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Comptes Rendus Physique
Volume 7, n° 3-4
pages 391-397 (avril-mai 2006)
Doi : 10.1016/j.crhy.2006.01.006
Statistical mechanics of the self-gravitating gas: Thermodynamic limit, instabilities and phase diagrams
Mécanique statistique du gaz auto-gravitant : limite thermodynamique, instabilités et diagrammes de phase

Hector J. de Vega a, b, , Norma G. Sanchez b
a LPTHE, laboratoire associé au CNRS UMR 7589, université Pierre et Marie Curie (Paris VI) et Denis Diderot (Paris VII), 4, place Jussieu, 75252 Paris, cedex 05, France 
b Observatoire de Paris, LERMA, laboratoire associé au CNRS UMR 8112, 61, avenue de lʼObservatoire, 75014 Paris, France 

Corresponding author.

We show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when  , keeping   fixed, that is, with   fixed. We develop Monte Carlo simulations, analytic mean field methods (MF) and low density expansions. We compute the equation of state and find it to be locally  , that is a local ideal gas equation of state. The system is in a gaseous phase for   and collapses into a very dense object for   in the CE with the pressure becoming large and negative. The isothermal compressibility diverges at  . We compute the fluctuations around mean field for the three ensembles. We show that the particle distribution can be described by a Haussdorf dimension  . To cite this article: H.J. de Vega, N.G. Sanchez, C. R. Physique 7 (2006).

The full text of this article is available in PDF format.

Nous montrons que la limite de volume infini existe pour le gaz auto-gravitant à lʼequilibre thermique dans les trois ensembles (EGC, EC, EMC) quand  , avec   fixe, cʼest à dire   fixe. Nous utilisons les simulations Monte Carlo, la méthode du champ moyen et les developpements à basse densité. Nous calculons lʼéquation dʼétat et nous trouvons quʼelle est localement  , cʼest-à-dire, lʼéquation dʼun gaz parfait local . Le système est dans une phase gazeuse pour   et sʼeffondre dans un objet très dense pour   dans lʼensemble canonique avec une pression grande et négative. La compressibilité isothermique diverge à  . Nous calculons les fluctuations autour du champ moyen pour les trois ensembles. Nous montrons que la distribution des particules est décrite par une dimension de Haussdorf  . Pour citer cet article : H.J. de Vega, N.G. Sanchez, C. R. Physique 7 (2006).

The full text of this article is available in PDF format.

Keywords : Self-gravitating gas, Mean field, Gravitational collapse

Mots-clés : Gaz auto-gravitant, Champ moyen, Effondrement gravitationnel

© 2006  Académie des sciences@@#104156@@
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