Testing a non-local 1-equation turbulent convection model: A solar model

Context: Turbulent convection models treat stellar convection more physically than standard mixing-length theory by including non-local effects. We recently successfully applied the Kuhfuss version to convective cores in main sequence stars. Its usefulness for convective envelopes remains to be tested. Aims: The solar convective envelope constitutes a viable test bed for investigating the usefulness of the 1-equation Kuhfuss turbulent convection model. Methods: We used the one-dimensional stellar evolution code GARSTEC to calculate a standard solar model with the 1-equation Kuhfuss turbulent convection model, and compared it to helioseismic measurements and a solar model using standard mixing-length theory. Additionally, we investigated the influence of the additional free parameters of the convection model on the solar structure. Results: The 1-equation Kuhfuss model reproduces the sound-speed profile and the lower boundary of the convective region less well than the mixing-length model, because the inherent non-local effects overestimate the amount of convective penetration below the Schwarzschild boundary. We trace this back to the coupling of the temperature gradient to the convective flux in the 1-equation version of the Kuhfuss theory. Conclusions: The temperature stratification of the solar convective envelope is not well modelled by the 1-equation Kuhfuss turbulent convection model, and the more complex 3-equation version is needed to improve the modelling of convection in the envelopes of 1D stellar evolution models.