  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.
