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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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