Ring-shaped instability of nonequilibrium models of disk-like self-gravitating systems

In this work, we study the problem of the formation of a ring-shaped structure based on three nonequilibrium disk composite models with an anisotropic velocity diagram, which we constructed. These models are based on a nonstationary generalization of the well-known equilibrium isotropic disk model of Bisnovatyi-Kogan and Zeldovich. Corresponding nonstationary analogues of the dispersion equation for the ring-shaped perturbation mode of the models are introduced. Based on the results of numerical calculations of these equations, a comparative analysis of the three nonequilibrium disk models is carried out, in particular, with respect to the gravitational instability of the ring-shaped perturbation mode. The mechanisms and initial physical conditions for the formation of ring-shaped structures in disk-like self-gravitating systems at the early stage of their evolution have been identified.