On the evolution of a stellar system in the context of the virial equation

TL;DR

This paper explores how stellar systems evolve towards virial equilibrium, revealing that certain properties stabilize while others continue to grow, leading to core-halo structures.

Contribution

It provides a detailed analysis of the relaxation process in stellar systems using the virial equation, highlighting the timescale and behavior of key parameters.

Findings

Virial equilibrium is reached after about 2-3 dozen dynamic times.

The virial ratio and radii fluctuate and stabilize, while the RMS radius grows indefinitely.

A small core and extended halo form during evolution.

Abstract

The virial equation is used to clarify the nature of the dynamic evolution of a stellar system. Compared to the kinetic equation, it gives a deeper but incomplete description of the process of relaxation to a quasi-stationary state, which here means the fulfillment of the virial theorem. Analysis shows that the time to reach the virial equlibrium state $T_v$ is about two to three dozen dynamic time periods $T_d$. Namely, during $T_v$ the virial ratio, the mean harmonic radius, and the root-mean-square radius of the system fluctuate, and then the first two characteristics stabilize near their equilibrium values, while the root-mean-square radius continues to grow (possibly ad infinitum). This indicates a fundamentally different behavior of the moment of inertia of the system relative to the center of gravity and its potential energy, leading to the formation of a relatively small equilibrium core and an extended halo.