Stellar dynamos with $\vecΩ\times \vec{J}$ effect

Abstract

We study axisymmetric mean-field dynamo models containing differential rotation, the $α$ effect and the additional turbulent induction effects. The additional effects result from the combined action of rotation and an inhomogeneity of the large-scale magnetic field. The best known of them is the $\vecΩ\times\vec{J}$ effect. We also include anisotropic diffusion and a new dynamo term which is of third order in the rotation vector $\vecΩ$ The model calculations are carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities according to a standard model of the solar interior. In addition, we consider a dynamo model for a full sphere which is solely based on the joint induction effects of rotation and an inhomogeneity of the large-scale magnetic field, without differential rotation and the $α$ effect (a $δ^{2}$ dynamo model). This kind of dynamo model may be relevant for fully convective stars.