One‐Dimensional Convective Thermal Evolution Calculation Using a Modified Mixing Length Theory: Application to Saturnian Icy Satellites

Solid‐state thermal convection plays a major role in the thermal evolution of solid planetary bodies. Solving the equation system for thermal evolution considering convection requires 2‐D or 3‐D modeling, resulting in large calculation costs. A 1‐D calculation scheme based on mixing length theory (MLT) requires a much lower calculation cost and is suitable for parameter studies. A major concern for the MLT scheme is its accuracy due to a lack of detailed comparisons with higher dimensional schemes. In this study, I quantify its accuracy via comparisons of thermal profiles obtained by 1‐D MLT and 3‐D numerical schemes. To improve the accuracy, I propose a new definition of the mixing length ( l ), which is a parameter controlling the efficiency of heat transportation due to convection, for a bottom‐heated convective layer. Adopting this new definition of l , I investigate the thermal evolution of Saturnian icy satellites, Dione and Enceladus, under a wide variety of parameter conditions. Calculation results indicate that each satellite requires several tens of GW of heat to possess a thick global subsurface ocean suggested from geophysical analyses. Dynamical tides may be able to account for such an amount of heat, though the reference viscosity of Dione's ice and the ammonia content of Dione's ocean need to be very high. Otherwise, a thick global ocean in Dione cannot be maintained, implying that its shell is not in a minimum stress state.