Post-collapse dynamics of self-gravitating Brownian particles in D dimensions

TL;DR

This paper investigates the post-collapse behavior of self-gravitating Brownian particles in D dimensions, revealing ensemble-dependent structures like Dirac peaks and binary-like formations, consistent with thermodynamic predictions.

Contribution

It provides a detailed analysis of post-collapse dynamics in both canonical and microcanonical ensembles for self-gravitating Brownian particles in arbitrary dimensions.

Findings

Formation of Dirac peaks with increasing mass in canonical ensemble

Self-similar density evolution outside the peak

Binary-like structures with high-temperature halos in microcanonical ensemble

Abstract

We address the post-collapse dynamics of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, the post-collapse evolution is marked by the formation of a Dirac peak with increasing mass. The density profile outside the peak evolves self-similarly with decreasing central density and increasing core radius. In the microcanonical ensemble, the post-collapse regime is marked by the formation of a ``binary''-like structure surrounded by an almost uniform halo with high temperature. These results are consistent with thermodynamical predictions.