Advanced astrophysics

311 Pages·2003·2.061 MB·English

by  Neb Duric

ADVANCED ASTROPHYSICS
Thisbookdevelopsthebasicunderlyingphysicsrequiredforafuller,richerunder-
standingofthescienceofastrophysicsandtheimportantastronomicalphenomena
it describes. The Cosmos manifests phenomena in which physics can appear in
itsmostextreme,andthereforemoreinsightful,forms.Aproperunderstandingof
phenomena such as black holes, quasars and extrasolar planets requires that we
understandthephysicsthatunderliesallofastrophysics.Consequently,developing
astrophysicalconceptsfromfundamentalphysicshasthepotentialtoachievetwo
goals:toderiveabetterunderstandingofastrophysicalphenomenafromfirstprin-
ciples and to illuminate the physics from which the astrophysics is developed. To
thatend,astrophysicaltopicsaregroupedaccordingtotherelevantareasofphysics.
Thebookisidealasatextforgraduatestudentsandasareferenceforestablished
researchers.
The author obtained his PhD in 1984 from the University of Toronto where he
earned the Royal Astronomical Society of Canada Gold Medal for academic ex-
cellence.AfterabriefpostdoctoralstintattheUniversityofBritishColumbia,he
joinedthefacultyattheUniversityofNewMexicowherehepursuedhisinterestsin
radioastronomy.Hehasbeenteachingforthepast17years,earningan“excellence
inteaching”awardforthegraduatecoursesonwhichthisbookisbased.Dr.Duric
has over 100 scientific publications and has authored and/or edited five books. In
addition,hehasdevelopedanumberofonlineclasses,includingacompletelyinter-
active,web-basedfreshmanastronomycourse.Heistherecipientofthe“Regent’s
Fellowship”, the highest honour that UNM bestows on its faculty. His research
has taken him around the world to over a dozen countries, accounting in part, for
the global perspective that characterizes his book. Dr. Duric is a member of the
AmericanAstronomicalSocietyandtheCanadianAstronomicalSociety.

ADVANCED ASTROPHYSICS
NEB DURIC
UniversityofNewMexico
  
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge  , United Kingdom
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521819671
© Neb Duric 2004
This book 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 2003
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Contents
Preface pagexiii
PartI Classicalmechanics 1
1 Orbitalmechanics 3
1.1 Universalgravitation 3
1.1.1 Centerofmass 3
1.1.2 Reducedmass 4
1.2 Kepler’slaws 5
1.2.1 Planetaryorbits 9
1.3 Binarystars 11
1.3.1 Visualbinaries 11
1.3.2 Theapparentorbit 11
1.3.3 Thetrueorbit 12
1.3.4 Determiningtheorbitalelements 14
1.3.5 Spectroscopicbinaries 14
1.3.6 Themassfunction 17
1.3.7 Summaryofbinarystarstudies 18
1.3.8 Mass–luminosityrelation 19
1.4 Extrasolarplanets 20
1.4.1 Theastrometricmethod 21
1.4.2 Theradialvelocitymethod 22
1.4.3 Thetransitmethod 24
1.5 References 25
1.6 Furtherreading 25
2 Galaxydynamics 26
2.1 Potentialsofarbitrarymatterdistributions 26
2.2 Dynamicsofthindisks 27
v
vi Contents
2.3 Rotationcurvesofdiskgalaxies 30
2.3.1 Rotationcurvesofrealspiralgalaxies 31
2.4 N-bodygravitationalsystems 34
2.4.1 Equationofmotion 34
2.4.2 TheVirialtheorem 35
2.4.3 Clustersofgalaxies 36
2.5 References 39
2.6 Furtherreading 39
3 Cosmicexpansionandlargescalestructure 40
3.1 TheexpansionoftheUniverse 40
3.1.1 Thecosmologicalconstant 42
3.2 Large-scalecosmicstructure 45
3.2.1 Overview 45
3.2.2 Correlationfunctionsofgalaxies 46
3.2.3 Darkmatterandlarge-scalestructure 47
3.2.4 Hotandcolddarkmatter 51
3.2.5 TheJeans’massandgravitationalstability 52
3.2.6 Possiblemodelsofstructureformation 54
3.3 References 55
3.4 Furtherreading 55
PartII Statisticalmechanics 57
4 Overviewofstatisticalmechanics 59
4.1 Thermodynamics 59
4.2 Classicalstatisticalmechanics 61
4.3 Quantumstatisticalmechanics 63
4.3.1 Bose–Einsteinstatistics 64
4.3.2 Fermi–Diracstatistics 64
4.4 Photondistributionfunction 65
4.5 Thermodynamicequilibrium 66
4.6 Furtherreading 68
5 TheearlyUniverse 69
5.1 The3Kbackgroundradiation 69
5.1.1 Historyofthebackgroundradiation 69
5.1.2 Evolutionofenergydensity 70
5.2 Galaxyformation 71
5.3 Localcosmologyandnucleosynthesis 72
5.3.1 Overview 72
5.3.2 Primordialhelium 73
5.4 Reactionrates 75
5.4.1 Introduction 75
Contents vii
5.4.2 Barrierpenetration 77
5.4.3 Estimatingreactionrates 81
5.4.4 DestructionofD 82
5.4.5 FormationofD 82
5.4.6 Formationof4He 83
5.5 ParticleequilibriaintheearlyUniverse 83
5.5.1 Overview 83
5.5.2 Chemicalequilibrium 86
5.5.3 TheearlyUniverse 87
5.5.4 Theneutron–protonratio 87
5.5.5 Reactionfreeze-out 88
5.5.6 Reactiontimescale 90
5.5.7 Formationofdeuterium 91
5.6 Furtherreading 93
6 Stellarstructureandcompactstars 94
6.1 Hydrostaticequilibrium 94
6.2 Fermiondegeneracy 97
6.2.1 Whitedwarfequationofstate 100
6.2.2 Mass–radiusrelationforwhitedwarfs 100
6.3 Internalstructureofwhitedwarfs 100
6.3.1 Relationshipbetweenpressureand
energydensity 101
6.3.2 Relatingelectronnumberdensitytothe
massdensity 104
6.3.3 Othersourcesofpressure 105
6.3.4 Equationofstate 105
6.3.5 Internalstructureofwhitedwarfs 105
6.3.6 Estimatingtheradiusandmassofa
whitedwarf 107
6.4 Stabilityofcompactstars 109
6.4.1 Totalenergy 109
6.4.2 Electroncapture 110
6.4.3 Maximumdensity 111
6.5 Structureofneutronstars 114
6.5.1 Overview 114
6.5.2 Liquidlayer 115
6.5.3 Thecrust 117
6.5.4 Thecore 119
6.6 Pulsars 119
6.7 Furtherreading 121
viii Contents
PartIII Electromagnetism 123
7 Radiationfromacceleratingcharges 125
7.1 TheLienard–Wiechertpotential 125
7.1.1 Scalarandvectorpotentials 125
7.1.2 Green’sfunctionsolution 126
7.1.3 TheL–Wpotentials 127
7.2 Electricandmagneticfieldsofamovingcharge 128
7.2.1 Movingchargeatconstantvelocity 129
7.2.2 Radiationfromacceleratingcharges–thefarzone 131
7.2.3 Angulardistributionofradiation 131
7.2.4 Totalemittedpower 133
7.3 Furtherreading 134
8 Bremsstrahlungandsynchrotronradiation 135
8.1 Bremsstrahlung 135
8.1.1 Singleparticlecollisions 135
8.1.2 Radiationfromanensembleofparticles 137
8.2 Synchrotronradiation 138
8.2.1 Totalpower 139
8.2.2 Thereceivedspectrum 140
8.2.3 Spectrumofapower-lawenergydistribution 141
8.3 Furtherreading 143
9 Highenergyprocessesinastrophysics 144
9.1 Neutronstars 144
9.2 Supernovaremnants 145
9.2.1 Particleacceleration 145
9.3 Radiogalaxies 148
9.4 GalacticX-raysources 152
9.4.1 Theenergysource 153
9.4.2 Maximumluminosity/Eddingtonlimit 153
9.4.3 Characteristictemperature 154
9.4.4 Masstransfer 154
9.5 Accretiondisks 154
9.5.1 Diskhydrodynamics 156
9.5.2 Theemissionspectrumofthedisk 157
9.6 Pulsarsrevisited 159
9.6.1 Theradiationfield 160
9.6.2 Radiatedpower 161
9.6.3 TheBrakingIndex 162
9.6.4 Thestaticmagneticfield 162
9.6.5 Thestaticelectricfield 162
Contents ix
9.7 Reference 163
9.8 Furtherreading 163
10 Electromagneticwavepropagation 164
10.1 EMwavesinanun-magnetizedplasma 165
10.1.1 Dispersionmeasure 166
10.2 EMwavesinamagnetizedmedium 167
10.2.1 Rotationmeasure 170
10.3 Reference 172
10.4 Furtherreading 172
PartIV Quantummechanics 173
11 Thehydrogenatom 175
11.1 Structureofthehydrogenatom 175
11.1.1 Case1 r → ∞ 177
11.1.2 Case2 r → 0 177
11.1.3 Whataboutthein-between? 178
11.1.4 Normalizing R(r) 179
11.2 Totalwavefunction 181
11.3 Probabilityfunctions 181
11.4 Energyeigenstatesandtransitions 185
11.5 Furtherreading 185
12 Theinteractionofradiationwithmatter 187
12.1 Non-relativistictreatment 187
12.2 SingleparticleHamiltonian 188
12.3 Separationofstaticandradiationfields 189
12.3.1 Relativeimportanceof H ,H and H 189
0 1 2
12.4 Radiativetransitions 190
12.4.1 Semi-classicalapproach 190
12.4.2 TheHamiltonianoftheradiationfield 191
12.4.3 TheperturbationHamiltonian 192
12.4.4 Time-dependentperturbationtheory 193
12.5 Absorptionofphotons 194
12.5.1 Absorptioncross-sections 196
12.5.2 Dipoletransitionprobability 197
12.5.3 Bound–boundabsorptioncross-section 198
12.6 Spontaneousemission 199
12.7 Photoionization 200
12.7.1 Bound–freecross-sections 202
12.8 Selectionrules 203
12.8.1 Dipoleselectionrules 204
12.8.2 Electricquadrupoletransitions 205