Cluster--cluster strong lensing: expectations and detection methods

ABSTRACT We calculate the all-sky number of galaxy clusters that are expected to be gravita-tionally lensed by foreground massive clusters. We describe the redshift and numberdistributions of clusters using a Press-Schechter analysis, and model the foregroundlensing clusters as singular isothermal spheres. If Ω m = 0.3 and Ω Λ = 0.7, we ex-pect ∼ 30 cluster-cluster strong lensing events that involve foreground X-ray lumi-nous clusters with total mass greater than 7.5 × 10 14 h −1 M⊙, or X-ray luminosityL x (2 − 10keV) ∼> 8 × 10 44 h −2 ergss −1 , and background clusters with total massgreater than 10 14 h −1 M⊙. The number expected in an open universe with Ω m = 0.3is less than ∼ 4. Because of uncertainty in σ 8 , the root-mean-square density fluc-tuations in spheres of radius 8h −1 Mpc, the exact number of such lensing events isuncertain by a factor of about 5. We examine methods to detect cluster-cluster lensingevents based on optical, X-ray, and Sunyaev-Zel’dovich effect observations.Key words: cosmology: observations — gravitational lensing — galaxies: clusters —galaxies: clusters: individual: Cl0024+17