In this paper we present a model for the short (1 s) population of gamma-ray bursts. In this model heated neutron stars in a close binary system near its last stable orbit emit a large amount of neutrinos (~1053 ergs). A fraction of these neutrinos will annihilate to form an e+e- pair plasma wind that will, in turn, expand and recombine to photons that make the gamma-ray burst. We study neutrino annihilation and show that a substantial fraction (~) of the energy deposited into e+e- pairs comes from interstar neutrinos, where each member of the neutrino pair originates from each neutron star. Thus, in addition to the annihilation of neutrinos blowing off of a single star, there is a new source of baryon-free plasma that is deposited between the stars. To model the e+e- pair plasma wind between stars, we do three-dimensional relativistic numerical hydrodynamic calculations. We find that the timescale for these bursts, deriving from the baryon-free plasma, is less than 1 s and that they will have a hot spectrum ~5 MeV. The energy in bursts is of the order of 1052 ergs.
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