Chemical mixing by internal gravity waves in intermediate mass stars

Abstract

Observations have made it clear that additional mixing is needed compared to standard stellar evolution models. While convection zones are clearly well mixed, chemical mixing near convective boundaries and across radiative zone is still not well described. Over the years, different transport mechanisms were included in the stellar evolution models to explain the observed anomalies such as Nitrogen abundances in B stars (Gies & Lambert, 1992) and He discrepancy in O type stars (Herrero et al., 1992). In this work, we studied mixing induced by Internal Gravity Waves (IGWs), which are naturally occurring waves that propagate in stably stratified fluids with gravity as the restoring force. We studied wave mixing in intermediate-mass stars with a convective core and a radiative envelope. In these stars, IGWs are generated at the convective–radiative interface and propagate outwards into extended radiation zone. We conducted two–dimensional (2D) hydrodynamic simulations which couple the convective and radiative regions in stars. We consider an equatorial slice of the star with the simulation domain extending up to 80 - 90 % of the radius of the star, using a background reference state model from the 1D stellar evolution code MESA. In order to study the mixing by IGWs, we introduced tracer particles into our two-dimensional (2D) hydrodynamic simulations and tracked their trajectories over time. This work is an extension of the work by Rogers & McElwaine (2017) to different masses (3, 7, and 20 M⊙) and ages (ZAMS, midMS, and TAMS). We find that the mixing profile changes dramatically across ages. In younger stars, we find that the measured diffusion coefficient increases toward the surface (as previously seen in Rogers & McElwaine (2017)). However, in older stars, the initial increase in the diffusion profile is followed by a decreasing trend toward the surface. This is due to the extra damping experienced by the waves at the turning point (radius at which the waves lose their wave-like properties), which is located at a lower fraction of the total stellar radius and the Brunt– V¨ais¨al¨a frequency spike. We also find that mixing is stronger in more massive stars due to the stronger convective driving along with the lower average Brunt–V¨ais¨al¨a frequency, which results in higher amplitude waves within the radiative zone. Hence, future stellar evolution models should include this variation. In order to aid the inclusion of this mixing in 1D stellar evolution models, we present a simple prescription that can be included in 1D models (Varghese et al., 2023). We then extended our analysis to understand the effects of rotation on wave mixing. For this, we chose a stellar model age and mass and ran the hydrodynamic models with varying rotation rates from Ω = 1×10−5 to 1×10−4 rads−1 and obtained the mixing profiles for each model. We found that the rotation increases the overall damping experienced by waves throughout the radiation zone, thus leading to decreased mixing.We also investigated the convective core overshooting in stellar models across masses and ages. Here, we conduct a detailed analysis of the mixing profile near the convective– radiative interface to find a prescription to constrain the shape and the extent of mixing by overshooting motions. We study how the overshoot depth varies across age and mass. We find that a Gaussian function could explain the overshoot profiles for all the models, and we measured the overshoot depth as the distance at which the Gaussian fit is still valid.