Structure and stability of the magnetic solar tachocline

Rather weak fossil magnetic fields in the radiative core can produce the solar tachocline if the field is poloidal and almost horizontal in the tachocline region, i.e. if the field is confined within the core. This particular field geometry is shown to result from a shallow (<~1Mm) penetration of the meridional flow existing in the convection zone into the radiative core. I.e., two conditions are crucial for a magnetic tachocline theory: (i) the presence of meridional flow of a few meters per second at the base of the convection zone, and (ii) a magnetic diffusivity inside the tachocline smaller than 10^8 cm^2s^-1. Numerical solutions for both confined poloidal fields and the resulting tachocline structures are presented. We find that the tachocline thickness runs as <I>B</I>_p^-1/2 with the poloidal field amplitude falling below 5% of the solar radius for <I>B</I>^p > 5 mG. The resulting toroidal field amplitude inside the tachocline of about 100 G does not depend on the <I>B</I>^p. The hydromagnetic stability of the tachocline is only briefly discussed. For the hydrodynamic stability of latitudinal differential rotation we found that the critical 29% of the 2D theory of Watson (1981) are reduced to only 21% in 3D for marginal modes of about 6 Mm radial scale.