# Statistical mechanics of gravitating gas like galaxy

## TL;DR

This paper develops a statistical mechanics framework for self-gravitating gases like galaxies, introducing the concept of gravitational haziness to describe equilibrium states and deriving related equations of state.

## Contribution

It introduces the concept of gravitational haziness as a key parameter and constructs a kinetic equation for self-gravitating gases, deriving equilibrium distributions and a galaxy equation of state.

## Key findings

- Defined the most probable state using gravitational haziness.
- Derived a particle distribution function analogous to Maxwell-Boltzmann.
- Formulated a galaxy equation of state incorporating gravitational haziness.

## Abstract

The most probable state of an infinite self-gravitating gas in the dynamical equilibrium is defined by `gravitational haziness', a parameter representing many-body effects and formally like the temperature in the case of thermal equilibrium. A kinetic equation is constructed using a concept of statistical equipartition of the virial among subsystems of the self-gravitating gas. A closed equation for the gravitational potential is conjectured as a special property of the kinetic equation. An equilibrium particle distribution function in the phase space, an analog of the Maxwell-Boltzmann weight, and a galaxy equation of state are found for all `gravitational haziness'. The first law of a `hazydynamics' (thermodynamics) states that the total mass of an astronomical stellar collection is the sum of the Archimedes displaced mass and an excess `gobbled' mass determined by the `gravitational haziness' and history.