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

TL;DR

This paper studies how galaxy-cluster mergers affect the distribution of the largest Einstein radii, finding that mergers increase expected values and that current observations largely agree with the standard cosmological model, though some discrepancies exist at lower redshifts.

Contribution

It introduces the impact of cluster mergers on the order statistics of Einstein radii and compares theoretical predictions with observational data, highlighting the importance of mergers in lensing statistics.

Findings

Mergers increase the expected largest Einstein radii by about 10%.

Current data at high redshift agrees with $ m extit{ extbf{ extLambda} CDM}$ predictions.

Discrepancies at lower redshifts suggest the need for more precise measurements.

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 $0.1 \leq z \leq 0.55$. 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.