Three-dimensional magneto-shear instabilities in the solar tachocline - II. Axisymmetric case

A Boussinesq model of the development of non-axisymmetric (in particular m= 1) three-dimensional magneto-shear instabilities in the solar tachocline was presented in Paper I. However, there it was erroneously concluded that the axisymmetric (m= 0) modes are stable, and they were not discussed further. Here it is shown that, although m= 0 modes are indeed stable for broad magnetic profiles, they are strongly unstable to radial shredding (high radial wavenumber) instabilities on the poleward shoulders of toroidal magnetic bands at high field strengths (roughly 40-100 kG depending on bandwidth and latitude). These instabilities have growth rates comparable to or greater than those for tipping instabilities (m= 1) in many cases, but both are strongly stabilized by gravitational stratification characteristic of the upper radiative core. Weaker fields are m= 0 stable (though weakly m= 1 unstable), even in neutral gravitational stratification (convection zone).