Consistent Solar Models Including the $^7$Li and $^3$He Constraints

Abstract

Improvements induced by helioseismology show that microscopic diffusion cannot be neglected in solar models. Helium and metal diffusion is now generally introduced in the computations. They cannot however explain the observed lithium depletion. Macroscopic motions are needed to bring up to the convection zone the nuclearly depleted matter. Such motions also lead to a better agreement between the sound velocity in the model and that deduced from the inversion of seismic modes. On the other hand, they must not bring up too much $^3$He, as we now know that the $^3$He/$^4$He ratio cannot have changed by more than 10 percent during these last 3 Gyr. Here we present new consistent solar models in which the $^3$He constraint is satisfied. The fact that $^3$He must remain constant while $^7$Li must be depleted leads to strong constraints on the effective macroscopic diffusion coefficient allowed below the solar convection zone.