Degree-one convection and the origin of Enceladus' dichotomy

Recently, the Cassini spacecraft has detected ongoing geologic activity near the south pole of Saturn's moon Enceladus. In contrast, the satellite's north-polar region is heavily cratered and appears to have been geologically inactive for a long time. We propose that this hemispheric dichotomy is caused by interior dynamics with degree-one convection driving the south-polar activity. We investigate a number of core sizes and internal heating rates for which degree-one convection occurs. The numerical simulations imply that a core radius of less than 100±20 km and an energy input at a rate of 3.0 to 5.5 GW would be required for degree-one convection to prevail. This is within the range of the observed thermal power release near Enceladus' south pole. Provided that Enceladus is not fully differentiated, degree-one convection is found to be a viable mechanism to explain Enceladus' hemispheric dichotomy.     

A model for the temperature-dependence of tidal dissipation in convective plumes on icy satellites: Implications for Europa and Enceladus

To explain the formation of surface features on Europa, Enceladus, and other satellites, many authors have postulated the spatial localization of tidal heating within convective plumes. However, the concept that enhanced tidal heating can occur within a convective plume has not been rigorously tested. Most models of this phenomenon adopt a tidal heating with a temperature-dependence derived for an incompressible, homogeneous (zero-dimensional) Maxwell material, but it is unclear whether this formulation is relevant to the heterogeneous situation of a warm plume surrounded by cold ice. To determine whether concentrated dissipation can occur in convective plumes, we develop a two-dimensional model to compute the volumetric dissipation rate for an idealized, vertically oriented, isolated convective plume obeying a Maxwellian viscoelastic compressible rheology. We apply the model to the Europa and Enceladus ice shells, and we investigate the consequences for partial melting and resurfacing processes on these bodies. We find that the tidal heating is strongly temperature dependent in a convective ice plume and could produce elevated temperatures and local partial melting in the ice shells of Europa and Enceladus. Our calculation provides the first quantitative verification of the hypothesis by Sotin et al. [Sotin, C., Head, J.W., Tobie, G., 2002. Geophys. Res. Lett. 29. 74-1] and others that the tidal dissipation rate is a strong function of temperature inside a convective plume. On Europa, such localized heating could help allow the formation of domes and chaos terrains by convection. On Enceladus, localized tidal heating in a thermal plume could explain the concentrated activity at the south pole and its associated heat transport of 2-7 GW.     

Tidal heating and the long-term stability of a subsurface ocean on Enceladus

Tidal dissipation has been suggested as the heat source for the south polar thermal anomaly on Enceladus. We find that under present-day conditions and assuming Maxwellian behavior, tidal dissipation is negligible in the silicate core. Dissipation may be significant in the ice shell if the shell is decoupled from the silicate core by a subsurface ocean. We have run a series of self-consistent convection and conduction models in 2D axisymmetric and 3D spherical geometry in which we include the spatially-variable tidal heat production. We find that in all cases, the shell removes more heat from the interior than can be produced in the core by radioactive decay, resulting in cooling of the interior and the freezing of any ocean. Under likely conditions, a 40-km thick ocean made of pure water would freeze solid on a ∼30 Ma timescale. An ocean containing other chemical components will have a lower freezing point, but even a water-ammonia eutectic composition will only prolong the freezing, not prevent it. If the eccentricity of Enceladus were higher (e?0.015) in the past, the increased dissipation in the ice shell may have been sufficient to maintain a liquid layer. We cannot therefore rule out the presence of a transient ocean, as a relic of an earlier era of greater heating. If the eccentricity is periodically pumped up, the ocean may have thickened and thinned on a similar timescale as the orbital evolution, provided the ocean never froze completely. We conclude that the current heat flux of Enceladus and any possible subsurface ocean is not in steady-state, and is the remnant of an epoch of higher eccentricity and tidal dissipation.     

Enceladus: Present internal structure and differentiation by early and long-term radiogenic heating

Pre-Cassini images of Saturn's small icy moon Enceladus provided the first indication that this satellite has undergone extensive resurfacing and tectonism. Data returned by the Cassini spacecraft have proven Enceladus to be one of the most geologically dynamic bodies in the Solar System. Given that the diameter of Enceladus is only about 500 km, this is a surprising discovery and has made Enceladus an object of much interest. Determining Enceladus' interior structure is key to understanding its current activity. Here we use the mean density of Enceladus (as determined by the Cassini mission to Saturn), Cassini observations of endogenic activity on Enceladus, and numerical simulations of Enceladus' thermal evolution to infer that this satellite is most likely a differentiated body with a large rock-metal core of radius about 150 to 170 km surrounded by a liquid water-ice shell. With a silicate mass fraction of 50% or more, long-term radiogenic heating alone might melt most of the ice in a homogeneous Enceladus after about 500 Myr assuming an initial accretion temperature of about 200 K, no subsolidus convection of the ice, and either a surface temperature higher than at present or a porous, insulating surface. Short-lived radioactivity, e.g., the decay of ²⁶Al, would melt all of the ice and differentiate Enceladus within a few million years of accretion assuming formation of Enceladus at a propitious time prior to the decay of ²⁶Al. Long-lived radioactivity facilitates tidal heating as a source of energy for differentiation by warming the ice in Enceladus so that tidal deformation can become effective. This could explain the difference between Enceladus and Mimas. Mimas, with only a small rock fraction, has experienced relatively little long-term radiogenic heating; it has remained cold and stiff and less susceptible to tidal heating despite its proximity to Saturn and larger eccentricity than Enceladus. It is shown that the shape of Enceladus is not that of a body in hydrostatic equilibrium at its present orbital location and rotation rate. The present shape could be an equilibrium shape corresponding to a time when Enceladus was closer to Saturn and spinning more rapidly, or more likely, to a time when Enceladus was spinning more rapidly at its present orbital location. A liquid water layer on Enceladus is a possible source for the plume in the south polar region assuming the survivability of such a layer to the present. These results could place Enceladus in a category similar to the large satellites of Jupiter, with the core having a rock-metal composition similar to Io, and with a deep overlying ice shell similar to Europa and Ganymede. Indeed, the moment of inertia factor of a differentiated Enceladus, C/MR², could be as small as that of Ganymede, about 0.31.     

Photometric and spectral analysis of the distribution of crystalline and amorphous ices on Enceladus as seen by Cassini

Photometric and spectral analysis of data from the Cassini Visual and Infrared Mapping Spectrometer (VIMS) has yielded significant results regarding the properties and composition of the surface of Saturn's satellite Enceladus. We have obtained spectral cubes of this satellite, containing both spatial and spectral information, with a wavelength distribution in the infrared far more extensive than from any previous observations and at much higher spatial resolution. Using a composite mosaic of the satellite, we map the distribution of crystalline and amorphous ices on the surface of Enceladus according to a “crystallinity factor” and also the depth of the temperature- and structure-dependent 1.65 micron water-ice band. These maps show the surface of Enceladus to be mostly crystalline, with a higher degree of crystallinity at the “tiger-stripe” cracks and a larger amorphous signature between these stripes. These results suggest recent geological activity at the “tiger stripe” cracks and an intriguing atmospheric environment over the south pole where amorphous ice is produced either through intense radiative bombardment, flash-freezing of cryovolcanic liquid, or rapid condensation of water vapor particles on icy microspherules or on the surface of Enceladus.     

Atmospheric control of the cooling rate of impact melts and cryolavas on Titan’s surface

As on Earth, Titan’s atmosphere plays a major role in the cooling of heated surfaces. We have assessed the mechanisms by which Titan’s atmosphere, dominantly N₂ at a surface pressure of 1.5 × 10⁵ Pa, cools a warm or heated surface. These heated areas can be caused by impacts generating melt sheets and (possibly) by endogenic processes emplacing cryolavas (a low-temperature liquid that freezes on the surface). We find that for a cooling cryolava flow, lava lake, or impact melt body, heat loss is mainly driven by atmospheric convection. Radiative heat loss, a dominant heat loss mechanism with terrestrial silicate lava flows, plays only a minor role on Titan. Long-term cooling and solidification are dependent on melt sheet or flow thickness, and also local climate, because persistent winds will speed cooling. Relatively rapid cooling caused by winds reduces the detectability of these thermal events by instruments measuring surface thermal emission. Because surface temperature drops by ≈50% within ≈1 day of emplacement, fresh flows or impact melt may be difficult to detect via thermal emission unless an active eruption is directly observed. Cooling of flow or impact melt surfaces are orders of magnitude faster on Titan than on airless moons (e.g., Enceladus or Europa).Although upper surfaces cool fast, the internal cooling and solidification process is relatively slow. Cryolava flow lengths are, therefore, more likely to be volume (effusion) limited, rather than cooling-limited. More detailed modeling awaits constraints on the thermophysical properties of the likely cryomagmas and surface materials.     

Arecibo radar observations of Rhea, Dione, Tethys, and Enceladus

We have measured the bulk radar reflectance properties of the mid-size saturnian satellites Rhea, Dione, Tethys, and Enceladus with the Arecibo Observatory's 13 cm wavelength radar system during the 2004 through 2007 oppositions of the Saturn system. Comparing to the better studied icy Galilean satellites, we find that the total reflectivities of Rhea and Tethys are most similar to Ganymede while Dione is most similar to Callisto. Enceladus' reflectivity falls between those of Ganymede and Europa. The mean circular polarization ratios of the saturnian satellites range from ∼0.8 to 1.2, and are on average lower than those of the icy Galilean satellites at this wavelength although still larger than expected for single reflections off the surface. The ratio for the trailing hemisphere of Enceladus may be the exception with a value ?0.56. The 13 cm wavelength radar albedos and polarization ratios may be systematically lower than similar results from the Cassini orbiter's RADAR instrument at 2.2 cm wavelength [Ostro, S.J., and 19 colleagues, 2006. Icarus 183, 479-490]. Overall, these reflectivities and polarization properties, together with the shapes of the echo spectra, suggest subsurface multiple scattering to be the dominant reflection mechanism although operating less efficiently than on the large icy moons of Jupiter. All these saturnian moons and icy jovian moons are atmosphere-less, low temperature water ice surfaces, and any differences in radar properties may be indicative of differences in composition or the effects of various processes that modify the regolith structure. The degree of variation in radar properties with wavelength on each satellite may constrain the thickness and efficiency of the scattering layer.     

Shapes of the saturnian icy satellites and their significance

The sizes and shapes of six icy saturnian satellites have been measured from Cassini Imaging Science Subsystem (ISS) data, employing limb coordinates and stereogrammetric control points. Mimas, Enceladus, Tethys, Dione and Rhea are well described by triaxial ellipsoids; Iapetus is best represented by an oblate spheroid. All satellites appear to have approached relaxed, equilibrium shapes at some point in their evolution, but all support at least 300 m of global-wavelength topography. The shape of Enceladus is most consistent with a homogeneous interior. If Enceladus is differentiated, its shape and apparent relaxation require either lateral inhomogeneities in an icy mantle and/or an irregularly shaped core. Iapetus supports a fossil bulge of over 30 km, and provides a benchmark for impact modification of shapes after global relaxation. Satellites such as Mimas that have smoother limbs than Iapetus, and are expected to have higher impact rates, must have relaxed after the shape of Iapetus was frozen.     

Magnetic portraits of Tethys and Rhea

The Cassini spacecraft made a single flyby each of Saturn's icy moons Tethys and Rhea in late 2005. The magnetic field observations from these flybys provide unique portraits of the magnetic properties of these moons. These are the first observations of interactions of these inert moons with the sub-magnetosonic plasma of Saturn's magnetosphere. Because the upstream field and plasma conditions are extremely stable, we are able to observe the interaction in great detail. One of the major findings of this study is that the region of plasma depletion is greatly elongated along the field direction in a sub-magnetosonic interaction. Based on the consideration of field aligned velocities of thermal ions, we show that overlapping particle shadow wings form downstream of an inert moon such that in each of the particle shadow wings, particles of specific field aligned velocities are depleted. Other major findings of this study are: (1) Tethys and Rhea are devoid of any internal magnetic field; (2) No induction generated field was observed, as expected because of the extremely weak primary inducing (time varying) field; (3) There is no appreciable mass-loading of Saturn's magnetosphere from Tethys and Rhea; (4) We predict that wave particles interactions would be generated that smooth out the phase space holes created by the moon/plasma interaction. These waves serve to isotropize the plasma distribution function.     

Electrical properties of Titan's surface from Cassini RADAR scatterometer measurements

We report regional-scale low-resolution backscatter images of Titan's surface acquired by the Cassini RADAR scatterometer at a wavelength of 2.18-cm. We find that the average angular dependence of the backscatter from large regions and from specific surface features is consistent with a model composed of a quasi-specular Hagfors term plus a diffuse cosine component. A Gaussian quasi-specular term also fits the data, but less well than the Hagfors term. We derive values for the mean dielectric constant and root-mean-square (rms) slope of the surface from the quasi-specular term, which we ascribe to scattering from the surface interface only. The diffuse term accommodates contributions from volume scattering, multiple scattering, or wavelength-scale near-surface structure. The Hagfors model results imply a surface with regional mean dielectric constants between 1.9 and 3.6 and regional surface roughness that varies between 5.3° and 13.4° in rms-slope. Dielectric constants between 2 and 3 are expected for a surface composed of solid simple hydrocarbons, water ice, or a mixture of both. Smaller dielectric constants, between 1.6 and 1.9, are consistent with liquid hydrocarbons, while larger dielectric constants, near 4.5, may indicate the presence of water-ammonia ice [Lorenz, R.D., 1998. Icarus 136, 344-348] or organic heteropolymers [Thompson, W.R., Squyres, S.W., 1990. Icarus 86, 336-354]. We present backscatter images corrected for angular effects using the model residuals, which show strong features that correspond roughly to those in 0.94-μm ISS images. We model the localized backscatter from specific features to estimate dielectric constant and rms slope when the angular coverage is within the quasi-specular part of the backscatter curve. Only two apparent surface features are scanned with angular coverage sufficient for accurate modeling. Data from the bright albedo feature Quivira suggests a dielectric constant near 2.8 and rms slope near 10.1°. The dark albedo feature Shangri-La is best fit by a Hagfors model with a dielectric constant close to 2.4 and an rms slope near 9.5°. From the modeled backscatter curves, we find the average radar albedo in the same linear (SL) polarization to be near 0.34. We constrain the total-power albedo in order to compare the measurements with available groundbased radar results, which are typically obtained in both senses of circular polarization. We estimate an upper limit of 0.4 on the total-power albedo, a value that is significantly higher than the 0.21 total albedo value measured at 13 cm [Campbell, D., Black, G., Carter, L., Ostro, S., 2003. Science 302, 431-434]. This is consistent with a surface that has more small-scale structure and is thus more reflective at 2-cm than 13-cm. We compare results across overlapping observations and observe that the reduction and analysis are repeatable and consistent. We also confirm the strong correlations between radar and near-infrared images.     

Plasma, plumes and rings: Saturn system dynamics as recorded in global color patterns on its midsize icy satellites

New global maps of the five inner midsize icy saturnian satellites, Mimas, Enceladus, Tethys, Dione, and Rhea, have been constructed in three colors (UV, Green and near-IR) at resolutions of 1 km/pixel. The maps reveal prominent global patterns common to several of these satellites but also three major color features unique to specific satellites or satellite subgroups. The most common features among the group are first-order global asymmetries in color properties. This pattern, expressed on Tethys, Dione and Rhea, takes the form of a ∼1.4-1.8 times enhancement in redness (expressed as IR/UV ratio) of the surface at the center of the trailing hemisphere of motion, and a similar though significantly weaker IR/UV enhancement at the center of the leading hemisphere. The peak in redness on the trailing hemisphere also corresponds to a known decrease in albedo. These double hemispheric asymmetries are attributable to plasma and E-ring grain bombardment on the trailing and leading hemispheres, respectively, for the outer three satellites Tethys, Dione and Rhea, whereas as E-ring bombardment may be focused on the trailing hemisphere of Mimas due to its orbital location interior to Enceladus. The maps also reveal three major deviations from these basic global patterns. We observe the previously known dark bluish leading hemisphere equatorial band on Tethys but have also discovered a similar band on Mimas. Similar in shape, both features match the surface patterns expected for irradiation of the surface by incident MeV electrons that drift in a direction opposite to the plasma flow. The global asymmetry on Enceladus is offset ∼40° to the west compared to the other satellites. We do not consider Enceladus in detail here, but the global distribution of bluish material can be shown to match the deposition pattern predicted for plume fallback onto the surface (Kempf, S., Beckmann, U., Schmidt, S. [2010]. Icarus 206, 446-457. doi:10.1016/j.icarus.2009.09.016). E-ring deposition on Enceladus thus appears to mask or prevent the formation of the lenses and hemispheric asymmetries we see on the other satellites. Finally, we observe a chain of discrete bluish splotches along the equator of Rhea. Unlike the equatorial bands of Tethys and Mimas, these splotches form a very narrow great circle ?10-km wide (north-to-south) and appear to be related to surface disruption, exposing fresh, bluish ice on older crater rims. This feature is unique to Rhea and may have formed by impact onto its surface of orbiting material.     

Physisorption of CO2 on non-ice materials relevant to icy satellites

CO₂ is known to adsorb onto clay and other minerals when a significant atmospheric pressure is present. We have found that CO₂ can also adsorb onto some clays when the CO₂ partial pressure is effectively zero under ultra-high vacuum (UHV) if cooled to the surface temperatures of the icy satellites of Jupiter and Saturn. The strength of adsorption and the spectral characteristics of the adsorbed CO₂ infrared (IR) ν₃ absorption band near 4.25 μm depend on the composition and temperature of the adsorbent. CO₂ remains adsorbed onto the clay mineral montmorillonite for >10 s of min when exposed to a vacuum of ∼1×¹⁰⁻⁸ Torr at ∼125 K. CO₂ does not adsorb onto serpentine, goethite, or palagonite under these conditions. A small amount may adsorb onto kaolinite. When heated above 150 K under vacuum, the CO₂ desorbs from the montmorillonite within a few minutes. The ν₃ absorption band of CO₂ adsorbed onto montmorillonite at 125 K is similar to that of the CO₂ detected on the saturnian and Galilean satellites and is markedly different from CO₂ adsorbed onto montmorillonite at room temperature. We infer the adsorption process is physisorption and postulate that this mechanism may explain the presence and spectral characteristics of the CO₂ detected in the surfaces of these outer satellites.     

Constraining the surface properties of Saturn's icy moons, using Cassini/CIRS emissivity spectra

We have conducted a search for emissivity features in the thermal infrared spectrum of the icy satellites of Saturn, Phoebe, Iapetus, Enceladus, Tethys, and Hyperion, observed by the Composite Infrared Spectrometer (CIRS) on board the Cassini spacecraft. Despite the heterogeneity of the composition of these bodies depicted by Earth-based and Cassini/VIMS observations, the CIRS spectra of all satellites are undistinguishable from black-body spectra, with no detectable emissivity feature. However, several materials, which have been detected on the surface of the same bodies, present emissivity features in the analyzed spectral range. In particular, water ice presents features with sufficient contrast to be detected by CIRS. Here we study the physical causes of the absence of features by simulating the effects of intimate mixtures using models of directional emissivity for optically thick surfaces for different particle sizes and abundances, and porosities. The simulations include a set of materials detected on the Phoebe's surface, like water ice, hydrated silicates, and organics. We find that featureless spectra can be produced in three scenarios: (1) ice particles with large sizes, (2) mixtures of ices dominated by dark contaminants, and (3) small particles with large porosity. Constraints imposed by the NIR spectra of the satellites favors the latter scenario as the more likely explanation to the absence of emissivity features on the icy satellites of Saturn.     

Monte Carlo simulations of the water vapor plumes on Enceladus

Monte Carlo simulations are used to model the July 14, 2005 UVIS stellar occultation observations of the water vapor plumes on Enceladus. These simulations indicate that the observations can be best fit if the water molecules ejected along the Tiger Stripes in the South Polar region of Enceladus have a vertical surface velocity of 300-500 m/s at the surface. The high surface velocity suggests that the plumes on Enceladus originate from some depth beneath the surface. The total escape rate of water molecules is 4-6×¹⁰²⁷ s⁻¹, or 120-180 kg/s, consistent with previous works, and more than 100 times the estimated mass escape rate for ice particles. The average deposition rate in the South Polar region is on the order of 10¹¹ cm⁻² s⁻¹, yielding a resurfacing rate as high as 3×¹⁰⁻⁴ cm/yr. The globally averaged deposition rate of water molecules is about one order of magnitude lower.     

Unstable extension of Enceladus' lithosphere

Regions near Enceladus' equator, Sarandib and Diyar Planitia, contain extensive sets of parallel ridges and troughs that may be diagnostic of the region's formation conditions. We present photoclinometry profiles across these ridges and troughs, which indicate that they are periodic, low-slope features with dominant wavelengths of 3 to 4 km and amplitudes between 100 and 400 m. The morphology of these terrains is consistent with formation via unstable extension of the lithosphere. Our numerical modeling demonstrates that unstable extension can generate large-scale topography under Enceladus-like conditions. Comparison of our photoclinometry profiles with the dominant wavelengths produced by our numerical model permits estimation of the background heat flow at the time the Sarandib-Diyar province formed. We estimate heat flows of 110 to , suggesting that resurfacing of the planitiae was accompanied by strong, localized heating. The extension necessary to produce the ridges and troughs may have been caused by now-inactive diapirs, internal phase changes, or other mechanisms. Our heat flux estimates imply elastic thickness at the time of resurfacing of 0.4 to 1.4 km, which are sufficient to have allowed satellite reorientation if the province was underlain by a low-density region. It is therefore plausible that Enceladus has experienced multiple heating events, each leading to localized resurfacing and global reorientation.     

Enceladus' south polar sea

Recent observations of the south pole of Saturn's moon Enceladus by the Cassini spacecraft have revealed an active world, powered by internal heat. In this paper, we propose that localized subsurface melting on Enceladus has produced an internal south polar sea. Evidence for this localized sea comes from the shape of Enceladus, which does not match a differentiated body at its current orbital position. We show that melting induced by the observed heat flow at the south pole produces a large enough pit to match the shape of Enceladus with a differentiated rock and ice interior. Numerical modeling of melting and ice flow shows that the sea produced beneath the south pole is stable against inflow of ductile ice from its surroundings for the duration of the heating. The shape modification due to melting also produces a negative degree-two gravity anomaly, which can reorient the spin axis of Enceladus in order to place the sea at the pole.     

The oxidation state of hydrothermal systems on early Enceladus

The discovery of CO₂, CH₄, and N₂ in a plume at Enceladus provides useful clues about the chemistry and evolution of this moon of Saturn. Here, we use chemical equilibrium and kinetic calculations to estimate the oxidation state of hydrothermal systems on early Enceladus, with the assumption that the plume's composition was inherited from early hydrothermal fluids. Chemical equilibrium calculations are performed using the CO₂/CH₄ ratio in the plume, and kinetic calculations are conducted using equations from fluid dynamics and chemical kinetics. Our results suggest that chemical equilibrium between CO₂ and CH₄ would have been reachable at temperatures above ∼200 °C in hydrothermal systems. The oxidation state of the hydrothermal systems would have been close to the pyrrhotite-pyrite-magnetite (PPM) or fayalite-magnetite-quartz (FMQ) redox buffer (i.e., terrestrial-like) if the plume's CO₂ and CH₄ equilibrated in hydrothermal systems long ago. As for minerals, we suggest that iron metal would have been oxidized to magnetite by the escape of H₂ from the early satellite. Our calculations also indicate that, assuming CO₂ and CH₄ reached chemical equilibrium, magnetite would not have been oxidized to hematite in hydrothermal systems, perhaps due to insufficient H₂ escape. It is shown that, if Enceladus accreted as much NH₃ as comets contain, the presence of N₂ and deficiency of NH₃ in the plume can be understood in the context of chemical equilibrium in the C-N-O-H system. We conclude by proposing an evolutionary hypothesis in which the fairly oxidized nature of the plume can be explained by a brief episode of oxidation caused by short-lived radioactivity. These suggestions can be rigorously tested by acquiring gravity and isotopic data in the future.     

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.     

Tidal evolution of Mimas, Enceladus, and Dione

The tidal evolution through several resonances involving Mimas, Enceladus, and/or Dione is studied numerically with an averaged resonance model. We find that, in the Enceladus-Dione 2:1 e-Enceladus type resonance, Enceladus evolves chaotically in the future for some values of k₂/Q. Past evolution of the system is marked by temporary capture into the Enceladus-Dione 4:2 ee^′-mixed resonance. We find that the free libration of the Enceladus-Dione 2:1 e-Enceladus resonance angle of 1.5° can be explained by a recent passage of the system through a secondary resonance. In simulations with passage through the secondary resonance, the system enters the current Enceladus-Dione resonance close to tidal equilibrium and thus the equilibrium value of tidal heating of 1.1(18,000/QS) GW applies. We find that the current anomalously large eccentricity of Mimas can be explained by passage through several past resonances. In all cases, escape from the resonance occurs by unstable growth of the libration angle, sometimes with the help of a secondary resonance. Explanation of the current eccentricity of Mimas by evolution through these resonances implies that the Q of Saturn is below 100,000. Though the eccentricity of Enceladus can be excited to moderate values by capture in the Mimas-Enceladus 3:2 e-Enceladus resonance, the libration amplitude damps and the system does not escape. Thus past occupancy of this resonance and consequent tidal heating of Enceladus is excluded. The construction of a coherent history places constraints on the allowed values of k₂/Q for the satellites.