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.     

Thermal convection with a water ice I rheology: Implications for icy satellite evolution

We model stagnant-lid convection for water ice I using a multicomponent rheology, combining grain boundary sliding, dislocation and diffusion creep mechanisms. For the superplastic flow-dislocation creep rheology, dislocation creep (n=4) dominates the deformation within the actively convecting sublayer whilst superplastic flow (n=1.8) is the dominant process within the stagnant-lid whilst for the superplastic flow-diffusion creep rheology, superplastic flow is the dominant deformation mechanism within the convecting sublayer while diffusion creep (n=1) is the dominant deformation process in the stagnant-lid. These results suggest deformation in the actively convecting sublayer is likely to be dominated by the mechanism with the largest stress exponent. We also provide heat flux scaling relationships for the superplastic flow, basal slip, dislocation creep-superplastic flow and superplastic flow-diffusion creep rheologies and provide a simple parameterized convection model of an icy satellite thermal evolution.     

Seas under ice: Stability of liquid-water oceans within icy worlds

The present-day existence of internal oceans under the outer ice shell of several icy satellites of the Solar System has been recently proposed. The presence of antifreeze substances decreasing ice’s melting point (and tidal heating in Europa’s case) has been generally believed to allow the stability of such oceans; limited cooling of the water (ice plus liquid) layer, due to stability against convection or to stagnant lid convection in the icy shell, have been also considered. Here we propose that even pure liquid-water oceans could survive today within several icy worlds, and we consider some factors affecting thermal modeling in these bodies. So, the existence of such oceans would be a natural consequence of the physical properties of water ice, independently from the addition of antifreeze substances or any other special conditions. The inclusion of these substances would contribute to expand the conditions for water to stay liquid and to increase ocean’s volume.     

Thermal-orbital evolution of Io and Europa

Coupled thermal-orbital evolution models of Europa and Io are presented. It is assumed that Io, Europa, and Ganymede evolve in the Laplace resonance and that tidal dissipation of orbital energy is an internal heat source for both Io and Europa. While dissipation in Io occurs in the mantle as in the mantle dissipation model of Segatz et al. (1988, Icarus 75, 187), two models for Europa are considered. In the first model dissipation occurs in the silicate mantle while in the second model dissipation occurs in the ice shell. In the latter model, ice shell melting and variations of the shell thickness above an ocean are explicitly included. The rheology of both the ice and the rock is cast in terms of a viscoelastic Maxwell rheology with viscosity and shear modulus depending on the average temperature of the dissipating layer. Heat transfer by convection is calculated using a parameterization for strongly temperature-dependent viscosity convection. Both models are consistent with the present orbital elements of Io, Europa, and Ganymede. It is shown that there may be phases of quasi-steady evolution with large or small dissipation rates (in comparison with radiogenic heating), phases with runaway heating or cooling and oscillatory phases during which the eccentricity and the tidal heating rate will oscillate. Europa's ice thickness varies between roughly 3 and 70 km (dissipation in the silicate layer) or 10 and 60 km (dissipation in the ice layer), suggesting that Europa's ocean existed for geological timescales. The variation in ice thickness, including both convective and purely conductive phases, may be reflected in the formation of different geological surface features on Europa. Both models suggest that at present Europa's ice thickness is several tens of km thick and is increasing, while the eccentricity decreases, implying that the satellites evolve out of resonance. Including lithospheric growth in the models makes it impossible to match the high heat flux constraint for Io. Other heat transfer processes than conduction through the lithosphere must be important for the present Io.     

Equilibrium Convection on a Tidally Heated and Stressed Icy Shell of Europa for a Composite Water Ice Rheology

Water ice I rheology is a key factor for understanding the thermal and mechanical state of the outer shell of the icy satellites. Ice flow involves several deformation mechanisms (both Newtonian and non-Newtonian), which contribute to different extents depending on the temperature, grain size, and applied stress. In this work I analyze tidally heated and stressed equilibrium convection in the ice shell of Europa by considering a composite viscosity law which includes diffusion creep, basal slip, grain boundary sliding and dislocation creep, and. The calculations take into account the effect of tidal stresses on ice flow and use grain sizes between 0.1 and 100 mm. An Arrhenius-type relation (useful for parameterized convective models) is found then by fitting the calculated viscosity between 170 and 273 K to an exponential regression, which can be expressed in terms of pre-exponential constant and effective activation energy. I obtain convective heat flows between ~40 and ~60 mW m^?2, values lower than those usually deduced (~100 mW m^?2) from geological indicators of lithospheric thermal state, probably indicating heterogeneous tidal heating. On the other hand, for grain sizes larger than ~0.3 mm the thicknesses of the ice shell and convective sublayer are ~20–30 km and ~5–20 km respectively, values in good agreement with the available information for Europa. So, some fundamental geophysical characteristics of the ice shell of Europa could be arising from the properties of the composite water ice rheology.     

Coupled convection and tidal dissipation in Europa’s ice shell using non-Newtonian grain-size-sensitive (GSS) creep rheology

We present self-consistent, fully coupled two-dimensional (2D) numerical models of thermal evolution and tidal heating to investigate how convection interacts with tidal dissipation under the influence of non-Newtonian grain-size-sensitive creep rheology (plausibly resulting from grain boundary sliding) in Europa’s ice shell. To determine the thermal evolution, we solved the convection equations (using finite-element code ConMan) with the tidal dissipation as a heat source. For a given heterogeneous temperature field at a given time, we determined the tidal dissipation rate throughout the ice shell by solving for the tidal stresses and strains subject to Maxwell viscoelastic rheology (using finite-element code Tekton). In this way, the convection and tidal heating are fully coupled and evolve together. Our simulations show that the tidal dissipation rate can have a strong impact on the onset of thermal convection in Europa’s ice shell under non-Newtonian GSS rheology. By varying the ice grain size (1-10 mm), ice-shell thickness (20-120 km), and tidal-strain amplitude (0-4 × 10⁻⁵), we study the interrelationship of convection and conduction regimes in Europa’s ice shell. Under non-Newtonian grain-size-sensitive creep rheology and ice grain size larger than 1 mm, no thermal convection can initiate in Europa’s ice shell (for thicknesses <100 km) without tidal dissipation. However, thermal convection can start in thinner ice shells under the influence of tidal dissipation. The required tidal-strain amplitude for convection to occur decreases as the ice-shell thickness increases. For grain sizes of 1-10 mm, convection can occur in ice shells as thin as 20-40 km with the estimated tidal-strain amplitude of 2 × 10⁻⁵ on Europa.     

Effects of plasticity on convection in an ice shell: Implications for Europa

Europa's surface exhibits numerous pits, uplifts, and disrupted chaos terrains that have been suggested to result from convection in the ice shell. To test this hypothesis, we present numerical simulations of convection in an ice shell including the effects of plasticity, which provides a simple continuum representation for brittle or semibrittle deformation along discrete fractures. Plastic deformation occurs when stresses reach a specified yield stress; at lower stresses, the fluid flow follows a Newtonian, temperature-dependent viscosity. Four distinct modes of behavior can occur. For yield stresses exceeding ∼1 bar, plastic effects are negligible and stagnant-lid convection, with no surface motion and minimal topography, results. At intermediate yield stresses, a stagnant lid forms but deforms plastically, leading to surface velocities up to several millimeters per year. Slightly smaller yield stresses allow episodic, catastrophic overturns of the upper conductive lid, with (transient) stagnant lids forming in between overturn events. The smallest yield stresses allow continual recycling of the upper lid, with simultaneous, gradual ascent of warm ice to the surface and descent of cold, near-surface ice into the interior. The exact yield stresses over which each regime occurs depend on the ice-shell thickness, melting-temperature viscosity, and activation energy for viscous creep. To form hummocky matrix and translate chaos plates by several kilometers, substantial surface strain must accompany chaos formation, and the three plasticity-dominated convection modes described here can provide such deformation. Our simulations suggest that, if yield stresses of ∼0.2-1 bar are relevant to Europa, then convection in Europa's ice shell can produce chaos-like structures at the surface. However, our simulations have difficulty explaining Europa's numerous pits and uplifts. When plasticity forces the upper lid to participate in the convection, dynamic topography of ∼50-100-m amplitude results, but the topographic structures generally have diameters of 30-100 km, an order of magnitude wider than typical pits and uplifts. None of our simulations produced isolated pits or uplifts of any diameter.     

Giant impacts and the initiation of plate tectonics on terrestrial planets

Earth is the only terrestrial planet with present-day lithosphere recycling through plate tectonics. However, theoretical models of mantle convection based on general considerations find that all the terrestrial planets should be operating in the stagnant lid regime, in which the planets are one-plated and there is no lithosphere recycling. The stagnant lid regime is a consequence of the strong viscosity contrast across the convective layer, and therefore the upper lid (roughly equivalent to the lithosphere) must be sufficiently weakened in order to be mobilized. Here I propose that giant impacts could have provided the upper layer weakening required for surface recycling, and hence for plate tectonics, to initiate on the early Earth. Additionally, giant impacts originated lithosphere thickness and density differences, which might contribute to the initiation of subduction. Impacts are more energetic for Earth than for Mars, which could explain the likely early existence of plate tectonics on the Earth whereas Mars never had lithosphere recycling. On the other hand, convection on Mercury and the Moon might be sluggish or even inexistent, implying a reduced influence of giant impacts on their internal dynamics, whereas there is no record of the earliest geological history of Venus, which obscures any discussion on the influence of giant impacts on their internal dynamics.     

Tidal dissipation within large icy satellites: Applications to Europa and Titan

This paper describes a new approach based on variational principles to calculate the radial distribution of tidal energy dissipation in any satellite. The advantage of the model with respect to classical solutions, is that it relates in a straightforward way the radial distribution of the time-averaged dissipation rate to its sensitivity to the corresponding distribution of viscoelastic parameters. This method is applied to Io-, Europa-, and Titan-like interiors, and it is tested against the results obtained by two classical methods by determining global dissipation as well as radial and lateral distributions within satellite interiors. By exploring systematically the different parameters defining the interior models, we demonstrate that the presence of a deep ocean below an outer ice layer strongly influences the tidal dissipation distribution in both the outer ice layer and in the innermost part of the satellite. On the one hand, the ocean by imposing a large radial displacement at the base of the outer ice I layer, controls the distribution of tidal strain rate within the outer layer, making the tidal strain rate field very weakly sensitive to the viscosity variations. Conversely, in the high-pressure ice layer below the ocean, both tidal strain rate and dissipation are very sensitive to any variation of the ice viscosity. On the other hand, for identical structures of the mantle and of the core, the presence of a subsurface ocean reduces the strength of dissipation in the silicate mantle. The existence of a liquid layer within Europa makes models of the silicate mantle less dissipative than the predictions for Io.     

The impact of a weak south pole on thermal convection in Enceladus’ ice shell

Enceladus exhibits a strong hemispheric dichotomy of tectonism and heat flux, with geologically young, heavily tectonized terrains and a high heat flux in the South Polar Terrain (SPT) and relatively ancient terrains with presumably lower heat fluxes over the rest of the satellite. To understand the convective pattern and its relationship with surface tectonics, we present three-dimensional numerical models of convection in Enceladus’ ice shell including basal heating and tidal heating. Our thermal boundary conditions exhibit no north–south asymmetries, but because the tectonism at the SPT may weaken the ice there, we impose a mechanically weak lithosphere within the SPT. The weakening is parameterized by adopting a reduced viscosity contrast within the SPT. Without such a weak zone, convection (if any) resides in stagnant-lid mode and exhibits no hemispheric dichotomy. In the presence of such an SPT weak zone, however, we find vigorous convection in the ice underneath the SPT, with convective plumes rising close to the surface. In contrast, only stagnant lid convection, or no convection at all, occurs elsewhere over the satellite. Away from the SPT, the heat flux in our models is small (5–10 mW m^?2) and the surface strains are small enough to imply surface ages >10⁹ years. Within the SPT, however, our models yield peak heat fluxes of ～70–200 mW m^?2, implying heat flows integrated across the SPT of up to 5 GW, similar to that inferred from Cassini thermal observations. The surface strains in our models are high enough near the south pole to cause intense tectonism and imply surface ages of ～10⁶–10⁷ years, consistent with age estimates of the SPT.     

The temperature of Europa's subsurface water ocean

A 100 km deep liquid water ocean probably underlies the icy exterior of Jupiter's satellite Europa. The long-term persistence of a liquid ocean beneath an ice shell presents a thermal conundrum: Is the temperature of the ocean equal to the freezing point of water at the bottom of the ice shell, or is it equal to the somewhat warmer temperature at which water attains its maximum density? We argue that most of the ocean is at the temperature of maximum density and that the bulk of the vigorously convecting ocean is separated from the bottom of the ice shell by a thin “stratosphere” of stably stratified water which is at the freezing point, and therefore buoyant. If Europa's subsurface water ocean is warm, it could explain the widespread geologic evidence for apparent melt-through events observed on its surface and may constrain the overall age of its surface.     

The production of Ganymede's magnetic field

One of the great discoveries of NASA's Galileo mission was the presence of an intrinsically produced magnetic field at Ganymede. Generation of the relatively strong (750 nT) field likely requires dynamo action in Ganymede's metallic core, but how such a dynamo has been maintained into the present epoch remains uncertain. Using a one-dimensional, three layer thermal model of Ganymede, we find that magnetic field generation can only occur if the sulfur mass fraction in Ganymede's core is very low (?3%) or very high (?21%), and the silicate mantle can cool rapidly (i.e. it has a viscosity like wet olivine). However, these requirements are not necessarily compatible with cosmochemical and physical models of the satellite. We therefore investigate an alternative scenario for producing Ganymede's magnetic field in which passage through an eccentricity pumping Laplace-like resonance in Ganymede's past enables present day dynamo action in the metallic core. If sufficient tidal dissipation occurs in Ganymede's silicate mantle during resonance passage, silicate temperatures can undergo a runaway which prevents the core from cooling until the resonance passage ends. The rapid silicate and core cooling that follows resonance escape triggers dynamo action via thermal and/or compositional convection. To test the feasibility of this mechanism we couple our thermal model with an orbital evolution model to examine the effects of resonance passage on Ganymede's silicate mantle and metallic core. We find that, contrary to expectations, there are no physically plausible scenarios in which tidal heating in the silicates is sufficient to cause the thermal runaway necessary to prevent core cooling. These findings are robust to variations in the silicate rheology, tidal dissipation factor of Jupiter (QJ), structure of the ice shell, and the inclusion of partial melting in the silicate mantle. Resonance passage therefore appears unlikely to explain Ganymede's magnetic field and we must appeal to the special conditions described above to explain the presence of the field.     

Heat flow, lenticulae spacing, and possibility of convection in the ice shell of europa

Two opposing models to explain the geological features observed on Europa’s surface have been proposed. The thin-shell model states that the ice shell is only a few kilometers thick, transfers heat by conduction only, and can become locally thinner until it exposes an underlying ocean on the satellite’s surface. According to the thick-shell model, the ice shell may be several tens of kilometers thick and have a lower convective layer, above which there is a cold stagnant lid that dissipates heat by conduction. Whichever the case, from magnetic data there is strong support for the presence of a layer of salty liquid water under the ice. The present study was performed to examine whether the possibility of convection is theoretically consistent with surface heat flows of ∼100-200 mW m⁻², deduced from a thin brittle lithosphere, and with the typical spacing of 15-23 km proposed for the features usually known as lenticulae. It was obtained that under Europa’s ice shell conditions convection could occur and also account for high heat flows due to tidal heating of the convective (nearly isothermal) interior, but only if the dominant water ice rheology is superplastic flow (with activation energy of 49 kJ mol⁻¹; this is the rheology thought dominant in the warm interior of the ice shell). In this case the ice shell would be ∼15-50 km thick. Furthermore, in this scenario explaining the origin of the lenticulae related to convective processes requires ice grain size close to 1 mm and ice thickness around 15-20 km.     

Thermal Equilibrium States of Europa's Ice Shell: Implications for Internal Ocean Thickness and Surface Heat Flow

Ice-shell thickness and ocean depth are calculated for steady state models of tidal dissipation in Europa's ice shell using the present-day values of the orbital elements. The tidal dissipation rate is obtained using a viscoelastic Maxwell rheology for the ice, the viscosity of which has been varied over a wide range, and is found to strongly increase if an (inviscid) internal ocean is present. To determine steady state values, the tidal dissipation rate is equated to the heat-transfer rate through the ice shell calculated from a parameterized model of convective heat transfer or from a thermal conduction model, if the ice layer is found to be stable against convection. Although high dissipation rates and heat fluxes of up to 300 mWm⁻² are, in principle, possible for Europa, these values are unrealistic because the states for which they are obtained are thermodynamically unstable. Equilibrium models have surface heat flows around 20 mWm⁻² and ice-layer thicknesses around 30 km, which is significantly less than the total thickness of the H₂O-layer. These results support models of Europa with ice shells a few tens of kilometers thick and around 100-km-thick subsurface oceans.     

The influence of mantle melting on the evolution of Mars

We present a parameterized convection model of Mars by incorporating a new heat-flow scaling law for stagnant-lid convection, to better understand how the evolution of Mars may be affected by mantle melting. Melting in the mantle during convection leads to the formation of a compositionally buoyant lithosphere, which may also be intrinsically more viscous by dehydration. The consequences of these melting effects on the evolution of terrestrial planets have not been explored before. The temporal evolution of crust and lithospheric mantle is modeled in a self-consistent manner considering mantle melting, convective instability, and the rewetting of dehydrated lithosphere from below by hydrogen diffusion. Though the effect of compositional buoyancy turns out to be minimal, the introduction of viscosity contrast between wet and dry mantle can considerably slow mantle cooling and sometimes lead to non-monotonic core cooling. Furthermore, with or without dehydration stiffening, our model predicts that the martian mantle must have been degassed more extensively (>80%) than previously suggested (<10%); the loss of such a large amount of water from the mantle to surface has significant implications about the role of water in the early surface and climate evolution of Mars.     

Stagnant lid convection in the mid-sized icy satellites of Saturn

Thermal history models for the mid-sized saturnian satellites Mimas, Tethys, Dione, Iapetus, and Rhea have been calculated assuming stagnant lid convection in undifferentiated satellites and varying parameter values over broad ranges. Of all five satellites under consideration, only Dione, Rhea and Iapetus do show significant internal activities related to convective overturn for extended periods of time. The interiors of Mimas and Tethys do not convect or do so only for brief periods of time early in their thermal histories. Although we use lower densities than previous models, our calculations suggest higher interior temperatures but also thicker rigid shells above the convecting regions. Temperatures in the stagnant lid will allow melting of ammonia-dihydrate. Dione, Rhea and Iapetus may differentiate early and form early oceans, Iapetus only if ammonia is present. Mimas and Tethys with ammonia may differentiate if they accreted in an optically thick nebula with ambient temperatures around 250 K. Our models suggest that the outer shells of the satellites are largely primordial in composition even if the satellites differentiated. In these cases the deep interior may be layered with a pure ice shell underlain by an ammonia dihydrate layer and a rock core.     

Coupling the atmosphere with interior dynamics: Implications for the resurfacing of Venus

We calculated 2D and 3D mantle convection models for Venus using digitized atmosphere temperatures from the model of Bullock and Grinspoon (Bullock, M.A., Grinspoon, D.H. [2001]. Icarus 150, 19–37) to study the interaction between interior dynamics and atmosphere thermal evolution. The coupling between atmosphere and interior occurs through mantle degassing and the effect of varying concentrations of the greenhouse gas H₂O on the surface temperature. Exospheric loss of hydrogen to space is accounted for as a H₂O sink. The surface temperature enters the mantle convection model as a boundary condition.Our results suggest a self-consistent feedback mechanism between the interior and the atmosphere resulting in spatial–temporal surface renewal. Greenhouse warming of the atmosphere results in an increase in the surface temperature. Whenever the surface temperature reaches a critical value, the viscosity difference across the lithosphere becomes smaller than about 10⁵ and the surface becomes locally mobile. The critical surface temperature depends on the activation energy for mantle creep, the stress exponent in the non-Newtonian mantle rheology law, and the mantle temperature. Surface renewal together with surface lava flow may explain why the surface of Venus is young on average, i.e. not older than a few hundred million years.The mobilization of the near-surface lithosphere increases the rate of heat removal from the mantle and thereby the interior cooling rate. The enhanced cooling results in a reduction of the water outgassing rates. As a consequence of decreasing water concentrations in the atmosphere, the surface temperature decreases. Our model calculations suggest that Venus should have been geologically active until recently. This is in agreement with several lines of observational evidence from thermal emissivity measurements and crater distribution analyses.     

Viscosity of the Martian mantle and its initial temperature: Constraints from crust formation history and the evolution of the magnetic field

The rheology of the Martian mantle and the planet's initial temperature is constrained with thermal evolution models that include crust growth and test the conditions for magnetic field generation in the core. As observations we use the present-day average crustal thickness of 50-120 km as estimated from the Mars Global Surveyor gravity and topography data, the evidence for the crust being produced mostly early, with a rate declining from the Noachian to the Hesperian, and the evidence for an early magnetic field that likely existed for less than a billion years. We use the fact that the rate of crust growth is a function of temperature, which must be above the solidus in the sub-lithosphere mantle, and the mantle convection speed because the latter determines the rate at which melt can be replenished. The convection speed is a strong function of viscosity which, in turn, is a strong function of temperature and also of the water content of the mantle. We use a viscosity parameterization with a reference viscosity evaluated at 1600 K the value of which can be characteristic of either a dry or a wet mantle. We further consider the Fe-FeS phase diagram for the core and compare the core liquidus estimated for a sulphur content of 14% as suggested by the SNC meteorite compositions with the core temperatures calculated for our cooling models. Two data sets of the Fe-FeS eutectic temperature have been used that differ by about 200 K [Böhler, R., 1996. Fe-FeS eutectic temperatures at 620 kbar. Phys. Earth Planet. Inter. 96, 181-186; Fei, Y., Bertka, C.M., Finger, L.W., 1997. High-pressure iron-sulphur compound, Fe₃S₂, and melting relations in the Fe-FeS system. Science 275, 1621-1623] at Martian core-mantle boundary pressure and in the eutectic composition by 5 wt%. The differences in eutectic temperature and composition translate into a difference of about 400 K in liquidus temperature for 14 wt% sulphur.We find it premature to rule out specific mantle rheologies on the basis of the presently available crustal thickness and crust growth evidence. Rather a trade-off exists between the initial mantle temperature and the reference viscosity. Both a wet mantle rheology with a reference viscosity less than 10²⁰ Pas and a dry mantle rheology with a reference viscosity of 10²¹ Pas or more can be acceptable if initial mantle temperatures between roughly 1700 and 2000 K are allowed. To explain the magnetic field history, the differences in liquidus temperatures matter. For a liquidus temperature of about 1900 K at the Martian core-mantle boundary as calculated from the Böhler et al. eutectic, a dry mantle rheology can best explain the lack of a present-day dynamo. For a liquidus temperature of about 1500 K at the core-mantle boundary as calculated from the Fei et al. eutectic all models are consistent with the observed lack of dynamo action. The reason lies with the fact that at 14 wt% S the Martian core would be close to the eutectic composition if the Fei et al. data are correct. As inner core growth is unlikely for an almost eutectic core, the early field would have been generated by a thermally driven dynamo. Together with the measured strength of the Martian crustal magnetization this would prove the feasibility of a strong thermally driven dynamo.     

Implications of large elastic thicknesses for the composition and current thermal state of Mars

The martian elastic lithosphere thickness Te has recently been constrained by modeling the geodynamical response to loading at the martian polar caps and Te was found to exceed 300 km at the north pole today. Geological evidence suggests that Mars has been volcanically active in the recent past and we have reinvestigated the martian thermal evolution, identifying models which are consistent with Te>300 km and the observed recent magmatic activity. We find that although models satisfying both constraints can be constructed, special assumptions regarding the concentration and distribution of radioactive elements, the style of mantle convection and/or the mantle's volatile content need to be made. If a dry mantle rheology is assumed, strong plumes caused by, e.g., a strongly pressure dependent mantle viscosity or endothermic phase transitions near the core-mantle boundary are required to allow for decompression melting in the heads of mantle plumes. For a wet mantle, large mantle water contents of the order of 1000 ppm are required to allow for partial mantle melting. Also, for a moderate crustal enrichment of heat producing, elements the planet's bulk composition needs to be 25 and 50% sub-chondritic for dry and wet mantle rheologies, respectively. Even then, models resulting in a globally averaged elastic thicknesses of Te>300 km are difficult to reconcile with most elastic thickness estimates available for the Hesperian and Amazonian periods. It therefore seems likely that large elastic thicknesses in excess of 300 km are not representative for the bulk of the planet and that Te possibly shows a large degree of spatial heterogeneity.     

Subsurface oceans and deep interiors of medium-sized outer planet satellites and large trans-neptunian objects

The detection of induced magnetic fields in the vicinity of the jovian satellites Europa, Ganymede, and Callisto is one of the most surprising findings of the Galileo mission to Jupiter. The observed magnetic signature cannot be generated in solid ice or in silicate rock. It rather suggests the existence of electrically conducting reservoirs of liquid water beneath the satellites' outermost icy shells that may contain even more water than all terrestrial oceans combined. The maintenance of liquid water layers is closely related to the internal structure, composition, and thermal state of the corresponding satellite interior. In this study we investigate the possibility of subsurface oceans in the medium-sized icy satellites and the largest trans-neptunian objects (TNO's). Controlling parameters for subsurface ocean formation are the radiogenic heating rate of the silicate component and the effectiveness of the heat transfer to the surface. Furthermore, the melting temperature of ice will be significantly reduced by small amounts of salts and/or incorporated volatiles such as methane and ammonia that are highly abundant in the outer Solar System. Based on the assumption that the satellites are differentiated and using an equilibrium condition between the heat production rate in the rocky cores and the heat loss through the ice shell, we find that subsurface oceans are possible on Rhea, Titania, Oberon, Triton, and Pluto and on the largest TNO's 2003 UB₃₁₃, Sedna, and 2004 DW. Subsurface oceans can even exist if only small amounts of ammonia are available. The liquid subsurface reservoirs are located deeply underneath an ice-I shell of more than 100 km thickness. However, they may be indirectly detectable by their interaction with the surrounding magnetic fields and charged particles and by the magnitude of a satellite's response to tides exerted by the primary. The latter is strongly dependent on the occurrence of a subsurface ocean which provides greater flexibility to a satellite's rigid outer ice shell.