Modeling stellar interiors with rotational mixing: what has been achieved? what needs to be done?

Jean-Paul Zahn

Abstract. The standard model of stellar structure, although it presently includes convective overshoot, microscopic diffusion, gravitational settling and radiative acceleration, is still unable to account for various observational facts, and there is now a large consensus that some "extra mixing" must occur in the radiation zones. To account for such mixing, the minimalist approach consists in introducing a parametrized turbulent diffusivity, and to adjust it so as to match the observations. A better way is to strive to implement the physical processes that may be responsible for this mixing, in particular shear-induced turbulence and large-scale meridional circulation, which both are linked with the differential rotation of the star. To describe that rotational mixing, as we call it, one has thus to follow the evolution of the internal rotation profile. By making some plausible assumptions, its is possible to reduce the advection of angular momentum through the 2-D circulation to a 1-D process, and that of the chemical elements to a vertical diffusion. It is then possible to implement these transports in a 1-D stellar evolution code. In massive stars, angular momentum is transported mainly by the meridional circulation, and there is good agreement between the observations and the predictions based on the rotational mixing. This not so for solar-type stars where another, more efficient mechanism is required to transport angular momentum. A fossil magnetic field has been invoked, but recently it has been shown that such a field would connect with the convection zone, and imprint its differential rotation on the radiation zone, which is not observed. The other candidate is the transport of angular momentum by the internal gravity waves that are emitted at the base of the convection zone; although their treatment is still somewhat crude, it appears that they can explain both the quasi-uniform rotation of the solar interior, and the depletion of lithium observed in such stars.