Angular momentum transport in magnetized stellar radiative zones. IV. Ferraro's theorem and the solar tachocline

We consider the circumstances under which the latitudinal differential rotation of the solar convective envelope can (or cannot) be imprinted on the underlying radiative core through the agency of a hypothetical weak, large-scale poloidal magnetic field threading the solar radiative interior. We do so by constructing steady, two-dimensional axisymmetric solutions to the coupled momentum and induction equations under the assumption of a purely zonal flow and time-independent poloidal magnetic field. Our results show that the structure of the interior solutions is entirely determined by the boundary conditions imposed at the core-envelope interface. Specifically, in the high Reynolds number regime a poloidal held having a nonzero component normal to the core-envelope interface can lead to the transmission of significant differential rotation into the radiative interior. In contrast, for a poloidal field that is contained entirely within the radiative core, any differential rotation is confined to a thin magnetoviscous boundary layer located immediately beneath the interface, as well as along the rotation/magnetic axis. We argue that a magnetically decoupled configuration is more likely to be realized in the solar interior. Consequently, the helioseismically inferred lack of differential rotation in the radiative core does not necessarily preclude the existence of a weak, large-scale poloidal field therein. We suggest that such a field may well be dynamically significant in determining the structure of the solar tachocline.