The Dynamical Stability of a Fat Disk with Constant Specific Angular Momentum

Abstract

We examine the stability of stationary, axisymmetric, rotating tori with constant specific angular momentum and uniform entropy as a model of quasars and active galactic nuclei. Using the linearized perturbation equation, we solve the two dimensional eigenvalue problem numerically. It is found that such tori are unstable in almost all the cases for global nonaxisymmetric modes, although they are marginally stable for local, axisymmetric modes. The growth rate decreases as the radial width of the torus becomes either sufficiently small or sufficiently large. The rotational energy is always reduced in the unstable modes for the fixed total angular momentum.