Effect of Local Treatments of Convection upon the Solar P-mode Excitation Rates

We compute, for several solar models, the rates P at which the solar radial p modes are expected to be excited. The solar models are computed with two different local treatments of convection : the classical mixinglength theory (MLT hereafter) and Canuto et al. (1996, CGM hereafter)’s formulation. For one set of solar models (EMLT and ECGM models), the atmosphere is gray and assumes Eddington’s approximation. The models only assume one mixing-length parameter and reproduce the solar radius at solar age but not the Balmer line profiles. For a second set of models (KMLT and KCGM models), the atmosphere is built using a T (τ) law which has been obtained from a Kurucz’s model atmosphere computed with the same local treatment of convection. The mixing-length parameter in the model atmosphere is chosen so as to provide a good agreement between synthetic and observed Balmer line profiles, while the mixing-length parameter in the interior model is calibrated so that the model reproduces the solar radius at solar age. For the MLT treatment, the rates P do depend significantly on the properties of the atmosphere. Indeed differences in P between the EMLT model and the KMLT are found very large. On the other hand, for the CGM treatment, differences in P between the ECGM and the KCGM models are very small compared to the error bars attached to the seismic measurements. The excitation rates P for modes from the EMLT model are significantly under-estimated compared with the solar seismic constraints. The KMLT model results in intermediate values for P and shows also an important discontinuity in the temperature gradient and the convective velocity. On the other hand, the KCGM model and the ECGM model yield values for P closer to the seismic data than the EMLT and KMLT models. We conclude that the solar p-mode excitation rates provide valuable constraints and according to the present investigation cleary favor the CGM treatment with respect to the MLT.