Calibrating chemical mixing induced by internal gravity waves based on hydrodynamical simulations

Context. Internal gravity waves (IGWs) have been shown to contribute to the transport of chemical elements in stars with a convective core and radiative envelope. Recent two-dimensional hydrodynamical simulations of convection in intermediate-mass stars have provided estimates of the chemical mixing efficiency of such waves. The chemical diffusion coefficient from IGW mixing is described by a constant A, times the squared wave velocity. However, the value of A remains unconstrained by such simulations. Aims. This work aims to investigate what values A can take in order to reproduce the observed nitrogen surface abundances of the most nitrogen-enriched massive stars. Furthermore, we discuss the prevalence of IGW mixing compared to rotational mixing. Methods. We provide an implementation of these (time-dependent) mixing profiles predicted from hydrodynamical simulations in the one-dimensional stellar evolution code <ns0:monospace>MESA</ns0:monospace>. We computed evolution tracks for stars between 3 and 30 M⊙ with this new implementation for IGW mixing and studied the evolution for the surface abundances of isotopes involved in the CNO cycle, particularly the nitrogen-14 isotope. Results. We show that this one-dimensional framework that predicts the chemical diffusion coefficient from IGW mixing yields consistent morphologies of the mixing profile in comparison with hydrodynamical simulations. We find that the value of A must increase with mass in order to reproduce the most nitrogen-enriched stars. If we assume these calibrated values for A, mixing by IGWs is a potential mechanism to reproduce well-mixed stars without needing rapid rotation. Conclusions. We have provided observational limits on the efficiency of IGW mixing for future theoretical studies. Furthermore, future asteroseismic modelling efforts that take IGW mixing into account will be able to place additional constraints on the convective core mass, as our models predict that the convective core would be significantly more massive if IGW mixing is indeed efficient.