Instabilities in a nonstationary model of self-gravitating disks. II. Warp modes of vertical oscillations

Gravitational instabilities with respect to warp modes of vertical oscillations are examined for nonlinearly nonequilibrium disk models with isotropic and anisotropic velocity diagrams. Nonstationary analogs of the dispersion relations for vertical oscillations in these models are derived in a general form. A detailed study is made of the major large scale oscillatory modes, which correspond primarily to the most common type of warp in the form of an integral sign, as well as to dome-shaped, U-shaped, and precessional warps. Critical diagrams showing the initial virial relation as a function of the rotation parameter for the nonstationary model are constructed for each of these vertical oscillation modes. A comparative analysis is made of the growth rates of the instabilities for these modes in order to determine the dependence of the characteristic times for their appearance on the basic physical parameters of the two models.