Incomplete-exclusion Statistical Mechanics in Non-collisional Violent Relaxation of Celestial Objects

TL;DR

This paper introduces a modified statistical mechanics framework for celestial systems undergoing violent relaxation, accounting for partial exclusion effects that better reflect real galaxy interactions.

Contribution

It develops an incomplete-exclusion equilibrium distribution, extending Lynden-Bell's theory to more accurately model non-collisional gravitational systems.

Findings

Derived an incomplete-exclusion distribution analogous to Fermi states.

Enhanced understanding of equilibrium states in celestial violent relaxation.

Provides a new theoretical tool for astrophysical modeling.

Abstract

Violent relaxation has been proposed half a century ago to bear responsibility for non-collisional dynamics and formation of gravitationally bound systems of extended celestial objects (agglomeration of stars, galaxies, clusters of galaxies) when reaching an approximate equilibrium state which can be described thermodynamically. The Lynden-Bell equilibrium distribution of such systems, resulting from a spatial exclusion principle, had been shown to be an analog to the Fermi distribution of states in solid state physics. Real extended objects like galaxies do not completely exclude each other, however. Permitting for partial exclusion leads to a modification of the equilibrium distribution. Here we show that this case can be treated in analogy to a hypothetical incomplete population of Fermi states. An incomplete-exclusion equilibrium distribution is obtained which enters the violent relaxation theory.