Local [ITAL]N[/ITAL]-Body Simulations for the Distribution and Evolution of Particle Velocities in Planetary Rings

Abstract

Distribution and evolution of particle velocities in planetary rings of one- and two-size components are investigated by a local N-body simulation with periodic boundary conditions, which includes collisions and gravitational interactions between particles. Evolution of rms eccentricities and inclinations for a system of low optical depth is found to be well predicted by the numerical results of three-body orbit calculations. The Kolmogorov-Smirnov test is performed to examine the particle velocity distribution, and it is found that the distribution of orbital eccentricities and inclinations of particles in a disk with low optical depth can be well approximated by a Rayleigh distribution when the restitution coefficient of particles is small enough (0.6) to achieve an equilibrium state, whereas excess of high-velocity particles is found in more elastic cases in which velocity dispersion increases monotonically. When the optical depth is larger and the disk of particles becomes gravitationally unstable, however, effects of collective wakes become important. Theoretical results based on three-body orbit calculations fail to predict the evolution in this case, and eccentricities and inclinations deviate from the Rayleigh distribution.