Additional results for unstable stratified toroidal magnetic fields in stars

Abstract

General conditions for adiabatic instability of weak axisymmetric toroidal magnetic fields are obtained. In particular all fields which haveH _ϕ=0 and ∂H ²_ϕ /∂δ>0 simultaneously are unstable. This includes all fields which exist near to the axis of symmetry and, indeed, any without an infinite current density anywhere. A detailed discussion is given of fields with an angular dependenceH ²_ϕ ∼|P _ℓ (cos θ)|. These fields are dynamically unstable with respect to both axisymmetric and non-axisymmetric perturbations for all values of the azimuthal wave number |m|. The maximum growth rates are independent ofm and they are largest for the fields that are defined in the regions closest to the polar axis.