THE OSCILLATIONS AND STABILITY OF MAGNETIZED ACCRETION DISCS

The modes of oscillation and instability of linearized, axisymmetric a nd nonaxisymmetric disturbances in magnetized, annular differentially rotating flows, appropriate to accretion discs, are studied. It is ass umed that the fluid is incompressible and homogeneous to enable the st udy to focus on the interaction of vertical and toroidal magnetic fiel ds with the sheared flow. Sufficient conditions for stability are foun d for non-axisymmetric modes. A heuristic derivation of a sufficient c ondition for axisymmetric stability is made when only toroidal fields are present. It is shown that the growth rate of the instability for a lmost all modes is bounded by the strength of the magnetic fields and may vary with the vertical wavenumber and azimuthal wavenumber. There always exist modes for which the growth rates are unbounded. Wave ener gy and angular momentum for modes are constructed to understand how th e disturbances are transported. The normal-mode spectrum is computed, including the possible growth rates. The evolution of linear axisymmet ric and non-axisymmetric perturbations is then studied as an initial-v alue problem.