Hahn, J.M., Porco, C., Spitale, J. (2010). "An Nbody Integrator for Planetary Rings" American Astronomical Society, DPS meeting #42, #50.09.


Abstract
An Nbody integrator has been developed to simulate large-scale phenomena in planetary rings, such as the confinement of the outer edge of Saturn's B ring by Mimas' m=2 Lindblad resonance, and the propagation of spiral density waves in the A ring. The code tracks N particles whose motions trace the perturbed ring's streamlines. Accelerations on those particles due to ring gravity, pressure, and viscosity are then simple functions of the particles' positions and velocities relative to those streamlines. A second-order kick-drift scheme (Wisdom & Holman 1991, Saha & Tremaine 1992) is used to advance the particles' epicyclic orbit elements over time, with the kicks given by the rate equations of Longaretti and Borderies (1991). Simulating a narrow but well-resolved annulus in the ring typically requires execution times of ~10 minutes on a desktop PC using only N~1000 particles. A simulation of the B ring's sharp outer edge, as well as the propagation of nonlinear spiral density waves, will be shown in the conference poster. We also plan to extend this 2D model to 3D, so as to simulate spiral bending waves. Another goal of this program is to study resonant perturbations in a dense and incompressible ring, which can experience vertical displacements due to a satellite's horizontal forcing. Such rings are suspected to be unstable (Borderies et al 1985), which can account for the B ring-edge's m<>2 modes (Spitale & Porco 2009, 2010). We also hope to have preliminary results from a study of this scenario at conference time.