Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices

TL;DR

This paper derives a simplified Virial theorem for rotating self-gravitating Brownian particles and 2D point vortices, enabling analysis of their dynamics without solving complex equations.

Contribution

It introduces a new form of the Virial theorem for these systems and establishes an analogy between self-gravitating particles and point vortices.

Findings

Simplified Virial theorem for 2D systems

Analogy between gravitational systems and vortex dynamics

General results without solving the Smoluchowski-Poisson system

Abstract

We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form that can be used to obtain general results about the dynamics of the system without being required to solve the Smoluchowski-Poisson system explicitly. We also develop the analogy between self-gravitating systems and two-dimensional point vortices and derive a Virial-like relation for the vortex system.