The stationary state and gravitational temperature in a pure self-gravitating system

TL;DR

This paper investigates the equilibrium and thermodynamic properties of large self-gravitating gaseous systems, introducing a gravitational temperature concept and analyzing their stability.

Contribution

It proposes a method to estimate the critical mass for long-range gravitational systems and introduces the gravitational temperature and thermal capacity for stability analysis.

Findings

Identifies the stationary state as a Tsallis equilibrium.

Defines a gravitational temperature incorporating gravitational potential.

Introduces gravitational thermal capacity for stability assessment.

Abstract

The pure self-gravitating system in this paper refers to a multi-body gaseous system where the self-gravity plays a dominant role and the intermolecular interactions can be neglected. Therefore its total mass must be much more than a limit mass, the minimum mass of the system exhibiting long-range nature. Thee method to estimate the limit mass is then proposed. The nonequlibrium stationary state in the system is identical to the Tsallis equilibrium state, at which the Tsallis entropy approaches to its maximum. On basis of this idea, we introduce a new concept of the temperature whose expression includes the gravitational potential and therefore we call it gravitational temperature. Accordingly, the gravitational thermal capacity is also introduced and it can be used to verify the thermodynamic stability of the astrophysical systems.