Characterizing the Cluster Lens Population

We present a detailed investigation into which properties of cold dark matter halos make them effective strong gravitational lenses. The cross sections for giant arc formation of 878 clusters from a high-resolution N-body simulation of the ΛCDM cosmology are measured by ray tracing through 13,594 unique projections. We measure concentrations, axis ratios, orientations, and the amount of substructure of each cluster, and compare the lensing weighted distribution of each quantity to that of the cluster population as a whole. We find that NFW profiles provide just as good a fit to lensing clusters as they do to the total cluster population; however, the concentrations of lensing clusters are on average 34% larger than the typical cluster in the Universe. Despite this bias, the anomalously high concentrations of lensing clusters (c > 14) recently measured by several groups from combined strong and weak lensing analyses (Kneib et al. 2003; Gavazzi et al. 2003; Broadhurst et al. 2005b), appear to be inconsistent with the concentration distribution in our simulations, which predict < 2% of lensing clusters should have concentrations this high. No correlation is found between strong lensing cross section and the amount of substructure, indicating that the population of cluster lenses is no more relaxed or disturbed than typical clusters in the Universe. Lensing clusters tend to have their principal axis aligned with the the line of sight: the median angle is |cos θ| = 0.67. We introduce several different types of simplified dark matter halos, and use them to isolate which properties of CDM clusters make them effective gravitational lenses. Projections of halo substructure onto small radii and the large scale mass distribution of clusters do not significantly influence strong lensing cross sections. The abundance of giant arcs is primarily determined by the mass distribution within an average overdensity of ∼ 10, 000. The clumpy cores of dark matter halos result in ∼ 25−60% more giant arcs than smooth ellipsoids of the same total mass. A multiple lens plane ray tracing algorithm is used to show that projections of large scale structure increase strong lensing cross sections by a modest amount . 7%. We revisit the question of whether there is an excess of giant arcs detected for high redshift clusters in the Red-Sequence Cluster Survey (Gladders et al. 2003) and find that the number of high redshift (z & 0.6) lensing clusters is in good agreement with ΛCDM, although our simulations predict more low redshift (z . 0.6) lensing clusters than were observed. Subject headings: dark matter – galaxies: clusters: cosmology: theory – methods: numerical – clusters: general – large scale structure of the universe – gravitational lensing