Size of the smallest particles in Saturn's rings

Abstract

Spacecraft and ground-based observations have shown that particles in Saturn's main rings have a power-law distribution roughly between centimeter and ten meters, but sub-centimeter particles appear to be lacking. Recent studies based on Cassini observations suggest that the minimum particle size is on the order of millimeters, although their abundance is lower than is expected from the extrapolation of the power-law distribution for the larger size range. Cohesive force between particles has been proposed to explain the paucity of sub-centimeter particles, but its strength depends on impact velocity. In order to better understand recent Cassini observations about small ring particles, we examine impact velocity (vimp) between ring particles using N-body simulation including size distribution. We find that most collisions take place at low velocities with vimp≲0.1 cm s−1; even in dense rings where particles' velocity dispersion is enhanced by gravitational wakes, they collide at such low velocities because particles tend to move coherently in the wakes. This velocity is too low to detach sub-centimeter particles that are attached to the surface of large ones due to the cohesive force, explaining their paucity in the main rings. On the other hand, impacts at higher velocities occasionally occur, either as collision between particles in the high-velocity tail in dilute rings, or as collisions between adjacent wakes in the case of dense rings. Such infrequent high-velocity impacts release millimeter-sized particles strongly attached to the surface of large ones, explaining the observed free millimeter-sized particles with relatively low abundance. Our results suggest that studies of small particles in Saturn's rings would provide constraints on the cohesive force between icy particles, which is important not only for the origin and evolution of planetary rings but also for other astrophysical problems including dust evolution and planetesimal formation in protoplanetary disks.