Linear kinetic theory of instabilities of a gravitating stellar disk

Linear kinetic theory is developed to describe collective oscillations (and their instabilities) propagating in a rapidly rotating disk of stars, repr esenting a highly flattened galaxy. The analysis is carried out for the spe cial case of a self-gravitating, infinitesimally thin, and spatially inhomo geneous system, taking into account the effects both of thermal movements o f stars and of gravitational encounters between stars and giant molecular c louds of an interstellar medium. The star-cloud encounters are described wi th the use of the Landau collision integral. The dynamics of gravity pertur bations with rare interparticle encounters is considered. Such a disk is tr eated by employing the well elaborated mathematical formalisms from plasma perturbation theory using normal-mode analysis. In particular, the method o f solving the Boltzmann equation is applied by integration along paths, neg lecting the influence of star-cloud encounters on the distribution of stars in the zeroth-order approximation. We are especially interested in importa nt kinetic effects due to wave-star resonances, which we have little knowle dge about. The kinetic effects are introduced via a minor drift motion of s tars which is computed from the equations of stellar motion in an unperturb ed central force field of a galaxy. The dispersion laws for two main branch es of disk's oscillations, that is the classical Jeans branch and an additi onal gradient branch, are deduced. The resonant Landau-type instabilities o f hydrodynamically stable Jeans and gradient gravity perturbations is consi dered to be a long-term generating mechanism for propagating density waves, thereby leading to spiral-like and/or ring-like patterns in the flat galax ies.