Comparison of an X-ray selected sample of massive lensing clusters with
  the MareNostrum Universe LCDM simulation
  A long-standing problem of strong lensing by galaxy clusters regards the
observed high rate of giant gravitational arcs as compared to the predictions
in the framework of the "standard" cosmological model. Recently, few other
inconsistencies between theoretical expectations and observations have been
claimed which regard the large size of the Einstein rings and the high
concentrations of few clusters with strong lensing features. All of these
problems consistently indicate that observed galaxy clusters may be
gravitational lenses stronger than expected. We use clusters extracted from the
MareNostrum Universe to build up mock catalogs of galaxy clusters selected
through their X-ray flux. We use these objects to estimate the probability
distributions of lensing cross sections, Einstein rings, and concentrations for
the sample of 12 MACS clusters at $z>0.5$ presented in Ebeling et al. (2007)
and discussed in Zitrin et al. (2010). We find that simulated clusters produce
$\sim 50%$ less arcs than observed clusters do. The medians of the
distributions of the Einstein ring sizes differ by $\sim 25%$ between
simulations and observations. We estimate that, due to cluster triaxiality and
orientation biases affecting the lenses with the largest cross sections, the
concentrations of the individual MACS clusters inferred from the lensing
analysis should be up to a factor of $\sim 2$ larger than expected from the
$\Lambda$CDM model. The arc statistics, the Einstein ring, and the
concentration problems in strong lensing clusters are mitigated but not solved
on the basis of our analysis. Nevertheless, due to the lack of redshifts for
most of the multiple image systems used for modeling the MACS clusters, the
results of this work will need to be verified with additional data. The
upcoming CLASH program will provide an ideal sample for extending our
comparison (abridged).
