Energetics of a Black Hole-Accretion Disk System with Magnetic Connection: Limit of Low Accretion Rate

Abstract We consider the energetics of a black hole-accretion disk system with magnetic connection: a Keplerian disk is connected to a Kerr black hole by a large-scale magnetic field. We assume that 1) the magnetic field is locked to the inner boundary of the disk and corotates with it, and 2) the accretion rate is low, but the accretion from the disk can still provide a sufficient amount of cold plasma particles in the transition region so that the magnetohydrodynamics approximation is valid. By finding solutions that smoothly pass the fast critical point near the equatorial plane, we find that a system with a fast rotating black hole and that with a slow rotating black hole behave very differently. For a black hole with $a \gt a_\mathrm{cr} \equiv 0.3594 \,M a > a_\mathrm{cr} \equiv 0.3594 \,M$, where $M$ is the mass and $a$ is the specific angular momentum of the black hole, the spinning energy of the black hole is efficiently extracted and transported to the disk, thus increasing the radiation efficiency of the disk by orders of magnitude. For a black hole with $0 \leq a < a_\mathrm{cr}$, the inner region of the disk is disrupted by the magnetic field and the inner boundary moves out to a radius where the angular velocity of the disk is equal to the spinning angular velocity of the black hole. As a result, the disk may have an extremely low radiation efficiency if $0\leq a/M \ll 1$.