Stellar evolution with rotation and magnetic fields I. The relative importance of rotational and magnetic effects

We compare the current effects of rotation in stellar evolution to those of the magnetic field created by the Tayler instability. In stellar regions, where a magnetic field can be generated by the dynamo due to differential rotation (Spruit 2002), we find that the growth rate of the magnetic instability is much faster than for the thermal instability. Thus, meridional circulation is small with respect to the magnetic fields, both for the transport of angular momentum and of chemical elements. Also, the horizontal coupling by the magnetic field, which reaches values of a few 105 G, is much more important than the effects of the horizontal turbulence. The field, however, is not sufficient to distort the shape of the equipotentials. We impose the condition that the energy of the magnetic field created by the TaylerSpruit dynamo cannot be larger than the energy excess present in the differential rotation. This leads to a criterion for the existence of the magnetic field in stellar interiors. Numerical tests are made in a rotating star model of ...rotating with an initial velocity of 300 km s -1. We find that the coefficients of diffusion for the transport of angular momentum by the magnetic field are several orders of magnitude larger than the transport coefficients for meridional circulation and shear mixing. The same applies to the diffusion coefficients for the chemical elements; however, very close to the core, the strong (mu)-gradient reduces the mixing by the magnetic instability to values not too different from the case without magnetic field. We also find that magnetic instability is present throughout the radiative envelope, with the exception of the very outer layers, where differential rotation is insufficient to build the field, a fact consistent with the lack of evidence of strong fields at the surface of massive stars. However, the equilibrium situation reached by a rotating star with magnetic field and rotation is still to be ascertained.