| |
| |
| Preface | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| An overview of the observations | |
| |
| |
| Stars | |
| |
| |
| The Galaxy | |
| |
| |
| Other galaxies | |
| |
| |
| Elliptical galaxies | |
| |
| |
| Spiral galaxies | |
| |
| |
| Lenticular galaxies | |
| |
| |
| Irregular galaxies | |
| |
| |
| Open and globular clusters | |
| |
| |
| Groups and clusters of galaxies | |
| |
| |
| Black holes | |
| |
| |
| |
| Collisionless systems and the relaxation time | |
| |
| |
| The relaxation time | |
| |
| |
| |
| The cosmological context | |
| |
| |
| Kinematics | |
| |
| |
| Geometry | |
| |
| |
| Dynamics | |
| |
| |
| The Big Bang and inflation | |
| |
| |
| The cosmic microwave background | |
| |
| |
| Problems | |
| |
| |
| |
| Potential Theory | |
| |
| |
| |
| General results | |
| |
| |
| The potential-energy tensor | |
| |
| |
| |
| Spherical systems | |
| |
| |
| Newton's theorems | |
| |
| |
| 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 | |
| |
| |
| |
| Multipole expansion | |
| |
| |
| |
| The potentials of spheroidal and ellipsoidal systems | |
| |
| |
| Potentials of spheroidal shells | |
| |
| |
| Potentials of spheroidal systems | |
| |
| |
| Potentials of ellipsoidal systems | |
| |
| |
| Ferrers potentials | |
| |
| |
| Potential-energy tensors of ellipsoidal systems | |
| |
| |
| |
| The potentials of disks | |
| |
| |
| 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 potential of our Galaxy | |
| |
| |
| The bulge | |
| |
| |
| The dark halo | |
| |
| |
| The stellar disk | |
| |
| |
| The interstellar medium | |
| |
| |
| The bulge as a bar | |
| |
| |
| |
| Potentials from functional expansions | |
| |
| |
| Bi-orthonormal basis functions | |
| |
| |
| Designer basis functions | |
| |
| |
| |
| Poisson solvers for N-body codes | |
| |
| |
| 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 | |
| |
| |
| Problems | |
| |
| |
| |
| The Orbits of Stars | |
| |
| |
| |
| Orbits in static spherical potentials | |
| |
| |
| Spherical harmonic oscillator | |
| |
| |
| Kepler potential | |
| |
| |
| Isochrone potential | |
| |
| |
| Hyperbolic encounters | |
| |
| |
| Constants and integrals of the motion | |
| |
| |
| |
| Orbits in axisymmetric potentials | |
| |
| |
| Motion in the meridional plane | |
| |
| |
| Surfaces of section | |
| |
| |
| Nearly circular orbits: epicycles and the velocity ellipsoid | |
| |
| |
| |
| Orbits in planar non-axisymmetric potentials | |
| |
| |
| Two-dimensional non-rotating potential | |
| |
| |
| Two-dimensional rotating potential | |
| |
| |
| Weak bars | |
| |
| |
| Lindblad resonances | |
| |
| |
| Orbits trapped at resonance | |
| |
| |
| |
| Numerical orbit integration | |
| |
| |
| 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 | |
| |
| |
| |
| Angle-action variables | |
| |
| |
| 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 | |
| |
| |
| Summary | |
| |
| |
| |
| Slowly varying potentials | |
| |
| |
| Adiabatic invariance of actions | |
| |
| |
| Applications | |
| |
| |
| Harmonic oscillator | |
| |
| |
| Eccentric orbits in a disk | |
| |
| |
| Transient perturbations | |
| |
| |
| Slow growth of a central black hole | |
| |
| |
| |
| Perturbations and chaos | |
| |
| |
| Hamiltonian perturbation theory | |
| |
| |
| Trapping by resonances | |
| |
| |
| Levitation | |
| |
| |
| From order to chaos | |
| |
| |
| Irregular orbits | |
| |
| |
| Frequency analysis | |
| |
| |
| Liapunov exponents | |
| |
| |
| |
| Orbits in elliptical galaxies | |
| |
| |
| The perfect ellipsoid | |
| |
| |
| Dynamical effects of cusps | |
| |
| |
| Dynamical effects of black holes | |
| |
| |
| Problems | |
| |
| |
| |
| Equilibria of Collisionless Systems | |
| |
| |
| |
| The collisionless Boltzmann equation | |
| |
| |
| Limitations of the collisionless Boltzmann equation | |
| |
| |
| Finite stellar lifetimes | |
| |
| |
| Correlations between stars | |
| |
| |
| Relation between the DF and observables | |
| |
| |
| An example | |
| |
| |
| |
| Jeans theorems | |
| |
| |
| 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] | |
| |
| |
| |
| DFs for spherical systems | |
| |
| |
| 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 | |
| |
| |
| |
| DFs for axisymmetric density distributions | |
| |
| |
| 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 | |
| |
| |
| |
| DFs for razor-thin disks | |
| |
| |
| Mestel disk | |
| |
| |
| Kalnajs disks | |
| |
| |
| |
| Using actions as arguments of the DF | |
| |
| |
| Adiabatic compression | |
| |
| |
| Cusp around a black hole | |
| |
| |
| Adiabatic deformation of dark matter | |
| |
| |
| |
| Particle-based and orbit-based models | |
| |
| |
| N-body modeling | |
| |
| |
| Softening | |
| |
| |
| Instability and chaos | |
| |
| |
| Schwarzschild models | |
| |
| |
| |
| The Jeans and virial equations | |
| |
| |
| 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 | |
| |
| |
| Spherical systems | |
| |
| |
| The tensor virial theorem and observational data | |
| |
| |
| |
| Stellar kinematics as a mass detector | |
| |
| |
| Detecting black holes | |
| |
| |
| Extended mass distributions of elliptical galaxies | |
| |
| |
| Dynamics of the solar neighborhood | |
| |
| |
| |
| The choice of equilibrium | |
| |
| |
| The principle of maximum entropy | |
| |
| |
| Phase mixing and violent relaxation | |
| |
| |
| Phase mixing | |
| |
| |
| Violent relaxation | |
| |
| |
| Numerical simulation of the relaxation process | |
| |
| |
| Problems | |
| |
| |
| |
| Stability of Collisionless Systems | |
| |
| |
| |
| Introduction | |
| |
| |
| Linear response theory | |
| |
| |
| Linearized equations for stellar and fluid systems | |
| |
| |
| |
| The response of homogeneous 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 | |
| |
| |
| |
| General theory of the response of stellar systems | |
| |
| |
| The polarization function in angle-action variables | |
| |
| |
| The Kalnajs matrix method | |
| |
| |
| The response matrix | |
| |
| |
| |
| The energy principle and secular stability | |
| |
| |
| The energy principle for fluid systems | |
| |
| |
| The energy principle for stellar systems | |
| |
| |
| The relation between the stability of fluid and stellar systems | |
| |
| |
| |
| The response of spherical 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 stability of uniformly rotating systems | |
| |
| |
| The uniformly rotating sheet | |
| |
| |
| Kalnajs disks | |
| |
| |
| Maclaurin spheroids and disks | |
| |
| |
| Problems | |
| |
| |
| |
| Disk Dynamics and Spiral Structure | |
| |
| |
| |
| Fundamentals of spiral structure | |
| |
| |
| Images of spiral galaxies | |
| |
| |
| 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 | |
| |
| |
| |
| Wave mechanics of differentially rotating disks | |
| |
| |
| 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 | |
| |
| |
| |
| Global stability of differentially rotating disks | |
| |
| |
| 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 | |
| |
| |
| Summary | |
| |
| |
| |
| Damping and excitation of spiral structure | |
| |
| |
| 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 | |
| |
| |
| |
| Bars | |
| |
| |
| Observations | |
| |
| |
| The pattern speed | |
| |
| |
| Dynamics of bars | |
| |
| |
| Weak bars | |
| |
| |
| Strong bars | |
| |
| |
| The vertical structure of bars | |
| |
| |
| Gas flow in bars | |
| |
| |
| Slow evolution of bars | |
| |
| |
| |
| Warping and buckling of disks | |
| |
| |
| Warps | |
| |
| |
| Kinematics of warps | |
| |
| |
| Bending waves with self-gravity | |
| |
| |
| The origin of warps | |
| |
| |
| Buckling instability | |
| |
| |
| Problems | |
| |
| |
| |
| Kinetic Theory | |
| |
| |
| |
| Relaxation processes | |
| |
| |
| Relaxation | |
| |
| |
| Equipartition | |
| |
| |
| Escape | |
| |
| |
| Inelastic encounters | |
| |
| |
| Binary formation by triple encounters | |
| |
| |
| Interactions with primordial binaries | |
| |
| |
| |
| General results | |
| |
| |
| Virial theorem | |
| |
| |
| Liouville's theorem | |
| |
| |
| Reduced distribution functions | |
| |
| |
| Relation of Liouville's equation to the collisionless Boltzmann equation | |
| |
| |
| |
| The thermodynamics of self-gravitating systems | |
| |
| |
| 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 | |
| |
| |
| |
| The evolution of spherical stellar systems | |
| |
| |
| Mass loss from stellar evolution | |
| |
| |
| Evaporation and ejection | |
| |
| |
| The maximum lifetime of a stellar system | |
| |
| |
| Core collapse | |
| |
| |
| After core collapse | |
| |
| |
| Equipartition | |
| |
| |
| Tidal shocks and the survival of globular clusters | |
| |
| |
| Binary stars | |
| |
| |
| Soft binaries | |
| |
| |
| Hard binaries | |
| |
| |
| Reaction rates | |
| |
| |
| Inelastic encounters | |
| |
| |
| 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 | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Collisions and Encounters of Stellar Systems | |
| |
| |
| |
| Dynamical friction | |
| |
| |
| The validity of Chandrasekhar's formula | |
| |
| |
| 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 | |
| |
| |
| |
| High-speed encounters | |
| |
| |
| 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 | |
| |
| |
| |
| Tides | |
| |
| |
| 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 | |
| |
| |
| |
| Encounters in stellar disks | |
| |
| |
| Scattering of disk stars by molecular clouds | |
| |
| |
| Scattering of disk stars by spiral arms | |
| |
| |
| Summary | |
| |
| |
| |
| Mergers | |
| |
| |
| Peculiar galaxies | |
| |
| |
| Grand-design spirals | |
| |
| |
| Ring galaxies | |
| |
| |
| Shells and other fine structure | |
| |
| |
| Starbursts | |
| |
| |
| The merger rate | |
| |
| |
| Problems | |
| |
| |
| |
| Galaxy Formation | |
| |
| |
| |
| Linear structure formation | |
| |
| |
| Gaussian random fields | |
| |
| |
| Filtering | |
| |
| |
| The Harrison-Zeldovich power spectrum | |
| |
| |
| Gravitational instability in the expanding universe | |
| |
| |
| Non-relativistic fluid | |
| |
| |
| Relativistic fluid | |
| |
| |
| |
| Nonlinear structure formation | |
| |
| |
| Spherical collapse | |
| |
| |
| The cosmic web | |
| |
| |
| Press-Schechter theory | |
| |
| |
| The mass function | |
| |
| |
| The merger rate | |
| |
| |
| Collapse and virialization in the cosmic web | |
| |
| |
| |
| N-body simulations of clustering | |
| |
| |
| The mass function of halos | |
| |
| |
| Radial density profiles | |
| |
| |
| Internal dynamics of halos | |
| |
| |
| The shapes of halos | |
| |
| |
| Rotation of halos | |
| |
| |
| Dynamics of halo substructure | |
| |
| |
| |
| Star formation and feedback | |
| |
| |
| Reionization | |
| |
| |
| Feedback | |
| |
| |
| Mergers, starbursts and quiescent accretion | |
| |
| |
| The role of central black holes | |
| |
| |
| Origin of the galaxy luminosity function | |
| |
| |
| |
| Conclusions | |
| |
| |
| Problems | |
| |
| |
| Appendices | |
| |
| |
| |
| Useful numbers | |
| |
| |
| |
| Mathematical background | |
| |
| |
| Vectors | |
| |
| |
| 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 | |
| |
| |
| |
| Special functions | |
| |
| |
| 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 | |
| |
| |
| |
| Mechanics | |
| |
| |
| 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 | |
| |
| |
| |
| Delaunay variables for Kepler orbits | |
| |
| |
| |
| Fluid mechanics | |
| |
| |
| Basic equations | |
| |
| |
| Continuity equation | |
| |
| |
| Euler's equation | |
| |
| |
| Energy equation | |
| |
| |
| Equation of state | |
| |
| |
| The ideal gas | |
| |
| |
| Sound waves | |
| |
| |
| Energy and momentum in sound waves | |
| |
| |
| Group velocity | |
| |
| |
| |
| Discrete Fourier transforms | |
| |
| |
| |
| The Antonov-Lebovitz theorem | |
| |
| |
| |
| The Doremus-Feix-Baumann theorem | |
| |
| |
| |
| Angular-momentum transport in disks | |
| |
| |
| Transport in fluid and stellar systems | |
| |
| |
| Transport in a disk with stationary spiral structure | |
| |
| |
| Transport in perturbed axisymmetric disks | |
| |
| |
| Transport in the WKB approximation | |
| |
| |
| |
| Derivation of the reduction factor | |
| |
| |
| |
| The diffusion coefficients | |
| |
| |
| |
| The distribution of binary energies | |
| |
| |
| 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 | |
| |
| |
| References | |
| |
| |
| Index | |