MHD effects on fingering convection in stars: the problem with parasites

Fingering convection is an important source of mixing in stars, which are low Prandtl number fluids. Quantifying transport by fingering convection is therefore crucial to a better understanding of stellar evolution. In the absence of magnetic fields, Brown et al. have shown that fingering-induced fluxes measured in DNS are well-predicted by a so-called "parasitic" model, in which the primary fingering instability is assumed to saturate due to the growth of secondary shear instabilities between the fingers. Recent work [Harrington & Garaud, ApJ 2019] extended this analysis to include a vertical magnetic field, and found that a similar parasitic model could account for the increase in turbulent fluxes with magnetic field strength observed in simulations. However, this analysis was limited to a small region of parameter space. Here we show that lowering the magnetic Prandtl number and exploring a broader range of stratifications reveals discrepancies between the parasitic saturation model and the DNS results. We propose some explanations, and discuss implications of our findings for other systems where parasitic saturation models are used, such as the MRI in accretion disks and GSF instability in stars.