Fokker–planck Treatment of Collisional Stellar Dynamics

  • Marc Freitag
Part of the Lecture Notes in Physics book series (LNP, volume 760)

In this chapter, I explain how the evolution of an N-body system can be described using a formalism explicitly based on the distribution function in phase space. Such an approach can be contrasted with direct N-body simulations in which the trajectories of a large number of particles are integrated. Because trajectories with close initial conditions diverge exponentially in gravitational N-body systems (Goodman et al. 1993; Hemsendorf & Merritt 2002, and references therein), most results of N-body simulations must be interpreted statistically. It is therefore interesting to consider the simulation methods that treat the gravitational system in an explicitly statistical way.


Globular Cluster Massive Black Hole Stellar System Core Collapse Stellar Cluster 
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  1. Aarseth S. J., 1971, Ap&SS, 13, 324CrossRefADSGoogle Scholar
  2. Alexander T., 2007, in Livio M., Koekemoer A. M., eds, 2007 STScI Spring Symposium: Black Holes. (astro-ph/0708.0688)Google Scholar
  3. Amaro-Seoane P., Freitag M., Spurzem R., 2004, MNRAS, 352, 655CrossRefADSGoogle Scholar
  4. Baumgardt H., Hut P., Heggie D. C., 2002, MNRAS, 336, 1069CrossRefADSGoogle Scholar
  5. Bettwieser E., Spurzem R., 1986, A&A, 161, 102zbMATHADSGoogle Scholar
  6. Binney J., Tremaine S., 1987, Galactic Dynamics. Princeton Univ. Press, Princeton, NJzbMATHGoogle Scholar
  7. Breeden J. L., Cohn H. N., Hut P., 1994, ApJ, 421, 195CrossRefADSGoogle Scholar
  8. Chandrasekhar S., 1943, Rev. Mod. Phys., 15, 1zbMATHCrossRefADSMathSciNetGoogle Scholar
  9. Chandrasekhar S., 1960, Principles of Stellar Dynamics. Dover, enlarged editionGoogle Scholar
  10. Chang J. S., Cooper G., 1970, J. Comp. Phys., 6, 1zbMATHCrossRefADSGoogle Scholar
  11. Chernoff D. F., Weinberg M. D., 1990, ApJ, 351, 121CrossRefADSGoogle Scholar
  12. Cohn H., 1979, ApJ, 234, 1036CrossRefADSGoogle Scholar
  13. Cohn H., 1980, ApJ, 242, 765CrossRefADSGoogle Scholar
  14. Cohn H., 1985, in Goodman J., Hut P., eds, Proc. IAU Symp. 113, Dynamics of Star Clusters. Reidel, Dordrecht, p. 161Google Scholar
  15. Cohn H., Hut P., Wise M., 1989, ApJ, 342, 814CrossRefADSGoogle Scholar
  16. Cohn H., Kulsrud R. M., 1978, ApJ, 226, 1087CrossRefADSMathSciNetGoogle Scholar
  17. Cuadra J., Nayakshin S., Springel V., Di Matteo T., 2005, MNRAS, 360, L55ADSGoogle Scholar
  18. David L. P., Durisen R. H., Cohn H. N., 1987a, ApJ, 313, 556CrossRefADSGoogle Scholar
  19. David L. P., Durisen R. H., Cohn H. N., 1987b, ApJ, 316, 505CrossRefADSGoogle Scholar
  20. Drukier G. A., 1993, MNRAS, 265, 773ADSGoogle Scholar
  21. Drukier G. A., 1995, 100, 347Google Scholar
  22. Drukier G. A., Cohn H. N., Lugger P. M., Yong H., 1999, ApJ, 518, 233CrossRefADSGoogle Scholar
  23. Drukier G. A., Fahlman G. G., Richer H. B., 1992, ApJ, 386, 106CrossRefADSGoogle Scholar
  24. Dull J. D., Cohn H. N., Lugger P. M., Murphy B. W., Seitzer P. O., Callanan P. J., Rutten R. G. M., Charles P. A., 1997, ApJ, 481, 267CrossRefADSGoogle Scholar
  25. Einsel C., Spurzem R., 1999, MNRAS, 302, 81CrossRefADSGoogle Scholar
  26. Einsel M., 1996, PhD thesis, Christian-Albrechts-Universität zu KielGoogle Scholar
  27. Fiestas J., 2006, PhD thesis, Heidelberg UniversityGoogle Scholar
  28. Fiestas J., Spurzem R., Kim E., 2006, MNRAS, 373, 677CrossRefADSGoogle Scholar
  29. Freitag M., Amaro-Seoane P., Kalogera V., 2006a, ApJ, 649, 91CrossRefADSGoogle Scholar
  30. Freitag M., Benz W., 2002, A&A, 394, 345zbMATHCrossRefADSGoogle Scholar
  31. Freitag M., Rasio F. A., Baumgardt H., 2006b, MNRAS, 368, 121ADSGoogle Scholar
  32. Gao B., Goodman J., Cohn H., Murphy B., 1991, ApJ, 370, 567CrossRefADSGoogle Scholar
  33. Giersz M., Heggie D. C., 1994, MNRAS, 268, 257ADSGoogle Scholar
  34. Giersz M., Heggie D. C., 1996, MNRAS, 279, 1037ADSGoogle Scholar
  35. Giersz M., Heggie D. C., 2003, MNRAS, 339, 486CrossRefADSGoogle Scholar
  36. Giersz M., Heggie D. C., 2007, in Vesperini E,. Giersz M., Sills A., eds, Dynamical Evolution of Dense Stellar Systems. Proceedings of IAU Symposium No.,246. (astro-ph/0711.0523)Google Scholar
  37. Giersz M., Spurzem R., 1994, MNRAS, 269, 241ADSGoogle Scholar
  38. Gnedin O. Y., Lee H. M., Ostriker J. P., 1999, ApJ, 522, 935CrossRefADSGoogle Scholar
  39. Gnedin O. Y., Ostriker J. P., 1997, ApJ, 474, 223CrossRefADSGoogle Scholar
  40. Goodman J., 1983a, ApJ, 270, 700CrossRefADSGoogle Scholar
  41. Goodman J., 1983b, PhD thesis, Princeton UniversityGoogle Scholar
  42. Goodman J., 1984, ApJ, 280, 298CrossRefADSGoogle Scholar
  43. Goodman J., Heggie D. C., Hut P., 1993, ApJ, 415, 715CrossRefADSGoogle Scholar
  44. Grabhorn R. P., Cohn H. N., Lugger P. M., Murphy B. W., 1992, ApJ, 392, 86CrossRefADSGoogle Scholar
  45. Heggie D., Hut P., 2003, The Gravitational Million-Body Problem Cambridge Univ. Press, CambridgezbMATHGoogle Scholar
  46. Hemsendorf M., Merritt D., 2002, ApJ, 580, 606CrossRefADSGoogle Scholar
  47. Hénon M., 1960, Annales d’Astrophysique, 23, 668ADSGoogle Scholar
  48. Hénon M., 1961, Annales d’Astrophysique, 24, 369ADSGoogle Scholar
  49. Hénon M., 1973, in Martinet L., Mayor M., eds, Lectures of the 3rd Advanced Course of the Swiss Society for Astronomy and Astrophysics. Obs. de Gèneve, Gèneve, p. 183Google Scholar
  50. Hénon M., 1975, in Hayli A., ed., Proc. IAU Symp. 69, Dynamics of Stellar Systems. Reidel, Dordrecht, p. 133Google Scholar
  51. Hopman C., Alexander T., 2006, ApJ Lett., 645, L133CrossRefADSGoogle Scholar
  52. Hurley J. R., Pols O. R., Aarseth S. J., Tout C. A., 2005, MNRAS, 363, 293CrossRefADSGoogle Scholar
  53. Inagaki S., Saslaw W. C., 1985, ApJ, 292, 339CrossRefADSGoogle Scholar
  54. Inagaki S., Wiyanto P., 1984, PASJ, 36, 391ADSGoogle Scholar
  55. Jeans J. H., 1915, MNRAS, 76, 70ADSGoogle Scholar
  56. Kim E., Einsel C., Lee H. M., Spurzem R., Lee M. G., 2002, MNRAS, 334, 310CrossRefADSGoogle Scholar
  57. Kim E., Lee H. M., Spurzem R., 2004, MNRAS, 351, 220CrossRefADSGoogle Scholar
  58. Kim E., Yoon I., Lee H. M., Spurzem R., 2008, MNRAS, 383, 2ADSGoogle Scholar
  59. Kim S. S., Lee H. M., Goodman J., 1998, ApJ, 495, 786CrossRefADSGoogle Scholar
  60. Lee H. M., 1987a, ApJ, 319, 801CrossRefADSGoogle Scholar
  61. Lee H. M., 1987b, ApJ, 319, 772CrossRefADSGoogle Scholar
  62. Lee H. M., 1995, MNRAS, 272, 605ADSGoogle Scholar
  63. Lee H. M., Fahlman G. G., Richer H. B., 1991, ApJ, 366, 455CrossRefADSGoogle Scholar
  64. Lee H. M., Ostriker J. P., 1987, ApJ, 322, 123CrossRefADSGoogle Scholar
  65. Lee H. M., Ostriker J. P., 1993, ApJ, 409, 617CrossRefADSGoogle Scholar
  66. Lightman A. P., Shapiro S. L., 1977, ApJ, 211, 244CrossRefADSGoogle Scholar
  67. Lin D. N. C., Tremaine S., 1980, ApJ, 242, 789CrossRefADSGoogle Scholar
  68. Louis P. D., Spurzem R., 1991, MNRAS, 251, 408ADSGoogle Scholar
  69. Merritt D., 1983, ApJ, 264, 24CrossRefADSGoogle Scholar
  70. Merritt D., 1984, ApJ, 276, 26CrossRefADSGoogle Scholar
  71. Merritt D., 1985, ApJ, 289, 18CrossRefADSGoogle Scholar
  72. Merritt D., 1999, PASP, 111, 129CrossRefADSGoogle Scholar
  73. Merritt D., 2008, preprint (astro-ph/0802.3186)Google Scholar
  74. Merritt D., Harfst S., Bertone G., 2007a, Phys. Rev. D, 75, 043517CrossRefADSGoogle Scholar
  75. Merritt D., Mikkola S., Szell A., 2007b, ApJ, 671, 53CrossRefADSGoogle Scholar
  76. Murali C., Weinberg M. D., 1997a, MNRAS, 288, 749ADSGoogle Scholar
  77. Murali C., Weinberg M. D., 1997b, MNRAS, 291, 717ADSGoogle Scholar
  78. Murali C., Weinberg M. D., 1997c, MNRAS, 288, 767ADSGoogle Scholar
  79. Murphy B. W., Cohn H. N., 1988, MNRAS, 232, 835ADSGoogle Scholar
  80. Murphy B. W., Cohn H. N., Durisen R. H., 1991, ApJ, 370, 60CrossRefADSGoogle Scholar
  81. Perets H. B., Hopman C., Alexander T., 2007, ApJ, 656, 709CrossRefADSGoogle Scholar
  82. O’Leary R. M., Kocsis B., Loeb A., 2008, preprint (astro-ph/0807.2638)Google Scholar
  83. Quinlan G. D., 1996, New Astronomy, 1, 255CrossRefADSGoogle Scholar
  84. Quinlan G. D., Shapiro S. L., 1989, ApJ, 343, 725CrossRefADSGoogle Scholar
  85. Quinlan G. D., Shapiro S. L., 1990, ApJ, 356, 483CrossRefADSGoogle Scholar
  86. Rosenbluth M. N., MacDonald W. M., Judd D. L., 1957, Physical Review, 107, 1zbMATHCrossRefADSMathSciNetGoogle Scholar
  87. Saslaw W. C., 1985, Gravitational Physics of Stellar and Galactic Systems. Cambridge Univ. Press, CambridgeGoogle Scholar
  88. Shin J., Kim S. S., Takahashi K., 2008, MNRAS, 386, L67ADSGoogle Scholar
  89. Spitzer L., 1987, Dynamical evolution of globular clusters. Princeton Univ. Press, Princeton, NJGoogle Scholar
  90. Spitzer L. J., Shapiro S. L., 1972, ApJ, 173, 529CrossRefADSGoogle Scholar
  91. Spurzem R., Takahashi K., 1995, MNRAS, 272, 772ADSGoogle Scholar
  92. Statler T. S., Ostriker J. P., Cohn H. N., 1987, ApJ, 316, 626CrossRefADSGoogle Scholar
  93. Takahashi K., 1995, PASJ, 47, 561ADSGoogle Scholar
  94. Takahashi K., 1996, PASJ, 48, 691ADSGoogle Scholar
  95. Takahashi K., 1997, PASJ, 49, 547ADSGoogle Scholar
  96. Takahashi K., Inagaki S., 1991, PASJ, 43, 589CrossRefADSGoogle Scholar
  97. Takahashi K., Lee H. M., Inagaki S., 1997, MNRAS, 292, 331ADSGoogle Scholar
  98. Takahashi K., Portegies Zwart S. F., 2000, ApJ, 535, 759CrossRefADSGoogle Scholar
  99. Takahashi K., Sensui T., Funato Y., Makino J., 2002, PASJ, 54, 5ADSGoogle Scholar
  100. Williams R. J. R., Baker A. C., Perry J. J., 1999, MNRAS, 310, 913CrossRefADSGoogle Scholar
  101. Wiyanto P., Kato S., Inagaki S., 1985, PASJ, 37, 715ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Marc Freitag
    • 1
  1. 1.University of Cambridge Institute of AstronomyCambridgeCB3 0HAUK

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