Thermal equilibrium in Europaʹs ice shell

Models of tidal-convective equilibrium for Europaʹs ice shell are computed using a laboratory-derived composite flow law for ice. Volume diffusion creep is found to dominate the flow law at equilibrium, and thus the thickness of the shell is strongly dependent on the poorly known grain size of the ice. This grain size is, however, constrained to be less than a few millimeters if equilibrium is achieved at the current eccentricity. Europaʹs ice shell cannot be thinner than about 16 km in equilibrium at present, since tidal dissipation cannot generate enough heat in such a thin shell to balance the heat transport. No conductive equilibria are found; this is likely due to the fact that most of a conductive shell must be cold if temperature gradients are to be large enough to carry the heat. A minimum eccentricity of about 0.0025 (about 1/4 the present value) below which there are no equilibria is also found.