3D hydrodynamic simulations of massive main-sequence stars. I. Dynamics and mixing of convection and internal gravity waves

We performed 3D hydrodynamic simulations of the inner $\approx 50\%$ radialextent of a $25\ \mathrm{M_\odot}$ star in the early phase of the main sequenceand investigate core convection and internal gravity waves in the core-envelopeboundary region. Simulations for different grid resolutions and drivingluminosities establish scaling relations to constrain models of mixing for 1Dapplications. As in previous works, the turbulent mass entrainment rateextrapolated to nominal heating is unrealistically high ($1.58\times 10^{-4}\mathrm{M_\odot/yr}$), which is discussed in terms of the non-equilibriumresponse of the simulations to the initial stratification. We measurequantitatively the effect of mixing due to internal gravity waves excited bycore convection interacting with the boundary in our simulations. The wavepower spectral density as a function of frequency and wavelength agrees wellwith the GYRE eigenmode predictions based on the 1D spherically averaged radialprofile. A diffusion coefficient profile that reproduces the sphericallyaveraged abundance distribution evolution is determined for each simulation.Through a combination of eigenmode analysis and scaling relations it is shownthat in the $N^2$-peak region, mixing is due to internal gravity waves andfollows the scaling relation $D_\mathrm{IGW-hydro} \propto L^{4/3}$ over a$\gtrapprox 2\ \mathrm{dex}$ range of heating factors. Different extrapolationsof the mixing efficiency down to nominal heating are discussed. If internalgravity wave mixing is due to thermally-enhanced shear mixing, an upper limitis $D_\mathrm{IGW} \lessapprox 2$ to $3\times 10^4\ \mathrm{cm^2/s}$ at nominalheating in the $N^2$-peak region above the convective core.