The strongest gravitational lenses

Abstract

Context. The Einstein radius of a gravitational lens is a key characteristic. It encodes information about decisive quantities such as halo mass, concentration, triaxiality, and orientation with respect to the observer. Therefore, the largest Einstein radii can potentially be utilised to test the predictions of the ΛCDM model. Aims. Hitherto, studies have focussed on the single largest observed Einstein radius. 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. Methods. We obtain the order statistics of Einstein radii by a Monte Carlo approach, based on the semi-analytic modelling of the halo population on the past lightcone. After sampling the order statistics, we fit a general extreme value distribution to the first-order distribution, which allows us to derive analytic relations for the order statistics of the Einstein radii. Results. We find that the Einstein radii of the 12 MACS clusters are not in conflict with the ΛCDM expectations. Our exclusion criteria indicate that, in order to exhibit tension with the concordance model, one would need to observe approximately twenty Einstein radii with θ eff > ∼ 30 , ten with θ eff > ∼ 35 , five with θ eff > ∼ 42 , or one with θ eff > ∼ 74 in the redshift range 0.5 ≤ z ≤ 1.0 on the full sky (assuming a source redshift of z s = 2). 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. Conclusions. A framework that allows the individual and joint order distributions of the n-largest Einstein radii to be derived is presented. From a statistical point of view, we do not see any evidence of an Einstein ring problem even for the largest Einstein radii of the studied MACS sample. This conclusion is consolidated by the large uncertainties that enter the lens modelling and to which the largest Einstein radii are particularly sensitive.

SARCS strong-lensing galaxy groups

“…In particular, including baryonic physics allows for a modification of the central mass distribution through radiative cooling and feedback processes, resulting in higher concentrations (e.g., Mead et al 2010;Fedeli 2012). Finally, Waizmann et al (2012Waizmann et al ( , 2014, used the statistics of extreme values to show that very large Einstein radii are rare but not in conflict with Λ-CDM cosmology.…”

Simulation-based marginal likelihood for cluster strong lensing cosmology

“…There have been four other works in the literature that analyse the strong lensing statistics of the high-z MACS clusters and compare them to predictions from simulations (Horesh et al 2011;Meneghetti et al 2011;Zitrin et al 2011;Waizmann et al 2014). Several factors could lead to disagreements with our findings presented in Sec.…”

“…Einstein radii were found to be about 1.4 times larger than predicted by ΛCDM, measured by comparing the medians of the total distributions. A recent study by Waizmann et al (2014) takes a different approach to the strong lensing comparison by using order statistics. Semi-analytic models of cluster lensing and mass function are combined with general extreme value distributions to determine 'exclusion constraints' on the n-largest observed Einstein radii; the high-z MACS sample is found to be consistent with ΛCDM.…”

“…The studies of Horesh et al (2011) and Meneghetti et al (2011) employ directly the results from N-body and non-radiative gas simulations, while Zitrin et al (2011) andWaizmann et al (2014) use semi-analytic models. In the present work, we have 10 The values of θ E,med as quoted in Meneghetti et al (2011) are based on the earlier mass models, prior to the availability of HST data within the CLASH and Frontier Fields programmes.…”

Cluster strong lensing: a new strategy for testing cosmology with simulations

“…Killedar et al In the present work, we take the well-studied z > 0.5 MACS clusters as our case in point (Horesh et al (2010), Meneghetti et al (2011), Waizmann et al (2014). We propose a Bayesian approach to the strong lensing cosmological test, employing clusters modelled within ΛCDM hydrodynamic simulations which include the effects of stellar and AGN feedback.…”