Stochastic orbital migration of small bodies in Saturn's rings

Many small moonlets that create propeller structures have been found in Saturn's rings by the Cassini spacecraft. We study the dynamical evolution of such 20-50 m sized bodies, which are embedded in Saturn's rings. We estimate the importance of various interaction processes with the ring particles on the moonlet's eccentricity and semi-major axis analytically. For low ring surface densities, the main effects on the evolution of the eccentricity and the semi-major axis are found to be caused by collisions and the gravitational interaction with particles in the vicinity of the moonlet. For high surface densities, the gravitational interaction with self-gravity wakes becomes important. We also perform realistic three-dimensional, collisional N-body simulations with up to a quarter of a million particles. A new set of pseudo shear periodic boundary conditions is used, which reduces the computational costs by an order of magnitude compared to previous studies. Our analytic estimates are confirmed to within a factor of two. On short timescales the evolution is always dominated by stochastic effects caused by collisions and gravitational interaction with self-gravitating ring particles. These result in a random walk of the moonlet's semi-major axis. The eccentricity of the moonlet quickly reaches an equilibrium value owing to collisional damping. The average change in semi-major axis of the moonlet after 100 orbital periods is 10-100m. This translates to an offset in the azimuthal direction of several hundred kilometres. We expect that such a shift is easily observable.