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For more than a decade now, it has been controversial whether or not the high rate of
giant gravitational arcs and the largest observed Einstein radii are consistent with the
standard cosmological model. Recent studies indicate that mergers provide an efficient
mechanism to substantially increase the strong-lensing efficiency of individual clusters.
Based on purely semi-analytic methods, we investigated the statistical impact of cluster
mergers on the distribution of the largest Einstein radii and the optical depth for giant
gravitational arcs of selected cluster samples. Analysing representative all-sky
realizations of clusters at redshifts z < 1 and
assuming a constant source redshift of zs = 2.0, we find that
mergers increase the number of Einstein radii above 10″ (20″) by ~35% (~55%). Exploiting the tight correlation between Einstein radii and lensing
cross sections, we infer that the optical depth for giant gravitational arcs with a
length-to-width ratio ≥ 7.5 of those clusters with Einstein radii above 10″ (20″) increases by ~45% (~85%). Our findings suggest that cluster mergers significantly
influence in particular the statistical lensing properties of the strongest gravitational
lenses. We conclude that semi-analytic studies must inevitably take these events into
account before questioning the standard cosmological model on the basis of the largest
observed Einstein radii and the statistics of giant gravitational arcs
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