Magnetic shear-flow instability in thin accretion disks. Structure and magnetic configurations of accretion disk-dynamo models

The possibility that the magnetic shear-flow instability (also 'Balbus-Hawley' instability) might give rise to turbulence in a thin accretion disk is investigated through numerical simulations. The study is linear and the fluid disk is supposed to be incompressible and differentially rotating with a simple velocity profile with #OMEGA##propor to#R"-"q. The simplicity of the model is counterbalanced by the fact that the study is fully global in all the three spatial directions with boundaries on each side; finite diffusivities are also allowed. The investigation is carried out also for several values of the azimuthal wavenumber of the perturbations in order to analyse whether nonaxisymmetric modes might be preferred which may produce, in a nonlinear extension of the study, a self-sustained magnetic field. We find the final pattern steady, with similar kinetic and magnetic energies and the angular momentum always transported outwards. Despite the differential rotation there are only small differences for the eigenvalues for various nonaxisymmetric eigensolutions. Axisymmetric instabilities are by no means preferred, in fact for our Prandtl numbers between 0.1 and 1 the azimuthal wavenumbers m=0, 1, 2 appear to be equally readily excited. The equatorial symmetry is quadrupolar for the magnetic field and dipolar for the flow field system. The maximal magnetic field strength to cause the instability is practically independent of the magnetic Prandtl number. With typical white-dwarf values, a magnetic amplitude of 10"5 G is estimated. (orig.)SIGLEAvailable from TIB Hannover: RR 7310(99-08/09) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman