Care and feeding of frogs

TL;DR

This paper investigates the dynamics of propeller moonlets in Saturn's rings, extending the frog resonance model with numerical experiments to understand their libration behavior and compare it with observations.

Contribution

It introduces an extended frog resonance model including feedback and disk torques, providing insights into propeller moonlet librations and their dependence on disk interactions.

Findings

Frog librations depend on the delay time t_diff exceeding the libration period P_lib.

Damping from Lindblad torques can suppress librations if feedback is weak.

The model can reproduce the observed libration period of Bleriot but not its amplitude.

Abstract

"Propellers" are features in Saturn'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, "Bl\'eriot," 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 gap'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 Bl\'eriot, the frog resonance model can reproduce the observed libration period P_lib ~ 4 yr. However, our simple feedback prescription suggests that Bl\'eriot'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.