How Predator-Prey Dynamics Creates ‘Straw’ in the Strongest Density Waves

<p>The Cassini cameras detected elongated structures in Saturn&#8217;s ring in highly perturbed regions near ring edges and within the strongest density waves. These &#8216;straw&#8217; features are likely triggered by the periodic forcing arising from the nearby moons. We investigate the temporal response to this forcing by interpretation of the ring occultation counting statistics. The varying geometry of Cassini star occultations by Saturn&#8217;s rings constrains both the size and shape of structures that block starlight. Statistics of UVIS star occultations measure structures as small as meters, on times scales of minutes to decades. We calculate the excess variance, skewness and kurtosis including the effects of irregular particle shadows, along with a granola bar model (<strong>GBM</strong>) for gaps, ghosts and clumps. We then use the statistics of ring occultations observed by the Cassini UVIS High Speed Photometer to characterize structures in Saturn&#8217;s rings. Skewness for small <strong>&#964; </strong>has a different sign for transparent and opaque structures, and can distinguish gaps from clumps. The higher order central moments are more sensitive to the extremes of the size distribution and opacity.</p> <p>To calculate the expected variance, skewness and kurtosis, we use the moments approach of Showalter and Nicholson (1990), extended to higher moments and removing their restrictions on fractional particle area &#948; <<1 and line-of-sight optical depth &#964; <<1. We include Poisson contributions, but ignore Sheppard&#8217;s corrections for data compression; and use the exact formulas, not Taylor expansions. The measured Cassini occultation statistics show the expected extrema and zero crossings. The observed excess variance shows aggregate growth following the passage of a density wave crest. For self-gravity wakes in the A ring, we find wake width <strong>W</strong> = 18-29m; typical wavelength <strong>S</strong>+<strong>W</strong> ~ 60m; <strong>H</strong>/<strong>W</strong> < 0.12, thus vertical height <strong>H </strong>< 4m. These results are consistent with a simple dynamical model of the rings, analogous to an ecological <strong><em>Predator-Prey</em></strong> interaction. Compression drives aggregation, which lags the forcing. Perturbed by passing density waves, <strong>self-gravity wakes </strong>grow and erode on orbital timescales with a full amplitude of <strong>60%, </strong>and a phase lag