The varying geometry of Cassini star occultations by Saturn's rings constrains both the size and shape of structures that block starlight. We extend the approach of Showalter and Nicholson (1990, who first used the observed variance of the stellar counts to calculate the size of the ring particles from the Voyager ring occultation) to higher moments and remove their restrictions on fractional particle area delta < < 1 and line-of-sight optical depth tau < < 1. We calculate the excess variance, skewness and kurtosis including the effects of irregular particle shadows, adopting a rectangular parallelepiped model of self-gravity wakes which can also be extended to model irregularly spaced gaps, ghosts, and clumps. Particles in Saturn's background C ring and the C ring ramp are matched by spheres with effective radius a(eff) = 2.5 m, with no evidence for gaps or ghosts in these 2 regions. The A ring statistics are dominated by self-gravity wakes. The skewness and kurtosis require transparent regions like those seen in high resolution Cassini occultations and indicated by numerical simulations. Transparent gaps between self-gravity wakes demonstrate dynamic processes which prevent the rings from achieving uniformity. The changing wake structures show density waves can trigger aggregation, consistent with a Predator-Prey model of ring dynamics (Esposito et al. 2012). Perturbed by passing density waves, self-gravity wakes grow and erode on orbital timescales with a full amplitude of 50 %, and a phase lag Delta phi similar to 60 degrees. We speculate that the collisions or azimuthal instabilities of these wakes may lead to the straw features seen in Cassini images. Ejecta from collisions and erosion may be forming the dusty haloes around the density waves. Similar resonant perturbations from a forming protoplanet could trigger growth at its resonant locations in a debris disk.

Cassini’s Ultraviolet Imaging Spectrograph (UVIS) observed 276 stellar occultations of Saturn’s rings over the course of its mission. During these occultations, UVIS’ High-Speed Photometer (HSP) collected photon count measurements through the rings at a typical radial resolution of 10 meters from a wide range of viewing angles. Because photon counts are Poisson distributed, the variance of the starlight is approximately equal to its mean in the absence of occulting ring material. When the star passes behind the rings from the point-of view of the spacecraft, the finite sizes of the ring particles result in an excess variance above the mean caused by correlation in the blocking of photons. Showalter and Nicholson (1990, Icarus, 87, 285) and Colwell et al. (2018, Icarus, 300, 150) interpreted this excess variance in terms of an effective particle or clump size, RE, which depends on the length scale of shadows cast by particles and clumps. In the A ring however, where ring particles aggregate into trailing spiral structures called self-gravity wakes (Colwell et al., 2006, Colwell et al., 2007, Hedman et al., 2007, Nicholson and Hedman (2010), the assumptions of Showalter and Nicholson (1990) and Colwell et al. (2018) of uncorrelated spherical particles are invalid.Here we expand their analyses to account for the presence of self-gravity wakes, ephemeral agglomerations of ring particles under the competing influence of their mutual self-gravity and Keplerian shear, by introducing free parameters S(wake separation), and W (wake width) into a direct calculation of higher order statistical moments of excess variance, skewness, and kurtosis from the expectation value of the random variate, ring transparency (T). We use the granola bar model of self-gravity wakes (Colwell et al. 2006) to calculate the autocovariance of the measured signal. In this work we compare the values of these higher order moments in the peaks and troughs of the Janus 2:1, Pandora 5:4, Janus 5:4, and Janus 6:5 density waves, which exist in regions in which self-gravity wakes are prominent. We compare the best-fit combinations of S and W to the excess variance for many combinations of S and W from different ring regions to reveal trends in the variation of wake properties by ring region. The sum S+W is constrained by the measured dispersion of the waves which gives the local surface mass density. We use this value to determine the Toomre most-unstable wavelength which we assume to be equal to the self-gravity wake wavelength (S+W) (Julian and Toomre, 1966). The second order moment, skewness (S), measures the asymmetry of the distribution and is indicative of either large clumps or small gaps in the rings nicknamed "ghosts" (Baillie et al., 2012). The presence of a few small gaps (high transparency outliers in the distribution) may lead to a positive skewness. The presence of too many gaps, however, increases the symmetry of the distribution as the gaps are no longer outliers. We take the ratio of S to τ to account for the correlation between the two variables (S is proportional to τ when τ ≳ 1). We occasionally observe that the ratio in the troughs differs by more than one standard deviation from the ratio in the peaks of the density waves. Our results indicate that either there are more gaps (positive outliers) present in the troughs than in the peaks or that there are so many gaps in the peaks that they no longer stand out as outliers of the distribution.We apply this analysis technique to a multitude of occultations across a variety of ring elevation (B) and azimuthal (f) angles to survey wake parameter variation across these regions. ReferencesBaillié, K., Colwell, J.E., Lissauer, J.J., Esposito, L.W., Sremčević, M., 2011. Waves in Cassini UVIS stellar occultations 2: The C ring. Icarus 216, 292-308.Colwell, J.E., et al., 2006. Gravitational wakes in Saturn’s A ring measured by stellar occultations from Cassini. Geophys. Res. Lett. 33.Colwell, J.E., Esposito, L.W., Sremčević, M., Stewart, G.R., McClintock, W.E., 2007. Self-gravity wakes and radial structure of Saturn’s B ring. Icarus 190, 127-144. Colwell, J. E., Esposito, L. W., Cooney, J. Particle sizes in Saturn’s rings from UVIS stellar occultations 1. Variations with ring region. Icarus 300, 150. Hedman, M. M., et al., 2007. Self-gravity wake structures in Saturn’s A ring revealed by Cassini-VIMS. The Astronomical Journal 133(6), 2624-2629.Jerousek, R. G., Colwell, J. E., Nicholson, P. D., Hedman, M. M., Esposito, L. W., 2016. Small Particles and Self-Gravity Wakes in Saturn’s Rings from UVIS and VIMS Stellar Occultations. Icarus 279, 36-50.Julian, W.H. and Toomre, A. (1966). Non-axisymmetric responses of differentially rotating disks of stars. Astrophys. J., 146. 810-830.Nicholson, P. D., and Hedman, M. M., 2010. Self-Gravity Wake Parameters in Saturn’s A and B Rings. Icarus 206, 410-423.Showalter, M. R., and Nicholson, P. D., 1990. Saturn's rings through a microscope: Particle size constraints from the Voyager PPS scan. Icarus 87, 285-306.Spilker, L. J., et al., 2004. Saturn A ring surface mass densities from spiral density wave dispersion behavior. Icarus 171, 372–390.

The varying geometry of Cassini star occultations by Saturn’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 of gaps, ghosts and clumps. The widths W and separation S of rectangular clumps play an analogous role to the relative size of the particle shadows, δ. In the first model considered, our calculations are based on the moments of the transparency T in that part of the ring A sampled by the occultation, thus extending the work of Showalter and Nicholson (1990) to larger τ and δ, and to higher central moments, without their simplifying assumptions. We also calculate these statistics using an approach based on the autocovariance, autocoskewness and autocokurtosis. These new approaches compare well to the formula for excess variance from Showalter and Nicholson in the region where all are accurate, δτ≪1. Skewness for small τ has a different sign for transparent and opaque structures, distinguishing gaps from clumps. The higher order central moments are more sensitive to the extremes of the size distribution and opacity. We explain the upward curvature of the dependence of normalized excess variance for Saturn’s background C ring by the observation of Jerousek etal (2018) that the measured optical depth is correlated with particle size. For a linear dependence Reff = 12 * (τ – 0.08) + 1.8m from Jerousek’s results, we match the curvature of normalized excess variance, the skewness and the kurtosis in the region between 78,000 and 84,600km from Saturn. Statistics calculated from the granola bar model give different predictions from individual particles. The different τ dependence suggests that the wave crests compress the gaps more than the wakes, and produce more regularity among the clumps; and larger and more opaque self-gravity wakes in the wave crests, with transparent ghosts. The UVIS observations fall between the most regular and the most irregular granola bar models. We compare selected occultations (Eckert etal 2020) at different values of the elevation B to estimate the flattening and axial ratio of ring particles and clumps. In Ring C, we find spheres: The statistical measures from multiple occultations follow the expected dependence on sin B, e.g. Showalter & Nicholson (1990). However, in the Janus 2:1 and Mimas 5:3 density waves, the excess variance for stars β Cen, λ Sco and σ Sgr shows no B dependence. This is exactly the expectation for completely flat (H/W =0) self-gravity wakes that we have derived from the autocovariance of the wake shadows. A closer analysis of this particular case gives H/W < 0.04, different from Colwell etal (2007), suggesting wakes are more like linguine than granola bars.

The high-speed photometer of Cassini’s Ultraviolet Imaging Spectrograph (UVIS) collected data from stellar occultations across Saturn’s rings at unprecedented high resolution over a wide range of viewing geometries. Because photon counts are described by Poisson statistics, we expect a variance equal to the mean in the absence of intervening ring material. However, most ring ‘particles’ are truly aggregates of smaller particles, ranging from micron-size dust to tens of meter-sized boulders, and if the sizes of these aggregates are not small relative to the field-of-view over a single integration period, they introduce excess variance from which we can glean further information about the sizes of particles and clumps. This is particularly relevant in the A ring, where non-axisymmetric self-gravity wakes are ubiquitous. Larger elongated clumps nicknamed straw have been directly imaged in the troughs of strong density waves (Porco et al., 2005, Science, 307, 1226-1236). In this work we present a survey of the statistical moments of variance and skewness for several ring stellar occultations at two strong density waves from different ring regions, Janus 2:1 and Mimas 5:3, over a variety of viewing angles. The line-of-sight distance from Cassini to the rings affects the measurement area due to the scattered signal and diffraction, and different viewing angles provide measurements of the same ring material with different aspects to potentially reveal the three-dimensional structure of clumps. We calculate an effective particle size per integration area, R, derived by Colwell et al., (2018, Icarus, 300, 150-166) and find similar values for R in both peaks and troughs across density waves as well as within density waves and in adjacent regions. We observe strong statistical similarity between troughs and regions adjoining the waves with overall higher skewness in the A ring, indicating more clumping and greater asymmetry in this region than in the inner B ring region.

&lt;p&gt;The Cassini cameras detected elongated structures in Saturn&amp;#8217;s ring in highly perturbed regions near ring edges and within the strongest density waves. These &amp;#8216;straw&amp;#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&amp;#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 (&lt;strong&gt;GBM&lt;/strong&gt;) 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&amp;#8217;s rings. Skewness for small &lt;strong&gt;&amp;#964; &lt;/strong&gt;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.&lt;/p&gt; &lt;p&gt;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 &amp;#948; &lt;&lt;1 and line-of-sight optical depth &amp;#964; &lt;&lt;1. We include Poisson contributions, but ignore Sheppard&amp;#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 &lt;strong&gt;W&lt;/strong&gt; = 18-29m; typical wavelength &lt;strong&gt;S&lt;/strong&gt;+&lt;strong&gt;W&lt;/strong&gt; ~ 60m; &lt;strong&gt;H&lt;/strong&gt;/&lt;strong&gt;W&lt;/strong&gt; &lt; 0.12, thus vertical height &lt;strong&gt;H &lt;/strong&gt;&lt; 4m. These results are consistent with a simple dynamical model of the rings, analogous to an ecological &lt;strong&gt;&lt;em&gt;Predator-Prey&lt;/em&gt;&lt;/strong&gt; interaction. Compression drives aggregation, which lags the forcing. Perturbed by passing density waves, &lt;strong&gt;self-gravity wakes &lt;/strong&gt;grow and erode on orbital timescales with a full amplitude of &lt;strong&gt;60%, &lt;/strong&gt;and a phase lag

The Saturnian moon Enceladus presents a unique opportunity to sample the contents of a subsurface liquid water ocean in situ via the continuous plume formed over its south polar terrain using a multi-flyby mission architecture. Previous analyses of the plume's composition by Cassini revealed an energy-rich system laden with salts and organic compounds, representing an environment containing most of the ingredients for life as we know it. Following in the footsteps of the Cassini-Huygens mission, we present Astrobiology eXploration at Enceladus (AXE), a New Frontiers class Enceladus mission concept study carried out during the 2021 NASA Planetary Science Summer School program at the Jet Propulsion Laboratory, California Institute of Technology. We demonstrate that a scientifically compelling geophysical and life-detection mission to Enceladus can be carried out within the constraints of a New Frontiers-5 cost cap using a modest instrument suite, requiring only a narrow angle, high-resolution telescopic imager, a mass spectrometer, and a high-gain antenna for radio communications and gravity science measurements. Using a multi-flyby mission architecture, AXE would evaluate the habitability and potential for life at Enceladus through a synergistic combination of in situ chemical analysis measurements aimed at directly detecting the presence of molecular biosignatures, along with geophysical and geomorphological investigations to contextualize chemical biosignatures and further evaluate the habitability of Enceladus over geologic time.

The varying geometry of Cassini star occultations by Saturn’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 of gaps, ghosts (local openings) and self-gravity wakes. In this model, the widths W and separation S of rectangular clumps play an analogous role to the size of the particle shadows, R. In the first model considered, our calculations are based on the moments of the transparency T in the ring region sampled by the occultation, thus extending the work of Showalter and Nicholson (1990) to larger τ and fractional area δ, and to higher central moments, without their simplifying assumptions. We also calculate these statistics using an approach based on the autocovariance, autocoskewness and autocokurtosis. These new approaches compare well to the formula for excess variance from Showalter and Nicholson in the region where all are accurate, δτ≪1. Skewness for small τ has a different sign for transparent and opaque structures, distinguishing gaps from clumps. The higher order central moments are calculated from higher powers of the shadow size, thus more sensitive to the extremes of the size distribution. We explain the τ dependence of the excess variance for Saturn’s background C ring by the observation of Jerousek etal(2018) that the measured optical depth is correlated with particle size in the region between 78,000 and 84,600km from Saturn. Statistics calculated from the granola bar model give different predictions from those based on individual spherical particles. The density waves clearly show compression that triggers clump growth, as predicted by the Predator-Prey model (Esposito etal. 2012, Icarus 217, 103-114). The radial profiles and observed τ dependence suggest that the wave crests compress the gaps more than the wakes, along with broader self-gravity wakes in the wave crests, including transparent ghosts. The UVIS observations fall between the most regular and the most irregular granola bar models. Analysis of ring transparency favors irregularly-spaced elongated clumps. A closer analysis of this particular case gives H/W < 0.12, smaller than Colwell etal. (2007, Icarus 190, 127-144), suggesting wakes are more like linguine than granola bars.

EXPLORATION AT ENCELADUS (AXE). K. Marshall Seaton, Ethan R. Burnett, C. Adeene Denton, Bryce Doerr Kamak Ebadi, Stephanie Eckert, Ian. T. W. Flynn, Szilárd Gyalay, Casey I. Honniball, Shayna Hume, Corbin L. Kling, Julian C. Marohnic, Julia Milton, Claire A. Mondro, Raquel G. Nuno, Caoimhe M. Rooney, Beck E. Strauss, Gaia Stucky de Quay Alfred Nash, Jennifer Scully. Georgia Institute of Technology, Atlanta, GA 30332, United States (kseaton6@gatech.edu). University of Colorado, Boulder. Purdue University. Massachusetts Institute of Technology. Jet Propulsion Laboratory, California Institute of Technology. University of Central Florida. University of Pittsburgh. University of California, Santa Cruz. NASA Goddard Space Flight Center. National Air and Space Museum, Smithsonian Institution. University of Maryland, College Park. University of Tennessee, Knoxville. University of California, Los Angeles. NASA Ames Research Center. National Institute of Standards and Technology. Harvard University.

The Ultraviolet Imaging Spectrograph (UVIS) on the Cassini spacecraft observed 275 ring stellar occultations from July 2004 until August 2017. We use stellar occultation data from the UVIS High Speed Photometer (HSP) to characterize the smallest particles at ring edges by modeling observed diffraction signatures. We identify these signatures as spikes in the signal caused by particles near the ring edge diffracting light into the detector and increasing the signal above that of the star alone. The shape and amplitude of the diffraction signature depend on the size and abundance of the smallest particles and are therefore indicative of the lower limits of the particle size distribution at the edge. We analyze the outer edge of the A ring and B ring and the edges of the Encke Gap, Keeler Gap, the so-called "Strange" ringlet (R6), Huygens ringlet and Titan ringlet. Other edges do not have sufficient contrast and sharp enough edges for this analysis at UVIS wavelengths. We find minimum particle sizes ranging from 4.5 mm to 66 mm and average power law indices ranging from 3.0-3.2. Overall, we find that the edges of the narrow ringlets in the Cassini Division and C ring exhibit fewer diffraction signatures than the outer A ring region. Our results, in conjunction with previous results by Becker et al. (2016), indicate that edges directly perturbed by satellite resonances show a greater population of sub-cm particles than the sharp edges of ringlets that are confined by other mechanisms. Our results are similarly consistent with Esposito et al. (2012), who propose that regions perturbed by satellite resonances can be explained by a predator-prey model of aggregation and fragmentation. Large aggregates may form at these strong resonant locations that may in turn accelerate the ring particles and lead to more disruptive collisions producing a population of smaller particles that result in the diffraction signatures analyzed here. This is in agreement with Bodmva et al. (2012) who find that the mean ring particle radius decreases as relative collision velocity increases.

We now know that the outer solar system is host to at least six diverse planetary ring systems, each of which is a scientifically compelling target with the potential to inform us about the evolution, history and even the internal structure of the body it adorns. These diverse ring systems represent a set of distinct local laboratories for understanding the physics and dynamics of planetary disks, with applications reaching beyond our Solar System. We highlight the current status of planetary rings science and the open questions before the community to promote continued Earth-based and spacecraft-based investigations into planetary rings. As future spacecraft missions are launched and more powerful telescopes come online in the decades to come, we urge NASA for continued support of investigations that advance our understanding of planetary rings, through research and analysis of data from existing facilities, more laboratory work and specific attention to strong rings science goals during future mission selections.

We give calculations for the excess variance, excess skewness and excess kurtosis with formulas that combine the effects of cylindrical shadows, along with gaps, ghosts and clumps (all calculated for the granola bar model for rectangular clumps and gaps). Wherever the rings have significant gaps or clumps, those will dominate the statistics over the individual ring particles contribution. We have refined an overlap correction for multiple shadows, which is important for larger optical depth. This correction results from summing a geometric series, and is similar to the empirical formula, eq. (22) in Colwell et al (2018). The comparison to Monte Carlo calculations is improved for large particle size by including the edge effects when large particles cross the edges of the viewing area A in Cassini UVIS occultations. As a check, we can explain the upward curvature of the dependence of normalized excess variance for Saturn’s background C ring by the observation of Jerousek etal (2018) that the increased optical depth is directly correlated with effective particle size. Assuming a linear dependence Reff = 12 * (tau – 0.08) + 1.8m, we match both the curvature of excess variance E and the skewness Gamma in the region between 78,000 and 84,600km from Saturn. This explanation requires no gaps or ghosts (Baillie etal 2013) in this region of Saturn’s C ring.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Frontiers in Planetary Rings Science A Science White Paper for the Planetary Science and Astrobiology Decadal Survey 2023-2032 Shawn Brooks, Tracy Becker, Kevin Baillie, Heidi Becker, E Bradley, Joshua Colwell, Jeffrey Cuzzi, Imke De Pater, Stephanie Eckert, Maryame Elmoutamid, et al.