Dynamics of Galaxies

474 Pages·2014·17.443 MB·English

by  Bertin G.

Dynamics of Galaxies
Giuseppe Bertin
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DynamicsofGalaxies
SecondEdition
Our understanding of galaxies, thebuilding blocks of theUniverse, has
advanced significantly in recent years. New observations from ground-
andspace-basedtelescopes,thediscoveryofdarkmatter,andnewinsights
into its distribution have been instrumental in this. This textbook pro-
videsgraduatestudentswithamodernintroductiontothegravitationally
determinedstructureandevolutionofgalaxies.Readerswillalsobenefit
fromdetaileddiscussionsoftheissuesinvolvedintheprocessofmodel-
ingcomplexstellarsystems.Additionally,thetextprovidesanaccessible
framework for interpretingobservations and devising new observational
tests.
Basedontheauthor’sextensiveteachingexperience,thisSecondEdi-
tion features an up-to-date view of basic phenomenology, a discussion
ofthestructureofdarkhalosingalaxies, thedynamicsofquasi-relaxed
stellar systems and globular clusters, galaxies and gravitational lens-
ing, and an introduction to self-gravitating accretion disks. Extended
problem sets are available from the accompanying resources website:
www.cambridge.org/9781107000544.
GiuseppeBertinisprofessorofphysicsattheUniversityofMilan,Italy;
previously,hewasonthefacultyoftheScuolaNormaleSuperiore,Pisa.
HehasalsoheldseveralpositionsattheMassachusettsInstituteofTech-
nology and has been a member of the Kavli Institute for Theoretical
Physics,UniversityofCalifornia,SantaBarbara(in2006and2009).Heis
alsoauthorofSpiralStructureinGalaxies:ADensityWaveTheorywith
C. C. Lin, published by MIT Press, and editor of the proceedings of a
seriesofthreeinternationalworkshopsonplasmasinthelaboratoryand
intheUniverse.HewaselectedtoItaly’sAccademiaNazionaledeiLin-
ceiin2013,thesameyearhereceiveditsPremioNazionaledelPresidente
dellaRepubblicainScience.

Dynamics of Galaxies
SecondEdition
GIUSEPPE BERTIN
Universita` degliStudidiMilano
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
CambridgeUniversityPressispartoftheUniversityofCambridge.
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Informationonthistitle:www.cambridge.org/9781107000544
(cid:1)c CambridgeUniversityPress2000
(cid:1)c GiuseppeBertin2014
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2000
Secondedition2014
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationData
Bertin,G.(Giuseppe),author.
Dynamicsofgalaxies/GiuseppeBertin,UniversitaDegliStudidiMilano.–Secondedition.
pages cm
Includesbibliographicalreferencesandindex.
ISBN978-1-107-00054-4(hardback)
1. Galaxies. I. Title.
QB857.B47 2014
(cid:2)
523.112–dc23 2013030425
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URLsforexternalorthird-partyInternetWebsitesreferredtointhispublication
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Contents
PrefacetotheFirstEdition,2000 pagexiii
PrefacetotheSecondEdition xv
Acknowledgments xvii
PARTI BASICPHENOMENOLOGY 1
1 Scales 3
Notes 7
2 ObservationalWindows 9
2.1 Radio 11
2.2 Millimetric 12
2.3 Infrared 12
2.4 Optical 13
2.5 Ultraviolet 14
2.6 XRays 15
2.7 OtherSources 16
Notes 17
3 Classifications 19
3.1 HubbleClassification 20
3.2 MorphologyofEllipticalGalaxies 21
3.3 MorphologyofSpiralGalaxies 22
Notes 25
4 Photometry,Kinematics,andDarkMatter 29
4.1 LuminosityProfiles 30
4.1.1 ExponentialDisks 30
4.1.2 TheR1/4Law 32
4.1.3 AzimuthalStructure 33
4.2 DopplerLineShiftsandLinewidths 34
4.2.1 RotationCurvesofSpiralGalaxies 34
4.2.2 KinematicProfilesofEllipticalGalaxies 37
4.3 GlobalScalingLaws 39
4.3.1 Luminosity-VelocityRelationforSpiralGalaxies 40
4.3.2 TheRisingPartoftheRotationCurvesofSpiralGalaxies 40
4.3.3 TheFundamentalPlaneofEllipticalGalaxies 42
4.3.4 TheMassoftheCentralBlackHole:Velocity-DispersionRelation
forSpheroids 44
4.4 DarkMatterandCosmology 44
Notes 47
vi Contents
5 BasicQuestions,SemiempiricalApproach,andthe
DynamicalWindow 53
5.1 Structure 54
5.1.1 MorphologyandPatternFormationinComplexSystems 55
5.2 FormationandEvolution 56
5.2.1 TheCosmologicalContext 57
5.3 ModelingandSomeFundamentalQuestions 58
5.4 RelationtoOtherBranchesofAstrophysics 58
PARTII PHYSICALMODELS 59
6 Self-GravityandRelationtoPlasmaPhysics 61
6.1 GravityandSelf-Gravity 63
6.2 CollectiveBehavior 63
6.3 AConciseDictionary 64
Notes 65
7 RelaxationTimes,AbsenceofThermodynamicalEquilibrium 66
7.1 Two-StarRelaxationTimes 66
7.1.1 HeuristicAnalysis 66
7.1.2 FullExpressionsfortheRelaxationTimes 67
7.1.3 SettingtheParameterDependence 69
7.1.4 RelationtoOtherTimeScales 69
7.2 CollisionalityandDynamicalFrictioninInhomogeneousSystems 70
7.2.1 AdequacyoftheClassicalLocalDescription 70
7.2.2 Slow,NonadiabaticEvolutionofEllipticalGalaxiesInduced
byDynamicalFriction 71
7.2.3 OtherAstrophysicalEffectsRelatedtoCollisionality 74
7.2.4 RelaxationProcessesinGlobularClusters 74
7.3 CollisionlessRelaxationProcesses 76
7.3.1 PhaseMixing 76
7.3.2 ResonancesandCollectiveModes 76
7.3.3 ViolentRelaxation 77
Notes 78
8 Models 82
8.1 SystemsofManyParticles 82
8.2 ContinuumLimitandStellarDynamics 84
8.3 FluidLimitandFluidModels 85
8.3.1 AnExampleofMomentEquations 87
8.3.2 EquationsforaZero-ThicknessBarotropicFluidDisk 87
8.4 VirialEquations 88
8.5 AsymptoticsversusToyModels 89
8.5.1 MatchedAsymptoticExpansions 91
Notes 92
9 EquilibriumandStability:SymmetryandSymmetryBreaking 95
9.1 TheJeansTheorem 96
9.1.1 ASelf-ConsistentCollisionlessPlasmaConfigurationwith
aCurrentSheet 97
9.2 SymmetryBreaking 99
9.2.1 AnElementaryExamplefromClassicalMechanics 99
9.2.2 ClassificationofModes 101
Contents vii
9.3 Motivationforperturbationanalyses 102
9.4 SpiralGalaxiesversusEllipticalGalaxies 103
Notes 104
10 ClassicalEllipsoids 105
10.1 EllipsoidalFiguresofEquilibrium 106
10.1.1 SomePropertiesofHomogeneousEllipsoids 106
10.1.2 ClassificationoftheEquilibriumConfigurations 108
10.2 RigidlyRotatingEquilibriumEllipsoids 110
10.2.1 AxisymmetricalMaclaurinSpheroids 111
10.2.2 TriaxialJacobiEllipsoids 111
10.2.3 ExtremizingtheMechanicalEnergy 112
10.2.4 TensorVirialEquations 112
10.3 TheMechanismofBifurcation 113
10.3.1 LinearModalAnalysis 113
10.3.2 DynamicalandSecularStability 115
10.3.3 ThermodynamicalAnalogueofPhaseTransitions 115
11 IntroductiontoDispersiveWaves 119
11.1 HyperbolicWaves 120
11.2 DispersiveWaves 122
11.2.1 FourierAnalysis 122
11.2.2 ModulationTheory 124
11.2.3 DynamicsofRayTracinginInhomogeneousMedia 125
11.3 WaterWaves 126
11.3.1 DerivationoftheDispersionRelation 126
11.3.2 Regimes 127
11.3.3 Examples 128
Notes 129
12 JeansInstability 131
12.1 HomogeneousFluidModel 131
12.1.1 InhomogeneousSystemsandRelationtotheVirial
Theorem 132
12.1.2 ElectrostaticPlasmaWaves 133
12.1.3 SimpleGeneralizations 133
12.2 HomogeneousKineticModelandLandauDamping 134
12.2.1 PlasmaDispersionFunction 135
12.2.2 MarginalStabilityandtheFluidLimit 136
12.3 KineticAnalysisofaPlane-ParallelSlab 137
12.3.1 Bounceorbitexpansion 138
Notes 138
PARTIII SPIRALGALAXIES 141
13 Orbits 143
13.1 ActionandAngleVariables 145
13.2 EpicyclicOrbits 146
13.3 RotatingFrame 149
13.4 TrappingattheLagrangianPoints 149
13.4.1 TrappingofaChargedParticleontheTopofaHill 152
13.5 EquationsfortheGuidingCenters 153
13.5.1 LarmorOscillationsandDrifts 153
viii Contents
13.5.2 StarDriftsandStellarHydrodynamics 155
13.6 ExactOrbitsandtheProblemofSelf-Consistency 157
13.6.1 Three-DimensionalOrbitsandPolar-RingGalaxies 157
13.6.2 ExactOrbitsinNonaxisymmetricalDisks 158
13.6.3 OrbitalResponseandSelf-Consistency 159
Notes 160
14 TheBasicState:VerticalandHorizontalEquilibriumof
theDisk 162
14.1 VerticalEquilibrium 163
14.1.1 TheIsothermalSelf-GravitatingSlab 163
14.1.2 TheInhomogeneousDiskandStudyoftheSolar
Neighborhood 164
14.2 Quasi-MaxwellianDistributionFunctionforaCoolDisk 168
14.3 ExactModels 169
14.3.1 Density-PotentialPairs 169
14.3.2 DistributionFunctionfortheIsothermalSelf-SimilarDisk 171
14.4 AReferenceBasicStateinViewoftheProblemofSpiralStructure 172
14.5 AReferenceBasicStateinViewoftheProblemofDarkMatter 175
14.6 TheProblemofExtraplanarGas 177
Notes 180
15 DensityWaves 184
15.1 DispersionRelations 187
15.1.1 DispersionRelationforTightlyWoundWavesinaDiskofStars 187
15.1.2 TheQuadraticDispersionRelationforaFluidOne-Component
Model 190
15.1.3 TheCubicDispersionRelationfortheFluidModel 190
15.1.4 Finite-ThicknessEffects 191
15.2 MarginalStability 191
15.2.1 FortheQuadraticDispersionRelationoftheFluidModel 192
15.2.2 FortheQuadraticDispersionRelationoftheFluidModelwith
FiniteThickness 192
15.2.3 FortheQuadraticDispersionRelationofaFluidFully
Self-GravitatingDiskwithFiniteThickness 193
15.2.4 FortheZero-ThicknessCaseinStellarDynamics 193
15.2.5 FortheCubicDispersionRelationoftheFluidModel 194
15.3 WaveBranches 195
15.3.1 GroupPropagationandWaveAction 197
15.3.2 PropagationDiagrams 198
15.4 TurningPointsandResonances 199
15.5 DynamicalMechanisms 200
15.5.1 ParameterRegimes 200
15.5.2 FeedbackandMaintenance 201
15.5.3 OverreflectionandExcitation 203
15.5.4 WaveCyclesforSelf-ExcitedModes 204
15.6 EquationsoftheHomogeneousShearingSheet 205
Notes 206
16 RolesofGas 210
16.1 WavesandEffectiveStabilityinaTwo-ComponentDisk 211
16.1.1 Two-Fluid,Zero-ThicknessDispersionRelation 211
16.1.2 MarginalStabilityandDecoupling 212