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

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 oil 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 similar to 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 z(1) greater than or similar to 0.5 and sources near z(s) = 2. 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.