| Preface |
| Introduction / Chapter 1： |
| An overview of the observations / 1.1： |
| Collisionless systems and the relaxation time / 1.2： |
| The relaxation time |
| The cosmological context / 1.3： |
| Potential Theory / Chapter 2： |
| General results / 2.1： |
| The potential-energy tensor |
| Spherical systems / 2.2： |
| Potential-density pairs for attened systems / 2.3： |
| Multipole expansion / 2.4： |
| The potentials of spheroidal and ellipsoidal systems / 2.5： |
| The potentials of disks / 2.6： |
| The potential of our Galaxy / 2.7： |
| Potentials from functional expansions / 2.8： |
| Poisson solvers for N-body codes / 2.9： |
| The Orbits of Stars / Chapter 3： |
| Orbits in static spherical potentials / 3.1： |
| Orbits in axisymmetric potentials / 3.2： |
| Orbits in planar non-axisymmetric potentials / 3.3： |
| Numerical orbit integration / 3.4： |
| Angle-action variables / 3.5： |
| Slowly varying potentials / 3.6： |
| Perturbations and chaos / 3.7： |
| Orbits in elliptical galaxies / 3.8： |
| Equilibria of Collisionless Systems / Chapter 4： |
| The collisionless Boltzmann equation / 4.1： |
| Jeans theorems / 4.2： |
| DFs for spherical systems / 4.3： |
| DFs for axisymmetric density distributions / 4.4： |
| DFs for razor-thin disks / 4.5： |
| Using actions as arguments of the DF / 4.6： |
| Particle-based and orbit-based models / 4.7： |
| The Jeans and virial equations / 4.8： |
| Stellar kinematics as a mass detector / 4.9： |
| The choice of equilibrium / 4.10： |
| Stability of Collisionless Systems / Chapter 5： |
| The response of homogeneous systems / 5.1： |
| General theory of the response of stellar systems / 5.3： |
| The energy principle and secular stability / 5.4： |
| The response of spherical systems / 5.5： |
| The stability of uniformly rotating systems / 5.6： |
| Disk Dynamics and Spiral Structure / Chapter 6： |
| Fundamentals of spiral structure / 6.1： |
| Wave mechanics of differentially rotating disks / 6.2： |
| Global stability of differentially rotating disks / 6.3： |
| Damping and excitation of spiral structure / 6.4： |
| Bars / 6.5： |
| Warping and buckling of disks / 6.6： |
| Kinetic Theory / Chapter 7： |
| Relaxation processes / 7.1： |
| The thermodynamics of self-gravitating systems / 7.2： |
| The Fokker Planck approximation / 7.4： |
| The evolution of spherical stellar systems / 7.5： |
| Summary / 7.6： |
| Collisions and Encounters of Stellar Systems / Chapter 8： |
| Dynamical friction / 8.1： |
| High-speed encounters / 8.2： |
| Tides / 8.3： |
| Encounters in stellar disks / 8.4： |
| Mergers / 8.5： |
| Galaxy Formation / Chapter 9： |
| Linear structure formation / 9.1： |
| Nonlinear structure formation / 9.2： |
| N-body simulations of clustering / 9.3： |
| Star formation and feedback / 9.4： |
| Conclusions / 9.5： |
| Useful numbers / Appendices A： |
| Mathematical background / B： |
| Special functions / C： |
| Mechanics / D： |
| Delaunay variables for Kepler orbits / E： |
| Fluid mechanics / F： |
| Discrete Fourier transforms / G： |
| The Antonov Lebovitz theorem / H： |
| The Doremus Feix Baumann theorem / I： |
| Angular-momentum transport in disks / J： |
| Derivation of the reduction factor / K： |
| The diffusion coefficients / L： |
| The distribution of binary energies / M： |
| References |
| Index |
| Stars / 1： |
| The Galaxy |
| Other galaxies |
| Elliptical galaxies |
| Spiral galaxies |
| Lenticular galaxies |
| Irregular galaxies |
| Open and globular clusters |
| Groups and clusters of galaxies |
| Black holes |
| Kinematics |
| Geometry |
| Dynamics |
| The Big Bang and inflation |
| The cosmic microwave background |
| Problems |
| Newton's theorems / 2： |
| Potential energy of spherical systems |
| Potentials of some simple systems |
| Point mass |
| Homogeneous sphere |
| Plummer model |
| Isochrone potential |
| Modified Hubble model |
| Power-law density model |
| Two-power density models |
| Potential-density pairs for flattened systems |
| Kuzmin models and generalizations |
| Logarithmic potentials |
| Poisson's equation in very flattened systems |
| Potentials of spheroidal shells |
| Potentials of spheroidal systems |
| Potentials of ellipsoidal systems |
| Ferrers potentials |
| Potential-energy tensors of ellipsoidal systems |
| Disk potentials from homoeoids |
| The Mestel disk |
| The exponential disk |
| Thick disks |
| Disk potentials from Bessel functions |
| Application to axisymmetric disks |
| Disk potentials from logarithmic spirals |
| Disk potentials from oblate spheroidal coordinates |
| The bulge |
| The dark halo |
| The stellar disk |
| The interstellar medium |
| The bulge as a bar |
| Bi-orthonormal basis functions |
| Designer basis functions |
| Direct summation |
| Softening |
| Tree codes |
| Cartesian multipole expansion |
| Particle-mesh codes |
| Periodic boundary conditions |
| Vacuum boundary conditions |
| Mesh refinement |
| P[superscript 3]M codes |
| Spherical-harmonic codes |
| Simulations of planar systems |
| Spherical harmonic oscillator / 3： |
| Kepler potential |
| Hyperbolic encounters |
| Constants and integrals of the motion |
| Motion in the meridional plane |
| Surfaces of section |
| Nearly circular orbits: epicycles and the velocity ellipsoid |
| Two-dimensional non-rotating potential |
| Two-dimensional rotating potential |
| Weak bars |
| Lindblad resonances |
| Orbits trapped at resonance |
| Symplectic integrators |
| Modified Euler integrator |
| Leapfrog integrator |
| Runge-Kutta and Bulirsch-Stoer integrators |
| Multistep predictor-corrector integrators |
| Multivalue integrators |
| Adaptive timesteps |
| Individual timesteps |
| Regularization |
| Burdet-Heggie regularization |
| Kustaanheimo-Stiefel (KS) regularization |
| Orbital tori |
| Time averages theorem |
| Action space |
| Hamilton-Jacobi equation |
| Angle-action variables for spherical potentials |
| Angle-action variables for flattened axisymmetric potentials |
| Stackel potentials |
| Epicycle approximation |
| Angle-action variables for a non-rotating bar |
| Adiabatic invariance of actions |
| Applications |
| Harmonic oscillator |
| Eccentric orbits in a disk |
| Transient perturbations |
| Slow growth of a central black hole |
| Hamiltonian perturbation theory |
| Trapping by resonances |
| Levitation |
| From order to chaos |
| Irregular orbits |
| Frequency analysis |
| Liapunov exponents |
| The perfect ellipsoid |
| Dynamical effects of cusps |
| Dynamical effects of black holes |
| Limitations of the collisionless Boltzmann equation / 4： |
| Finite stellar lifetimes |
| Correlations between stars |
| Relation between the DF and observables |
| An example |
| Choice of f and relations between moments |
| DF depending only on H |
| DF depending on H and L |
| DF depending on H and L[subscript z] |
| Ergodic DFs for systems |
| Ergodic Hernquist, Jaffe and isochrone models |
| Differential energy distribution |
| DFs for anisotropic spherical systems |
| Models with constant anisotropy |
| Osipkov-Merritt models |
| Other anisotropic models |
| Differential-energy distribution for anisotropic systems |
| Spherical systems defined by the DF |
| Polytropes and the Plummer model |
| The isothermal sphere |
| Lowered isothermal models |
| Double-power models |
| Michie models |
| DF for a given axisymmetric system |
| Axisymmetric systems specified by f(H, L[subscript z]) |
| Fully analytic models |
| Rowley models |
| Rotation and flattening in spheroids |
| The Schwarzschild DF |
| Mestel disk |
| Kalnajs disks |
| Adiabatic compression |
| Cusp around a black hole |
| Adiabatic deformation of dark matter |
| N-body modeling |
| Instability and chaos |
| Schwarzschild models |
| Jeans equations for spherical systems |
| Effect of a central black hole on the observed velocity dispersion |
| Jeans equations for axisymmetric systems |
| Asymmetric drift |
| Spheroidal components with isotropic velocity dispersion |
| Virial equations |
| Scalar virial theorem |
| The tensor virial theorem and observational data |
| Detecting black holes |
| Extended mass distributions of elliptical galaxies |
| Dynamics of the solar neighborhood |
| The principle of maximum entropy |
| Phase mixing and violent relaxation |
| Phase mixing |
| Violent relaxation |
| Numerical simulation of the relaxation process |
| Linear response theory / 5： |
| Linearized equations for stellar and fluid systems |
| Physical basis of the Jeans instability |
| Homogeneous systems and the Jeans swindle |
| The response of a homogeneous fluid system |
| The response of a homogeneous stellar system |
| Unstable solutions |
| Neutrally stable solutions |
| Damped solutions |
| Discussion |
| The polarization function in angle-action variables |
| The Kalnajs matrix method |
| The response matrix |
| The energy principle for fluid systems |
| The energy principle for stellar systems |
| The relation between the stability of fluid and stellar systems |
| The stability of spherical systems with ergodic DFs |
| The stability of anisotropic spherical systems |
| Physical basis of the radial-orbit instability |
| Landau damping and resonances in spherical systems |
| The uniformly rotating sheet |
| Maclaurin spheroids and disks |
| Images of spiral galaxies / 6： |
| Spiral arms at other wavelengths |
| Dust |
| Relativistic electrons |
| Molecular gas |
| Neutral atomic gas |
| HII regions |
| The geometry of spiral arms |
| The strength and number of arms |
| Leading and trailing arms |
| The pitch angle and the winding problem |
| The pattern speed |
| The anti-spiral theorem |
| Angular-momentum transport by spiral-arm torques |
| Preliminaries |
| Kinematic density waves |
| Resonances |
| The dispersion relation for tightly wound spiral arms |
| The tight-winding approximation |
| Potential of a tightly wound spiral pattern |
| The dispersion relation for fluid disks |
| The dispersion relation for stellar disks |
| Local stability of differentially rotating disks |
| Long and short waves |
| Group velocity |
| Energy and angular momentum in spiral waves |
| Numerical work on disk stability |
| Swing amplifier and feedback loops |
| The swing amplifier |
| Feedback loops |
| Physical interpretation of the bar instability |
| The maximum-disk hypothesis |
| Response of the interstellar gas to a density wave |
| Response of a density wave to the interstellar gas |
| Excitation of spiral structure |
| Excitation by companion galaxies |
| Excitation by bars |
| Stationary spiral structure |
| Excitation of intermediate-scale structure |
| Observations |
| Dynamics of bars |
| Strong bars |
| The vertical structure of bars |
| Gas flow in bars |
| Slow evolution of bars |
| Warps |
| Kinematics of warps |
| Bending waves with self-gravity |
| The origin of warps |
| Buckling instability |
| Relaxation / 7： |
| Equipartition |
| Escape |
| Inelastic encounters |
| Binary formation by triple encounters |
| Interactions with primordial binaries |
| Virial theorem |
| Liouville's theorem |
| Reduced distribution functions |
| Relation of Liouville's equation to the collisionless Boltzmann equation |
| Negative heat capacity |
| The gravothermal catastrophe |
| The Fokker-Planck approximation |
| The master equation |
| Fokker-Planck equation |
| Weak encounters |
| Local encounters |
| Orbit-averaging |
| Fluctuation-dissipation theorems |
| Diffusion coefficients |
| Heating of the Galactic disk by MACHOs |
| Relaxation time |
| Numerical methods |
| Fluid models |
| Monte Carlo methods |
| Numerical solution of the Fokker-Planck equation |
| N-body integrations |
| Checks and comparisons |
| Mass loss from stellar evolution |
| Evaporation and ejection |
| The maximum lifetime of a stellar system |
| Core collapse |
| After core collapse |
| Tidal shocks and the survival of globular clusters |
| Binary stars |
| Soft binaries |
| Hard binaries |
| Reaction rates |
| Stellar systems with a central black hole |
| Consumption of stars by the black hole |
| The effect of a central black hole on the surrounding stellar system |
| The validity of Chandrasekhar's formula / 8： |
| Applications of dynamical friction |
| Decay of black-hole orbits |
| Galactic cannibalism |
| Orbital decay of the Magellanic Clouds |
| Dynamical friction on bars |
| Formation and evolution of binary black holes |
| Globular clusters |
| Mass loss |
| Return to equilibrium |
| Adiabatic invariance |
| The distant-tide approximation |
| Disruption of stellar systems by high-speed encounters |
| The catastrophic regime |
| The diffusive regime |
| Disruption of open clusters |
| Disruption of binary stars |
| Dynamical constraints on MACHOs |
| Disk and bulge shocks |
| High-speed interactions in clusters of galaxies |
| The restricted three-body problem |
| The sheared-sheet or Hill's approximation |
| The epicycle approximation and Hill's approximation |
| The Jacobi radius in Hill's approximation |
| Tidal tails and streamers |
| Scattering of disk stars by molecular clouds |
| Scattering of disk stars by spiral arms |
| Peculiar galaxies |
| Grand-design spirals |
| Ring galaxies |
| Shells and other fine structure |
| Starbursts |
| The merger rate |
| Gaussian random fields / 9： |
| Filtering |
| The Harrison-Zeldovich power spectrum |
| Gravitational instability in the expanding universe |
| Non-relativistic fluid |
| Relativistic fluid |
| Spherical collapse |
| The cosmic web |
| Press-Schechter theory |
| The mass function |
| Collapse and virialization in the cosmic web |
| The mass function of halos |
| Radial density profiles |
| Internal dynamics of halos |
| The shapes of halos |
| Rotation of halos |
| Dynamics of halo substructure |
| Reionization |
| Feedback |
| Mergers, starbursts and quiescent accretion |
| The role of central black holes |
| Origin of the galaxy luminosity function |
| Appendices |
| Vectors / A： |
| Curvilinear coordinate systems |
| Vector calculus |
| Fourier series and transforms |
| Abel integral equation |
| Schwarz's inequality |
| Calculus of variations |
| Poisson distribution |
| Conditional probability and Bayes's theorem |
| Central limit theorem |
| Delta function and step function |
| Factorial or gamma function |
| Error function, Dawson's integral, and plasma dispersion function |
| Elliptic integrals |
| Legendre functions |
| Spherical harmonics |
| Bessel functions |
| Single particles |
| Systems of particles |
| Lagrangian dynamics |
| Hamiltonian dynamics |
| Hamilton's equations |
| Poincare invariants |
| Poisson brackets |
| Canonical coordinates and transformations |
| Extended phase space |
| Generating functions |
| Basic equations |
| Continuity equation |
| Euler's equation |
| Energy equation |
| Equation of state |
| The ideal gas |
| Sound waves |
| Energy and momentum in sound waves |
| The Antonov-Lebovitz theorem |
| The Doremus-Feix-Baumann theorem |
| Transport in fluid and stellar systems |
| Transport in a disk with stationary spiral structure |
| Transport in perturbed axisymmetric disks |
| Transport in the WKB approximation |
| The evolution of the energy distribution of binaries |
| The two-body distribution function in thermal equilibrium |
| The distribution of binary energies in thermal equilibrium |
| The principle of detailed balance |
図書
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