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Abstract We present 3D hydrodynamical simulations of core convection with a stably stratified envelope of a 25M_⊙star in the early phase of the main sequence. We use the explicit gas-dynamics codePPMstar, which tracks two fluids and includes radiation pressure and radiative diffusion. Multiple series of simulations with different luminosities and radiative thermal conductivities are presented. The entrainment rate at the convective boundary, internal gravity waves in and above the boundary region, and the approach to dynamical equilibrium shortly after a few convective turnovers are investigated. We perform very long simulations on 896³grids accelerated by luminosity boost factors of 1000, 3162 and 10,000. In these simulations, the growing penetrative convection reduces the initially unrealistically large entrainment. This reduction is enabled by a spatial separation that develops between the entropy gradient and the composition gradient. The convective boundary moves outward much more slowly at the end of these simulations. Finally, we present a 1D method to predict the extent and character of penetrative convection beyond the Schwarzschild boundary. The 1D model is based on a spherically averaged reduced entropy equation that takes the turbulent dissipation as input from the 3D hydrodynamic simulation and takes buoyancy and all other energy sources and sinks into account. This 1D method is intended to be ultimately deployed in 1D stellar evolution calculations and is based on the properties of penetrative convection in our simulations carried forward through the local thermal timescale. 

ABSTRACT Recent photometric observations of massive stars have identified a low-frequency power excess which appears as stochastic low-frequency variability in light-curve observations. We present the oscillation properties of high-resolution hydrodynamic simulations of a $$25\,\,{\rm{M}_\odot }$$ star performed with the PPMstar code. The model star has a convective core mass of $$\approx 12\,\,{\rm{M}_\odot }$$ and approximately half of the envelope simulated. From this simulation, we extract light curves from several directions, average them over each hemisphere, and process them as if they were real photometric observations. We show how core convection excites waves with a similar frequency as the convective time-scale in addition to significant power across a forest of low and high angular degree l modes. We find that the coherence of these modes is relatively low as a result of their stochastic excitation by core convection, with lifetimes of the order of 10s of days. Thanks to the still significant power at higher l and this relatively low coherence, we find that integrating over a hemisphere produces a power spectrum that still contains measurable power up to the Brunt–Väisälä frequency. These power spectra extracted from the stable envelope are qualitatively similar to observations, with the same order of magnitude yet lower characteristic frequency. This work further shows the potential of long-duration, high-resolution hydrodynamic simulations for connecting asteroseismic observations to the structure and dynamics of core convection and the convective boundary.