On the nature of the hydrodynamic stability of accretion disks

The linear stability of accretion disks is revisited. The governing equations are expanded asymptotically and solved to first order in the expansion parameter $ϵ$ defined by the ratio of the disk’s vertical thickness to its radial extent. Algebraically growing solutions are found for global perturbations on the radial accretion flow of thin inviscid compressible Keplerian disks. The algebraic temporal behavior is exhibited in the vertical velocities and the thermodynamic variables and has the form $t\sin {\mathrm{\Omega }}_{0}t$ locally in the disk where ${\mathrm{\Omega }}_0$ is the Keplerian rotation rate. The physical implications and relations to the Solberg-Hoiland stability criteria are discussed.