Galactic Dynamics


Since it was first published in 1987, Galactic Dynamics has 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, making Galactic Dynamics the most authoritative introduction to galactic astrophysics available to advanced undergraduate students, ...
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Since it was first published in 1987, Galactic Dynamics has 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, making Galactic Dynamics the 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 original classic text is the definitive introduction to the field.

About the Author:
James Binney is professor of physics at the University of Oxford. His books include Galactic Astronomy

About the Author:
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

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Product Details

Meet the Author

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.
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Table of Contents

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