The Crater Production Functions for Mimas

Introduction: The highly successful Voyager [1,2] and Cassini [3] imaging experiments revealed high quality imaging data that allows for a reasonably good analysis of the crater distributions on the Saturnian satellites [4,5,6]. The observed crater distributions appear to conflict with theoretical crater distributions that are derived from observed projectile populations [6,7]. In order to compare relative crater frequencies across different diameter ranges of measured craters a model of the crater production function is required. This function is fitted to the measured crater distribution and crater frequencies at a specific reference diameter can be determined from the function. Crater frequencies from measurements on high-and low-resolution imaging data or large and small areas can be compared relative to each other at the reference diameter. This technique is also used for the determination of absolute surface ages were the absolute age is derived from a chronology function, which is valid only at one specific crater diameter. If the used crater production function does not reflect the observed crater size-frequency distribution over large diameter ranges reasonably well, relative stratigraphy as well as absolute dating of the investigated surfaces becomes nearly impossible. In this presentation we compare crater production functions for Mimas that are derived from the observed size-distribution of comets [7] and from the lunar crater size-distribution [8] with the observed crater distribution on Mimas. Scaling the lunar crater production function to Mimas: For the scaling of the production function we rely on the Ivanov scaling laws [9], which require knowledge about several parameters. They are mostly well known or can be deduced from known parameters or observations. In the case of the Saturnian satellites the projectile densities and impact velocities are not well known, because the source of the impacting projectiles is still in discussion. Because of missing apex-/antapex asymmetries and the missing focusing effect of Saturn [6], we assume a planetocentric projectile source with impact velocities on the order of 600 m/s. Furthermore, scaling the lunar crater production function [8] to Mimas requires the transition from a basaltic to an icy target. The affected scaling parameters are the simple to complex transition and the strength to gravity transition. On Mimas the ~135 km Herschel crater is clearly of complex character. If the classic 1/g approach [10] is applied using the lunar value of 15 km [8], the smallest simple crater on Mimas is expected to