AN ANALYTIC PARAMETERIZATION OF SELF-GRAVITY WAKES IN SATURN'S RINGS, WITH APPLICATION TO OCCULTATIONS AND PROPELLERS

摘要

We have developed a semianalytic method of parameterizing N-body simulations of self-gravity wakes in Saturn's rings, describing their photometric properties by means of only six numbers: three optical depths and three weighting factors. These numbers are obtained by fitting a sum of three Gaussians to the results of a density-estimation procedure that finds the frequencies of various values of local density within a simulated ring patch. Application of our parameterization to a suite of N-body simulations implies that rings dominated by self-gravity wakes appear to be mostly empty space, with more than half of their surface area taken up by local optical depths around 0.01. Such regions will be photometrically inactive for all viewing geometries. While this result might be affected by our use of identically sized particles, we believe the general result that the distribution of local optical depths is trimodal, rather than bimodal as previous authors have assumed, is robust. The implications of this result for the analysis of occultation data are more conceptual than practical, as we find that occultations can only distinguish between bimodal and trimodal models at very low opening angles. Thus, the only adjustment needed in existing analyses of occultation data is that the model parameter τgap should be interpreted as representing the area-weighted average optical depth within the gaps (or inter-wake regions), keeping in mind the possibility that the optical depth within those inter-wake regions may vary significantly. The most significant consequence of our results applies to the question of why "propeller" structures observed in the mid-A ring are seen as relative-bright features, even though the most prominent features of simulated propellers are regions of relatively low density. Our parameterization of self-gravity wakes lends preliminary quantitative support to the hypothesis that propellers would be bright if they involve a local and temporary disruption of self-gravity wakes. Even though the overall local density is lower within the propeller-shaped structure surrounding an embedded central moonlet, disruption of the wakes would flood these same regions with more "photometrically active" material (i.e., material that can contribute to the rings' local optical depth), raising their apparent brightnesses in agreement with observations. We find for a wide range of input parameters that this mechanism indeed can plausibly make propellers brighter than the wake-dominated background, though it is also possible for propellers to blend in with the background or even to remain dark. We suggest that this mechanism be tested by future detailed numerical models.