Trapping of Magnetic Flux by the Plunge Region of a Black Hole Accretion Disk

The existence of the radius of marginal stability means that accretion flowsaround black holes invariably undergo a transition from a MHD turbulentdisk-like flow to an inward plunging flow. We argue that the plunging inflowcan greatly enhance the trapping of large scale magnetic field on the blackhole, and therefore may increase the importance of the Blandford-Znajek (BZ)effect relative to previous estimates that ignore the plunge region. We supportthis hypothesis by constructing and analyzing a toy-model of the dragging andtrapping of a large scale field by a black hole disk, revealing a strongdependence of this effect on the effective magnetic Prandtl number of the MHDturbulent disk. Furthermore, we show that the enhancement of the BZ effectdepends on the geometric thickness of the accretion disk. This may be, at leastin part, the physical underpinnings of the empirical relation between theinferred geometric thickness of a black hole disk and the presence of a radiojet.