Excitation of Gravity Waves by Fingering Convection, and the Formation of Compositional Staircases in Stellar Interiors

Fingering convection (or thermohaline convection) is a weak yet important kind of mixing that occurs in stably stratified stellar radiation zones in the presence of an inverse mean molecular weight gradient. Brown et al. recently proposed a new model for mixing by fingering convection, which contains no free parameter. and was found to fit the results of direct numerical simulations in almost all cases. Notably, however, they found that mixing was substantially enhanced above their predicted values in the few cases where large-scale gravity waves, followed by thermo-compositional layering, grew spontaneously from the fingering convection. This effect is well. known in the oceanographic context. and is attributed to the excitation of the so-called collective instability.. In this work, we build on the results of Brown et al. and of Traxler et al. to determine the conditions under which the collective instability may be expected. We find that it is only relevant in stellar regions that have a relatively large Prandtl number (the ratio of the kinematic viscosity to the thermal diffusivity), O(10(-3)) or larger. This implies that the collective instability cannot occur in main-sequence stars, where the Prandtl number is always much smaller than this (except in the outer layers of surface convection zones, where fingering is irrelevant anyway). It could in principle be excited in regions of high electron degeneracy, during He core flash, or in the interiors of white dwarfs. We discuss the implications of our findings for these objects, from both a theoretical and. an observational point of view.