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.
We have identified an important source of mixing in stellar radiation zones, that would arise whenever two conditions are satisfied: (1) the presence of an inverse vertical compositional gradient, and (2) the presence of densitycompensating horizontal gradients of temperature (alternatively, entropy) and composition. The former can be caused naturally by any off-center burning process, by atomic diffusion, or by surface accretion. The latter could be caused by rotation, tides, meridional flows, etc. The linear instability and its nonlinear development have been well-studied in the oceanographic context. It is known to drive the formation of stacks of fingering layers separated by diffusive interfaces, called intrusions. Using 3D numerical simulations of the process in the astrophysically-relevant region of parameter space, we find similar results, and demonstrate that the material transport in the intrusive regime can be highly enhanced compared with pure diffusion, even in systems which would otherwise be stable to fingering (thermohaline) convection.
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