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

Abstract

We investigate the possibility that gamma-ray bursts are powered by a central engine consisting of a black hole with an external magnetic field anchored in a surrounding disk or torus. The energy source is then the rotation of the black hole, and it is extracted electromagnetically via a Poynting flux, a mechanism first proposed by Blandford and Znajek (Mon. Nat. R. Astron. Soc. 179 (1997) 433) for AGN. Our reanalysis of the strength of the Blandford–Znajek power shows that the energy extraction rate of the black hole has been underestimated by a factor 10 in previous works. Accounting both for the maximum rotation energy of the hole and for the efficiency of electromagnetic extraction, we find that a maximum of 9% of the rest mass of the hole can be converted to a Poynting flow, i.e. the energy available to produce a gamma-ray burst is 1.6×10 53( M/ M ⊙) erg for a black hole of mass M. We show that the black holes formed in a variety of gamma-ray burst scenarios probably contain the required high angular momentum. To extract the energy from a black hole in the required time of ≲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 makes the Poynting flux from the hole dominate that of the disk. Thereby we demonstrate that the Poynting energy extracted need not be dominated by the disk, nor is limited to the binding energy of the disk. This means that the Blandford–Znajek mechanism remains a very good candidate for powering gamma-ray bursts.