The role of viscosity and cooling mechanisms in the stability of accretion disks

A dispersion relation for linearized perturbation of a geometrically thin accretion disk is derived for an arbitrary viscosity law and cooling mechanism. Using this equation, we formulate the necessary and sufficient conditions for the stability of a disk. The conditions which are imposed on the viscosity and the cooling process are general and can be used as an a priori check if a particular choice of mechanisms leads to a stable disk. It is shown that the conditions cannot be satisfied by any one of the relevant cooling mechanisms with the standard viscosity law. Small variations in this law lead, however, to a stable configuration.