Magnetic Flares Near Black Holes

Abstract

Magnetic flaring interactions are investigated between a black hole and an ionized accretion disk. For the electrodynamics in the presence of a black hole we use the 3 + 1-split as described by Thorne, Price and Macdonald (1986). This allows us to treat the problem in a quasi-classical manner.

We assume that magnetic fields created in the disk and extending into a force-free corona, form a connection between the disk and the black hole’s horizon as one of the foot points is transported across the innermost stable orbit. Relative motions between plasma at both ends of the link set up an electrical circuit formed by the linking magnetic fields, the well-conducting disk and the horizon. We assume that the Alfvén crossing time of the circuit is less than the shearing time. Then the coronal part of the circuit evolves along a sequence of force-free states.

If the total resistance of the circuit (including the horizon part) is large enough a steady state may be possible with a slipping circuit and an azimuthal magnetic field component which is smaller than the poloidal component. In general however a steady state is not possible because of the large magnetic Reynolds number of such an astrophysical system. Then kinetic energy, either from the rotating hole or from the accreting matter, is stored periodically in the form of force-free magnetic fields and released in field relaxations by reconnection. These magnetic Bares resemble those in a system which consists of a magnetic neutron star and an accretion disk (Aly and Kuijpers, 1990; Kuijpers, 1990). We consider both a non-rotating and a maximally rotating black hole and derive under what conditions magnetic flares can be expected. We find that the energy release in the form of a sequence of magnetic explosions can be a substantial fraction of the Eddington luminosity.