Resonant excitation of density waves in Saturnʹs rings: the effect of interparticle collisions

Kinetic theory with the phenomenological Bhatnagar-Gross-Krook binary collision integral is used to study the small amplitude oscillations and their stability of a collisional planetary ring system of identical particles. A differentially rotating, spatially homogeneous disk is considered, with the property that both the epicyclic frequency and the angular velocity of differential rotation exceeds the frequency of inelastic (physical) collisions between particles, that is, a disk with rare collisions is considered. The stabilizing influence of collisions on the growth rate of the oscillating resonant type instability, studied in the first paper of the series, is shown. Also it is shown that in low optical depth regions of Saturnʹs rings rare collisions cannot suppress the resonant excitation of spiral density waves investigated by Griv (Planet. Space Sci. 44, 579–587, 1996) in the first paper of the present series.