Convective mixing in distant and close-in giant planets -- Dependences on the initial composition, luminosity, bloating and semi-convection

Abstract

Recent structure models of Jupiter suggest the existence of an extended region in the deep interior with a high heavy element abundance, referred to as a dilute core. This finding has led to increased interest in modelling the formation and evolution processes with the goal of understanding how and under what circumstances such a structure is formed and retained, to in turn better understand the relation between atmospheric and bulk metallicity. We modelled the evolution of giant planets, varying various parameters relevant for the convective mixing process, such as the mixing length parameter and the size of the mesh, and parameters related to the general evolution, such as the orbital distance and the initial luminosity. We in particular studied hot Jupiters and find that the effect of bloating on the mixing process is small but can in some cases inhibit convective mixing by lowering the intrinsic luminosity for a given entropy. Semi-convection can significantly lower the extent of a dilute core if it is strong enough. We find that dilute cores are unable to persist for initial luminosities much higher than 3 x 1e3 LJ for a Jupiter-like planet for the initial heavy element profiles we studied. From this we conclude that, based on our model, it is unlikely that a large number of giant planets retain a dilute core throughout their evolution, although this is dependent on the assumptions and limitations of our method. Future work should focus on improving the link between formation and evolution models so that the mixing process is accurately modelled throughout a planet's lifetime and on improving the understanding of how to model convection near radiative-convective boundaries.