, Volume 51, Issue 3, pp 410–423 | Cite as

Instabilities in a nonstationary model of self-gravitating disks. I. Bar and ring perturbation modes

  • S. N. NuritdinovEmail author
  • K. T. Mirtadjieva
  • Mariam Sultana


The instabilities of bar and ring mode perturbations against the background of a disk oscillating nonlinearly in its own plane are examined in a disk model which is a nonstationary generalization of the well known Bisnovatyi-Kogan-Zel'dovich model. Nonstationary analogs corresponding to a dispersion relation are found for these two oscillation modes. The results of the calculations are presented in the form of critical dependences of the initial virial ratio on the degree of rotation. A comparative analysis of the growth rates of the gravitational instability for these modes is also carried out. The bar mode instability occurs if the initial total kinetic energy of the disk is no more than 10.4% of the initial potential energy. The mechanism is associated with an instability in the radial motions which is aperiodic for small values of the rotation parameter Ω < 0.1, but is otherwise oscillatory. Calculations show that a ring structure can be formed as a result of an instability in the radial motions if the initial total energy of the model is no more than 5.2% of the initial potential energy, regardless of the value of Ω.


models self-gravitating disk 


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  1. 1.
    G. S. Bisnovatyi-Kogan and Ya. B. Zel'dovich, Astrofizika 6, 387 (1970).ADSGoogle Scholar
  2. 2.
    M. G. Abramyan, Dynamics of embedded gravitating systems [in Russian], Dissertation abstract, Erevan (1986).Google Scholar
  3. 3.
    V. A. Antonov, Uchen. zapiski LGU 32, 79 (1976).MathSciNetGoogle Scholar
  4. 4.
    J. Binney and S. Tremaine, Galactic dynamics, Princeton University Press (1987), p.733.Google Scholar
  5. 5.
    V. A. Antonov and S. N. Nuritdinov, Astron. zh. 58, 1158 (1981).zbMATHADSGoogle Scholar
  6. 6.
    S. N. Nuritdinov, Astron. zh. 62, 506 (1985).ADSGoogle Scholar
  7. 7.
    S. N. Nuritdinov, Astron. zh. 68, 763 (1991).ADSMathSciNetGoogle Scholar
  8. 8.
    S. N. Nuritdinov, The Dynamics of Gravitating Systems and the Methods of Analytic Celestial Mechanics [in Russian], Nauka, Alma-Ata (1987), p. 65.Google Scholar
  9. 9.
    A. J. Kalnajs, Astrophys. J. 175, 63 (1972).CrossRefADSGoogle Scholar
  10. 10.
    A. M. Fridman and V. L. Polyachenko, Physics of gravitating systems, Springer-Verlag, New-York (1984).Google Scholar
  11. 11.
    I. G. Malkin, The Theory of Stability of Motion [in Russian], Nauka, Moscow (1967).Google Scholar
  12. 12.
    S. N. Nuritdinov and M. Usarova, Problems in the Physics and Dynamics of Stellar Systems [in Russian], Tashkent State Univ., Tashkent (1989), p. 49.Google Scholar
  13. 13.
    R. Buta, Astrophys. J. Suppl. Ser. 96, 39 (1995).CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • S. N. Nuritdinov
    • 1
    • 2
    Email author
  • K. T. Mirtadjieva
    • 2
    • 1
  • Mariam Sultana
    • 3
  1. 1.Institute of AstronomyAcademy of Sciences of the Republic of UzbekistanTashkentUzbekistan
  2. 2.Department of AstronomyNational University of UzbekistanTashkentUzbekistan
  3. 3.Federal UniversityKarachiPakistan

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