The strongest gravitational lenses: IV. The order statistics of the largest Einstein radii with cluster mergers

Abstract

Based on techniques developed in the previous papers of this series, we investigate the impact of galaxy-cluster mergers on the order statistics of the largest Einstein radii. We show that the inclusion of mergers significantly shifts the extreme value distribution of the largest Einstein radius to higher values, typically increasing the expected value by $\sim 10\%$. A comparison with current data reveals that the largest observed Einstein radius agrees excellently well with the theoretical predictions of the $\Lambda$CDM model at redshifts $z>0.5$. At redshifts $z<0.5$, our results are somewhat more controversial. Although cluster mergers also increase the expected values of the order statistics of the $n$ largest Einstein radii by $\sim 10\%$, the theoretically expected values are notably lower ($\sim 3\sigma$ deviation for $n=12$) than the largest Einstein radii of a selected sample of SDSS clusters in the redshift range $0.1\le z\le 0.55$. The uncertainties of the observed Einstein radii are still large, however, and thus the measurements need to be carefully revised in future works. Therefore, given the premature state of current observational data, overall, there is still no reliable statistical evidence for observed Einstein radii to exceed the theoretical expectations of the standard cosmological model.

arXiv comment9 pages, 7 figures, 1 table; accepted for publication in A&A

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• RELICS: Strong-lensing analysis of the massive clusters MACS J0308.9+2645 and PLCK G171.9-40.7
• A Very Large (${\theta }_E\gtrsim 40$") Strong Gravitational Lens Selected with the Sunyaev-Zel'dovich Effect: PLCK G287.0+32.9 ($z$ = 0.38)
• RELICS: A Very Large (${\theta }_E\sim 40"$) Cluster Lens -- RXC J0032.1+1808
• Strong Lensing Analysis of the Powerful Lensing Cluster MACS J2135.2-0102 ($z$=0.33)