Existence of the Magnetorotational Instability

By posing and solving a global axisymmetric eigenvalue problem on an infinite domain with modes vanishing at zero and infinity for a differentially rotating MHD plasma, the conditions for the occurrence of apurely growing low- frequency mode known as the magnetorotational instability (MRI) are mapped. It is shown that the MRI criterion drawn from the ''local dispersion relation'' is at bestinadequate and may even bemisleading. The physics of the MRI is rather nuanced. It is dictated by the details of the radial profile of the rotation velocity (r) and not just by the sign and the magnitude of its gradient, 0. The salient features of the class of profiles for which the MRI-like eigenmodes may occur are given along with the eigenspectrum. For a variety of other profiles, it is shown that an unstable mag- netorotational mode is not a valid eigensolution. Subject headinggs: accretion, accretion disks — MHD