Bridging the Prandtl number gap: 3D simulations of thermohaline convection in astrophysical regimes

TL;DR

This paper demonstrates that 3D simulations of thermohaline convection can be performed at realistic stellar Prandtl numbers, confirming the validity of existing chemical mixing models across a wide parameter range, and suggesting other physics must explain observational discrepancies.

Contribution

The study extends 3D thermohaline convection simulations to stellar Prandtl numbers, validating the Brown, Garaud, & Stellmach (2013) model in realistic regimes.

Findings

Simulations at Prandtl numbers as low as 10^{-6} are feasible.

The chemical mixing model remains consistent across studied regimes.

Discrepancies with observations are not due to Prandtl number limitations.

Abstract

Thermohaline convection (also known as fingering convection or thermohaline mixing) occurs in stellar radiation zones where a sufficient inversion of the mean molecular weight is present. This process mixes chemicals radially and occurs in a variety of stars, including near the luminosity bump on the red giant branch and potentially in polluted white dwarfs. Previous efforts to characterize this process using 3D simulations have been restricted to regimes far from actual stars: The Prandtl number $\Pr$--the ratio of the kinematic viscosity to thermal diffusivity--assumes values as low as $10^{-6}$ in stars, but 3D simulations have been restricted to $\Pr \gtrsim 10^{-2}$. For this reason, disagreements between observations and simulations are routinely dismissed as stemming from this $\Pr$ gap. This letter bridges this gap and demonstrates that 3D simulations of thermohaline convection can be performed in stellar parameter regimes. Using a suite of simulations spanning previously studied regimes with $\Pr \gtrsim 10^{-2}$ down to $\Pr = 10^{-6}$, we demonstrate that the chemical mixing model of Brown, Garaud, & Stellmach (2013) remains consistent with 3D simulations across both regimes. Therefore, tensions between this model and observations cannot be dismissed as resulting from a $\Pr$ gap, and must be resolved by considering additional physics.