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

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.