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Preface | |

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Introduction | |

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An overview of the observations | |

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Stars | |

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The Galaxy | |

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Other galaxies | |

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Elliptical galaxies | |

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Spiral galaxies | |

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Lenticular galaxies | |

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Irregular galaxies | |

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Open and globular clusters | |

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Groups and clusters of galaxies | |

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Black holes | |

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Collisionless systems and the relaxation time | |

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The relaxation time | |

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The cosmological context | |

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Kinematics | |

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Geometry | |

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Dynamics | |

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The Big Bang and inflation | |

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The cosmic microwave background | |

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Problems | |

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Potential Theory | |

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General results | |

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The potential-energy tensor | |

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Spherical systems | |

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Newton's theorems | |

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Potential energy of spherical systems | |

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Potentials of some simple systems | |

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Point mass | |

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Homogeneous sphere | |

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Plummer model | |

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Isochrone potential | |

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Modified Hubble model | |

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Power-law density model | |

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Two-power density models | |

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Potential-density pairs for flattened systems | |

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Kuzmin models and generalizations | |

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Logarithmic potentials | |

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Poisson's equation in very flattened systems | |

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Multipole expansion | |

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The potentials of spheroidal and ellipsoidal systems | |

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Potentials of spheroidal shells | |

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Potentials of spheroidal systems | |

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Potentials of ellipsoidal systems | |

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Ferrers potentials | |

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Potential-energy tensors of ellipsoidal systems | |

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The potentials of disks | |

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Disk potentials from homoeoids | |

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The Mestel disk | |

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The exponential disk | |

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Thick disks | |

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Disk potentials from Bessel functions | |

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Application to axisymmetric disks | |

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Disk potentials from logarithmic spirals | |

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Disk potentials from oblate spheroidal coordinates | |

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The potential of our Galaxy | |

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The bulge | |

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The dark halo | |

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The stellar disk | |

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The interstellar medium | |

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The bulge as a bar | |

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Potentials from functional expansions | |

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Bi-orthonormal basis functions | |

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Designer basis functions | |

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Poisson solvers for N-body codes | |

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Direct summation | |

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Softening | |

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Tree codes | |

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Cartesian multipole expansion | |

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Particle-mesh codes | |

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Periodic boundary conditions | |

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Vacuum boundary conditions | |

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Mesh refinement | |

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P[superscript 3]M codes | |

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Spherical-harmonic codes | |

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Simulations of planar systems | |

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Problems | |

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The Orbits of Stars | |

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Orbits in static spherical potentials | |

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Spherical harmonic oscillator | |

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Kepler potential | |

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Isochrone potential | |

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Hyperbolic encounters | |

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Constants and integrals of the motion | |

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Orbits in axisymmetric potentials | |

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Motion in the meridional plane | |

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Surfaces of section | |

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Nearly circular orbits: epicycles and the velocity ellipsoid | |

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Orbits in planar non-axisymmetric potentials | |

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Two-dimensional non-rotating potential | |

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Two-dimensional rotating potential | |

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Weak bars | |

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Lindblad resonances | |

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Orbits trapped at resonance | |

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Numerical orbit integration | |

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Symplectic integrators | |

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Modified Euler integrator | |

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Leapfrog integrator | |

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Runge-Kutta and Bulirsch-Stoer integrators | |

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Multistep predictor-corrector integrators | |

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Multivalue integrators | |

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Adaptive timesteps | |

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Individual timesteps | |

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Regularization | |

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Burdet-Heggie regularization | |

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Kustaanheimo-Stiefel (KS) regularization | |

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Angle-action variables | |

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Orbital tori | |

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Time averages theorem | |

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Action space | |

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Hamilton-Jacobi equation | |

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Angle-action variables for spherical potentials | |

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Angle-action variables for flattened axisymmetric potentials | |

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Stackel potentials | |

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Epicycle approximation | |

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Angle-action variables for a non-rotating bar | |

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Summary | |

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Slowly varying potentials | |

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Adiabatic invariance of actions | |

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Applications | |

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Harmonic oscillator | |

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Eccentric orbits in a disk | |

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Transient perturbations | |

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Slow growth of a central black hole | |

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Perturbations and chaos | |

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Hamiltonian perturbation theory | |

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Trapping by resonances | |

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Levitation | |

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From order to chaos | |

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Irregular orbits | |

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Frequency analysis | |

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Liapunov exponents | |

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Orbits in elliptical galaxies | |

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The perfect ellipsoid | |

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Dynamical effects of cusps | |

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Dynamical effects of black holes | |

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Problems | |

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Equilibria of Collisionless Systems | |

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The collisionless Boltzmann equation | |

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Limitations of the collisionless Boltzmann equation | |

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Finite stellar lifetimes | |

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Correlations between stars | |

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Relation between the DF and observables | |

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An example | |

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Jeans theorems | |

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Choice of f and relations between moments | |

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DF depending only on H | |

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DF depending on H and L | |

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DF depending on H and L[subscript z] | |

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DFs for spherical systems | |

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Ergodic DFs for systems | |

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Ergodic Hernquist, Jaffe and isochrone models | |

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Differential energy distribution | |

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DFs for anisotropic spherical systems | |

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Models with constant anisotropy | |

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Osipkov-Merritt models | |

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Other anisotropic models | |

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Differential-energy distribution for anisotropic systems | |

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Spherical systems defined by the DF | |

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Polytropes and the Plummer model | |

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The isothermal sphere | |

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Lowered isothermal models | |

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Double-power models | |

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Michie models | |

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DFs for axisymmetric density distributions | |

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DF for a given axisymmetric system | |

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Axisymmetric systems specified by f(H, L[subscript z]) | |

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Fully analytic models | |

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Rowley models | |

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Rotation and flattening in spheroids | |

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The Schwarzschild DF | |

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DFs for razor-thin disks | |

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Mestel disk | |

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Kalnajs disks | |

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Using actions as arguments of the DF | |

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Adiabatic compression | |

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Cusp around a black hole | |

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Adiabatic deformation of dark matter | |

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Particle-based and orbit-based models | |

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N-body modeling | |

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Softening | |

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Instability and chaos | |

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Schwarzschild models | |

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The Jeans and virial equations | |

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Jeans equations for spherical systems | |

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Effect of a central black hole on the observed velocity dispersion | |

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Jeans equations for axisymmetric systems | |

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Asymmetric drift | |

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Spheroidal components with isotropic velocity dispersion | |

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Virial equations | |

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Scalar virial theorem | |

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Spherical systems | |

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The tensor virial theorem and observational data | |

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Stellar kinematics as a mass detector | |

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Detecting black holes | |

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Extended mass distributions of elliptical galaxies | |

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Dynamics of the solar neighborhood | |

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The choice of equilibrium | |

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The principle of maximum entropy | |

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Phase mixing and violent relaxation | |

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Phase mixing | |

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Violent relaxation | |

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Numerical simulation of the relaxation process | |

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Problems | |

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Stability of Collisionless Systems | |

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Introduction | |

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Linear response theory | |

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Linearized equations for stellar and fluid systems | |

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The response of homogeneous systems | |

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Physical basis of the Jeans instability | |

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Homogeneous systems and the Jeans swindle | |

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The response of a homogeneous fluid system | |

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The response of a homogeneous stellar system | |

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Unstable solutions | |

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Neutrally stable solutions | |

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Damped solutions | |

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Discussion | |

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General theory of the response of stellar systems | |

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The polarization function in angle-action variables | |

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The Kalnajs matrix method | |

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The response matrix | |

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The energy principle and secular stability | |

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The energy principle for fluid systems | |

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The energy principle for stellar systems | |

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The relation between the stability of fluid and stellar systems | |

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The response of spherical systems | |

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The stability of spherical systems with ergodic DFs | |

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The stability of anisotropic spherical systems | |

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Physical basis of the radial-orbit instability | |

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Landau damping and resonances in spherical systems | |

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The stability of uniformly rotating systems | |

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The uniformly rotating sheet | |

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Kalnajs disks | |

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Maclaurin spheroids and disks | |

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Problems | |

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Disk Dynamics and Spiral Structure | |

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Fundamentals of spiral structure | |

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Images of spiral galaxies | |

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Spiral arms at other wavelengths | |

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Dust | |

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Relativistic electrons | |

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Molecular gas | |

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Neutral atomic gas | |

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HII regions | |

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The geometry of spiral arms | |

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The strength and number of arms | |

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Leading and trailing arms | |

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The pitch angle and the winding problem | |

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The pattern speed | |

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The anti-spiral theorem | |

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Angular-momentum transport by spiral-arm torques | |

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Wave mechanics of differentially rotating disks | |

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Preliminaries | |

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Kinematic density waves | |

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Resonances | |

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The dispersion relation for tightly wound spiral arms | |

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The tight-winding approximation | |

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Potential of a tightly wound spiral pattern | |

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The dispersion relation for fluid disks | |

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The dispersion relation for stellar disks | |

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Local stability of differentially rotating disks | |

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Long and short waves | |

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Group velocity | |

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Energy and angular momentum in spiral waves | |

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Global stability of differentially rotating disks | |

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Numerical work on disk stability | |

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Swing amplifier and feedback loops | |

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The swing amplifier | |

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Feedback loops | |

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Physical interpretation of the bar instability | |

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The maximum-disk hypothesis | |

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Summary | |

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Damping and excitation of spiral structure | |

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Response of the interstellar gas to a density wave | |

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Response of a density wave to the interstellar gas | |

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Excitation of spiral structure | |

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Excitation by companion galaxies | |

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Excitation by bars | |

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Stationary spiral structure | |

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Excitation of intermediate-scale structure | |

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Bars | |

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Observations | |

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The pattern speed | |

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Dynamics of bars | |

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Weak bars | |

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Strong bars | |

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The vertical structure of bars | |

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Gas flow in bars | |

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Slow evolution of bars | |

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Warping and buckling of disks | |

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Warps | |

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Kinematics of warps | |

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Bending waves with self-gravity | |

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The origin of warps | |

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Buckling instability | |

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Problems | |

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Kinetic Theory | |

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Relaxation processes | |

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Relaxation | |

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Equipartition | |

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Escape | |

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Inelastic encounters | |

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Binary formation by triple encounters | |

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Interactions with primordial binaries | |

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General results | |

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Virial theorem | |

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Liouville's theorem | |

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Reduced distribution functions | |

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Relation of Liouville's equation to the collisionless Boltzmann equation | |

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The thermodynamics of self-gravitating systems | |

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Negative heat capacity | |

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The gravothermal catastrophe | |

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The Fokker-Planck approximation | |

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The master equation | |

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Fokker-Planck equation | |

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Weak encounters | |

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Local encounters | |

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Orbit-averaging | |

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Fluctuation-dissipation theorems | |

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Diffusion coefficients | |

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Heating of the Galactic disk by MACHOs | |

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Relaxation time | |

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Numerical methods | |

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Fluid models | |

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Monte Carlo methods | |

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Numerical solution of the Fokker-Planck equation | |

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N-body integrations | |

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Checks and comparisons | |

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The evolution of spherical stellar systems | |

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Mass loss from stellar evolution | |

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Evaporation and ejection | |

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The maximum lifetime of a stellar system | |

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Core collapse | |

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After core collapse | |

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Equipartition | |

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Tidal shocks and the survival of globular clusters | |

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Binary stars | |

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Soft binaries | |

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Hard binaries | |

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Reaction rates | |

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Inelastic encounters | |

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Stellar systems with a central black hole | |

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Consumption of stars by the black hole | |

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The effect of a central black hole on the surrounding stellar system | |

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Summary | |

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Problems | |

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Collisions and Encounters of Stellar Systems | |

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Dynamical friction | |

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The validity of Chandrasekhar's formula | |

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Applications of dynamical friction | |

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Decay of black-hole orbits | |

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Galactic cannibalism | |

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Orbital decay of the Magellanic Clouds | |

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Dynamical friction on bars | |

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Formation and evolution of binary black holes | |

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Globular clusters | |

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High-speed encounters | |

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Mass loss | |

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Return to equilibrium | |

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Adiabatic invariance | |

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The distant-tide approximation | |

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Disruption of stellar systems by high-speed encounters | |

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The catastrophic regime | |

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The diffusive regime | |

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Disruption of open clusters | |

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Disruption of binary stars | |

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Dynamical constraints on MACHOs | |

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Disk and bulge shocks | |

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High-speed interactions in clusters of galaxies | |

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Tides | |

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The restricted three-body problem | |

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The sheared-sheet or Hill's approximation | |

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The epicycle approximation and Hill's approximation | |

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The Jacobi radius in Hill's approximation | |

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Tidal tails and streamers | |

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Encounters in stellar disks | |

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Scattering of disk stars by molecular clouds | |

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Scattering of disk stars by spiral arms | |

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Summary | |

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Mergers | |

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Peculiar galaxies | |

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Grand-design spirals | |

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Ring galaxies | |

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Shells and other fine structure | |

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Starbursts | |

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The merger rate | |

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Problems | |

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Galaxy Formation | |

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Linear structure formation | |

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Gaussian random fields | |

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Filtering | |

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The Harrison-Zeldovich power spectrum | |

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Gravitational instability in the expanding universe | |

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Non-relativistic fluid | |

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Relativistic fluid | |

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Nonlinear structure formation | |

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Spherical collapse | |

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The cosmic web | |

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Press-Schechter theory | |

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The mass function | |

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The merger rate | |

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Collapse and virialization in the cosmic web | |

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N-body simulations of clustering | |

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The mass function of halos | |

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Radial density profiles | |

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Internal dynamics of halos | |

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The shapes of halos | |

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Rotation of halos | |

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Dynamics of halo substructure | |

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Star formation and feedback | |

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Reionization | |

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Feedback | |

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Mergers, starbursts and quiescent accretion | |

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The role of central black holes | |

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Origin of the galaxy luminosity function | |

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Conclusions | |

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Problems | |

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Appendices | |

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Useful numbers | |

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Mathematical background | |

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Vectors | |

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Curvilinear coordinate systems | |

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Vector calculus | |

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Fourier series and transforms | |

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Abel integral equation | |

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Schwarz's inequality | |

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Calculus of variations | |

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Poisson distribution | |

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Conditional probability and Bayes's theorem | |

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Central limit theorem | |

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Special functions | |

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Delta function and step function | |

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Factorial or gamma function | |

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Error function, Dawson's integral, and plasma dispersion function | |

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Elliptic integrals | |

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Legendre functions | |

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Spherical harmonics | |

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Bessel functions | |

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Mechanics | |

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Single particles | |

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Systems of particles | |

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Lagrangian dynamics | |

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Hamiltonian dynamics | |

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Hamilton's equations | |

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Poincare invariants | |

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Poisson brackets | |

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Canonical coordinates and transformations | |

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Extended phase space | |

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Generating functions | |

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Delaunay variables for Kepler orbits | |

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Fluid mechanics | |

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Basic equations | |

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Continuity equation | |

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Euler's equation | |

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Energy equation | |

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Equation of state | |

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The ideal gas | |

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Sound waves | |

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Energy and momentum in sound waves | |

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Group velocity | |

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Discrete Fourier transforms | |

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The Antonov-Lebovitz theorem | |

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The Doremus-Feix-Baumann theorem | |

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Angular-momentum transport in disks | |

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Transport in fluid and stellar systems | |

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Transport in a disk with stationary spiral structure | |

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Transport in perturbed axisymmetric disks | |

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Transport in the WKB approximation | |

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Derivation of the reduction factor | |

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The diffusion coefficients | |

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The distribution of binary energies | |

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The evolution of the energy distribution of binaries | |

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The two-body distribution function in thermal equilibrium | |

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The distribution of binary energies in thermal equilibrium | |

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The principle of detailed balance | |

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References | |

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Index | |