Scaling of convection in high-pressure ice layers of large icy moons and implications for habitability

Abstract

The existence of a high-pressure (HP) ice layer between the silicate core and the liquid ocean in large icy moons and ocean worlds is usually seen as a barrier to habitability, preventing a direct contact and therefore transfer of nutrients from the core to the liquid ocean. More recently, several studies challenged that hypothesis and showed that exchanges were possible under specific conditions, allowing transport of salts toward the ocean. In our study, we consider an effect not taken into account in the previous works, which is the dynamical implications of the phase equilibrium at the ice–ocean interface allowing a non-zero vertical velocity at the surface of the HP ice layer. This effect, which can be modeled as a phase change boundary condition for the ice layer, has a significant impact on the flow dynamics and enables exchanges with the ocean by fusion and crystallization at the top interface of the HP ice layer, even without partial melting in the bulk of the ice layer. For the same conditions as standard convective systems, it also leads to faster mass transfer in the bulk. These exchanges are directly linked to the melting capacity of the ice at the interface between the HP ice layer and the core, depending on the efficiency of convection in the liquid ocean. This is controlled by a dimensionless parameter noted Φ. Considering this boundary condition at the interface between the HP ice layer and the liquid ocean, we propose a scaling of the bottom temperature and the top vertical velocity as function of the Rayleigh number, in the case of a fixed heat flux from the core, a rigid or free-slip bottom boundary and various values of Φ.