This is the version of the paper from arXiv.org. Subsequently published as Monthly Notices of the Royal Astronomical Society, 2006, 372, pp.1351-1356, available from http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2966.2006.10942.x. The definitive version is available from www.blackwell-synergy.com.Cosmological long-duration gamma-ray bursts (LGRBs) are thought to originate from the core collapse to black holes of stripped massive stars. Those with sufficient rotation form a centrifugally-supported torus whose collapse powers the GRB. We investigate the role of tidal locking within a tight binary as a source of the necessary angular momentum. We find that the binary orbit must be no wider than a few solar radii for a torus to form upon core collapse. Comparing this criterion to the observed population of binaries containing two compact objects suggests that rotation may have been important in the formation of up to 50% of the observed systems. As these systems created a neutron star and not a black hole they presumably did not produce highly luminous GRBs. We suggest instead that they make the subset of GRBs in the relatively local universe which have much lower luminosity
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