Force‐Free Magnetosphere of an Accretion Disk–Black Hole System. II. Kerr Geometry

We consider a stationary axisymmetric force-free degenerate magnetosphere ofa rotating Kerr black hole surrounded by a thin Keplerian infinitely-conductingaccretion disk. We focus on the closed-field geometry characterize by a directmagnetic coupling between the disk and the hole's event horizon. We first arguethat the hole's rotation necessarily limits the radial extent of the force-freelink on the disk surface: the faster the hole rotates, the smaller themagnetically-connected inner part of the disk has to be. We then show that thisis indeed the case by solving numerically the Grad--Shafranov equation--themain differential equation describing the structure of the magnetosphere. Animportant element in our approach is the use of the regularity condition at theinner light cylinder to fix the poloidal current as a function of the poloidalmagnetic flux. As an outcome of our computations, we are able to chart out themaximum allowable size of the portion of the disk that is magneticallyconnected to the hole as a function of the black hole spin. We also calculatethe angular momentum and energy transfer between the hole and the disk thattakes place via the direct magnetic link. We find that both of these quantitiesgrow rapidly and that their deposition becomes highly concentrated near theinner edge of the disk as the black hole spin is increased.Comment: 45 pages, 12 figures. Accepted for publication in the Astrophysical Journa