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 $\approx 50\%$ radial extent of a $25\ \mathrm{M_\odot}$ star in the early phase of the main sequence and investigate core convection and internal gravity waves in the core-envelope boundary region. Simulations for different grid resolutions and driving luminosities establish scaling relations to constrain models of mixing for 1D applications. As in previous works, the turbulent mass entrainment rate extrapolated to nominal heating is unrealistically high ($1.58\times 10^{-4}\ \mathrm{M_\odot/yr}$), which is discussed in terms of the non-equilibrium response of the simulations to the initial stratification. We measure quantitatively the effect of mixing due to internal gravity waves excited by core convection interacting with the boundary in our simulations. The wave power spectral density as a function of frequency and wavelength agrees well with the GYRE eigenmode predictions based on the 1D spherically averaged radial profile. A diffusion coefficient profile that reproduces the spherically averaged abundance distribution evolution is determined for each simulation. Through a combination of eigenmode analysis and scaling relations it is shown that in the $N^2$-peak region, mixing is due to internal gravity waves and follows the scaling relation $D_\mathrm{IGW-hydro} \propto L^{4/3}$ over a $\gtrapprox 2\ \mathrm{dex}$ range of heating factors. Different extrapolations of the mixing efficiency down to nominal heating are discussed. If internal gravity wave mixing is due to thermally-enhanced shear mixing, an upper limit is $D_\mathrm{IGW} \lessapprox 2$ to $3\times 10^4\ \mathrm{cm^2/s}$ at nominal heating in the $N^2$-peak region above the convective core.