Galactic dynamics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2008
|
| Edition: | 2. ed. |
| Series: | Princeton series in astrophysics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 885, [16] S. Ill., graph. Darst. |
| ISBN: | 9780691130279 9780691130262 |
Staff View
MARC
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| 100 | 1 | |a Binney, James |d 1950- |e Verfasser |0 (DE-588)171978153 |4 aut | |
| 245 | 1 | 0 | |a Galactic dynamics |c James Binney and Scott Tremaine |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2008 | |
| 300 | |a XVI, 885, [16] S. |b Ill., graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Princeton series in astrophysics | |
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| _version_ | 1804137629594157056 |
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| adam_text | Contents
Preface xiii
1 Introduction 1
1.1 An overview of the observations 5
• Stars 5 • The Galaxy 11 • Other galaxies 19 Elliptical
galaxies 20 Spiral galaxies 25 t Lenticular galaxies 28
Irregular galaxies 28 • Open and globular clusters 29 • Groups
and clusters of galaxies 30 • Black holes 32
1.2 Collisionless systems and the relaxation time 33
• The relaxation time 34
1.3 The cosmological context 37
• Kinematics 38 • Geometry 39 • Dynamics 40 • The Big
Bang and inflation 45 • The cosmic microwave background 48
Problems 52
2 Potential Theory 55
2.1 General results 56
The potential-energy tensor 59
2.2 Spherical systems 60
• Newton s theorems 60 Potential energy of spherical sys-
tems 63 • Potentials of some simple systems 63 t Point
mass 63 Homogeneous sphere 63 Plummer model 65
t Isochrone potential 65 Modified Hubble model 66
o Power-law density model 68 Two-power density models 70
2.3 Potential-density pairs for flattened systems 72
• Kuzmin models and generalizations 72 • Logarithmic poten-
tials 74 • Poisson s equation in very flattened systems 77
2.4 Multipole expansion 78
2.5 The potentials of spheroidal and ellipsoidal systems 83
• Potentials of spheroidal shells 84 • Potentials of spheroidal
systems 87 • Potentials of ellipsoidal systems 94 Ferrers
potentials 95 Potential-energy tensors of ellipsoidal systems 95
vi Contents
2.6 The potentials of disks 96
• Disk potentials from homoeoids 96 The Mestel disk 99 t The
exponential disk 100 Thick disks 102 • Disk potentials from
Bessel functions 103 S Application to axisymmetric disks 106
• Disk potentials from logarithmic spirals 107 • Disk potentials
from oblate spheroidal coordinates 109
2.7 The potential of our Galaxy 110
The bulge 111 The dark halo 112 The stellar disk 112
t The interstellar medium 112 The bulge as a bar 117
2.8 Potentials from functional expansions 118
Bi-orthonormal basis functions 120 Designer basis func-
tions 120
2.9 Poisson solvers for N-body codes 122
• Direct summation 123 Softening 123 • Tree codes 125
Cartesian multipole expansion 127 • Particle-mesh codes 129
Periodic boundary conditions 131 Vacuum boundary con-
ditions 132 Mesh refinement 135 P3M codes 135
• Spherical-harmonic codes 136 • Simulations of planar sys-
tems 137
Problems 137
3 The Orbits of Stars 142
3.1 Orbits in static spherical potentials 143
c Spherical harmonic oscillator 147 i Kepler potential 147
Isochrone potential 149 Hyperbolic encounters 153
• Constants and integrals of the motion 155
3.2 Orbits in axisymmetric potentials 159
• Motion in the meridional plane 159 • Surfaces of section 162
• Nearly circular orbits: epicycles and the velocity ellipsoid 164
3.3 Orbits in planar non-axisymmetric potentials 171
• Two-dimensional non-rotating potential 171 • Two-
dimensional rotating potential 178 • Weak bars 188
Lindblad resonances 188 Orbits trapped at resonance 193
3.4 Numerical orbit integration 196
• Symplectic integrators 197 [ Modified Euler integrator 197
t Leapfrog integrator 200 • Runge-Kutta and Bulirsch-Stoer
integrators 201 • Multistep predictor-corrector integrators 202
• Multivalue integrators 203 • Adaptive timesteps 205
• Individual timesteps 206 • Regularization 208 Burdet-
Heggie regularization 208 Kustaanheimo-Stiefel (KS) regular-
ization 210
3.5 Angle-action variables 211
• Orbital tori 212 Time averages theorem 215 Action
space 216 Hamilton-Jacobi equation 217 • Angle-action
variables for spherical potentials 220 • Angle-action variables for
flattened axisymmetric potentials 226 i Stackel potentials 226
Contents
Epicycle approximation 231 • Angle-action variables for a non-
rotating bar 234 • Summary 236
3.6 Slowly varying potentials 237
• Adiabatic invariance of actions 237 • Applications 238
Harmonic oscillator 238 Eccentric orbits in a disk 240
Transient perturbations 240 Slow growth of a central black
hole 241
3.7 Perturbations and chaos 243
• Hamiltonian perturbation theory 243 • Trapping by reso-
nances 246 Levitation 250 • From order to chaos 253
Irregular orbits 256 t Frequency analysis 258 t Liapunov
exponents 260
3.8 Orbits in elliptical galaxies 262
• The perfect ellipsoid 263 • Dynamical effects of cusps 263
• Dynamical effects of black holes 266
Problems 268
4 Equilibria of Collisionless Systems 274
4.1 The collisionless Boltzmann equation 275
• Limitations of the collisionless Boltzmann equation 278 t Finite
stellar lifetimes 278 t Correlations between stars 279 • Relation
between the df and observables 280 An example 282
4.2 Jeans theorems 283
• Choice of / and relations between moments 285 DF de-
pending only on H 285 DF depending on H and L 286
t DF depending on H and Lz 286
4.3 DFs for spherical systems 287
• Ergodic DFs for systems 288 Ergodic Hernquist. Jaffe and
isochrone models 290 t Differential energy distribution 292
• DFs for anisotropic spherical systems 293 Models with
constant anisotropy 294 Osipkov-Merritt models 297
o Other anisotropic models 298 o Differential-energy distribu-
tion for anisotropic systems 299 • Spherical systems defined
by the DF 299 Polytropes and the Plummer model 300
The isothermal sphere 302 t Lowered isothermal models 307
Double-power models 311 Michie models 312
4.4 DFs for axisymmetric density distributions 312
• DF for a given axisymmetric system 312 • Axisymmetric sys-
tems specified by f(H,Lz) 314 Fully analytic models 314
t Rowley models 318 Rotation and flattening in spheroids 320
• The Schwarzschild DF 321
4.5 DFs for razor-thin disks 329
• Mestel disk 329 • Kalnajs disks 330
4.6 Using actions as arguments of the DF 333
• Adiabatic compression 335 Cusp around a black hole 336
Adiabatic deformation of dark matter 337
viii Contents
4.7 Particle-based and orbit-based models 338
• N-body modeling 339 Softening 341 Instability and
chaos 341 • Schwarzschild models 344
4.8 The Jeans and virial equations 347
• Jeans equations for spherical systems 349 Effect of a central
black hole on the observed velocity dispersion 350 • Jeans equa-
tions for axisymmetric systems 353 t Asymmetric drift 354
t Spheroidal components with isotropic velocity dispersion 356
• Virial equations 358 Scalar virial theorem 360
Spherical systems 361 The tensor virial theorem and ob-
servational data 362
4.9 Stellar kinematics as a mass detector 365
• Detecting black holes 366 • Extended mass distributions of
elliptical galaxies 370 • Dynamics of the solar neighborhood 372
4.10 The choice of equilibrium 376
• The principle of maximum entropy 377 • Phase mix-
ing and violent relaxation 379 Phase mixing 379
Violent relaxation 380 • Numerical simulation of the relaxation
process 382
Problems 387
5 Stability of Collisionless Systems 394
5.1 Introduction 394
• Linear response theory 396 • Linearized equations for stellar
and fluid systems 398
5.2 The response of homogeneous systems 401
• Physical basis of the Jeans instability 401 • Homogeneous
systems and the Jeans swindle 401 • The response of a ho-
mogeneous fluid system 403 • The response of a homo-
geneous stellar system 406 i Unstable solutions 410
Neutrally stable solutions 411 Damped solutions 412
• Discussion 416
5.3 General theory of the response of stellar systems 417
• The polarization function in angle-action variables 418 • The
Kalnajs matrix method 419 • The response matrix 421
5.4 The energy principle and secular stability 423
• The energy principle for fluid systems 423 • The energy princi-
ple for stellar systems 427 • The relation between the stability of
fluid and stellar systems 431
5.5 The response of spherical systems 432
• The stability of spherical systems with ergodic DFs 432 • The
stability of anisotropic spherical systems 433 Physical basis of
the radial-orbit instability 434 • Landau damping and resonances
in spherical systems 437
5.6 The stability of uniformly rotating systems 439
• The uniformly rotating sheet 439 • Kalnajs disks 444
• Maclaurin spheroids and disks 449
Contents
Problems 450
6 Disk Dynamics and Spiral Structure 456
6.1 Fundamentals of spiral structure 458
• Images of spiral galaxies 460 • Spiral arms at other wave-
lengths 462 Dust 464 Relativistic electrons 465
Molecular gas 465 Neutral atomic gas 465 o HII re-
gions 467 • The geometry of spiral arms 468 The
strength and number of arms 468 Leading and trailing
arms 469 c The pitch angle and the winding problem 471
The pattern speed 474 • The anti-spiral theorem 477
• Angular-momentum transport by spiral-arm torques 478
6.2 Wave mechanics of differentially rotating disks 481
• Preliminaries 481 o Kinematic density waves 481
Resonances 484 • The dispersion relation for tightly wound
spiral arms 485 The tight-winding approximation 485
Potential of a tightly wound spiral pattern 486 The dispersion
relation for fluid disks 488 The dispersion relation for stellar
disks 492 • Local stability of differentially rotating disks 494
• Long and short waves 497 • Group velocity 499
• Energy and angular momentum in spiral waves 503
6.3 Global stability of differentially rotating disks 505
• Numerical work on disk stability 505 • Swing ampli-
fier and feedback loops 508 t The swing amplifier 508
Feedback loops 512 t Physical interpretation of the bar
instability 513 • The maximum-disk hypothesis 515
• Summary 517
6.4 Damping and excitation of spiral structure 518
• Response of the interstellar gas to a density wave 518
• Response of a density wave to the interstellar gas 522
• Excitation of spiral structure 524 Excitation by companion
galaxies 524 Excitation by bars 525 t Stationary spiral struc-
ture 525 o Excitation of intermediate-scale structure 526
6.5 Bars 528
• Observations 528 t The pattern speed 531 • Dynamics of
bars 533 Weak bars 534 Strong bars 535 The vertical
structure of bars 536 o Gas flow in bars 536 Slow evolution of
bars 539
6.6 Warping and buckling of disks 539
• Warps 539 Kinematics of warps 540 Bending
waves with self-gravity 542 l The origin of warps 544
• Buckling instability 548
Problems 552
7 Kinetic Theory 554
7.1 Relaxation processes 555
Relaxation 555 Equipartition 556 Escape 556 Inelastic
Contents
encounters 557 Binary formation by triple encounters 557
O Interactions with primordial binaries 558
7.2 General results 559
• Virial theorem 559 • Liouville s theorem 561 • Reduced
distribution functions 563 • Relation of Liouville s equation to
the collisionless Boltzmann equation 565
7.3 The thermodynamics of self-gravitating systems 567
• Negative heat capacity 567 • The gravothermal catastrophe 568
7.4 The Fokker—Planck approximation 573
• The master equation 573 • Fokker-Planck equation 574
i Weak encounters 574 Local encounters 576 Orbit-
averaging 577 • Fluctuation-dissipation theorems 578
• Diffusion coefficients 580 Heating of the Galactic disk by
MACHOs 583 • Relaxation time 586 • Numerical meth-
ods 588 Fluid models 588 Monte Carlo methods 592
Numerical solution of the Fokker-Planck equation 593
i N-body integrations 594 Checks and comparisons 595
7.5 The evolution of spherical stellar systems 596
• Mass loss from stellar evolution 600 • Evaporation and ejec-
tion 602 o The maximum lifetime of a stellar system 605 • Core
collapse 606 • After core collapse 609 • Equipartition 612
• Tidal shocks and the survival of globular clusters 615
• Binary stars 616 Soft binaries 618 Hard binaries 620
Reaction rates 621 • Inelastic encounters 625 • Stellar sys-
tems with a central black hole 629 Consumption of stars by
the black hole 629 The effect of a central black hole on the
surrounding stellar system 631
7.6 Summary 633
Problems 634
8 Collisions and Encounters of Stellar Systems 639
8.1 Dynamical friction 643
The validity of Chandrasekhar s formula 646 • Applications
of dynamical friction 647 Decay of black-hole orbits 647
Galactic cannibalism 649 Orbital decay of the Magellanic
Clouds 650 Dynamical friction on bars 651 Formation and
evolution of binary black holes 652 Globular clusters 654
8.2 High-speed encounters 655
Mass loss 657 Return to equilibrium 657 t Adiabatic
invariance 658 • The distant-tide approximation 658
• Disruption of stellar systems by high-speed encounters 661
The catastrophic regime 662 The diffusive regime 663
Disruption of open clusters 664 Disruption of binary
stars 665 Dynamical constraints on MACHOs 668
t Disk and bulge shocks 669 High-speed interactions in clus-
ters of galaxies 672
Contents
8.3 Tides 674
• The restricted three-body problem 675 • The sheared-sheet
or Hill s approximation 678 o The epicycle approximation and
Hill s approximation 679 The Jacobi radius in Hill s approxima-
tion 680 • Tidal tails and streamers 681
8.4 Encounters in stellar disks 685
• Scattering of disk stars by molecular clouds 687 • Scattering of
disk stars by spiral arms 691 • Summary 695
8.5 Mergers 695
• Peculiar galaxies 696 • Grand-design spirals 698
• Ring galaxies 699 • Shells and other fine structure 701
• Starbursts 705 • The merger rate 708
Problems 710
9 Galaxy Formation 716
9.1 Linear structure formation 717
• Gaussian random fields 719 Filtering 720 The Harrison
Zeldovich power spectrum 721 • Gravitational instability in the
expanding universe 722 t Non-relativistic fluid 722 o Relativistic
fluid 726
9.2 Nonlinear structure formation 733
• Spherical collapse 733 • The cosmic web 735 • Press -Schechter
theory 739 l The mass function 744 The merger rate 746
• Collapse and virialization in the cosmic web 748
9.3 N-body simulations of clustering 751
• The mass function of halos 752 • Radial density profiles 753
• Internal dynamics of halos 756 i The shapes of halos 756
Rotation of halos 757 Dynamics of halo substructure 759
9.4 Star formation and feedback 760
Reionization 760 t Feedback 761 Mergers, starbursts and
quiescent accretion 762 The role of central black holes 764
o Origin of the galaxy luminosity function 765
9.5 Conclusions 765
Problems 766
Appendices
A Useful numbers 770
B Mathematical background 771
• Vectors 771 • Curvilinear coordinate systems 773
• Vector calculus 775 • Fourier series and transforms 778
• Abel integral equation 780 • Schwarz s inequality 780
• Calculus of variations 781 • Poisson distribution 781
• Conditional probability and Bayes s theorem 782 • Central
limit theorem 783
xii Contents
C Special functions 785
• Delta function and step function 785 • Factorial or gamma
function 786 • Error function, Dawson s integral, and plasma
dispersion function 786 • Elliptic integrals 787 • Legendre
functions 788 • Spherical harmonics 789 • Bessel functions 790
D Mechanics 792
• Single particles 792 • Systems of particles 794 • Lagrangian
dynamics 797 • Hamiltonian dynamics 797 Hamilton s equa-
tions 797 Poincare invariants 799 Poisson brackets 800
Canonical coordinates and transformations 800 Extended
phase space 803 t Generating functions 803
E Delaunay variables for Kepler orbits 805
F Fluid mechanics 807
• Basic equations 807 Continuity equation 807 Euler s equa-
tion 808 Energy equation 810 l Equation of state 811
• The ideal gas 812 • Sound waves 813 Energy and momen-
tum in sound waves 814 • Group velocity 817
G Discrete Fourier transforms 818
H The Antonov—Lebovitz theorem 822
I The Doremus—Feix—Baumann theorem 823
J Angular-momentum transport in disks 825
• Transport in fluid and stellar systems 825 • Transport in a disk
with stationary spiral structure 826 • Transport in perturbed axi-
symmetric disks 828 • Transport in the WKB approximation 829
K Derivation of the reduction factor 830
L The diffusion coefficients 833
M The distribution of binary energies 838
• The evolution of the energy distribution of binaries 838 • The
two-body distribution function in thermal equilibrium 839 • The
distribution of binary energies in thermal equilibrium 839 • The
principle of detailed balance 841
References 842
Index 857
|
| adam_txt |
Contents
Preface xiii
1 Introduction 1
1.1 An overview of the observations 5
• Stars 5 • The Galaxy 11 • Other galaxies 19 Elliptical
galaxies 20 Spiral galaxies 25 t Lenticular galaxies 28
Irregular galaxies 28 • Open and globular clusters 29 • Groups
and clusters of galaxies 30 • Black holes 32
1.2 Collisionless systems and the relaxation time 33
• The relaxation time 34
1.3 The cosmological context 37
• Kinematics 38 • Geometry 39 • Dynamics 40 • The Big
Bang and inflation 45 • The cosmic microwave background 48
Problems 52
2 Potential Theory 55
2.1 General results 56
The potential-energy tensor 59
2.2 Spherical systems 60
• Newton's theorems 60 Potential energy of spherical sys-
tems 63 • Potentials of some simple systems 63 t Point
mass 63 Homogeneous sphere 63 Plummer model 65
t Isochrone potential 65 Modified Hubble model 66
o Power-law density model 68 Two-power density models 70
2.3 Potential-density pairs for flattened systems 72
• Kuzmin models and generalizations 72 • Logarithmic poten-
tials 74 • Poisson's equation in very flattened systems 77
2.4 Multipole expansion 78
2.5 The potentials of spheroidal and ellipsoidal systems 83
• Potentials of spheroidal shells 84 • Potentials of spheroidal
systems 87 • Potentials of ellipsoidal systems 94 Ferrers
potentials 95 Potential-energy tensors of ellipsoidal systems 95
vi Contents
2.6 The potentials of disks 96
• Disk potentials from homoeoids 96 The Mestel disk 99 t The
exponential disk 100 Thick disks 102 • Disk potentials from
Bessel functions 103 S Application to axisymmetric disks 106
• Disk potentials from logarithmic spirals 107 • Disk potentials
from oblate spheroidal coordinates 109
2.7 The potential of our Galaxy 110
The bulge 111 The dark halo 112 The stellar disk 112
t The interstellar medium 112 The bulge as a bar 117
2.8 Potentials from functional expansions 118
Bi-orthonormal basis functions 120 Designer basis func-
tions 120
2.9 Poisson solvers for N-body codes 122
• Direct summation 123 Softening 123 • Tree codes 125
Cartesian multipole expansion 127 • Particle-mesh codes 129
Periodic boundary conditions 131 Vacuum boundary con-
ditions 132 Mesh refinement 135 P3M codes 135
• Spherical-harmonic codes 136 • Simulations of planar sys-
tems 137
Problems 137
3 The Orbits of Stars 142
3.1 Orbits in static spherical potentials 143
c Spherical harmonic oscillator 147 i Kepler potential 147
Isochrone potential 149 Hyperbolic encounters 153
• Constants and integrals of the motion 155
3.2 Orbits in axisymmetric potentials 159
• Motion in the meridional plane 159 • Surfaces of section 162
• Nearly circular orbits: epicycles and the velocity ellipsoid 164
3.3 Orbits in planar non-axisymmetric potentials 171
• Two-dimensional non-rotating potential 171 • Two-
dimensional rotating potential 178 • Weak bars 188
Lindblad resonances 188 Orbits trapped at resonance 193
3.4 Numerical orbit integration 196
• Symplectic integrators 197 [ Modified Euler integrator 197
t Leapfrog integrator 200 • Runge-Kutta and Bulirsch-Stoer
integrators 201 • Multistep predictor-corrector integrators 202
• Multivalue integrators 203 • Adaptive timesteps 205
• Individual timesteps 206 • Regularization 208 Burdet-
Heggie regularization 208 Kustaanheimo-Stiefel (KS) regular-
ization 210
3.5 Angle-action variables 211
• Orbital tori 212 Time averages theorem 215 Action
space 216 Hamilton-Jacobi equation 217 • Angle-action
variables for spherical potentials 220 • Angle-action variables for
flattened axisymmetric potentials 226 i Stackel potentials 226
Contents
Epicycle approximation 231 • Angle-action variables for a non-
rotating bar 234 • Summary 236
3.6 Slowly varying potentials 237
• Adiabatic invariance of actions 237 • Applications 238
Harmonic oscillator 238 Eccentric orbits in a disk 240
Transient perturbations 240 Slow growth of a central black
hole 241
3.7 Perturbations and chaos 243
• Hamiltonian perturbation theory 243 • Trapping by reso-
nances 246 Levitation 250 • From order to chaos 253
Irregular orbits 256 t Frequency analysis 258 t Liapunov
exponents 260
3.8 Orbits in elliptical galaxies 262
• The perfect ellipsoid 263 • Dynamical effects of cusps 263
• Dynamical effects of black holes 266
Problems 268
4 Equilibria of Collisionless Systems 274
4.1 The collisionless Boltzmann equation 275
• Limitations of the collisionless Boltzmann equation 278 t Finite
stellar lifetimes 278 t Correlations between stars 279 • Relation
between the df and observables 280 An example 282
4.2 Jeans theorems 283
• Choice of / and relations between moments 285 DF de-
pending only on H 285 DF depending on H and L 286
t DF depending on H and Lz 286
4.3 DFs for spherical systems 287
• Ergodic DFs for systems 288 Ergodic Hernquist. Jaffe and
isochrone models 290 t Differential energy distribution 292
• DFs for anisotropic spherical systems 293 Models with
constant anisotropy 294 Osipkov-Merritt models 297
o Other anisotropic models 298 o Differential-energy distribu-
tion for anisotropic systems 299 • Spherical systems defined
by the DF 299 Polytropes and the Plummer model 300
The isothermal sphere 302 t Lowered isothermal models 307
Double-power models 311 Michie models 312
4.4 DFs for axisymmetric density distributions 312
• DF for a given axisymmetric system 312 • Axisymmetric sys-
tems specified by f(H,Lz) 314 Fully analytic models 314
t Rowley models 318 Rotation and flattening in spheroids 320
• The Schwarzschild DF 321
4.5 DFs for razor-thin disks 329
• Mestel disk 329 • Kalnajs disks 330
4.6 Using actions as arguments of the DF 333
• Adiabatic compression 335 Cusp around a black hole 336
Adiabatic deformation of dark matter 337
viii Contents
4.7 Particle-based and orbit-based models 338
• N-body modeling 339 Softening 341 Instability and
chaos 341 • Schwarzschild models 344
4.8 The Jeans and virial equations 347
• Jeans equations for spherical systems 349 Effect of a central
black hole on the observed velocity dispersion 350 • Jeans equa-
tions for axisymmetric systems 353 t Asymmetric drift 354
t Spheroidal components with isotropic velocity dispersion 356
• Virial equations 358 Scalar virial theorem 360
Spherical systems 361 The tensor virial theorem and ob-
servational data 362
4.9 Stellar kinematics as a mass detector 365
• Detecting black holes 366 • Extended mass distributions of
elliptical galaxies 370 • Dynamics of the solar neighborhood 372
4.10 The choice of equilibrium 376
• The principle of maximum entropy 377 • Phase mix-
ing and violent relaxation 379 Phase mixing 379
Violent relaxation 380 • Numerical simulation of the relaxation
process 382
Problems 387
5 Stability of Collisionless Systems 394
5.1 Introduction 394
• Linear response theory 396 • Linearized equations for stellar
and fluid systems 398
5.2 The response of homogeneous systems 401
• Physical basis of the Jeans instability 401 • Homogeneous
systems and the Jeans swindle 401 • The response of a ho-
mogeneous fluid system 403 • The response of a homo-
geneous stellar system 406 i Unstable solutions 410
Neutrally stable solutions 411 Damped solutions 412
• Discussion 416
5.3 General theory of the response of stellar systems 417
• The polarization function in angle-action variables 418 • The
Kalnajs matrix method 419 • The response matrix 421
5.4 The energy principle and secular stability 423
• The energy principle for fluid systems 423 • The energy princi-
ple for stellar systems 427 • The relation between the stability of
fluid and stellar systems 431
5.5 The response of spherical systems 432
• The stability of spherical systems with ergodic DFs 432 • The
stability of anisotropic spherical systems 433 Physical basis of
the radial-orbit instability 434 • Landau damping and resonances
in spherical systems 437
5.6 The stability of uniformly rotating systems 439
• The uniformly rotating sheet 439 • Kalnajs disks 444
• Maclaurin spheroids and disks 449
Contents
Problems 450
6 Disk Dynamics and Spiral Structure 456
6.1 Fundamentals of spiral structure 458
• Images of spiral galaxies 460 • Spiral arms at other wave-
lengths 462 Dust 464 Relativistic electrons 465
Molecular gas 465 Neutral atomic gas 465 o HII re-
gions 467 • The geometry of spiral arms 468 The
strength and number of arms 468 Leading and trailing
arms 469 c The pitch angle and the winding problem 471
The pattern speed 474 • The anti-spiral theorem 477
• Angular-momentum transport by spiral-arm torques 478
6.2 Wave mechanics of differentially rotating disks 481
• Preliminaries 481 o Kinematic density waves 481
Resonances 484 • The dispersion relation for tightly wound
spiral arms 485 The tight-winding approximation 485
Potential of a tightly wound spiral pattern 486 The dispersion
relation for fluid disks 488 The dispersion relation for stellar
disks 492 • Local stability of differentially rotating disks 494
• Long and short waves 497 • Group velocity 499
• Energy and angular momentum in spiral waves 503
6.3 Global stability of differentially rotating disks 505
• Numerical work on disk stability 505 • Swing ampli-
fier and feedback loops 508 t The swing amplifier 508
Feedback loops 512 t Physical interpretation of the bar
instability 513 • The maximum-disk hypothesis 515
• Summary 517
6.4 Damping and excitation of spiral structure 518
• Response of the interstellar gas to a density wave 518
• Response of a density wave to the interstellar gas 522
• Excitation of spiral structure 524 Excitation by companion
galaxies 524 Excitation by bars 525 t Stationary spiral struc-
ture 525 o Excitation of intermediate-scale structure 526
6.5 Bars 528
• Observations 528 t The pattern speed 531 • Dynamics of
bars 533 Weak bars 534 Strong bars 535 The vertical
structure of bars 536 o Gas flow in bars 536 Slow evolution of
bars 539
6.6 Warping and buckling of disks 539
• Warps 539 Kinematics of warps 540 Bending
waves with self-gravity 542 l The origin of warps 544
• Buckling instability 548
Problems 552
7 Kinetic Theory 554
7.1 Relaxation processes 555
Relaxation 555 Equipartition 556 Escape 556 Inelastic
Contents
encounters 557 Binary formation by triple encounters 557
O Interactions with primordial binaries 558
7.2 General results 559
• Virial theorem 559 • Liouville's theorem 561 • Reduced
distribution functions 563 • Relation of Liouville's equation to
the collisionless Boltzmann equation 565
7.3 The thermodynamics of self-gravitating systems 567
• Negative heat capacity 567 • The gravothermal catastrophe 568
7.4 The Fokker—Planck approximation 573
• The master equation 573 • Fokker-Planck equation 574
i Weak encounters 574 Local encounters 576 Orbit-
averaging 577 • Fluctuation-dissipation theorems 578
• Diffusion coefficients 580 Heating of the Galactic disk by
MACHOs 583 • Relaxation time 586 • Numerical meth-
ods 588 Fluid models 588 Monte Carlo methods 592
Numerical solution of the Fokker-Planck equation 593
i N-body integrations 594 Checks and comparisons 595
7.5 The evolution of spherical stellar systems 596
• Mass loss from stellar evolution 600 • Evaporation and ejec-
tion 602 o The maximum lifetime of a stellar system 605 • Core
collapse 606 • After core collapse 609 • Equipartition 612
• Tidal shocks and the survival of globular clusters 615
• Binary stars 616 Soft binaries 618 Hard binaries 620
Reaction rates 621 • Inelastic encounters 625 • Stellar sys-
tems with a central black hole 629 Consumption of stars by
the black hole 629 The effect of a central black hole on the
surrounding stellar system 631
7.6 Summary 633
Problems 634
8 Collisions and Encounters of Stellar Systems 639
8.1 Dynamical friction 643
The validity of Chandrasekhar's formula 646 • Applications
of dynamical friction 647 Decay of black-hole orbits 647
Galactic cannibalism 649 Orbital decay of the Magellanic
Clouds 650 Dynamical friction on bars 651 Formation and
evolution of binary black holes 652 Globular clusters 654
8.2 High-speed encounters 655
Mass loss 657 Return to equilibrium 657 t Adiabatic
invariance 658 • The distant-tide approximation 658
• Disruption of stellar systems by high-speed encounters 661
The catastrophic regime 662 The diffusive regime 663
Disruption of open clusters 664 Disruption of binary
stars 665 Dynamical constraints on MACHOs 668
t Disk and bulge shocks 669 High-speed interactions in clus-
ters of galaxies 672
Contents
8.3 Tides 674
• The restricted three-body problem 675 • The sheared-sheet
or Hill's approximation 678 o The epicycle approximation and
Hill's approximation 679 The Jacobi radius in Hill's approxima-
tion 680 • Tidal tails and streamers 681
8.4 Encounters in stellar disks 685
• Scattering of disk stars by molecular clouds 687 • Scattering of
disk stars by spiral arms 691 • Summary 695
8.5 Mergers 695
• Peculiar galaxies 696 • Grand-design spirals 698
• Ring galaxies 699 • Shells and other fine structure 701
• Starbursts 705 • The merger rate 708
Problems 710
9 Galaxy Formation 716
9.1 Linear structure formation 717
• Gaussian random fields 719 Filtering 720 The Harrison
Zeldovich power spectrum 721 • Gravitational instability in the
expanding universe 722 t Non-relativistic fluid 722 o Relativistic
fluid 726
9.2 Nonlinear structure formation 733
• Spherical collapse 733 • The cosmic web 735 • Press -Schechter
theory 739 l The mass function 744 The merger rate 746
• Collapse and virialization in the cosmic web 748
9.3 N-body simulations of clustering 751
• The mass function of halos 752 • Radial density profiles 753
• Internal dynamics of halos 756 i The shapes of halos 756
Rotation of halos 757 Dynamics of halo substructure 759
9.4 Star formation and feedback 760
Reionization 760 t Feedback 761 Mergers, starbursts and
quiescent accretion 762 The role of central black holes 764
o Origin of the galaxy luminosity function 765
9.5 Conclusions 765
Problems 766
Appendices
A Useful numbers 770
B Mathematical background 771
• Vectors 771 • Curvilinear coordinate systems 773
• Vector calculus 775 • Fourier series and transforms 778
• Abel integral equation 780 • Schwarz's inequality 780
• Calculus of variations 781 • Poisson distribution 781
• Conditional probability and Bayes's theorem 782 • Central
limit theorem 783
xii Contents
C Special functions 785
• Delta function and step function 785 • Factorial or gamma
function 786 • Error function, Dawson's integral, and plasma
dispersion function 786 • Elliptic integrals 787 • Legendre
functions 788 • Spherical harmonics 789 • Bessel functions 790
D Mechanics 792
• Single particles 792 • Systems of particles 794 • Lagrangian
dynamics 797 • Hamiltonian dynamics 797 Hamilton's equa-
tions 797 Poincare invariants 799 Poisson brackets 800
Canonical coordinates and transformations 800 Extended
phase space 803 t Generating functions 803
E Delaunay variables for Kepler orbits 805
F Fluid mechanics 807
• Basic equations 807 Continuity equation 807 Euler's equa-
tion 808 Energy equation 810 l Equation of state 811
• The ideal gas 812 • Sound waves 813 Energy and momen-
tum in sound waves 814 • Group velocity 817
G Discrete Fourier transforms 818
H The Antonov—Lebovitz theorem 822
I The Doremus—Feix—Baumann theorem 823
J Angular-momentum transport in disks 825
• Transport in fluid and stellar systems 825 • Transport in a disk
with stationary spiral structure 826 • Transport in perturbed axi-
symmetric disks 828 • Transport in the WKB approximation 829
K Derivation of the reduction factor 830
L The diffusion coefficients 833
M The distribution of binary energies 838
• The evolution of the energy distribution of binaries 838 • The
two-body distribution function in thermal equilibrium 839 • The
distribution of binary energies in thermal equilibrium 839 • The
principle of detailed balance 841
References 842
Index 857 |
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| author | Binney, James 1950- Tremaine, Scott |
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| classification_tum | PHY 971f |
| ctrlnum | (OCoLC)427483182 (DE-599)BVBBV023301111 |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023301111 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:46:40Z |
| indexdate | 2024-07-09T21:15:20Z |
| institution | BVB |
| isbn | 9780691130279 9780691130262 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016485567 |
| oclc_num | 427483182 |
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| physical | XVI, 885, [16] S. Ill., graph. Darst. |
| publishDate | 2008 |
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| publisher | Princeton Univ. Press |
| record_format | marc |
| series2 | Princeton series in astrophysics |
| spelling | Binney, James 1950- Verfasser (DE-588)171978153 aut Galactic dynamics James Binney and Scott Tremaine 2. ed. Princeton [u.a.] Princeton Univ. Press 2008 XVI, 885, [16] S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Princeton series in astrophysics Cúmulos estelares Galaxias Sternhaufen (DE-588)4183148-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Galaxie (DE-588)4057375-8 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Galaxie (DE-588)4057375-8 s Dynamik (DE-588)4013384-9 s DE-604 Sternhaufen (DE-588)4183148-2 s Dynamisches System (DE-588)4013396-5 s 1\p DE-604 Tremaine, Scott Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016485567&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Binney, James 1950- Tremaine, Scott Galactic dynamics Cúmulos estelares Galaxias Sternhaufen (DE-588)4183148-2 gnd Dynamisches System (DE-588)4013396-5 gnd Galaxie (DE-588)4057375-8 gnd Dynamik (DE-588)4013384-9 gnd |
| subject_GND | (DE-588)4183148-2 (DE-588)4013396-5 (DE-588)4057375-8 (DE-588)4013384-9 |
| title | Galactic dynamics |
| title_auth | Galactic dynamics |
| title_exact_search | Galactic dynamics |
| title_exact_search_txtP | Galactic dynamics |
| title_full | Galactic dynamics James Binney and Scott Tremaine |
| title_fullStr | Galactic dynamics James Binney and Scott Tremaine |
| title_full_unstemmed | Galactic dynamics James Binney and Scott Tremaine |
| title_short | Galactic dynamics |
| title_sort | galactic dynamics |
| topic | Cúmulos estelares Galaxias Sternhaufen (DE-588)4183148-2 gnd Dynamisches System (DE-588)4013396-5 gnd Galaxie (DE-588)4057375-8 gnd Dynamik (DE-588)4013384-9 gnd |
| topic_facet | Cúmulos estelares Galaxias Sternhaufen Dynamisches System Galaxie Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016485567&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT binneyjames galacticdynamics AT tremainescott galacticdynamics |