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Galactic Dynamics

ISBN-10: 0691130272
ISBN-13: 9780691130279
Edition: 2nd 2008 (Revised)
List price: $105.00 Buy it from $103.17
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Description: Since it was first published in 1987,Galactic Dynamicshas become the most widely used advanced textbook on the structure and dynamics of galaxies and one of the most cited references in astrophysics. Now, in this extensively revised and updated  More...

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Book details

List price: $105.00
Edition: 2nd
Copyright year: 2008
Publisher: Princeton University Press
Publication date: 1/27/2008
Binding: Paperback
Pages: 904
Size: 6.00" wide x 9.25" long x 1.75" tall
Weight: 2.508
Language: English

Since it was first published in 1987,Galactic Dynamicshas become the most widely used advanced textbook on the structure and dynamics of galaxies and one of the most cited references in astrophysics. Now, in this extensively revised and updated edition, James Binney and Scott Tremaine describe the dramatic recent advances in this subject, makingGalactic Dynamicsthe most authoritative introduction to galactic astrophysics available to advanced undergraduate students, graduate students, and researchers. Every part of the book has been thoroughly overhauled, and many sections have been completely rewritten. Many new topics are covered, including N-body simulation methods, black holes in stellar systems, linear stability and response theory, and galaxy formation in the cosmological context. Binney and Tremaine, two of the world's leading astrophysicists, use the tools of theoretical physics to describe how galaxies and other stellar systems work, succinctly and lucidly explaining theoretical principles and their applications to observational phenomena. They provide readers with an understanding of stellar dynamics at the level needed to reach the frontiers of the subject. This new edition of the classic text is the definitive introduction to the field.

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

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