Strong lensing in the MareNostrum Universe II: scaling relations and
  optical depths
  The strong lensing events that are observed in compact clusters of galaxies
can, both statistically and individually, return important clues about the
structural properties of the most massive structures in the Universe.
Substantial work is ongoing in order to understand the degree of similarity
between the lensing cluster population and the population of clusters as a
whole, with members of the former being likely more massive, compact, and
substructured than members of the latter. In this work we exploit synthetic
clusters extracted from the {\sc MareNostrum Universe} cosmological simulation
in order to estimate the correlation between the strong lensing efficiency and
other bulk properties of lensing clusters, such as the virial mass and the
bolometric X-ray luminosity. We found that a positive correlation exist between
all these quantities, with the substantial scatter being smaller for the
luminosity-cross section relation. We additionally used the relation between
the lensing efficiency and the virial mass in order to construct a synthetic
optical depth that agrees well with the true one, while being extremely faster
to be evaluated. We finally estimated what fraction of the total giant arc
abundance is recovered when galaxy clusters are selected according to their
dynamical activity or their X-ray luminosity. Our results show that there is a
high probability for high-redshift strong lensing clusters to be substantially
far away from dynamical equilibrium, and that $30-40\%$ of the total amount of
giant arcs are lost if looking only at very X-ray luminous objects.
