A study of convective core overshooting as a function of stellar mass based on two-dimensional hydrodynamical simulations

We perform two-dimensional numerical simulations of core convection for zero-age-main-sequence stars covering a mass range from 3 $M_\odot$ to 20 $M_\odot$. The simulations are performed with the fully compressible time-implicit code MUSIC. We study the efficiency of overshooting, which describes the ballistic process of convective flows crossing a convective boundary, as a function of stellar mass and luminosity. We also study the impact of artificially increasing the stellar luminosity for 3 $M_\odot$ models. The simulations cover hundreds to thousands of convective turnover timescales. Applying the framework of extreme plume events previously developed for convective envelopes, we derive overshooting lengths as a function of stellar masses. We find that the overshooting distance ($d_{\rm ov}$) scales with the stellar luminosity ($L$) and the convective core radius ($r_{\rm conv}$). We derive a scaling law $d_{\rm ov} \propto L^{1/3} r_{\rm conv}^{1/2}$ which is implemented in a 1D stellar evolution code and the resulting stellar models are compared to observations. The scaling predicts values for the overshooting distance that significantly increase with stellar mass, in qualitative agreement with observations. Quantitatively, however, the predicted values are underestimated for masses $\gtrsim 10 M_\odot$. Our 2D simulations show the formation of a nearly-adiabatic layer just above the Schwarzschild boundary of the convective core, as exhibited in recent 3D simulations of convection. The most luminous models show a growth in size with time of the nearly-adiabatic layer. This growth seems to slow down as the upper edge of the nearly-adiabatic layer gets closer to the maximum overshooting length and as the simulation time exceeds the typical thermal diffusive timescale in the overshooting layer.