The strongest gravitational lenses: III. The order statistics of the largest Einstein radii

TL;DR

This study uses order statistics and semi-analytic modeling to analyze the largest Einstein radii in galaxy clusters, testing their consistency with the LCDM model and deriving analytic relations for their distribution.

Contribution

It extends previous analyses by employing order statistics and a Monte Carlo approach to better understand the distribution of Einstein radii and their implications for cosmological models.

Findings

The 12 MACS clusters' Einstein radii are consistent with LCDM expectations.

Approximately twenty Einstein radii >30" would be needed to challenge the model.

Larger Einstein radii are less aligned and less triaxial on average.

Abstract

The Einstein radius (ER) of a gravitational lens encodes information about decisive quantities such as halo mass, concentration, triaxiality, and orientation with respect to the observer. Thus, the largest Einstein radii can potentially be utilised to test the predictions of the LCDM model. Hitherto, studies have focussed on the single largest observed ER. We extend those studies by employing order statistics to formulate exclusion criteria based on the n largest Einstein radii and apply these criteria to the strong lensing analysis of 12 MACS clusters at z>0.5. We obtain the order statistics of Einstein radii by a MC approach, based on the semi-analytic modelling of the halo population on the past lightcone. After sampling the order statistics, we fit a GEV distribution to the first-order distribution, which allows us to derive analytic relations for the order statistics of the Einstein radii. We find that the Einstein radii of the 12 MACS clusters are not in conflict with the LCDM expectations. Our exclusion criteria indicate that, in order to exhibit tension with the concordance model, one would need to observe approximately twenty Einstein radii >30", ten >35" or five >42" in the range of 0.5<z<1.0 on the full sky. Furthermore, we find that, with increasing order, the haloes with the largest Einstein radii are on average less aligned along the line-of-sight and less triaxial. In general, the cumulative distribution functions steepen for higher orders, giving them better constraining power. (abridged)