A statistically complete survey for arc-like features in images of distant rich clusters of galaxies.

Using data from an earlier search for supernovae in distant clusters, we have constructed a homogeneous set of V images for 19 rich clusters with mean redshift z¯¯¯=0.32z¯=0.32. By considering the images above a fixed surface brightness limit, the data for extended arc-like features which might arise from gravitational lensing of background sources. A list of 20 candidate arcs is presented. We examine the usefulness of such a catalogue for deriving the background source redshift distribution, NzNz. Whilst the number and shape distribution of arc candidates is consistent with the lensing hypothesis, cluster velocity dispersions of very high precision would be needed to provide useful constraints on the fraction of high-redshift galaxies to faint limits. We show how, in principle, a likelihood ratio test based on the radial distribution of arcs in a single well-studied cluster could determine whether a significant fraction of the faint galaxy population is at high redshift. This test also provides a means of determining accurate cluster velocity dispersions at any redshift