Simulating the Formation of Fine-Scale Structure in Saturn's Rings

Planetary ring dynamics is reviewed, based on the results of local 3-dimensional simulations, which utilize a co-moving calculation cell with periodic boundary conditions. Various factors afiecting the local balance between collisional dissipation and viscous gain of energy from the systematic velocity fleld are considered, including gravitational encounters and collective gravitational forces besides physical impacts. Simulation examples of the efiects of difierent forms of the coe‐cient of restitution are given. Viscous stability properties are also discussed: examples of both instabilities and overstabilities are given and brie∞y discussed in the context of observed structures in Saturn’s rings. x1. Introduction Saturn’s rings consist of cm to meter-sized icy particles revolving on nearly circular, almost co-planar orbits. The ring evolution is governed by the orbital motion, the frequent impacts between ring particles, their mutual self-gravity, and the perturbations exerted by both external satellites and by embedded moonlets. In the dense main rings (the A and B rings) particles collide even 10{100 times per orbital revolution. Although the orbital velocities are » 20 km/s, the random velocities related to orbital eccentricities and inclinations are small, indicating impact velocities below » 0.5 cm/s (corresponds to ring vertical thickness » 10 meters). Such gentle impacts do not lead to fragmentation, but still dissipate a signiflcant fraction of random kinetic energy in each collision. This loss is balanced by the viscous gain of energy from the difierential rotation around the planet (orbital speeds increase inward), establishing a local steady-state in a time scale of few tens of impacts/particle. 16),21),56) Details of the resulting balance (velocity dispersion, geometric thickness, viscosity) are determined by the frequency and elasticity of impacts, and the internal density and size distribution of particles. 43) Depending on the implied viscosity-density relation, the ring can be either stable or unstable against the growth of local perturbations. For example, dense rings composed of quite inelastic particles can become viscously overstable, which is likely to relate to the strictly axisymmetric small-scale oscillations observed in several locations of Saturn’s A and B rings. 9),58) The importance of ring particles’ mutual gravity for shaping the local structure of Saturn’s rings has been strikingly demonstrated by the Cassini stellar 8),9),19) and radio occultation measurements, 58) which conflrm the presence of unresolved trailing structures (self-gravity wakes 41) ) throughout the A and B rings. These structures arise as a superposition of tiny perturbations excited around each individual ring particle, amplifled by the interplay of shear and gravity (swing-ampliflcation mechanism 61) ). Such structures were envisioned by Alar Toomre already decades