Collisionless relaxation in galactic dynamics and the evolution of long-range order

Annals of the New York Academy of Sciences

Volumn 848, Issue , 1998, Pages 28-47

  Kandrup, Henry E ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASTRONOMY; CONFERENCE PAPER; COSMOS; DYNAMICS; EVOLUTION; GRAVITY; MATHEMATICAL MODEL;

EID: 0031854176     PISSN: 00778923     EISSN: None     Source Type: Book Series    
DOI: 10.1111/j.1749-6632.1998.tb08956.x     Document Type: Conference Paper

References (64)

1. MIHALAS, D. & J. BINNEY 1981. Galactic Astronomy. Freeman. San Francisco, CA.
2. BlNNEY, J. & S. TREMAINE. 1987. Galactic Dynamics. Princeton University Press. Princeton, NJ.
3. SCHWEIZER, F. 1986. Colliding and merging galaxies. Science. 231: 227-234.
4. MAOZ, E. 1991. What damps small perturbations in stellar systems. Astrophys. J. 375: 687-690.
5. LYNDEN-BELL, D. 1967. Statistical mechanics of violent relaxation in stellar systems. Mon. Not. R. Astr. Soc. 136: 101-121.
6. CHANDRASEKHAR, S. 1943. Principles of Stellar Structure. University of Chicago Press. Chicago, IL.
7. KANDRUP, H.E. 1981. A generalized Landau equation for a system with a self-consistent mean field: Derivation from an N-particle Liouville equation. Astrophys. J. 244: 316-330.
8. HERTEL, P. & W. THIRRING. 1971. Free energy of gravitating fermions. Commun. Math. Phys. 24: 22-36.
9. RYBICKI, G. 1971. Exact stastistical mechanics of a one-dimensional self-gravitating system. Astrophys. Space Sei. 14: 56-72.
10. MINEAU, P., M.R. FEIX & J.L. ROUET 1990. Numerical simulations of violent relaxation and formation of phase space holes in gravitational systems. Astron. Astrophys. 228: 344-349.
11. LUWEL, M. & G. SEVERNE. 1985. Collisions mixing in 1-dimensioanl gravitational systems initially in a stationary waterbag configuration. Astron. Astrophys. 152: 305-314.
12. YAWN, K.R. & B.N. MILLER. 1997. Ergodic properties and equilibrium of onedimensional self-gravitating systems. Phys. Rev. E. 56: 2429-2436.
13. MORRISON, P.J. 1980. the Maxwell-Vlasov equations as a continous Hamiltonian system. Phys. Lett. A. 80: 383-386.
14. KANDRUP, H.E. 1990. Geometric approach to secular and nonlinear stability for spherical star clusters. Astrophys. J. 351: 104-113.
15. MORRISON, P.J. & S. ELIEZER. 1986. Spontaeous symmetry breaking and neutral stability in the noncanonical Hamiltonian formalis. Phys. Rev. A. 33: 4205-4214.
16. BARTHOLOMEW, P. 1971. On the theory of stability of galaxies. Mon. Not. R. Astr. Soc. 151: 333-350.
17. PFAFFELMOSER, K. 1992. Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data. J. Diff. Eqns. 95: 281-303.
18. SCHAEFFER, J. 1991. Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions. Commun. Part. Diff. Eqns. 16: 1313-1335.
19. KORMENDY, J. & D. RICHSTONE. 1995. Inward bound -the search for supermassive black holes in galactic nuclei. Ann. Rev. Astron. Astrophys. 33: 581-624.
20. BATT, J. 1987. Asymptotic properties of spherically symmetric self-gravitating systems for t → ∞. Transport Theory and Statistical Physics 16: 763-778.
21. LOUIS, P. D. & O.E. GERHART. 1988. Can galaxies oscillate? A self-consistent model of a non-stationary stellar system. Mon. Not. R. Astr. Soc. 233: 337-365.
22. SRIDHAR, S. 1989. Undamped oscillations of homogeneous collisionless stellar systems. Mon. Not. R. Astr. Soc. 201: 1159-1163.
23. KING, I. 1962. The structure of star clusters. I. An empirical density law. Astron. J. 67:471-485.
24. DE VAUCOULEUR, G. 1948. Recherches sur les nébuleuses extragalactiques. Ann. D'astrophysique. 11: 247-287.
25. LAUER, T.R., E.A. AJHAR, Y.-L. BYUN, A. DRESSLER, S.M. FABER, C. GRILL-MAIR, J. KORMENDY, D. RICHSTONE & S. TREMAINE. 1995. The centers of early-type galaxies with HST. I. An observational study. Astron. J. 110: 2622-2654.
26. LANDAU, L.D. & E.M. LiFSHirz.1958. Statistical Physics. Pergamon. London.
27. IPSER, J.R. & G. HORWITZ. 1979. The problems of maximizing functionals in Newtonian stellar dynamics and its relation to thermodynamic and dynamical stability. Astrophys. J. 232: 863-873.
28. HOLM, D.D., G.E. MARSDEN, T. RATIU & A. WEINSTEIN. 1985. Nonlinear stability of fluid and plasma equilibria. Phys. Repts. 123: 1-116.
29. KANDRUP, H.E., M.E. MAHON & H. SMITH. 1993. Energy and phase space mixing for self-gravitating systems of stars. Astron. Astrophys. 271: 440-450.
30. CONTOPOULOS, G. 1994. Private communication.
31. VAN ALBADA, T.S. 1982. Dissipationless galaxy formation and the r1'4 law. Mon. Not. R. Astr. Soc. 201: 939-955.
32. QUINN, P. J. & W.H. ZUREK. 1988. The angular momentum distribution in galactic halos. Astrophys. J. 331: 1-18.
33. KANDRUP, H.E., M.E. MAHON & H. SMITH. 1993. Energy and phase space mixing for self-gravitating systems of stars. Astron. Astrophys. 271: 440-450.
34. KANDRUP, H.E. 1993. Non-violent relaxation of colliding galaxies. In Advances In Gravitation and Cosmology. B.R. lyer, A.R. Prasanna, R.K. Varma & C.V. Vishveshwara, Eds. Wiley Eastern. New Delhi.
35. LANDAU, L.D. 1946. On the vibrations of the electronic plasma. Soviet Phys. JETP. 10: 25.
36. STIX, T.H. 1962. The Theory Of Plasma Waves. Mcgraw-Hill. New York.
37. CASE, K.M. 1959. Plasma oscillations. Ann. Phys. (NY) 7: 349-364.
38. VAN KAMPEN, N.G. 1955. On the theory of stationary waves in plasmas. Physica 21: 949-963.
39. HABIB, S., H.E. KANDRUP & P.P. YIP. 1986. Gravitational Landau damping. Astrophys. J. 309: 176-182.
40. MONTGOMERY, D. 1963. Nonlinear Landau damping of oscillations in a bounded plasma. Phys. Fluids A . 6: 1109-1114.
41. CHANNELL, P.J. 1995. Canonical integration of the collisionless Boltzmann equation. Ann. N. Y. Acad. Sei. 751: 152-161.
42. KANDRUP, H.E. 1994. Is There Chaos In BEDLAM? University of Florida preprint.
43. CHANNELL, P.J. 1994. Private communication.
44. KANDRUP, H.E. & M.E. MAHON. 1994. Relaxation and stochasticity in a truncated Toda lattice. Phys. Rev. E . 49: 3735-3747.
45. MAHON, M.E., R.A. ABERNATHY, B.O. BRADLEY & H.E. KANDRUP. 1995. Transient ensemble dynamics in time-independent galactic potentials. Mon. Not. R. Astr. Soc. 275: 443-453.
46. KANDRUP, H.E. 1994. Reduced Hamiltonian descriptions. Phys. Rev. D. 50: 2425-2430.
47. KUBO, R., M. TODA & N. HASHITSUME. 1991. Statistical Physics II. Springer-Verlag. New York.
48. CHANDRASEKHAR, S. 1943. Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15: 1-89.
49. MATHER, J.N. 1982. Existence of quasi-periodic orbits for twist homeomorphisms of the annulus. Topology. 21: 457-467.
50. ARNOLD, V.I. 1964. Small denominators and problems of stability of motion in classical and celestial mechanics. Russian Math. Surveys. 18: 85-191.
51. CONTOPOULOS, G. 1971. Orbits in highly perturbed dynamical systems. Astron. J. 76: 147-156.
52. LIEBERMAN, M.A. & A. LlCHTENBERG. J. 1972. Stochastic and adiabatic behaviour of particles accelerated by periodic forces. Phys. Rev. A 5: 1852-1866.
53. HABIB, S., H.E. KANDRUP & M.E. MAHON. 1996. Chaos and noise in a truncated Toda potential. Phys. Rev. E. 53: 5473-5476.
54. HABIB, S., H.E. KANDRUP & M.E. MAHON. 1997. Chaos and noise in galactic potentials. Astrophys. J. 480: 155-166.
55. LICHTENBERG, A.J. & M.A. LlEBERMAN. 1992. Regular and Chaotic Dynamics. Springer-Verlag. New York.
56. MILLER, R.H. 1964. Irreversibility in small stellar dynamical systems. Astrophys. J. 140: 250-256.
57. KANDRUP, H.E. & H. SMITH. 1991. On the sensitivity of the Af-body problem to small changes in initial conditions. Astrophys. J. 374: 255-265.
58. KANDRUP, H.E. & H. SMITH. 1992. On the sensitivity of the N-body problem to small changes in initial conditions. II. Astrophys. J. 386: 635-645.
59. KANDRUP, H.E., H. SMITH. & D.E. WILLMES. 1992. On the sensitivity of the TV-body problem to small changes in initial conditions. III. Astrophys. J. 399: 627-633.
60. GOODMAN, J., D. HEGGIE & P. HUT. 1994. On the exponential instability of N-body systems. Astrophys. J. 415: 715-723.
61. KANDRUP, H.E., M.E. MAHON & H. SMITH. 1992. On the sensitivity of the N-body problem to small changes in initial conditions. III. Astrophys. J. 428: 458-465.
62. OGORODNIKOV, K.F. 1965. Dynamics of Stellar Systems. Macmillan. New York.
63. KLIMONTOVICH, Yu. L. 1983. The Kinetic Theory of Electromagnetic Processes. Springer-Verlag. New York.
64. LYNDEN-BELL, D. & R. WOOD. 1968. The gravo-thermal catastrophe in isothermal spheres and the onset of Red-Giant structure for stellar systems. Mon. Not. R. Astr. Soc. 138: 495-525.