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, rapidly (and nonuniformly) rotating, two-dimensional, and collisional particulate disk against small-amplitude gravity perturbations. A gas-kinetic theory 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 disturbances (e.g. those produced by a spontaneous perturbation and/or a companion system) the disk is subdivided into numerous irregular ringlets, with size and spacing of the order of 4πρ ≈ 2πh, where ρ ≈ cr/κ is the mean epicyclic radius, cr is the radial dispersion of random velocities of particles, κ is the local epicyclic frequency, and h ≈ 2ρ is the typical thickness of the system. The present research is aimed above all at explaining the origin of various structures in highly flattened, rapidly rotating systems of mutually gravitating particles. In particular, it is suggested that forthcoming Cassini spacecraft high-resolution images may reveal this kind of hyperfine ∼ 2πh < ∼ 100 m structure in the main rings A, B, and C of the Saturnian ring system.