A fast method for computing strong-lensing cross sections: application to merging clusters

¹ Zentrum für Astronomie, ITA, Universität Heidelberg, Albert-Überle-Str. 2, 69120 Heidelberg, Germany e-mail: cosimo@ita.uni-heidelberg.de
² Dipartimento di Astronomia, Università di Bologna, via Ranzani 1, 40127 Bologna, Italy
³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85740 Garching, Germany

Received: 5 July 2005
Accepted: 28 September 2005

Abstract

Strong gravitational lensing by irregular mass distributions, such as galaxy clusters, is generally not quantified well by cross sections of analytic mass models. Computationally expensive ray-tracing methods have so far been necessary for accurate cross-section calculations. We describe a fast, semi-analytic method here that is based on surface integrals over high-magnification regions in the lens plane and demonstrate that it yields reliable cross sections even for complex, asymmetric mass distributions. The method is faster than ray-tracing simulations by factors of ~30 and thus suitable for large cosmological simulations, saving large amounts of computing time. We apply this method to a sample of galaxy cluster-sized dark matter haloes with simulated merger trees and show that cluster mergers approximately double the strong-lensing optical depth for lens redshifts and sources near . We believe that this result hints at one possibility for understanding the recently detected high arcs abundance in clusters at moderate and high redshifts, and is thus worth studying further.