Statistical mechanics of the self-gravitating gas: Thermodynamic limit, instabilities and phase diagrams

We show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when ( N , V ) → ∞ , keeping N / V 1 / 3 fixed, that is, with η ≡ G m 2 N V 1 / 3 T 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 p ( r → ) = T ρ V ( r → ) , that is a local ideal gas equation of state. The system is in a gaseous phase for η < η T = 1.51024 … and collapses into a very dense object for η > η T in the CE with the pressure becoming large and negative. The isothermal compressibility diverges at η = η T . We compute the fluctuations around mean field for the three ensembles. We show that the particle distribution can be described by a Haussdorf dimension 1 < D < 3 . To cite this article: H.J. de Vega, N.G. Sanchez, C. R. Physique 7 (2006).