  We have used the two-degree field (2dF) multi-fibre spectrograph of the
Anglo-Australian Telescope to search for candidate members of the unusual
globular cluster omega Centauri at and beyond the cluster tidal radius.
Velocities with an accuracy of ~10 kms-1 were obtained for 4105 stars selected
to lie in the vicinity of the lower giant branch in the cluster
colour-magnitude diagram and which cover an area on the sky of ~2.4x3.9 deg2
centered on the cluster. Within the velocity interval 190-270 kms-1, the
cluster member candidates have a steeply declining surface density distribution
consistent with the adopted tidal radius of 57`. For stars in the sample beyond
the tidal radius, an analysis of line-strengths from the spectra, as well as
radial velocities, identifies only six stars as possible candidates for
extra-tidal association with the cluster. If all six of these stars are indeed
related to the cluster, then a maximum of 0.7 +/- 0.2 per cent of the total
cluster mass is contained in the region between one and two tidal radii. Given
this limit, we conclude that there is no compelling evidence for any
significant extra-tidal population in omega Cen. The effects of tidal shocks on
the outer parts of the cluster are consistent with this limit. Theories for the
origin of omega Cen frequently suggest that the cluster is the former nucleus
of a tidally stripped dwarf galaxy. Our results require that the stripping
process must have been largely complete at early epochs, consistent with
dynamical models of the process. The stripped former dwarf galaxy stars are
therefore now widely distributed around the Galaxy.
