Cratering and age of the small Saturnian satellites

The small ($\le$ 135 km mean radius) saturnian satellites are closely related to the rings and together they constitute a complex dynamical system where formation and destruction mechanisms compete against each other. We model the cratering process by Centaur objects on the small saturnian satellites, and compare our results with the observational crater counts obtained from the Voyager and Cassini missions. Using a theoretical model previously developed we calculate the crater production on these satellites considering two slopes of the size-frequency distribution (SFD) for the smaller objects of the Centaur population and compare our results with the available observations. In addition, we consider the case of catastrophic collisions between these satellites and Centaur objects and calculate the age of formation of those satellites that suffer one or more disruptions. In general we find that the observed crater distributions are best modeled by the crater size distribution corresponding to the $s_2 = 3.5$ index of the SFD of impactors with diameters smaller than 60 km. However, for crater diameters $D \lesssim 3-8$ km (which correspond to impactor diameters $d \sim 0.04 - 0.15$ km), the observed distributions become flatter and deviate from our results, which may evidence processes of erosion and/or crater saturation at small crater sizes or a possible break in the SFD of impactors at $d \sim 0.04 - 0.15$ km to a much shallower differential slope of $\sim -1.5$. Our results suggest that Pan, Daphnis, Atlas, Aegaeon, Methone, Anthe, Pallene, Calypso and Polydeuces suffered one or more catastrophic collisions over the age of the Solar System, the younger being associated to arcs with ages of $\sim10^8$ years. We have also calculated the satellites' surface ages, which indicate ongoing resurfacing processes.