Galactic Dynamics

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  • Edition: 2nd
  • Format: Paperback
  • Copyright: 2008-01-07
  • Publisher: Princeton Univ Pr

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Since it was first published in 1987,Galactic Dynamicshas become the most widely used advanced textbook on the structure and dynamics of galaxies and one of the most cited references in astrophysics. Now, in this extensively revised and updated edition, James Binney and Scott Tremaine describe the dramatic recent advances in this subject, makingGalactic Dynamicsthe most authoritative introduction to galactic astrophysics available to advanced undergraduate students, graduate students, and researchers. Every part of the book has been thoroughly overhauled, and many sections have been completely rewritten. Many new topics are covered, including N-body simulation methods, black holes in stellar systems, linear stability and response theory, and galaxy formation in the cosmological context. Binney and Tremaine, two of the world's leading astrophysicists, use the tools of theoretical physics to describe how galaxies and other stellar systems work, succinctly and lucidly explaining theoretical principles and their applications to observational phenomena. They provide readers with an understanding of stellar dynamics at the level needed to reach the frontiers of the subject. This new edition of the classic text is the definitive introduction to the field.

Author Biography

James Binney is professor of physics at the University of Oxford. His books include "Galactic Astronomy". Scott Tremaine is the Richard Black Professor of Astrophysics at the Institute for Advanced Study and a member of the National Academy of Sciences. Both are fellows of the Royal Society.

Table of Contents

Prefacep. xiii
Introductionp. 1
An overview of the observationsp. 5
Starsp. 5
The Galaxyp. 11
Other galaxiesp. 19
Elliptical galaxiesp. 20
Spiral galaxiesp. 25
Lenticular galaxiesp. 28
Irregular galaxiesp. 28
Open and globular clustersp. 29
Groups and clusters of galaxiesp. 30
Black holesp. 32
Collisionless systems and the relaxation timep. 33
The relaxation timep. 34
The cosmological contextp. 37
Kinematicsp. 38
Geometryp. 39
Dynamicsp. 40
The Big Bang and inflationp. 45
The cosmic microwave backgroundp. 48
Problemsp. 52
Potential Theoryp. 55
General resultsp. 56
The potential-energy tensorp. 59
Spherical systemsp. 60
Newton's theoremsp. 60
Potential energy of spherical systemsp. 63
Potentials of some simple systemsp. 63
Point massp. 63
Homogeneous spherep. 63
Plummer modelp. 65
Isochrone potentialp. 65
Modified Hubble modelp. 66
Power-law density modelp. 68
Two-power density modelsp. 70
Potential-density pairs for flattened systemsp. 72
Kuzmin models and generalizationsp. 72
Logarithmic potentialsp. 74
Poisson's equation in very flattened systemsp. 77
Multipole expansionp. 78
The potentials of spheroidal and ellipsoidal systemsp. 83
Potentials of spheroidal shellsp. 84
Potentials of spheroidal systemsp. 87
Potentials of ellipsoidal systemsp. 94
Ferrers potentialsp. 95
Potential-energy tensors of ellipsoidal systemsp. 95
The potentials of disksp. 96
Disk potentials from homoeoidsp. 96
The Mestel diskp. 99
The exponential diskp. 100
Thick disksp. 102
Disk potentials from Bessel functionsp. 103
Application to axisymmetric disksp. 106
Disk potentials from logarithmic spiralsp. 107
Disk potentials from oblate spheroidal coordinatesp. 109
The potential of our Galaxyp. 110
The bulgep. 111
The dark halop. 112
The stellar diskp. 112
The interstellar mediump. 112
The bulge as a barp. 117
Potentials from functional expansionsp. 118
Bi-orthonormal basis functionsp. 120
Designer basis functionsp. 120
Poisson solvers for N-body codesp. 122
Direct summationp. 123
Softeningp. 123
Tree codesp. 125
Cartesian multipole expansionp. 127
Particle-mesh codesp. 129
Periodic boundary conditionsp. 131
Vacuum boundary conditionsp. 132
Mesh refinementp. 135
P[superscript 3]M codesp. 135
Spherical-harmonic codesp. 136
Simulations of planar systemsp. 137
Problemsp. 137
The Orbits of Starsp. 142
Orbits in static spherical potentialsp. 143
Spherical harmonic oscillatorp. 147
Kepler potentialp. 147
Isochrone potentialp. 149
Hyperbolic encountersp. 153
Constants and integrals of the motionp. 155
Orbits in axisymmetric potentialsp. 159
Motion in the meridional planep. 159
Surfaces of sectionp. 162
Nearly circular orbits: epicycles and the velocity ellipsoidp. 164
Orbits in planar non-axisymmetric potentialsp. 171
Two-dimensional non-rotating potentialp. 171
Two-dimensional rotating potentialp. 178
Weak barsp. 188
Lindblad resonancesp. 188
Orbits trapped at resonancep. 193
Numerical orbit integrationp. 196
Symplectic integratorsp. 197
Modified Euler integratorp. 197
Leapfrog integratorp. 200
Runge-Kutta and Bulirsch-Stoer integratorsp. 201
Multistep predictor-corrector integratorsp. 202
Multivalue integratorsp. 203
Adaptive timestepsp. 205
Individual timestepsp. 206
Regularizationp. 208
Burdet-Heggie regularizationp. 208
Kustaanheimo-Stiefel (KS) regularizationp. 210
Angle-action variablesp. 211
Orbital torip. 212
Time averages theoremp. 215
Action spacep. 216
Hamilton-Jacobi equationp. 217
Angle-action variables for spherical potentialsp. 220
Angle-action variables for flattened axisymmetric potentialsp. 226
Stackel potentialsp. 226
Epicycle approximationp. 231
Angle-action variables for a non-rotating barp. 234
Summaryp. 236
Slowly varying potentialsp. 237
Adiabatic invariance of actionsp. 237
Applicationsp. 238
Harmonic oscillatorp. 238
Eccentric orbits in a diskp. 240
Transient perturbationsp. 240
Slow growth of a central black holep. 241
Perturbations and chaosp. 243
Hamiltonian perturbation theoryp. 243
Trapping by resonancesp. 246
Levitationp. 250
From order to chaosp. 253
Irregular orbitsp. 256
Frequency analysisp. 258
Liapunov exponentsp. 260
Orbits in elliptical galaxiesp. 262
The perfect ellipsoidp. 263
Dynamical effects of cuspsp. 263
Dynamical effects of black holesp. 266
Problemsp. 268
Equilibria of Collisionless Systemsp. 274
The collisionless Boltzmann equationp. 275
Limitations of the collisionless Boltzmann equationp. 278
Finite stellar lifetimesp. 278
Correlations between starsp. 279
Relation between the DF and observablesp. 280
An examplep. 282
Jeans theoremsp. 283
Choice of f and relations between momentsp. 285
DF depending only on Hp. 285
DF depending on H and Lp. 286
DF depending on H and L[subscript z]p. 286
DFs for spherical systemsp. 287
Ergodic DFs for systemsp. 288
Ergodic Hernquist, Jaffe and isochrone modelsp. 290
Differential energy distributionp. 292
DFs for anisotropic spherical systemsp. 293
Models with constant anisotropyp. 294
Osipkov-Merritt modelsp. 297
Other anisotropic modelsp. 298
Differential-energy distribution for anisotropic systemsp. 299
Spherical systems defined by the DFp. 299
Polytropes and the Plummer modelp. 300
The isothermal spherep. 302
Lowered isothermal modelsp. 307
Double-power modelsp. 311
Michie modelsp. 312
DFs for axisymmetric density distributionsp. 312
DF for a given axisymmetric systemp. 312
Axisymmetric systems specified by f(H, L[subscript z])p. 314
Fully analytic modelsp. 314
Rowley modelsp. 318
Rotation and flattening in spheroidsp. 320
The Schwarzschild DFp. 321
DFs for razor-thin disksp. 329
Mestel diskp. 329
Kalnajs disksp. 330
Using actions as arguments of the DFp. 333
Adiabatic compressionp. 335
Cusp around a black holep. 336
Adiabatic deformation of dark matterp. 337
Particle-based and orbit-based modelsp. 338
N-body modelingp. 339
Softeningp. 341
Instability and chaosp. 341
Schwarzschild modelsp. 344
The Jeans and virial equationsp. 347
Jeans equations for spherical systemsp. 349
Effect of a central black hole on the observed velocity dispersionp. 350
Jeans equations for axisymmetric systemsp. 353
Asymmetric driftp. 354
Spheroidal components with isotropic velocity dispersionp. 356
Virial equationsp. 358
Scalar virial theoremp. 360
Spherical systemsp. 361
The tensor virial theorem and observational datap. 362
Stellar kinematics as a mass detectorp. 365
Detecting black holesp. 366
Extended mass distributions of elliptical galaxiesp. 370
Dynamics of the solar neighborhoodp. 372
The choice of equilibriump. 376
The principle of maximum entropyp. 377
Phase mixing and violent relaxationp. 379
Phase mixingp. 379
Violent relaxationp. 380
Numerical simulation of the relaxation processp. 382
Problemsp. 387
Stability of Collisionless Systemsp. 394
Introductionp. 394
Linear response theoryp. 396
Linearized equations for stellar and fluid systemsp. 398
The response of homogeneous systemsp. 401
Physical basis of the Jeans instabilityp. 401
Homogeneous systems and the Jeans swindlep. 401
The response of a homogeneous fluid systemp. 403
The response of a homogeneous stellar systemp. 406
Unstable solutionsp. 410
Neutrally stable solutionsp. 411
Damped solutionsp. 412
Discussionp. 416
General theory of the response of stellar systemsp. 417
The polarization function in angle-action variablesp. 418
The Kalnajs matrix methodp. 419
The response matrixp. 421
The energy principle and secular stabilityp. 423
The energy principle for fluid systemsp. 423
The energy principle for stellar systemsp. 427
The relation between the stability of fluid and stellar systemsp. 431
The response of spherical systemsp. 432
The stability of spherical systems with ergodic DFsp. 432
The stability of anisotropic spherical systemsp. 433
Physical basis of the radial-orbit instabilityp. 434
Landau damping and resonances in spherical systemsp. 437
The stability of uniformly rotating systemsp. 439
The uniformly rotating sheetp. 439
Kalnajs disksp. 444
Maclaurin spheroids and disksp. 449
Problemsp. 450
Disk Dynamics and Spiral Structurep. 456
Fundamentals of spiral structurep. 458
Images of spiral galaxiesp. 460
Spiral arms at other wavelengthsp. 462
Dustp. 464
Relativistic electronsp. 465
Molecular gasp. 465
Neutral atomic gasp. 465
HII regionsp. 467
The geometry of spiral armsp. 468
The strength and number of armsp. 468
Leading and trailing armsp. 469
The pitch angle and the winding problemp. 471
The pattern speedp. 474
The anti-spiral theoremp. 477
Angular-momentum transport by spiral-arm torquesp. 478
Wave mechanics of differentially rotating disksp. 481
Preliminariesp. 481
Kinematic density wavesp. 481
Resonancesp. 484
The dispersion relation for tightly wound spiral armsp. 485
The tight-winding approximationp. 485
Potential of a tightly wound spiral patternp. 486
The dispersion relation for fluid disksp. 488
The dispersion relation for stellar disksp. 492
Local stability of differentially rotating disksp. 494
Long and short wavesp. 497
Group velocityp. 499
Energy and angular momentum in spiral wavesp. 503
Global stability of differentially rotating disksp. 505
Numerical work on disk stabilityp. 505
Swing amplifier and feedback loopsp. 508
The swing amplifierp. 508
Feedback loopsp. 512
Physical interpretation of the bar instabilityp. 513
The maximum-disk hypothesisp. 515
Summaryp. 517
Damping and excitation of spiral structurep. 518
Response of the interstellar gas to a density wavep. 518
Response of a density wave to the interstellar gasp. 522
Excitation of spiral structurep. 524
Excitation by companion galaxiesp. 524
Excitation by barsp. 525
Stationary spiral structurep. 525
Excitation of intermediate-scale structurep. 526
Barsp. 528
Observationsp. 528
The pattern speedp. 531
Dynamics of barsp. 533
Weak barsp. 534
Strong barsp. 535
The vertical structure of barsp. 536
Gas flow in barsp. 536
Slow evolution of barsp. 539
Warping and buckling of disksp. 539
Warpsp. 539
Kinematics of warpsp. 540
Bending waves with self-gravityp. 542
The origin of warpsp. 544
Buckling instabilityp. 548
Problemsp. 552
Kinetic Theoryp. 554
Relaxation processesp. 555
Relaxationp. 555
Equipartitionp. 556
Escapep. 556
Inelastic encountersp. 557
Binary formation by triple encountersp. 557
Interactions with primordial binariesp. 558
General resultsp. 559
Virial theoremp. 559
Liouville's theoremp. 561
Reduced distribution functionsp. 563
Relation of Liouville's equation to the collisionless Boltzmann equationp. 565
The thermodynamics of self-gravitating systemsp. 567
Negative heat capacityp. 567
The gravothermal catastrophep. 568
The Fokker-Planck approximationp. 573
The master equationp. 573
Fokker-Planck equationp. 574
Weak encountersp. 574
Local encountersp. 576
Orbit-averagingp. 577
Fluctuation-dissipation theoremsp. 578
Diffusion coefficientsp. 580
Heating of the Galactic disk by MACHOsp. 583
Relaxation timep. 586
Numerical methodsp. 588
Fluid modelsp. 588
Monte Carlo methodsp. 592
Numerical solution of the Fokker-Planck equationp. 593
N-body integrationsp. 594
Checks and comparisonsp. 595
The evolution of spherical stellar systemsp. 596
Mass loss from stellar evolutionp. 600
Evaporation and ejectionp. 602
The maximum lifetime of a stellar systemp. 605
Core collapsep. 606
After core collapsep. 609
Equipartitionp. 612
Tidal shocks and the survival of globular clustersp. 615
Binary starsp. 616
Soft binariesp. 618
Hard binariesp. 620
Reaction ratesp. 621
Inelastic encountersp. 625
Stellar systems with a central black holep. 629
Consumption of stars by the black holep. 629
The effect of a central black hole on the surrounding stellar systemp. 631
Summaryp. 633
Problemsp. 634
Collisions and Encounters of Stellar Systemsp. 639
Dynamical frictionp. 643
The validity of Chandrasekhar's formulap. 646
Applications of dynamical frictionp. 647
Decay of black-hole orbitsp. 647
Galactic cannibalismp. 649
Orbital decay of the Magellanic Cloudsp. 650
Dynamical friction on barsp. 651
Formation and evolution of binary black holesp. 652
Globular clustersp. 654
High-speed encountersp. 655
Mass lossp. 657
Return to equilibriump. 657
Adiabatic invariancep. 658
The distant-tide approximationp. 658
Disruption of stellar systems by high-speed encountersp. 661
The catastrophic regimep. 662
The diffusive regimep. 663
Disruption of open clustersp. 664
Disruption of binary starsp. 665
Dynamical constraints on MACHOsp. 668
Disk and bulge shocksp. 669
High-speed interactions in clusters of galaxiesp. 672
Tidesp. 674
The restricted three-body problemp. 675
The sheared-sheet or Hill's approximationp. 678
The epicycle approximation and Hill's approximationp. 679
The Jacobi radius in Hill's approximationp. 680
Tidal tails and streamersp. 681
Encounters in stellar disksp. 685
Scattering of disk stars by molecular cloudsp. 687
Scattering of disk stars by spiral armsp. 691
Summaryp. 695
Mergersp. 695
Peculiar galaxiesp. 696
Grand-design spiralsp. 698
Ring galaxiesp. 699
Shells and other fine structurep. 701
Starburstsp. 705
The merger ratep. 708
Problemsp. 710
Galaxy Formationp. 716
Linear structure formationp. 717
Gaussian random fieldsp. 719
Filteringp. 720
The Harrison-Zeldovich power spectrump. 721
Gravitational instability in the expanding universep. 722
Non-relativistic fluidp. 722
Relativistic fluidp. 726
Nonlinear structure formationp. 733
Spherical collapsep. 733
The cosmic webp. 735
Press-Schechter theoryp. 739
The mass functionp. 744
The merger ratep. 746
Collapse and virialization in the cosmic webp. 748
N-body simulations of clusteringp. 751
The mass function of halosp. 752
Radial density profilesp. 753
Internal dynamics of halosp. 756
The shapes of halosp. 756
Rotation of halosp. 757
Dynamics of halo substructurep. 759
Star formation and feedbackp. 760
Reionizationp. 760
Feedbackp. 761
Mergers, starbursts and quiescent accretionp. 762
The role of central black holesp. 764
Origin of the galaxy luminosity functionp. 765
Conclusionsp. 765
Problemsp. 766
Useful numbersp. 770
Mathematical backgroundp. 771
Vectorsp. 771
Curvilinear coordinate systemsp. 773
Vector calculusp. 775
Fourier series and transformsp. 778
Abel integral equationp. 780
Schwarz's inequalityp. 780
Calculus of variationsp. 781
Poisson distributionp. 781
Conditional probability and Bayes's theoremp. 782
Central limit theoremp. 783
Special functionsp. 785
Delta function and step functionp. 785
Factorial or gamma functionp. 786
Error function, Dawson's integral, and plasma dispersion functionp. 786
Elliptic integralsp. 787
Legendre functionsp. 788
Spherical harmonicsp. 789
Bessel functionsp. 790
Mechanicsp. 792
Single particlesp. 792
Systems of particlesp. 794
Lagrangian dynamicsp. 797
Hamiltonian dynamicsp. 797
Hamilton's equationsp. 797
Poincare invariantsp. 799
Poisson bracketsp. 800
Canonical coordinates and transformationsp. 800
Extended phase spacep. 803
Generating functionsp. 803
Delaunay variables for Kepler orbitsp. 805
Fluid mechanicsp. 807
Basic equationsp. 807
Continuity equationp. 807
Euler's equationp. 808
Energy equationp. 810
Equation of statep. 811
The ideal gasp. 812
Sound wavesp. 813
Energy and momentum in sound wavesp. 814
Group velocityp. 817
Discrete Fourier transformsp. 818
The Antonov-Lebovitz theoremp. 822
The Doremus-Feix-Baumann theoremp. 823
Angular-momentum transport in disksp. 825
Transport in fluid and stellar systemsp. 825
Transport in a disk with stationary spiral structurep. 826
Transport in perturbed axisymmetric disksp. 828
Transport in the WKB approximationp. 829
Derivation of the reduction factorp. 830
The diffusion coefficientsp. 833
The distribution of binary energiesp. 838
The evolution of the energy distribution of binariesp. 838
The two-body distribution function in thermal equilibriump. 839
The distribution of binary energies in thermal equilibriump. 839
The principle of detailed balancep. 841
Referencesp. 842
Indexp. 857
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