Constraints on the long-term existence of dilute cores in giant planets

TL;DR

This study investigates the stability and layering behavior of dilute cores in giant planets like Saturn and Jupiter through direct numerical simulations, revealing conditions under which these cores can persist or evolve over time.

Contribution

It demonstrates that the gamma-instability leads to layer formation in double-diffusive convection under various boundary conditions, providing new constraints on planetary core evolution.

Findings

Convective layers form due to gamma-instability when stratification drops below a critical threshold.

Layers grow and eventually occupy the entire domain, indicating a universal behavior.

Saturn's current stable core suggests this threshold has not been reached, informing planetary formation models.

Abstract

Ring seismology has recently revealed the presence of internal gravity waves inside Saturn that extend up to 60% of Saturn's radius starting from the center, in what is recognized today as Saturn's stably-stratified dilute core. Similarly, gravity measurements on Jupiter suggest the existence of a dilute core of still poorly constrained radial extent. These cores are likely in a double-diffusive regime, which prompt the question of their long-term stability. Indeed, previous DNS (Direct Numerical Simulations) 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 letter, 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 DNS 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.