Black hole magnetosphere with small-scale flux tubes

There is observational evidence that the X-ray continuum source that creates the broad fluorescent emission lines in some Seyfert galaxies may be compact and located at a few gravitational radii above the black hole. We consider the possibility that this compact source may be powered by small-scale flux tubes near the black hole that are attached to the orbiting accretion disc. As a first step, this paper investigates the salient features of black hole magnetospheres that contain small-scale, disc-hole linking `closed' flux tubes, using the force-free approximation in an axisymmetric setting. We find that the extent of the closed zone is a result of the balance between the black hole spin induced twist in the closed zone and the confinement pressure of the external (open) field of the disc. The maximal extent of the closed zone, for a typical external confinement, is usually a few gravitational radii. The pressure competition between the closed zone and the external confinement could in principle lead to interesting dynamics and dissipation relevant for the compact X-ray corona.