Care and Feeding of Frogs

Details Care and Feeding of Frogs Care and Feeding of Frogs

Jan 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aj....143....9p&link_type=abstract

The Astronomical Journal, Volume 143, Issue 1, article id. 9 (2012).

Astronomy and Astrophysics

Astronomy

1

Planets And Satellites: Dynamical Evolution And Stability, Planets And Satellites: Rings

Scientific paper

"Propellers" are features in Saturn's A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion (Tiscareno et al.) the longitude residuals of the best-observed propeller, "Blériot," appear consistent with a sinusoid of period ~4 years. Pan & Chiang 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 delay, 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 delay exceeds the frog libration period P lib, and if damping from Lindblad torques balances driving from co-orbital torques. If t delay Lt 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's t delay ~ 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.

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