BEHAVIOR OF SECTORAL INSTABILITIES DEPENDING ON THE PARAMETERS OF THE GENERALIZED MODEL OF A SELF-GRAVITATING DISK

In this work, we investigate the problem of gravitational instability in a generalized model of a nonlinearly radially pulsating disk with an anisotropic velocity diagram relative to sectoral modes of perturbations. This model is a non-stationary generalization of the equilibrium self-gravitating disk by Bisnovatyi-Kogan and Zeldovich. Exact expressions are obtained for the main physical characteristics of the generalized model, such as the components of the kinetic energy of the pulsating disk, velocity dispersions in the radial and transverse directions, the global anisotropy parameter, and others. We also found non-stationary analogs of dispersion equations (NADE) against the background of this generalized model for sectoral modes of perturbations. Based on the results of numerical calculations of NADE, graphs comparing the instability increments depending on the initial virial ratio of the system for various values of the parameters α and β, characterizing the difference and degree of anisotropy of nonlinearly non-stationary models of the self-gravitating disk, were constructed. In particular, it is shown that the development of bar-like mode instability will be the same for all anisotropic models, as the NADE of this mode does not depend on the parameters α and β. The work is partially based on a talk presented at the Modern Stellar Astronomy 2024 conference.

self-gravitating disk, non-stationary model, sectoral modes of perturbations, gravitational instability, instability increment