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 arcsproduced in matched simulated and observed cluster samples. The observed sampleconsists of 10 X-ray selected clusters at redshifts z ~ 0.2 imaged with HST bySmith et al. The simulated dataset is produced by lensing the Hubble DeepField, which serves as a background source image, with 150 realizations(different projections and shifts) of five simulated z = 0.2 clusters from aLambdaCDM N-body simulation. The real and simulated clusters have similarmasses, the real photometric redshift is used for each background source, andall the observational effects influencing arc detection in the real dataset,including light from cluster galaxies, are simulated in the artificial dataset.We develop, and apply to both datasets, an objective automatic arc-findingalgorithm. We find consistent arc statistics in the real and in the simulatedsample, with an average of ~ 1 detected giant (length to width ratio >= 10) arcper cluster and ~ 0.2 giant luminous (R<22.3 mag) arc per cluster. Thus, takinginto account a realistic source population and observational effects, theclusters predicted by LambdaCDM have the same arc-production efficiency as theobserved clusters. If, as suggested by other studies, there is a discrepancybetween the predicted and the observed total number of arcs on the sky, it mustbe the result of differences between the redshift dependent cluster massfunctions, and not due to differences in the lensing efficiency of the mostmassive clusters.