Stationary Relativistic MHD Flows

Abstract

It is widely accepted that the formation of jets in active galactic nuclei and in young stellar sources is ultimately related to the existence of gaseous disks around some central object. Rotating black holes are still thought to be the prime-mover behind the activity detected in centers of galaxies, while, in the case of protostellar jets, rapidly rotating stars and disks are responsible for the ejection of bipolar outflows. in both cases, magnetic fields are invoked for the acceleration and the collimation of these outflows.

MHD flows near rapidly rotating compact objects must include the general relativistic effects of the underlying metric. Relativistic jet flows on the parsec-scale in active galactic nuclei have to be based on special relativistic elements which go beyond the traditional Newtonian MHD description. We give a comprehensive introduction into the theory of relativistic MHD for rapidly rotating compact objects with special emphasis on axisymmetric flows. In addition, we show that accreting black holes dispose of two different energy channels — the accretion power as well as dissipation of rotational energy of a black hole by means of magnetic processes. The angular momentum can only be tapped from black holes by interaction with rotating magnetospheres that are built up e.g. by the inner accretion disk.

The gravitational field of rotating black holes is more complex than that of Newtonian objects. In addition to the ordinary gravitational force, the rapid rotation of compact objects also generates the gravitomagnetic force which couples with electromagnetic fields over Maxwell’s equations. This effect has interesting consequences e.g. for the time-evolution of magnetic fields advected from the interstellar matter towards the black hole. The shearing of the absolute space around rapidly rotating black holes acts as a gravitomagnetic dynamo effect which amplifies any seed field near a rotating object. This process will provide the dipolar magnetic structures that are behind the bipolar outflows seen as relativistic jets in elliptical galaxies. The magnetic fields also influence the accretion towards the rotating black hole. For sufficiently rapidly rotating holes, the accretion can carry negative angular momentum inwards, spinning down in this way the black hole. For extremely fast rotating holes, accretion could even occur with total negative energy.

The presence of magnetic fields near rotating black holes has other consequences. The rapid rotation of the disk-magnetosphere initiates outflows which are collimated on the scale of a few hundred Schwarzschild radii into cylindrical relativistic jets. Solutions of the force-balance equation are discussed which demonstrate the mechanism. The structure of the magnetic fields dragged along into the parsec-scale jets is essential for the understanding of the emission mechanisms of flat-spectrum quasars and BL Lac objects. Self-collimation also works in the protostellar case, since typical jet radii derived from observations are of the order of a few light cylinder radii, which makes Newtonian MHD obsolete on this scale.