Hydrodynamic stability in accretion disks under the combined influence of shear and density stratification

The hydrodynamic stability of accretion disks is considered. The particular question is whether the combined action of a (stable) vertical density stratification and a (stable) radial differential rotation gives rise to a new instability for nonaxisymmetric modes of disturbances. The existence of such an instability is not suggested by the well-known Solberg-Høiland criterion. It is also not suggested by a local analysis for disturbances in general stratifications of entropy and angular momentum which is presented in our Sect. 2. This confirms the results of the Solberg-Høiland criterion also for nonaxisymmetric modes within the frame of ideal hydrodynamics but only in the frame of a short-wave approximation for small m. As a necessary condition for stability we find that only conservative external forces are allowed to influence the stable disk. As magnetic forces are never conservative, linear disk instabilities should only exist in the magnetohydrodynamical regime which indeed contains the magnetorotational instability as a much-promising candidate. To overcome some of the used approximations in a numerical approach, the equations of the compressible adiabatic hydrodynamics are integrated, imposing initial nonaxisymmetric velocity perturbations with $m=1$ to $m=200$. Only solutions with decaying kinetic energy are found. The system always settles in a vertical equilibrium stratification according to pressure balance with the gravitational potential of the central object