Derivation of an equation of pair correlation function from BBGKY hierarchy in a weakly coupled self gravitating system

TL;DR

This paper derives an equation for the pair correlation function in a weakly coupled, inhomogeneous self-gravitating system using BBGKY hierarchy, aiding the study of star cluster thermodynamics.

Contribution

It introduces a novel derivation of the pair correlation function equation from BBGKY hierarchy for inhomogeneous gravitational systems.

Findings

Equation applicable to star cluster cores in quasi thermal equilibrium

Potential to analyze thermodynamic properties of aged star clusters

Provides a theoretical framework for gravitational correlation studies

Abstract

An equation of pair correlation function has been derived from the first two members of BBGKY hierarchy in a weakly coupled inhomogeneous self gravitating system in quasi thermal equilibrium. This work may be useful to study the thermodynamic properties of the central region of a star cluster which is older than a few or more central relaxation time.