Galactic Dynamics

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ISBN: 9780691130279 | 0691130272
Cover: Paperback
Copyright: 1/7/2008

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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.

Preface	p. xiii
Introduction	p. 1
An overview of the observations	p. 5
Stars	p. 5
The Galaxy	p. 11
Other galaxies	p. 19
Elliptical galaxies	p. 20
Spiral galaxies	p. 25
Lenticular galaxies	p. 28
Irregular galaxies	p. 28
Open and globular clusters	p. 29
Groups and clusters of galaxies	p. 30
Black holes	p. 32
Collisionless systems and the relaxation time	p. 33
The relaxation time	p. 34
The cosmological context	p. 37
Kinematics	p. 38
Geometry	p. 39
Dynamics	p. 40
The Big Bang and inflation	p. 45
The cosmic microwave background	p. 48
Problems	p. 52
Potential Theory	p. 55
General results	p. 56
The potential-energy tensor	p. 59
Spherical systems	p. 60
Newton's theorems	p. 60
Potential energy of spherical systems	p. 63
Potentials of some simple systems	p. 63
Point mass	p. 63
Homogeneous sphere	p. 63
Plummer model	p. 65
Isochrone potential	p. 65
Modified Hubble model	p. 66
Power-law density model	p. 68
Two-power density models	p. 70
Potential-density pairs for flattened systems	p. 72
Kuzmin models and generalizations	p. 72
Logarithmic potentials	p. 74
Poisson's equation in very flattened systems	p. 77
Multipole expansion	p. 78
The potentials of spheroidal and ellipsoidal systems	p. 83
Potentials of spheroidal shells	p. 84
Potentials of spheroidal systems	p. 87
Potentials of ellipsoidal systems	p. 94
Ferrers potentials	p. 95
Potential-energy tensors of ellipsoidal systems	p. 95
The potentials of disks	p. 96
Disk potentials from homoeoids	p. 96
The Mestel disk	p. 99
The exponential disk	p. 100
Thick disks	p. 102
Disk potentials from Bessel functions	p. 103
Application to axisymmetric disks	p. 106
Disk potentials from logarithmic spirals	p. 107
Disk potentials from oblate spheroidal coordinates	p. 109
The potential of our Galaxy	p. 110
The bulge	p. 111
The dark halo	p. 112
The stellar disk	p. 112
The interstellar medium	p. 112
The bulge as a bar	p. 117
Potentials from functional expansions	p. 118
Bi-orthonormal basis functions	p. 120
Designer basis functions	p. 120
Poisson solvers for N-body codes	p. 122
Direct summation	p. 123
Softening	p. 123
Tree codes	p. 125
Cartesian multipole expansion	p. 127
Particle-mesh codes	p. 129
Periodic boundary conditions	p. 131
Vacuum boundary conditions	p. 132
Mesh refinement	p. 135
P[superscript 3]M codes	p. 135
Spherical-harmonic codes	p. 136
Simulations of planar systems	p. 137
Problems	p. 137
The Orbits of Stars	p. 142
Orbits in static spherical potentials	p. 143
Spherical harmonic oscillator	p. 147
Kepler potential	p. 147
Isochrone potential	p. 149
Hyperbolic encounters	p. 153
Constants and integrals of the motion	p. 155
Orbits in axisymmetric potentials	p. 159
Motion in the meridional plane	p. 159
Surfaces of section	p. 162
Nearly circular orbits: epicycles and the velocity ellipsoid	p. 164
Orbits in planar non-axisymmetric potentials	p. 171
Two-dimensional non-rotating potential	p. 171
Two-dimensional rotating potential	p. 178
Weak bars	p. 188
Lindblad resonances	p. 188
Orbits trapped at resonance	p. 193
Numerical orbit integration	p. 196
Symplectic integrators	p. 197
Modified Euler integrator	p. 197
Leapfrog integrator	p. 200
Runge-Kutta and Bulirsch-Stoer integrators	p. 201
Multistep predictor-corrector integrators	p. 202
Multivalue integrators	p. 203
Adaptive timesteps	p. 205
Individual timesteps	p. 206
Regularization	p. 208
Burdet-Heggie regularization	p. 208
Kustaanheimo-Stiefel (KS) regularization	p. 210
Angle-action variables	p. 211
Orbital tori	p. 212
Time averages theorem	p. 215
Action space	p. 216
Hamilton-Jacobi equation	p. 217
Angle-action variables for spherical potentials	p. 220
Angle-action variables for flattened axisymmetric potentials	p. 226
Stackel potentials	p. 226
Epicycle approximation	p. 231
Angle-action variables for a non-rotating bar	p. 234
Summary	p. 236
Slowly varying potentials	p. 237
Adiabatic invariance of actions	p. 237
Applications	p. 238
Harmonic oscillator	p. 238
Eccentric orbits in a disk	p. 240
Transient perturbations	p. 240
Slow growth of a central black hole	p. 241
Perturbations and chaos	p. 243
Hamiltonian perturbation theory	p. 243
Trapping by resonances	p. 246
Levitation	p. 250
From order to chaos	p. 253
Irregular orbits	p. 256
Frequency analysis	p. 258
Liapunov exponents	p. 260
Orbits in elliptical galaxies	p. 262
The perfect ellipsoid	p. 263
Dynamical effects of cusps	p. 263
Dynamical effects of black holes	p. 266
Problems	p. 268
Equilibria of Collisionless Systems	p. 274
The collisionless Boltzmann equation	p. 275
Limitations of the collisionless Boltzmann equation	p. 278
Finite stellar lifetimes	p. 278
Correlations between stars	p. 279
Relation between the DF and observables	p. 280
An example	p. 282
Jeans theorems	p. 283
Choice of f and relations between moments	p. 285
DF depending only on H	p. 285
DF depending on H and L	p. 286
DF depending on H and L[subscript z]	p. 286
DFs for spherical systems	p. 287
Ergodic DFs for systems	p. 288
Ergodic Hernquist, Jaffe and isochrone models	p. 290
Differential energy distribution	p. 292
DFs for anisotropic spherical systems	p. 293
Models with constant anisotropy	p. 294
Osipkov-Merritt models	p. 297
Other anisotropic models	p. 298
Differential-energy distribution for anisotropic systems	p. 299
Spherical systems defined by the DF	p. 299
Polytropes and the Plummer model	p. 300
The isothermal sphere	p. 302
Lowered isothermal models	p. 307
Double-power models	p. 311
Michie models	p. 312
DFs for axisymmetric density distributions	p. 312
DF for a given axisymmetric system	p. 312
Axisymmetric systems specified by f(H, L[subscript z])	p. 314
Fully analytic models	p. 314
Rowley models	p. 318
Rotation and flattening in spheroids	p. 320
The Schwarzschild DF	p. 321
DFs for razor-thin disks	p. 329
Mestel disk	p. 329
Kalnajs disks	p. 330
Using actions as arguments of the DF	p. 333
Adiabatic compression	p. 335
Cusp around a black hole	p. 336
Adiabatic deformation of dark matter	p. 337
Particle-based and orbit-based models	p. 338
N-body modeling	p. 339
Softening	p. 341
Instability and chaos	p. 341
Schwarzschild models	p. 344
The Jeans and virial equations	p. 347
Jeans equations for spherical systems	p. 349
Effect of a central black hole on the observed velocity dispersion	p. 350
Jeans equations for axisymmetric systems	p. 353
Asymmetric drift	p. 354
Spheroidal components with isotropic velocity dispersion	p. 356
Virial equations	p. 358
Scalar virial theorem	p. 360
Spherical systems	p. 361
The tensor virial theorem and observational data	p. 362
Stellar kinematics as a mass detector	p. 365
Detecting black holes	p. 366
Extended mass distributions of elliptical galaxies	p. 370
Dynamics of the solar neighborhood	p. 372
The choice of equilibrium	p. 376
The principle of maximum entropy	p. 377
Phase mixing and violent relaxation	p. 379
Phase mixing	p. 379
Violent relaxation	p. 380
Numerical simulation of the relaxation process	p. 382
Problems	p. 387
Stability of Collisionless Systems	p. 394
Introduction	p. 394
Linear response theory	p. 396
Linearized equations for stellar and fluid systems	p. 398
The response of homogeneous systems	p. 401
Physical basis of the Jeans instability	p. 401
Homogeneous systems and the Jeans swindle	p. 401
The response of a homogeneous fluid system	p. 403
The response of a homogeneous stellar system	p. 406
Unstable solutions	p. 410
Neutrally stable solutions	p. 411
Damped solutions	p. 412
Discussion	p. 416
General theory of the response of stellar systems	p. 417
The polarization function in angle-action variables	p. 418
The Kalnajs matrix method	p. 419
The response matrix	p. 421
The energy principle and secular stability	p. 423
The energy principle for fluid systems	p. 423
The energy principle for stellar systems	p. 427
The relation between the stability of fluid and stellar systems	p. 431
The response of spherical systems	p. 432
The stability of spherical systems with ergodic DFs	p. 432
The stability of anisotropic spherical systems	p. 433
Physical basis of the radial-orbit instability	p. 434
Landau damping and resonances in spherical systems	p. 437
The stability of uniformly rotating systems	p. 439
The uniformly rotating sheet	p. 439
Kalnajs disks	p. 444
Maclaurin spheroids and disks	p. 449
Problems	p. 450
Disk Dynamics and Spiral Structure	p. 456
Fundamentals of spiral structure	p. 458
Images of spiral galaxies	p. 460
Spiral arms at other wavelengths	p. 462
Dust	p. 464
Relativistic electrons	p. 465
Molecular gas	p. 465
Neutral atomic gas	p. 465
HII regions	p. 467
The geometry of spiral arms	p. 468
The strength and number of arms	p. 468
Leading and trailing arms	p. 469
The pitch angle and the winding problem	p. 471
The pattern speed	p. 474
The anti-spiral theorem	p. 477
Angular-momentum transport by spiral-arm torques	p. 478
Wave mechanics of differentially rotating disks	p. 481
Preliminaries	p. 481
Kinematic density waves	p. 481
Resonances	p. 484
The dispersion relation for tightly wound spiral arms	p. 485
The tight-winding approximation	p. 485
Potential of a tightly wound spiral pattern	p. 486
The dispersion relation for fluid disks	p. 488
The dispersion relation for stellar disks	p. 492
Local stability of differentially rotating disks	p. 494
Long and short waves	p. 497
Group velocity	p. 499
Energy and angular momentum in spiral waves	p. 503
Global stability of differentially rotating disks	p. 505
Numerical work on disk stability	p. 505
Swing amplifier and feedback loops	p. 508
The swing amplifier	p. 508
Feedback loops	p. 512
Physical interpretation of the bar instability	p. 513
The maximum-disk hypothesis	p. 515
Summary	p. 517
Damping and excitation of spiral structure	p. 518
Response of the interstellar gas to a density wave	p. 518
Response of a density wave to the interstellar gas	p. 522
Excitation of spiral structure	p. 524
Excitation by companion galaxies	p. 524
Excitation by bars	p. 525
Stationary spiral structure	p. 525
Excitation of intermediate-scale structure	p. 526
Bars	p. 528
Observations	p. 528
The pattern speed	p. 531
Dynamics of bars	p. 533
Weak bars	p. 534
Strong bars	p. 535
The vertical structure of bars	p. 536
Gas flow in bars	p. 536
Slow evolution of bars	p. 539
Warping and buckling of disks	p. 539
Warps	p. 539
Kinematics of warps	p. 540
Bending waves with self-gravity	p. 542
The origin of warps	p. 544
Buckling instability	p. 548
Problems	p. 552
Kinetic Theory	p. 554
Relaxation processes	p. 555
Relaxation	p. 555
Equipartition	p. 556
Escape	p. 556
Inelastic encounters	p. 557
Binary formation by triple encounters	p. 557
Interactions with primordial binaries	p. 558
General results	p. 559
Virial theorem	p. 559
Liouville's theorem	p. 561
Reduced distribution functions	p. 563
Relation of Liouville's equation to the collisionless Boltzmann equation	p. 565
The thermodynamics of self-gravitating systems	p. 567
Negative heat capacity	p. 567
The gravothermal catastrophe	p. 568
The Fokker-Planck approximation	p. 573
The master equation	p. 573
Fokker-Planck equation	p. 574
Weak encounters	p. 574
Local encounters	p. 576
Orbit-averaging	p. 577
Fluctuation-dissipation theorems	p. 578
Diffusion coefficients	p. 580
Heating of the Galactic disk by MACHOs	p. 583
Relaxation time	p. 586
Numerical methods	p. 588
Fluid models	p. 588
Monte Carlo methods	p. 592
Numerical solution of the Fokker-Planck equation	p. 593
N-body integrations	p. 594
Checks and comparisons	p. 595
The evolution of spherical stellar systems	p. 596
Mass loss from stellar evolution	p. 600
Evaporation and ejection	p. 602
The maximum lifetime of a stellar system	p. 605
Core collapse	p. 606
After core collapse	p. 609
Equipartition	p. 612
Tidal shocks and the survival of globular clusters	p. 615
Binary stars	p. 616
Soft binaries	p. 618
Hard binaries	p. 620
Reaction rates	p. 621
Inelastic encounters	p. 625
Stellar systems with a central black hole	p. 629
Consumption of stars by the black hole	p. 629
The effect of a central black hole on the surrounding stellar system	p. 631
Summary	p. 633
Problems	p. 634
Collisions and Encounters of Stellar Systems	p. 639
Dynamical friction	p. 643
The validity of Chandrasekhar's formula	p. 646
Applications of dynamical friction	p. 647
Decay of black-hole orbits	p. 647
Galactic cannibalism	p. 649
Orbital decay of the Magellanic Clouds	p. 650
Dynamical friction on bars	p. 651
Formation and evolution of binary black holes	p. 652
Globular clusters	p. 654
High-speed encounters	p. 655
Mass loss	p. 657
Return to equilibrium	p. 657
Adiabatic invariance	p. 658
The distant-tide approximation	p. 658
Disruption of stellar systems by high-speed encounters	p. 661
The catastrophic regime	p. 662
The diffusive regime	p. 663
Disruption of open clusters	p. 664
Disruption of binary stars	p. 665
Dynamical constraints on MACHOs	p. 668
Disk and bulge shocks	p. 669
High-speed interactions in clusters of galaxies	p. 672
Tides	p. 674
The restricted three-body problem	p. 675
The sheared-sheet or Hill's approximation	p. 678
The epicycle approximation and Hill's approximation	p. 679
The Jacobi radius in Hill's approximation	p. 680
Tidal tails and streamers	p. 681
Encounters in stellar disks	p. 685
Scattering of disk stars by molecular clouds	p. 687
Scattering of disk stars by spiral arms	p. 691
Summary	p. 695
Mergers	p. 695
Peculiar galaxies	p. 696
Grand-design spirals	p. 698
Ring galaxies	p. 699
Shells and other fine structure	p. 701
Starbursts	p. 705
The merger rate	p. 708
Problems	p. 710
Galaxy Formation	p. 716
Linear structure formation	p. 717
Gaussian random fields	p. 719
Filtering	p. 720
The Harrison-Zeldovich power spectrum	p. 721
Gravitational instability in the expanding universe	p. 722
Non-relativistic fluid	p. 722
Relativistic fluid	p. 726
Nonlinear structure formation	p. 733
Spherical collapse	p. 733
The cosmic web	p. 735
Press-Schechter theory	p. 739
The mass function	p. 744
The merger rate	p. 746
Collapse and virialization in the cosmic web	p. 748
N-body simulations of clustering	p. 751
The mass function of halos	p. 752
Radial density profiles	p. 753
Internal dynamics of halos	p. 756
The shapes of halos	p. 756
Rotation of halos	p. 757
Dynamics of halo substructure	p. 759
Star formation and feedback	p. 760
Reionization	p. 760
Feedback	p. 761
Mergers, starbursts and quiescent accretion	p. 762
The role of central black holes	p. 764
Origin of the galaxy luminosity function	p. 765
Conclusions	p. 765
Problems	p. 766
Appendices
Useful numbers	p. 770
Mathematical background	p. 771
Vectors	p. 771
Curvilinear coordinate systems	p. 773
Vector calculus	p. 775
Fourier series and transforms	p. 778
Abel integral equation	p. 780
Schwarz's inequality	p. 780
Calculus of variations	p. 781
Poisson distribution	p. 781
Conditional probability and Bayes's theorem	p. 782
Central limit theorem	p. 783
Special functions	p. 785
Delta function and step function	p. 785
Factorial or gamma function	p. 786
Error function, Dawson's integral, and plasma dispersion function	p. 786
Elliptic integrals	p. 787
Legendre functions	p. 788
Spherical harmonics	p. 789
Bessel functions	p. 790
Mechanics	p. 792
Single particles	p. 792
Systems of particles	p. 794
Lagrangian dynamics	p. 797
Hamiltonian dynamics	p. 797
Hamilton's equations	p. 797
Poincare invariants	p. 799
Poisson brackets	p. 800
Canonical coordinates and transformations	p. 800
Extended phase space	p. 803
Generating functions	p. 803
Delaunay variables for Kepler orbits	p. 805
Fluid mechanics	p. 807
Basic equations	p. 807
Continuity equation	p. 807
Euler's equation	p. 808
Energy equation	p. 810
Equation of state	p. 811
The ideal gas	p. 812
Sound waves	p. 813
Energy and momentum in sound waves	p. 814
Group velocity	p. 817
Discrete Fourier transforms	p. 818
The Antonov-Lebovitz theorem	p. 822
The Doremus-Feix-Baumann theorem	p. 823
Angular-momentum transport in disks	p. 825
Transport in fluid and stellar systems	p. 825
Transport in a disk with stationary spiral structure	p. 826
Transport in perturbed axisymmetric disks	p. 828
Transport in the WKB approximation	p. 829
Derivation of the reduction factor	p. 830
The diffusion coefficients	p. 833
The distribution of binary energies	p. 838
The evolution of the energy distribution of binaries	p. 838
The two-body distribution function in thermal equilibrium	p. 839
The distribution of binary energies in thermal equilibrium	p. 839
The principle of detailed balance	p. 841
References	p. 842
Index	p. 857
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Galactic Dynamics

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