Saturn's icy satellites: Thermal and structural models

Thermal histories of the small icy Saturnian satellites Mimas, Tethys, Dione, Rhea, and Iapetus are constructed by assuming that they formed as homogeneous ice-silicate mixtures. The models include effects of radiogenic and accretional heating, conductive and subsolidus convective heat transfer, and lithospheric growth. Accretional heating is unlikely to have melted the water ice in the interiors of these bodies and solid state creep of the predominately ice material precludes melting by radiogenic heating. Mimas is so small that its thermal evolution is essentially purely conductive; at present it is a cold, nearly isothermal body. Any subsolidus convection or thermal activity in Mimas would have been confined to a brief period in its early history and would have been due to a warm formation. The four largest satellites are big enough and contain sufficient heat-producing silicates that solid state convection beneath a rigid lithosphere is inevitable independent of initial conditions. Dione and Rhea have convective interiors for most of their thermal histories, while Tethys and Iapetus have mainly conductive thermal histories with early periods of convective 0activity. The thermal histories of the five satellites for the last 4 by are independent of initial conditions; at present they have cold, conductive interiors. The model thermal histories are qualitatively consistent with the appearances of these satellites: Mimas has an ancient heavily cratered surface, Tethys and probably Iapetus have both heavily cratered and more lightly cratered areas, and Dione and Rhea have extensively modified surfaces. Because of their similar sizes and densities, Mimas and Enceladus are expected to have similar surfaces and thermal histories, but instead Enceladus has the most modified surface of all the small icy Saturnian satellites. Our results suggest a heat source for Enceladus, in addition to radiogenic and accretional heating; tidal dissipation is a possibility. Because the water ice in these bodies does not melt, resurfacing must be accomplished by the melting of a low-melting-temperature minor component such as ammonia hydrate.     

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.     

On the stability of hypothetical satellites coorbital to Mimas or Enceladus

In the present work, we study the stability of hypothetical satellites that are coorbital with Enceladus and Mimas. We performed numerical simulations of 50 particles around the triangular Lagrangian equilibrium points of Enceladus and Mimas taking into account the perturbation of Mimas, Enceladus, Tethys, Dione, Titan and the oblateness of Saturn. All particles remain on tadpole orbits after 10 000 yr of integration. Since in the past the orbit of Enceladus and Mimas expanded due to the tidal perturbation, we also simulated the system with Enceladus and Mimas at several different values of semimajor axes. The results show that in general the particles remain on tadpole orbits. The exceptions occur when Enceladus is at semimajor axes that correspond to 6:7, 5:6 and 4:5 resonances with Mimas. Therefore, if Enceladus and Mimas had satellites librating around their Lagrangian triangular points in the past, they would have been removed if Enceladus crossed one of these first-order resonances with Mimas.     

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.     

The orbital-thermal evolution and global expansion of Ganymede

The tectonically and cryovolcanically resurfaced terrains of Ganymede attest to the satellite's turbulent geologic history. Yet, the ultimate cause of its geologic violence remains unknown. One plausible scenario suggests that the Galilean satellites passed through one or more Laplace-like resonances before evolving into the current Laplace resonance. Passage through such a resonance can excite Ganymede's eccentricity, leading to tidal dissipation within the ice shell. To evaluate the effects of resonance passage on Ganymede's thermal history we model the coupled orbital-thermal evolution of Ganymede both with and without passage through a Laplace-like resonance. In the absence of tidal dissipation, radiogenic heating alone is capable of creating large internal oceans within Ganymede if the ice grain size is 1 mm or greater. For larger grain sizes, oceans will exist into the present epoch. The inclusion of tidal dissipation significantly alters Ganymede's thermal history, and for some parameters (e.g. ice grain size, tidal Q of Jupiter) a thin ice shell (5 to 20 km) can be maintained throughout the period of resonance passage. The pulse of tidal heating that accompanies Laplace-like resonance capture can cause up to 2.5% volumetric expansion of the satellite and contemporaneous formation of near surface partial melt. The presence of a thin ice shell and high satellite orbital eccentricity would generate moderate diurnal tidal stresses in Ganymede's ice shell. Larger stresses result if the ice shell rotates non-synchronously. The combined effects of satellite expansion, its associated tensile stress, rapid formation of near surface partial melt, and tidal stress due to an eccentric orbit may be responsible for creating Ganymede's unique surface features.     

Crater modification and geologic activity in Enceladus' heavily cratered plains: Evidence from the impact crater distribution

Although we can observe current activity on Saturn's satellite Enceladus with Cassini, insight into past activity is best achieved (for now) through studying the impact crater distributions. Furthermore, approximation of terrain ages can only be attained through calculations using crater densities and estimations of impact rates in the saturnian system. Here we focus on what the impact crater distribution in Enceladus' heavily cratered plains can tell us about Enceladus' geologic history. We use Cassini ISS images to count craters in the heavily cratered plains on Enceladus, along with Rhea, Dione, Tethys and Mimas as references, to develop and compare their size-frequency distributions. Comparisons of our counts show that Enceladus' cratered plains distribution is unique in that it appears to have a relative deficiency of craters for diameters ?2 km and ?6 km compared to the other satellites' heavily cratered plains. Our data also indicates that the impact crater density within the cratered plains changes with latitude. Specifically, both the north and south mid-latitude regions have approximately three times higher density than the equatorial region. We hypothesize that the “missing” small and large craters in Enceladus' cratered plains is due to a combination of viscous relaxation of the larger craters, and burial of the relaxed large craters and small craters by south polar plume and possibly E-ring material. We also conclude that the spatial density distribution is not consistent with recent polar wander.     

Cassini RPWS observations of dust in Saturn's E Ring

The Cassini radio and plasma wave science (RPWS) instrument is sensitive to few-micron dust grains impacting on the spacecraft at relative speeds of order 10 km/s. Through the first year or so of operations in orbit at Saturn, the RPWS has made a number of both inclined and equatorial crossings of the E ring, particularly near the orbit of Enceladus. Assuming water ice grains, the typical size particle detected by the RPWS has a radius of a few microns. Peak impact rates of about 50 s⁻¹ are found near the orbit of Enceladus corresponding to densities of order 5×10⁻⁴ m⁻³. The variation of dust fluxes as a function of height above or below the equator is well described by a Gaussian distribution with a scale height of about 2800 km although there is usually some non-Gaussian variation near the peak fluxes suggesting some structure in the core of the ring. Offsets of the peak number densities are typically of the order of a few hundred km from the geometric equator. A near-equatorial radial profile through the orbit of Enceladus shows a sharply peaked distribution at the orbit of the moon. A size distribution averaged over several passes through the orbit of Enceladus is determined which varies as m^−2.80. The peak in dust number density at the orbit of Enceladus is consistent with previous optical measurements and strongly supports the suggestion that Enceladus is a primary source for E ring particles.     

The three-dimensional structure of Saturn’s E ring

Saturn’s diffuse E ring consists of many tiny (micron and sub-micron) grains of water ice distributed between the orbits of Mimas and Titan. Various gravitational and non-gravitational forces perturb these particles’ orbits, causing the ring’s local particle density to vary noticeably with distance from the planet, height above the ring-plane, hour angle and time. Using remote-sensing data obtained by the Cassini spacecraft in 2005 and 2006, we investigate the E-ring’s three-dimensional structure during a time when the Sun illuminated the rings from the south at high elevation angles (>15°). These observations show that the ring’s vertical thickness grows with distance from Enceladus’ orbit and its peak brightness density shifts from south to north of Saturn’s equator plane with increasing distance from the planet. These data also reveal a localized depletion in particle density near Saturn’s equatorial plane around Enceladus’ semi-major axis. Finally, variations are detected in the radial brightness profile and the vertical thickness of the ring as a function of longitude relative to the Sun. Possible physical mechanisms and processes that may be responsible for some of these structures include solar radiation pressure, variations in the ambient plasma, and electromagnetic perturbations associated with Saturn’s shadow.     

Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites

We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect each giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet’s centrifugal radius (where the specific angular momentum of the collapsing giant planet gaseous envelope achieves centrifugal balance, located at rCJ ∼ 15R_J for Jupiter and rCS ∼ 22R_S for Saturn) and an optically thin, extended outer disk out to a fraction of the planet’s Roche-lobe (R_H), which we choose to be ∼R_H/5 (located at ∼150 R_J near the inner irregular satellites for Jupiter, and ∼200R_S near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk may result from the nebula gas flowing into the protoplanet during the time of giant planet gap-opening (or cessation of gas accretion). For the sake of specificity, we use a solar composition “minimum mass” model to constrain the gas densities of the inner and outer disks of Jupiter and Saturn (and also Uranus). Our model has Ganymede at a subnebula temperature of ∼250 K and Titan at ∼100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 and 90 K, respectively.Our model has Callisto forming in a time scale ∼10⁶ years, Iapetus in 10⁶-10⁷ years, Ganymede in 10³-10⁴ years, and Titan in 10⁴-10⁵ years. Callisto takes much longer to form than Ganymede because it draws materials from the extended, low density portion of the disk; its accretion time scale is set by the inward drift times of satellitesimals with sizes 300-500 km from distances ∼100R_J. This accretion history may be consistent with a partially differentiated Callisto with a ∼300-km clean ice outer shell overlying a mixed ice and rock-metal interior as suggested by Anderson et al. (2001), which may explain the Ganymede-Callisto dichotomy without resorting to fine-tuning poorly known model parameters. It is also possible that particulate matter coupled to the high specific angular momentum gas flowing through the gap after giant planet gap-opening, capture of heliocentric planetesimals by the extended gas disk, or ablation of planetesimals passing through the disk contributes to the solid content of the disk and lengthens the time scale for Callisto’s formation. Furthermore, this model has Hyperion forming just outside Saturn’s centrifugal radius, captured into resonance by proto-Titan in the presence of a strong gas density gradient as proposed by Lee and Peale (2000). While Titan may have taken significantly longer to form than Ganymede, it still formed fast enough that we would expect it to be fully differentiated. In this sense, it is more like Ganymede than like Callisto (Saturn’s analog of Callisto, we expect, is Iapetus). An alternative starved disk model whose satellite accretion time scale for all the regular satellites is set by the feeding of planetesimals or gas from the planet’s Roche-lobe after gap-opening is likely to imply a long accretion time scale for Titan with small quantities of NH₃ present, leading to a partially differentiated (Callisto-like) Titan. The Cassini mission may resolve this issue conclusively. We briefly discuss the retention of elements more volatile than H₂O as well as other issues that may help to test our model.     

Evidence for the existence of additional small satellites of Saturn

Imaging data are presented which indicate that small satellites exist in the Saturnian system in addition to those whose orbits had been firmly established by the time of the Voyager 2 encounter with Saturn. The noise characteristics of the Voyager camera system, the images themselves, and the best current interpretation of them are discussed. No two observations could be connected with motion of a single object. The orbital distance of the object with the most convincing image was found to lie midway between the orbital radii of Mimas and Enceladus if equatorial motion is assumed. However, if the object has an inclination comparable to Mimas's (∼11^°.5°), its orbital distance could lie anywhere in the Mimas-Enceladus region. The object appeared to trail Mimas by ∼ 30° (or ∼ 180° out of phase with the “Mimas ghost”) but also trailed Enceladus by ∼ 65°, opening the possibility that the object could reside at the Enceladus L₅ point. At this position it could be a source of E-ring material and the vertical excursions due to its inclined motion (equivalent to ∼ 1 arcsec as viewed from the Earth) could provide an explanation for the vertical extent and structure of the E ring.     

Oceans in the icy Galilean satellites of Jupiter?

Equilibrium models of heat transfer by heat conduction and thermal convection show that the three satellites of Jupiter—Europa, Ganymede, and Callisto—may have internal oceans underneath ice shells tens of kilometers to more than a hundred kilometers thick. A wide range of rheology and heat transfer parameter values and present-day heat production rates have been considered. The rheology was cast in terms of a reference viscosity ν₀ calculated at the melting temperature and the rate of change A of viscosity with inverse homologous temperature. The temperature dependence of the thermal conductivity k of ice I has been taken into account by calculating the average conductivity along the temperature profile. Heating rates are based on a chondritic radiogenic heating rate of 4.5 pW kg⁻¹ but have been varied around this value over a wide range. The phase diagrams of H₂O (ice I) and H₂O + 5 wt% NH₃ ice have been considered. The ice I models are worst-case scenarios for the existence of a subsurface liquid water ocean because ice I has the highest possible melting temperature and the highest thermal conductivity of candidate ices and the assumption of equilibrium ignores the contribution to ice shell heating from deep interior cooling. In the context of ice I models, we find that Europa is the satellite most likely to have a subsurface liquid ocean. Even with radiogenic heating alone the ocean is tens of kilometers thick in the nominal model. If tidal heating is invoked, the ocean will be much thicker and the ice shell will be a few tens of kilometers thick. Ganymede and Callisto have frozen their oceans in the nominal ice I models, but since these models represent the worst-case scenario, it is conceivable that these satellites also have oceans at the present time. The most important factor working against the existence of subsurface oceans is contamination of the outer ice shell by rock. Rock increases the density and the pressure gradient and shifts the triple point of ice I to shallower depths where the temperature is likely to be lower then the triple point temperature. According to present knowledge of ice phase diagrams, ammonia produces one of the largest reductions of the melting temperature. If we assume a bulk concentration of 5 wt% ammonia we find that all the satellites have substantial oceans. For a model of Europa heated only by radiogenic decay, the ice shell will be a few tens of kilometers thinner than in the ice I case. The underlying rock mantle will limit the depth of the ocean to 80-100 km. For Ganymede and Callisto, the ice I shell on top of the H₂O-NH₃ ocean will be around 60- to 80-km thick and the oceans may be 200- to 350-km deep. Previous models have suggested that efficient convection in the ice will freeze any existing ocean. The present conclusions are different mainly because they are based on a parameterization of convective heat transport in fluids with strongly temperature dependent viscosity rather than a parameterization derived from constant-viscosity convection models. The present parameterization introduces a conductive stagnant lid at the expense of the thickness of the convecting sublayer, if the latter exists at all. The stagnant lid causes the temperature in the sublayer to be warmer than in a comparable constant-viscosity convecting layer. We have further modified the parameterization to account for the strong increase in homologous temperature, and therefore decrease in viscosity, with depth along an adiabat. This modification causes even thicker stagnant lids and further elevated temperatures in the well-mixed sublayer. It is the stagnant lid and the comparatively large temperature in the sublayer that frustrates ocean freezing.     

Viscosity of the lithosphere of Enceladus

High resolution Voyager II images of Enceladus reveal that some regions on its surface are highly cratered; the most heavily cratered surfaces probably date back to a period of heavy bombardment. The forms of many of the craters on Enceladus are similar to those of fresh lunar craters, but many of the craters are much shallower in depth, and the floors of some craters are bowed up. The flattering of craters and bowing up of the floors are indicative of viscous relaxation of the topography. Analysis of the forms of the flattened craters suggests that the viscosity at the top of the lithosphere, in the most heavily cratered regions, is between 10²⁴ and 10²⁵ P. The exact time scale for the collapse of the craters is not known, but probably was between 100 my and 4 gy. The flattened craters are located in distinct zones that are adjacent to zones, of similar age, where craters have not flattened. The zones where flattened craters occur possibly are regions in which the heat flow was (or is) higher than that in the adjacent terrains. Because the temperature at the top of the lithosphere of Enceladus would be less than or equal to that of Ganymede and Callisto, if it is covered by a thick regolith, and because the required viscosity on Enceladus is one to two orders of magnitude less than that for Ganymede and Callisto, it can be concluded that the lithospheric material on Enceladus is different from that of Ganymede and Callisto. Enceladus probably has a mixture of ammonia ice and water ice in the lithosphere, whereas the lithospheres of Ganymede and Callisto are composed primarily of water ice.     

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.     

The E-ring in the vicinity of Enceladus: II. Probing the moon's interior—The composition of E-ring particles

The population of Saturn's outermost tenuous E-ring is dominated by tiny water ice particles. Active volcanism on the moon Enceladus, embedded in the E-ring, has since late 2005 been known to be a major source of particles replenishing the ring. Therefore particles in the vicinity of Enceladus may provide crucial information about the dynamical and chemical processes occurring below the moon's icy surface. Here we present a statistical evaluation of more than 2000 impact ionisation mass spectra of Saturn's E-ring particles, with sizes predominantly below 1 μm, detected by the Cosmic Dust Analyser onboard the Cassini spacecraft. We focus on the identification of non-water features in spectra otherwise dominated by water ice signatures. Here we specify the categorisation of two different spectrum types, which probably represent two particle populations. Type I spectra imply pure water ice particles, whereas in Type II spectra organic compounds and/or silicate minerals are identified as impurities within the icy particles. This finding supports the hypothesis of a dynamic interaction of Enceladus' rocky core with liquid water.     

Tidal dissipation,orbital evolution,and the nature of Saturn's inner satellites

Estimates of tidal damping times of the orbital eccentricities of Saturn's inner satellites place constraints on some satellite rigidities and dissipation functions Q. These constraints favor rock-like rather than ice-like properties for Mimas and probably Dione. Photometric and other observational data are consistent with relatively higher densities for these two satellites, but require lower densities for Tethys, Enceladus, and Rhea. This leads to a nonmonotonic density distribution for Saturn's inner satellites, apparently determined by different mass fractions of rocky materials. In spite of the consequences of tidal dissipation for the orbital eccentricity decay and implications for satellite compositions, tidal heating is not an important contributor to the thermal history of any Saturnian satellite.     

Shell thickness variations and the long-wavelength topography of Titan

The long-wavelength topography of Titan has an amplitude larger than that expected from tidal and rotational distortions at its current distance from Saturn. This topography is associated with small gravity anomalies, indicating a high degree of compensation. Both observations can be explained if Titan has a floating, isostatically-compensated ice shell with a spatially-varying thickness. The spatial variations arise because of laterally-variable tidal heating within the ice shell. Models incorporating shell thickness variations result in an improved fit to the observations and a degree-two tidal Love number h_2t consistent with expectations, without requiring Titan to have moved away from Saturn. Our preferred models have a mean shell thickness of ≈100 km in agreement with the observed gravity anomalies, and a heat flux appropriate to a chondritic Titan. Shell thickness variations are eliminated by convection; we therefore conclude that Titan’s ice shell is not convecting at the present day.     

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).     

On the thermal history of Saturn’s satellites Titan and Enceladus

The thermal histories of two geologically active satellites of Saturn—Titan and Enceladus—are discussed. During the Cassini mission, it was found that there are both nitrogen-containing compounds—NH₃ and N₂-and CO₂ and CH₄ in the water plumes of Enceladus; at that, ammonia is the prevailing form. This may testify that during evolution, the material of the satellite was warmed up to T ∼ 500–600 K, when NH₃ (the form of nitrogen capable of being accreted) could only be partly converted into N₂. Contrary to Enceladus, the temperature inside Titan probably reached values higher than 800 K or even higher than 1000 K, since the process of the chemical dissociation of ammonia was completely finished on this satellite and its atmosphere contains only molecular nitrogen. While the internal heating of Titan up to high temperatures can be explained by its large mass, the heating source for Enceladus’ interior is far from evident. Such traditional heating sources as the energy of gravitational differentiation and the radiogenic heating due to shortliving ²⁶Al and ⁶⁰Fe could not be effective. The first one is because of the small size of Enceladus (RE ≈ 250 km), and the inefficiency of the second one is caused by the fact that the satellite was formed not earlier than 8–10 Myr after the formation of calcium and aluminum-enriched inclusions in carbonaceous chondrites (CAI), i.e., after ²⁶Al had completely decayed. In the present paper, we propose other heating mechanisms-the heat of long-living radioactive elements and tidal heat, which could provide the observed chemical composition of the water plumes of Enceladus rather than only the differentiation of its protomatter into the ironstone core and the ice mantle.     

Mass-radius relationships in icy satellites

Using published laboratory data for H₂O ice, we have developed a modeling technique by which the bulk density, density and temperature profile, rotational moment of inertia, central pressure, and location of the rock-ice interface can all be obtained as a function of the radius, the heliocentric distance, and the silicate composition. Models of the interiors of Callisto, Ganymede, Europa, Rhea, and Titan are given, consistent with present mass and radius data. The radius and mass of spheres of ice under self-gravitation for two different temperature classes are given (103 and 77°K). Measurements of mass, radius, and I/MR² by spacecraft can be interpreted by this model to yield substantial information about the internal structure and the ice: rock ratio of the icy satellites of Jupiter and Saturn.