[Paper Review] The strongest gravitational lenses: I. The statistical impact of cluster mergers

Matthias Redlich, Matthias Bartelmann+2 more|May 31, 2012

Galaxies: Formation, Evolution, Phenomena53 references31 citations

TL;DR

This study uses semi-analytic modeling to assess how cluster mergers statistically enhance strong gravitational lensing, finding they increase the number of Einstein radii above 10'' and 20'' by 35% and 55%, respectively, and boost the optical depth for giant arcs by 45% and 85%. The results show mergers significantly amplify the lensing efficiency of the strongest clusters, implying they must be included in cosmological tests based on extreme lensing observations.

ABSTRACT

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 arcsec (20 arcsec) 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 arcsec (20 arcsec) 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.

Motivation & Objective

• To investigate the statistical impact of cluster mergers on the distribution of the largest Einstein radii and optical depth for giant arcs in galaxy clusters.
• To address the long-standing tension between observed strong lensing properties and predictions of the standard cosmological model (ΛCDM).
• To develop and apply a new semi-analytic method that incorporates merger dynamics into statistical lensing studies, overcoming limitations of small simulation sample sizes.
• To assess whether mergers can explain the observed excess of giant arcs and unusually large Einstein radii without challenging ΛCDM.
• To provide a conservative estimate of merger effects by sampling merger orientations randomly, avoiding overestimation from idealized alignment assumptions.

Proposed method

• The study employs a semi-analytic model of triaxial gravitational lenses using analytic expressions for deflection angles, avoiding computationally expensive numerical integrations.
• It models clusters as triaxial dark matter haloes with realistic concentration-mass relations and varying axis ratios, improving upon previous spherically symmetric or fixed-ellipticity approximations.
• Mergers are simulated by randomly sampling the relative orientation and approach direction of merging substructures, avoiding the idealized assumption of perfect alignment with the main halo's major axis.
• The lensing cross sections for giant arcs are computed using three different algorithms, with adjustments to ensure consistency and reliability in estimating strong-lensing efficiency.
• The statistical impact is quantified by comparing lensing properties—Einstein radii and optical depth—between isolated clusters and those undergoing mergers in large all-sky realizations at z < 1.
• The analysis assumes a fixed source redshift of z_s = 2.0 and leverages the tight correlation between Einstein radii and lensing cross sections to infer optical depth enhancements.

Experimental results

Research questions

• RQ1 To what extent do cluster mergers increase the number of Einstein radii exceeding 10'' and 20'' in the ΛCDM framework?
• RQ2 How do mergers affect the optical depth for giant gravitational arcs with a length-to-width ratio ≥ 7.5 in the strongest lenses?
• RQ3 Are the observed largest Einstein radii and high arc abundances consistent with ΛCDM when merger effects are properly accounted for?
• RQ4 How does the statistical lensing efficiency of clusters change during mergers compared to isolated systems?
• RQ5 Does the random sampling of merger orientations lead to a conservative estimate of the merger boost, compared to idealized aligned configurations?

Key findings

• Cluster mergers increase the number of Einstein radii above 10'' by approximately 35%, and above 20'' by approximately 55% compared to isolated clusters.
• The optical depth for giant arcs with a length-to-width ratio ≥ 7.5 increases by about 45% for clusters with Einstein radii above 10'', and by about 85% for those above 20''.
• The study confirms that mergers significantly enhance the strong-lensing efficiency of the most powerful gravitational lenses, particularly in the extreme tail of the distribution.
• The results suggest that semi-analytic studies must include merger effects before rejecting the standard cosmological model based on extreme lensing observations.
• The conservative sampling of merger orientations implies that the actual boost from mergers may be even higher than estimated, as idealized aligned mergers produce stronger enhancements.
• The findings are consistent with previous numerical studies but provide a more statistically robust estimate by overcoming the sample-size limitations of simulations.