SCALE-INVARIANT MODE IN COLLISIONLESS SPHERICAL STELLAR SYSTEMS

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Abstract

An analytical solution of the perturbed equations is obtained, which exists in all ergodic models of collisionless spherical stellar systems with a single length parameter. This solution corresponds to variations of this parameter, that is, the stretching/contraction of the sphere keeping the total mass constant. During the process, the system remains in an equilibrium state. The simplicity of the solution makes it possible to explicitly give expressions for the distribution function, potential, and density in all orders of perturbation theory. This, in turn, helps to clarify the concept of perturbation energy, which, being a second-order magnitude in amplitude, cannot be calculated in linear theory. The expression for the 2nd-order perturbation energy does not match the well-known quadratic form for perturbation energy derived from 1st-order perturbations in linear theory. However, both of these energies are integrals of motion and differ only by a constant. The obtained solution can be used to control the correctness of codes and the accuracy of calculations in the numerical study of collisionless stellar models.

About the authors

E. V. Polyachenko

Institute of Astronomy of the Russian Academy of Sciences

Author for correspondence.
Email: epolyach@inasan.ru
Russia, Moscow

I. G. Shukhman

Institute of Solar-Terrestrial Physics of Siberian Branch of RAS

Author for correspondence.
Email: shukhman@iszf.irk.ru
Russia, Irkutsk

References

  1. J. Binney and S. Tremaine, Galactic Dynamics: 2nd ed. (Princeton Univ. Press, NJ, 2008), BT.
  2. А. Б. Михайловский, А. М. Фридман, Я. Г. Эпельбаум, ЖЭТФ 59, 1608 (1970).
  3. В. Л. Поляченко, И. Г. Шухман, Астрон. журн. 50, 97 (1973).
  4. В. Л. Поляченко, И. Г. Шухман, Астрон. журн. 50, 721 (1973).
  5. А. Г. Морозов, В. Л. Поляченко, И. Г. Шухман, Астрон. журн. 51, 75 (1974).
  6. J. Kalnajs, Astrophys. J. 205, 751 (1976).
  7. В. Л. Поляченко, И. Г. Шухман, Астрон. журн. 58, 933, (1981).
  8. E. V. Polyachenko, Monthly Not. Roy. Astron. Soc. 348, 345 (2004).
  9. E. V. Polyachenko, Monthly Not. Roy. Astron. Soc. 357, 559 (2005).
  10. C. Hamilton and T. Heinemann, arXiv:2011.14812 [astro-ph.GA] (2020).
  11. C. Hamilton, Monthly Not. Roy. Astron. Soc. 501, 3371 (2021).
  12. J. Y. Lau and J. Binney, Monthly Not. Roy. Astron. Soc. 507, 2241 (2021).
  13. J. Y. Lau and J. Binney, Monthly Not. Roy. Astron. Soc. 507, 2562 (2021).
  14. A. M. Fridman and V. L. Polyachenko, Physics of Gravitating Systems (Berlin: Springer-Verlag, 1984).
  15. P. L. Palmer, Stability of Collisionless Stellar Systems: Mechanisms for the Dynamical Structure of Galaxies (Dordrecht, Boston: Kluwer Academic Publishers, 1994).
  16. M. D. Weinberg, Astrophys. J. 421, 481 (1994).
  17. D. C. Heggie, P. G. Breen, and A. L. Varri, Monthly Not. Roy. Astron. Soc. 492, 6019 (2020).
  18. S. D. Mathur, Monthly Not. Roy. Astron. Soc. 243, 529 (1990).
  19. N. G. van Kampen, Physica 21(6), 949 (1955).
  20. Л. Д. Ландау, ЖЭТФ 16, 574 (1946).
  21. E. V. Polyachenko, I. G. Shukhman, and O. I. Borodina, Monthly Not. Roy. Astron. Soc. 503, 660 (2021).
  22. E. V. Polyachenko and I. G. Shukhman, Phys. Fluids 34(6), id. 064108 (2022).
  23. Ц. Ц. Линь, Теория гидродинамической устойчивости (М.: ИЛ, 1958).
  24. J. Barré, A. Olivetti, and Y. Y. Yamaguchi, J. Physics A: Mathematical and Theoretical 44(41), id. 405502 (2011).
  25. R. King, Astron. J. 71, 64 (1966).
  26. S. Tremaine, Astrophys. J. 625, 143 (2005).
  27. E. V. Polyachenko, V. L. Polyachenko, and I. G. Shukh-man, Monthly Not. Roy. Astron. Soc. 386, 1966 (2008).
  28. E. V. Polyachenko and I. G. Shukhman, Monthly Not. Roy. Astron. Soc. 451, 5120 (2015).
  29. M. Hénon, Ann. d’Astrophysique 23, 474 (1960).
  30. L. Hernquist, Astrophys. J. 356, 359 (1990).
  31. W. Jaffe, Monthly Not. Roy. Astron. Soc. 202, 995 (1983).
  32. H. C. Plummer, Monthly Not. Roy. Astron. Soc. 71, 460 (1911).
  33. R. W. Nelson and S. Tremaine, Monthly Not. Roy. Astron. Soc. 306, 1 (1999).
  34. M. Held, J. Atmospher. Sci. 42, 2280 (1985).

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