Thermodynamics of self-gravitating systems

Details Thermodynamics of self-gravitating systems Thermodynamics of self-gravitating systems

2001-07-16

arxiv.org/abs/cond-mat/0107345v3

Phys.Rev. E66 (2002) 036105

Physics

Condensed Matter

Statistical Mechanics

54 pages. 25 figures. Submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.66.036105

Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a ``gravothermal catastrophe'': it can achieve ever increasing values of entropy by developing a dense and hot ``core'' surrounded by a low density ``halo''. In this paper, we study the phase transition between ``equilibrium'' states and ``collapsed'' states with the aid of a simple relaxation equation [Chavanis, Sommeria and Robert, Astrophys. J. 471, 385 (1996)] constructed so as to increase entropy with an optimal rate while conserving mass and energy. With this numerical algorithm, we can cover the whole bifurcation diagram in parameter space and check, by an independent method, the stability limits of Katz [Mon. Not. R. astr. Soc. 183, 765 (1978)] and Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)]. When no equilibrium state exists, our relaxation equation develops a self-similar collapse leading to a finite time singularity.

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