A gas-kinetic stability analysis of self-gravitating and collisional particulate disks with application to Saturn's rings

Linear theory is used to determine the stability of the self-gravitating, r apidly land nonuniformly) rotating, two-dimensional, and collisional partic ulate disk against small-amplitude gravity perturbations. A gas-kinetic the ory approach is used by exploring the combined system of the Boltzmann and the Poisson equations. The effects of physical collisions between particles are taken into account by using in the Boltzmann kinetic equation a Krook model integral of collisions modified to allow collisions to be inelastic. It is shown that as a direct result of the classical Jeans instability and a secular dissipative-type instability of small-amplitude gravity disturban ces (e.g. those produced by a spontaneous perturbation and/or a companion s ystem) the disk is subdivided into numerous irregular ringlets, with size a nd spacing of the order of 4 pi rho approximate to 2 pi h, where rho approx imate to c(r)/K is the mean epicyclic radius, c(r) is the radial dispersion of random velocities of particles, re is the local epicyclic frequency, an d h approximate to 2 rho is the typical thickness of the system. The presen t research is aimed above all at explaining the origin of various structure s in highly flattened, rapidly rotating systems of mutually gravitating par ticles. In particular, it is suggested that forthcoming Cassini spacecraft high-resolution images may reveal this kind of hyperfine similar to 2 pi h less than or similar to 100 m structure in the main rings A, B, and C of th e Saturnian ring system. (C) 2000 Elsevier Science Ltd. All rights reserved .