Paper detail

Care and feeding of frogs

&#34;Propellers&#34; are features in Saturn&#39;s A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion (Tiscareno 2010); the longitude residuals of the best-observed propeller, &#34;Blériot,&#34; appear consistent with a sinusoid of period ~4 years. Pan and Chiang (2010) proposed that propeller moonlets librate in &#34;frog resonances&#34; 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 gap&#39;s 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 Blériot, the frog resonance model can reproduce the observed libration period P_lib ~ 4 yr. However, our simple feedback prescription suggests that Blériot&#39;s 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.