What Confines the Rings of Saturn?

Abstract

The viscous spreading of planetary rings is believed to be counteracted by satellite torques, through either an individual resonance or overlapping resonances. For the A ring of Saturn, it has been commonly believed that the satellite Janus alone can prevent the ring from spreading, via its 7:6 Lindblad resonance. We discuss this common misconception and show that, in reality, the A ring is confined by the contributions from the group of satellites Pan, Atlas, Prometheus, Pandora, Janus, Epimetheus, and Mimas, whose cumulative torques from various resonances gradually decrease the angular momentum flux transported outward through the ring via density and bending waves. We further argue that this decrease in angular momentum flux occurs through “flux reversal.” Furthermore, we use the magnitude of the satellites’ resonance torques to estimate the effective viscosity profile across the A ring, showing that it decreases with radius from ∼50 cm 2 s −1 to less than ∼10 cm 2 s −1 . The gradual estimated decrease of the angular momentum flux and effective viscosity are roughly consistent with results obtained by balancing the shepherding torques from Pan and Daphnis with the viscous torque at the edges of the Encke and Keeler gaps, as well as the edge of the A ring. On the other hand, the Mimas 2:1 Lindblad resonance alone seems to be capable of confining the edge of the B ring, and contrary to the situation in the A ring, we show that the effective viscosity across the B ring is relatively constant at ∼24–30 cm 2 s −1 .