The Detection and Statistics of Giant Arcs Behind CLASH Clusters

We developed an algorithm to find and characterize gravitationally lensed galaxies (arcs) to perform a comparison of the observed and simulated arc abundance. Observations are from the Cluster Lensing And Supernova survey with Hubble (CLASH). Simulated CLASH images are created using the MOKA package and also clusters selected from the high resolution, hydrodynamical simulations, MUSIC, over the same mass and redshift range as the CLASH sample. The algorithm' s arc elongation accuracy, completeness and false positive rate are determined and used to compute an estimate of the true arc abundance. We derive a lensing efficiency of $4 \pm 1$ arcs (with length $\ge 6"$ and length-to-width ratio $\ge 7$) per cluster for the X-ray selected CLASH sample, $4 \pm 1$ arcs per cluster for the MOKA simulated sample and $3 \pm 1$ arcs per cluster for the MUSIC simulated sample. The observed and simulated arc statistics are in full agreement. We measure the photometric redshifts of all detected arcs and find a median redshift $z_s = 1.9$ with 33% of the detected arcs having $z_s > 3$. We find that the arc abundance does not depend strongly on the source redshift distribution but is sensitive to the mass distribution of the dark matter halos (e.g. the $c-M$ relation). Our results show that consistency between the observed and simulated distributions of lensed arc sizes and axial ratios can be achieved by using cluster-lensing simulations that are carefully matched to the selection criteria used in the observations.