Dynamical stability of two-dimensional accretion flows: An analytic study

We solve the eigenvalue problem for nonaxisymmetric normal modes (the "Papaloizou-Pringle" instability) in a two-dimensional shearing flow with steady accretion. We use asymptotic techniques to derive (analytically) explicit expressions for eigenfunctions of the unstable modes, and their growth rate. These expressions allow us to demonstrate the stabilizing effect of transonic accretion and to identify the physical cause for this stabilization. accretion, accretion disks instabilities.