Angular momentum transport from magnetoconvection and the magnetic modulation of the solar differential rotation

In order to explain the modulation of the solar rotation law during the activity minima and maxima the angular momentum transport by rotating magnetoconvection is numerically simulated when a convective box is penetrated by an inclined azimuthal magnetic field. Turbulence-induced kinetic and magnetic stresses {\em and} the Maxwell stress of the large-scale magnetic background field are the basic transporters. Without rotation the sign of the total stress naturally depends on the signs of the field components as positive (negative) $B_\theta B_\phi$ transport the angular momentum poleward (equatorward). For fast enough rotation, however, the turbulence-originated $\Lambda$ effect starts to dominate the transport of the angular momentum. The simulations show that positive angles between the azimuthal field and the two meridional magnetic field components (as expected to be realized by induction of solar-type rotation laws) reduce the inward radial as well as the equatorward latitudinal transport by the rotating magnetoconvection. In accordance with the observations the magnetically influenced rotation law at the solar surface proves to be flatter than the nonmagnetic one even displaying a slightly decelerated equator .