The strongest gravitational lenses

Waizmann, Jean-Claude; Redlich, Matthias; Bartelmann, Matthias

doi:10.1051/0004-6361/201219944

Cited by 27 publications

(38 citation statements)

References 64 publications

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“…3, where the cdfs based on the MC data are presented. It can be seen nicely that the MC simulated data exhibits the steepening of the cdf with the increasing order that has also been found for the order statistics of the most massive and most distant galaxy clusters in Waizmann et al (2012). As a result, while the first order F (n) is broad and allows the largest Einstein radius to be realised in a wide range, the higher orders are confined to an increasingly narrow range of radii.…”

Section: The Distributions Of the Order Statistics Of The Effective Esupporting

confidence: 65%

“…The adopted method for the semi-analytic modelling of the distribution of Einstein radii has already been thoroughly presented in two previous papers of this series (see Redlich et al 2012;Waizmann et al 2012, and references therein). Thus, we only repeat the most important definitions and relations that are needed to follow this work.…”

Section: Semi-analytic Modelling Of the Distribution Of Einstein Radiimentioning

confidence: 99%

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The strongest gravitational lenses

Waizmann

Redlich

Meneghetti

et al. 2014

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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.

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Section: The Distributions Of the Order Statistics Of The Effective Esupporting

confidence: 65%

Section: Semi-analytic Modelling Of the Distribution Of Einstein Radiimentioning

confidence: 99%

The strongest gravitational lenses

Waizmann

Redlich

Meneghetti

et al. 2014

A&A

Self Cite

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“…(1)) outside the virial radius, we alternatively force all sampled axis ratios a sc to lie within the range of two standard deviations. Since this manipulation may affect the statistics of the largest predicted Einstein radii, we will investigate the consequences in our follow-up work (Waizmann et al 2012). The numerical value of the free parameter A e depends on the underlying cosmology.…”

Section: Triaxial Gravitational Lensesmentioning

confidence: 99%

“…), within a reasonably short time. This ability is important for our follow-up work, where we plan to employ methods of extreme value statistics to investigate the probability distribution of the largest Einstein radius expected within a ΛCDM cosmology (Waizmann et al 2012). We require our new approach to be fully self-consistent within the framework of the extended Press-Schechter theory (Lacey & Cole 1993), which means that in particular the predicted merger rates and the Press-Schechter mass function (cf.…”

Section: Impact Of Cluster Mergers On the Statistics Of The Largest Ementioning

confidence: 99%

“…The simulated boxes might simply be too small to contain a sufficient number of extraordinarily strong gravitational lenses, which forbids solid statistical conclusions. In a follow-up paper, we will show that this limitation is indeed decisive in the context of extreme value statistics (Waizmann et al 2012). Semi-analytic methods -admittedly based on a set of simplifying assumptions -can overcome this limitation because they are computationally less demanding and hence can be used to analyse large samples of particularly strong gravitational lenses within a comparably short time.…”

Section: Introductionmentioning

confidence: 99%

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The strongest gravitational lenses

Redlich

Bartelmann

Waizmann

et al. 2012

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For more than a decade now, it has been controversial whether or not the high rate of giant gravitational arcs and the largest observed Einstein radii are consistent with the standard cosmological model. Recent studies indicate that mergers provide an efficient mechanism to substantially increase the strong-lensing efficiency of individual clusters. Based on purely semi-analytic methods, we investigated the statistical impact of cluster mergers on the distribution of the largest Einstein radii and the optical depth for giant gravitational arcs of selected cluster samples. Analysing representative all-sky realizations of clusters at redshifts z < 1 and assuming a constant source redshift of z s = 2.0, we find that mergers increase the number of Einstein radii above 10 (20 ) by ∼35% (∼55%). Exploiting the tight correlation between Einstein radii and lensing cross sections, we infer that the optical depth for giant gravitational arcs with a length-to-width ratio ≥7.5 of those clusters with Einstein radii above 10 (20 ) increases by ∼45% (∼85%). Our findings suggest that cluster mergers significantly influence in particular the statistical lensing properties of the strongest gravitational lenses. We conclude that semi-analytic studies must inevitably take these events into account before questioning the standard cosmological model on the basis of the largest observed Einstein radii and the statistics of giant gravitational arcs.

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