Excitation of gravity waves by fingering convection, and the formation of compositional staircases in stellar interiors

TL;DR

This paper investigates the conditions under which gravity waves are excited by fingering convection in stellar interiors, focusing on the collective instability and its relevance in different stellar environments.

Contribution

It determines the specific stellar conditions, particularly Prandtl number thresholds, necessary for the collective instability to occur, extending previous models of fingering convection.

Findings

Collective instability is relevant only for Prandtl numbers around 10^{-3} or higher.

Main sequence stars are unlikely to experience this instability due to low Prandtl numbers.

Potential excitation of gravity waves in white dwarfs and during He core flash events.

Abstract

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. (2013) 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. (2013) and of Traxler et al. (2011b) to determine the conditions under which the collective instability may be expected. We find that it is only relevant in stellar regions which 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, both from a theoretical and from an observational point of view.