A model for the interior structure, evolution, and differentiation of Callisto

The recently measured dimensionless moment of inertia (MoI) factor for Callisto of 0.3549±0.0042 (Anderson et al., 2001, Icarus, 153, 157-161) poses a problem: its value cannot be explained by a model in which Callisto is completely differentiated into an ice shell above a rock shell and an iron core such as its neighboring satellite Ganymede nor can it be explained by a model of a homogeneous, undifferentiated ice-rock satellite. We show that Callisto may be incompletely differentiated into an outer ice-rock shell in which the volumetric rock concentration is close to the primordial one at the surface and decreases approximately linearly with depth, an ice mantle mostly depleted of rock, and an about 1800 km rock-ice core in which the rock concentration is close to the close-packing limit. The ice-rock shell thickness depends on uncertain rheology parameters and the heat flow and can be roughly 50 to 150 km thick. We show that if Callisto accreted from a mix of metal bearing rock and ice and if the average size of the rocks was of the order of meters to tens of meters, then Callisto may have experienced a gradual, but still incomplete unmixing of the two components. An ocean in Callisto at a depth of 100-200 km is difficult to obtain if the ice is pure H₂O and if the ice-rock lithosphere is 100 km or more thick; a water ocean is more plausible for ice contaminated by ammonia, methane or salts; or for pure H₂O at a depth of 400-600 km.     

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.     

Convective-conductive transitions and sensitivity of a convecting ice shell to perturbations in heat flux and tidal-heating rate: Implications for Europa

We investigate the response of conductive and convective ice shells on Europa to variations of heat flux and interior tidal-heating rate. We present numerical simulations of convection in Europa's ice shell with Newtonian, temperature-dependent viscosity and tidal heating. Modest variations in the heat flux supplied to the base of a convective ice shell, ΔF, can cause large variations of the ice-shell thickness Δδ. In contrast, for a conductive ice shell, large ΔF involves relatively small Δδ. We demonstrate that, for a fluid with temperature-dependent viscosity, the heat flux undergoes a finite-amplitude jump at the critical Rayleigh number Racr. This jump implies that, for a range of heat fluxes relevant to Europa, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. We show that, as a result, modest variations in heat flux near the critical Rayleigh number can force the ice shell to switch between the thin, conductive and thick, convective configurations over a ∼10⁷-year interval, with thickness changes of up to ∼10-30 km. Depending on the orbital and thermal history, such switches might occur repeatedly. However, existing evolution models based on parameterized-convection schemes have to date not allowed these transitions to occur. Rapid thickening of the ice shell would cause radial expansion of Europa, which could produce extensional tectonic features such as fractures or bands. Furthermore, based on interpretations for how features such as chaos and ridges are formed, several authors have suggested that Europa's ice shell has recently undergone changes in thickness. Our model provides a mechanism for such changes to occur.     

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 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.     

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.     

Micrometeorite impact annealing of ice in the outer Solar System

The spectra of water ice on the surfaces of icy satellites and Kuiper Belt Objects (KBOs) indicate that the surface ice on these bodies is in a crystalline state. This conflicts with theoretical models, which predict that radiation (galactic cosmic rays and solar ultraviolet) should damage the crystalline structure of ice on geologically short timescales. Temperatures are too low in the outer Solar System for the ice to anneal, and reflectance spectra of these bodies should match those of amorphous solid water (ASW). We assess whether the kinetic energy deposited as heat by micrometeorite impacts on outer Solar System bodies is sufficient to anneal their surface ice down to a near-infrared optical depth . We calculate the kinetic energy flux from interplanetary micrometeorite impacts, including gravitational focusing. We also calculate the thermal diffusion of impact heat in various surfaces and the rate of annealing of ice. We conclude that the rate of annealing from micrometeorite impacts is sufficient to explain the crystallinity of ice on nearly all the surfaces of the saturnian, uranian and neptunian satellites. We discuss how the model can be used in conjunction with spectra of KBOs to probe dust fluxes in the Kuiper Belt.     

Ultraviolet photolysis of amino acids in a 100 K water ice matrix: Application to the outer Solar System bodies

We report the rates of decomposition by ultraviolet (UV) photolysis of four amino acids in millimeter-thick crystalline water ice matrices at 100 K to constrain the survivability of these important organic molecules within ice lying near the surfaces of outer Solar System bodies. We UV-irradiated crystalline ice samples containing known concentrations of the amino acids glycine, aspartic acid, glutamic acid, and phenylalanine, then we measured the surviving concentrations using high performance liquid chromatography (HPLC) with fluorescence detection. From these experiments, we determine photolytic decomposition rates and half-lives. The half-life varies linearly with the ice thickness for all acids studied here. For example, glycine is the most resistant to photolytic destruction with a half-life of 50, 12, and 3.7 h in 1.6, 0.28, and 0.14 mm thick ices, respectively. We explain this linear variation of half-life with thickness as a consequence of extinction, mostly due to scattering, within these macroscopically thick ice samples. Applied to low latitude surface ice on Jupiter's satellite Europa, this analysis indicates that the concentration of any of these amino acids within the top meter of similar ice will be halved within a ∼10 year timescale.     

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.