GENERAL LOCAL STABILITY-CRITERIA FOR STRATIFIED, WEAKLY MAGNETIZED ROTATING SYSTEMS

We consider the local stability of laminar differential rotation in a weakly magnetized plasma to adiabatic axisymmetric disturbances. Our assumptions are considerably less restrictive than those of previous analyses. The angular velocity need not have cylindrical isorotational surfaces, and a priori convective stability is not assumed. In an unmagnetized gas, stability under these circumstances would be governed by the Hoiland criteria. These criteria change qualitatively when even a weak magnetic field is present. In a magnetized plasma, the new criteria for stability have the same general form exhibited by the purely hydrodynamical case, but with all angular momentum gradients replaced by angular velocity gradients. Our findings are in accord with those of Papaloizou & Szuszkiewicz, who, using very different methods, considered the stability of isorotational field configurations. The results presented here thus point very generally to angular velocity gradients, not angular momentum gradients, as the fundamental stability discriminants in rotating astrophysical plasmas.