Oceans in the icy Galilean satellites of Jupiter?

Abstract

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.

Introduction

Observations of electromagnetic induction signatures at Europa and Callisto have been interpreted as indicative of sublithosphere liquid water oceans in these satellites Khurana et al 1998, Neubauer 1998, Kivelson et al 1999, Kivelson et al 2000, Zimmer et al 2000. The magnetic field data gathered during several close fly-bys of Ganymede have also been proposed to be in part due to induction in an ocean in this satellite as well (Kivelson et al., 2002). If these interpretations are correct, then the magnetic field data will allow estimates of the thickness of the ice layers covering the oceans. For Europa, the strength of the induced signal suggests an ocean underneath a thin ice shell a few tens of kilometers thick. Hussmann et al. (2002) have shown that tidal heating in such an ice shell can keep a subsurface europan ocean from freezing. For Ganymede and Callisto the oceans are at greater depths of 100 km or more. For Europa, the existence of an ocean underneath tens of kilometers of ice is supported by geological evidence (Pappalardo et al., 1999) and some authors favor even thinner ice layers (e.g., Greenberg et al 1998, Kattenhorn 2002. Similar geologic evidence is not available for Ganymede and Callisto. At least for Callisto, the inferred existence of an ocean is surprising since this satellite is incompletely differentiated Anderson et al 2001, Sohl et al 2002 and shows little sign of past endogenic activity (as witnessed by its old surface).

Subsurface oceans on satellites are possible because of the anomalous melting behavior of ice I for which the melting temperature decreases with pressure until it joins the ice I/ice II transition and the ice III melting curve in a triple point at a pressure of 207 MPa and a temperature of 251.15 K (Chizov, 1993; Fig. 1 ). This triple point pressure translates into different depths for the three satellites because of their differing masses and, possibly, ice shell densities. For Europa, assuming an ice shell density of 1000 kg m⁻³, a depth of 160 km is obtained, about as deep as the thickness of the water layer, which is believed to be around 150 km Anderson et al 1998, Sohl et al 2002. The depth of the minimum melting temperature is about 145 km in Ganymede if an ice shell density of 1000 kg m⁻³ is assumed. This density is reasonable since Ganymede is most likely differentiated (Anderson et al., 1996). For Callisto, the ice shell density could be about 1600 kg m⁻³ if the satellite is undifferentiated or has a mostly undifferentiated, cold and stiff outer shell. The value is calculated from the density of ice I, a concentration of rock of about 50 wt%, and a rock density of 3500 kg m⁻³. With the latter ice shell density, the depth to the triple point pressure is about 104 km. If the outer shell in Callisto were pure ice, the depth to the triple point would be about 166 km.

It is possible that the melting point is even further depressed if the ice in the satellites is not pure H₂O but contains other components such as ammonia, methane, and/or salts (e.g., Kargel, 1992). The phase diagram of the water–ammonia system is well studied (e.g., Hogenboom et al 1997, Sotin et al 1998 and can serve as a model. Ammonia hydrates are predicted condensates in the satellites of Jupiter (e.g., Lewis, 1971) and the concept of internal layers of ammonia–water liquid is well developed in the literature (see, e.g., Kargel 1998, Sotin et al 1998 for reviews). The water–ammonia liquidus temperature depends on pressure and on the concentration of ammonia in the water. The liquidus surface in a concentration–pressure–temperature phase diagram contains the points 5 wt% NH₃, P = 0.1 MPa, and T = 266.92 K; the low-pressure peritectic at 32.1 wt% NH₃, 0.1 MPa, and 176 K, and the high-pressure eutectic at 29 wt% NH₃, 170 MPa, and 176 K. The solidus up to 170 MPa is an isothermal surface at 176 K to a good approximation.

The evolution of an ice shell and ocean will depend not only on the bulk concentration of ammonia but also, to some extent, on the initial conditions. If the shell grew on top of an ocean with some initial concentration of ammonia and began from zero thickness, then the shell will be pure water ice. The composition of the ocean will be determined by the mass of the water ice removed from the ocean and the constancy of the ammonia mass. The ice shell bottom temperature will be the liquidus temperature and will be determined by the composition of the ocean and the pressure at the bottom of the lid. As the shell thickens, the shell bottom temperature will describe a path on the liquidus surface. Grasset and Sotin (1996) have suggested a possible path on the liquidus surface starting at 5 wt% NH₃, P = 0.1 MPa, and T = 266.92 K and continuing to the high-pressure eutectic at 29 wt% NH₃, 170 MPa, and 176 K (compare Fig. 1). The pressure of 170 MPa is equivalent to a depth of about 130 km on Europa, 120 km on Ganymede, and 135 km on Callisto.

If the satellite were initially at subsolidus temperatures and was warmed to reach the ammonia hydrate solidus, a partial melt would form at a temperature of 176 K and mostly independent of pressure. The composition of the liquid, under these circumstances, will be around 30 wt% ammonia, decreasing slightly with pressure, because the composition along the eutectic/peritectic is almost constant. The solid phase in the partial melt will be H₂O ice. Since the ice is less dense than the fluid, the ice will tend to float on top of the forming ocean. The rate at which the ice will separate and float will depend on the rheology and the concentration of the melt in the solid. As the temperature increases, water will dilute the melt. The increasing concentration of the melt will further the formation of an ocean by facilitating the gravitational separation of ice from the melt. The composition of the ocean once formed and the temperature at the base of the ice shell will be determined by the pressure at the base of the ice shell, the bulk concentration of ammonia, and the liquidus surface.

Since we are interested in equilibrium configurations, we will neglect any rates of separation of the ice from the liquid. Rather, we assume that ice and melt have separated and that the composition of the ocean and the temperature at the bottom of the ice shell are given by the Grasset and Sotin (1996) liquidus.

For Europa, it is possible to attribute the existence of an ocean to tidal heating. This is not possible for Ganymede and Callisto; tidal heating is negligible at their present orbital distances and eccentricities. On these satellites, oceans must be due to radiogenic heating or to heat buried at depth and released through satellite cooling. It has been speculated (e.g., Malhotra 1991, Showman and Malhotra 1997, Showman et al 1997 that Ganymede went through a phase of intense tidal heating perhaps as little as 1 Gyr ago when it passed into the present resonance through a 3:2 resonance. During such a transition, the eccentricity would have increased by as much as a factor of 10, which would have increased the heating rate by approximately a factor of 2 above the radiogenic heating rate (Spohn and Breuer, 1998).

In this paper, we will investigate the possibility of present oceans in the Galilean satellites as a consequence of an assumed heat flow from below the ocean. That heat flow may be due to radiogenic heating, tidal heating, and/or satellite cooling, but the model is general and does not a priori attribute the heat flow to a particular mechanism.