Methods for ray-tracing thermal modelling of Saturn's main rings

The thermal emission and temperatures of the main rings of Saturn depend on the energy the ring particles absorb, reflect and scatter and/or on their Bond albedo, emissivity, thermal inertia, rotation rate and porosity. However, the energy that each particle absorbs also depends on the amount of energy (e.g., solar energy) that reaches its surface and this latter on the local optical depth, that controls the mutual eclipsing between neighbouring particles and, in general, all shadowing effects on the rings. On the other hand, thermal models of the rings of Saturn based on the energy balance equation strongly depend on a function that described how the non-shadowed area of ring particles changes with solar elevation. Experimental and analytical shadowing functions have been proposed by [6] and [1], respectively. In this work, we propose shadowing functions based on the creation of 3D arrays of spherical particles that simulate specific regions of the main rings of Saturn. The methods implemented to obtain these shadowing functions follow the next general steps: • Arrays are created as a collection of spherical particles with a size distribution that follows a power law constrained to the optical depth of the region of study based on the UVIS instrument data. • The particles of the arrays are then reordered to add some relevant dynamical features observed in actual rings (e.g., wake structures in the case of optically-thick rings). • Under different illumination geometries, images of these arrays are rendered using ray tracing. From these images, an analysis of their pixel brightness values allows us to determine the non-shadowed fractional area of the particles in order to compose the corresponding shadowing functions.