Gasdynamical Stability of Shear Flow in Spiral Arms of Disk Galaxies

Abstract

Using a linear, finite difference hydrodynamic code, we investigate the dynamical stability of gas flow within the spiral arms of disk galaxies by considering an initial value problem. Assuming a shock to be present, we test the postshock stability of the flow in the presence of rapidly varying shear, which is characteristic of the region adjacent to shocks in spiral arms. Our method involves carrying out a linearized perturbation analysis on the postshock flow. The perturbations have a simple plane wave form in the azimuthal direction. We include radial as well as azimuthal velocities in the background flow. The region under investigation extends from the shock front to the location at which the radial velocity becomes supersonic. This is a semiglobal calculation in the sense that its extent is small on a galactic scale but encompasses postshock flow structure. We do not consider sell-gravity here. Despite the existence of several potentially destabilizing elements, the flows examined were found to be linearly stable, in general agreement with millimeter-wave observations of laminar flow structure in M51. In particular, the shock is Kelvin-Helmholtz stable, and the inner hard-wall boundary conditions do not lead to global Papaloizou-Pringle instabilities. The key stabilizing feature of the flow appears to be the presence of radial velocity. We suggest that radial flow stabilizes galactic shocks by altering the nature of the dynamics at the corotation radius of the semiglobal mode. Since fluid elements of the unperturbed system cannot comove with the modal pattern speed, energy exchange is profoundly affected. This may also at least partly account for why it is that accretion markedly stabilizes disks that are linearly unstable to Papaloizou-Pringle modes.