Statistics of giant arcs in galaxy clusters

We study the expected properties and statistics of giant arcs produced by galaxy clusters in a ACDM (cold dark matter) universe and investigate how the characteristics of CDM clusters determine the properties of the arcs they generate. Because of the triaxiality and substructure of CDM halos, the giant-arc cross section for individual clusters varies by more than an order of magnitude as a function of viewing angle. In addition, the shallow density cusps and triaxiality of CDM clusters cause systematic alignments of giant arcs that should be testable with larger samples from forthcoming lensing surveys. We compute the predicted statistics of giant arcs for the ACDM model and compare them with results from previous surveys. The predicted arc statistics are in excellent agreement with the numbers of giant arcs observed around low-redshift (0.2 ≲ z ≲ 0.6) clusters from the Extended Medium-Sensitivity Survey sample; however, there are hints of a possible excess of arcs observed around high-redshift (z ≳ 0.6) clusters. This excess, if real, appears to be due to the presence of highly massive or concentrated clusters at high redshifts.