The Blandford-Znajek process as a central engine for a gamma-ray burst

We investigate the possibility that gamma-ray bursts are powered by a centr al engine consisting of a black hole with an external magnetic field anchor ed in a surrounding disk or torus. The energy source is then the rotation o f the black hole, and it is extracted electromagnetically via a Poynting fl ux, a mechanism first proposed by Blandford and Znajek (Mon. Nat, R. Astron . Sec. 179 (1997) -133) for AGN. Our reanalysis of the strength of the Blan dford-Znajek power shows that the energy extraction rate of the black hole has been underestimated by a factor 10 in previous works. Accounting both f or the maximum rotation energy of the hole and for the efficiency of electr omagnetic extraction? we find that a maximum of 9% of the rest mass of the hole call be converted to a Poynting flow, i.e. the energy available to pro duce a gamma-ray burst is 1.6 x 10(S3)(M/M.) erg for a black hole of mass M . We show that the black holes formed in a variety of gamma-ray burst scena rios probably contain the required high angular momentum. To extract the en ergy from a black hole in the required time of less than or similar to 1000 s a field of 10(15) G near the black hole is needed, We give an example of a disk-plus-field structure that both delivers the required field and make s the Poynting Aux from the hole dominate that of the disk. Thereby we demo nstrate that the Poynting energy extracted need not be dominated by the dis k, nor is limited to the binding energy of the disk. This means that the Bl andford-Znajek mechanism remains a very good candidate for powering gamma-r ay bursts. (C) 2000 Elsevier Science B.V. All rights reserved.