Statement of the problem

Most studies of light scattering in planetary rings have assumed layers which are many particles thick, plane parallel, and homogeneous. However, real rings may be thin, vertically warped, and clumpy. We have developed a ray tracing code which calculates the light scattered by an arbitrary distribution of particles. This approach promises to clarify a number of puzzling observations of the Saturnian and Uranian rings.

(1) Many studies have concluded that Saturn's rings are many particles thick (e.g. Lumme et al. 1983), whereas dynamical calculations predict that optically thick rings should be physically thin (Wisdom & Tremaine 1988 and references therein). Lumme et al. argue that the particles in Saturn's B Ring fill only 2% of the volume of the ring, while Wisdom and Tremaine predict a filling factor of 20% or more.

The claim that Saturn's rings are thick is based on their observed opposition surge, a rapid brightening (0.3 mag in the V band) which occurs at phase angles below about 1.5°. The surge is attributed to particles covering their own shadows near opposition. Shadowing can occur either between discrete particles, or within the surface structure of a particle. The range in phase angle over which the brightening takes place is proportional to the volume filling factor of the ring or surface. Thus the very narrow opposition effect of Saturn's rings implies a very porous ring, unless individual particles backscatter extremely strongly.