On the Coupling between Helium Settling and Rotation-Induced Mixing in Stellar Radiative Zones: I- Analytical Approach

In the presence of rotation-induced mixing, element diffusion still occurs in stellar radiative zones, although at a slower rate than in the case of a complete stability of the stellar gas. As a consequence, helium settling leads to vertical $\displaystyle \mu $-gradients which, due to the meridional circulation, turn into horizontal fluctuations. Up to now, the feed-back effect of this process on the rotation-induced mixing was currently neglected in the computations of abundance variations in stellar surfaces, or artificially reduced. Here we analyse its consequences and derive an approximate analytical solution in a quasi-stationary case. We also discuss the relative importance of the various physical effects which influence the meridional circulation velocity. In a second paper (Th\'eado and Vauclair 2002a), we will present a complete 2D numerical simulation of this process while a third paper (Th\'eado and Vauclair 2002b) will be devoted to special applications to Pop I stars.