The Lensed Arc Production Efficiency of Galaxy Clusters: A Comparison of Matched Observed and Simulated Samples

We compare the statistical properties of giant gravitationally lensed arcs produced in matched simulated and observed cluster samples. The observed sample consists of 10 X-ray-selected clusters at redshifts zc ~0.2 imaged with HST by Smith et al. The simulated data set is produced by lensing the Hubble Deep Field, which serves as a background source image, with 150 realizations (different projections and shifts) of five simulated zc = 0.2 clusters from a (lambda)CDM N-body simulation. The real and simulated clusters have similar masses, the real photometric redshift is used for each background source, and all the observational effects influencing arc detection in the real data set, including light from cluster galaxies, are simulated in the artificial data set. We develop, and apply to both data sets, an objective automatic arc-finding algorithm. We find consistent arc statistics in the real and in the simulated sample, with an average of ~1 detected giant (length-to-width ratio l/w >=10) arc per cluster and ~0.2 giant luminous (RST < 22.3 mag) arcs per cluster. Thus, taking into account a realistic source population and observational effects, the clusters predicted by (lambda)CDM have the same arc production efficiency as the observed clusters. If, as suggested by other studies, there is a discrepancy between the predicted and the observed total number of arcs on the sky, it must be the result of differences between the redshift-dependent cluster mass functions and not due to differences in the lensing efficiency of the most massive clusters.