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On spherically symmetric gravitational collapse

Publication ,  Journal Article
Brenner, MP; Witelski, TP
Published in: Journal of Statistical Physics
January 1, 1998

This paper considers the dynamics of a classical problem in astrophysics, the behavior of spherically symmetric gravitational collapse starting from a uniform, density cloud of interstellar gas. Previous work on this problem proposed a universal self-similar solution for the collapse yielding a collapsed mass much smaller than the mass contained in the initial cloud. This paper demonstrates the existence of a second threshold not far above the marginal collapse threshold - above which the asymptotic collapse is not universal. In this regime, small changes in the initial data or weak stochastic forcing leads to qualitatively different collapse dynamics. In the absence of instabilities, a progressing wave solution yields a collapsed uniform core with infinite density. Under some conditions the instabilities ultimately lead to the well-known self-similar dynamics. However, other instabilities can cause the density profile to become non-monotone and produce a shock in the velocity. In presenting these results, we outline pitfalls of numerical schemes that can arise when computing collapse.

Duke Scholars

Published In

Journal of Statistical Physics

DOI

ISSN

0022-4715

Publication Date

January 1, 1998

Volume

93

Issue

3-4

Start / End Page

863 / 899

Related Subject Headings

  • Fluids & Plasmas
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Brenner, M. P., & Witelski, T. P. (1998). On spherically symmetric gravitational collapse. Journal of Statistical Physics, 93(3–4), 863–899. https://doi.org/10.1023/b:joss.0000033167.19114.b8
Brenner, M. P., and T. P. Witelski. “On spherically symmetric gravitational collapse.” Journal of Statistical Physics 93, no. 3–4 (January 1, 1998): 863–99. https://doi.org/10.1023/b:joss.0000033167.19114.b8.
Brenner MP, Witelski TP. On spherically symmetric gravitational collapse. Journal of Statistical Physics. 1998 Jan 1;93(3–4):863–99.
Brenner, M. P., and T. P. Witelski. “On spherically symmetric gravitational collapse.” Journal of Statistical Physics, vol. 93, no. 3–4, Jan. 1998, pp. 863–99. Scopus, doi:10.1023/b:joss.0000033167.19114.b8.
Brenner MP, Witelski TP. On spherically symmetric gravitational collapse. Journal of Statistical Physics. 1998 Jan 1;93(3–4):863–899.
Journal cover image

Published In

Journal of Statistical Physics

DOI

ISSN

0022-4715

Publication Date

January 1, 1998

Volume

93

Issue

3-4

Start / End Page

863 / 899

Related Subject Headings

  • Fluids & Plasmas
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences