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C.C. Porco, M.J. Pantazopoulou (LPL/UofA), D. Richardson, T. Quinn (U. Washington), T.J.J. Kehoe (LPL/UofA)
Particle disks, such as planetary rings, of varying thickness differ in the manner in which they scatter light. Consequently, high resolution observations of a ring's light-scattering properties may be used to infer ring thickness, and hence the collisional environment, at various locales. The usual approach to this problem has utilized classical radiative transfer techniques, which strictly apply to many-particle-thick rings. However, there is reason to believe that Saturn's rings, for example, may be very thin, with vertical thickness comparable to the largest particles, a circumstance in which the classical techniques have limited utility.
We have developed a geometric ray-tracing code that scatters rays from a light source at arbitrary illumination angle, into a computer-generated patch of ring particles of pre-determined photometric properties, and collects 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 observations of Saturn's A ring. We can reproduce classical analytical results when vertically thick particle distributions are used, and we find good agreement with Voyager imaging results when thin particle distributions are used: ie, in regimes where classical theory fails. This work has allowed us to set limits on the thickness of Saturn's A ring and to demonstrate that the rings are thinner than classical radiative treatments assume.
We have also applied our light scattering code to realistic numerical ring ('patch') simulations in which gravitational wakes have been observed to form. We have demonstrated that such wakes are the likely cause of the well-known azimuthal brightness asymmetry in Saturn's A ring.