Regolith depth growth on an icy body orbiting Saturn and evolution of bidirectional reflectance due to surface composition changes

Using a Markov chain model, we consider the regolith growth on a small body in orbit around Saturn, subject to meteoritic bombardment, and assuming all impact ejecta are re-collected. We calculate the growth of regolith and the fractional pollution, assuming an initial pure ice body and amorphous carbon as a pollutant. We extend the meteorite flux of Cuzzi and Estrada (Cuzzi, J., Estrada, P. [1998]. Icarus 132, 1–35) to larger sizes to consider the effect of disruption of the moonlet on other moonlets in the ensemble. This is a relatively small effect, completely negligible for moonlets of 1 m radius. For the given impact model, fractional pollution reaches 22% for 1 m bodies, but only 3% for 10 m bodies, 1.7% for 20 m bodies, and 1% for 30 m bodies after 4 byr. By considering an ensemble of moonlets, which have identical cross-sections for releasing and capturing ejecta, this analysis can be extended to a model of particles in Saturn’s rings, where the calculated spectra can be compared to observed ring spectra. The measured spectral reflectance of Saturn’s rings from Cassini observations therefore constrains the size and age of the ring particles. The comparison between 1 m, 10 m, 20 m, and 30 m particles confirms that for larger ring mass, the current rings would be less polluted; for the largest particles, we expect negligible changes in the UV spectrum after 4 byr of meteoritic bombardment. We consider two end members for mixing of the meteoritic material: areal and intimate. Given the uncertainties in the actual mixing of the meteoritic infall and in its composition (as a worst case, we assume the meteoritic material is 100% amorphous carbon, intimately mixed) initially pure ice 30 m ring particles would darken after 4 byr of exposure by 15%.