Characterizing strong lensing galaxy clusters using the Millennium-XXL and MOKA simulations

In this paper, we investigate the strong lensing statistics in galaxyclusters. We extract dark matter haloes from the Millennium- XXL simulation, compute their Einstein radius distribution, and find a very good agreement with Monte Carlo predictions produced with the MOKA code. The distribution of the Einstein radii is well described by a lognormal distribution, with a considerable fraction of the largest systems boosted by different projection effects. We discuss the importance of substructures and triaxiality in shaping the size of the critical lines for cluster size haloes. We then model and interpret the different deviations, accounting for the presence of a Brightest Central Galaxy (BCG) and two different stellar mass density profiles. We present scaling relations between weak lensing quantities and the size of the Einstein radii. Finally, we discuss how sensible is the distribution of the Einstein radii on the cosmological parameters Omega(M) - sigma(8) finding that cosmologies with higher Omega(M) and sigma(8) possess a large sample of strong lensing clusters. The Einstein radius distribution may help distinguish Planck13 and WMAP7 cosmology at 3 sigma.