Onset of Convection affected by Internal Heating - Implications for Europa and Enceladus

Europa and Enceladus present two bodies in our Solar System that, besides Earth, contain liquid water and therefore the chance of extraterrestrial life. Regarding the state and evolution of their H₂O-layer there are still many open questions. One important mechanism is the heat transport through the outer solid ice shell. It is still unclear whether the ice shells are in a conductive state or if convection takes place. One significant parameter determining if its possible that convection can set in is the ice shell thickness which is unknown for both icy moons. Since both celestial bodies are in the vicinity of enormous planets, namely Jupiter and Saturn, they are subjected to significant tidal forces. These forces can result in additional heating of the ice shell. Due to this further energy source convection might be possible for ice shell thicknesses smaller than predicted by Rayleigh-Bénard convection.
We numerically investigate how an additional uniform internal heating affects the point for the onset of convection in a two-dimensional Cartesian system that is also heated from below. The point for the onset of convection is characterized by the critical Rayleigh number that describes the strength of convection. With an increasing internal heat production rate, the critical Rayleigh number decreases, meaning that less force is required to initiate convection compared to a purely basally heated system. Furthermore, we use these results to derive corresponding minimum ice shell thicknesses. Depending on the viscosity of the ice, we find values between 8 km and 83 km for a system without internal heating that are reduced to 1.5 km to 15 km for the largest investigated heating rate for Europa. For Enceladus, our results yield thicknesses of 22 km to 223 km (no heating) down to 3 km to 30 km (largest heating). Comparing these values to actual estimations of the ice shell thickness for the moons exhibit a realistic chance for Europa’s ice shell to convect but only a small likelihood for Enceladus’ ice shell.