Thermal convection in the outer shell of large icy satellites

Evolution of large icy satellites is controlled by heat transfer across the outer ice I layer. After the core overturn a possible structure consists o f a silicate core and a shell of molten ices. As the satellite cools down, the primordial ocean crystallizes. If the outer layer is thick enough, conv ection is very likely to occur in it. We have used the results of a recent two-dimensional numerical model of convection including variable viscosity to estimate the vigor and the efficiency of convection in this layer, Visco sity variations induce the apparition of a stagnant lid at the top of the f luid, which reduces the efficiency of heat transfer. In the present study, the Rayleigh number Ra and the heat flux Phi are computed as a function of the thickness of the layer, assuming that the ice flow is Newtonian. Calcul ations are first made for a generic satellite of radius R = 2500 km and mea n density [rho] = 1.9 g/cm(3). It is then shown that variations of +/-500 k m on the radius and +/-0.5 g/cm(3) on the mean density do not induce signif icant differences in the values of Ra and Phi. On the other hand, variation s of the reference viscosity mu (o), and of the activation energy E induce major differences. The reference viscosity is equal to the viscosity close to the melting point, and its possible value yields around mu (o) = 5x10(13 ) pa s. A possible value of E is 60 kJ/mol, For these values of the rheolog ical parameters we find that the initial ocean may crystallize completely i n similar to3.6 Gyr. Higher values of mu (o) and/or E reduce significantly the vigor and the efficiency of convection. The influence of the compositio n of the initial ocean is also investigated. The presence of ammonia reduce s the convective strength and the heat flux. The upper structure of icy sat ellites is discussed as a function of the rheological and compositional par ameters, The presence of a sub-surface ocean could be explained by either t he presence of volatiles in the initial ocean or the presence of additional heat sources, such as tidal dissipation.