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Short note on conditional collapse of self-gravitating system with positive total energy

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  • Ahn, Jaewook
  • Choi, Jung-Il

Abstract

In this study, we first show a finite time collapse of a three-dimensional Smoluchowski–Poisson system in the micro-canonical ensemble (i.e., μSP system) with positive total energy. Using a precise estimation of the bound of the gravitational contribution to total energy, we provide blow-up conditions on the initial state of the μSP system. The conditions indicate that highly clustered self-gravitating particles in the μSP system induce a finite time collapse, even for positive total energy.

Suggested Citation

  • Ahn, Jaewook & Choi, Jung-Il, 2018. "Short note on conditional collapse of self-gravitating system with positive total energy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 205-209.
    • Handle: RePEc:eee:phsmap:v:507:y:2018:i:c:p:205-209
    DOI: 10.1016/j.physa.2018.04.108
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    References listed on IDEAS

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    1. Chavanis, P.H. & Sire, C., 2005. "On the interpretations of Tsallis functional in connection with Vlasov–Poisson and related systems: Dynamics vs thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 419-446.
    2. Lemou, Mohammed & Chavanis, Pierre-Henri, 2010. "Escape of stars from gravitational clusters in the Chandrasekhar model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1021-1040.
    3. Chavanis, Pierre-Henri, 2007. "Critical mass of bacterial populations and critical temperature of self-gravitating Brownian particles in two dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 392-412.
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