Angular momentum transport in magnetized stellar radiative zones. III. The solar light-element abundances

We calculate the depletion of the trace elements lithium and beryllium within a solar-mass star during the course of its evolution from the zero-age main sequence to the age of the present-day Sun. In the radiative layers beneath the convection zone, we assume that these elements are transported by the turbulent fluid motions that result from instability of the shear how associated with internal differential rotation. This turbulent mixing is modeled as a diffusion process, using a diffusion coefficient that is taken to be proportional to the gradient of the angular velocity distribution inside the star. We study the evolution of the light-element abundances produced by rotational mixing for models in which internal angular momentum redistribution takes place either by hydrodynamic or by hydromagnetic means. Since models based on these alternative mechanisms for angular-momentum transport predict similar surface rotation rates late in the evolution, we explore the extent to which light-element abundances make it possible to distinguish between them. In the case of an internally magnetized star, our computations indicate that both the details of the surface abundance evolution and the magnitude of the depletion at solar age can depend sensitively on the assumed strength and configuration of the poloidal magnetic field inside the star. For a configuration with no direct magnetic coupling between the radiative and convective portions of the stellar interior, the depletion of lithium calibrated to the solar lithium depletion at the solar age is similar at all ages to the lithium depletion of a model in which angular-momentum transport occurs solely by hydrodynamical processes. However, the two models can be distinguished on the basis of their respective beryllium depletions, with the depletion of the magnetic model being significantly smaller than that of the nonmagnetic model.