Identifying and Characterizing Local Gaps in Saturn’s Rings from Skewness of Cassini UVIS Stellar Occultation Data

The Ultraviolet Imaging Spectrograph (UVIS) high-speed photometer (HSP) aboard the Cassini spacecraft collected stellar occultation data for stars of various brightness and viewing geometries as they were occulted by Saturn’s rings. We calculate the variance and skewness of the occultation light curves, and we analyze these statistical moments as functions of both optical depth and ring plane radius. Typical radial resolution of the occultations is 10-20 meters allowing for statistical moments to be calculated from 1000 points at 10 km radial sampling in the rings. We derived an analytic expression for skewness (S) as a function of optical depth assuming a ring composed of identical spherical particles, analogous to the normalized excess variance (E) relationship to optical depth used by Showalter and Nicholson (1990) and Colwell et al. (2018) to determine an effective particle size across the rings. We compared the results for effective particle size derived from S and E. Some regions, such as the inner B ring, return similar R-effective values, while others, such as the C ring plateaus, show distinctly different values. Skewness is a measure of the asymmetry of the distribution of photon counts in a measurement sample, while the variance is related to the spread of the distribution. Thus, agreement in the derived values of R-effective from S and E indicates an absence of clumps or local holes (nicknamed “ghosts”) in the rings that would lead to unusually small or large values of S, respectively. Regions of the rings where the values of R-effective from skewness (R_S) disagree with those derived from E (R_E) thus indicate the presence of ghosts or clumps that skew the distribution of photon counts in those regions. We use Monte-Carlo simulations of a simplified ring system composed of identical spherical particles interspersed with clumps and ghosts to determine the effects of these phenomena on S and compare to data. We also use simulated occultations through N-body simulations of the rings to calculate E and S where ghosts due to small moonlets or boulders are prevalent. We find variations in the suggested number of ghosts, presumed to be openings due to the same phenomena that create propeller structures in the A ring, across the rings, including in regions where there are no obvious optical depth signatures.