3D Simulations of Convective Entrainment in Gas Giants: Rotation and Decreasing Luminosity as Barriers to Mixing

Observations from Juno and Cassini suggest that Jupiter and Saturn may possess fuzzy cores -- central regions where the abundance of heavy elements varies smoothly with depth. Such gradients pose a longstanding puzzle for models of planetary evolution and formation, which predict that vigorous convection would homogenize the interior of gas giants within the first $\sim 10^6$--$10^8~\mathrm{years}$ of cooling. Previous 3D simulations and analytic predictions for the propagation of a convection zone into a stable region have demonstrated that the rapid rotation of gas giants can significantly slow convective mixing, but not enough to stop it. Another piece of the puzzle is luminosity. Gas giants cool as they age, and with that comes a declining heat flux over time. Recent ideas suggest that when this declining luminosity is combined with rotational effects, convection may stall. We explore this possibility using 3D hydrodynamic simulations that include both rotation and a surface cooling flux that decreases as $1/t$. Our results demonstrate that, even without rotation, a declining luminosity can suppress mixing sufficiently to preserve an initial compositional gradient in the deep interior of gas giants. If confirmed by more realistic simulations, this may help to explain the long-term survival of fuzzy cores.