Collision mechanics and the structure of planetary ring edges

A numerical simulation of collisional evolution, originally developed to model planetary accretion processes, is applied to a hypothetical ring with parameters modeled after Saturn's rings in order to study changes in radial structure near ring edges. The tendency of rings to spread so as to conserve angular momentum while energy is dissipated in collisions is confirmed if random motion is in equilibrium. Even with no energy loss (coefficient of restitution in velocity ε = 1), spreading occurs becase random motion is increasing. With a moderately side-scattering collisional model, characteristic of collisions of nonrotating spheres (the slippery “billiard-ball” model), random motion increases for ε > 0.63, in agreement with analytical models. For isotropic scattering, which may be more realistic given particle rotation, damping dominates for ε up to 0.83. As long as random motion is damped, ring edges may contract rather than spread, producing concentrations of material just inside the ring edges reminiscent of results of earlier stimulation which did not precisely conserve angular momentum.