Binary neutron star mergers are plausible progenitor candidates for short gamma-ray bursts ( GRBs ) ; however , a detailed explanation of their central engine is still lacking .
The annihilation of neutrino pairs has been proposed as one of the possible powering mechanisms .
We present calculations of the energy and momentum deposition operated by neutrino pair annihilation above merger remnants .
Starting from the results of a detailed , three-dimensional simulation of the aftermath of a binary neutron star merger , we compute the deposition rates over a time scale comparable to the life time of the disk ( t \approx 0.4 s ) , assuming a long-lived massive neutron star ( MNS ) .
We model neutrino emission using a spectral leakage scheme and compute the neutrino annihilation rates using a ray-tracing algorithm .
We find that the presence of the MNS increases the energy deposition rate by a factor \sim 2 , mainly due to the annihilation of radiation coming from the MNS with radiation coming from the disk .
We compute the impact of relativistic effects and discover that , despite they can significantly change the local rate intensity , the volume-integrated results are only marginally decreased .
The cumulative deposited energy , extrapolated to 1 sec , is \approx 2.2 \times 10 ^ { 49 } { erg } .
A comparison with the inferred short GRB energetics reveals that in most cases this energy is not large enough , even assuming small jet opening angles and a long-lived MNS .
Significantly more intense neutrino luminosities ( a factor 5-10 larger ) are required to explain most of the observed short GRB .
We conclude that it is unlikely that neutrino pair annihilation can explain the central engine of short GRBs alone .