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W.B. McKinnon (Dept. Earth and Planetary Sci., Washington Univ./SwRI, Boulder)
The combination of radiogenic and tidal heating in Europa's rock and metal core plus tidal heating within the floating ice shell itself leads to thickness estimates for the shell of under 20 km. For a nominal core tidal {\it Q} of 25 and the presence of a liquid iron-sulfur inner core (to allow greater flexing), the average ice shell thickness is just under 15 km. In a way, the high heat flows implied stabilize the ice shell against convective overturn. Using the temperature-dependent viscosity convection scaling of Solomatov and coworkers, I have found that convection is not initiated in ice shells under 25 km thick for ice grain sizes greater than 1 mm (grain size being the controlling parameter for grain-boundary sliding, the dominant deformation mechanism). Only if the grain size is rather small (under 0.2 mm) is the viscosity low enough that convection is possible in ice shells as thin as 10 km. This result is less forgiving than those based on earlier parameterized convection formulae, and suggests that it may be very difficult to initiate solid-state convection in shells well under 10 km thick, unless some argument can be made that warm ice should have a steady-state grain size under 0.1 mm, which seems unlikley given terrestrial experience. This suggests that diapiric instabilities on Europa may be just that, and not the manifestation of steady convection. On the other hand, one can envisage a situation in which Europa's heat flow drops (say, due to oscillation of its orbital eccentricity, or a convective fluctuation in its rock mantle), which leads to thickening of the ice shell and initiation of convection at its base. At the threshold for convective instability, the heat flow (Nusselt number) more than doubles, but the tidal heating in the (warm part of the) ice shell may increase by more than a factor of 5! Clearly, this situation is not stable, and a new steady-state configuration may arise, {\it if it exists.} In any event, this shell must thin, not thicken.