The strongest gravitational lenses II. Is the large Einstein radius of MACS J0717.5+3745 in conflict with ΛCDM?

Context. With the amount and quality of galaxy cluster data increasing, the question arises whether or not the standard cosmological model can 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. Aims. We aim to evaluate the occurrence probability of the large observed Einstein radius of MACS J0717.5+3745 within the standard Lambda CDM cosmology. In particular, we want to model the distribution function of the single largest Einstein radius in a given cosmological volume and to study which underlying assumptions and effects have the strongest impact on the results. Methods. 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. Results. We find that the distribution of the maximum Einstein radius 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 Einstein radius of MACS J0717.5+3745, finding that this system is not in tension with Lambda CDM. 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 (type-II) Frechet distribution. Conclusions. With a multitude of effects that strongly influence the distribution of the single largest Einstein radius, it is more than doubtful that the standard Lambda CDM 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 Einstein radius (greater than or similar to 100 '') than that of MACS J0717.5+3745 would have to be observed.