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Cluster strong lensing in the Millennium Simulation: The effect of galaxies and structures along the line-of-sight

We use ray-tracing through the Millennium simulation to study how secondary matter structures along the line-of-sight and the stellar mass in galaxies affect strong cluster lensing, in particular the cross-section for giant arcs. Furthermore, we investigate the distribution of the cluster Einstein radii and the radial distribution of giant arcs. We find that additional structures along the line-of-sight increase the strong-lensing optical depth by ~10-25%, while strong-lensing cross-sections of individual clusters are frequently boosted by as much as ~50%. The enhancement is mainly due to structures that are not correlated with the lens. Cluster galaxies increase the strong-lensing optical depth by up to a factor of 2, while interloping galaxies are not significant. We conclude that these effects need to be taken into account for predictions of the giant arc abundance, but they are not large enough to fully account for the reported discrepancy between predicted and observed abundances. Furthermore, we find that Einstein radii defined via the area enclosed by the critical curve are 10-30% larger than those defined via radial surface mass density profiles. The contributions of radial and tangential arcs to the radial distribution of arcs can be clearly distinguished. The radial distribution of tangential arcs is very broad and extends out to several Einstein radii. Thus, individual arcs are not well suited for constraining Einstein radii.