Mixing by Internal Gravity Waves in Stars: Assessing Numerical Simulations Against Theory

TL;DR

This study evaluates the effectiveness of internal gravity waves in mixing stellar material through simulations and theory, finding that current models underestimate the complexity and face numerical challenges in accurately measuring mixing rates.

Contribution

It compares theoretical predictions with hydrodynamical simulations and tracer particle methods, highlighting limitations and challenges in modeling stellar mixing by IGWs.

Findings

Neither thermal diffusion nor shearing sufficiently mix stars to correct models.

Tracer particle methods can artificially inflate diffusion coefficients.

Diffusion models may not be suitable for certain simulation timescales.

Abstract

Here we present a study of radial chemical mixing in non-rotating massive main-sequence stars driven by internal gravity waves (IGWs), based on multi-dimensional hydrodynamical simulations with the fully compressible code MUSIC. We examine two proposed mechanisms of material mixing in stars by IGWs that are commonly quoted, relating to thermal diffusion and sub-wavelength shearing. Thermal diffusion provides a non-restorative effect to the waves, leaving material displaced from its previous equilibrium, while shearing arising within the waves drives weak localised flows, mixing the fluid there. Using IGW spectra from the simulations, we evaluate theoretical predictions of mixing rates due to these mechanisms. We show, for $20M_\odot$ main-sequence stars, that neither of these mechanisms are likely to create mixing sufficient to correct inaccuracies in current stellar evolution models. Furthermore, we compare these predictions to results obtained from Lagrangian tracer particles, following a method recently used for global simulations of stellar interiors to measure mixing by IGWs in their radiative zones. We demonstrate that tracer particle methods face significant numerical challenges in measuring the small diffusion coefficients predicted by the aforementioned theories, for which they are prone to yielding artificially enhanced coefficients. Diffusion coefficients based on such methods are currently used with stellar evolution codes for asteroseismic studies, but should be viewed with caution. Finally, in a case where tracer particles do not suffer from numerical artefacts, we suggest that a diffusion model is not suitable for timescales typically considered by two-dimensional numerical simulations.