Devil in the details: statistics of chord occultations of Saturn's rings

Over the 13-years Cassini was in orbit around Saturn the Ultraviolet Imaging Spectrograph (UVIS) highspeed photometer (HSP) occultations of UV bright stars as they passed behind the rings with sampling cadences of 1, 2, or 8 ms. In 80 of these occultations, the occultation point traced a chord across the rings so that the occultation point moved parallel to the ring particles in the neighborhood of the minimum ring plane radius, rmin, of the occultation. Some of these occultations provided spatial sampling at or below the Fresnel scale (~10 m) in the frame of the ring particles. Near the rmin, many of these occultations provide long broadly featureless tracks since there is no radial motion of the occultation point, while others resolve azimuthally limited ring structure. We compute the first four statistical moments of photons counted by the UVIS HSP around rmin for each of these chord occultations. The variance of this distribution beyond that expected by Poisson counting statistics constrains the cross-section weighted average shadow size of the ring particles and hence the radius of their (circular) shadows, aeff. However, the variance may be dominated by larger structures such as self-gravity wakes and/or azimuthally limited underdense regions which have signatures in the next higher moments, skewness and kurtosis. We report the effective particle radii, aeff at the locations of each chord's minimum and discuss the implications of the statistics on the dominant azimuthal ring structure at each location. Values of aeff are generally consistent with Colwell et al. 2018 but pinpoint only specific ring radii, albeit with more precision.