DYNAMICS OF THE SHARP EDGES OF BROAD PLANETARY RINGS

This paper describes a model of a broad planetary ring whose sharp edge is confined by a satellite’s mth Lindblad resonance (LR). This model uses the streamline formalism of Borderies et al. to calculate the ring’s internal forces, namely, ring gravity, pressure, and viscosity. The model also allows for the possibility of a drag force that can affect small ring particles directly, and large ring particles indirectly via collisions with the small. The model calculates the streamlines ’ forced eccentricities e, their longitudes of periapse ω̃, and the surface density σ throughout the perturbed ring. This model is then applied to the outer edge of Saturn’s B ring, which is maintained by an m = 2 inner LR with the satellite Mimas. A suite of ring models are used to illustrate how a ring’s perturbed state depends on the ring’s physical properties: its surface density, its viscosity, the ring particles ’ dispersion velocity, and the strength of the hypothetical drag force. A comparison of simulations with the outer B ring’s observed properties suggests that the ring’s surface density there is 10 σ 280 gm cm−2 in the ring’s outermost ∼40 km. The ring’s sharp edge identifies the site where the ring’s viscous torque precisely counterbalances the perturbing satellite’s gravitational torque on the ring. However, an examination of several seemingly conventional viscous B ring models shows that they all fail, by wide margins, to balance these torques at the ring’s outer edge. This is partly due to the ring’s self-gravity, which tends to reduce forced eccentricities near the resonance. But this is also due to the fact tha