Index of Objects

Home , Abell 370, NGC 1300, NGC 1379, NGC 1549, NGC 1566, NGC 2300

Cambridge University Press 978-1-107-00054-4 - Dynamics of Galaxies: Second Edition Giuseppe Bertin Index More information

Index of objects

Galaxies NGC 3198, 31, 36, 175–6, 178, 255, 276, 283, NGC 221 (= M32), 20, 321, 350 285, 287, 293 NGC 224 (= M31), 4–5, 48, 80, 282–3, 289, NGC 3344, 264 321, 350, 381 NGC 3377, 321 NGC 309, 258, 265, 288 NGC 3379, 32–3, 314, 342, 344, 347, 371, 373, NGC 598 (= M33), 223–4, 381 376, 379, 385–6 NGC 628 (= M74), 23, 174, 259, 261, 265 NGC 3521, 36 NGC 720, 375, 377 NGC 3741, 259 NGC 801, 36, 284 NGC 3923, 386 NGC 821, 379 NGC 3938, 264 NGC 3998, 159 NGC 891, 24, 177, 180, 182 NGC 4013, 276 NGC 936, 264 NGC 4038, 75 NGC 1035, 284 NGC 4039, 75 NGC 1058, 259 NGC 4244, 27 NGC 1068, 445–6 NGC 4254 (= M99), 223–4, 256, 258, 261, 264 NGC 1300, 13, 225, 254, 256 NGC 4258 (= M106), 294, 321–2, 350, 445 NGC 1316, 386 NGC 4278, 378 NGC 1344, 387 NGC 4321 (= M100), 23, 224, 254, 264–5 NGC 1365, 225 NGC 4374, 33, 373, 387, 405–6 NGC 1379, 410–1 NGC 4406, 386 NGC 1399, 351, 373, 376, 379, 385–6, NGC 4472 (= M49), 347, 349–50, 370–3, 375–6, 405–6 379, 385–6, 405–6 NGC 1404, 373, 405–6 NGC 4486 (= M87), 5, 8, 20, 72, 80, 321, 350–1, NGC 1407, 388 376, 379, 385–6 NGC 1549, 22 NGC 4494, 379 NGC 1566, 21 NGC 4550, 37 NGC 1637, 265, 288 NGC 4552, 33, 410–1 NGC 2300, 382 NGC 4559, 177 NGC 2403, 28, 31, 177 NGC 4565, 27 = NGC 2599 ( UGC 4458), 36 NGC 4594 (= M104), 321 NGC 2663, 37 NGC 4596, 264 NGC 2683, 36 NGC 4622, 223, 254, 256–7, 288 NGC 2685, 159 NGC 4636, 5, 373, 375, 379, 385–6, 405–6 NGC 2841, 22 NGC 4649 (= M60), 379, 386 NGC 2859, 253 NGC 4650, 159 NGC 2903,174, 293 NGC 4725, 174 NGC 2915, 259, 261 NGC 4762, 27 NGC 2974, 378 NGC 5018, 37 NGC 2997, 23, 224, 258, 264–5 NGC 5044, 382 NGC 3031 (= M81), 17–8, 22–3, 163, 186, 249, NGC 5055 (= M63), 267 252, 257, 262–4 NGC 5077, 380 NGC 3079, 445–6, 449 NGC 5128 (= Cen A), 352, 379, 386–7 NGC 3108, 379 NGC 5194 (= M51), 12, 27, 224, 252, 255–6, 263–4 NGC 3115, 49, 321 NGC 5195, 224

456 Index of objects

NGC 5236 (= M83), 21, 264 ESO 510-G13, 23 NGC 5266, 379 ESO 603-G21, 159 NGC 5364, 21 NGC 5371, 174 II Zw 73, 159 NGC 5457 (= M101), 23–4, 264–5 Globular clusters NGC 5907, 24, 27, 47 NGC 104 (= 47 Tuc), 336–7, 351 NGC 6946, 23–4, 27, 259–60, NGC 2419, 331, 341 264–5 NGC 5139 (= ω Cen), 337, 351 NGC 7079, 264 NGC 6341 (= M92), 331 NGC 7796, 372, 374 NGC 7078 (= M15), 337

UGC 463, 264, 294 Clusters of galaxies UGC 2259, 292 UGC 2885, 36, 284, 292 Abell 370 (A370), 425 UGC 7321, 177 Abell 496 (A496), 388 UGC 7576, 159 Abell 520 (A520), 296 Abell 1758 (A1758), 434 UGC 12591, 36, 49 Abell 2218 (A2218), 5 Bullet, 15, 296, 375, 384, IC 342, 264 388, 427 IC 2006, 378 Coma, 51, 383, 388, 431 Ring, 296, 388 ESO 199-IG12, 159 Ursa Major, 8, 32, 40–1, 296 ESO 474-G26, 159 Virgo, 5, 8, 10, 20, 23, 46

Index

Abel inversion, 166, 316–7 stationary phase, 123, 245 accretion, 14, 24, 177, 392, 403, 405–6 steepest descent, 123 accretion disks, 63, 103, 109, 403, 435–49 two-scale analysis, 165 active disk, 442 atomic deuterium, 16 advection-dominated, 439 atomic hydrogen, 9–10, 12, 16–7, 24, 35, 40, 47, 159, α-disks, 438 177–80, 447 external irradiation, 438, 442, 444–5 21-cm line, 9, 11, 16, 34, 282, 317 and flat rotation curves, 441–2, 445–7 in elliptical galaxies, 55, 104, 377–9, 386, 435, 447 line profiles, 445, 447, 449 and Jeans instability, 12 luminosity, 437 and modeling of the basic state, 86, 162, 173–4, 218 optically thin, 438, 442 and rotation curves, 9, 34–6, 49, 167, 280, 282–3, 285 role of self-gravity, 439–47 in tests of density-wave theory, 17, 257 self-regulated, 439–47 and warps, 24, 266–7, 276 spectral energy distribution, 442–4 atomic nuclei, α decay of, 246 steady-state, 439–47 thickness, 438–9, 441 ballerina effect, 275 transition regions, 441 Balmer lines, 14 action and angle variables, 145, 152, 186, 301 barred spiral structure, 27, 223, 228, 240–1, 249, 288. See active disk, 174, 188, 216, 232, 288 also modes, global: bar active galactic nuclei, 7, 12–4, 18, 403, 435, 438, 445, in the near infrared, 27, 223, 228 adiabatic growth, 72, 290, 402 basic state, 54, 56, 82, 95, 99, 101–2, 113–4, 131–8, linearized equations, 324 162–83 models, 321–5 for disks, 88, 103 adiabatic invariant, 143, 154–5, 157, 223 for elliptical galaxies, 104 adiabatic response, 138, 357 evolution of, 180, 219, 229–30, 243–4, 248, 250, 261, age gradients, 252, 261 280, 287, 305, 313–5, 323–4, 355, 364–7, 391–6, Airy functions, 124 402, 413 Alfvén resonance, 81, 276 reference, for disk stability analyses, 172–4 Alfvén velocity, 275 reference, for the problem of dark halos, 175–7 amplitude modulation of spiral arms, 223, 228, 240, BBGKY hierarchy, 85 253, 256 bending waves, 61, 101, 119, 157–8, 184, 265–79 amplitude of spiral structure. See arm-interarm contrast action conservation, 269, 289 (or arm strength) analogy with a flag flapping in the wind, 270, 278, 289 angular-diameter distance, 412, 420, 429 angular-momentum density, 269 anisotropic harmonic oscillator, 304–5, 312 on a current sheet (in the heliosphere), 273–6 anisotropy radius, 339 and disk-halo interaction, 270–2, 278 arm-interarm contrast (or arm strength), 23, 224, 228, group velocity, 269 243, 258, 261, 285 homogeneous slab model, 269–72 asymptotic methods (or analysis), 62, 90–2, 94, 121, 124, inhomogeneous disk, 272–3 190–1, 234, 236, 344, 441 wave packets, 267, 270–1 Laplace integration, 340 wave trains, 269 matched asymptotic expansions (or matching), 91–2, Bessel functions, 170, 189, 193, 221, 237–9 121, 186, 207, 231, 237, 239, 276, 333 Big Bang, 4, 45, 57 ordering, 46, 91–2, 188, 190–1, 207, 219, 232–3, 344 Bohr-Sommerfeld quantum condition, 239 phase-integral, 94, 237 Boltzmann entropy. See entropy functional

458 Index

bounce frequency, 137–8, 164 and statistical mechanics, 394–401 bounce orbit and violent relaxation, 77–8 average, 324, 359 color gradients, 30 expansion, 138 across spiral arms, 252, 261–2 boundary conditions, 62–3, 65, 82, 90–2, 98, 177, 182, comoving coordinates. See Lagrangian coordinates 292, 320, 327, 333, 340–1 (description) for bending modes, 273 compact ellipticals, 20 for bending waves on a current sheet, 276 concordance cosmological model, 10, 46–7, 57 and dispersive waves, 122, 126–8 conspiracy, 35–6, 40–1, 286–7, 348, 408 for global spiral modes, 186–7, 189, 201, 204, 231–3 continuum limit, 58, 64, 72, 84–5, 143, 394 for modes in spherical systems, 360–1, 394 controlled thermonuclear research, 65 for selection of quasi-spherical models, 339–40 convective amplification and damping, 270–1 for a steady cooling flow, 404 cooling flows, 402–8 in two-turning point problem, 234–5, 238, 246 fit for a set of x-ray bright galaxies, 406 boundary layer, 91–2, 437 core radius, 320, 330 Boussinesq equation, 128 Coriolis force, 64, 134 box orbits, 306, 309, 311 corotation boxiness, 21, 33, 38, 335, 344 circle or radius, 149–52, 155, 185, 189, 197–9, 203–6, boxlets, 311 216, 221, 260, 269 Boyle law, 392–3 empirical determination, 252, 256–7, 262–4 bremsstrahlung (free-free emission), 11, 383, 403, 442 for normal and barred modes, 240–2, 248, 253–4 bulge, 7, 21, 23, 29–32, 36, 38, 48, 57, 74, 87–8, 90, 103, resonance, 149–50, 189, 222–3 157–8, 162–3, 167–8, 171–80, 200, 249, 254, 267, turning point, 238–9 283–4, 286, 300, 322, 352 zone or region, 64, 157, 186, 203–6, 231, 235 Burgers equation, 121 corrugations, 23, 266, 276, 355. See also warps cosmic acceleration equation, 46 capture of satellites, 71–4, 365 cosmic age or time, 46, 414 cat’s eyes, 156–7 cosmic background radiation, 9–10, 45–6, 57, 429 causality condition, 128, 135 cosmic chemical composition, 404 cD galaxies, 7, 20, 38, 74, 406 cosmic ether, 45 Cepheid variables, 10, 46 cosmic expansion equation, 46 Cerenkovˇ cone, 129 cosmic rays, 16, 18, 62, 274 Chebyshev polynomials, 305 cosmic shear, 429–30, 433. See also gravitational lensing chemical evolution of galaxies, 14 cosmological constant (). See parameter: cosmological circular velocity, 34, 36, 168, 346, 349, 372, 409, 425, dark energy () circularity function, 317 Coulomb logarithm, 68, 71, 79, 85 circularization of orbits, 71–2, 379 counterrotation, 37, 39, 168 classification of galaxies coupling dynamical, 54, 253–5 of disk and halo, 271 luminosity, 21 of modes, 258 morphology (Hubble), 19–20, 26, 103, 248–9, 254, 391 cross correlation technique, 49 regularity, 22 current sheet, 61 clusters of galaxies, 4–7, 9–10, 15–16, 20, 32, 37–8, in a plasma slab (Harris pinch), 97–9 40–4, 46, 49–51, 56, 74, 104, 280–1, 294, 296, 375, in the heliosphere, 273–6, 279 380–5, 388, 402–8, 418–9, 425–32 cusps coexistence, 27, 243, 249, 251, 254, 257, 262. See also in collisionless dynamical models, 316, 346, 373 modes, global: coexistence collisional, 323, 351 Cole-Hopf transformation, 121 cosmological, 290–1, 373 collisional Boltzmann equation, 351 and gravitational lensing, 425 collisionless Boltzmann equation, 58, 64, 84–8, 96–7, and gravothermal catastrophe, 392 120, 131, 157, 181, 299, 304, 360, 394, 396 power law and massive black holes, 322–5, 371 for linear adiabatic growth, 323–5 cyclotron frequency. See Larmor (cyclotron) gyration for linear perturbations, 134–8, 187–189, 219–22, 356–62 dark energy. See parameter: cosmological collisionless collapse, 56, 318, 370–1 dark energy () as physical basis of f∞ models, 337–49 dark matter and properties of galaxy cores, 343 baryonic and nonbaryonic, 45–6, 285 and radial-orbit instability, 73, 362–4 central cusps, 290–1, 373

Index 459

cold, 47, 290, 398 for two-component systems, 349 and cosmology, 44–7, 427–32 density waves dynamical arguments, 288–9 action density, 196–200, 208, 221, 237, 259 in elliptical galaxies, 370–81 analogy in magnetized plasma, 189 in groups and clusters, 381–5 angular momentum density, 189, 197–8, 203–5, 222, hot, 47 244, 258, 261 and modeling, 87–8, 172–80, 253–6, 270–3, 347–9, branches (short, long, open, trailing, leading), 195–9 408–11 with complex wave number, 207, 220–1 nonspherical isothermal halo, 175–7 dispersion relations, 187–91 size of dark halos, 42, 48, 427 energy density, 189, 197–8, 203–5, 222, 258 shapes of dark halos, 164–8, 175–7, 283, 285, 290, finite-thickness effects, 191–4, 217, 227, 250, 260, 265 375, 427–8, 441 fluid reduction factor, 190, 211 in the solar neighborhood and in our Galaxy, 164–8, group propagation, 197–8 289–90 kinematic, 150, 273 in spiral galaxies, 280–94 observational tests, 184–7, 189, 223–6, 229–30, 241, substructures, 26, 291, 425, 430 243–5, 247–50, 252–61 Debye length, 64–5, 79, 85, 98, 133 ODE representation, 232–5 decoupling regime of heavy disks (B, of high J), 194–7, 199–205, of cold gas from a cooling flow, 403–6 253–6 in the cosmological context, 47, 381 regime of light disks (A, of low J), 194–7, 199–205, of gas and stars, 194, 212–9, 254 253–6 in the geometry of the basic state, 162, 436 shock scenario, 185, 226, 252 between morphological and regularity classification, 22 stability conditions, 191–7, 203–6, 211–5 between optical and x-ray isophotes, 375, 384 stellar reduction factor, 189, 220 between shape and rotation, 301 tightly wound, 184–91 of visible and dark matter dynamics, 287 in two-component disks, 211–5 of wave and star motion, 202, 247 wave cycles, 202–5, 231, 237–40, 242. See also of wave dynamics in the linear theory, 101 feedback; and overreflection deductive approach, 54, 57–8, 62, 82, 85–6, 103, 172, wave packet, 199–200, 202–3, 205–7, 249 230, 253, 315, 408 wave trains, 200, 206 degeneracy descriptive approach, 53, 315, 317–8, 346 age-metallicity, 14 detailed angular-momentum conservation, 72, 394, 397–8 dark matter and pressure anisotropy in ellipticals, diamagnetic current, 169 371–4 differential rotation, 34, 110, 116, 134, 144–5, 149, 187, of different m values in perturbations to a spherical 202, 208, 210, 247, 253, 335, 352, 447 model, 358 luminous and dark matter in spirals, 175–8, 255, 287 diffusion equation, 85, 436, 439 mass-sheet in gravitational lensing, 426–30 dimming, cosmological, 430 of spherical models, 319 dipole, 115 in the statistical mechanical context, 395, 402 Disk Mass Project, 182, 255, 286 density-potential pairs, 162, 168–9, 316–8 disk shocking, 331 for cusp modeling, 346 disk truncation, 30, 273, 441, 443 exponential disk, 170 disk-halo interaction, 270–2. See also bending waves isochrone sphere, 303 diskiness, 21, 33, 38, 335, 344 isothermal slab, 163–4 dispersive waves, 62, 64, 91, 101, 119–29, 131, 187, 197, Maclaurin disk, 170, 182 269. See also density waves MOND, 292 dispersion relation, 119, 122, 124–8 perfect ellipsoid, 310 group velocity, 123, 125, 128–9 perfect sphere, 304 phase velocity, 124, 128–9 Plummer sphere, 321 in physical space, 122, 124. See also modulation theory pseudoisothermal sphere, 175 wave action, 124 / and R1 4 law, 346 wave branches, 119, 122, 128. See also propagation regularized self-similar disk, 171 diagrams self-similar disk, 170 wave energy, 124 singular isothermal sphere, 320 in wave number space, 124, 205–6 Stäckel, 316 wave packet, 119, 121, 123–5, 129 density-priority models, 316–7, 365 wave train, 119, 124 for tangentially biased models, 350 dissipation-driven instabilities, 64, 100, 113, 115, 152

460 Index

dissipative collapse, 285, 384, 391–2, 396, 402–8, collisionless (stellar dynamical) counterparts and 435, 447 analogues, 110, 117, 182, 367, 369 dissipative interstellar medium, 7, 12, 55, 74, 83, 162, Dedekind adjoint solutions, 108–9, 114 172–3, 210, 229, 251, 261 Dirichlet–Riemann linear flow, 108, 113 and self-regulation, 173, 201, 210, 218–9, 244, heterogeneous, 109–110, 310 250–1 Jacobi, 105–18, 253 and settling of polar rings, 160, 268 gravitational energy, 107 and shock formation, 121, 210, 226, 247 Maclaurin spheroids, 105–18, 170, 182, 207, 230, distance estimators, 40, 43–4, 336, 422, 429 253, 367 distance modulus, 412 modal analysis, 113–5 distribution-function priority models, 315, 318–9, 337, potential inside, 106 349–50, 352 potential outside, 107 Doppler-shifted frequency, 137, 187, 190, 195 Riemann, 109, 114 double adiabatic theory, 157 Roche, 109 drift, 143, 155 elliptical integrals, 106–7, 170 asymmetric, 168–9, 286 ellipticity, 117, 375, 428 diamagnetic, 169 complex, 426, 433 E × B, 153–4 profile, 21, 179, 334–6, 345, 352 magnetic gradient, 153–4 emission-weighted temperature, 376 polarization, 155 energy distribution N(E), 338, 343, 395 of young stars away from spiral arms, 261 energy principles, 366–7 dual morphology. See coexistence entropy functional, 393–4, 395, 397–400, 416 dumbbell galaxies, 74 epicyclic motion (epicycles), 22, 35, 146–56, 168, 186, dust extinction, 14 206, 210, 220, 222, 254, 257, 278, 311, 317 dust lanes, 21, 185, 223 complete expansion, 148 dwarf ellipticals and dwarf spheroidals, 19, 26, 44, 55, frequency, 65, 134, 147, 301–3 291, 313–4, 371, 380, 382, 387 to two orders, 148, 168 equation of state, 86, 98, 110, 132, 318, 323, 404 dynamical exclusion principle, 394–5 baroclinic, 180 dynamical friction, 68, 70–5, 85, 270–1, 290, 293, 379, barotropic, 88, 110, 178, 180 382–3 for collisionless plasma, 157 dynamical window, 53–4, 104, 243, 365 isothermal, 163, 320 polytropic, 110 early-type galaxies, 20–1, 31–2, 48, 56, 73, 90, 373–4, equipartition, 68, 75–6, 80, 89 379–80, 386–7, 407, 414, 427–30, 447 equipotential surfaces, 110 eccentricity, 105–16 equivalent acoustic (or effective thermal) speed (or ecliptic plane, 273–4 velocity dispersion), 88, 173, 180, 190, 216, effective potential, 145–6 399, 438 effective radius (or half-luminosity radius), 33, 43, 50, escape velocity (and escape energy), 181–2, 326, 332 371, 374, 408–9, 412, 429 Eulerian coordinates (description), 206 eigenstates in quantum mechanics, 101, 253 evanescent waves, 198–9, 235, 238, 276 eigenvalue problem evaporation, 75, 331, 392 for the construction of f∞ models, 341 exponential length (or scale) for disks, 30, 35, 41, 175, for modes on a spherical system, 360 210, 226, 248, 254, 256, 260, 263 for spiral modes, 229–39 extraplanar gas, 55, 177–80, 281 eikonal equation, 125 extrasolar planets, 419, 424, 435 Einstein Cross, 422 extratidal light, 331, 352 Einstein ring, 289, 421, 427. See also gravitational lensing electromagnetic plasmas (and plasma physics), 53, 57–8, feedback. See also density waves: wave cycles 61–5, 69, 76, 82, 84–7, 90–1, 93, 95, 103, 115, 118, of bending waves, 271 130, 133, 143, 154–7, 169, 185, 187, 207–8, 253, of density waves from the central regions, 202–4, 261, 319, 347, 359, 366, 392, 396, 437 231, 249 Einstein-de Sitter cosmological model, 46, 412 and x-ray emission from ellipticals or clusters, 408 ellipsoidal coordinates, 306–9 Fermi-Dirac statistic, 394 ellipsoids, classical, 38, 89–90, 95, 101–2, 105–18, 152, Feynman, on gravitation, 3, 45 288, 310 figure rotation, 110, 268, 301, 310, 314 applications in different fields, 105 fine-grained and coarse-grained, 76, 395 bifurcation theory, 108–9, 113–6, 253 fire-hose instability, 269, 369

Index 461

flaring, 445 globular clusters, 3–4, 39, 44–5, 55, 57, 65, 74, 79, 83, flattening, 20, 108, 111, 114, 324, 335, 369 85, 290–1, 313–4, 318–9, 341, 371, 380, 435 bulge, 157, 182 age, 325 Earth, 149 core radius, 330 globular clusters, 335–6 and dynamical friction, 69–74, 396 halo, 157, 177, 179, 288 in elliptical galaxies, 4, 20, 72 ellipticals, 26, 34, 38, 111 density distribution in our Galaxy, 4, 290 fast-rotating stars, 116 and gravitational lensing, 424 flocculent spirals, 22, 228, 248, 254–5, 263. See also and gravothermal catastrophe, 351, 392–3 classification of galaxies: regularity as kinematic tracers, 158, 379, 386 fluid limit, 85–8, 136–7, 190 as King models, 326–37 fluid model, 53, 85–8, 394 and MOND, 291, 387 and behavior at resonances, 219–23 post-core-collapse phase, 330 for density waves, 206–7, 210–9 relaxation time, 74–5, 79–80 for disk-halo interaction, 271 rotating, 334–7 for global spiral modes, 229–45 shapes, 325–6 f∞ models, 337–49 as triaxial stellar systems with isotropic pressure, 332–4 core and nuclear structure, 342–3 truncation, 325, 331–2, 346–7, 352, 393, 401 density profile, 342 graininess (or granularity), 64, 83, 85 generalized to negative temperature, 340, 365 grand-design spiral structure, 55, 184, 247–65 and gravothermal catastrophe, 344 alternative scenarios, 244–5, 263 as limit of fn family, 340 in the gaseous outer disk, 17, 259–61 and measurements of the mass-to-light ratio, 344, 349 as generally bisymmetric, 22, 228, 258 nonspherical, 344–5 as generally long-lived, 184, 187, 202, 247–65. 1/4 and R law, 344, 349 See also quasi-stationary spiral structure selection criterion, 340 as generally trailing, 204 stability, 362–6 and global modes, 210, 240, 247–65 from statistical mechanics, 396–8 in the near infrared, 22–3, 223–4, 228, 243, 245, 255 two-component (i.e., with dark matter), 347–9 gravitational lensing, 5, 9–10, 48, 58, 177, 281, 289–91, (ν) f models, 340, 396–401 370, 380, 384, 387, 418–34 and gravothermal catastrophe, 398–400 arcs, 5, 424–5 Fokker-Planck equation, 85, 319, 323 by an axisymmetric lens, 421, 424–5 force-free magnetic configurations, 396, 415 caustics, 425 form factor (q), 342, 346 complex ellipticity, 426, 433 Fourier analysis, 101, 122–4, 127, 134–7, 188, 205, 242, critical density, 419–21, 424 248, 359 critical lines, 424–5 Fourier quotient technique, 49 deflection potential, 420–1 Fourier-Bessel transform, 170 double, 431–2 Friedmann-Lemaˆıtre cosmological model, 46, 412 of extended sources, 421, 423, 425 frozen-in condition in a plasma, 276, 396 Jacobian matrix, 423–6, 431 FU Orionis objects, 442–7 magnification, 423–4, 426–7, 429–31 and MOND, 294, 384, 427 galactic fountain, 182 multiple images, 9, 16, 419, 421–2, 424–5 galactic longitude, 144–5 by a point mass, 420 galaxy-galaxy interactions, 5, 7, 19, 56, 65, 74, 280. See polarization, 425–6, 428–9 also merging ray tracing equation, 419–20, 423–5 galaxy-galaxy lensing, 48, 427–9, 433. See also reduced shear, 426 gravitational lensing refraction index, 419 gamma functions, 171, 327 shear matrix, 423, 426 gamma rays, 10, 16 surface brightness conservation, 423, 430 gas-to-star density ratio, 5, 30, 164, 174 time delays and measurement of the Hubble constant, in our Galaxy, 165 51–2, 421–2, 427, 429 Gauss theorem and jump condition, 134, 164, 233 gravitational waves, 16, 18 geostationary satellites, 152 gravothermal catastrophe, 76, 133, 330, 344, 351, 392–5, Gibbs free energy, 115 398–401, 416 global description of stellar systems, 325–349 gravothermal oscillations, 393 global temperature, 399–400, 416 groove instability, 222

462 Index

guiding-center orbits, 61, 65, 143, 145, 147, 153–8, exceptional, 305 160, 168 isolating, 304–11, 316, 339–40 gyrogravothermal catastrophe, 393 local, 305 quasi, 305, 309, 319 half-mass radius, 79, 303–4, 319, 321, 328, 339, 342, third, 304–5, 339 346, 348, 398 integration along the characteristics (or along the halo. See dark matter unperturbed orbits), 120, 131, 138, 148 Hankel functions, 238, 246 interstellar medium (ISM), 12, 15, 17, 22–3, 54–5, 58, heat equation, 121 70, 74, 210, 219, 223, 247, 250, 252, 263, heating of the disk, 218–9, 250–2, 438–40 377, 403 heavy disks. See density waves: regime of heavy disks magnetic fields, 11–2, 82, 377, 403 (B, of high J) intracluster medium (ICM), 5, 9, 15–6, 281, 375, 383–4, helicity integral, 396 388, 403–4 Hessian, 157 irrotational flow, 126 Hickson compact group, 383 isophotes, 21, 33, 334, 344, 378, 382 hierarchical formation, 39, 414 offset of optical and x-ray, 375, 377, 384 high-temperature plasmas, 64, 69, 97, 144 twist, 21–2, 33, 55, 299, 316, 355 high-velocity clouds, 24, 183 isothermal nonspherical halo. See dark matter high-velocity stars, 182 isothermal self-gravitating slab, 163–7, 193, 319 HI. See atomic hydrogen isothermal self-similar disk, 171–3 HII regions (warm ionized gas), 11, 14, 21–2, 177, 180, isothermal sphere, 175, 177, 282, 290, 319–27, 330, 371, 185, 380 380, 392–4, 416, 423, 428, 441 Hill surface, 333 isovelocity contours, 267, 378 Holmberg radius, 30, 267 iteration methods, 172, 177, 182, 324, 333, 335, 405 homology, 38, 343, 409–11, 428 Hubble constant (H ), 8, 43, 46, 51–2, 292, 384, 412–3, 0 Jacobi integral, 149, 151, 155, 312, 332 422, 427, 433 Jacobian, 397 dimensionless or reduced (h), 46, 412–3 Jeans equations. See moment equations Hubble Deep Field, 8, 11, 17 Jeans, on galaxy classification, 20, 26 Hubble profile, modified, 310, 320, 345 Jeans, on modifying the law of gravity, 291 Hubble time, 3, 46, 65, 70, 250, 314, 381, 403, 406 Jeans instability, 12, 131–9, 208, 248, 394 Hubble Ultra Deep Field, 4, 8 in accretion disks, 439–42 hurricanes, 24–5, 249 homogeneous fluid model, 131–2 hydrostatic equilibrium, 15, 163, 193, 281, 323, 374–7, homogeneous kinetic model, 134–7 383, 402–5, 418 in one-component disks, 191–5 hyperbolic waves, 119–21 rotating homogeneous fluid model, 133–4 characteristics, 120–1, 125, 131, 135, 137–8, 143 slab kinetic model, 137–8 wave breaking, 121 hypervelocity stars, 158 in two-component disks, 210–5 Jeans length, 64–5, 79, 98, 132, 134, 392 Jeans theorem, 64, 85, 95–8, 299–300, 304–5, 311, ignorable coordinates, 101, 305 314–5, 339 incompressible fluid, 84, 105, 110, 113, 122, 126, (J,Q) diagram, 195, 201 271–2, 276 inflationary scenario, 47, 118 inhomogeneities, 62–3, 79, 96–7, 131, 154, 355, 366, KandK (near-infrared bands), 9, 19, 22–3, 26–7, 30, 40, 369, 393–4, 429 53, 55, 223–8, 240–6, 254–8, 263–4, 281, 288, 409, and basic state of the disk, 89–91, 96, 137, 158, 163–5 449 and bending waves, 269, 272–3 KAM theorem, 311 and density waves, 184, 186–7, 198–202, 205, 219, 229 Kelvin circulation theorem, 117, 396 and dispersive waves, 121, 124–5 Kelvin modes, 113 and transport processes, 58, 69–75 Kelvin-Helmholtz instability, 270 and virial theorem, 132 Keplerian decline, 34, 181, 282, 436–7, 441–2, 445–7 initial conditions, 53, 56–7, 62, 72, 77, 82, 122, 250, 252, kernel (potential theory of a disk), 169, 232 261, 315, 337, 363, 391, 394, 397, 400, 436 kinematic limit, 132, 150, 273 initial mass function (IMF), 13 kinematic tracers, 370, 374–80 integrability, 58, 157, 300, 312, 314 discrete, 379 integrals of the motion, 85, 96–8, 137–8, 145, 299–300, King models. See globular clusters 314–5 Klein-Gordon equation, 122

Index 463

Korteweg-de Vries equation, 128, 130 Mach number, 129 Kuzmin theorem, 316 Magellanic Clouds (LMC and SMC), 5, 18, 74, 270, 277, 289, 295, 381 Lagrange multipliers, 397–8, 402 magnetic islands, 156–7 Lagrangian coordinates (description), 108, 113, 206 magnetic mirror, 143 Lagrangian points. See trapping magnetic reconnection, 117, 157, 207, 275 Landau damping, 64, 76, 134–8, 270 magnetic sectors. See solar sectors at resonances for density waves, 189, 207, 211, magnetically confined plasmas, 64–5, 149, 157 219–23 magnetohydrodynamics (MHD), 81, 86–7, 139, 157, 216, at resonances in spherical systems, 360, 366 275–6, 396 Lane-Emden equation, 321, 323 and conservation laws, 396 Langer’s transformation, 235–7 marginal stability, 102, 136–7, 192–5. See also modes, Laplace equation, 126, 149 global: neutral; density waves: stability conditions Larmor (cyclotron) gyration, 65, 143–4, 153–5 for the cubic dispersion relation (and relation to the late-type galaxies, 5, 20–1, 32, 36, 48, 264, 284, swing amplifier), 194–5 294, 387 for the gravothermal catastrophe, 394 leading waves, 195–7, 202–5, 252–3. See also density and radial orbit instability, 364, 366–7 waves for a thick self-gravitating fluid disk, 193 Legendre polynomials, 149, 182 for two-component disks, 212–5 generalized, 357 mass estimators, 370, 382 Lenz vector, 311 mass segregation, 75, 80, 392 libration, 152, 156 mass-to-light ratio, 14, 30–1, 36, 40, 55, 175, 315–6, 318, light disks. See density waves: regime of light disks 343, 348–9, 404, 409–10 (A, of low J) in clusters and groups, 381–4 likelihood, 176 cumulative, 349, 373 Lindblad diagram, 352 and dark matter in ellipticals, 370–81 Lindblad resonances, 149–52, 195, 198–9, 203, 207, 245, and dark matter in spirals, 280–96 250–1 massive black holes, 7, 9, 44, 55, 76, 281, 294, 314, different behavior of gas and stars, 211, 219–22, 242, 321–5, 351, 353, 365, 369, 373, 389, 408, 424 258–9 and the Galactic Center, 6, 445 ILR, exposed, 203, 242, 252 and accretion disks, 435–6, 445, 449 linear limit, 95, 99, 101 influence radius, 324 line-of-sight velocity profiles (or line profiles), 39, 315, preexisting collisionless collapse, 402 317, 349, 372, 374. See also accretion disks material arms, 249 linkage of vortex lines, 396 matrix equation, 245, 361, 368 Liouville theorem, 84 maximum disk (maximal disk), 36, 41, 167, 175, 177, local description of stellar systems, 70–1, 299, 319–25 182, 250, 255, 258–9, 264, 285–8, 348 Local Group, 4–5, 20, 381–2, 387 maximum value of the distribution function logarithmic spirals, 205 (constraint), 395 and α-spectrum, 242 Maxwellian distribution, 69, 78, 96–7, 134, 319–21, long-axis tubes, 307–9 339–40, 347 lookback time, 391, 408, 413 for a plasma current sheet, 97–8 lopsidedness, 26, 258–9 quasi (for disks), 162, 168–9, 181, 188 Lorentz force, 64. See also Larmor (cyclotron) gyration quasi (for spherical systems), 318, 325–32 loss cone, 182 and statistical mechanics, 78, 96, 396–402 low-luminosity galaxies, 7, 33, 38, 55–6, 291, 313, 319, Mayer cluster expansion, 94 371, 410 mean gravitational field (and potential), 29, 34–5, 63, 66, low-surface-brightness (LSB) galaxies, 20, 29, 32, 36, 42, 83–5, 143, 145, 147, 299, 337, 402, 419 48, 287 mean surface brightness (SBe), 43–4, 50 luminosity distribution of galaxies, 7, 313, 326, 380, 410 merging, 7, 19, 56, 72–4, 323, 337, 365, 383, 394, 396, luminosity profiles, 30–33. See also cusps; core radius 409, 414 exponential law, 30–2 meridional circulation, 180 / R1 4 law, 32–3. See also f∞ models metastable models, 364 / R1 n law, 33 microlensing, 289, 418, 424, 433. See also gravitational universality. See homology lensing luminous-dark-matter decomposition, 36, 41, 167, 172, migration of stars, 252 175–7, 255, 282–7, 348–9, 371, 410 Milky Way galaxy (our Galaxy), 3–4, 10, 16, 27, 34, 51, Lyman lines, 14 145, 167, 181, 222, 255, 283, 381

464 Index

minor-axis rotation, 39 particle-mesh or mean-field codes, 83 modeling, 58 resolution in phase space, 219, 252 disk, 172–7 and spiral modes, 218–9, 244, 250–2, 262–5 elliptical galaxies, 313–9 tree codes, 83 two-component disk, 215–8 softening, 83, 89 modes, global, 229–46, 356–61, 394 near infrared (near IR). See K and K’ (near-infrared ballooning, 207 bands) bar, 240–2, 253–6 negative global temperature, 399–400 bending, 268, 271, 273, 277–8 negative specific heat, 89, 351, 392, 394 continuous spectrum, 244–5, 367 negative temperature, 340, 364–366 coexistence, 243, 251, 254, 257 negative-energy waves and modes, 64, 198, 208 damped versus self-excited, 240, 244, 367 negative-mass instability, 222 discrete spectrum, 244–5. See also Bohr-Sommerfeld neutral hydrogen. See atomic hydrogen quantum condition neutrino mass, 47 eigenfunction, 229, 232, 240–2, 254, 358, 366, 394 Noether theorem, 311 eigenvalue. See eigenvalue problem nonlinear equilibration (or saturation), 102, 210, 229, exact integrodifferential problem, 227, 231–2, 241, 360 244, 253, 257–8, 265 g, 113 nonmodal scenarios, 244–5, 249 Kelvin (or f modes), 113 nonparametric inversion, 317 matrix equation, 245, 361, 368 normal (nonbarred) spiral structure, 210, 218. See also moderately unstable, 102, 201, 240, 243, 251, 253 modes, global: normal (nonbarred) neutral, 99–100, 113–4, 229, 271, 288 in the near infrared, 223–6, 228 neutral tilt, 273 nucleosynthesis, 18, 58 normal (nonbarred), 240–2, 253–6 observational tests, 252–61 oblate, 31, 38, 73, 106–8, 273, 285, 309, 318, 335, 340, p, 113 355, 358, 365, 369, 374 pulsation, 114 ocean waves, 22, 260 quasi (of black holes), 246 O(4) invariance, 311 spiral prototypes, 199, 242, 248, 254–5 Oort, on spiral structure, 22, 27, 227, 244, 248, 251, 262 survey, 173–4, 191, 218, 230, 240–3, 250, 253–4, 256, 262 Oort constants, 144–5, 290 toroidal, 114, 369 Oort mass discrepancy, 145, 165–7, 181, 255, 280, 289 transverse-shear (bending), 113 optically thick, 438, 443 with two-blob (or two-lump) structure, 205, 240, optically thin, 403, 438, 442 253, 258 orbit superposition (Schwarzschild method), 64, 160, 300, in two-component disks, 211, 215–9, 231, 250, 254, 310–2, 316–7, 373 258, 271 Ostriker-Peebles criterion, 106, 115, 118, 288, 367, 369 modified Newtonian dynamics (MOND), 291–6, 375, overreflection, 198–9, 203–4, 231, 239, 251–3 384, 387, 427 overstability, 369 modulation theory, 124–5, 130 molecules, 22, 35–6, 54, 104, 162, 210, 218, 322 parameter CO, 10, 12, 17, 445 anomalous viscosity, 438 (giant) molecular clouds, 4, 165, 218, 252, 256, axisymmetric stability (Q), 90, 165, 201, 439 264, 281 central potential (#), 327, 337, 399–400 molecular hydrogen, 10, 12, 16, 285, 393, 445 concentration (C, for King models), 99, 327 and spiral structure, 210, 218, 252, 256, 264–5 cosmic rotation (λ), 39 water maser emission, 16, 445–6 cosmological dark energy (), 46, 56, 413, 429–31 moment equations, 86–7, 317–8, 364, 369, 373 cosmological density (m), 46, 56, 413, 429–31 effective stability, 194, 213, 215–8, 449 N-body simulations, 26, 49, 57, 70–4, 80, 82–4, 89–90, epicyclic (ε), 174, 188, 232 92–3, 182, 288, 290–1, 295, 315, 344–5, 352, 356, gas-to-star density (α), 211, 215–8 362, 364, 366–9, 385, 391, 393, 398, 425 gas-to-star temperature (β), 211, 215–8 of black-hole growth, 351 global anisotropy, 342, 362 of collisionless collapse, 78, 318, 337–9, 341, 353, Hubble constant, dimensionless (h), 45 363–5, 394–5, 397–401, 415 impact (b), 67–8, 79 direct codes, 83 local anisotropy, 338–40 excessive heating, 83, 262 magnetic support in plasmas, 64 and MOND, 292, 296 nonaxisymmetric stability (J), 191, 201

Index 465

for the onset of the gravothermal catastrophe, 392–4 potential photometric index (n), 33 Earth, 149, 152 plasma (g), 85 Eddington (or Stäckel), 90, 306, 309–11, 316, 337, 369 rotation strength, 334 harmonic, 71, 147, 302, 304, 324 rotational support (t), 107, 367 isochrone, 148, 303, 340, 342 self-gravity (ε0), 165, 174 Keplerian, 145, 147–8, 302, 304, 324, 436–9 thickness, 165, 191 logarithmic, 63, 171, 302–3, 321, 324, 371, 428 threshold acceleration for MOND (a0), 293 rotating Stäckel, 312 tidal strength, 332 precession, 149, 152, 157, 266–8, 291 vorticity (f), 109, 111, 115 pressure anisotropy, 38, 54, 64, 72, 86, 111, 157, 269, WKB (|rk|), 188, 232–3 392. See also pressure tensor parametric instability, 268 and axisymmetric equilibrium, 111, 317–8 parity, 101 and closure of moment equations, 86–7, 318 even perturbations, 101, 229, 275 for a cool disk, 66, 87, 147, 168 odd perturbations, 101, 275 in globular clusters, 75, 330, 335–7 partitions of phase space, 85, 397 and impact on density waves, 208 passive evolution, 56, 409, 414 and integrals of the motion, 96, 300, 316 passive role, 211, 218, 243, 253, 442 and modeling of elliptical galaxies, 310, 313–4, pattern formation, 55–6, 128–9, 184, 187, 250–3, 337–41, 350, 352, 372, 398–401 262–3, 270 and radial orbit instability, 355, 362–6 pattern frequency (or speed), 184–5, 189, 195, 202–3, pressure tensor, 34, 86–7 221, 249, 251–3, 256–7, 259, 261–4, 269–70, radially biased, 73, 337–41, 363–6, 368 300. See also corotation tangentially biased, 72, 75, 311, 347, 370 phase diagram, 213, 216 principal planes, 21, 109, 268, 311 phase transitions, 105, 115–7 principal range of spiral structure, 189, 195, 212, 220 photodissociation regions, 17 prolate, 73, 106–7, 273, 300, 307, 309, 333–4, 340, 355, plane capacitor, 164 358, 364–5 planetary nebulae, 39, 379, 386–7 propagation diagrams, 189, 198–200, 202–3, 205, 241–2, plasma dispersion function, 135–7, 139, 221, 270 254. See also density waves: branches (short, long, plasma frequency, 64 open, trailing, leading) plasma (Langmuir) waves, 133, 138 in two-component disks, 216–7, 227 Poincaré proper motions, 167, 326, 336, 381 on dark matter, 51 pseudo-phase-space density, 398 on relaxation, 80 pseudoisothermal sphere, 175, 423 Poincaré pears, 109, 114. See also ellipsoids, classical Poincaré-Wavre theorem, 183 quadratic programming technique, 374 Poisson brackets, 84, 356 quadrupole, 115, 149, 152, 310, 425–6, 433 Poisson equation, 61, 84, 96, 132, 135, 300–1, 319, 321, quasi-circular orbits, 72–4, 89, 144, 146–52, 162, 332–3, 335, 339, 356–7, 421 301, 372 for the axisymmetric case, 165 quasi-neutrality in plasmas, 63, 90 for an electrostatic plasma, 133 quasi-stationary spiral structure, 19, 24, 55, 159, 202, 226 for even perturbations on a thin disk, 134 hypothesis, 184–7, 241, 247–52, 267 in MOND, 292 and modal theory, 226, 230, 240, 243–5, 248–52, in polar cylindrical coordinates, 88 256–8, 267 for reduced potential, 233 for a self-gravitating finite-thickness disk, radial action, 72, 146, 302, 323–5 163–5 radial orbit instability, 73, 356, 362–5, 368, 399 for the spherical case, 320, 327, 341 radiation boundary condition, 128 in spherical coordinates, 356–7 radio continuum, 10–12 for tightly wound perturbations, 211, 232–3, ray tracing, 121, 125, 419–20, 423–5. See also 245 gravitational lensing polytropic ellipsoids, 110 Rayleigh’s criterion for rotating fluids, 147 polytropic sphere, 320–1 reduced mass, 68 generalized, 369 regimes, 56, 62, 70, 97, 132, 269, 292, 323. See also loaded, 323 parameter; density waves Population I, 13, 19, 22–3, 210–1, 243, 258 for models of elliptical galaxies, 344, 398–401 Population II, 22, 165, 210–1, 258 for models of globular clusters, 347, 367 population synthesis models, 14 for water waves, 127–9

466 Index

relaxation, 54, 58, 70–81, 84, 95, 143, 318, 323, 395 second-order phase transitions, 105, 115–7 in N-body codes, 83, 250–2, 262 secular instability, 100, 104, 115, 117, 394. See also collisionless, 76–8, 392, 395 dissipation-driven instabilities incomplete (or partial), 78, 97, 301, 337–49, 392, seeing, 11, 33, 322, 423, 427 396–401 self-regulation, 173, 201, 210, 218–9, 226–7, 231, 244, in globular clusters, 80, 325–37, 351 248–51, 257 and MOND, 293 in accretion disks, 439–47 phase mixing, 76 semiempirical approach, 53–8, 62, 82, 87, 102, 184–6, times, 66–70, 84–5 229–30, 243, 247–9, 253, 268, 291, 301, 314–5, violent, 77–8, 301, 394, 402 347, 438 resistivity, 69, 86, 115, 275–6, 396 separable potential, 292, 307 resonance, 71–2, 76, 84, 138, 276, 300, 359–60, 366. See separatrix, 157, 160 also Alfvén resonance; density waves; Lindblad SgrA,6,281 resonances shear Alfvén waves, 275 response to tidal driving, 102–3, 244–5, 252, 262, 367 shear flow, 65, 149, 156–7, 186 restricted three-body problem, 65, 152 sheared magnetic configuration, 65, 149, 156–7, 207 reversed-field pinch plasma configuration, 396 shearing sheet model, homogeneous, 90, 186, 203, ringed galaxies. See rings 205–7 rings, 21, 23, 221, 248, 258, 436 shielding, 138 HI in an elliptical galaxy, 378–9, 447 shock waves, 121. See also density waves: shock scenario planetary, 63–4, 268, 436, 439, 447–8 short-axis tubes, 307–9 polar, 55, 157–9, 177, 268, 285 similarity solutions, 402, 416 of test particles, 272, 278 single-particle dynamics, 35, 54, 64, 105, 143, 158, 160, Roche volume (lobe), 75, 332–3. See also ellipsoids, 202, 278, 299–300 classical singular perturbations, 91, 115 rotating bowl, 99–101 sinking satellites, 70–4, 79 rotating stars, 110, 116 slab model, 164, 166, 186, 193–4, 207, 269, 439 rotation curve, 29, 34–7, 40, 50, 55–6, 280–7 even perturbations, 101, 275 decomposition. See luminous-dark-matter odd perturbations, 101, 275 decomposition slide-away (or runaway) tails, 69 for our Galaxy, 145, 167, 283 slow nonadiabatic evolution, 71–3, 290 radio versus optical, 48, 283 small-scale spiral activity, 27, 103, 187, 210, 248–51, representative for pure-disk spirals, 177 254, 258 Rutherford cross section, 69 smoothed particle hydrodynamics (SPH) codes and Rydberg states, 312 simulations, 263, 440, 442 softening. See N-body simulations Sandage, on classification, 19, 26 solar nebula, 435 SAURON survey, 385 solar neighborhood, 18, 134, 172, 181, 255, 280–1, 286 scaling laws, 39–44, 50, 56, 313–4, 392, 408, 412–3, density determination, 164–7, 181, 289–90, 313 429–31 kinematics, 3, 34, 143–5, 151, 158, 191 baryonic Tully-Fisher relation in spirals, 50 pressure anisotropy, 34, 66, 269, 392 fundamental plane relation, 42–4, 56, 354, 391, solar sectors, 273–6 408–14 solar wind, 273 luminosity-size, 414 solenoidal field, 292 luminosity-velocity relation in spirals (Tully-Fisher), solid-body rotation, 73, 108–9, 133, 147, 191, 335, 353 40–1 soliton, 130 luminosity-velocity-dispersion relation in ellipticals sonic point, 404, 416 (Faber-Jackson), 42 sound waves, 64, 122, 132, 212, 220, 247 mass of the central black holes in spheroids, space probe 44, 445 Helios, 78 mass-luminosity relation in ellipticals, 408–10 Pioneer, 273–4, 293 mass-radius relation, 40 Rosetta, 293 optical-x-ray luminosity relation in ellipticals, 407 Ulysses, 278 rising part of the rotation curve in spirals Viking, 24 (scale length R), 40–2, 50 Voyager, 436 surface brightness-radius relation in ellipticals, 44 spherical harmonics, 83, 113, 355, 357 Schrödinger equation, 8, 246 generalized, 357 SDSS (Sloan Digital Sky Survey), 26, 380, 387, 421 spherical pendulum. See rotating bowl

Index 467

spherical stellar wind problem, 273, 416 HST (Hubble Space Telescope), 4, 8, 10, 24, 53, spheroidal coordinates, 307, 309 224–5, 322, 325, 381 standing wave (patterns), 128, 202, 204, 248, 250, 253 INTEGRAL, 10 star formation rate (SFR), 14, 263 IRAS, 10 statistical mechanics of self-gravitating systems, 58, 61, ISO, 10 76, 318. See also gravothermal catastrophe JWST, 11 and collisonless collapse, 76, 394–5 Keck,6,11 and incomplete violent relaxation, 77, 301, 340, 396–8 Magellan, 15 and degeneracy, 402 NTT, 6 stellar hydrodynamics, 86, 155–7, 206 Observatoire Midi-Pyrenees, 5 stellar populations, 14, 40, 56–7, 82, 162, 181, 280–2, Planck, 10, 52, 433 287, 290, 370, 372–3, 381, 414. See also ROSAT, 9, 18, 375, 377, 382–5, 405 Population I; Population II SAX, 10 strong lensing, 51, 384, 424–5, 427, 429, 431. See also SIM, 11 gravitational lensing SKA, 11 structural stability, 340, 401 Spitzer, 10, 26, 226 Sturm-Liouville problems, 235 Subaru, 422 subsonic ﬂow, 404, 416 Swift, 10 SU(3) invariance, 311 Uhuru, 9 supernova, 10, 46, 109, 177, 404 VLA (Very Large Array), 378 rate, 404–5 VLT, 6, 11, 13, 23, 116, 225 SN1987A, 18 WIYN, 225 superparticles, 83 WMAP, 10 supersonic motion, 129, 416 WSRT (Westerbork Synthesis Radio Telescope), 41 surface waves, 134 XMM (XMM-Newton), 9, 375, 382, 384–5, 388 swing, 195, 203, 206, 251–2 thermal conductivity, 121, 394 symmetry breaking, 22–3, 26, 58, 95–104, 152 thermal instability, 404 in classical ellipsoids, 105, 113, 117 thermodyamical equilibrium, 66, 78, 95–6 by density waves, 152, 184–7, 204, 448 thermodynamical limit, 85, 96 and group theory, 117 thermodynamical potential, 394 by perturbations on a current sheet, 273–6 thermodynamical (global) temperature, 364, and phase transitions, 115–6 399–400 by the presence of a massive disk, 175–77 thermostat, dynamical. See self-regulation in quantum mechanics, 101, 104 tidal interaction. See galaxy-galaxy interactions; response of the ray-tracing matrix in gravitational to tidal driving lensing, 431 tidal (truncation) radius, 326, 352 in slab geometry, 101 tidal torque, 39 in spherical geometry, 301, 315, 356–67 tilted-ring model, 266–267 by tides, 332–4 time scale, 58, 65, 218, 247. See also relaxation synchrotron emission, 11 Alfv´en, 65 cooling, 7, 15, 210, 219, 391, 403, 442 telescope crossing, 69–70, 77, 365 AGILE, 10 dynamical, 3, 65, 70, 102, 115, 364, 391, 442 ALMA, 11, 442 for evolution associated with spiral torques, 261 Anglo-Australian Observatory, 20 for group propagation, 205, 239, 267–8 ASCA, 383 topological invariant, 396 Auger, 18 toroidal structure, 337, 352, 367 CFHT, 428, 430, 433 in a plasma, 65, 103, 149, 157 CGRO (Compton Gamma Ray Observatory), 10 trailing waves, 195–7, 202–5, 220–1, 238, 251–3, Chandra, 9, 15, 375, 382, 384–5, 388 259–60. See also density waves COBE, 10 transient evolution or rapidly evolving behavior, 19, 187, Dwingeloo, 283 201, 203, 210, 231, 244, 248–9, 252, 256, 261, 268 E-ELT, 11 transport processes, 58, 61, 79, 86, 103, 124–5, 272–4, Einstein, 9, 375 278, 403. See also density waves Fermi, 10 angular momentum, 205, 222, 244, 258, 261, 435–6, GAIA, 11, 17 439–40, 448 Herschel, 10 anomalous, 438–40, 448 Hipparcos, 10, 165, 167, 289 energy, 124, 404, 438–41, 448

468 Index

trapping anomalous (or turbulent), 438, 448 of a charged particle on top of a hill, 152–3 diffusion, 436 at Lagrangian points, 149–57, 160 ion, 276 at Lindblad resonances, 152 physical prescription, 438–40 magnetic, 62, 143–4 Vlasov equation, 61, 84, 163, 168. See also collisionless triaxiality, 21, 54, 90, 96, 101–18, 160, 182, 253, 268, Boltzmann equation 285, 290, 292, 299–301, 306–11, 314–9, 326, 332–5, vortensity, 222 351, 355, 358, 365, 369–70, 374–5, 380 vorticity, 108–9, 126, 206, 222, 260 triple point, 213, 215 in electron plasmas, 62 truncated models, 75, 181, 273, 318, 325–37, 346–7, 352, integral, 396 360, 392–3, 401 islands, 156 T Tauri stars, 442–4 turbulent warps, 23–4, 35, 55, 90, 103, 177, 266–79, 288–9. See behavior, 249 also bending waves dissipation, 219 amplitude and amplitude profile, 269–70, 276, 289 energy density, 3 in our Galaxy, 27, 266 motions in the atmosphere, 11 in the stellar disk, 266 speed (velocity dispersion) in the gas, 35, 86, 103, 180, waser, 204. See also overreflection; density waves: 377, 380, 449 wave cycles turning points, 146, 199–200, 203, 208, 231, 323, water waves, 119, 122, 125–30, 134 325. See also density waves capillary forces, 126 for dispersive waves, 124 deep, 128 for three-dimensional orbits, 306–7 shallow, 127–8 three-turning-point problem, 246 ship, 128–9 two-turning-point problem, 234–9 water-bag model, 350, 415 uniform solutions through, 235–7 wave bands, 10–1, 19, 40, 223, 226–7, 263, 409 TW Hydrae, 443 wave barrier (and Q barrier), 202–4, 252. See also twisting of isophotes. See isophotes: twist feedback two-component models, 97, 164–5, 182, 210–9, wave breaking. See hyperbolic waves 227, 250, 254, 258, 270–1, 345–9, 354, 371–4. See wave cycles. See density waves also density waves: in two-component disks wave packet. See density waves; dispersive waves two-stream instability, 84, 270–1, 289, 369 wave train. See density waves; dispersive waves weak (or statistical) lensing, 384, 425–33. See also V/σ plot, 38 gravitational lensing velocity and velocity-dispersion profiles, 34. See also WIMPs, 47 dark matter; rotation curve winding dilemma, 202, 247, 249, 266 in disks, 34–7, 40–2, 172–80, 215–9 WKB (or WKBJ), 124, 186–207, 232–9 in ellipticals, 37–9, 343–4, 349, 371–4 for bending waves, 269–73, 278 in globular clusters, 331, 336–7 dispersion relation and wave action, 208, 236–7 velocity dispersion tensor. See pressure tensor local versus global theory, 186, 232–9 velocity ellipsoid, 34, 66, 168, 181, 300 and observed pitch angles, 151, 259–60 vertex of stellar motions, 168, 181 for open spirals, 190–1 violent instabilities, 102–3, 201, 231, 243, 254, 288, 340, and shearing sheet model, 205–6 355, 364–5, 367, 369, 396 for tightly wound spirals, 186–93, 196–202 virial coefficient, 409–12 x-ray binaries, 15, 109, 403, 438 equations, 88–9 x-ray emission (from ellipticals, groups, and clusters), equilibrium, 78, 89, 107, 116, 281, 337, 408 15–6, 281, 374–77, 382–3 in relation to Jeans instability, 132–3 from cooling flows, 403–8 mass, 383 β model, 383 ratio, 77, 338, 400 in relation to relaxation, 69 tensor, second-order, 89, 108, 112–4, 369 Yukawa potential, 292 theorem, 39, 107, 341, 382, 409 for two-component system, 348 zero-frequency limit, 138, 325, See also marginal stability viscosity, 86, 100, 115, 121, 396, 436–40, 445 zero-thickness limit, 88, 272–3, 276