Magneto-rotational overstability in accretion disks

¹ FOM-Institute for Plasma Physics Rijnhuizen, PO Box 1207, 3430 BE Nieuwegein, The Netherlands e-mail: blokland@rijnh.nl
² Association EURATOM-FOM, Trilateral Euregio Cluster

Received: 22 December 2004
Accepted: 13 April 2005

Abstract

We present analytical and numerical studies of magnetorotational instabilities occuring in magnetized accretion disks. These calculations are performed for general radially stratified disks in the cylindrical limit. We elaborate on earlier analytical results and confirm and expand them with numerical computations of unstable eigenmodes of the full set of linearised compressible MHD equations. We compare these solutions with those found from approximate local dispersion equations from WKB analysis.
In particular, we investigate the influence of a nonvanishing toroidal magnetic field component on the growth rate and oscillation frequency of magnetorotational instabilities in Keplerian disks. These calculations are performed for a constant axial magnetic field strength. We find the persistence of these instabilities in accretion disks close to equipartition. Our calculations show that these eigenmodes become overstable (complex eigenvalue), due to the presence of a toroidal magnetic field component, while their growth rate reduces slightly.
Furthermore, we demonstrate the presence of magneto-rotational overstabilities in weakly magnetized sub-Keplerian rotating disks. We show that the growth rate scales with the rotation frequency of the disk. These eigenmodes also have a nonzero oscillation frequency, due to the presence of the dominant toroidal magnetic field component. The overstable character of the MRI increases as the rotation frequency of the disk decreases.