Boundary Layer Circulation in Disk-Halo Galaxies - Part Three - the Dispersion Relation for Local Disturbances and Large-Scale Spiral Waves

Abstract

This paper concerns the geometry and physical properties of waves which arise from a shear-flow (i.e. inflection point) instability of the galactic boundary layer circulation. This circulation was shown to exist in the meridional plane of a model galaxy containing a gaseous disk embedded in a rotating gaseous halo. Previously derived equations describe the local effects of Boussinesq perturbations, in the form of spiral waves with aribitrary pitch angle, on the model disk-halo system. The equations are solved asymptotically for large values of the local Reynolds number. In passing to the limit of inviscid waves, it is possible to derive a locally valid dispersion relation. A perturbation technique is developed whereby the inviscid wave eigenvalues can be corrected for the effects of small but finite viscosity. In this way the roles of the buoyancy force, Coriolis acceleration, viscous stresses, and their interactions can be studied. It is found that, locally, the most unstable inviscid waves are leading and open with large azimuthal wavenumbers. However, these waves display little or no coherence over the face of the disk and so would not emerge as modes in a global analysis.The geometry of the dominant inviscid waves is found to be leading, tightlymore » wound spirals. Viscous corrections shift the dominant wave form to trailing, tightly wound spirals with small azimuthal wavenumbers. These waves grow on a time scale of about 10/sup 7/ years. It is suggested that these waves can initiate spiral structure in galaxies during disk formation and that a subsequent transition to a self-gravitating acoustical mode with the same spiral geometry may occur. This transition becomes possible once the contrast in gas densities between the disk and surrounding halo becomes sufficiently large.« less