# Galactic Dynamics

, by Binney, James**Note:**Supplemental materials are not guaranteed with Rental or Used book purchases.

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

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.

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.

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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