Standard Solar Models in the Light of New Helioseismic Constraints. II. Mixing below the Convective Zone

In previous work, we have shown that recent updated standard solar models cannot reproduce the radial profile of the sound speed at the base of the convective zone and fail to predict the photospheric lithium abundance. In parallel, helioseismology has shown that the transition from differential rotation in the convective zone to almost uniform rotation in the radiative solar interior occurs in a shallow layer called the tachocline. This layer is presumably the seat of a large-scale circulation and of turbulent motions. Here we introduce a macroscopic transport term in the structure equations that is based on a hydrodynamical description of the tachocline proposed by Spiegel & Zahn, and we calculate the mixing induced within this layer. We discuss the influence of different parameters that represent the tachocline thickness, the Brunt-Väisälä frequency at the base of the convective zone, and the time dependence of this mixing process along the Sun's evolution. We show that the introduction of such a process inhibits the microscopic diffusion by about 25%. Starting from models including a pre-main-sequence evolution, we obtain (1) a good agreement with observed photospheric chemical abundance of light elements such as 3 He, 4 He, 7 Li, and 9 Be; (2) a smooth composition gradient at the base of the convective zone; and (3) a significant improvement of the sound-speed square difference between the seismic Sun and the models in this transition region when we allow the photospheric heavy-element abundance to adjust, within the observational incertitude, as a result of the action of this mixing process. The impact on neutrino predictions is also discussed.