Evolution of a stellar system in the context of the virial equation

Abstract

The virial equation is used to clarify the nature of the dynamic evolution of a stellar system. The methods used are based on analytical and numerical modeling of evolution, as well as on an approach long used in the nonlinear theory of oscillations. It is shown that the mean harmonic radius of a system with negative total energy never exceeds two times the equilibrium value. The time to reach the virial equlibrium state $T_v$ is about two to three dozen dynamic time periods $T_d$. For systems not in close proximity to virial equilibrium, the virial ratio, the mean harmonic radius, and the root mean square radius of the system fluctuate during $T_v$; then the virial ratio and mean harmonic radius stabilize near their equilibrium values, while the root mean square radius continues to increase (possibly ad infinitum). Thus, the moment of inertia of the system relative to the center of gravity and its potential energy have significantly different behavior, which leads to the formation of a relatively small quasi-equilibrium core and an extended halo.