Characterizing the Cluster Lens Population

We present a detailed investigation into which properties of CDM halos makethem effective strong gravitational lenses. Strong lensing cross sections of878 clusters from an N-body simulation are measured by ray tracing through13,594 unique projections. We measure concentrations, axis ratios,orientations, and the amount of substructure of each cluster, and compare thelensing weighted distribution of each quantity to that of the clusterpopulation as a whole. The concentrations of lensing clusters are on average34% larger than the typical cluster in the Universe. Despite this bias, theanomalously high concentrations (c >14) recently measured by several groups,appear to be inconsistent with the concentration distribution in oursimulations, which predict < 2% of lensing clusters should have concentrationsthis high. No correlation is found between lensing cross section and the amountof substructure. We introduce several types of simplified dark matter halos,and use them to isolate which properties of CDM clusters make them effectivelenses. Projections of halo substructure onto small radii and the large scalemass distribution of clusters do not significantly influence cross sections.The abundance of giant arcs is primarily determined by the mass distributionwithin an average overdensity of ~ 10,000. A multiple lens plane ray tracingalgorithm is used to show that projections of large scale structure increasethe giant arc abundance by a modest amount <7%. We revisit the question ofwhether there is an excess of giant arcs behind high redshift clusters in theRCS survey and find that the number of high redshift (z > 0.6) lenses is ingood agreement with LCDM, although our simulations predict more low redshift (z< 0.6) lenses than were observed. (abridged)Comment: 19 pages, 15 figures. Submitted to Ap