Instabilities in a nonstationary model of self-gravitating disks. IV. Generalization of the models and comparison of results

Abstract

A generalized phase model of a radially nonstationary disk with an anisotropic velocity diagram is constructed which has an exact nonlinear nonstationarity law and is a nonequilibrium extension of the equilibrium disk of Bisnovatyi-Kogan and Zel’dovich. For a comparative analysis of the instabilities of the generalized model with respect to horizontal and vertical oscillatory modes, nonstationary analogs of the dispersion relations are obtained for these modes. An analysis of these results shows that the parameters characterizing the difference and degree of anisotropy of nonlinearly nonstationary models have opposite effects on the horizontal and vertical oscillations of a disk. We also compare the horizontal and vertical oscillatory modes against the background of nonstationary models with isotropic and anisotropic velocity diagrams. For small and moderate disk rotation parameters, it is found that the vertical modes dominate the horizontal modes, while the opposite picture is seen on approaching the maximum rotation.