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

We perform two-dimensional (2D) numerical simulations of core convection for zero-age main-sequence stars covering a mass range from 3 to 20 M-circle dot. 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-circle dot models. The simulations cover hundreds to thousands of convective turnover time-scales. 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(ov)) scales with the stellar luminosity (L) and the convective core radius (r(conv)). We derive a scaling law d(ov) proportional to L(1/3)r(conv)(1/2), which is implemented in a one-dimensional 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 greater than or similar to 10 M-circle dot. Our 2D simulations show the formation of a nearly adiabatic layer just above the Schwarzschild boundary of the convective core, as exhibited in recent three-dimensional 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 time-scale in the overshooting layer.