Abstract
Hyper-accretion discs around black holes emit copious neutrinos and anti-neutrinos. A fraction of the emitted neutrinos convert to electron-positron plasma above the disc through the annihilation reaction $\nu\bar\nu\to e^+e^-$. This process may drive relativistic jets associated with GRB explosions. We calculate the efficiency of energy deposition by neutrinos. Our calculation is fully relativistic and based on a geodesic-tracing method. We find that the efficiency of neutrino heating is a well-defined function of (i) accretion rate and (ii) spin of the black hole. It is practically independent of the details of neutrino transport in the opaque zone of the disc. The results help identify accretion discs whose neutrino emission can power GRBs.
Highlights
A plausible model for the central engines of gamma-ray bursts (GRBs) pictures a transient, hyper-accreting disc formed around a rotating black hole
The disc is a source of copious neutrinos and anti-neutrinos, which partially annihilate above the disc and turn into e± pairs, ν + ν → e− + e+
The two processes of e± creation considered in this paper (Section 2.3) give the total energy deposition rate E = Eνν+ EνB
Summary
A plausible model for the central engines of gamma-ray bursts (GRBs) pictures a transient, hyper-accreting disc formed around a rotating black hole (see Beloborodov 2008 for a recent review). The disc is a source of copious neutrinos and anti-neutrinos, which partially annihilate above the disc and turn into e± pairs, ν + ν → e− + e+. This process was proposed as a possible mechanism for creating relativistic, e±-dominated jets that could power observed GRBs (Eichler et al 1989). Its accurate calculation requires a detailed relativistic model for the neutrino source — the accretion disc — as well as tracing the neutrino propagation in the Kerr spacetime of the black hole. Our work has three motivations: (i) A relativistic calculation of ννannihilation has never been done for a realistic accretion disc around a spinning black hole.
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