A NUMERICAL SIMULATION OF PLANETARY RINGS. II: MASS SEGREGATION, RING CONFINEMENT, AND GAP FORMATION.

We consider a numerical model of planetary rings in which particles interact through mutual attraction and inelastic collisions. Arbitrary mass distributions are allowed. Various situations are simulated: (i) The evolution of an isolated ring made of particles with different masses. 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 particles. 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. Theoretical approximations are derived in a number of limiting cases and are shown to be in good agreement with numerical results.