Stellar evolution with rotation and magnetic fields - II. General equations for the transport by Tayler-Spruit dynamo

We further develop the Tayler-Spruit dynamo theory, based on the most efficient instability for generating magnetic fields in radiative layers of differentially rotating stars. We avoid the simplifying assumptions that either the mu- or the T-gradient dominates, but we treat the general case and we also account for the nonadiabatic effects, which favour the growth of the magnetic field. The general equation leads to the same analytical solutions in the limiting cases considered by Spruit (2002). Numerical models of a 15 M-circle dot star with a magnetic field are performed. The differences between the asymptotic solutions and the general solution demonstrate the need to use the general solution. Stars with a magnetic field rotate almost as a solid body. Several of their properties (size of the core, MS lifetimes, tracks, abundances) are closer to those of models without rotation than with rotation only. In particular, the observed N/C or N/H excesses in OB stars are better explained by our previous models with rotation only than by the present models with magnetic fields that predict no nitrogen excesses. We show that there is a complex feedback loop between the magnetic instability and the thermal instability driving meridional circulation. Equilibrium of the loop, with a small amount of differential rotation, can be reached when the velocity U-magn of the growth of the magnetic instability is of the same order as the velocity U-circ of the meridional circulation. This opens the possibility for further magnetic models, but at this stage we do not know the relative importance of the magnetic fields due to the Tayler instability in stellar interiors.