Ray-tracing thermal modelling of Saturn's main rings

Abstract

The observations of the Cassini spacecraft gave new perspectives to our understanding of the rings of Saturn and their thermal studies due to their large variety of observation geometries. However, we still know little about the ring particles' physical and, particularly, thermal properties, which is the reason why a number of observations are not easy to explain. Nevertheless, the observed temperature profiles of the rings can be reproduced by considering the rings' general structural properties like local optical depth, τ, and, for the optically-thick rings, wake properties like the ratios H/W or wake thickness to wake width, and S/W or wake separation to wake width; as well as their main energy input sources (e. g., direct and reflected solar energy and Saturn's infrared energy).In this work, we assume that the main rings (C, B, Cassini Division and A rings) are monolayers and study the temperature variations with solar elevation angle, B′, of ten of their regions with a simple thermal balance equation that depends on the rings' shadowing behaviour due to the illumination geometry (B′) and the arrangement of particles across the rings (τ). The shadowing is a key feature, which we reproduce with a numerical function obtained via ray tracing from arrays of spherical particles (C(B′,τ)). Using the former model, we fit Cassini Composite Infrared Spectrometer (CIRS) temperature data with the Bond albedo, AV, and the so-called rotation parameter, f (which represents the rotation status of the ring particles) as only parameters. These parameters are two of the most important physical properties that define the rings' temperatures.With our method, we are able to reproduce the CIRS data temperature trends of the selected regions reasonably well. For evaluation purposes we compare the derived Bond albedo values with those obtained with the Cassini Imaging Science Subsystem (ISS) at wavelengths in the range 451 ≲ λ ≲ 650nm. The comparison suggests a dominance of slow rotators. Additionally, we evaluate the differences obtained when using either a numerical or an analytical shadowing function (in particular, that by (Altobelli et al., 2008)) in the thermal model. The differences between these two approaches reflect some details of the structure of the ring regions we study.