The strongest gravitational lenses

I. The statistical impact of cluster mergers

¹ Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
e-mail: matthias.redlich@stud.uni-heidelberg.de
² Dipartimento di Astronomia, Università di Bologna, via Ranzani 1, 40127 Bologna, Italy
³ INAF – Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
⁴ INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵ Department of Astronomy, University of Florida, 211 Bryant Space Science Center, Gainesville, FL 32611, USA

Received: 31 May 2012
Accepted: 3 September 2012

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″ (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.