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Title:
Boundary Layer Circulation in Disk-Halo Galaxies - Part Three - the Dispersion Relation for Local Disturbances and Large-Scale Spiral Waves
Authors:
Waxman, A. M.
Publication:
Astrophysical Journal Supplement, Vol. 41, P. 647, 1979 (ApJS Homepage)
Publication Date:
12/1979
Origin:
KNUDSEN
DOI:
10.1086/190635
Bibliographic Code:
1979ApJS...41..647W

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. In a previous paper we derived the equations governing the stability of such a flow. The equations describe the local effects of Boussinesq perturbations, in the form of spiral waves with arbitrary pitch angle, on the model disk-halo system. Ultimately, we are interested in those local waves which display a coherent spiral geometry over a large part of the disk. The equations are solved asymptotically for large values of the local Reynolds number. In passing to the limit of inviscid waves, we are able to derive a locally valid dispersion relation. We also develop a technique whereby we may correct the inviscid wave eigenvalues for the effects of small but finite viscosity. In this way we can study the roles of the buoyancy force, Coriolis acceleration, viscous stresses, and their interactions. 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. Restricting ourselves to waves with long coherence lengths, we find the geometry of the dominant inviscid waves to be leading, tightly 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 l0 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.

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