SIMULATIONS OF THE DYNAMICAL AND LIGHT-SCATTERING BEHAVIOR OF SATURN'S RINGS AND THE DERIVATION OF RING PARTICLE AND DISK PROPERTIES

Abstract

We study the light-scattering behavior of Saturn's rings for the purpose of deducing the nature and distribution of the particles comprising them and the collisional and dynamical environments in which they reside. To this end, we have developed two complex numerical codes to apply to this objective. One is a geometric ray-tracing code that scatters rays from a light source at an arbitrary illumination angle into a computer-generated patch of ring particles of predetermined photometric properties and size distribution, and counts the rays that emerge into arbitrary viewing directions. The code accounts for singly and multiply scattered light as well as the illumination of the rings by the planet Saturn. We examine the light-scattering behavior of various realizations of particle distribution, ring thickness, and optical depth—assuming macroscopic, backscattering particles with radii in the centimeter-to-meter range—and have compared our experimental results with classical analytical single-scattering and numerical multiple-scattering calculations, and with Cassini images of Saturn's A and C rings. We can reproduce the classical photometric results when vertically thick particle distributions are used, and we find good agreement with the observations when physically thin particle distributions are used, that is, in regimes where classical theory fails. This work has allowed us to demonstrate that the particles in the low optical depth portion of the C ring reflect about 32% of the incident sunlight in a manner similar to that of the jovian moon, Callisto. Those orbiting beyond the Encke gap in Saturn's A ring are nearly twice as reflective, and are slightly more forward scattering than those in the C ring. The A ring vertical full thickness beyond the Encke gap is likely to be very thin, ~10 m. The thickness of the C ring is not discernible from this work. The optically thicker A and B rings are darker at high phase than classical calculations predict because they are so thin. We have also incorporated the capability to realistically simulate a patch of colliding, self-gravitating particles in Saturn's gravity field into a sophisticated N-body parallel tree code. This code can model dissipative collisions among several million particles with optional sliding friction. We have applied our light-scattering code to simulations of Saturn's A ring produced by this patch code in which gravitational wakes have been observed to form. We have demonstrated, as have others, that such wakes are the likely cause of the well-known azimuthal brightness asymmetry in Saturn's A ring. We match the asymmetry amplitude and shape, as observed primarily in low-solar-phase Voyager images, by assuming a velocity-dependent restitution law that yields a coefficient of restitution ~3.5 times lower at the velocity dispersions appropriate for the smallest particles in Saturn's rings than previously assumed; Cassini data are consistent with these results. We simultaneously find a particle albedo and phase function consistent with those deduced from photometric analyses of Cassini images taken on approach to Saturn. These results suggest that the ring particle collisions in Saturn's A ring are more lossy than previously expected, a result possibly due to particle surface roughness, a regolith, and/or a large degree of porosity, all of which would lower the coefficient of restitution.