Non-Axisymmetric Responses of Differentially Rotating Disks of Stars

This paper examines the dynamical responses and, incidentally, the stability of certain extremely thin, Cartesian models for relatively small portions of the differentially rotating stellar disks of ordinary spiral galaxies. These models incorporate a spatially constant epicyclic frequency, unperturbed surface density, Schwarzschild velocity distribution, and rate of rectilinear shear; motions perpendicular to their planes are not considered here. A small-perturbation analysis of the collision-free Boltzmann equation for these models shows that their infinitesimal, "non-axisymmetric" initial disturbances eventually must all phase-damp away. However, even when their remaining "axisymmetric" instabilities have been avoided by a sufficient velocity dispersion, these shearing star disk models remain responsive in a remarkably spiral4ike and vigorous manner to such perturbing gravity forces as might in reality arise from discrete, orbiting aggregates of interstellar material. It must be cautioned, though, that these results strictly apply only to the comparatively "local" models discussed herein and not necessarily to complete star disks.