Spitale, J. N., Porco, C. C. (2009). "Chaotic Behavior of the Kinematics of the Outer Edge of Saturn's B-ring" American Astronomical Society, DPS meeting #41, #25.05.


Abstract
The association between the outer edge of Saturn's B-ring and the 2:1 inner Lindblad resonance with Mimas has long been recognized. The ring is expected to respond to the resonance by taking the shape of a body-centered ellipse (i.e., azimuthal wavenumber m=2) with one short axis pointed toward Mimas. Previous studies (e.g., Porco et al. (1984, Icarus), Hedman et al. (submitted to AJ)) have indeed shown the pattern to have one radial minimum oriented in the general direction of Mimas, though neither precisely, nor uniformly. Because those studies typically sampled the ring at widely space intervals, their results represent a time-average of the ring's behavior, suggesting that the ring is typically in a state of libration about the expected orientation. Indeed, Hedman et al. obtained a significantly better fit to their data after including a libration term in their model. Here, we use several thousand Cassini ISS images to solve for the ring elements independently at each of 18 epochs spanning about four years from 2005 to 2009. Instead of librating, the ring edge appears to circulate, with one radial maximum sliding past Mimas during 2006. Moreover, during the 2005-2009 period, the m=2 eccentricity varied regularly, decreasing to nearly zero in 2006. In the simplest model for the 2:1 resonance, this would imply that the free and forced eccentricities are nearly equal, so the system is balanced on the boundary between libration and circulation, such that small perturbations may push it either way. Because free eccentricities tend to be damped out by viscous forces, it is not yet clear why we find the ring in such a state.