Rotational mixing in low-mass stars II. Self-consistent models of Pop II RGB stars

In this paper we study the effects of rotation in low-mass, low-metallicity RGB stars. We present the first evolutionary models taking into account self-consistently the latest prescriptions for the transport of angular momentum by meridional circulation and shear turbulence in stellar interiors as well as the associated mixing processes for chemicals computed from the ZAMS to the upper RGB. We discuss in details the uncertainties associated with the physical description of the rotational mixing and study carefully their effects on the rotation profile, diffusion coefficients, structural evolution, lifetimes and chemical signatures at the stellar surface. We focus in particular on the various assumptions concerning the rotation law in the convective envelope, the initial rotation velocity distribution, the presence of mean molecular weight gradients and the treatment of the horizontal and vertical turbulence. This exploration leads to two main conclusions : (1) After the completion of the first dredge-up, the degree of differential rotation (and hence mixing) is maximised in the case of a differentially rotating convective envelope (i.e., j_CE(r) = cst), as anticipated in previous studies. (2) Even with this assumption, and contrary to some previous claims, the present treatment for the evolution of the rotation profile and associated meridional circulation and shear turbulence does not lead to enough mixing of chemicals to explain the abundance anomalies in low-metallicity field and globular cluster RGB stars observed around the bump luminosity. This study raises questions that need to be addressed in a near future. These include for example the interaction between rotation and convection and the trigger of additional hydrodynamical instabilities.