Letter to the Editor

Nonaxisymmetric modes of MRI in dissipative Keplerian disks

¹ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany e-mail: [lkitchatinov;gruediger]@aip.de
² Institute for Solar-Terrestrial Physics, PO Box 291, Irkutsk 664033, Russia e-mail: kit@iszf.irk.ru
³ Pulkovo Astronomical Observatory, St. Petersburg 196140, Russia

Received: 19 February 2010
Accepted: 17 March 2010

Abstract

Aims. Deviations from the axial symmetry are necessary to maintain self-sustained MRI-turbulence by a dynamo mechanism. We define the parameter region where the nonaxisymmetric MRI modes are excited and study their geometries and growth rates.

Methods. The linear eigenvalue problem for global nonaxisymmetric modes of standard-MRI in Keplerian disks is solved numerically with allowance for finite diffusion.

Results. For small magnetic Prandtl numbers the microscopic viscosity completely drops out of the analysis so that the stability maps and the growth rates expressed in terms of the magnetic Reynolds number Rm and the Lundquist number S do not depend on the magnetic Prandtl number Pm. The minimum magnetic field for the onset of nonaxisymmetric MRI grows with the rotation rate. For a given S all nonaxisymmetric modes disappear for a sufficiently large Rm. This is a consequence of the radial fine-structure of the nonaxisymmetric modes resulting from the winding effect of differential rotation. It is this fine-structure which also provides serious resolution problems for the numerical simulation of MRI at large Rm.

Conclusions. For weak magnetic fields slightly above the critical value for the onset of MRI only axisymmetric modes are unstable. Nonaxisymmetric modes need stronger fields and not too large Rm. If Pm is small its real value does not play any role in MRI.