GLOBAL AXISYMMETRIC MAGNETOROTATIONAL INSTABILITY WITH DENSITY GRADIENTS

We examine global incompressible axisymmetric perturbations of a differentially rotatingMHD plasmawith radial density gradients. It is shown that the standard magnetorotational instability (MRI) criterion drawn from the local dispersion relation is often misleading. If the equilibrium magnetic field is either purely axial or purely toroidal, the problem reduces to finding the global radial eigenvalues of an effective potential. The standard Keplerian profile in-cluding the origin is mathematically ill-posed, and thus any solution will depend strongly on the inner boundary. We find a class of unstable modes localized by the form of the rotation and density profiles, with reduced dependence on boundary conditions. Subject headinggs: accretion, accretion disks — instabilities — MHD 1. BACKGROUND It is often stated that the magnetorotational instability (MRI; Chandrasekhar 1961; Balbus & Hawley 1991, hereafter BH91) in accretion disks is a ‘‘local’ ’ instability, i.e., normal modes are driven unstable by the local value of the rotational flow shear. Implicit in this analysis is the assumption that equilibrium rota