Two numerical models designed to reproduce Saturn ring temperatures as measured by Cassini-CIRS

•Saturn’s rings temperature modeling.•Radial profile of emissivity and thermal relaxation time.•Analytical temperature anisotropy function.

We present two numerical models designed to reproduce the temperatures of the illuminated Saturn rings as measured by the CASSINI-CIRS instrument. Our models are constrained by all available temperature measurements performed on the illuminated rings since SOI. Both models reproduce well the variations of temperature under any illumination and observation geometry. One model is derived from a purely numerical data mining approach, relying on the implementation of a Neural Network that treats the data set globally. This model is used as a test of coverage completeness of the observational parameter space, driving our ability to characterize the rings thermal response. The second (analytical) model is derived using simple physical considerations, by treating the rings as a surface rather than as a collection of individual particles, combined with an empirical anisotropy function to describe the temperature resulting from the Sun’s and Saturn’s heating. The thermal response of this ring-surface is parameterized by its Bond albedo and emissivity, thermal relaxation time and a set of geometrical parameters quantifying the anisotropy of the temperature measurements depending on azimuth and elevation of the observer with respect to the ring plane, as well as on the solar elevation. Both models provide formulae to predict the ring temperature, that will ease the benchmarking of future physical models against data. The physical model is applied to fit the temperature of tens of different radial slices, allowing us to constrain the combined emissivity and albedo, thermal relaxation time and anisotropy parameters of the ring slabs with the highest radial resolution achieved so far with CIRS. Using for the first time all observation geometries available for illuminated rings, we are confident that our values are as unbiased as possible against observation geometry. The thermal relaxation time appears to be short, a few tens of minutes, and independent of the radial distance across the whole ring. A study of the temperature anisotropy suggests inter-particle shadowing is important in the B ring and in the outer A ring regions.