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Astronomy Reports

, Volume 63, Issue 4, pp 263–273 | Cite as

Strong Shock in a Uniform Expanding Universe. Approximate and Exact Solutions of Self-Similar Equations

  • G. S. Bisnovatyi-KoganEmail author
  • S. A. PanafidinaEmail author
Article

Abstract

Self-similar solution is obtained for propagation of a strong shock, in a flat expanding dusty Friedman universe. Approximate analytic solution was obtained earlier, using relation between self-similar variables, equivalent to the exact energy conservation integral, which was obtained by L.I. Sedov for the strong explosion in the static uniform medium. Here, numerical integration of self-similar equation is performed, providing an exact solution of the problem, which is rather close to the approximate analytic one. The differences between these solutions are most apparent in the vicinity of the shock. For a polytropic equation of state, self-similar solutions exist in a more narrow interval of the adiabatic power than in the static case.

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References

  1. 1.
    N. R. Tanvir, arXiv:1307.6156v1 [astro–ph.CO] (2013).Google Scholar
  2. 2.
    K. P. Stanyukovich, Nonstationary Motion of Continuous Media ( Gostekhizdat, Moscow, 1955) (in Russian).Google Scholar
  3. 3.
    G. I. Taylor, Proc. Royal Soc. London. Series A 201, 175 (1950).ADSGoogle Scholar
  4. 4.
    L. I. Sedov, Soviet Physics Doklady 52 (1) (1946).Google Scholar
  5. 5.
    G. S. Bisnovatyi–Kogan, Gravitation and Cosmology 21, 236 (2015) (arXiv:1408.1981v2).ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Ya. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics. Volume 2. The Atructure and Evolution of the Universe (University of Chicago Press, Chicago, IL, 1983).Google Scholar
  7. 7.
    E. Bertschinger, Astrophys. J. 268, 17 (1983).ADSCrossRefGoogle Scholar
  8. 8.
    M. A. Eremin and I. G. Kovalenko, Astron. Astrophys. 335, 370 (1998).ADSGoogle Scholar
  9. 9.
    I. G. Kovalenko and P. A. Sokolov, Astron. Astrophys. 270, 1 (1993).ADSGoogle Scholar
  10. 10.
    S. Ikeuchi, K. Tomisaka, and J. P. Ostriker, Astrophys. J. 265, 583 (1983).ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    L.M. Ozernoi and V.V. Chernomordik, SovietAstron. 22, 141 (1978).ADSGoogle Scholar
  12. 12.
    J. Shwarz, J. P. Ostriker, and A. Yahil, Astrophys. J. 202, 1 (1975).ADSCrossRefGoogle Scholar
  13. 13.
    E. T. Vishniac, J. P. Ostriker, and E. Bertschinger, Astrophys. J. 291, 399 (1985).ADSCrossRefGoogle Scholar
  14. 14.
    E. Bertschinger, Astrophys. J. 295, 1 (1985).ADSCrossRefGoogle Scholar
  15. 15.
    Ya.M. Kazhdan, Soviet Astron. 30, 261 (1986).ADSGoogle Scholar
  16. 16.
    L. Ciotti and A. D’Ercole, Astron. Astrophys. 215, 347 (1989).ADSGoogle Scholar
  17. 17.
    J. P. Ostriker and C. F. McKee, Rev. Modern Physics 60, 1 (1988).ADSCrossRefGoogle Scholar
  18. 18.
    L. I. Sedov, Metody podobiya i razmernostei v mekhanike (Nauka, Moscow, 1977) (in Russian).Google Scholar
  19. 19.
    L. D. Landau and E. M. Lifshitz, Hydrodynamics (Nauka, Moscow, 1988) (in Russian).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Space Research Institute RASMoscowRussia
  2. 2.National Research Nuclear University MEPhIMoscowRussia
  3. 3.Moscow Institute of Physics and Technology MIPTDolgoprudnyi, Moscow regionRussia

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