The strongest gravitational lenses: II. Is the large Einstein radius of
  MACS J0717.5+3745 in conflict with LCDM?
  Can the standard cosmological model be questioned on the basis of a single
observed extreme galaxy cluster? Usually, the word extreme refers directly to
cluster mass, which is not a direct observable and thus subject to substantial
uncertainty. Hence, it is desirable to extend studies of extreme clusters to
direct observables, such as the Einstein radius (ER). We aim to evaluate the
occurrence probability of the large observed ER of MACS J0717.5 within the
standard LCDM cosmology. In particular, we want to model the distribution
function of the single largest ER in a given cosmological volume and to study
which underlying assumptions and effects have the strongest impact on the
results. We obtain this distribution by a Monte Carlo approach, based on the
semi-analytic modelling of the halo population on the past lightcone. After
sampling the distribution, we fit the results with the general extreme value
(GEV) distribution which we use for the subsequent analysis. We find that the
distribution of the maximum ER is particularly sensitive to the precise choice
of the halo mass function, lens triaxiality, the inner slope of the halo
density profile and the mass-concentration relation. Using the distributions so
obtained,we study the occurrence probability of the large ER of MACS J0717.5,
finding that this system is not in tension with LCDM. We also find that the GEV
distribution can be used to fit very accurately the sampled distributions and
that all of them can be described by a Frechet distribution. With a multitude
of effects that strongly influence the distribution of the single largest ER,
it is more than doubtful that the standard LCDM cosmology can be ruled out on
the basis of a single observation. If, despite the large uncertainties in the
underlying assumptions, one wanted to do so, a much larger ER (> 100 arcsec)
than that of MACS J0717.5 would have to be observed.
