Stability of the Stellar Disks of Flat Galaxies. I. A Collisionless, Homogeneous System

A differentially rotating stellar disk, representing highly flattened galaxies, is studied by employing the linear kinetic theory to determine its stability against small-amplitude gravity perturbations. The analysis is carried out for the special case of an infinitely thin, spatially homogeneous system, taking into account the effects of random (residual) movements of stars, but neglecting collisions. The influence of drift motion on the stability of disk oscillations is investigated. This minor motion of a star, whose value may be determined from the higher order approximation of Lindblad's epicyclic theory, is analogous to the grad B drift of an electrically charged particle in a plasma and is related to the differential rotation of the system. In classical stellar dynamics, this drift has been known as the asymmetric drift. Within the local approximation of the WKB method, it is shown that a disk rotating differentially could be unstable due to either a gravitational Jeans-type instability or an oscillating kinetic-type instability (overstability). To suppress Jeans instabilities, a generalized local stability criterion must be satisfied, which indicates that in a differentially rotating disk, nonaxisymmetric perturbations are more unstable than axisymmetric ones. A Jeans-stable disk is still unstable to oscillatory growing perturbations. The etiology of this oscillating instability is the resonant interaction of drifting stars with Jeans-stable waves at the corotation resonance: nonaxisymmetric Jeans-stable modes of the differentially rotating disk are modified by drifts and can become unstable. It is similar to the instability of the Cherenkov type (the inverse Landau damping effect) in plasmas, and it is due to the nature of the differential rotation of the galactic system. The growth rates of the amplitudes of the excited waves are exponentially small, excepting the corotation resonant regions of the system. As drift motion always exists in the differentially rotating disk, the oscillating instability can be considered to be a long-term generating mechanism for propagating density waves, thereby leading to spiral-like patterns in the flat galaxies. It is suggested also that because of the resonant interaction of stars with the gravitational field of the oscillatory growing waves, the rate of relaxation of a disk toward equilibrium can be enhanced. This collisionless collective relaxation will be accompanied by a secular increase in the stellar velocity dispersion and a redistribution of the surface mass density to a more peaked distribution. The latter may assist in the formation of a condensed nucleus of a galaxy.