The Christiansen Effect in Saturn’s narrow dusty rings and the spectral identification of clumps in the F ring

Stellar occultations by Saturn’s rings observed with the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft reveal that dusty features such as the F ring and the ringlets in the Encke and the Laplace Gaps have distinctive infrared transmission spectra. These spectra show a narrow optical depth minimum at wavelengths around 2.87 μm. This minimum is likely due to the Christiansen Effect, a reduction in the extinction of small particles when their (complex) refractive index is close to that of the surrounding medium. Simple Mie-scattering models demonstrate that the strength of this opacity dip is sensitive to the size distribution of particles between 1 and 100 μm across. Furthermore, the spatial resolution of the occultation data is sufficient to reveal variations in the transmission spectra within and among these rings. In both the Encke Gap ringlets and F ring, the opacity dip weakens with increasing local optical depth, which is consistent with the larger particles being concentrated near the cores of these rings. The Encke Gap ringlets also show systematically weaker opacity dips than the F ring and Laplace Gap ringlet, implying that the former has a smaller fraction of grains less than ∼30 μm across. However, the strength of the opacity dip varies most dramatically within the F ring; certain compact regions of enhanced optical depth lack an opacity dip and therefore appear to have a greatly reduced fraction of grains in the few-micron size range. Such spectrally-identifiable structures probably represent a subset of the compact optically-thick clumps observed by other Cassini instruments. These variations in the ring’s particle size distribution can provide new insights into the processes of grain aggregation, disruption and transport within dusty rings. For example, the unusual spectral properties of the F-ring clumps could perhaps be ascribed to small grains adhering onto the surface of larger particles in regions of anomalously low velocity dispersion.     

Saturn’s F ring grains: Aggregates made of crystalline water ice

We present models of the near-infrared (1-5 μm) spectra of Saturn’s F ring obtained by Cassini’s Visual and Infrared Mapping Spectrometer (VIMS) at ultra-high phase angles (177.4-178.5°). Modeling this spectrum constrains the size distribution, composition, and structure of F ring particles in the 0.1-100 μm size range. These spectra are very different from those obtained at lower phase angles; they lack the familiar 1.5 and 2 μm absorption bands, and the expected 3 μm water ice primary absorption appears as an unusually narrow dip at 2.87 μm. We have modeled these data using multiple approaches. First, we use a simple Mie scattering model to constrain the size distribution and composition of the particles. The Mie model allows us to understand the overall shapes of the spectra in terms of dominance by diffraction at these ultra-high phase angles, and also to demonstrate that the 2.87 μm dip is associated with the Christiansen frequency of water ice (where the real refractive index passes unity). Second, we use a combination of Mie scattering with Effective Medium Theory to probe the effect of porous (but structureless) particles on the overall shape of the spectrum and depth of the 2.87 μm band. Such simple models are not able to capture the shape of this absorption feature well. Finally, we model each particle as an aggregate of discrete monomers, using the Discrete Dipole Approximation (DDA) model, and find a better fit for the depth of the 2.87 μm feature. The DDA models imply a slightly different overall size distribution. We present a simple heuristic model which explains the differences between the Mie and DDA model results. We conclude that the F ring contains aggregate particles with a size distribution that is distinctly narrower than a typical power law, and that the particles are predominantly crystalline water ice.     

Hydrodynamical simulations of viscous overstability in Saturn’s rings

We perform axisymmetric hydrodynamical simulations that describe the nonlinear outcome of the viscous overstability in dense planetary rings. These simulations are particularly relevant for Cassini observations of fine-scale structure in Saturn’s A and B-ring, which take the form of periodic microstructure on the 0.1 km scale, and irregular larger-scale variations on 1-10 km. Nonlinear wavetrains dominate all the simulations, and we associate them with the observed periodic microstructure. The waves can undergo small chaotic fluctuations in their phase and amplitude, and may be punctuated by more formidable ‘wave defects’ distributed on longer scales. It is unclear, however, whether the defects are connected to the irregular larger-scale variations observed by Cassini. The long-term behaviour of the simulations is dominated by the imposed boundary conditions, and more generally by the limitations of the local model we use: the shearing box. When periodic boundary conditions are imposed, the system eventually settles on a uniform travelling wave of a predictable wavelength, while reflecting boundaries, and boundaries with buffer zones, maintain a disordered saturated state. The simulations omit self-gravity, though we examine its influence in future work.     

How the Enceladus dust plume feeds Saturn’s E ring

Pre-Cassini models of Saturn’s E ring [Horányi, M., Burns, J., Hamilton, D., 1992. Icarus 97, 248-259; Juhász, A., Horányi, M., 2002. J. Geophys. Res. 107, 1-10] failed to reproduce its peculiar vertical structure inferred from Earth-bound observations [de Pater, I., Martin, S.C., Showalter, M.R., 2004. Icarus 172, 446-454]. After the discovery of an active ice-volcanism of Saturn’s icy moon Enceladus the relevance of the directed injection of particles for the vertical ring structure of the E ring was swiftly recognised [Juhász, A., Horányi, M., Morfill, G.E., 2007. Geophys. Res. Lett. 34, L09104; Kempf, S., Beckmann, U., Moragas-Klostermeyer, G., Postberg, F., Srama, R., Economou, T., Schmidt, J., Spahn, F., Grün, E., 2008. Icarus 193, 420-437]. However, simple models for the delivery of particles from the plume to the ring predict a too small vertical ring thickness and overestimate the amount of the injected dust.Here we report on numerical simulations of grains leaving the plume and populating the dust torus of Enceladus. We run a large number of dynamical simulations including gravity and Lorentz force to investigate the earliest phase of the ring particle life span. The evolution of the electrostatic charge carried by the initially uncharged grains is treated selfconsistently. Freshly ejected plume particles are moving in almost circular orbits because the Enceladus orbital speed exceeds the particles’ ejection speeds by far. Only a small fraction of grains that leave the Hill sphere of Enceladus survive the next encounter with the moon. Thus, the flux and size distribution of the surviving grains, replenishing the ring particle reservoir, differs significantly from the flux and size distribution of the particles freshly ejected from the plume. Our numerical simulations reproduce the vertical ring profile measured by the Cassini Cosmic Dust Analyzer (CDA) [Kempf, S., Beckmann, U., Moragas-Klostermeyer, G., Postberg, F., Srama, R., EconoDmou, T., Smchmidt, J., Spahn, F., Grün, E., 2008. Icarus 193, 420-437]. From our simulations we calculate the deposition rates of plume particles hitting Enceladus’ surface. We find that at a distance of 100 m from a jet a 10 m sized ice boulder should be covered by plume particles in 10⁵-10⁶ years.     

Total particulate mass in Enceladus plumes and mass of Saturn’s E ring inferred from Cassini ISS images

The eclipse mosaic (PIA08329) of the Saturn system, taken on September 15, 2006 when Cassini was in Saturn’s shadow, contains numerous color images of the Enceladus plume and the E ring at phase angles ranging from 173° to 179°. These forward-scattering observations sample the diffraction peak for particle radii in the 1–5 μm range. The phase angle dependence and total brightness are sensitive indicators of the total mass of solid material in the plume. We fit the data with a variety of particle shapes and size distributions, and find that the median radius of the equivalent-volume sphere is 3.1 μm, with an uncertainty of ±0.5 μm. The total mass of particles in the plume is (1.45 ± 0.5) × 10⁵ kg. We have not considered variations with altitude in the particle size and shape distribution, and we leave that for another paper. We find that the brightness of the E ring varies with position in the orbit, not only because of the viewing geometry, e.g., variations in phase angle, but also because of some unknown intrinsic variability. The total mass of solid material in the E ring is (12 ± 5.5) × 10⁸ kg. For the plume, the production rate of particles – the mass per unit time leaving the vents is 51 ± 18 kg s⁻¹. We estimate that 9% of these particles are escaping from Enceladus, implying lifetimes of ∼8 years for the E ring particles. Based on three comparisons with vapor amounts from ultraviolet spectroscopy, the ice/vapor ratio is in the range 0.35–0.70. This high ratio poses a problem for theories in which particles form by condensation from the gas phase, and could indicate that particles are formed as spray from a liquid reservoir.     

Stability of co-orbital ring material with applications to the Janus-Epimetheus system

An analytical model that describes the evolution of ring particles that are co-orbital with two larger bodies on near-circular and near-planar orbits has been formulated. This can be used to estimate the lifetime of the particles within the ring. All the examples investigated, such as the Janus-Epimetheus (JE) system, indicate that the particles should be removed from the co-orbital region within half a synodic period (∼4 years for JE). Numerical modelling confirms the predictions of the model. When the masses are on eccentric orbits the particles remain within the co-orbital system for longer. Our results suggest that the ring associated with Janus and Epimetheus must be continually fed with material, probably by meteoroid impacts on the two satellites.     

Moonlet induced wakes in planetary rings: Analytical model including eccentric orbits of moon and ring particles

Saturn’s rings host two known moons, Pan and Daphnis, which are massive enough to clear circumferential gaps in the ring around their orbits. Both moons create wake patterns at the gap edges by gravitational deflection of the ring material (Cuzzi, J.N., Scargle, J.D. [1985]. Astrophys. J. 292, 276-290; Showalter, M.R., Cuzzi, J.N., Marouf, E.A., Esposito, L.W. [1986]. Icarus 66, 297-323). New Cassini observations revealed that these wavy edges deviate from the sinusoidal waveform, which one would expect from a theory that assumes a circular orbit of the perturbing moon and neglects particle interactions. Resonant perturbations of the edges by moons outside the ring system, as well as an eccentric orbit of the embedded moon, may partly explain this behavior (Porco, C.C., and 34 colleagues [2005]. Science 307, 1226-1236; Tiscareno, M.S., Burns, J.A., Hedman, M.M., Spitale, J.N., Porco, C.C., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, C.C., Tiscareno, M.S., Burns, J.A., Dones, L. [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, C.C., Tiscareno, M.S. [2009]. Astron. J. 138, 272-286). Here we present an extended non-collisional streamline model which accounts for both effects. We describe the resulting variations of the density structure and the modification of the nonlinearity parameter q. Furthermore, an estimate is given for the applicability of the model. We use the streamwire model introduced by Stewart (Stewart, G.R. [1991]. Icarus 94, 436-450) to plot the perturbed ring density at the gap edges.We apply our model to the Keeler gap edges undulated by Daphnis and to a faint ringlet in the Encke gap close to the orbit of Pan. The modulations of the latter ringlet, induced by the perturbations of Pan (Burns, J.A., Hedman, M.M., Tiscareno, M.S., Nicholson, P.D., Streetman, B.J., Colwell, J.E., Showalter, M.R., Murray, C.D., Cuzzi, J.N., Porco, C.C., and the Cassini ISS team [2005]. Bull. Am. Astron. Soc. 37, 766), can be well described by our analytical model. Our analysis yields a Hill radius of Pan of 17.5 km, which is 9% smaller than the value presented by Porco (Porco, C.C., and 34 colleagues [2005]. Science 307, 1226-1236), but fits well to the radial semi-axis of Pan of 17.4 km. This supports the idea that Pan has filled its Hill sphere with accreted material (Porco, C.C., Thomas, P.C., Weiss, J.W., Richardson, D.C. [2007]. Science 318, 1602-1607). A numerical solution of a streamline is used to estimate the parameters of the Daphnis-Keeler gap system, since the close proximity of the gap edge to the moon induces strong perturbations, not allowing an application of the analytic streamline model. We obtain a Hill radius of 5.1 km for Daphnis, an inner edge variation of 8 km, and an eccentricity for Daphnis of 1.5 × 10⁻⁵. The latter two quantities deviate by a factor of two from values gained by direct observations (Jacobson, R.A., Spitale, J., Porco, C.C., Beurle, K., Cooper, N.J., Evans, M.W., Murray, C.D. [2008]. Astron. J. 135, 261-263; Tiscareno, M.S., Burns, J.A., Hedman, M.M., Spitale, J.N., Porco, C.C., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767), which might be attributed to the neglect of particle interactions and vertical motion in our model.     

Self-gravity wake parameters in Saturn’s A and B rings

An increasing body of evidence shows that, at the sub-km level, Saturn’s main A and B rings are dominated by an ever-changing pattern of elongated, canted structures known as self-gravity wakes. Best known for causing azimuthal variations in the rings’ reflectivity, these structures also have a profound influence on how the transmission of the rings varies with both longitude and opening angle, B (Colwell et al. [2006] Geophys. Res. Lett. 33, 7201; Colwell et al. [2007] Icarus 190, 127-144; Hedman et al. [2007] Astron. J. 133, 2624-2629). We use data from three stellar occultations observed by Cassini’s Visual and Infrared Mapping Spectrometer (VIMS) to measure the transmission of the rings as a function of B, when viewed parallel to the wakes. These data are used to constrain properties of the self-gravity wakes as a function of radius across the A and B rings: specifically the fractional width of the gaps between the wakes, G/λ, and the average normal optical depth in the gaps, τ_G. We find that the overall normal optical depth of the rings, τ_n is primarily controlled by G/λ, which varies between <0.05 and ∼0.70 in the A and B rings. The gaps, however, are not completely empty, being filled by material — possibly cm-sized ring particles — with an average normal optical depth which varies from 0.12 to ∼0.4. In addition to regional variations, local variations in τ_G are seen in the regular structure which dominates the inner B ring, and in the environs of strong density waves in the A ring. The same model applied to the lower optical depth Cassini Division reveals very little evidence of self-gravity wakes, except where τ_n exceeds ∼0.25.     

The opposition and tilt effects of Saturn’s rings from HST observations

The two major factors contributing to the opposition brightening of Saturn’s rings are (i) the intrinsic brightening of particles due to coherent backscattering and/or shadow hiding on their surfaces, and (ii) the reduced interparticle shadowing when the solar phase angle α → 0°. We utilize the extensive set of Hubble Space Telescope observations (Cuzzi, J.N., French, R.G., Dones, L. [2002]. Icarus 158, 199–223) for different elevation angles B and wavelengths λ to disentangle these contributions. We assume that the intrinsic contribution is independent of B, so that any B dependence of the phase curves is due to interparticle shadowing, which must also act similarly for all λ’s. Our study complements that of Poulet et al. (Poulet, F., Cuzzi, J.N., French, R.G., Dones, L. [2002]. Icarus 158, 224), who used a subset of data for a single B ∼ 10°, and the French et al. (French, R.G., Verbiscer, A., Salo, H., McGhee, C.A., Dones, L. [2007b] PASP 119, 623–642) study for the B ∼ 23° data set that included exact opposition. We construct a grid of dynamical/photometric simulation models, with the method of Salo and Karjalainen (Salo and Karjalainen [2003]. Icarus 164, 428–460), and use these simulations to fit the elevation-dependent part of opposition brightening. Eliminating the modeled interparticle component yields the intrinsic contribution to the opposition effect: for the B and A rings it is almost entirely due to coherent backscattering; for the C ring, an intraparticle shadow hiding contribution may also be present.Based on our simulations, the width of the interparticle shadowing effect is roughly proportional to B. This follows from the observation that as B decreases, the scattering is primarily from the rarefied low filling factor upper ring layers, whereas at larger B’s the dense inner parts are visible. Vertical segregation of particle sizes further enhances this effect. The elevation angle dependence of interparticle shadowing also explains most of the B ring tilt effect (the increase of brightness with elevation). From comparison of the magnitude of the tilt effect at different filters, we show that multiple scattering can account for at most a 10% brightness increase as B → 26°, whereas the remaining 20% brightening is due to a variable degree of interparticle shadowing. The negative tilt effect of the middle A ring is well explained by the the same self-gravity wake models that account for the observed A ring azimuthal brightness asymmetry (Salo, H., Karjalainen, R., French, R.G. [2004]. Icarus 170, 70–90; French, R.G., Salo, H., McGhee, C.A., Dones, L. [2007]. Icarus 189, 493–522).     

Saturn’s wayward shepherds: the peregrinations of Prometheus and Pandora

Saturn’s narrow F ring is flanked by two nearby small satellites, Prometheus and Pandora, discovered in Voyager images taken in 1980 and 1981 (Synnott et al., 1983, Icarus 53, 156-158). Observations with the Hubble Space Telescope (HST) during the ring plane crossings (RPX) of 1995 led to the unexpected finding that Prometheus was ∼19° behind its predicted orbital longitude, based on the Synnott et al. (1983) Voyager ephemeris (Bosh and Rivkin, 1996 Science 272, 518-521; Nicholson et al., 1996, Science 272, 509-515). Whereas Pandora was at its predicted location in August 1995, McGhee (2000, Ph.D. thesis, Cornell University) found from the May and November 1995 RPX data that Pandora also deviates from the Synnott et al. (1983) Voyager ephemeris. Using archival HST data from 1994, previously unexamined RPX images, and a large series of targeted WFPC2 observations between 1996 and 2002, we have determined highly accurate sky-plane positions for Prometheus, Pandora, and nine other satellites found in our images. We compare the Prometheus and Pandora measurements to the predictions of substantially revised and improved ephemerides for the two satellites based on an extensive analysis of a large set of Voyager images (Murray et al., 2000, Bull. Am. Astron. Soc. 32, 1090; Evans, 2001 Ph.D. thesis, Queen Mary College). From December 1994 to December 2000, Prometheus’ orbital longitude lag was changing by −0.71° year⁻¹ relative to the new Voyager ephemeris. In contrast, Pandora is ahead of the revised Voyager prediction. From 1994 to 2000, its longitude offset changed by +0.44° year⁻¹, showing in addition an ∼585 day oscillatory component with amplitude Δλ_CR0 = 0.65 ± 0.07° whose phase matches the expected perturbation due to the nearby 3:2 corotation resonance with Mimas, modulated by the 71-year libration in the longitude of Mimas due to its 4:2 resonance with Tethys. We determine orbital elements for freely precessing equatorial orbits from fits to the 1994-2000 HST observations, from which we conclude that Prometheus’ semimajor axis was 0.31 km larger, and Pandora’s was 0.20 km smaller, than during the Voyager epoch. Subsequent observations in 2001-2002 reveal a new twist in the meanderings of these satellites: Prometheus’ mean motion changed suddenly by an additional −0.77° year⁻¹, equivalent to a further increase in semimajor axis of 0.33 km, at the same time that Pandora’s mean motion changed by +0.92° year⁻¹, corresponding to a change of −0.42 km in its semimajor axis. There is an apparent anticorrelation of the motions of these two moons seen in the 2001-2002 observations, as well as over the 20-year interval since the Voyager epoch. This suggests a common origin for their wanderings, perhaps through direct exchange of energy between the satellites as the result of resonances, possibly involving the F ring.     

The smallest particles in Saturn’s A and C Rings

Radio occultations of Saturn’s main rings by spacecraft suggest a power law particle size-distribution down to sizes of the order of 1 cm (Marouf, E.A., Tyler, G.L., Zebker, H.A., Simpson, R.A., Eshleman, V.R. [1983]. Icarus 54, 189–211; Zebker, H.A., Marouf, E.A., Tyler, G.L. [1985]. Icarus 64, 531–548.). The lack of optical depth variations between ultraviolet and near-IR wavelengths indicate a lack of micron-sized particles. Between these two regimes, the particle-size distribution is largely unknown. A cutoff where the particle-size distribution turns over must exist, but the position and shape of it is not clear from existing studies.     

New Cassini RADAR results for Saturn’s icy satellites

Cassini radar tracks on Saturn’s icy satellites through the end of the Prime Mission in 2008 have increased the number of radar albedo estimates from 10 (Ostro et al., 2006) to 73. The measurements sample diverse subradar locations (and for Dione, Rhea, and Iapetus almost always use beamwidths less than half the target angular diameters), thereby constraining the satellites’ global radar albedo distributions. The echoes result predominantly from volume scattering, and their strength is thus strongly sensitive to ice purity and regolith maturity. The combination of the Cassini data set and Arecibo 13-cm observations of Enceladus, Tethys, Dione, Rhea (Black et al., 2007), and Iapetus (Black et al., 2004) discloses an unexpectedly complex pattern of 13-to-2-cm wavelength dependence. The 13-cm albedos are generally smaller than 2-cm albedos and lack the correlation seen between 2-cm and optical geometric albedos. Enceladus and Iapetus are the most interesting cases. We infer from hemispheric albedo variations that the E-ring has a prominent effect on the 13-cm radar “lightcurve”. The uppermost trailing-side regolith is too fresh for meteoroid bombardment to have developed larger-scale heterogeneities that would be necessary to elevate the 13-cm radar albedo, whereas all of Enceladus is clean and mature enough for the 2-cm albedo to be uniformly high. For, Iapetus, the 2-cm albedo is strongly correlated with optical albedo: low for the optically dark, leading-side material and high for the optically bright, trailing-side material. However, Iapetus’ 13-cm albedo values show no significant albedo dichotomy and are several times lower than 2-cm values, being indistinguishable from the weighted mean of 13-cm albedos for main-belt asteroids, 0.15 ± 0.10. The leading side’s optically dark contaminant must be present to depths of at least one to several decimeters, so 2-cm albedos can mimic the optical dichotomy; however, it does not have to extend any deeper than that. The fact that both hemispheres of Iapetus look Asteroid-like at 13 cm means that coherent backscattering itself is not nearly as effective as it is at 2 cm. Since Iapetus’ entire surface is mature regolith, the wavelength dependence must involve composition, not structure. Either the composition is a function of depth everywhere (with electrical loss much greater at depths greater than a decimeter or two), or the intrinsic electrical loss of some pervasive constituent is much higher at 13 cm than at 2 cm. Ammonia is a candidate for such a contaminant. If ammonia’s electrical properties do not depend on frequency, and if ammonia is globally much less abundant within the upper one or two decimeters than at greater depths, then coherent backscattering would effectively be shut down at 13 cm, explaining the Asteroid-like 13-cm albedo.     

A primordial origin for the atmospheric methane of Saturn’s moon Titan

The origin of Titan’s atmospheric methane is a key issue for understanding the origin of the saturnian satellite system. It has been proposed that serpentinization reactions in Titan’s interior could lead to the formation of the observed methane. Meanwhile, alternative scenarios suggest that methane was incorporated in Titan’s planetesimals before its formation. Here, we point out that serpentinization reactions in Titan’s interior are not able to reproduce the deuterium over hydrogen (D/H) ratio observed at present in methane in its atmosphere, and would require a maximum D/H ratio in Titan’s water ice 30% lower than the value likely acquired by the satellite during its formation, based on Cassini observations at Enceladus. Alternatively, production of methane in Titan’s interior via radiolytic reactions with water can be envisaged but the associated production rates remain uncertain. On the other hand, a mechanism that easily explains the presence of large amounts of methane trapped in Titan in a way consistent with its measured atmospheric D/H ratio is its direct capture in the satellite’s planetesimals at the time of their formation in the solar nebula. In this case, the mass of methane trapped in Titan’s interior can be up to ∼1300 times the current mass of atmospheric methane.     

Accretion of Saturn’s mid-sized moons during the viscous spreading of young massive rings: Solving the paradox of silicate-poor rings versus silicate-rich moons

The origin of Saturn’s inner mid-sized moons (Mimas, Enceladus, Tethys, Dione and Rhea) and Saturn’s rings is debated. Charnoz et al. [Charnoz, S., Salmon J., Crida A., 2010. Nature 465, 752–754] introduced the idea that the smallest inner moons could form from the spreading of the rings’ edge while Salmon et al. [Salmon, J., Charnoz, S., Crida, A., Brahic, A., 2010. Icarus 209, 771–785] showed that the rings could have been initially massive, and so was the ring’s progenitor itself. One may wonder if the mid-sized moons may have formed also from the debris of a massive ring progenitor, as also suggested by Canup [Canup, R., 2010. Nature 468, 943–946]. However, the process driving mid-sized moon accretion from the icy debris disks has not been investigated in details. In particular, Canup’s (2010) model does not seem able to explain the varying silicate contents of the mid-sized moons (from 6% to 57% in mass). Here, we explore the formation of large objects from a massive ice-rich ring (a few times Rhea’s mass) and describe the fundamental properties and implications of this new process. Using a hybrid computer model, we show that accretion within massive icy rings can form all mid-sized moons from Mimas to Rhea. However in order to explain their current locations, intense dissipation within Saturn (with Q_p < 2000) is required. Our results are consistent with a satellite origin tied to the rings formation at least 2.5 Gy ago, both compatible with either a formation concurrent to Saturn or during the Late Heavy Bombardment. Tidal heating related to high-eccentricity post-accretional episodes may induce early geological activity. If some massive irregular chunks of silicates were initially present within the rings, they would be present today inside the satellites’ cores which would have accreted icy shells while being tidally expelled from the rings (via a heterogeneous accretion process). These moons may be either mostly icy, or, if they contain a significant amount of rock, already differentiated from the ice without the need for radiogenic heating. The resulting inner mid-sized moons may be significantly younger than the Solar System and a ∼1 Gyr formation delay is possible between Mimas and Rhea. The rings resulting from this process would evolve to a state compatible with current mass estimates of Saturn’s rings, and nearly devoid of silicates, apart from isolated silicate chunks coated with ice, interpreted as today Saturn’s rings’ propellers and ring-moons (like Pan or Daphnis).     

Estimating the masses of Saturn’s A and B rings from high-optical depth N-body simulations and stellar occultations

We have completed a series of local N-body simulations of Saturn’s B and A rings in order to identify systematic differences in the degree of particle clumping into self-gravity wakes as a function of orbital distance from Saturn and dynamical optical depth (a function of surface density). These simulations revealed that the normal optical depth of the final configuration can be substantially lower than one would infer from a uniform distribution of particles. Adding more particles to the simulation simply piles more particles onto the self-gravity wakes while leaving relatively clear gaps between the wakes. Estimating the mass from the observed optical depth is therefore a non-linear problem. These simulations may explain why the Cassini UVIS instrument has detected starlight at low incidence angles through regions of the B ring that have average normal optical depths substantially greater than unity at some observation geometries [Colwell, J.E., Esposito, L.W., Srem?evi?, M., Stewart, G.R., McClintock, W.E., 2007. Icarus 190, 127-144]. We provide a plausible internal density of the particles in the A and B rings based upon fitting the results of our simulations with Cassini UVIS stellar occultation data. We simulated Cassini-like occultations through our simulation cells, calculated optical depths, and attempted to extrapolate to the values that Cassini observes. We needed to extrapolate because even initial optical depths of >4 (σ > 240 g cm⁻²) only yielded final optical depths no greater than 2.8, smaller than the largest measured B ring optical depths. This extrapolation introduces a significant amount of uncertainty, and we chose to be conservative in our overall mass estimates. From our simulations, we infer the surface density of the A ring to be , which corresponds to a mass of . We infer a minimum surface density of for Saturn’s B ring, which corresponds to a minimum mass estimate of . The A ring mass estimate agrees well with previous analyses, while the B ring is at least 40% larger. In sum, our lower limit estimate is that the total mass of Saturn’s ring system is 120-200% the mass of the moon Mimas, but significantly larger values would be plausible given the limitations of our simulations. A significantly larger mass for Saturn’s rings favors a primordial origin for the rings because the disruption of a former satellite of the required mass would be unlikely after the decay of the late heavy bombardment of planetary surfaces.     

Negative diffusion in planetary rings with a nearby moon

This paper analyzes a process that has been observed in simulations of numerous systems where ring material is strongly perturbed by a nearby moon. If the ring particles can be imparted with a forced eccentricity on the order of 10⁻⁵ in a single pass by the moon, particle orbits are observed to move towards regions of higher density as a result of the organized collisions that occur in the dense peaks of the satellite wake. The width of the ring can decrease by as much as 90% if the forced eccentricity is greater than 3 × 10⁻⁵ and the unperturbed geometric optical depth is greater than 0.03. The fractional change in ring width is relatively insensitive to the particle size so long as the particle radius is much less than the product of the semimajor axis and the forced eccentricity. Including a power law particle size distribution with slope of −2.8 spanning a decade in particle radius reduces the fractional width change by about 10% compared to the uniform particle-size case. Adding gravitational interactions between ring particles only has a significant effect on ring confinement if the unperturbed geometric optical depth exceeds .03, but a 40% reduction in ring width is still achieved in a self-gravitating ring of geometric optical depth 0.3 if the forced eccentricity exceeds 3 × 10⁻⁵. This process does not require the material to be in resonance with the moon, nor does it have any minimum mass constraints because particle self-gravity is not required. The collisional damping of satellite wakes therefore provides a simple mechanism by which a single moon can reduce the radial extent of any ringlet that is close to it and has sufficient optical depth for collisions to be significant.     

Morphology and variability of the Titan ringlet and Huygens ringlet edges

We present a forward modeling approach for determining, in part, the ring particle spatial distribution in the vicinity of sharp ring or ringlet edges. Synthetic edge occultation profiles are computed based on a two-parameter particle spatial distribution model. One parameter, h, characterizes the vertical extent of the ring and the other, δ, characterizes the radial scale over which the ring optical depth transitions from the background ring value to zero. We compare our synthetic occultation profiles to high resolution stellar occultation light curves observed by the Cassini Ultraviolet Imaging Spectrograph (UVIS) High Speed Photometer (HSP) for occultations by the Titan ringlet and Huygens ringlet edges.More than 100 stellar occultations of the Huygens ringlet and Titan ringlet edges were studied, comprising 343 independent occultation cuts of the edges of these two ringlets. In 237 of these profiles the measured light-curve was fit well with our two-parameter edge model. Of the remaining edge occultations, 69 contained structure that could only be fit with extremely large values of the ring-plane vertical thickness (h > 1 km) or by adopting a different model for the radial profile of the ring optical depth. An additional 37 could not be fit by our two-parameter model.Certain occultations at low ring-plane incidence angles as well as occultations nearly tangent to the ring edge allow the direct measurement of the radial scale over which the particle packing varies at the edge of the ringlet. In 24 occultations with these particular viewing geometries, we find a wide variation in the radial scale of the edge. We are able to constrain the vertical extent of the rings at the edge to less than ∼300 m in the 70% of the occultations with appropriate viewing geometry, however tighter constraints could not be placed on h due to the weaker sensitivity of the occultation profile to vertical thickness compared to its sensitivity to δ.Many occultations of a single edge could not be fit to a single value of δ, indicating large temporal or azimuthal variability, although the azimuthal variation in δ with respect to the longitudes of various moons in the system did not show any discernible pattern.     

Saturn's dynamic D ring

The Cassini spacecraft has provided the first clear images of the D ring since the Voyager missions. These observations show that the structure of the D ring has undergone significant changes over the last 25 years. The brightest of the three ringlets seen in the Voyager images (named D72), has transformed from a narrow, <40-km wide ringlet to a much broader and more diffuse 250-km wide feature. In addition, its center of light has shifted inwards by over 200 km relative to other features in the D ring. Cassini also finds that the locations of other narrow features in the D ring and the structure of the diffuse material in the D ring differ from those measured by Voyager. Furthermore, Cassini has detected additional ringlets and structures in the D ring that were not observed by Voyager. These include a sheet of material just interior to the inner edge of the C ring that is only observable at phase angles below about 60°. New photometric and spectroscopic data from the ISS (Imaging Science Subsystem) and VIMS (Visual and Infrared Mapping Spectrometer) instruments onboard Cassini show the D ring contains a variety of different particle populations with typical particle sizes ranging from 1 to 100 microns. High-resolution images reveal fine-scale structures in the D ring that appear to be variable in time and/or longitude. Particularly interesting is a remarkably regular, periodic structure with a wavelength of ∼30 km extending between orbital radii of 73,200 and 74,000 km. A similar structure was previously observed in 1995 during the occultation of the star GSC5249-01240, at which time it had a wavelength of ∼60 km. We interpret this structure as a periodic vertical corrugation in the D ring produced by differential nodal regression of an initially inclined ring. We speculate that this structure may have formed in response to an impact with a comet or meteoroid in early 1984.     

Self-gravity wakes and radial structure of Saturn's B ring

We analyze stellar occultations by Saturn's rings observed with the Cassini Ultraviolet Imaging Spectrograph and find large variations in the apparent normal optical depth of the B ring with viewing angle. The line-of-sight optical depth is roughly independent of the viewing angle out of the ring plane so that optical depth is independent of the path length of the line-of-sight. This suggests the ring is composed of virtually opaque clumps separated by nearly transparent gaps, with the relative abundance of clumps and gaps controlling the observed optical depth. The observations can be explained with a model of self-gravity wakes like those observed in the A ring. These trailing spiral density enhancements are due to the competing processes of self-gravitational accretion of ring particles and Kepler shear. The B ring wakes are flatter and more closely packed than their neighbors in the A ring, with height-to-width ratios <0.1 for most of the ring. The self-gravity wakes are seen in all regions of the B ring that are not opaque. The observed variation in total B ring optical depth is explained by the amount of relatively empty space between the self-gravity wakes. Wakes are more tightly packed in regions where the apparent normal optical depth is high, and the wakes are more widely spaced in lower optical depth regions. The normal optical depth of the gaps between the wakes is typically less than 0.5 and shows no correlation with position or overall optical depth in the ring. The wake height-to-width ratio varies with the overall optical depth, with flatter, more tightly packed wakes as the overall optical depth increases. The highly flattened profile of the wakes suggests that the self-gravity wakes in Saturn's B ring correspond to a monolayer of the largest particles in the ring. The wakes are canted to the orbital direction in the trailing sense, with a trend of decreasing cant angle with increasing orbital radius in the B ring. We present self-gravity wake properties across the B ring that can be used in radiative transfer modeling of the ring. A high radial resolution (∼10 m) scan of one part of the B ring during a grazing occultation shows a dominant wavelength of 160 m due to structures that have zero cant angle. These structures are seen at the same radial wavelength on both ingress and egress, but the individual peaks and troughs in optical depth do not match between ingress and egress. The structures are therefore not continuous ringlets and may be a manifestation of viscous overstability.     

Long-term and large-scale viscous evolution of dense planetary rings

Planetary rings are common in the outer Solar System but their origin and long-term evolution is still a matter of debate. It is well known that viscous spreading is a major evolutionary process for rings, as it globally redistributes the disk’s mass and angular momentum, and can lead to the disk’s loosing mass by infall onto the planet or through the Roche limit. However, describing this process is highly dependent on the model used for the viscosity. In this paper we investigate the global and long-term viscous evolution of a circumplanetary disk. We have developed a simple 1D numerical code, but we use a physically realistic viscosity model derived from N-body simulations (Daisaka et al., 2001), and dependent on the disk’s local properties (surface mass density, particle size, distance to the planet). Particularly, we include the effects of gravitational instabilities (wakes) that importantly enhance the disk’s viscosity. This method allows to study the global evolution of the disk over the age of the Solar System.Common estimates of the disk’s spreading time-scales with constant viscosity significantly underestimate the rings’ lifetime. We show that, with a realistic viscosity model, an initially narrow ring undergoes two successive evolutionary stages: (1) a transient rapid spreading when the disk is self-gravitating, with the formation of a density peak inward and an outer region marginally gravitationally stable, and with an emptying time-scale proportional to (where M₀ is the disk’s initial mass), (2) an asymptotic regime where the spreading rate continuously slows down as larger parts of the disk become non-self-gravitating due to the decrease of the surface density, until the disk becomes completely non-self-gravitating. At this point its evolution dramatically slows down, with an emptying time-scale proportional to 1/M₀, which significantly increases the disk’s lifetime compared to the case with constant viscosity. We show also that the disk’s width scales like t^1/4 with the realistic viscosity model, while it scales like t^1/2 in the case of constant viscosity, resulting in much larger evolutionary time-scales in our model. We find however that the present shape of Saturn’s rings looks like a 100 million-years old disk in our simulations. Concerning Jupiter’s, Uranus’ and Neptune’s rings that are faint today, it is not likely that they were much more massive in the past and lost most of their mass due to viscous spreading alone.