Instability of thermal, viscous, and acoustic modes in thin accretion disks

A model for a thin gas disk in an external gravitational potential is examined in detail. A complete self-consistent system of hydrodynamic equations is used to study the dynamics of small nonaxisymmetric pinch perturbations in a thin gas disk, allowing for dissipative effects. The first and second viscosities are taken into account, and the opacity coefficient has an arbitrary dependence on the surface density sigma and half-thickness h. The possibilities of developing dissipative instabilities in accretion-disk models proposed by various authors are discussed. Both long-wavelength (compared to the disk thickness) and short-wavelength oscillations are considered. Good agreement between the results obtained with thin-disk and three-dimensional models is demonstrated.