Care and feeding of frogs

Propellers are features in Saturns A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion (Tiscareno 2010); the longitude residuals of the best-observed propeller, Bleriot, appear consistent with a sinusoid of period ~4 years. Pan and Chiang (2010) proposed that propeller moonlets librate in frog resonances with co-orbiting ring material. By analogy with the restricted three-body problem, they treated the co-orbital material as stationary in the rotating frame and neglected non-co-orbital material. Here we use simple numerical experiments to extend the frog model, including feedback due to the gaps motion, and drag associated with the Lindblad disk torques that cause Type I migration. Because the moonlet creates the gap, we expect the gap centroid to track the moonlet, but only after a time delay t_diff, the time for a ring particle to travel from conjunction with the moonlet to the end of the gap. We find that frog librations can persist only if t_diff exceeds the frog libration period P_lib, and if damping from Lindblad torques balances driving from co-orbital torques. If t_diff << P_lib, then the libration amplitude damps to zero. In the case of Bleriot, the frog resonance model can reproduce the observed libration period P_lib ~ 4 yr. However, our simple feedback prescription suggests that Bleriots t_diff ~ 0.01P_lib, which is inconsistent with the observed libration amplitude of 260 km. We urge more accurate treatments of feedback to test the assumptions of our toy models.

Stochastic flights of propellers

Kilometer-sized moonlets in Saturns A ring create S-shaped wakes called propellers in surrounding material. The Cassini spacecraft has tracked the motions of propellers for several years and finds that they deviate from Keplerian orbits having constant semimajor axes. The inferred orbital migration is known to switch sign. We show using a statistical test that the time series of orbital longitudes of the propeller Bleriot is consistent with that of a time-integrated Gaussian random walk. That is, Bleriots observed migration pattern is consistent with being stochastic. We further show, using a combination of analytic estimates and collisional N-body simulations, that stochastic migration of the right magnitude to explain the Cassini observations can be driven by encounters with ring particles 10-20 m in radius. That the local ring mass is concentrated in decameter-sized particles is supported on independent grounds by occultation analyses.