Magnetohydrodynamic instabilities and turbulence in accretion disks

In this paper we review the possibilities for magnetohydrodynamic processes to handle the angular momentum transport in accretion disks. Traditionally the angular momentum transport has been considered to be the result of turbulent viscosity in the disk, although the Keplerian flow in accretion disks is linearly stable towards hydrodynamic perturbations. It is on the other hand linearly unstable to some magnetohydrodynamic (MI-ID) instabilities. The most important instabilities are the Parker and Balbus-Hawley instabilities that are related to the magnetic buoyancy and the shear flow, respectively, We discuss these instabilities not only in the traditional MHD framework, but also in the context of slender flux tubes, that reduce the complexity of the problem while keeping most of the stability properties of the complete problem, In the non-linear regime the instabilities produce turbulence. Recent numerical simulations describe the generation of magnetic fields by a dynamo in the resulting turbulent flow, Eventually such a dynamo may generate a global magnetic field in the disk, The relation of the MHD-turbulence to observations of accretion disks is still obscure. It is commonly believed that magnetic fields can be highly efficient in transporting the angular momentum, but emission lines, short-time scale variability and non-thermal radiation, which a stellar astronomer would take as signs of magnetic variability, are more commonly observed during periods of low accretion rates.