Constraints on the Long-term Existence of Dilute Cores in Giant Planets

Post-Cassini ring seismology analysis suggests the existence of a stable stratification inside Saturn that extends from the center to similar to 60% of its radius, in what is recognized today as Saturn's dilute core. Similarly, gravity measurements on Jupiter suggest the existence of a dilute core of weekly constrained radial extent. These cores are likely in a double-diffusive regime, which prompts the question of their long-term stability. Indeed, previous direct numerical simulation (DNS) studies in triply periodic domains have shown that, in some regimes, double-diffusive convection tends to spontaneously form shallow convective layers, which coarsen until the region becomes fully convective. In this paper, we study the conditions for layering in double-diffusive convection using different boundary conditions, in which temperature and composition fluxes are fixed at the domain boundaries. We run a suite of DNSs varying microscopic diffusivities of the fluid and the strength of the initial stratification. We find that convective layers still form as a result of the previously discovered gamma-instability, which takes place whenever the local stratification drops below a critical threshold that only depends on the fluid diffusivities. We also find that the layers grow once formed, eventually occupying the entire domain. Our work thus recovers the results of previous studies, despite the new boundary conditions, suggesting that this behavior is universal. The existence of Saturn's stably stratified core, today, therefore suggests that this threshold has never been reached, which places a new constraint on scenarios for the planet's formation and evolution.