| Abstract
| - Aims. This paper aims at deciphering the dynamics of the envelope of a rotating star when some angular momentum loss due to mass loss is present. We especially wish to know when the spin-down flow forced by the mass loss supersedes the baroclinic flows that pervade the radiative envelope of rotating stars. Methods. We consider a Boussinesq fluid enclosed in a rigid sphere whose flows are forced both by the baroclinic torque, the spin-down of an outer layer, and an outward mass flux. The spin-down forcing is idealized in two ways: either by a rigid layer that imposes its spinning down velocity at some interface or by a turbulent layer that imposes a stress at this same interface to the interior of the star. Results. In the case where the layer is rigid and imposes its velocity, we find that, as the mass-loss rate increases, the flow inside the star shows two transitions: the meridional circulation associated with baroclinic flows is first replaced by its spin-down counterpart, while at much stronger mass-loss rates the baroclinic differential rotation is superseded by the spin-down differential rotation. When boundary conditions specify the stress instead of the velocity, we find just one transition as the mass-loss rate increases. Besides the two foregoing transitions, we find a third transition that separates an angular momentum flux dominated by stresses from an angular momentum flux dominated by advection. Thus, with this very simplified two-dimensional stellar model, we find three wind regimes: weak (or no wind), moderate, and strong. In the weak wind case, the flow in the radiative envelope is of baroclinic origin. In the moderate case, the circulation results from the spin-down while the differential rotation may either be of baroclinic or of spin-down origin, depending on the boundary conditions or more generally on the coupling between mass and angular momentum losses. For fast rotating stars, our model says that the moderate wind regime starts when mass loss is higher than ~ 10 -11M⊙/yr. In the strong wind case, the flow in the radiative envelope is mainly driven by angular momentum advection. This latter transition mass-loss rate depends on the mass and the rotation rate of the star, being around 10 -8M⊙/yr for a 3 M⊙ ZAMS star rotating at 200 km s -1 according to our model.
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