Ring–Ringlet Interactions

Abstract

This paper is motivated by the recent discovery of the single-sided shepherding observed in numerical simulations by975875;975875and explained by975875. It deals with the question of the confinement of the gap's edges. Gravitational perturbations exerted by the narrow ringlet on the gap's edges and the exchange of angular momentum between the ringlet and the gap's edges are studied. These results are applied to the ringlet and gap at 1.470Rpin Saturn's C ring. We find that if the ringlet's shape is dominated by them= 1 mode, then its surface density would have to be much smaller than generally thought, otherwise the perturbations exerted on the edges would have been observed in the Voyager data. If the ringlet's eccentricity is forced by the 2:1 Lindblad resonance with Prometheus, as suggested by Goldreich, Rappaport and Sicardy's explanation, then the perturbations exerted by the ringlet on the gap's edges are on the same order of magnitude as those exerted by Prometheus. The torque exerted by the ringlet is able to confine the gap's inner edge, but the flux of angular momentum due to the ringlet perturbations near the outer edge of the gap has the sign opposite to that expected for confinement. This suggests that either the gap's edges are, as the ringlet itself, confined by reversal of the viscous flux of angular momentum or that one or several satellites or big particles located within the gap are responsible for the confinement of its edges.