On the Coupling between Helium Settling and Rotation‐induced Mixing in Stellar Radiative Zones. I. Analytical Approach

Abstract

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 μ-gradients that, because of the meridional circulation, turn into horizontal fluctuations. Up to now, the feedback effect of this process on the rotation-induced mixing has been neglected in the computations of abundance variations in stellar surfaces or artificially reduced. Here we analyze its consequences and derive an approximate analytical solution in a quasi-stationary case. We also discuss the relative importance of the various physical effects that influence the meridional circulation velocity. In a second paper, we will present a complete two-dimensional numerical simulation of this process, while a third paper will be devoted to special applications to Population I stars.