Lensed arc statistics: comparison of Millennium-simulation galaxy
  clusters to Hubble Space Telescope observations of an X-ray selected sample
  It has been debated for a decade whether there is a large overabundance of
strongly lensed arcs in galaxy clusters, compared to expectations from
LambdaCDM cosmology. We perform ray tracing through the most massive halos of
the Millennium simulation at several redshifts in their evolution, using the
Hubble Ultra Deep Field as a source image, to produce realistic simulated
lensed images. We compare the lensed arc statistics measured from the
simulations to those of a sample of 45 X-ray selected clusters, observed with
the Hubble Space Telescope, that we have analysed in Horesh et al. (2010). The
observations and the simulations are matched in cluster masses, redshifts,
observational effects, and the algorithmic arc detection and selection. At
z=0.6 there are too few massive-enough clusters in the Millennium volume for a
proper statistical comparison with the observations. At redshifts 0.3<z<0.5,
however, we have large numbers of simulated and observed clusters, and the
latter are an unbiased selection from a complete sample. For these redshifts,
we find excellent agreement between the observed and simulated arc statistics,
in terms of the mean number of arcs per cluster, the distribution of number of
arcs per cluster, and the angular separation distribution. At z ~ 0.2 some
conflict remains, with real clusters being ~3 times more efficient arc
producers than their simulated counterparts. This may arise due to selection
biases in the observed subsample at this redshift, to some mismatch in masses
between the observed and simulated clusters, or to physical effects that arise
at low redshift and enhance the lensing efficiency, but which are not
represented by the simulations.
