Quasi-global, linear analysis of a magnetized disc

We consider the axisymmetric global modes of a uniformly magnetized accretion disc. We use a local disc model that incorporates vertical stratification but, except for velocity shear, ignores radial structure. Analytic expressions are obtained for the modes and their growth rates in the special case of a uniform vertical field, and the modes and growth rates are obtained numerically for more general orientations of the magnetic field. We find that, in general, the growing modes are overstable. We also report a new, global version of the instability of Balbus & Hawley that sets in for some, but not all, boundary conditions. This global instability can occur even when the magnetic field is strong. The existence of this global instability explains the difference between the instability criterion of Papaloizou & Szuszkiewicz and the instability criterion derived from a local analysis by Balbus & Hawley.