Stellar evolution models with overshooting based on 3-equation non-local theories

Context. Convective overshoot mixing is a critical ingredient of stellar structure models but is treated in most cases by ad hoc extensions of the mixing-length theory for convection. Advanced theories that are both more physical and numerically treatable are needed. Aims. Convective flows in stellar interiors are highly turbulent. This poses a number of numerical challenges for the modelling of convection in stellar interiors. We included an effective turbulence model in a 1D stellar evolution code in order to treat non-local effects within the same theory. Methods. We used a turbulent convection model that relies on the solution of second order moment equations. We implemented this into a state-of-the-art 1D stellar evolution code. To overcome a deficit in the original form of the model, we took the dissipation due to buoyancy waves in the overshooting zone into account. Results. We compute stellar models of intermediate mass main-sequence stars of between 1.5 and 8 M ⊙ . Overshoot mixing from the convective core and modified temperature gradients within and above it emerge naturally as a solution of the turbulent convection model equations. Conclusions. For a given set of model parameters, the overshooting extent determined from the turbulent convection model is comparable to other overshooting descriptions, the free parameters of which had been adjusted to match observations. The relative size of the mixed cores decreases with decreasing stellar mass without additional adjustments. We find that the dissipation by buoyancy waves constitutes a necessary and relevant extension of the turbulent convection model in use.