985.)

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; TiO bands developing strongly

O B A F G K M

la Ib II III IV V VI VII

Supergiants Supergiants Bright giants Giants Subgiants Main sequence (dwarfs) Subdwarfs White dwarfs

Luminosity class

a Boo (Arcturus) a CMi (Procyon) (3 Gem (Pollux) a Lyr (Vega) a UMi (polaris) a CMa (Sirius) a Cyg (Deneb) a Leo (Regulus) P Ori (Rigel) Sun

Examples: K2III F5 IV KOIII AO V F8Ib Al V A2 la B7 V B8Ia G2 V

Spectral type

Spectral type and luminosity class (MK, or Yerke's classification)

Class characteristics

Class

Henry Draper (HD) spectral classification Spectral type and luminosity class of the MK classification; dependence on color index B—V and visual absolute magnitude Mv. (Adapted from Unsoeld, A., The New Cosmos, Springer-Verlag, 1969.)


102

Hertzsprung-Russell diagram Hertzsprung-Russell or temperature luminosity diagram. (Adapted from Goldberg, L. & Dyer, E. R. in Science in Space, L. V. Berkner & H. Odishaw, eds., McGraw-Hill Book Company, 1961.) SPECTRAL TYPE

Su pergiants - 10 000

Somewhat aaea mom sequences

Population I Population I I Zero-age main sequence - 0.0001

+15 20

15

12

10 9 8 7

6

5

4

3

SURFACE TEMPERATURE (thousands of K)

Stars

103

Hertzsprung-Russell diagram with stellar examples. (From Kaler, J.B., Stars and their Spectra, Cambridge University Press, 1989, with permission.) O5

BO

-10-

AO

FO

GO

• ICyg 12

KO

P Cas

MO

M8

RWCep

^ ^ — - - — H R T O ta-0 ^ ^X"*^^^ -5-

-

-

• 6Aur

3etelgeuse

RCBr

-69° 202 Canopus

la

Antares

:•;:'./£

lOri c\^vv ^ ^ v/ii u \ ^îp CMa

£ Peg ;

:

• «A Vel •Polaris' •';/ RVTau 9Lyr

ii^-ii

•••:•'•]'f£;-^-: RegulusVV» $ Car

0-

ot UMa .

• • ^ • RRLyr

)J

aran

^'ra *

-

Capella Arcturus^/; ^ / \ ^—r-Tpniinv = ^ And Pollux :; V SBOO •

Fomalhaut « V Mv

Alde

1 PV ^

• TTau

0 Pic* 7 VirA,B

5-

^ n 3 Ori

V •——

N.

jcen

pcorn^ Cas N^g

E

ri £lnd

\

\

VI 10-

• HZ 21 ^ s ^ ^ ^ GD 358 • S ^ : ^ SiriusB*

\«nCasB \

\«BD-20°4123

\

Y» Wolf 630 A.B

40EriB3iv EG 159 • • >v Procyon B V G140-2 • * ^ S .

Kruger 6o(\

• G134-22

15-

\ Barnards

. Jr

LP658-2* L D7m O Q . uVCet • 1U w X U M a P701-29* J«Wolf359 VB8M VB10V

05

BO

AO

FO

MO

M8

104


An incomplete list of astrophysically important infrared and visible spectral features Identification

Wavelength (A)

Identification

He I CI Si I Si I Si I Si I Hell Hell Nal C III OI Hell OI He I Hla [0 1] [OI] Na I (D) Na I (D) He I Hell FeXIV Mgl Mgl [O III] [O III] He I HI/3 Hell C IV

10 830 10 691 10 689 10 627 10 603 10 371 10124 10120 9961 9710 8446 8237 7774 7065 6563 6363 (a) 6300 5896 5890 5876 5412 5303 5175 20°, 5 < m < 30 for zero obscuration, Am = 0, has been derived by Bahcall & Soniera (Ap. J. Supply 44, 73, 1980). (For non-zero obscuration, replace m by m — Am, where Ara v = 0.15 esc b and = 0.20 esc 6.) The units of A are stars mag deg and TV are stars -2

deg

1

D(l,b,m) = [1 + ioa(m-m*)] Md

i

with ^ = 2.55 X10"3, M* = + 2.20, Afb = — 6, Afd = + 19, a = 0.60,/3 = 0.05, 1/5 = 2.30 -8

-6

-4

-2

10

>

•5 s " v ^

-4

o

3 S1

7 1

s

s

i-J

3.

" S

90 80 70 60 50 40 30 20 £ 10 o

3. 1

li:

3 S1

=3.

r

•~1

S

—2 S ( ^

\

/

-50 / 5s ^ \ -60 \ \ -70 / / —-* -80 > 10s io r~" -90; !4 23 22 21 20 18 17 16 15 14 13 12 11 10 9 RIGHT ASCENSION (hr) ^

—

/

u ^^—^—

2

\

\

s

—o =^ -2

3.1 1.5 J 240

19''21"'22?3 +14°25'15" 19''21"'24?4 +14°24'43"

0.4... 0.5 0.071 0.024

0.5

15 46

-16°13'24" 220 -16°10'30" 280 -16°ll'3O" 190 11 19

2O''37"'13?7 20h37"'14?0 20 h 37'"14fl 20''37"'14?2

+42°08'55" +42°09'03" +42°08'54" +42°O9'15"

23''ll"'30?3 23''ll"'20?8 23 h ll'"36f7 23 h ll'"36f7

+61°12'56" 110 +61°13'45" 10 +61°12'00" 12 +61°ll'5O" 1.0

(From Physics of the Galaxy and Interstellar Springer-Verlag, 1987, with permission.)

Distance Linear diameter [kpc] [pc]

5.7 4.0 7.1 4.2

0.6

1 J '

0.10 0.32

1 >2.1 I

2.3 2.9 2.0

1 J '

0.4 0.7

| I | ' I

0.083 0.058 0.101 0.062

-> l2g | ' >

1.4 0.12 0.15 0.013

Matter, Scheffler, H. & Elsaesser, H.,

Compact HII regions (which are also observed as infrared sources) Compact components

Extended object W3

Radio source A1-A5 C

M42 M8 M17 W51 W75

NGC 7538 = S 158

W3 (OH) G209.0-19.4 A1-A4 S N G49.5-0.4d c DR21D B C

IR source IRS 1 IRS 4 IRS 8 IRe 1 IRe 1 IRe 2a IRS 2 IRS 1 DR21N IRS 2 IRS 1

*(20 (im)

*(20 //.m) (6 c m )

L IR

[1 ]

[Jy] 2 X 10 3 3 X 10 3 2 X 10 2 1.4 X 10 5 1.3 X 10 3 5 X 10 4 3 X 10 4 1.5 X 10 3 2

1 X 10 7 X 10 2 2 x 10 2

70 500 300 500 30

220 1 140 J 140 1 50 500 1 1700 J

3 X 105 -

2 X 105 4 X 105 5 X 104 5 X 106 5 X 106

6

X

3

X 1U

104

1 n4

The nieasured radiation flux at the earth at A = 20 //in and A = 6 cm {y = 5 GHz) are denoted by $(20 /Jin) and $(6 cm), respectively, -^TR is the total infrared luminosity of the source in units of solar luminosity LQ = 4 X 10" W. 1 jansky (Jy) = 10 W i n " 2 Hz" 1 . (From Physics of the Galaxy and Interstellar Springer-Verlag, 1987, "with permission.)

Matter, Scheffler, H. & Elsaesser, H.,

196

Radio astronomy

Compact HII regions (physical parameters) Object

E

(Nif

u

[K] [pccm" 6 ] [cm"3] [pccm~ 8400 10000 M42 8200 8000 NGC2237-46 8000 M20 8000 M8 M17, main source (S) 7700 8000 M16 7300 W51, main source W75, DR21 A B I 8400 C D NGC7538A1 A2 > / yuu B C 7000 NGC 7000 W3, A1-A5 W3(OH)

J J

2xlO 7 lxlO9 6xlO 6 3xl04 5xlO 4 4xlO 5 5xlO 6 4xlO 5 5xlO 7 5xlO 7 5xlO 7 9xlO 7 4xlO 7 8xlO 5 2xlO 6 7xlO 6 lxlO7 4xlO 3

6xlO 3 2xlO 5 5xlO 3 20 2

lxlO 6xlO 2 2xlO 3 2xlO 2 8xlO 2 2xlO 4 3xlO 4 3xlO 4 3xlO 4 lxlO3 4xlO 3 6xlO 3 lxlO5 10

83 54 55 80 50 64 170 120 190 36 27 49 27 60 14 26 12 100

Le

TW(HII)

s-1]

Me]

4xl049 3 x 1048 7xlO 4 8 2 x 1049 5 x 1048 1 x 1049 2xlO 5 0 7xl049 3xlO 5 0 2 x 1048 7xl047 4xl048 7xl047 8 x 1048 1 x 1047 7xl047 7xlO 4 6 4xl049

10 0.1 10

lxlO4 2xlO 2 2xlO 2 10 2

7xlO 2 10 2 0.2 0.1 0.4 0.1 33 0.1 0.3

0.002 2xlO 4

Mean electron temperature Te, emission measure E, root mean square electron density (N'i) , excitation parameter u, total number of Lyman continuum photons per s Lc and total mass of ionised hydrogen .M(HII) for a selection of HII regions. (From Physics of the Galaxy and Interstellar Matter, Schemer, H. & Elsaesser, H., Springer-Verlag, 1987, with permission)

Radio spectra

197

Radio spectra Spectra of typical radio sources. (Adapted from Kraus, J.D., Radio Astronomy, McGraw-Hill Co., 1966.) WAVELENGTH 1m 10 cm

10 m

100

1,000 FREQUENCY (MHz)

1 cm

10,000

1.633 4.497

405 MHz... 10.7 GHz

405 MHz... 10.7 GHz

GHz

405 MHz... 15

405 MHz... 15

405 MHz... 15

405 MHz... 10.7 GHz

405 MHz... 10.7 GHz

GHz

405 MHz... 15

7 GHz... 31

10 GHz... 31

3C161

3C218

3C227

3 C 249.1

3C286

3C295

3C348

3C353

DR21

NGC 7027

GHz

GHz

GHz

GHz

1.766

GHz

405 MHz... 15

3C147

1.32

1.81

2.944

4.963

1.485

1.480

1.230

3.460

±0.025

2.921

GHz

405 MHz... 15

3C123

±0.08

±0.05

±0.031

±0.045

±0.013

±0.018

±0.027

±0.055

±0.038

±0.016

±0.017

±0.030

2.345

GHz

a

405 MHz... 15

Frequency interval

3C48

Source

-0.127

-0.122

-0.034

-1.052

±0.759

±0.292

±0.288

-0.827

-0.910

±0.498

±0.012

±0.010

±0.001

±0.014

±0.009

±0.006

±0.007

±0.016

±0.011

±0.008

±0.006

±0.0001

-0.002 ±0.447

±0.001

±0.071

b

-

-

-0.109

-

-0.255

-0.124

-0.176

-

-

±0.001

±0.001

±0.001

±0.003

-

-

-

±0.001

±0.001

±0.001

±0.001

-0.194

-0.184

-0.124

-0.138

c

Spectral parameters log S[Jy] = a + b •logz/ [MHz] + c • log2 v [MHz]

Radio flux calibrators (a) Spectral parameters of telescope calibrators

T o a o S

CO

a,

93

S3

oo

CD

47 04 30 31 11 51 20 39 07

9 11 12 13 14 16 17 20 21

3C227 3 C 249.1 3C274 3C286 3C295 3C348 3C353 DR21 NGC 7027^

3C48 3C123 3C147 3C161 3C218

46.4 11.5 49.6 08.284 20.7 08.3 29.5 01.2 01.6

41.299 04.4 36.127 10.0 06.0

37 37 42 27 18

1 4 5 6 9

Source

position,

a [hms]

(b) Characteristics,

+ 7 +76 +12 +30 +52 + 4 - 0 +42 +42

+33 +29 +49 - 5 -12 -29 -12 + 10 - 8 +25

35.41 15 07.23 07 45 12 01 21 32.94 09 26 52 45 10

09 40 51 53 05 25 59 23 30 12 59 58 19 14 - 3

+ 1

+42 +39 +74 +81 +61 +29

bH [°]

20.3 6.1 625.0 25.1 54.1 168.1 131.1 -

39.4 119.2 48.2 41.2 134.6

5400 [Jy]

of telescope

6 ["" ']

and flux densities

12.1 4.0 365.0 19.7 36.3 86.8 88.2 -

25.6 77.7 33.9 28.9 76.0

[Jy]

5750

7.21 2.48 214 14.8 22.3 45.0 57.3 1.35

15.9 48.7 22.4 19.0 43.1

[Jy]

6.25 2.14 184 13.6 19.2 37.5 50.5 1.65

13.9 42.4 19.8 16.8 36.8

[Jy]

5l665

(3r2000.0)

5i400

calibrators

4.19 1.40 122 10.5 12.2 22.6 35.0 3.5

9.20 28.5 13.6 11.4 23.7

52700 [Jy]

2.52 0.77 71.9 7.30 6.36 11.8 21.2 5.7

5.24 16.5 7.98 6.62 13.5

55000 [Jy]

CD CD

93

Icr

fch

5'

Pi

[Jy]

[Jy] 3.31 10.6 5.10 4.18 8.81

1.71 0.47 48.1 5.38 3.65 7.19 14.2 21.6 -

3C227 3 C 249.1 3C274 3C286 3C295 3C348 3C353 DR21 NGC 7027(d) 1.02 0.23 28.1 3.44 1.61 20.0 6.16

[Jy] 1.72 5.63 2.65 2.14 -

5l5 000

0.73 20.0 2.55 0.92 19.0 5.86

[Jy] 1.11 3.71 1.71 -

522 235

GAL QSS GAL QSS GAL GAL GAL HII PN

s s s c~ c~ s c~

Th Th

c~ c~ s

C~ C~

Ident. QSS GAL QSS GAL GAL

Spec.

1 11 0.1 8 5 < 1

7 -

< 1 20 < 1 0.2 keV) (erg cm" 2 s" 1 )

740 220

1-5 x 1032

1.2 x 1038

2 x 10

37

L(X)max (2-11 keV) (erg s" 1 )

White dwarf

Sirius

Capella

Flare star

Dwarf nova (U Gem) Sub-dwarf

Blackhole candidate HDE 226868 IR/radio

Remarks

Flux density = (integrated 2 - 1 1 keV flux)/9keV; 1 /ijy = 0.242 x 1 0 ~ n erg cm" 2 s" 1 keV" 1 = 1.51 x 10~ 3 keV cm" 2 s" 1 keV" 1 . (Adapted from Bradt, H. V., Doxsey, R. E. and Jernigan, J. G., COSPAR Symposium on X-ray Astronomy, Innsbruck, Austria, May 31, 1978).

13 14 00 29 22 00

HZ 43

(a)

6 42 54 - 1 6 39 00

5 12 59.5 45 56 58

a CMa

a Aur

1 36 24 - 1 8 13 00

21 40 42.6 43 21 51

SS Cygni

UVCet

430 90

20 30 37.6 40 47 13

Cyg X - 3

20 5

260

1320

19 56 28.9 35 03 55.0

Cyg X - 1

Source

1950 S 1950

Of

Flux density (a) (2-11 keV) max (/iJy) min (fiJy)

Representative galactic sources: binaries and stars (cont.)

95

KTi e-t

J2 D

CO

CD

5

O

CD

a

o

a & Si

Pulsar

0 55 1

-30 -2 -32 10

12

14

-4

LOG FREQUENCY (Hz) -6

-

4

2 0 2 4 6 LOG PHOTON ENERGY (eV)

10

uu Q X 3

X-ray emission from a selection of low mass globular clusters

267

X-ray emission from a selection of low mass globular clusters Cluster NGC 6624 NGC 6441 Liller 1 Terzan 1 M15* Terzan 2 NGC 6712 NGC 1851 NGC 6440 NGC 5824 M79 M3 NGC 6541 ui Cen M22

Distance (kpc) 8.0 11.7 10.0 10.6 9.7 10.0 6.2 12.0 8.5 23.5 13.0 10.4 7.0 5.2 3.1

Log Lx (erg s" 1 ) 38.0 36.8 36.8 36.8 36.7 36.7 36.4 36.1 Transient 34.3 33.9 33.6 33.3 32.6-32.9 32.0-32.6

radiuscore (arcsec) 5 8 4 6 6 6 49 6 8 4 16 29 34 144 114

*M15 (NGC 7078) consists of two sources. Note: 1 kpc = 3.262 x 103 light years = 3.086 x 1019 m. The core radius, radiuscore, is defined to be the radius at which the surface brightness has dropped to half the central value. (Adapted from Exploring the X-ray Universe, Charles, P.A. and Seward, F.D., Cambridge University Press, 1995.) For a catalog of galactic globular clusters see Harris, W.E. 1996, AJ, 112, 1487 or http://www.physics.mcmaster.ca/Globular.html

X-ray emission from a selection of normal galaxies Galaxy NGC 507 NGC 720 NGC 4382 NGC 4472 M31 NGC 253 M81 M82

Type SO E SO E/S0 Sb Sc Sb Irr

Distance (Mpc) 98 32 28 28 0.68 3.1 3.4 3.4

Lx 0.2-4 keV (erg s" 1 ) 1.1 x 10 43 2.2 x 10 41 5.2 x 1040 1.1 x 1042 3.6 x 1039 7.4 x 1039 1.3 x 1040 3.5 x 1040

Note: Distance calculated from redshift for Ho = 50 km s" 1 Mpc- 1 , q0 = 0.5. 1 Mpc = 3.262 x 106 light years = 3.086 x 1022 m. (Adapted from Cosmic X-ray Sources, Seward, F., in Allen's Astro-physical Quantities, Cox, A.N., Ed., Springer, 2000.)

268

X-ray astronomy

The brightest X-ray emitting clusters of galaxies Cluster

a, 6 (2000)

Redshift Distance kT* 2-10 keV z (Mpc)

Lx (erg"1)

A426 (Perseus) 0318.6+4130 0.0183 110 £L3 1.4 x 1045 Ophiuchus 170 9-11 2 .5 x 10 45 Cluster 1712.4-23 22 0.028 43 2.4 3 X 10 M87 (Virgo) 12 30.8+12 23 0.0037 22 44 140 8.1 9 X 10 A1656 (Coma) 1259.8+2758 0.0235 Centaurus 64 10 6 X 10 43 Cluster 12 48.8-4119 0.0107 180 4.5 3 X 10 44 A2199 16 28.6+3931 0.0305 190 3.9 3 X 10 44 A496 0433.6-1314 0.0316 310 6.2 8 X 10 44 A85 00 41.6-09 20 0.0518 Note: Distance calculated from redshift for Ho = 50 km s"1 Mpc" 1 , q0 = 0.5. 1 Mpc = 3.262 x 106 light years = 3.086 x 1022 m. *kT is the cluster gas temperature in keV (Jones, C. and Forman, W., Ap. J., 511, 65, 1999.) (Adapted from Cosmic X-ray Sources, Seward, F., in Allen's Astrophysical Quantities, Cox, A.N., Ed., Springer, 2000.) X-ray properties of rich clusters (clusters with hundreds to thousands of galaxies) Lx (2-10 keV) ~ (10 42 - 5 -10 45 )/i- 2 erg s" 1 , kT ~ 2-14 keV, cluster core radius .Rc(X-ray) ~ (0.1-0.3)/!- 1 Mpc, ne ~ 3 x lO" 3 /! 1 / 2 cm" 3 , M g o s ( < 1.5ft"1 Mpc) ~ 10 13 - 5 M solar [range: (10 13 -10 14 )/i- 2 - 5 M solar ]

X-ray emission from a selection of active galaxies

269

X-ray emission from a selection of active galaxies Name

Redshift z

MRK348 NGC1068 Q0420-388 3C120 M81 NGC4151 3C273 M87 3C279 Cen A NGC5548 E1821+643 NGC6814 PKS 2155-304

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

Distance L x 0.2-4 keV (Mpc) (erg s" 1 ) 1 x 10 43 83 9 x 10 41 22 2 x 1046 24600 2 x 1044 200 5 x 1039 3.6 4 x 1042 20 6 x 1045 980 3 x 10 43 22 6 x 1045 3400 5 x 10 41 4.8 4 x 10 41 10 7 x 1045 1900 4 x 1042 30 2 x 1046 1100

Type

Seyfert 2 Seyfert 2 High redshift quasar VLBI radio galaxy Low luminosity AGN Seyfert 1.5 Radio loud quasar Radio galaxy Blazar Radio galaxy Seyfert 1 Radio quiet quasar Seyfert 1 BL Lac

Note: Distance calculated from redshift for Ho = 50 km s" 1 Mpc" 1 , q0 = 0.5. 1 Mpc = 3.262 x 106 light years = 3.086 x 1022 m. (Adapted from Cosmic X-ray Sources, Seward, F., in Allen's Astro-physical Quantities, Cox, A.N., Ed., Springer, 2000.)

X-ray astronomy

270 3C 273

The observed electromagnetic spectrum of the quasar 3C273 (3C273 is variable). (From Worrall, D. M. et. al, Ap. J., 232, 683, 1979.) -20

3C273

-25

i

fv oc ^"0.9

Distance: ^ z = 0.158; 1000 Mpc for /y o =50kms" 1 Mpc"1

N

-30

O

for log v 10 to 18

m v : 12.9-12.2 M v : -27.2 to-27.9 Av(absorption): 0.0 Coordinates: a = 12h 26m 33s (1950.0) 5 = 02°19 m 42 s

\

^

X-ray spectrum (2-60 keV, June-July, 1978): d/V ^ = 0.016 E"141photons cm"2 s"1 keV"1 -35 -

21

nH < 2.5 X 10 atoms cm"

\

\

2

X-ray luminosity (2-10 keV, June-July, 1978): L=1X

-40

10

15

LOG v (Hz)

20

\

\

\

Quasar X-ray luminosity

271

Quasar X-ray luminosity Quasar X-ray luminosity (0.5-4.5 keV) versus redshift. (Courtesy H. Tananbaum, Harvard/Smithsonian Center for Astrophysics, 1982.) 0537-286 47

•

3C446

10"

1548 +114 b

0420-388

82 .225+31 T IE 1227 + 0224 • 0938 + 119 2357-348 f

lio

46

• 3C263 3C279B"

3C47

CO

f a t •3C298*

IE 0438-1638 •

3C208

o

4C 10.43 PHL 891

DC >
27) leads to line emission with a mean energy of ( +kTe/2, hv = mec2 < +3fcTe/4,

{ +kTe,

Te < 107 K, 107 < Te < 1010 K,

Te > 10 10 K,

where mec2 = 510.9991 keV and Te is the temperature of the electrons and positrons. Nuclear de-excitation and radioactive decay See next page

299

Gamma-ray lines Gamma-ray lines Nucleosynthetic radioactive decay gamma-ray lines. Process

Half-life

Line Energy (keV)

|f Co + v

6.1 d

158.4 811.9

V e+ + v |f Co + e~ —y leFe + v

77 d

846.8 1238.8

sr C o + e -

272 d

122.1

2.6 y

1274.5 511.0

56 M

22AT xliNd

+

e

-

_ ^

^

22AT

FG

~h Z^

.

> 10iNe

•f e + + ^

| | Ti + e - —y |fSc + 1/ 2 2

~ 60 y

| A 1 ^ ?°Mg ••f e+ + ^ |A1 + e~ —y 2 |Mg + 1/

7.1 x 105 y

1- e~ + V

1.5 x 106 y 5.3 y

eo Co —> eo N i _

67.9 78.4 1808.7 511.0 1332.5 1173.2

(From Gehrels, N. and Paul, J., The New Gamma-ray Astronomy, in Physics Today, February, 1998.)

Gamma-ray

300

astronomy

Gamma-ray line features Observed gamma-ray line features. (From von Ballmoos, P. in TEV Gamma-ray Astrophysics, Voelk, H.J. and Aharonian, F.A., eds., Kluwer Academic Publishers, 1996.) Physical Process

Energy

Source

[keV] Nuclear de-excitation Fe (p, p', 7 ) 24 Mg (p, p', 7) 20 Ne (p, p', 7 ) 28 Si (p, p', 7) 12 C(p, p',7) 56

16

O (p, p', 7)

Radioactive decay Co(EC,7) 56 Fe

56

57

57

Co(EC,7) Fe Ti(EC) 44 Sc(/3+ 7 ) 26 Al(/3+ 7 ) 26 Mg 44

e e + Annihilation

Neutron Capture ^(71,7)^

56

Fe(n,7) 57 Fe

Cyclotron Lines * Redshifted line

847 1369 1634 1779 4439 4439 6129 6129

Flux

ph cm- 2 s- 1

Solar flares Solar flares Solar flares Solar flares Solar flares Orion Comp. Solar flares Orion Comp.

^ m.<j iM»f ....^

10 10 10" 1012 1013 1 0 U 1019 1 0 * 1017 1 0 * 1 0 " 1 0 M 1021

Energy (eV)

316

Cosmic rays

Vertical fluxes The vertical fluxes of different components of cosmic rays in the atmosphere. (From Hillas, A.M., Cosmic Rays, Pergamon Press, 1972.)

Hard Component Soft Component

0

muons E>.22 protons > 3 neutrons > 3 pions electrons >.O1 muons .027-22 protons .4-3 GEV

200 400 600 800 1000 Depth in atmosphere (g cm2)

317

Cutoff rigidity

Cutoff rigidity The Earth's magnetic field affects the penetration of charged particles in the vicinity of the Earth. The minimum rigidity (cutoff rigidity) necessary to reach some geomagnetic latitude A and geocentric radius R is given by: pc _ M cos4 A ze R? [(1 + cos# cos3 A) 1 / 2 + I ] 2 ' where M is the Earth's dipole moment, ( — ) is the magnetic rigidity of the particle; for charge z = 1 it is

\ze)

numerically equal, when expressed in volts, to the momentum in units

of ev/c, —2" ] « 60 x 109 volts, where i?o is the radius of the Earth, 9 is the angle between the direction of arrival of the particle and the tangent to the circle of latitude. (9 = 0 corresponds to arrival from the west for positive particles; 6 = 0 corresponds to arrival from the east for negative particles.)

Cosmic rays

318

Conversion from magnetic rigidity to kinetic energy per nucleon for electrons, protons and alpha particles. (From Smart, D.F. & Shea, M.A., in Handbook of Geophysics and the Space Environment, Jursa, A.S., ed., Air Force Geophysics Laboratory, 1985.)

O.I

1.0

RIGIDITY (109 volts)

10

K)1 100

Particle production in the atmosphere

319

Particle production in the atmosphere Schematic representation of the development of particle production in the atmosphere. (Adapted from Simpson et al, Phys. Rev., 90, 934, 1953.) Incident primary particle

Top of Atmosphere

Low energy nucleonic component (Disintegration product neutrons degenerate to 'slow' neutrons)

electronphoton component

hadron component

Sea Level N, P = high energy nucleons n, p = disintegration product nucleons -il

= nuclear disintegration

Cosmic rays

320

Gamma-ray production in the atmosphere Schematic diagram of gamma-ray production processes in the atmosphere. Neutrinos are ignored. (From Allkofer, O. C. & Grieder, P. K. F., Cosmic Rays on Earth, Physik Daten, ISSN 0344-8401, 1984.) TYPICAL ENERGY

PROCESS

A XV \ ^ P

ATMOSPHERIC NUCLEI

t ° DECAY

J

0.5Me V /^ I R

XCOMPTON

y

e"

>3GeV FRAGMENTS

200 MeV

\ +

ICOLLISIONSl

A\

50 MeV 16 L

* V

MULTIPLE COMPTON SCATTER PHOTOELECTRIC ABSORPTION

10 MeV

/NUCLEAR H RAYS 1 MeV 25KeV

Atmospheric depth

321

Atmospheric depth Relation between atmospheric depth and altitude for an isothermal atmosphere. (From Allkofer, O. C. & Grieder, P. K. F., Cosmic Rays on Earth, Physik Daten, ISSN 0344-8401, 1984.) 1000 'E u

500

en

LU Q

O LU

8 5

10

15

20 25 30

ALTITUDE(km) Relation between zenith angle and atmospheric depth at sea level in an isothermal atmosphere. (From Allkofer, O. C. & Grieder, P. K. F. Cosmic Rays on Earth, Physik Daten, ISSN 0344-8401, 1984.) 10s

CL Q 10A U

cr

UJ

x o 20°

40°

60°

ZENITH ANGLE 9

80°

Cosmic rays

322

Pressure and atmospheric thickness Relations between altitude and pressure, and altitude and depth in the real atmosphere. (After Cole, A. E. & Kantor, A. J., Air Force Reference Atmosphere, AFGL-TR-78-0051, 1978.)

103 1

84

-

72

-

10

1

I11"" ' ' 1

' I

102

id2 io3

id1 '

1

1

|IIMI|

1

/

-

60

-

34 MeV

LLJ U_

O

o

DC

u_

LU O

1/2

> 1

3H2 > ^--A

a %

k=0

Flat (Euclidean)

1/2

1

pc =

fc = - 1

Open

0 < g0 < ! / 2

0 < O0 < !

0. sinh(:r) = sin(x) for Qk < 0. For flk = 0, only the integral is evaluated. The three distances are related by: d,L = (1 + z)2dA = (1 + z)dM

360

Relativity and cosmology

The angular diameter distance (in units of the Hubble distance) for five cosmological models. Model A B C D E

"tot

1 0.1 1 0.01 1

I 0.1 0.1 0.01 0.01

0 0 0.9 0 0.99

~

10

Cosmology

361

Measurements of the Hubble constant HQ HQ in km s" 1 Mpc - l

100 50 57 ±3 100 ± 10 95 ± 4 95 ± 1 50 ± 7 85 ± 10 57 ± 1 67 ±8 87 ± 10 76 ±9 47 ± 7 86 ± 1 90 ± 10 87 ± 7 69 ± 8 55 ± 7 67 ± 7 58 ± 4 70 ± 7 64 + 8-6

Reference Baade, W. and Swope, H.H., Astron. J., 60, 151, 1955 Sandage, A., in Nuclei of Galaxies, North Holland, 1971 Sandage, A. and Tammann, G.A., Ap. J., 196, 313, 1975 De Vaucouleurs, G. and Bollinger, G., Ap. J., 233, 433, 1979 Aaronson, M., et al, Ap. J., 239, 12, 1980 De Vaucouleurs, G., Nature, 299, 303, 1982 Sandage, A. and Tammann, G.A., Nature, 307, 326, 1984 Pierce, M.J. and Tolly, R.B., Ap. J., 330, 579, 1988 Kraan-Kortweg, et a/., Ap. J., 331, 620, 1988 Van den Bergh, S., Astron. Ap. Rev., 1, 111, 1989 Tully, R.B., Astrophys. Ages and dating methods, Editiones Frontieres, 1990 Van den Bergh, S., P.A.S.P., 104, 861, 1992 Sandage, A. and Tammann, G.A., Ap. J., 415, 1, 1993 De Vaucouleurs, G., Ap. J., 415, 10, 1993 Tully, R.B., Proc. Nat. Acad. Sci., 90, 4806, 1993 Pierce, M.J., et a/., Nature, 371, 385, 1994 Tanvir, N.R., et a/., Nature, 377, 27, 1995 Sandage, A. and Tammann, G.A., Ap. J., 446, 1, 1995 Riess, A.G., Press, W.H., and Kirshner, R.P., Ap. J. (L), 438, L17, 1995 Sandage, A. et a/., Ap. J. (L), 460, L15, 1996 Freedman, W., American Astronomical Society Meeting 194, #39.0, 1999 Jha, S., Ap. J. Supp., 125, 73, 1999

(List to 1996 taken from Lang, K.R., Astrophysical Formulae, v. II, Springer-Verlag, 1999.)

fln. ol

Atomic physics

Wavelength of the more prominent L group lines (Angstrom) Siegbahn Sommerfeld transition 16 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 38 39

40 41 42 44 45 46 47 48 49 50 51 52 53 55 56 57 58 59 60 62 63

«2

Qfl

a'

Of

Lm -1Miv

illl - My

S Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Rb Sr Y

Zr Nb Mo Ru Rh Pd Ag Cd In Sn Sb Te I Cs Ba La Ce Pr Nd Sm Eu

36.27 31.37 27.37 24.31 21.53 19.40 17.57 15.93 14.53 13.306 12.229 11.27 10.415 9.652 8.972 8.358 7.3027 6.8486 6.4357

6.057 5.718 5.401 4.8437 4.5956 4.3666 4.1538 3.9564 3.7724 3.60151 3.4408 3.2910 3.1509 2.8956 2.7790 2.6689 2.5651 2.4676 2.3756 2.2057 2.1273

5.7120 5.3950 4.8357 4.5878 4.3585 4.1456 3.9478 3.7637 3.59257 3.4318 3.2820 3.1417 2.8861 2.7696 2.6597 2.5560 2.4577 2.3653 2.1950 2.1163

Ln - My

I e Lm

21.19 19.04 17.23 15.63 14.25 13.027 11.960 11.01 10.153 9.395 8.718 8.109

40.90 35.71 31.33 27.70 23.84 22.34 20.09 18.25 16.66 15.26 13.97 12.89 11.922 11.048 10.272 9.564

Pi

P

6.610 6.2039

5.8236 5.4803 5.1665 4.6110 4.3640 4.1373 3.9266 3.7301 3.5478 3.3779 3.2184 3.0700 2.9309 2.6778 2.5622 2.4533 2.3510 2.2539 2.1622 1.9936 1.9163

V V

- Mi Lu — Mi 83.75

23.28 19.76 17.86 16.28 14.87 13.61 12.56 11.587 10.711 9.939 9.235

7.822 P'l 7 Lm - Ny 5.5742 5.2260 4.9100 4.3619 4.1221 3.9007 3.6938 3.5064 3.3312 3.1686:L 3.0166 2.8761 2.7461 2.5064 2.3993 2.2980 2.2041 2.1148 2.0314 1.8781 1.8082

7.506 7.0310 7 6

Lm - Ny 5.3738 5.0248 4.1728 3.9357 3.7164 3.5149 3.3280 3.1553 2.99494 2.8451 2.7065 2.5775 2.3425 2.2366 2.1372 2.0443 1.9568 1.8738 1.7231 1.6543

Wavelength of the more prominent L group lines (Angstrom)

383

Wavelength of the more prominent L group lines (cont.) Siegbahn Sommerfeld transition

a2 a'

ax

Lin — Mj\r

Liu - My

64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 90 91 92

2.0526 1.9823 1.9156 1.8521 1.79202 1.7339 1.67942 1.6270 1.57704 1.52978 1.48438 1.4410 1.39866 1.3598 1.32155 1.28502 1.24951 1.21626 1.18408 1.15301 0.96585 0.9427 0.92062

2.0419 1.9715 1.9046 1.8410 1.78068 1.7228 1.66844 1.61617 1.56607 1.51885 1.47336 1.42997 1.38859 1.34847 1.31033 1.27377 1.23863 1.20493 1.17258 1.14150 0.95405 0.9309 0.90874

Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir

Pt Au Hg Tl Pb Bi Th Pa U

a

(From Smithsonian Physical Tables)

fh

I

P

E

Lu - My

Liu - Mi

1.8425 1.7727 1.7066 1.6435 1.58409 1.5268 1.4725 1.42067 1.3711 1.32423 1.27917 1.23603 1.19490 1.15540 1.11758 1.08128 1.04652 1.01299 0.98083 0.95002 0.76356 0.7407 0.71851

1.7419 1.6790 1.6198 1.5637 1.51094 1.4602 1.41261 1.36731 1.3235 1.28190 1.24203 1.2041 1.16884 1.13297 1.09974 1.06801 1.03770 1.00822 0.98083 0.95324 0.79192 0.7721 0.75307

V V

Lu - Mi 1.5886 1.5266 1.4697 1.4142 1.3611 1.3127 1.26512 1.21974 1.1765 1.13558 1.09630 1.0587 1.02296 0.98876 0.95599 0.92461 0.8946 0.86571 0.83801 0.81143 0.65176 0.6325 0.61359

384

Atomic physics

Main bound-bound electromagnetic transitions Transitions

Energy

Spectral region

Example

[eV]

Hyperfine structure

10

Radiofrequencies

21 cm hydrogen line

Spin-orbit coupling

10~ 5

Radiofrequencies

Molecular rotation

10~ 2 -10~ 4 Millimetric, infrared

1666 MHz transitions of OH molecule 1-0 transition of CO molecule at 2.6 mm H2 lines near 2/im

Molecular rotation1—10 vibration Atomic fine structure 1—10~^ Electronic transitions 10—10 of atoms, molecules and ions 10-104

Infrared Infrared Ultraviolet, visible, infrared Ultraviolet, X-ray

Ne II line at 12.8 fim Lyman, Balmer, etc. series of H, resonance lines of CI, Hel K,L shell electron lines

(Adapted from Lena, P., Observational Astrophysics, Springer-Verlag, 1986.) Bibliography Atomic, Molecular, & Optical Physics Handbook, Drake, G.W.F., ed., American Institute of Physics, 1996. Atomic Energy Levels, Moore, C.E., NBS Circular 467, US Government Printing Office. An Ultraviolet Multiplet Table, Moore, C.E., NBS Circular 488, US Government Printing Office. N o t e : Links to WWW resources which supplement the material in this chapter can be found at: http://www.astrohandbook.com

Chapter 12

Electromagnetic radiation And God said: c

V B=0

VxE+

1 r)R

c dt And there was light. - Unknown

c at

=0

Radiation by a point charge Blackbody radiation Planck functions Radiation curves Synchrotron radiation Single electron in a magnetic General distribution of electrons Power law distribution of electrons Cerenkov radiation Compton scattering Compton shift Energy of scattered photon Energy of struck electron Relation between the scattering angles Klein-Nishina cross-section Klein-Nishina differential cross-sections Inverse Compton scattering Total energy loss rate Spectra Hot plasma emission Bremsstrahlung from a hot plasma Non-thermal bremsstrahlung X-ray line emission from a hot plasma

field

387 388 388 389 390 390 391 391 392 393 393 393 393 393 394 396 396 396 397 398 398 398 398

386

Electromagnetic radiation

Radiative recombination radiation Maxwell's equations Conversion table Standard definitions in radiative transport theory Electromagnetic relations Maxwell's equations in various systems of units Spectrum nomogram Bibliography

399 399 400 401 402 403 404 404

Radiation by a point charge (cgs units)

387

Radiation by a point charge (cgs units) The Lienard- Wiechert potentials for a point charge e: =e A(x,t) = e

1 KR

A KR

The square bracket with subscript ret means that the quantity in brackets is to be evaluated at the retarded time, t' = t — [R(t')/c]. K = 1 — n • (3, where cf3 is the instantaneous velocity of the particle, and n = R/R is a unit vector directed from the position of the charge to the observation point. The electric field and magnetic fields: =e

B =n x E Total power radiated: P=\ o c-

/3) 2

where 7 = (1 — [32)~ll2, the Lorentz factor. If the charge is observed in a reference frame where its velocity is small compared to that of light,

388

Electromagnetic

Blackbody radiation (cgs units) Planck functions (brightness of a blackbody)

BAT) = ^ T> frn\

£>il>C

J-

- £ — — erg cm

B\(T) = —T— A

(exP ( w ) " l)

_o

_1

s

_1

cm sr

_1

2 3 i> 2hc2i>

v

kT I

Bv(T)dv

erg c m ^ s" 1 Hz" 1 s r ^

I

?

= Bx{T)d\

=

Rayleigh-Jeans law hv/kT « 1 BV(T) = 2 (-) kT Wien's law hv/kT » 1

Stefan-Boltzmann law /•OO

total emittance = -K I Jo 5 4 where a =

Bv(T)dv

= oT4 erg

2ir k

r—- = 5.67 x 10~ 5 erg cm" 2 deg~ 4 s^ 1 \bclh6

Wien displacement law Maximizing Bv: 10

Maximizing By.

z/m = 5.9 x 10 T Hz

i/m = 10.3 x 10 10 T Hz

Am = 0.51T" 1 cm

Am = 0.29T" 1 cm

radiation

389

Blackbody radiation (cgs units) Mean photon energy (M

_ /,v

1 volt m" 1 1 volt

1/3 x 10" 4 statvolt cm" 1 1/300 statvolt

Polarization

p

1 coul m~

3 x 10 statcoulombs cm"

Displacement

D

1 coul m

12TT x 105 statvolt cm" 1

Conductivity

a

1 mho m~

9 x 109 s" 1

Magnetic induction B

3 x 10 statcoulombs cm"

1 weber in"

10 gauss 1

Magnetic field

H

1 ampere-turn m" 4TT x 10" 3 oersted

Magnetization

M

1 weber in"

1/4TT x 10 gauss

(Adapted from Classical Electrodynamics, Jackson, J. D., John Wiley and Sons, 1962.)

Standard definitions in radiative transport theory

401

Standard definitions in radiative transport theory Quantity Symbol Specific intensity or radiance /„ Brightness

Units (cgs) erg cm" 2 s" 1 Hz" 1 sr" 1 erg cm" 2 s" 1 Hz" 1 sr" 1

Flux density

Bv = — /„ r Fv = / I^cosOd^l

erg cm~ 2 s^ 1 1A.TT1

Mean intensity

J^ = — / i^dfi

erg cm" 2 s" 1 Hz" 1

4TT J

uv = - / /^dO = —•/„ erg cm" 3 Hz" 1 c7 c Emission coefRcient j v erg cm" 3 s" 1 Hz" 1 sr" 1 4?r Emissivity e^ = —j v erg gm" 1 s" 1 Hz" 1 P (isotropic emission, p = density) Radiation density

Linear absorption coefiicient

av = n<jv (n = number density, av = cross-section)

cm" 1

Mean free path

lv = — av

cm

Optical depth

TV = / avds

dimensionless

f

J

Electromagnetic radiation

402

Electromagnetic relations Quantity Conversion factors: Charge: Potential: Magnetic field: Lorentz force: Maxwell equations:

Rationalized mks (SI)

Gaussian cgs

2.99792458 X 109 esu = 1 C = 1 A s = 1 V = 1 J C" 1 (1/299.792458) statvolt (ergs/esu) 10 4 gauss = 10 dyne/esu

= 1 T = 1 N A"1 m- 1

/ v V c V • D = 47rp

F = g(E + v x B)

\ '

F

c dt

c

V •B = 0

V x EH Constitutive relations: Linear media: Permitivity of free space: Permeability of free space: Fields from potentials:

Static potentials: (Coulomb gauge)

1 ^^ 1 /" 7dl

r - r: 7dl 4TT / r - r' 4TT

Relativistic transformations: (v is the velocity of the primed frame as seen in the unprimed frame)

EM

— En

EM

= En

E'±=7(E±H—vxBj

E'± = 7(Ej_ + v X B)

B

B

||

=B

II

||

=B

II 1

= c2 x 1(T 7 N A" 2 = 8.987 5 5 . . . x 109 m F " 1 ; 4TT

= 2.997 924 58 x 10s m s- l

(From Caso, C, et al., European Physical Journal, C3, 1, 1998)

4TT

X 10"

4TTM

D =E+P H=B -M

D = E + 4TTP H = B 4TTM

H = B

D = ( 1 / C 2 ) E + 4TTP

H = c 2 B - 4TTM

D = E + 4?rP

D,H

V x H = 4TTJ H

V X H = 4TTJ •

Qt

d~D

~dt

V-D

=

V D=p VxH

= dt

VxEH

V x E H

c dt

=0

=0 1 *r !

1

c y

0.1b 0.2'^

y

c '

10.0 fc .2 = O < if) 10

0.3 .0.4

- ^ -——

-

"f .-

Cs 1 3 7 -

—

•

-

;

To60 ,. -

—

__

I G AMMA-RAY ENERGY(MeV) 30

\

^ :

i

1

20

•

— •

1

3- 10

8.0 1

-

'

^0.6 0.8 1 0 2.0J 1.5=

i

:

j

=

\

\ *-Tota attenu 3tl n o

-7

.^

3

LOcN

v-

-r

:. l^^L

ft If

-='

a )sorptionâ/^b -

errr

- Tc ta

i~

3 6"

SODIUM IODIDE

ft

-

Mass attenuation coefficients for sodium iodide. The 'Compton total' attenuation coefficient ajp — o~a/p-\-as/p is shown explicity. (From Evans, R.D., op. cit.)

10'

PHOTON ENERGY (MeV)

p = 5.86 X 10' 3 g cm"3 at STP

Mass attenuation coefficient for photons in xenon. (Adapted from Chupp, E.L., Gamma-Ray Astronomy, D. Reidel Publishing Co., Dordrecht, 1976, with permission.) Attenuation of electromagnetic radiation 429

\

3

' r

\ \

\ —\

IC - 2

10-3

I0"

2

io-

1

JO

V

\

\

f>

*—

I

9.0) v L

j

4

" 1

A

10 I 10 PHOTON ENERGY (MeV)

- c

c

Iod de

3 p--= 4.51g =

vertical angle,

j

current (mA),

=

R = radius of ring (m). Photon flux integrated over all vertical angles

photons s" 1 mrad" 1 A" 1 , |

dedOdt

( ) ]

photons s" 1 mrad" 1 eV" 1 , for A > Ac d \ d 0 d t ' " • " " " "

V

[ ( ) ] photons s^ 1 mrad^ 1 A^ 1 .

V. Kostroun (Nuc. Inst. Meth., 172, 371, 1980) provides series expressions for the modified Bessel functions of fractional order which are suitable for evaluation with programmable calculators or desktop computers.

X-ray spectroscopy

459

X-ray spectroscopy Crystal spectroscopy Collimated single crystal Bragg spectrometer. Bragg condition: nX = 2ds'm6, where d is the effective spacing of the crystal planes that participate in the reflection. (Adapted from Burek, A., Space Sci. Inst., 2, 53, 1976.) Ci> ROTATION L A X I S CRYSTAL BRAGG ANGLE 0 B

DETECTOR

OPTICAL AXIS'

X-RAYS

Single crystal rocking curve C\ • #B + A = sin 1(nX/2doo), where A = refraction correction, doo = physical spacing of reflection planes, and #B = Bragg angle ignoring refraction. (Adapted from Burek, A., Space Sci. Inst, 2, 53, 1976.) /?„ = INTEGRATED REFLECTIVITY i.o

///o

PEAK REFLECTIVITY,

Experimental astronomy and astrophysics

460

Crystal

properties

Crystal

Density (g cm" 3 )

Quartz

2.66

Topaz

3.49-3.57

Calcite Silicon

2.710 2.33

Germanium

5.33

Beryl (golden) Sylvite Halite Fluorite

2.66 1.99 2.164 2.756 3.18

Aluminum

2.699

LiF

2.64

Graphite Mica Clinochlore

2.21 2.77-2.88 2.6-3.3 1.803

KBr

ADP EDDT

PET SHA KAP RAP T1AP CsAP NH 4 AP NaAP

1.538 1.39 1.3

1.636 1.94 2.7

2.178 1.415 1.504

Plane 1010 1011 2023 2243 303 040 400 200 211 111 220 200 111 220 200

1010 200 200 200 111 200 200 111 420 200 220 002 002 001 101 220 200 020 002 110 001 001 001 001 002 002

2d(A) 8.350 6.592 2.750 2.028 2.712 4.40 2.3246 4.64 6.083 6.284 3.840 5.44169 6.545 4.000 5.66897 15.9549 6.292 5.641 6.584 6.306 5.4744 4.057 4.676 1.80 4.027 2.848 6.708 19.84 28.392 10.648 5.305 7.50 8.808 8.742 13.98 26.5790 26.121 25.7567 25.68 26.14 26.42

Integrated reflectivity (0 = 60°) 6.25 x 10~ 5 (D) 1.23 x 10~ 4 (D) w l . 5 x HT 5 (D) « 6 x 10" 6 (D) (40°) 6 x 10" 5 (D) (43°) 1 x 10" 5 (D) 1.62 x 10~ 4 (D) 1.2 x 10~ 4 (D) 8 x 10~ 5 (D) 2.3 x 10" 4 (D) « 6 x 10" 5 (D)

10~ 4 -3 x 1 0 " 4 ( D ) 1.52 x 10~ 3 (S) w 2 x 10" 5 (S) 9.0 x 10" 5 (S) 1.4 x 10~ 5 (S) 1.15 x 10~ 4 (S) 2.2 x 10" 4 (S) 5 x 10~ 5 (S) 1.5 x 10" 4 (S) 7.0 x 10~ 4 (S) 1.5 x 10~ 4 (S)

D = double crystal; S = single crystal. (Adapted from Burek, A., Space Sci. Inst., 2, 53, 1976.)

X-ray spectroscopy

461

Useful characteristic lines for X-ray spectroscopy Wavelength(A)

Energy(keV)

Element

Designation

1.54 1.66 1.94 2.29 2.75 3.60 4.15 5.41 6.86 7.13 8.34 8.99 9.89 10.44 12.25 13.34 14.56 15.97 17.59 18.32 19.45 21.64 23.62 27.42 31.36 31.60 44.7 58.4 64.38 67.6 82.1 114

8.04 7.47 6.40 5.41 4.51 3.44 2.98 2.29 1.80 1.74 1.49 1.38 1.25 1.19 1.01 0.930 0.852 0.776 0.705 0.677 0.637 0.573 0.525 0.452 0.395 0.392 0.277 0.212 0.193 0.183 0.151 0.109

Cu Ni Fe Cr Ti Sn Ag Mo Sr Si Al Se Mg Ge Zn Cu Ni Co Fe F Mn Cr 0 Ti Ti N C

Kaly2 Kaly2 Ka\2 Ka\2 Ka1;2

w Mo B Zr Be

i«l,2 i«l,2 £"1,2 £«1,2

Ka1;2 Ka1;2 £«1,2

Ka1;2 £«1,2 La\ 2 £«1,2 £«1,2 £"1,2 £«1,2

Ka £«1,2 £"1,2

Ka £«1,2

LI Ka Ka

NyNyn MC, Ka M( Ka

Concave grating spectroscopy Concave grating equation: ±mA = d(sin a + sin /3), where m is the spectral order, d is the groove separation, a is the angle of incidence, and fi is the angle of diffraction. The negative sign applies when the spectrum lies between the central image (a = (3) and the tangent to the grating (sometimes referred to as the 'outside order'). When the spectrum lies between the incident beam and the central image, the positive sign must be used, and the spectrum is referred to as the 'inside order'. The signs of a and /3 are opposite when they lie on different sides of the grating normal.


462

Angular dispersion (a fixed): d(5 m dX d cos (3

Plate factor: dX

d cos (3

mR

dX

'

dl

cos/3 mR(l/d)

i o 4 l mm - l

where R is in meters, 1/d is the number of lines mm" 1 , and / is the distance along the Rowland circle. Grating (radius R)

Plate holder-

Optical layout of basic spectograph.

500 1000 1500 2000 A

Grazing incidence spectrograph.

(Adapted from Samson, J., Techniques of Vacuum Ultraviolet Spectroscopy; John Wiley and Sons, 1967.)

X-ray spectroscopy

463

Transmission grating spectroscopy Principle of the X-ray transmission grating, m is the diffraction order.

m = +2 transmision grating period = p m = +1

mX = p sin (6)

m =0 m = -1

incoming radiation wavelength = X

m = -2

An example partial spectrum (binary star Capella) produced by the Chandra X-ray Observatory's Low Energy Transmission Grating Spectrometer (LETGS). The spectral resolving power is > 1000 in the wavelength range 50-160 A. o o

XVI V XVI

iZ O i l 1 }

2

Si

XVI

X

XV

XV

•

o

=

1

—^Ju_ 10

1

iZ

(From Brinkman et a/., 2000, ApJ, 530, Llll)

•

•

1

JMUJ

40 wavelength

p

i ''

i

wavelength (A)

*

15

•

L

464


Reflection of X-rays vacuum reflected ray

boundary

n* (Hen* c = 1 — 6, c « y/(28)

Since (3^0,

for

S < 1.

reflection is not total for <j> < cf>c but is less than 1.

Away from an absorption edge, 6 « 2.70 x 10- 6 f ^ \

p (g cm- 3 )A 2 (A)

where Ze is the number of electrons associated with wavelengths greater than A. Ze = Z for A < Ak (K edge).


466

Calculated spectral reflectivity of an ideal surface as a function of normalized grazing angle (j>/(j>c for various values of /3/6. (After Hendrick, JOSA, 47, 165, 1957.)

>

LLJ CC

0.03

0.1 0.2 0.4 0.6 0.8 1.0 NORMALIZED ANGLE OF GRAZING INCIDENCE (0/0c)

Reflection of X-rays

467

Reflectivity vs. wavelength (energy) for various grazing angles and materials (Courtesy of M. Hettrick, Lawrence Berkeley Laboratory, Berkeley, CA.) Whenever possible, direct measurements should be made of grazing incidence reflectivity in the X-ray region because of uncertainties in the optical constants and the density of the material.

ATOMIC NUMBER KEY BOILING 30 65.37 POINT, °C 906 419.57 n MELTING* - • • POINT, ° C / I ZINCDENSITY

ATOMIC WEIGHT •SYMBOL NAME

7.14 1

(g cm" 3 )

Nickel

10"

101

10°

102

10 3

ENERGY (eV) I

105

104

I

11 i } i i

103

i

i

i

111 i i i i

102

i

o

WAVELENGTH (A)

i

11 i i i i i

10 4


468

Rhodium

icr 1

10°

io 1

10 2

10 3

ENERGY (eV) 105

104

103

102

o

101

WAVELENGTH (A) Ruthenium

10

10°

101

102

ENERGY (eV) 105

104

103

i

j

i

I n i i i

102

WAVELENGTH (A)

103

104


469

Tungsten

>

0.8

^

0.6

H

I-

o

74 183.85

LL

5930 3410 3410 19.3

y 0.4 LLJ

\l\l

WOLFRAM

ir °-2 10~1

I

I I M i l l

1

I

I I I I1 1

10 1

10°

10 2

10 3

104

ENERGY (eV) 111 I I i I I

105

i

111 i i i i i

104

i

111 I i i I i

103

I

111 i i i i i

102

i

LLL

WAVELENGTH (A) Rhenium

10

10°

101

10 2

ENERGY (eV) 105

104

103

102

WAVELENGTH (A)

10 3

10 4


470

Iridium

1.0

^

-

i l l

I I 1111

I

1 i j i Lj^1

|»

'

' I 1 I i ji

0.8

>o.e o

sJjK

LJJ _ j 0.4 LL " ~ LU CC 0.2 I

| r • *

\\ H \>

IRIDIUM

V

A7

_

-

30

\ °\

V\ \ \ \v\

1 1 1 1 1 1 ll

10,-1

1 I 1 I 1 J__

\

90°\

1

1

0.5°

/ v5° N ^ IA/

77 192.2 5300 2454 22.5

\r-—-

1

1 1 Mill 1

10°

10 2

10

\

_

10 3

104

103

104

ENERGY (eV) 105

104

103

10 2

WAVELENGTH (A) Osmium

10" 1

101

10°

102

ENERGY (eV) I in i i i i

10

5

i

Ini i i i i

10

4

i

h 11i i i i

10

3

t

In i i i i i

10

2

WAVELENGTH (A)

i

h11 l i i i

101


471

Platinum

1.0 0.8

i= o

ULJ I

06 0.4

LJJ

CC 0.2

78 195.09

~

4530

^

1769 P + 21.4 1 L PLATINUM

I

30

K

\\ U V^

\

-

\\

A \

101

10°

101-1

— A\lXl :

\ V

—k

\ I

\\ 8 \\ \ \°

\

I \

\ \\

\

10 3

104

10 3

104

10 2

ENERGY (eV) 104

105

103

102

WAVELENGTH (A) Gold

1.0

i

>" 0.8

O Jj 0.4 LJ_ LU

7 9 196.967 2970

1063 19.3

CC 0.2

Au

GOLD

10~1

10°

101

10 2

ENERGY (eV) 105

104

103

102

WAVELENGTH (A)


472

Reflectivity versus wavelength for various materials and grazing angles. (Adapted from Giacconi, R. et al., Space Science Review, 9, 3, 1969.) ENERGY (keV) 10

>

5

1.0

0.5

0.01

o

LLJ

0.01 WAVELENGTH (A)

Reflection of X-rays Photoabsorption nickel

473

cross sections and atomic scattering

factors

Edge Energies Nickel (Ni) K 8332.8 eV Lx 1008.6 eV Ml 110.8 eV Z = 28 L n 870.0 eV M n 68.0 eV Atomic Weight = 58.693 L m 852.7 eV M m 66.2 eV /xa (barns/atom) = ^(cm 2 /gm) x 97.46 E(keV)^(cm2/gm) = f2 X 716.92 ft*

I

f

10

100

/

I1 •L

s

f 10

10000

1000

> s

100

1000

10000

100

1000

10000

E(eV) (From Henke, B.L., Gullikson, E.M., Davis, J.C., Atomic Data and Nuclear Data Tables, 54, 240, 1993, with permission.)


474 Photoabsorption gold

cross sections and atomic scattering

Gold (Au) Li Z = 79 Atomic = 196.967 Ln weight Lin

Edge Energies 3424.9 eV N i 14352.8 eV M i 13733.6 eV M I I 3147.8 eV N I I 11918.7 eV Mm 2743.0 eV N i n M i v 2291.1 eV N i v M v 2205.7 eV N v

762.1 642.7 546.3 353.2 335.1 87.6 Nvi 83.9 NVII

fxa(barns/atom) = ^(cm 2 /gm) X 327.08 E(keV)//(cm2/gm) = f2 X 213.63

r 10

too •-T

K)00

/

/

10

Oi On Oni

107.2 e V 74.2 e V 57.2 e V

Y •"•/] 10000

1

\

\

9

eV eV eV eV eV eV eV

factors-

•Tti li

i!

X>0

100

1000

10000

1000

XXXX)

E(eV) (From Henke, B.L., Gullikson, E.M., Davis, J.C., Atomic Data and Nuclear Data Tables, 54, 291, 1993, with permission.)


475

Wolter type I mirror

system

- FOCAL SURFACE

The equations for a paraboloid and hyperboloid which are concentric and confocal can be written as: r2 = P2 + 2PZ + [Ae2Pd/(e2 - 1)] (paraboloid), 2 2 r*^ — o^

(hyperboloid), = e {d + Z)2 - Z2 where d is the distance from the system focus to the generating hyperbola's directrix, e is the eccentricity of this hyperbola, and P is the distance from the focus of the generating parabola to its directrix. The origin is at the focus for axial rays, Z is the coordinate along the axis of symmetry, and r is the radius of the surface at Z. RMS blur circle radius: (j —

and

10

tana

+ 4 tan 0 tan2 a radians

(a* and a£ are the grazing angles between the two surfaces and the path of an axial ray that strikes at an infinitesimal distance from the intersection). For most telescope designs: £ = 1. a = — tan- 1 / 4 0 = angle between incident rays and optical axis. Geometrical collecting area: A « 27rroLp tana. Effective collecting area: Ae(a,E) « AR2(a,E) « 8irZ0LpR2(a,E)a2, where R is the Fresnel reflectivity at energy E and mean grazing angle a. (Adapted from Van Speybroeck, L. & Chase, R., AP. Opt, 11, 440, 1972.)

476


Vacuum technology Vacuum nomograph. (Adapted from Roth, A., Vacuum Technology, North-Holland Pub. Co., 1976.) -Low

•+-—High—»f*

Ultra-high vacuum

Medium

10 l 8 --10 2 2

10-410-2•p 100102« 104-

-10-6 -10-4 -10-2 -100

-102 — 1 min - 1 0 min - 1 hr -10 4 - 1 0 hr 108- 1 day -106 - 1 week — 1 month 1010- 1 year -108 106-

106--1010 o

Air25°C

I

1Q4--1Q8 4

102-^106

|

i

10 102 ,' .'—r1100

Pressure (N rrT2)

100

10-2 10-4

10-2 10-4

10-6

10-8 10-10^

10-6 10-8 10-10 10-12 10-14

PRESSURE (Torr)

Pumping speed of an aperture of area A: ^-

= A(cm2)v/[1.32 x 10 7 T (K)/mol.wt] cm 3 s" 1 .

Kinetic theory of gases Mean free path, A = l/y/27rna2 viscosity, rj = pvX/3 heat conductivity, K = r]cve, mean speed, v = V[2.1 x 10 8 T (K)/mol.wt] cm s" 1 , where n = number of molecules cm" 3 , p = gas density in g cm" 3 , a = mol. diameter, cv = specific heat capacity at constant volume, e = 2.5 and 1.9 for monoatomic and diatomic gas, respectively.

477

Vacuum technology Rate at which molecules strike a surface: v = nu a /4 where n = the number density of molecules va = the average molecular velocity

v = 3.513 x 1022P(MT)-^2

cm"2 s"1

where P = pressure in Torr M = molecular weight T = temperature in K Mass of gas incident on unit area per unit time G = 5.833 x 1 0 - 2 P ( M T ) 1 / 2 g cm" 2 s" 1 where P, M and T are defined above. Time to form a monolayer: On the assumption that the molecular spacing is that of a close-packed (face-centered) lattice, the number of molecules per unit area to form a monomolecular layer is given by 7VS = 1.154O-2 where 3 cd m-2)

Scotopic V(A) (BOX 1Q- 5 cd m"- 2 )

0.00004 0.00012

0.0003 0.0008 0.0022 0.0055 0.0127

0.0004 0.0012 0.0040 0.0116 0.023

0.0270 0.0530 0.0950 0.157 0.239

0.038 0.060 0.091 0.139 0.208

0.339 0.456 0.576 0.713 0.842

0.323 0.503 0.710 0.862 0.954 0.995 0.995 0.952 0.870 0.757

0.948 0.999 0.953 0.849 0.697 0.531 0.365 0.243 0.155 0.0942

0.631 0.503 0.381 0.265 0.175

0.0561 0.0324 0.0188 0.0105 0.0058

0.107 0.061 0.032 0.017 0.0082

0.0032 0.0017 0.0009 0.0005 0.0002

0.0041 0.0021 0.00105 0.00052 0.00025 0.00012 0.00006 0.00003

0.0001

Photometry

489

K(X), spectral luminous efficacy for scotopic and photopic vision. Scotopic: max K = K (511 nm) = 1746 lm W" 1 . Photopic: max K = K (555 nm) = 680 In W" 1 2 SCOTOPIC-v^

I0

8 D

4

i

-

1

1

?

8 I 6

-

4

7i

2

O

c

E

/

I

A

t \

1 \

/ /

/ /

/

i

8 £

-

\

\

\ \

\ \

/

00

c/) O

i

3

/

•'

\

\ I \%\ t \ \ 1

2

i '

1

300

II

/ ( II 1 400 500 600 WAVELENGTH (nm)

\ \

\

i

11

J

700


490

Summary of typical sources/parameters monly used radiant energy sources

Lamp type Mercury short arc (high pressure) Xenon short arc

Xenon short

DC input power (watts)

Arc Luminous dimensions flux (mm) (lm)'

for the most com-

Luminous Average efficiency luminance (lm W~ ) (cd mm~ )

200

2.5 x 1.8

9500

150

1.3 x 1.0 12.£i x 6

3200 21 1 150 000 57

20 000

47.5

arc

Zirconium arc 100 Vortex-stabilized argon arc 24 800 Tungsten 1 light < 100 bulbs [ 1000 Fluorescent lamp standard 40 warm white Carbon arc, non-rotating 2000 15 800 rotating Deuterium 40 lamp

1.5 (diam.) 3 x 10 — —

—

250

2.5

250 300 3000 (in 3 mm x6 mm) 100

422 000 79 1630 21500

17

21.5 J

1400 10 to 25

2560

64

—

7.9 ] 16.3 >

36 800 18.4 1 175 to w5x 5 350 000 22.2 J 800 «8 x 8 1.0 (diam.) (Nominal irradiance at 250 nm at 2 30 cm = 0. 2n W cm" inn"1)

'Luminous flux $ in lumens from a source of total radiant power W(X) watts per unit wavelength:

$ = 680 / W(X)V(X)dX. Jo where V(X) represents the spectral luminous efficiency. Conversion table for various photometric

units

Luminous intensity (I) 1 candela (cd) = 1 lumen/steradian (lm sr^1) Luminous flux ($) [lumen (lm)] 4TT lumens = total flux from uniform point source of 1 candela Illuminance (E) 1 footcandle (fc) = 1 lumen foot"2 1 lux (lx) = 1 lumen m~2 = 0.0929 footcandle

491

Photometry Luminance (L) 1 footlambert (£L) = 1/TT candela foot" 2 . 1 nit (nt) = 1 candela m - 2 = 0.2919 footlambert

Luminance

values for various

sources Luminance Luminance (fL) (cd m " 2 )

Source Sun, as observed from Earth's surface at meridian Moon, bright spot, as observed from Earth's surface Clear blue sky Lightning flash Atomic fission bomb, 0.1 ms after firing, 90-ft diameter ball Tungsten filament lamp, gas-filled, 16 lm W~ Plain carbon arc, positive crater Fluorescent lamp, T-12 bulb, cool white, 430 mA, medium loading Colour television screen, average brightness

Typical values of natural scene

4.7 x 108 730 730 2300 2 x 10 10

1.6 x 109 2500 7900 7 x 10 10

6 x 10 11 2.6 x 106 4.7 x 106

2 x 10 12 9 x 106 1.6 x 10 7

2000 50

7000 170

illuminance

Sky condition

Approximate levels of illuminance (lux)

Direct sunlight Full daylight (not direct sunlight) Overcast day Very dark day Twilight Deep twilight Full moon Quarter moon Moonless, clear night sky Moonless, overcast night sky

1-1.3 x IO5 1-2 x 104 IO3 IO2 10 1 10" 1 10~2 IO- 3 1Q-4


492

Natural illuminance on the Earth for the hours immediately before and after sunset with a clear sky and no moon 10 6 10 5 —

—

•

,

10 4 10 3

J 102

\

\

LJJ \

\ \

10" 10": 10

V

"-4 ^3 ^ 2 ^T 0 1 2 3 HOURS BEFORE AND AFTER SUNSET

Radiant responsivity Calculation of radiant responsivity from lumminous responsivity for photocathodes: The response of a photocathode (in amperes) to the total radiation W(X) watts per unit wavelength is: aR(X)W(X)dX, where the relative spectral response of the photocathode is R(X) (i? max = 1) and a is the absolute radiant response at the peak of the response curve (amperes per watt). The light flus (in lumens) is given by: 680

fv(X)W(X)dX.

where V(X) is the spectral luminous efficiency. The luminous responsivity of the photocathode in amperes per lumen is then given by: ajR(X)W(X)dX D — 680 JV(X)W(X)dX and, therefore, _ 6S0SjV(X)W(X)dX a = jR(X)W(X)dX ' (The material in the preceding sections was adapted from Engstrom, R. W., Photomultiplier Handbook, RCA Corporation, 1980.)

a (av,ae) p (pVlpe) T(rj/,T e ) Q w (wv)

Luminous energy (quantity of light)

Luminous density Luminous flux

e

'watt per square meter, etc. Wm ^watt per steradian Wsr" watt per steradian and square centimeter Wsr c m " 'watt per steradian and square meter Wsr m~ one (numeric) —

E = d$/dA

E (Ee) / (/e) L (Le)

-3

= //

760

J3 J380 w = dQ/dV * = dQ/dt

a= p=

K(\)Qe\d\

/ L = d2 $/'du(dA cosfi) = dl/(dAcosO)(e) e = M/Mblackbody^)

lm-h lm-s lm-sm"'' lm

one (numeric) one (numeric) one (numeric) lumen-hour ^lumen-second (talbot) ' lumen-second per cubic meter 'lumen

Wcm~

erg cm ergs^ 1 W

watt per square centimeter

$ = dQ/dt M = d$/dA

J kWh

Symbol

quantities

M (M e )

Emissivity PHOTOMETRIC Absorptance Reflectance Transmittance

Radiant flux density at a surface Radiant exitance (radiant emittance)'™) Irradiance Radiant intensity Radiance

$ (<J>e)

Radiant

flux

w (we)

Radiant density

c Commonly used units' )

and radiometric

w =dQ/dV

Q (Qe)

RADIOMETRIC Radiant energy

Denning equation' '

photometric

erg 'joule kilowatt-hour 'joule per cubic meter erg per cubic centimeter erg per second twatt

Symbol' 0 '

Quantity(a)

Standard units, symbols, and defining equations for fundamental

to

01

o S

lumen per square foot footcandle (lumen per square foot) 'lux (lm m~ 2 ) phot (lm c m " ) 'candela (lumen per steradian) candela per unit area stilb (cd c m " 2 ) nit (t c d m~ 2 ) footlambert (cd per TV ft ) lambert (cd per 7r cm 2 ) apostilb (cd per TT m ) lumen watt" one (numeric)

M = d$/dA E = d^/dA

M (Mu) E (Eu)

/ (/jy) L (Lu)

K V

Luminous intensity (candlepower) Luminance (photometric brightness)

Luminous efficacy Luminous efficiency '

fc lx ph cd cd in~ 2 , etc. sb nt fL L asb lm W -

lm ft

Symbol

CD

a r e

{1'UJ is the solid angle through which flux from point source is radiated. {Photoelectronic Imaging Devices, Vol. 1, L.M. Biberman & S. Nudelman, eds., Plenum Press, 1971, with permission.)

^ 'iCmax is the maximum value of the K(X) function.

flux.

respectively, radiant exitance of a nieasured specinien and of a blackbody at the same temperature as the specimen.

w / $ i is the incident flux, $ a is absorbed flux, 4?r is reflected flux, ^ t is transmitted

{•> ' M and Mbiaekbody

^
ga

g

( rf )To be deprecated.

^-'International System (SI) unit indicated by dagger (f)

*> -'The equations in this column are given merely for identification.

l a /The symbols for photometric quantities are the same as those for the corresponding radiometric quantities. When it is necessary to differentiate them, the subscripts v and e, respectively should be used, e.g., Qu and Qc- Quantities may be restricted to a narrow "wavelength band by adding the word spectral and indicating the wavelength. The corresponding symbols are changed by adding a subscript A, e.g., Q\ for a spectral concentration or a A in parentheses, e.g., K(\), for a function of wavelength.

K = $^/$e V = K/Kmax^

/ = d^/dcu^1' L = d?Q/dco(dA cos 9) = dl/(dA cos 6)(e)

Commonly used u n i t s ^

Defining equation^

Symbol'0'-'

Quantity^ Luminous flux density at a surface Luminous exitance (luminous emittance)^ > Illumination (illuminance)

Standard units, symbols, and defining equations for fundamental photometric and radiometric quantities (cont.)

Photometry

495

Commercial lasers Wavelength

Type

Wavelength (cm)

(H 0.152 0.192 0.2-0.35 0.235-0.3 0.248 0.266 0.275-0.306 0.308 0.32-1.0 0.325 0.33-0.38 0.337 0.35-0.47 0.351 0.355 0.36-0.4 0.37-1.0 0.442 0.45-0.52 0.51 0.523 0.532 0.5435 0.578 0.594 0.612 0.628 0.6328

Molecular fluorine (F2) ArF excimer Doubled dye Tripled Ti-sapphire KrF excimer Quadrupled Nd Argon-ion XeCl excimer Pulsed dye He-Cd Neon Nitrogen Doubled Ti-sapphire XeF excimer Tripled Nd Doubled alexandrite CWdye He-Cd Ar-ion Copper vapor Doubled Nd-YLF Doubled Nd-YAG He-Ne Copper vapor He-Ne He-Ne Gold vapor He-Ne

0.635-0.66 0.647 0.67 0.68-1.13 0.694 0.72-0.8 0.75-0.9 0.98 1.047 or 1.053 1.061 1.064 1.15 1.2-1.6 1.313 1.32 1.4-1.6 1.523 1.54 1.54 1.75-2.5 2.3-3.3 2.6-3.0 3.3-29 3.39 3.6-4.0 5-6

9-11 40-100

Type InGaAlP diode Krypton ion GalnP diode Ti-sapphire Ruby Alexandrite GaAlAs diode InGaAs diode Nd-YLF Nd-glass Nd-YAG He-Ne InGaAsP diode Nd-YLF Nd-YAG Color center He-Ne Erbium-glass (bulk) Erbium-fiber (amplifier) Cobalt-MgF 2 Color center HF chemical Lead-salt diode He-Ne DF chemical Carbon monoxide Carbon dioxide Far-infrared gas

(From The Laser Guidebook, 2nd ed., Hecht, J., McGraw-Hill, 1991.)

Index of refraction of air The following formula gives the index of refraction of dry air at 15°C and a pressure of 101.325 kPa (1 atmos.; 760 Torr) and containing 0.03% by volume of carbon dioxide ("standard air"). The index of refraction is defined as n = A vac /A a i r , where A is the wavelength of the radiation. (n - 1) x 108 = 8342.13 + 2406030(130 - a2)'1 + 15997(38.9 - a 2 ) " 1 where a = 1/Avac and Avac has unit of /tm. The equation is valid for Avac from 200 nm to 2 /tm. If the air is at a temperature t in °C and a pressure p in pascals, a value of (n — 1) should be multiplied by - t) x 10~10] 96095.4(1 + 0.003661t)


496

Properties of optical materials Material

Useful Transmission Range Index of Refraction ( > 10% transmission) [wavelength (jtmi) in 2-mm Thickness in parentheses]

MgF 2

0.104-7 0.1216-9.7

CaF 2 BaF 2

0.125-12 0.1345-15

Sapphire (A12O3)

0.15-6.3

Fused silica (SiO2) Pyrex 7740 Vycor 7913

0.165-4 (d) 0.3-2.7 0.26-2.7

LiF

1.60(0.125), 1.34(4.3) no = 1.3777, na = 1.38950(0.589)(/) 1.47635(0.2288), 1.30756(9.724) 1.51217(0.3652), 1.39636(10.346) no = 1.8336(0.26520), no = 1.5864(5.577) (/) , n e slightly less than no 1.54715(0.20254), 1.40601(3.5) 1.474(0.589), ~ 1.5(2.2) 1.458(0.589)

As 2 S 3 RIR 2 RIR 20

0.6-0.13 ~ 0.4-4.7 ~ 0.4-5.5 0.13-12

2.84(1.0), 2.4(8) 1.75(2.2) 1.82(2.2) 1.393(0.185), 0.24(24)

RIR 12 Acrylic Silver chloride (AgCl)

~ 0.4-5.7 0.25-8.5 0.340-1.6 0.4-32

1.62(2.2) 1.71(2.0) 1.5066(0.4101), 1.4892(0.6563) 2.134(0.43), 1.90149(20.5)

Silver bromide (Ag'Br) Kel-F Diamond (Type IIA) NaCl

0.45-42 0.34-3.8 0.23-200 0.21-25

KBr KC1

0.205-25 0.18-30 0.19-~ 30 0.21-50

1.55995(0.538), 1.46324(25.14) 1.78373(0.19), 1.3632(23) 1.8226(0.226), 1.6440(0.538) 1.75118(0.365), 2.55990(39.22)

SrTiO 3 SrF 2

0.25-40 0.235-60 0.4-7.4 0.13-14

2.0548(0.248), 1.6381(1.083) 1.98704(0.297), 1.61925(53.12) 2.23(2.2), 2.19(4.3) 1.438(0.538)

Rutile (TiO 2 ) Thallium bromide (TIBr) Thallium bromoiodide (KRS-5) Thalliun chlorobroinide (KRS-6)

0.4-7 0.45-45 0.56-60 0.4-32

no = 2.5(1.0), ne = 2.7(1.0) (/) 2.652(0.436), 2.3(0.75) 2.62758(0.577), 2.21721(39.38) 2.3367(0.589), 2.0752(24)

ZnSe Irtran 2(ZnS)

0.5-22 0.6-15.6 1.1-15W 1.85-30 M

2.4(10.6) 2.26(2.2), 2.25(4.3) 3.42(5.0) 4.025(4.0), 4.002(12.0)

GaAs CdTe

Te

1-15 0.9-16 3.8-8

CaCO 3

0.25-3

3.5(1.0), 3.135(10.6) 2.83(1.0), 2.67(10.6) no = 6.37(4.3), n e = 4.93(4.3) (/) no = 1.90284(0.200), n e = 1.57796(0.198)(/) no = 1.62099(2.172), TI,, = 1.47392(3.324)

NaF

MgO

CsCl CsBr KI Csl

Si Ge

2.313(0.496), 2.2318(0.671) -

2.7151(0.2265), 2.4237(0.5461) 1.89332(0.185), 1.3403(22.3)

Properties of optical materials

497

Properties of optical materials (cont.) Material LiF MgF 2 CaF 2 BaF 2 A1 2 O 3 SiO2 Pyrex Vycor As 2 S 3

RIR2 RIR20 NaF

RIR12 MgO

Acrylic AgCl AgBr Kel-F Diamond NaCl

Thermal-Expansion Coefficient

(io-6/°c) 9 16 25 26

6.66^, 5.0^ 0.55 3.25 0.8 26 8.3 9.6 36 8.3 43

110-140 30 -

GaAs CdTe

0.8 44 48 50 9.4 9 51 60 8.5 4.2 5.5 5.7 4.5

Te

16.8

KBr

KC1 CsCl CsBr KI Csl

SrTiO 3 SrF 2 TiO 2 TIBr KRS-5 KRS-6 ZnSe ZnS Si Ge

CaCO 3

-

Knoop Hardness 100 415 158 65

1525-2000(c) 615

~ 600 109

~ 600 542 60 594 692 9.5

> 9.5 -

5700-10,400^ 18

7 19.5 5 620 130 880 12 40 39 150 354

1150 692 750 45 135

Melting Point

(°C)

870

1396 1360 1280 2040±10 1600 820 ( s ) 1200 300

~ 900 760 980

~ 900 2800 Distorts at 72 455 432 803 730 776 646 636 723 621

2080 1450 1825 460

414.5 423.5 800

1420 936

1238 1045 450 -

894.4^

(a) p a r a ii e i to c-axis. (") Perpendicular to c-axis. ( c ' Depends on crystal orientation. W Depends on grade. \e> Long-wavelength limit depends on purity of material. '-•'-' Birefringent {g> Softening temperature. ^ > Decomposition temperature. (From Building Scientific Apparatus, Moore, J.H., Davis, C.C., and Coplan, M.A.. Addison-Wesley Publishing Company, Inc., 1989.)

Magnification: Transverse: MT = 2/2/2/1 = —S2/S1 MT < O-Image inverted Longitudinal: ML = Ax 2 /Aî = —M\ ML < 0-No front to back inversion

Newtonian: x\X2 = —F2

Gaussian: 1/si + I/S2 = l/F

Thin lens If a lens can be characterized by a single focal length F measured from a single plane then the lens is "thin." Various relations hold among the quantities shown in the figure.

Theory of lenses

AX2

I

1

3

00

A thick lens cannot be characterized by a single focal length measured from a single plane. A single focal length F may be retained if it is measured from two planes, Hi, H2, at distances Pi, P2 from the vertices of the lens, Vi, V2. The two back focal lengths, BFLi and BFL2, are measured from the vertices. The thin lens equations may be used, provided all quantities are measured from the principal planes.

Thick lens

CO CO

I

S3

500


The lensmaker's

equation Pi—>

1 Pl = P1 = -

F(n - 1)TC F(n - 1)TC

Convex surfaces facing left have positive radii. In the above Ri > 0, R2 < 0. Principal plane offsets are positive to right. As illustrated, Pi > 0, P2 < 0. The thin lens focal length is given when Tc = 0. Numerical aperture NA = nosin(0MAx/2) ^MAX is the full angle of the cone of light rays that can pass through the system.

For small (/>:

//#(f-number) = F/D « 2 NA

Both f-number and NA refer to the system and not the exit lens.

Visible and ultraviolet light detectors

501

Visible and ultraviolet light detectors Photodiode Schematics of photodiodes (a) sealed with semi-transparent photocathode, (b) open (or sealed) with opaque photocathode. (From Timothy, J.G. & Madden, R.P. in Handbook on Synchrotron Radiation, E. Koch, ed., North-Holland Publishing Co., 1983, with permission.) Window

Guard ring

(a)

Semi-transparent photocathode Anode Anode (b)

Guard ring Opaque photocathode

(a) (116-254 nm) Incident UV photons cause the photocathode (usually semi-transparent cesium telluride deposited on a magnesium fluoride window) to emit low energy electrons, which are accelerated away by the electric field established by the anode potential (150 V). A calibrated picoammeter measures photocurrent. Quantum energy range (typ): 0.02-0.2 electrons per photon. (b) (5-122 nm) Incident UV photons cause the photocathode (usually aluminum with a 15 nm aluminum oxide layer) to emit low energy electrons, which are accelerated away by the electric field established by the anode potential (60-100 V). A calibrated picoammeter measures photocurrent. The useable range of photocurrents is approximately 10~9 to 10~15 amp. Quantum efficiency range (typ): 0.01-0.15 electrons per photon.


502

Quantum efficiencies of opaque Cs2Te and Csl photocathodes. (From Timothy, J.G. & Madden, R.P., op. cit.) 100.0 — I '

'

'

'

I '

'

'

]

I

T

r

,

[

,

,

\CsI (windowless) \

—

Csl (MgF2 window)

o

150 0.99975 -100 50 65

40 Front 70 80 0.99995 -100 13.5 45 16 Back 70 15 0.999985 -120 5 70

TI 800 x 800 15 12 x 12 50,000 200,000

RCA 320 x 512 30 10 x 15 350,000

Various typical CCD properties

1800 Front 40 12 0.99997 -35 2.3 45

Kodak 765 x 510 9 7 x 4.5 85,000 11 Back 90 9 0.99997 -120 1.2 142

Lorel (Ford) 3072 x 1024 15 46 x 15 > 140, 000 170, 000

o

O

o" 3

CD 3 (sapphire) SiO2 (fused quartz)

1040 A 1120 1220 1280 1340 1410 1600

514


UV fluorescent converters (wavelength shifters) Sodium salicylate Tetraphenyl butadiene Coronene p-Quaterphenyl

Diphenylstilbene p-Terphenyl Dimethyl POPOP POPOP

X-ray and gamma-ray detectors Detection principles - quantum efficiency In general, the quantum efficiency, e(E), for an incident photon of energy E is determined by the transmission of the detector window or any 'dead layer' and by the absorption of the detector medium: e{E) = e~{-Pllp^wPwtw(l

-

e^^/p)dPdtd)j

where (u/p)w and (fi/p)d are the mass absorption coefficients of the detector window (or 'dead layer') and detector medium, respectively, pw and pd are the densities of the detector window (or 'dead layer') and detector medium, respectively, and tw and td are the thicknesses of the detector window (or 'dead layer') and detector medium, respectively. Detection principles — point source detection with X-ray telescopes The fluctuation SNS in the number of counts from a point source of flux density F photons cm"2 s"1 keV"1 is given by: SNS = (AeSAEFt + fuBiAEt + AeSL0jBAEt)^2, where AeS = effective area (cm2) of telescope including detector, AE = energy interval (keV), t = observing time (s), / = focal length (cm) of telescope, u) = solid angle (sr) of picture element, Bi = internal background (ct cm"2 s"1 keV"1) of detector, J'D = diffuse X-ray background (photons cm"2 s"1 keV"1 sr" 1 ). The background, both internal and from diffuse X-rays, is assumed to be steady and well known. For a strong source, the signal-to-noise ratio NS/SNS = (AÂEFt)1!2 is given by the fluctuations in the source only. For a weak source, fluctuations in the background determine the signal-to-noise ratio: Ns = 6NS

X-ray and gamma-ray detectors

515

Scintillation detector Illustration representing a Nal scintillation detector showing sequence of events producing output from electron multiplier and various processes which contribute to response of detector to a gamma-ray source. (Adapted from Heath, R.L., Scintillation Spectrometry, USAEC Report, IDO-16880, 1964.) Source

Compton scattering photon

Pb shielding

U.V. photons produced from local excited states following ionization

tdiation II — Reflector Photocathode Pb X-ray -— Photomultiplier Photoelectroti emitted from cathode

Dynode (secondary electron emission)

Anode

LJJ

t

10"i E5a K X-ray 5

\

2

1^ ill

^"aOyr.Cs^ \\ 3"x3" Nal (Tl)

BejeksecJtter

5

k

Z

5 2 o

V

to

z 5 o ° 2

[

200 400 600 800 1000 1200 CHANNEL NUMBER A typical pulse-height spectrum obtained with a Nal(TI) spectrometer, illustrating the energy response of inorganic scintillators. The scale of the abscissa is 1 keV per channel.

P.E.

516


Gas proportional

counter

Since a proportional counter has internal gain, the system noise can be neglected and the energy resolution is: where

(A£)FWHM

= 2.35[(F + / ) f £ f / 2 eV,

E = energy deposited in counter (eV), F = Fano factor, / = a factor to account for variance in the gas gain, W = mean energy to form an ion pair (eV). As an example, for methane gas: F = 0.26 / = 0.75 W = 27 eV, so that for a proportional counter: = 2.6£ 1/2

^

(with E in keV).

Relative number of ion pairs collected in a gas-filled chamber as a function of the voltage across electrodes of the chamber. 10

O O

co I0 a: |IO

6

Geiger-Mueller . .. , region v limited proportionality , . \H y continuous ^^/ discharge recombination ionization chamber proportional region

£io 4 GO

I0

VOLTAGE BETWEEN ELECTRODES


517

Position sensitive gas proportional detector Readout system of detector. Incident photon is absorbed at point a; electrons drift toward anode-cathode planes. An avalanche at the anode (A) gives rise to pulse distributions at the cathodes (K\\ and K±). The position (X,Y) is obtained by analog summation and division. (Adapted from Bade, E. et al, Nucl. Inst. and Meth., 201, 193, 1982.)

Typical performance Spatial resolution: 0.25 mm (FWHM) at 1 keV. Energy resolution: E

= 2.2£ 1/2

(with E in keV).

Format: 10 cm x 10 cm. The solid-state detector (AE) F WHM

= 2.35[(^) 2 + (FrjE)}1/2 eV.

where rj = conversion factor (Si: 3.6 eV per electron-hole pair: Ge: 2.9 eV per electron-hole pair), a = detector rms noise (electrons), F = Fano factor (Si: 0.14; Ge: 0.13), E = photon or particle energy (eV).

518


Electron drift velocities Electron drift velocities in various gases. From Knoll, G.F., Radiation Detection and Measurement, John Wiley & Sons, 1989, with permission.) ELECTRON

DRIFT

VELOCITY

IN VARIOUS GASES

,1O 7

REDUCED ELECTRIC FIELD V c n r ' t o n r 1

519


Ionization and excitation data for a number of gases

Gas

Atomic number

First ionization potential (eV)

Second ionization potential (eV)

First excited state (eV)

Principal emission wavelengths 584 3888 5875 734 743 5400 5832 5852 6402 1048 1066 6965 7067 7503 8115 1236 5570 5870 1296 1470 4501 4624 4671 1215 4861 6562 1200 4110 1302 7771

He

2

24.48

54.40

20.9 19.8 meta

Ne

10

21.56

41.07

16.68 16.53 meta 16.62 meta

Ar

18

15.76

27.62

11.56 11.49 meta 11.66 meta

Kr

36

14.00

24.56

Xe

54

12.13

21.2

9.98 9.86 meta 10.51 meta 8.39 8.28 meta 9.4 meta

H

1

13.60

N

7

14.53

29.59

6.3

0

8

13.61

35.11

9.1

H2 N2

o2

I2

15.4 15.8 12.5 9.0

10.2

A

11.2 6.1 1.9

1782 2062

(Adapted from Rice-Evans, P., Spark, Streamer, Proportional and Drift Chambers, The Richelieu Press, London, 1974.)


520

Schematic diagram of a solid state detector. (Adapted from Enge, H., Introduction to Nuclear Physics, Addison-Wesley, 1966.) Particle \ \ \ G Id N ~ t y P e silicon

\ >

•

^

]

r

Signal

• -

www

[Depletion layer P-type silicon Metal

Charge-coupled device (CCD) X-rays

ONE PIXEL {

WIDTH

V }

MOS capacitor Metal electrode r ^ Dielectric SiO 2 2 to I $1 ! 2; / ^3 ^1

CharqeAVnr/ 1 -— J transfer Surface potential at Si/SiO 2 interface ' Silicon substrate

X-rays (Back-side illuminated)

where

(Vidt)2

id = dark current (electrons s" 1 ), a = rms readout noise (electrons),

keV,


521

TJ = mean energy required to produce one electron-hole pair (0.0036 keV for silicon), t = integration time (s), F = Fano factor (~ 0.15), E = energy of incident photon (keV). Expected quantum efficiency (defined as the probablity that an incident X-ray photon is detected as an 'event') vs. energy. The calculations consider only the interactions of X-rays in Si, for two hypothetical CCD's whose dead-layer and substrate thicknesses are separately within the range spanned by real devices. There will be a low energy cutoff (not shown) depending on the minimum signal which can be discriminated against the system noise. I

l

i

11 I I i I

I

I

!

I

i I i I

Si ABSORPTION EDGE 1.84 keV 1.0 y

-

0.5 -

/

-

/

1 EFF iciEr

o

D

D

a

i

-

/

-

/

;

i

0.10

-

B

0.1

/

;

/ / /

0.05

0.01

—

i

A

'Device A B

i

!

I I

0.5

Dead Layer

Substrate

0.5 micron Si 0.25 micron Si

200 micron Si" 30 micron Si -

I u I

I

1.0

£(keV)

MicroChannel plate detector Typical performance Spatial resolution: 20-30 /xm (FWHM). Quantum efficiency: 25% at 1.5 keV (Csl photocathode). Format: 25-100 mm in diameter.

I

1 i i i i l 10


522

Schematic diagram of a microchannel plate detector. (Adapted from Behr, A. in Landolt-Bornstein, subvol. 2a, Springer-Verlag, 1981.) 1 mm

X

Hollow

1 mm MicroChannel plate

I I

Burst of secondary electrons Nichrome contact

A

glass fibre Individual microchannel 7 Multiplied —êlectron J" output

Incident X-rays

Nichrome film contact Gain control (max voltage 1 kV)

Properties of common X-ray detectors

Detector Geiger counter Gas ionization in current mode Gas proportional Multiwire proportional chamber Scintillation [Nal(Tl)] Semiconductor [Si(Li)] Semiconductor (Ge)

Energy range (keV)

AE/E^ Dead Maximum at 5.9 keV time/event count rate (%) (/xs) (s" 1 )

3-50

none

200

104

0.2-50 0.2-50 3-50

n/a 15 20

n/a 0.2 0.2

io u ( 6 ) 105

105/anode wire

3-10 000 40

0.25

106

3.0 1-60 1-10 000 3.0

4-30 4-40

5 x 104 5 x 104

(°)FWHM. (6)Maximum count rate density is limited by space-charge effects to around 1011 photons s" 1 cm" 3 . (From Thompson, A.C. in X-ray Data Booklet, Lawrence Berkely Laboratory, University of California, 1986.)

523


Properties of intrinsic silicon and germanium

Atomic number Atomic weight Stable isotope mass numbers Density (300 K); g e m " 3 Atoms cm Dielectric constant Forbidden energy gap (300 K); eV Forbidden energy gap (0 K); eV Intrinsic carrier density (300 K); c m " Intrinsic resistivity (300 K); f2- cm Electron mobility (300 K); cm 2 V " 1 s " 1 Hole mobility (300 K); cm 2 V " 1 s " 1 Electron mobility (77 K); cm 2 V " 1 s " 1 Hole mobility (77 K); cm 2 V " 1 s " 1 Energy per electron-hole pair (300 K); eV Energy per electron-hole pair (77 K); eV Fano factor (77 K) Best gamma-ray energy resolution (77 K) (FWHM)

Si

Ge

14 28.09 28-29-30 2.33 4.96 x 10 22 12 1.115 1.165 1.5 x 10 10 2.3 x 105 1350 480 2.1 x 104 1.1 x 104 3.62 3.76 0.085-0.16 -

32 72.60 70-72-73-74-76 5.32 4.41 x 10 22 16 0.665 0.746 2.4 x 10 13 47 3900 1900 3.6 x 104 4.2 x 104 2.96 0.057-0.129 420 eV at 100 keV 920 eV at 661 keV 1300 eV at 1330 keV

(Adapted from Knoll, G.F., Radiation Detection and John Wiley & Sons, 1989.)

Measurement,

0.785 -

5.36

5.85

Ge(Li)

CdTe

1.6

-

-

-

-

-

-

-

1.85 1.47 1.84 1.80 Varies Varies

4.6

4.43

2.9

3.6

-

-

-

-

100 50 80 45 20-30 20-30

LN2 required during operation LN2 required during operation LN2 required during operation LN2 required during operation

Hygroscopic Non-hygroscopic Hygroscopic Non-hygroscopic Non-hygroscopic Non-hygroscopic

Scintillation conversion^) efficiency Notes (%)

26.7, 9.7, 3 1 iI -

26.7, 31.8

11.1

1.84

1.07, 33.2 0.68, 4.04 33.2, 36.0 33.2, 36.0 0.284 0.284

Index of refrac- Energy^) K-edge (keV) tW 6 ) (eV)

("'Room temperature, exponential decay constant. ' 'At emission maximum. (c)Per electron-hole pair. (d)Referred to Nal(Tl) with S-ll photocathode. (Adapted from Harshaw Scintillation Phosphors, The Harshaw Chemical Company.)

CdZnTe (CZT) 5.81

1.21

1.44

-

-

0.23 0.94 0.63 1.0 0.002-0.020 0.002-0.008

4100 4350 4200 5650 3500-4500 3500-4500

5.38 5.67 5.67 -

SCINTILLATORS Nal(Tl) 3.67 3.18 CaF 2 (Eu) 4.51 CsI(Na) 4.51 CsI(Tl) Plastics 1.06 Liquids 0.86 SOLID-STATE 2.35 Si(Li)

Material

Band A of max. Decay Density gap emission t i n i e ^ (g cm" 3 ) (eV) (A) (Ms)

Properties of scintillation and solid-state detector materials

"5

1to-

CO

9J

SS

O

3~

CD

CD

tq

524

Density (STP) (g cm- 3 )

33.16 (5.19, 4.86, 4.56) 35.97 1.84 11.10 (1.42, 1.41, 1.21

3.74 x 10" 3

5.85 x 10" 3

3.61

4.54

2.33 5.36

36

54

53

55

14 32

Xe

CRYSTALS Nal

Csl

Si Ge

0.284 0.867 3.203 (0.285,0.246, 0.244) 14.32 (1.92, 1.73, 1.67) 34.56 (5.46, 5.10, 4.78)

Shell energy^ (keV)

systems

Kr

PROPORTIONAL COUNTER GASES 0.713 x 10" 3 6 Methane (CH 4 ) 0.901 x 10~ 3 10 Ne 1.78 x 10~ 3 18 Ar

Atomic number, Z

Properties of materials used in X-ray detector

28.47, 32.30 (3.93, 4.22, 4.80) 30.81, 34.99 (4.28, 4.62, 5.28) 1.74, 1.83 9.88, 10.98 (1.19, 1.22)

29.67, 33.78 (4.10, 4.49, 5.30)

12.64, 14.12

0.277 0.849, 0.858 2.96

X-ray lines'6) (keV)

0.865 (0.13) 0.885 (0.15) 0.04 0.49 (0.01)

0.625 (0.04) 0.875 (0.14)

0.01 0.105

Fluorescence yield*c)

53 145

300

260

300

170

20 38 72

Energy at which photoelectric equals Compton cross-section (keV)

to

I

a,

op 93 S

.3

28

29

Ni

Cu

8.96

8.9

7.87

2.7

1.74

0.95

1

I

I

'

I

i i 11 i i 1 1

i

-

vS

Mil

£

>, 0.01 —

I

0.0001 —

X

III

I 200

,400 K / 1 ,800 K /

\

Radiation pressure

0.00001

1,000 K

\

Ml

\

III

o > 0.001 —

700 K \

III I

0

III I

!

i

1

400

\

i

\l

X

I

600 800 Altitude (km)

I

1000

|

1200

A temperature of 700 K corresponds to quiet solar conditions and 1700 K to active solar conditions. (From the Italian Aerospace Research Center, CIRA, 1972)

Approximate lifetimes for Earth satellites

541

Approximate lifetimes for Earth satellites e = 0.60

g j e = 0.40

LLJ

- e = 0.20 ^ e = 0.15 ^ e = 0.10 ITl 1 ^ e = 0.06 I I 7

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