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Regolith grain sizes of Saturn's rings inferred from Cassini-CIRS far-infrared spectra

We analyze far-infrared (10-650 cm$^{-1}$) emissivity spectra of Saturn's main rings obtained by the Cassini Composite Infrared Spectrometer (CIRS). In modeling of the spectra, the single scattering albedos of regolith grains are calculated using the Mie theory, diffraction is removed with the delta-Eddington approximation, and the hemispherical emissivities of macroscopic free-floating ring particles are calculated using the Hapke's isotropic scattering model. Only pure crystalline water ice is considered and the size distribution of regolith grains is estimated. We find that good fits are obtained if the size distribution is broad ranging from 1 $μ$m to 1-10 cm with a power law index of $ \sim 3$. This means that the largest regolith grains are comparable to the smallest free-floating particles in size and that the power law indices for both free-floating particles and regolith grains are similar to each other. The apparent relative abundance of small grains increases with decreasing solar phase angle (or increasing mean temperature). This trend is particularly strong for the C ring and is probably caused by eclipse cooling in Saturn's shadow, which relatively suppresses warming up of grains larger than the thermal skin depth ($\sim$ 1 mm) under subsequent solar illumination.