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

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.

18 pages, 13 figures; to be published in MNRAS

References in corpus (17)

• Probing the properties of convective cores through g modes: high-order g modes in SPB and gamma Doradus stars
• Rotational mixing in low-mass stars II. Self-consistent models of Pop II RGB stars
• On differential rotation and overshooting in solar-like stars
• The spectroscopic Hertzsprung-Russell diagram of Galactic massive stars
• Three-Dimensional Simulations of Massive Stars: I. Wave Generation and Propagation
• On the Chemical Mixing Induced by Internal Gravity Waves (IGW)
• Numerical Simulations of Penetration and Overshoot in the Sun
• Convective Overshoot and Macroscopic Diffusion in Pure-Hydrogen Atmosphere White Dwarfs
• Fully compressible simulations of waves and core convection in main-sequence stars
• Solar overshoot region and small-scale dynamo with realistic energy flux
• Calibrating Core Overshooting Parameters With Two-dimensional Hydrodynamical Simulations
• Benchmarking the Multi-dimensional Stellar Implicit Code MUSIC
• Two-dimensional simulations of solar-like models with artificially enhanced luminosity -- I. Impact on convective penetration
• Two-dimensional simulations of solar-like models with artificially enhanced luminosity. II. Impact on internal gravity waves
• Two-dimensional simulations of internal gravity waves in a 5 $M_{\odot }$ Zero-Age-Main-Sequence model
• Distribution and evolution of Li abundance in red clump stars can be explained by the internal gravity waves
• Effects of stratification on overshooting and waves atop the convective core of $5M_{\odot }$ main-sequence stars