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 z_s = 2.0, we find that mergers increase the number of
Einstein radii above 10 arcsec (20 arcsec) 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 arcsec (20 arcsec)
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.Comment: 23 pages, 18 figures; accepted for publication in Astronomy and
Astrophysics; v2: minor corrections (added clarifying comments; added Fig.
19) to match the accepted versio
