On the stability of magnetized accretion discs

Abstract

The shear instability of differentially rotating magnetized accretion discs is formulated as an eigenvalue problem. A monotonic instability caused by the presence of weak vertical magnetic fields, claimed by Balbus & Hawley on the basis of a local analysis, is shown to be absent whenever an azimuthal magnetic field is present. Instead the instability may take the form of overstable oscillations. A necessary condition for such an instability is obtained.