  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.
