Numerical Simulations of Ring Dynamics

Abstract

We consider a numerical model of planetary rings in which particles interact through mutual attraction and inelastic collisions. Arbitrary mass distributions are allowed. Our model is based on a Monte Carlo approach so that we can use a large number of particles. Various situations are simulated: (i) The evolution of an isolated narrow ring. The ring expands as a whole. Particles with a given mass acquire a well-defined relative density profile. Heavier particles concentrate near the center of the ring and lighter particles are pushed towards the edges, (ii) The confinement of a ring by shepherding satellites. Again a definite profile is obtained, and mass segregation is observed, (iii) The formation of a gap by a large particle (“moonlet”) imbedded into a uniform population of light paracles. A residual ringlet around the moonlet is observed. We study how the depth and width of the gap change with the mass of the moonlet.