Calibrating the α parameter of convective efficiency using observed stellar properties

Context. Synthetic model atmosphere calculations are still the most commonly used tool when determining precise stellar parameters and stellar chemical compositions. Besides three-dimensional models that consistently solve for hydrodynamic processes, one-dimensional models that use an approximation for convective energy transport play the major role. Aims. We use modern Balmer-line formation theory as well as spectral energy distribution (SED) measurements for the Sun and Procyon to calibrate the model parameter α that describes the efficiency of convection in our 1D models. Convection was calibrated over a significant range in parameter space, reaching from F-K along the main sequence and sampling the turnoff and giant branch over a wide range of metallicities. This calibration was compared to theoretical evaluations and allowed an accurate modeling of stellar atmospheres. Methods. We used Balmer-line fitting and SED fits to determine the convective efficiency parameter α. Both methods are sensitive to the structure and temperature stratification of the deeper photosphere. Results. While SED fits do not allow a precise determination of the convective parameter for the Sun and Procyon, they both favor values significantly higher than 1.0. Balmer-line fitting, which we find to be more sensitive, suggests that the convective efficiency parameter α is $\approx$ 2.0 for the main sequence and quickly decreases to $\approx$ 1.0 for evolved stars. These results are highly consistent with predictions from 3D models. While the values on the main sequence fit predictions very well, measurements suggest that the decrease of convective efficiency as stars evolve to the giant branch is more dramatic than predicted by models.