Simple model of violent relaxation of a spherical stellar system

TL;DR

This paper introduces a simplified hydrodynamic model for the violent relaxation process in spherical stellar systems, reducing complex equations to three core equations while ensuring energy conservation.

Contribution

It presents a novel simplified model that reduces the Jeans equations to three hydrodynamic equations for spherical stellar systems undergoing violent relaxation.

Findings

Model is consistent with energy conservation and virial theorem.

Simplifies analysis of violent relaxation in star clusters and galaxies.

Provides a basis for future detailed calculations.

Abstract

A spherical system with arbitrary mean velocities in the radial and transverse directions, but with zero dispersion of radial velocities, is considered as a model describing the violent relaxation of star clusters and galaxies. The model allows to reduce the infinite chain of Jeans' equations of moments to just three hydrodynamic equations. The found system of equations is consistent with the law of conservation of energy and the virial equation. This part of the work is devoted to a general description of the model, then the calculation results will be presented.