In September 2017, the Cassini spacecraft will point itself toward the surface of Saturn and end its 13-year mission of solving many of the mysteries of the ringed planet's system with a crash. This book is a dramatic, beautifully illustrated journey of discovery through the Saturn system. Cassini's instruments have revealed never seen before details including the only extraterrestrial lakes known in the solar system and have provided unprecedented views of the rings. It is a non-technical book for everyone who loves astronomy.

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.

A pattern of similar to 1 km wavelength ripples exhibiting a periodic beating pattern in Saturn's inner C ring (74,500- 77,765 km) was detected in low-inclination Cassini Radio Science Subsystem (RSS) occultation observations made in 2010 (Marouf et al., 2011). Initially interpreted as analogous to the similar to 30 km wavelength vertical corrugations with m = 1 discovered in the C and D rings in near-equinox Cassini Imaging Science Subsystem (ISS) images by Hedman et al. (2007, 2011), the shorter wavelength of these features suggested that they had evolved from a pair of impacts several centuries ago. However, important inconsistencies with this model prevented a secure identification of their origin. A comprehensive search has revealed additional detections of this pattern in Cassini RSS, Visual and Infrared Mapping Spectrometer (VIMS) and Ultraviolet Imaging Spectrograph (UVIS) occultations observed between 2008 and 2017 that show a significant decrease in the wavelength of the ripples over time, suggesting a much more recent origin than centuries ago. We identify the conspicuous beat pattern visible in the ripple structure as the interference of m = 0 and m = 2 vertical modes of similar amplitudes but slightly different frequencies, evolving over time and winding up at a rate governed by the mean motion of ring particles, rather than by the much slower node rate that is applicable to the m = 1 corrugations. From empirical fits to the observed time-dependent wavelengths of the two modes and power spectral analysis of individual optical depth profiles, we demonstrate that the short-wavelength vertical corrugations originated from the same event that produced the longer-wavelength m = 1 periodic structure in the rings. We infer an impact date of UTC 1983 Sep 19.25 +/- 5.5 d, taking into account a plausibly small contribution of ring self-gravity to the windup rates of the corrugations. No convincing signatures of counterpart m = 0 or m = 2 radial modes, or of vertical modes with m >= 3, are present in the occultation data, and no evidence of ripple structure is detectable beyond an orbital radius of 77,765 km. The measured amplitudes A0z and A2z of the newly-identified modes are anti-correlated with the ring optical depth. We detect a significant decrease in the amplitudes of both modes between 2008 and 2017. N-body numerical collisional simulations provide constraints on the vertical and radial ring viscosity that are compatible with the observed radial trend of mode amplitudes A0z and A2z and their variation with time. Assuming an effective particle size R =1 m, the inferred coefficient of restitution e similar to 0.5, with corresponding vertical and radial viscosities yz = 1.6 cm2 s-1and yr = 2.2 cm2 s-1at a radius of 75,500 km. The initial amplitudes of the m = 0 and m = 2 vertical modes are estimated to be similar to 4 to 7 times their observed values in 2017 in this region.

In September 2017, the Cassini spacecraft will point itself toward the surface of Saturn and end its 13-year mission of solving many of the mysteries of the ringed planet's system with a crash. This book is a dramatic, beautifully illustrated journey of discovery through the Saturn system. Cassini's instruments have revealed never seen before details including the only extraterrestrial lakes known in the solar system and have provided unprecedented views of the rings. It is a non-technical book for everyone who loves astronomy.

In September 2017, the Cassini spacecraft will point itself toward the surface of Saturn and end its 13-year mission of solving many of the mysteries of the ringed planet's system with a crash. This book is a dramatic, beautifully illustrated journey of discovery through the Saturn system. Cassini's instruments have revealed never seen before details including the only extraterrestrial lakes known in the solar system and have provided unprecedented views of the rings. It is a non-technical book for everyone who loves astronomy.

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 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.

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.

The satellite Mimas launches a bending wave -- a warping of the rings that propagates radially through self-gravity -- at the 5:3 inner vertical resonance with Saturn's rings. We present a modification of the linear bending wave theory which includes the effects of satellite self-gravity wakes on the particles in the wave. We show that, when treated as rigid, these wakes generate an extra layer of particles whose number density is proportional to the magnitude of the slope of the warped ring. Using a ray-tracing code we compare our predictions with those of linear bending wave theory and with 60 stellar occultations observed by the Cassini Ultraviolet Imaging Spectrograph (UVIS) and find that the extra layer of particles of our perturbed bending wave model has a considerable explanatory power for the UVIS dataset. Our best model explains the most discrepant and surprising features of the Mimas 5:3 bending wave; the enhancement of the signal for the cases of occultations with high ring opening angle and the bigger-than-expected viscosity, $\nu = 576 \, \mathrm{cm^2/s}$, which is more than double the viscosity computed from density waves. This shows that self-gravity wakes can be effective at transporting angular momentum in a vertically perturbed disk. Relative to neighboring density waves, we find a lower-than-expected value for the surface mass density, $\sigma = 36.7 \, \mathrm{g/cm^2}$, which suggests that the enhanced viscous interactions may be transporting material into the surrounding regions.

On the largest scales Saturn’s rings are often thought of as axisymmetric annuli varying only radially in optical depth with exceptions of spiral waves and eccentric ringlets. But on scales smaller than a few tens of km yet still larger than the largest common ring particles, the assumption of azimuthal symmetry breaks down. Structures such as “straw” in the troughs of density waves, partial gaps around propeller moonlets, and ephemeral particle aggregates such as self-gravity wakes are responsible for the predominant variations in optical depth. During the 13 year Cassini mission, the Ultraviolet Imaging Spectrograph (UVIS) high speed photometer (HSP) measured 80 stellar chord occultations of Saturn’s main rings. In the vicinity of the minimum ring plane radius of each chord, the occultation line-of-sight slewed across the ring plane tangent to the Keplerian motion of the ring particles. These occultations measured ultraviolet light in the wavelength range 110–190 nm with 1- or 2-ms ms integration times, providing optical depth measurements with resolution comparable to the Fresnel scale of ∼10 m in the frame co-moving with the local Keplerian speed. These high-resolution chord occultations reach their minimum ring radii over a broad range of radial locations within Saturn’s main rings and resolve non-axisymmetric structures in a wide variety of ring regions. We measure the azimuthal length scales and optical depth profiles of “ghosts”, or azimuthally limited gaps with radial scales less than 30 m (Baillié et al., 2013), in the C ring plateaus. We measure the length scale of transparent gaps and self-gravity wakes in the peaks and troughs of spiral density waves. We present optical depth profiles which resolve axisymmetric waves in the A and B rings and constrain the azimuthal length scale over which the waves remain axisymmetric to ∼ 1000 km. We combine autocorrelation length scales from stellar occultations which cut across the minimum ring radius of a chord occultation with line-of-sight trajectories from other occultations which are not tangent to the rings to constrain the morphology of the azimuthally and temporally averaged mesoscale structures at that ring radius. 2D autocorrelation profiles from stellar occultations show self-gravity wakes and axisymmetric waves often coexisting.

AbstractThe global energy budget is pivotal to understanding planetary evolution and climate behaviors. Assessing the energy budget of giant planets, particularly those with large seasonal cycles, however, remains a challenge without long-term observations. Evolution models of Saturn cannot explain its estimated Bond albedo and internal heat flux, mainly because previous estimates were based on limited observations. Here, we analyze the long-term observations recorded by the Cassini spacecraft and find notably higher Bond albedo (0.41 ± 0.02) and internal heat flux (2.84 ± 0.20 Wm−2) values than previous estimates. Furthermore, Saturn’s global energy budget is not in a steady state and exhibits significant dynamical imbalances. The global radiant energy deficit at the top of the atmosphere, indicative of the planetary cooling of Saturn, reveals remarkable seasonal fluctuations with a magnitude of 16.0 ± 4.2%. Further analysis of the energy budget of the upper atmosphere including the internal heat suggests seasonal energy imbalances at both global and hemispheric scales, contributing to the development of giant convective storms on Saturn. Similar seasonal variabilities of planetary cooling and energy imbalance exist in other giant planets within and beyond the Solar System, a prospect currently overlooked in existing evolutional and atmospheric models.

The Cassini Ultraviolet Imaging Spectrograph (UVIS) included a High-Speed Photometer (HSP), which observed hundreds of stellar occultations by Saturn’s ring system across a range of viewing geometries (Colwell et al. 2010). The unocculted time series data from the HSP follow Poisson counting statistics, such that the second and third central moments of the unocculted data should be equal to the mean photon rate of the star. When the star is occulted by the rings, the presence of ring particles introduces a correlation in the previously uncorrelated photons. This causes each of the central moments to deviate from their expected value. In particular, the second central moment, μ2, commonly known as the variance, becomes greater than the mean (Colwell et al. 2018). The third central moment, μ3, also deviates from this expectation upon occultation, but the nature of the deviation varies with optical depth. In particular, μ3 is less than its Poisson expectation for τ<0.33 and greater than this expectation for τ>0.33. The introduction of outlier features, namely small gaps (‘ghosts’, Baillié et al. (2013)) and clumps produce variable effects on the behavior of both μ2 and μ3, which is also dependent on optical depth.We compare the higher-order moments from Monte Carlo Simulations of a simplified ring system to those from the UVIS data to gain insight into the nature of such outliers in the C ring and Cassini Division. The behavior of the data in the C ring plateaus indicates that a small population of ∼ 10-m ghosts exists in this region, with a frequency of about 1 ghost per km of radial extent. In the background C ring, we find that particle sizes are positively correlated with optical depth and the data cannot be explained with a simple power-law size distribution. Instead, we are able to describe the behavior of the higher-order moments using a bent-power law size distribution of particles. We find similar behavior in the C Ring Ramp and Cassini Division Ramp. However, we cannot rule out nor confirm the presence of either ghosts or clumps in the background Cassini Division. In the Triple Band, the local ∼ 10-m ghost frequency oscillates between about 1 and 4 ghosts per km.

The Cassini Ultraviolet Imaging Spectrograph (UVIS) High Speed Photometer (HSP) observed 15 occultation traces of the bright star Hadar (Beta Centauri) in 2008-2009 at an elevation above the ring plane of 66.7 degrees. The combination of the high signal from this star (up to 600 counts per msec integration period) and its high elevation above the rings means these occultations provide the strongest constraints on the transparency of high optical depth regions as observed by UVIS. We use the excess variance that is introduced into the UVIS stellar occultation counting rates by the presence of ring particles to determine when the observed signal is purely background with no transmitted starlight. When the observed variance is equal to the mean, we identify the region as opaque. We have identified several regions that are opaque in the UVIS occultations in the B2 and B3 regions (Marouf et al. 2006). When comparing these regions between occultations of the same star, we discovered non-repeating, narrow regions where the transparency jumps from less than 1% up to as much as 20%. These regions are typically less than 100 m in radial extent and frequently less than 50 m. These regions do not repeat at the same location between occultations. In addition, we are able to take advantage of the fact that Hadar is a binary star and both components produce measurable signals in the HSP data. These partially transparent features produce two distinct signals in the occultation data if the azimuthal extent of the feature is at least as large as the projected separation of the two stars onto Saturn’s rings. In many cases we find that there is only one feature observed, indicating that the features are not only narrow in the radial direction but also of limited (< 100 m) extent in the azimuthal direction. We refer to these features as “phantoms” due to their similarity to the completely transparent regions identified in the C ring plateaus dubbed “ghosts” (Baillie et al. 2013). Figure 1 shows an example of an opaque region in the B2 region of the B ring in all 15 occultations of Hadar. In all but two of the 15 profiles there is a narrow spike with a transparency of 5% up to nearly 20% in the region between 100,090 km and 100,130 km. If a transparent region is observed in all occultations at the same location, we identify that as a boundary between two opaque regions rather than as a phantom. The region between ~100,140 – 100,160 km in Figure 1 has complicated structure that is not exactly repeated between the occultations but marks the boundary between two opaque regions. The phantoms, observed between 100,090 km and 100,130 km, do not repeat and are generally very narrow. The first 15 km of the next opaque region, seen from 100,165-100,180 km in Figure 1 are virtually free of phantom features. The projected separation of the two components of Hadar is less than 50 m in the azimuthal direction, and frequently phantoms are only seen to pass behind one of the two stars. The actual transparency of narrow phantoms is thus approximately twice as high as that shown in Figure 1, because the transparency is based on the combined brightness of the two components. Baillie et al. (2013) suggested that ghosts are the nearly empty openings in the background ring carved out by small moonlets akin to the propeller features imaged in the A ring. The situation may be similar for the phantoms, but the dynamics of neighboring ring particles resulting from embedded moonlets in the dense B ring may not produce the same orbital perturbations that give rise to propeller features. We will describe the distribution and characteristics of opaque regions and phantoms in the B2 and B3 regions.Figure 1: Transparency of 100 km of the B2 region of Saturn’s B ring showing an opaque region extending from approximately 100084 km to 100140 km, and part of another beginning at about 100162 km. Each curve is offset by 5% for clarity.Bibliography:Baillié, K., J. E. Colwell, L. W. Esposito, and M. C. Lewis 2013. Meter-sized Moonlet Population in Saturn’s C Ring and Cassini Division. Astron J.145, 171, doi:10.1088/0004-6256/145/6/171. Marouf, E. A., French, R. G., Rappaport, N. J., McGhee, C. A., Wong, K., Thomson, F. S., Anabtawi, A. 2006. Structure and properties of Saturn’s Ring B from Cassini radio occultations. Bull. Am. Astron. Soc. 38, 552.

&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

We determine the time-variable shape of the outer edge of Saturn’s B ring using the complete set of Cassini radio and stellar occultation data obtained between mid-2005 and the End-of-Mission in late 2017, considerably expanding the range and number of individual ring edge measurements used in previous analyses (Spitale and Porco, 2010; Nicholson et al., 2014a). During this 12-year interval, the dominant m=2 pattern driven by the Mimas 2:1 inner Lindblad resonance completed just over two rotations relative to Mimas, with a circulation period of 5.362 yr, while its radial amplitude varied from a minimum of 4 km to a maximum of 71 km. This circulation pattern has remained essentially unchanged over the full period of the observations. We confirm the existence of four additional perturbations with azimuthal wavenumbers m=1, 3, 4 and 5 and mean amplitudes ranging from 5 to 24 km, which we interpret as normal or edge modes, possibly triggered by viscous overstabilities in the dense B ring (Borderies et al., 1985; Longaretti, 2018). Fits of a simple WKB model to the observed pattern speeds of the edge modes with m≠1 suggest an average surface mass density in the outer 30 km of the B ring of ∼100 g cm−2, somewhat greater than the 50–70 g cm−2 inferred from density and bending waves in most other regions of this ring (Hedman and Nicholson, 2016). The m=1 mode, which extends further into the B ring, yields a more typical value of 60 g cm−2. Surprisingly, all four of these modes exhibit significant librations in their amplitudes and phases, with periods between 2.3 and 8.6 yr and amplitudes of 1.6 to 7.4 km. The origin of these librations is unknown and it is unclear if they are truly periodic and will maintain their amplitudes, periods, and phases over timescales of centuries. Their frequencies do not match those expected for interference between edge modes with varying numbers of radial nodes. Instead, they may represent periodic oscillations in the amplitudes of individual normal modes or nonlinear, non-resonant coupling between normal modes with different values of m, leading to long-term quasi-periodic variations in the mode amplitudes.

Using the complete set of stellar and radio occultation data from the Cassini mission, we fit a multimode model to the outer edge of Saturn's A ring, similar to that previously applied to the B ring edge by Spitale and Porco (2010) and Nicholson et al. (2014a). Our model takes into account the coorbital libration of the satellite Janus, whose 7:6 Lindblad resonance is believed to be responsible for maintaining the edge at its observed location. Consistent with previous analyses (Spitale and Porco, 2009; El Moutamid et al., 2016), we find that the shape of the ring's edge is dominated by a 7-lobed radial distortion that rotates with the same angular velocity as Janus during the periods when the satellite is on the inner leg of its 8-yr libration. The amplitude of this distortion is similar to 12 km, and one of the seven minima is aligned within a few degrees of the satellite's mean longitude. At times when Janus is on the outer leg of its libration, however, the 7-lobed pattern disappears completely. In addition to this resonantly-forced distortion, our data reveal the presence of a rich spectrum of normal modes sculpting the ring edge. When the 7-lobed pattern is present, the principal secondary mode has m = 5, while when the 7-lobed pattern is absent, the shape of the edge is dominated by modes with m = 9 and m = 12, all with radial amplitudes of 4-6 km. The data strongly suggest that the m = 5 mode actually persists, but at an undetectable level, throughout the latter period. Lower-amplitude modes are also seen with m = 3, 4, 6, 8, 10 and 18, though not at all times. The normal mode frequencies are consistent with a simple analytic model whereby each mode exists within a resonant cavity near the edge of the ring (Borderies et al., 1985; Longaretti, 2018), from which we estimate an average surface mass density in this region of similar to 20 g cm-2, consistent with that derived from weak density waves (Tiscareno and Harris, 2018). Despite the relative complexity of the best-fitting model, the RMS deviations between it and the observed edge radii range from 1.7 to 5.5 km, substantially exceeding the measurement errors of similar to 0.3 km and strongly suggesting the existence of additional, as-yet-uncharacterized perturbations. Contrary to previous analyses, we find no evidence for beating between the strong m = 7 signature due to Janus and a weaker signature due to its coorbital companion Epimetheus (Spitale and Porco, 2009) and only weak evidence for an m = -3 mode driven by a gravity anomaly within Saturn (El Moutamid et al., 2016).

We present the results of a series of laboratory low-speed impacts (< 4 m s −1 ) of centimeter-sized spherical projectiles into simulated dry and icy regolith samples. The target material was comprised of JSC-1 (Johnson Space Center) lunar simulant grains in the size range 100–250 μ m, mixed with similar-sized water ice grains. Impacts were performed under vacuum, either at room temperature for JSC-1 samples or at cryogenic temperatures (<150 K) for icy mixtures. We measured the ejecta masses from a collection plate and impact crater dimensions from post-impact crater photographs. We find that both the ejecta masses and crater diameters followed trends predicted by established scaling laws, albeit with different fitting parameters, and we were able to fit a strength regime π scaling to our measured crater diameters. The water ice in our target material took two forms: grains mixed with the regolith grains and frost from air condensation coating regolith grains. In both cases, the presence of water ice in the sample led to lower ejected masses and smaller crater sizes. In addition, our measured crater sizes were several orders of magnitude larger than expected for impacts into solid rock or water ice. Using our measured scaling parameters, we applied our findings to a planetary context for the study of secondary craters on icy moons, as well as eroding collisions occurring in Saturn’s rings. We found that the deviation of our measurements from solid targets and from commonly used scaling parameters allowed us to reconcile our measurements with the models in both cases.

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.