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 rota tion of the solar convective envelope can (or cannot) be imprinted on the u nderlying radiative core through the agency of a hypothetical weak, large-s cale poloidal magnetic held threading the solar radiative interior. We do s o by constructing steady, two-dimensional axisymmetric solutions to the cou pled momentum and induction equations under the assumption of a purely zona l flow and time-independent poloidal magnetic field. Our results show that the structure of the interior solutions is entirely determined by the bound ary conditions imposed at the core-envelope interface. Specifically, in the high Reynolds number regime a poloidal held having a nonzero component nor mal to the core-envelope interface can lead to the transmission of signific ant differential rotation into the radiative interior. In contrast, for a p oloidal field that is contained entirely within the radiative co:re, any di fferential rotation is confined to a thin magnetoviscous boundary layer loc ated immediately beneath the interface, as well as along the rotation/magne tic axis. We argue that a magnetically decoupled configuration is more like ly to be realized in the solar interior. Consequently, the helioseismically inferred lack of differential rotation in the radiative core does not nece ssarily preclude the existence of a we;ak, large-scale poloidal field there in. We suggest that such a held may well be dynamically significant in dete rmining the structure of the solar tachocline.