Proc. Neutrino Astrophysics - MPP Theory Group

From our torus models we find that the energy deposition rate by ν¯ν-annihilation near the
evacuated system axis is about ˙ Eν¯ν ≈ 5×10 50 erg/s. The corresponding annihilation efficiency
εa is of the order of ˙ Eν¯ν/Lν ≈ 5 × 10 −3 which is rather large because of the large νe and ¯νe
luminosities and because the torus geometry allows for a high reaction probability of neutrinos
with antineutrinos. In order to account for an observed GRB luminosity of Lγ ∼ 10 51 erg/s the
required focussing of the ν¯ν-annihilation energy is moderate, δΩ/(4π) = ˙ Eν¯ν/(2Lγ) ∼ 1/4,
corresponding to an opening angle of about 60 degrees. This value does not seem implausible
for the geometry of a thick accretion torus. Taking into account general relativistic effects
into the treatment of ν¯ν-annihilation reduces the above estimates only by about 10–50%.
In summary, our numerical simulations show that stellar mass black holes with accretion
tori that form after the merging of neutron star binaries have masses, lifetimes, and neutrino
luminosities that might provide enough energy by ν¯ν-annihilation to account for short and
not too powerful GRBs. The longer bursts and very energetic events, however, would require
an alternative explanation, e.g., failed supernovae (or “collapsars”) [9] where a stellar mass
black hole could have a more than 10 times more massive accretion torus than in the binary
neutron star scenario.
Acknowledgments
The calculations were performed at the Rechenzentrum Garching on an IBM SP2.
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