Accretion Disk Torqued by a Black Hole

If a Kerr black hole is connected to a disk rotating around it by a magneticfield, the rotational energy of the Kerr black hole provides an energy sourcefor the radiation of the disk in addition to disk accretion. The black holeexerts a torque on the disk, which transfers energy and angular momentumbetween the black hole and the disk. If the black hole rotates faster than thedisk, energy and angular momentum are extracted from the black hole andtransfered to the disk. The energy deposited into the disk is eventuallyradiated away by the disk, which will increase the efficiency of the disk. Ifthe black hole rotates slower than the disk, energy and angular momentum aretransfered from the disk to the black hole, which will lower the efficiency ofthe disk. With suitable boundary conditions, quasi-steady state solutions areobtained for a thin Keplerian disk magnetically coupled to a Kerr black hole.By ``quasi-steady state'' we mean that any macroscopic quantity at a givenradius in the disk slowly changes with time: the integrated change within onerotation period of the disk is much smaller than the quantity itself. We findthat, the torque produced by the magnetic coupling propagates only outward inthe disk, the total radiation flux of the disk is a superposition of theradiation flux produced by the magnetic coupling and that produced byaccretion. Most interestingly, a disk magnetically coupled to a rapidlyrotating black hole can radiate without accretion. Such a disk has an infiniteefficiency. For a specific example that the magnetic field touches the disk atthe inner boundary, the radial radiation profile is very different from that ofa standard accretion disk: the emissivity index is significantly bigger, mostradiation comes from a region which is closer to the center of the disk.Comment: 38 pages, including 9 figure