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 a ssumptions are considerably less restrictive than those of previous an alyses. The angular velocity need not have cylindrical isorotational s urfaces, and a priori convective stability is not assumed. In an unmag netized 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 criter ia for stability have the same general form exhibited by the purely hy drodynamical 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, consider ed the stability of isorotational field configurations. The results pr esented here thus point very generally to angular velocity gradients, not angular momentum gradients, as the fundamental stability discrimin ants in rotating astrophysical plasmas.