1998A&A...332..127B

The formulation of boundary conditions can have a significant influence on the solution of a system of differential equations. It is therefore important to apply a most realistic representation of the surface boundary conditions to the equations of stellar structure and evolution. With respect to previous models that usually employ some estimate of the surface temperature drawn from the Eddington approximation, a significant improvement of the outer boundary conditions is achieved by connecting models of stellar atmospheres to stellar structure models. Up to now stellar evolution calculations for late-type stars are calibrated using the well-observed properties of the present Sun. Including the physics of a plane-parallel atmospheric stratification it is necessary to account for a consistent description of the convective energy transfer in the outer layers of a cool star. At this step an apparent contradiction of the observations must be resolved: spectroscopic analysis of the Balmer lines emerging from solar-type stars using line-blanketed model atmospheres are usually carried out with reference to the Boehm-Vitense convection theory. To fit simultaneously the profiles of Hα and Hβ as well as higher series members a small mixing-length parameter α=l/H_p=0.5 is required. Models calibrated to the present Sun instead imply that the internal structure of the Sun follows a substantially higher value of α=1.5. This discrepancy cannot be removed in the context of Boehm-Vitense's convection theory. It is shown that the convection model of Canuto & Mazzitelli fits both the observed present Sun and the Balmer lines with a single common mixing-length parameter. The convection theory of Canuto & Mazzitelli thus offers for the first time a unified physical model of the Sun that is valid from the center to the upper photosphere.