Remarks about the thermodynamic limit in selfgravitating systems

Abstract

The present effort addresses the question about the existence of a well-defined thermodynamic limit for the astrophysical systems with the following power law form: to tend the number of particles, N, the total energy, E, and the characteristic linear dimension of the system, L, to infinity, keeping constant E/N^{Λ_{E}} and L/N^{Λ_{L}}, being Λ_{E} and Λ_{L} certain scaling exponent constant. This study is carried out for a system constituted by a non-rotating fluid under the influence of its own Newtonian gravitational interaction. The analysis yields that a thermodynamic limit of the above form will only appear when the local pressure depends on the energy density of fluid as $p=γε$, being $γ$ certain constant. Therefore, a thermodynamic limit with a power law form can be only satisfied by a reduced set of models, such as the selfgravitating gas of fermions and the Antonov isothermal model.