Constraints on cosmological parameters from clusters containing luminous arcs

It is well established that the luminous arcs seen in several clusters of galaxies are more distant galaxies imaged into a partial Einstein ring by the gravitational field of the intervening cluster. If the mass distribution in the cluster can be independently determined by the internal dynamics, then the mean angular distance of the arc from the cluster centre roughly the Einstein ring radius) depends upon the cosmological parameters. We investigate the possible constraints placed upon the cosmological constant and the density parameter by measurements of velocities of galaxies in such cluster lenses, In the case of A 370, a cluster lens with velocities measured for about 30 galaxies, the data are consistent with a zero cosmological constant, provided that the total mass distribution in the cluster is identical to that of the mean radial distribution of the galaxies. However, given the statistical uncertainty in the measured velocity dispersion, a wide range of cosmologies with non-zero cosmological constant is permitted. Closed models with an antipodal redshift less than 3 are excluded at the 90 per cent confidence level. No constraint can be placed upon the density parameter. If the assumption concerning the mass distribution is dropped, then nothing at all can be said about cosmology; however, for A370, the data are inconsistent at a 70 per cent confidence level with a mass distribution which is much more centrally condensed than the observed galaxy distribution. Multifrequency X-ray observations of the hot gas may place more definitive constraints upon the cosmological constant because the gas temperature and density distribution more directly trace the total mass distribution, and the statistical uncertainty is very much reduced.