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.     

Thermal convection in ice-I shells of Titan and Enceladus

Cassini-Huygens observations have shown that Titan and Enceladus are geologically active icy satellites. Mitri and Showman [Mitri, G., Showman, A.P., 2005. Icarus 177, 447-460] and McKinnon [McKinnon, W.B., 2006. Icarus 183, 435-450] investigated the dynamics of an ice shell overlying a pure liquid-water ocean and showed that transitions from a conductive state to a convective state have major implications for the surface tectonics. We extend this analysis to the case of ice shells overlying ammonia-water oceans. We explore the thermal state of Titan and Enceladus ice-I shells, and also we investigate the consequences of the ice-I shell conductive-convective switch for the geology. We show that thermal convection can occur, under a range of conditions, in the ice-I shells of Titan and Enceladus. Because the Rayleigh number Ra scales with δ³/ηb, where δ is the thickness of the ice shell and ηb is the viscosity at the base of the ice-I shell, and because ammonia in the liquid layer (if any) strongly depresses the melting temperature of the water ice, Ra equals its critical value for two ice-I shell thicknesses: for relatively thin ice shell with warm, low-viscosity base (Onset I) and for thick ice shell with cold, high-viscosity base (Onset II). At Onset I, for a range of heat fluxes, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. Switches between these states can cause large, rapid changes in the ice-shell thickness. For Enceladus, we demonstrate that an Onset I transition can produce tectonic stress of ∼500 bars and fractures of several tens of km depth. At Onset II, in contrast, we demonstrate that zero equilibrium states exist for a range of heat fluxes. For a mean heat flux within this range, the satellite experiences oscillations in surface heat flux and satellite volume with periods of ∼50-800 Myr even when the interior heat production is constant or monotonically declining in time; these oscillations in the thermal state of the ice-I shell would cause repeated episodes of extensional and compressional tectonism.     

Obliquity tides do not significantly heat Enceladus

Recently, Tyler [Tyler, R.H., 2009. Geophys. Res. Lett. 36, L15205; Tyler, R., 2011. Icarus, 211, 770-779] proposed that the tide due to an obliquity of greater than 0.1° might drive resonant flow in a liquid ocean at Enceladus, and that dissipation of the ocean’s kinetic energy may be an alternate source for the observed global heat flux. While there is currently no measurement of Enceladus’ obliquity, dissipation is expected to drive the spin pole to a Cassini state. Under this assumption, we find that Enceladus should occupy Cassini state 1 and that the obliquity of Enceladus should be less than 0.0015° for values of the degree-2 gravity coefficient C_2,2 between 1.0 × 10⁻³ and 2.5 × 10⁻³. Unless there is a significant free obliquity or the gravity coefficient C_2,2 has been significantly overestimated, it is unlikely that obliquity-driven flow in a subsurface ocean is the source of the extreme heat on Enceladus.     

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.     

Thermal evolution of Pluto and implications for surface tectonics and a subsurface ocean

Determining whether or not Pluto possesses, or once possessed, a subsurface ocean is crucial to understanding its astrobiological potential. In this study we use a 3D convection model to investigate Pluto’s thermal and spin evolution, and the present-day observational consequences of different evolutionary pathways. We test the sensitivity of our model results to different initial temperature profiles, initial spin periods, silicate potassium concentrations and ice reference viscosities. The ice reference viscosity is the primary factor controlling whether or not an ocean develops and whether that ocean survives to the present day. In most of our models present-day Pluto consists of a convective ice shell without an ocean. However if the reference viscosity is higher than 5 × 10¹⁵ Pa s, the shell will be conductive and an ocean should be present. For the nominal potassium concentration the present-day ocean and conductive shell thickness are both about 165 km; in conductive cases an ocean will be present unless the potassium content of the silicate mantle is less than 10% of its nominal value. If Pluto never developed an ocean, predominantly extensional surface tectonics should result, and a fossil rotational bulge will be present. For the cases which possess, or once possessed, an ocean, no fossil bulge should exist. A present-day ocean implies that compressional surface stresses should dominate, perhaps with minor recent extension. An ocean that formed and then re-froze should result in a roughly equal balance between (older) compressional and (younger) extensional features. These predictions may be tested by the New Horizons mission.     

Tidal dissipation in the solid cores of the major planets

If the orbital resonances in the Jovian and Saturnian satellite systems are the result of orbital evolution due to tidal dissipation then the present rates of energy dissipation ($\text{E}\text{dot}$) are >2 × 10²⁰ ergs sec^?1 (Jupiter) and ?2 × 10¹⁶ ergs sec^?1 (Saturn). These values of $\text{E}\text{dot}$ can be accounted for if the planets have rocky cores with volumes equal to those suggested by current models of the interiors and if the material of these cores is both solid and imperfectly elastic (Q_e ～ 34). The calculated values of Q_e are not strongly dependent on either the rigidity of the core or the densities of the core and the mantle. Thus, these quantities need not be known precisely. It may be significant that approximately the same value of Q_e is needed for all the major planets (Jupiter, Saturn, and Uranus) even though the values of $\text{E}\text{dot}$ for these planets differ by a factor greater than 10⁴.     

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.     

Mass and interior of Enceladus from Cassini data analysis

Gravity results are available from radio Doppler data acquired by the Deep Space Network during the encounter of the Cassini spacecraft with Enceladus in February 2005. We report the mass of Enceladus to be (1.0798±0.0016)×¹⁰²⁰ kg, which implies a density of . For a core made of hydrated silicates with a density of 2500 kg m⁻³ the core radius is ∼190 km and the quadrupole moment C₂₂∼1.4×¹⁰⁻³. If Enceladus is in hydrostatic equilibrium, the larger than previously anticipated density implies that the recently proposed secondary spin-orbit resonance cannot be present. Therefore, the source of endogenic activity of Enceladus remains unexplained.     

Effects of low-viscous layers and a non-zero obliquity on surface stresses induced by diurnal tides and non-synchronous rotation: The case of Europa

In this study we present a semi-analytical Maxwell-viscoelastic model of the variable tidal stress field acting on Europa’s surface. In our analysis, we take into account surface stresses induced by the small eccentricity of Europa’s orbit, the non-zero obliquity of Europa’s spin axis - both acting on a diurnal 3.55-days timescale - and the reorientation of the ice shell as a result of non-synchronous rotation (NSR). We assume that Europa’s putative ocean is covered by an ice shell, which we subdivide in a low-viscous and warm lower ice layer (asthenosphere, viscosity 10¹²-10¹⁷ Pa s), and a high-viscous and cold upper ice layer (lithosphere, viscosity 10²¹ Pa s).Viscoelastic relaxation influences surface stresses in two ways: (1) through viscoelastic relaxation in the lithosphere and (2) through the viscoelastic tidal response of Europa’s interior. The amount of relaxation in the lithosphere is proportional to the ratio between the period of the forcing mechanism and the Maxwell time of the high-viscous lithosphere. As a result, this effect is only relevant to surface stresses caused by the slow NSR mechanism. On the other hand, the importance of the viscoelastic response on surface stresses is proportional to the ratio between the relaxation time (τ_j) of a given viscoelastic mode j and the period of the forcing function. On a diurnal timescale the fast relaxation of transient modes related to the low viscosity of the asthenosphere can alter the magnitude and phase shift of the diurnal stress field at Europa’s surface. The effects are largest, up to 20% in magnitude and 7° in phase for ice rigidities lower than 3.487 GPa, when the relaxation time of the aforementioned transient modes approaches the inverse of the average angular rate of Europa’s orbit. On timescales relevant for NSR (>10⁴ years) the magnitude and phase shift of NSR surface stresses can be affected by viscoelastic relaxation of the ocean-ice boundary. This effect, however, becomes only important when the behavior of the lithosphere w.r.t. NSR approaches the fluid limit, i.e. for strong relaxation in the lithosphere. The combination of NSR and diurnal stresses for different amounts of viscoelastic relaxation of NSR stresses in the lithosphere leads to a large variety of global stress fields that can explain the formation of the large diversity of lineament morphologies observed on Europa’s surface. Variation of the amount of relaxation in the lithosphere is likely due to changes in the spin rate of Europa and/or the rheological properties of the surface.In addition, we show that a small obliquity(<1°) can have a considerable effect on Europa’s diurnal stress field. A non-zero obliquity breaks the symmetric distribution of stress patterns with respect to the equator, thereby affecting the magnitude and orientation of the principal stresses at the surface. As expected, increasing the value of Europa’s obliquity leads to larger diurnal stresses at the surface, especially when Europa is located 90° away from the nodes formed by the intersection of its orbital and equatorial planes.     

Tidal dynamical considerations constrain the state of an ocean on Enceladus

In previous work, solutions to the non-dissipative Laplace Tidal Equations (LTE) were used to provide bounds on the heat generated by the response of a subsurface ocean on Enceladus to an obliquity component of tidal forces. Here we improve these bounds using solutions from the LTE with a generic dissipation term explicitly added. We find solutions for a wider range of ocean tidal responses that include both unstratified (barotropic) and stratified (baroclinic) flow responses to obliquity as well as eccentricity components of the tidal forces. We consolidate the results in three ocean tidal scenarios on Enceladus that can explain the high heat fluxes (∼7 mW/m² globally averaged) inferred from measurements by the Cassini spacecraft: (1) a deep (1-50 km) barotropic ocean responding to obliquity tidal forces, where obliquity is at least 0.1°; (2) a shallow (∼360 m) barotropic ocean responding to eccentricity tidal forces; (3) a stratified (baroclinic) ocean responding to eccentricity tidal forces where the density-weighted “equivalent depth” (typically much smaller than the ocean’s physical depth) is near 360 m. The ocean is assumed to be global, but extensions for a semi-global case are also described. A more general result which is independent of the specific scenarios proposed is that an ocean attempting to freeze (with an associated decrease in its liquid depth, which affects the ocean’s dynamical response to the tidal forcing) must first pass through resonant configurations with a greatly increased generation of ocean tidal heat (exceeding 1 W/m² to 1 kW/m²) that would act to halt further freezing and stagnate the ocean state in this configuration so long as there is still orbital energy to provide the tidal forces. With an additional assumption that the ocean has evolved from a more energetic state where the depth of the liquid ocean was greater, we obtain the three scenarios proposed.     

Tidal rigidity of phobos

The Martian satellites Phobos and Deimos move along nearly circular coplanar, stable orbits and have created surfaces older than ～ 10⁹ years. The accretion hypothesis suggests that their primordial orbits were also very regular. However, tides raised on Mars and Phobos can substantially alter the semimajor axis a of Phobos' orbit over time. The effect of the Martian tidal torque alone on Phobos' orbit implies that the primordial e was ～0.1 to 0.2 about 4.6 × 10⁹ years ago if the present observed e = 0.015 is naively interpreted as a tidally damped remnant. Significant tidal friction in Phobos reduces the time scale for Phobos to achieve a crossing orbit with Deimos to less than 10⁹ years and permits the primodial e to approach unity. The consequences of orbital intersections cannot easily be resolved by assuming either a catastrophic origin for both satellites (namely, that both are fragments of a common parent body fractured by an impact) or that they were captured sequentially by Mars. Either hypothesis is difficult to accept, given that Deimos' orbit, which is only slightly affected by tides, is now so regular. An alternative scenario is proposed in this paper in which the observed e of Phobos results from several gravitational resonance excitations within the last 10⁹ years, assuming tidal friction in Phobos has had only a small effect on its orbit. In facr, both the primordial e and the inclination i may have been much smaller than presently observed. The constraints imposed on tidal friction in Phobos by both the apparent age of Phobos' surface (> 10⁹yrs) and the above scenario can be satisfied only of μQ > 10¹²dynes/cm². Since the Q factor is ～10², the rigidity μ > 10¹⁰dynes/cm². Thus Phobos should have substantial internal strength.     

Enceladus: A hypothesis for bringing both heat and chemicals to the surface

The eruptive plumes and large heat flow (～15 GW) observed by Cassini in the South Polar Region of Enceladus may be expressions of hydrothermal activity inside Enceladus. We hypothesize that a subsurface ocean is the heat reservoir for thermal anomalies on the surface and the source of heat and chemicals necessary for the plumes. The ocean is believed to contain dissolved gases, mostly CO₂ and is found to be relatively warm (～0 °C). Regular tidal forces open cracks in the icy crust above the ocean. Ocean water fills these fissures. There, the conditions are met for the upward movement of water and the dissolved gases to exsolve and form bubbles, lowering the bulk density of the water column and making the pressure at its bottom less than that at the top of the ocean. This pressure difference drives ocean water into and up the conduits toward the surface. This transportation mechanism supports the thermal anomalies and delivers heat and chemicals to the chambers from which the plumes erupt. Water enters these chambers and there its bubbles pop and loft an aerosol mist into the ullage. The exiting plume gas entrains some of these small droplets. Thus, nonvolatile chemical species in ocean water can be present in the plume particles. A CO₂ equivalent-gas molar fraction of ～4 × 10^?4 for the ocean is sufficient to support the circulation. A source of heat is needed to keep the ocean warm at ～0 °C (about two degrees above its freezing point). The source of heat is unknown, but our hypothesis is not dependent on any particular mechanism for producing the heat.     

Impact-induced N2 production from ammonium sulfate: Implications for the origin and evolution of N2 in Titan’s atmosphere

Chemical reactions and volatile supply through hypervelocity impacts may have played a key role for the origin and evolution of both planetary and satellite atmospheres. In this study, we evaluate the role of impact-induced N₂ production from reduced nitrogen-bearing solids proposed to be contained in Titan’s crust, ammonium sulfate ((NH₄)₂SO₄), for the replenishment of N₂ to the atmosphere in Titan’s history. To investigate the conversion of (NH₄)₂SO₄ into N₂ by hypervelocity impacts, we measured gases released from (NH₄)₂SO₄ that was exposed to hypervelocity impacts created by a laser gun. The sensitivity and accuracy of the measurements were enhanced by using an isotope labeling technique for the target. We obtained the efficiency of N₂ production from (NH₄)₂SO₄ as a function of peak shock pressure ranging from ∼8 to ∼45 GPa. Our results indicate that the initial and complete shock pressures for N₂ degassing from (NH₄)₂SO₄ are ∼10 and ∼25 GPa, respectively. These results suggest that cometary impacts on Titan (i.e., impact velocity v_i > ∼8 km/s) produce N₂ efficiently; whereas satellitesimal impacts during the accretion (i.e., v_i < 4 km/s) produce N₂ only inefficiently. Even when using the proposed small amount of (NH₄)₂SO₄ content in the crust (∼4 wt.%) (Fortes, A.D. et al., 2007. Icarus 188, 139-153), the total amount of N₂ provided through cometary impacts over 4.5 Ga reaches ∼2-6 times the present atmospheric N₂ (i.e., ∼7 × 10²⁰-2 × 10²¹ [mol]) based on the measured production efficiency and results of a hydrodynamic simulation of cometary impacts onto Titan. This implies that cometary impacts onto Titan’s crust have the potential to account for a large part of the present N₂ through the atmospheric replenishment after the accretion.     

Laboratory kinetics of C2H radical reactions with ethane, propane, and n-butane at T = 96-296 K: implications for Titan

The kinetics of the reactions of C₂H radical with ethane (k₁), propane (k₂), and n-butane (k₃) are studied over the temperature range of T = 96-296 K with a pulsed Laval nozzle apparatus that utilizes a pulsed laser photolysis-chemiluminescence technique. The C₂H decay profiles in the presence of both the alkane reactant and O₂ are monitored by the CH(A²Δ) chemiluminescence tracer method. The results, together with available literature data, yield the following Arrhenius expressions: k₁(T) = (0.51 ± 0.06) × 10⁻¹⁰ exp[(−76 ± 30)K/T] cm³ molecule⁻¹ s⁻¹ (T = 96-800 K), k₂(T) = (0.98 ± 0.32) × 10⁻¹⁰exp[(−71 ± 60)K/T] cm³ molecule⁻¹ s⁻¹ (T = 96-361 K), and k₃(T) = (1.23 ± 0.26) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ (T = 96-297 K). At T = 296 K, k₁ is measured as a function of total pressure and has little or no pressure dependence. The results from this work support a direct hydrogen abstraction mechanism for the title reactions. Implications to the atmospheric chemistry of Titan are discussed.     

Dione’s spectral and geological properties

We present a detailed analysis of the variations in spectral properties across the surface of Saturn’s satellite Dione using Cassini/VIMS data and their relationships to geological and/or morphological characteristics as seen in the Cassini/ISS images. This analysis focuses on a local region on Dione’s anti-saturnian hemisphere that was observed by VIMS with high spatial resolution during orbit 16 in October 2005. The results are incorporated into a global context provided by VIMS data acquired within Cassini’s first 50 orbits. Our results show that Dione’s surface is dominated by at least one global process. Bombardment by magnetospheric particles is consistent with the concentration of dark material and enhanced CO₂ absorption on the trailing hemisphere of Dione independent of the geology. Local regions within this terrain indicate a special kind of resurfacing that probably is related to large-scale impact process. In contrast, the enhanced ice signature on the leading side is associated with the extended ejecta of the fresh impact crater Creusa (∼49°N/76°W). Although no geologically active regions could be identified, Dione’s tectonized regions observed with high spatial resolution partly show some clean H₂O ice implying that tectonic processes could have continued into more recent times.     

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.     

Ion and neutral sources and sinks within Saturn's inner magnetosphere: Cassini results

Using ion-electron fluid parameters derived from Cassini Plasma Spectrometer (CAPS) observations within Saturn's inner magnetosphere as presented in Sittler et al. [2006a. Cassini observations of Saturn's inner plasmasphere: Saturn orbit insertion results. Planet. Space Sci., 54, 1197-1210], one can estimate the ion total flux tube content, N_IONL², for protons, H⁺, and water group ions, W⁺, as a function of radial distance or dipole L shell. In Sittler et al. [2005. Preliminary results on Saturn's inner plasmasphere as observed by Cassini: comparison with Voyager. Geophys. Res. Lett. 32(14), L14S04), it was shown that protons and water group ions dominated the plasmasphere composition. Using the ion-electron fluid parameters as boundary condition for each L shell traversed by the Cassini spacecraft, we self-consistently solve for the ambipolar electric field and the ion distribution along each of those field lines. Temperature anisotropies from Voyager plasma observations are used with (T_⊥/T_∥)_W⁺∼5 and (T_⊥/T_∥)_H⁺∼2. The radio and plasma wave science (RPWS) electron density observations from previous publications are used to indirectly confirm usage of the above temperature anisotropies for water group ions and protons. In the case of electrons we assume they are isotropic due to their short scattering time scales. When the above is done, our calculation show N_IONL² for H⁺ and W⁺ peaking near Dione's L shell with values similar to that found from Voyager plasma observations. We are able to show that water molecules are the dominant source of ions within Saturn's inner magnetosphere. We estimate the ion production rate S_ION∼10²⁷ ions/s as function of dipole L using N_H⁺, N_W⁺ and the time scale for ion loss due to radial transport τ_D and ion-electron recombination τ_REC. The ion production shows localized peaks near the L shells of Tethys, Dione and Rhea, but not Enceladus. We then estimate the neutral production rate, S_W, from our ion production rate, S_ION, and the time scale for loss of neutrals by ionization, τ_ION, and charge exchange, τ_CH. The estimated source rate for water molecules shows a pronounced peak near Enceladus’ L shell L∼4, with a value S_W∼2×10²⁸ mol/s.     

Chemical processes in Triton's atmosphere and surface

Liquid solutions of N₂ containing up to one-third CH₄ can exist on Triton's surface in regions T > 62.5°K. More generally, subsurface oceans of N₂ solution are expected to be stable beneath overlying, thermally insulating, less dense layers of the abundant light hydrocarbon products of radiochemical synthesis: C₂H₆, C₃H₈, and C₄H₁₀. Cosmic rays are the main source of energy, capable of producing synthesis of organic compounds from N₂CH₄ solutions on the surface. For baseline Triton models with R = 2500 km, ϱ = 2.1 g cm⁻³, and T_s = 65 or 55°K, respectively, 4 × 10⁻³ or 7 × 10⁻³ erg cm⁻² sec⁻¹ (49 or 87% of the total incident flux) is deposited within a few meters below the surface. Using yields from laboratory experiments, we estimate the quantities of products produced: over 4.5 billion years, the cosmic ray flux alone produces 2 to 4 m of organic product, about half of which is C₂H₆. For ocean depths <250 m, C₂H₆ will reach its saturation limit and form a surface “slick.” For ocean depths <10 km, all of the other products also oversaturate and exsolve, adding to the surface slick and/or to a denser bottom sediment. Products produced from solid N₂CH₄ mixtures will accumulate as evaporite deposits because of the rapid volatile transport (of N₂ and CH₄) over Triton's surface. The complex, reddish organic solid found in laboratory simulations is probably the source of Triton's reddish color. Estimated yields over 4.5 billion years (for 7 × 10⁻³ erg cm⁻² sec⁻¹) are 190 (C₂H₆), 58 (NH₃), 17 (HCN), 3.5 (HN₃), 2.5 (C₄H₁₀), 0.35 (CH₃CN), and 0.14 (C₂H₅N₃) g cm⁻². More basic laboratory work on the low-temperature, low-pressure solvent properties and phase equilibria of N₂-hydrocarbon systems is clearly needed.     

Exchange of ejecta between Telesto and Calypso: Tadpoles, horseshoes, and passing orbits

We have numerically integrated the orbits of ejecta from Telesto and Calypso, the two small Trojan companions of Saturn’s major satellite Tethys. Ejecta were launched with speeds comparable to or exceeding their parent’s escape velocity, consistent with impacts into regolith surfaces. We find that the fates of ejecta fall into several distinct categories, depending on both the speed and direction of launch.The slowest ejecta follow suborbital trajectories and re-impact their source moon in less than one day. Slightly faster debris barely escape their parent’s Hill sphere and are confined to tadpole orbits, librating about Tethys’ triangular Lagrange points L₄ (leading, near Telesto) or L₅ (trailing, near Calypso) with nearly the same orbital semi-major axis as Tethys, Telesto, and Calypso. These ejecta too eventually re-impact their source moon, but with a median lifetime of a few dozen years. Those which re-impact within the first 10 years or so have lifetimes near integer multiples of 348.6 days (half the tadpole period).Still faster debris with azimuthal velocity components ?10 m/s enter horseshoe orbits which enclose both L₄ and L₅ as well as L₃, but which avoid Tethys and its Hill sphere. These ejecta impact either Telesto or Calypso at comparable rates, with median lifetimes of several thousand years. However, they cannot reach Tethys itself; only the fastest ejecta, with azimuthal velocities ?40 m/s, achieve “passing orbits” which are able to encounter Tethys. Tethys accretes most of these ejecta within several years, but some 1% of them are scattered either inward to hit Enceladus or outward to strike Dione, over timescales on the order of a few hundred years.