Conclusions

Black hole rotation is, in principle, a more than sufficient source of energy for energizing even the most powerful relativistic jets. The viability of magnetic extraction of black hole spin energy does, however, hinge on the strength of the horizon-threading poloidal magnetic field that can be established by the accretion flow. In this paper, we have argued that the plunge region of the black hole accretion disk has an important role to play in enhancing the horizon-threading field well above the modest levels suggested by previous works. We support this hypothesis by constructing a toy-model (that is non-relativistic, assumes axisymmetry, and treats the fields away from the disk plane as potential) with which we can follow the dragging of an external magnetic field by the disk and its subsequent trapping by the plunge region. Our toy model suggests that the BZ effect can be enhanced above the canonical estimates of GA97 by a factor of $[1+xP_{\rm m}(h/r)]^2$ where $P_{\rm m}$ is the effective magnetic Prandtl number of the disk and $x\sim {\cal O}(r_{\rm dead}/r_{\rm ms})$. Even in cases where the effective magnetic diffusivity is small due to the MHD turbulence (i.e., $P_{\rm m}\sim 1$), the BZ effect can be enhanced by one order of magnitude (or more) above the GA97 value if the disk is geometrically-thick $h/r\approxgt r_{\rm ms}/r_{\rm dead}$. The $h/r$-dependence of this effect has an appealing resonance with the empirical evidence from GBHBs which points to a close connection between the existence of powerful black hole jets and the inferred properties of the accretion disk.

We thank Phil Armitage and Cole Miller for insightful discussions throughout this work. This research was supported by the National Science Foundation under grants PHY-990794 (CSR, MCB), AST-0205990, and AST-0307502 (MCB). Part of this work was carried out at the Kalvi Institute for Theoretical Physics at the University of California, Santa Barbara; CSR and MCB thank the members of KITP for their hospitality.