Cluster-cluster strong lensing: Expectations and detection methods

Abstract

We calculate the all-sky number of galaxy clusters that are expected to be gravitationally lensed by foreground massive clusters. We describe the redshift and number distributions of clusters using a Press-Schechter analysis, and model the foreground lensing clusters as singular isothermal spheres. If Ωm = 0.3 and ΩΛ = 0.7, we expect ∼ 30 cluster-cluster strong lensing events that involve foreground X-ray luminous clusters with total mass greater than 7.5 × 1014h-1 M⊙, or X-ray luminosity LX (2-10 keV) ≳8 × 1044h-2 ergs-1, and background clusters with total mass greater than 1014 h-1 M⊙. The number expected in an open universe with Ωm = 0.3 is less than ∼ 4. Because of uncertainty in σ8, the root-mean-square density fluctuation in spheres of radius 8 h-1 Mpc, the exact number of such lensing events is uncertain by a factor of about 5. We examine methods to detect cluster-cluster lensing events based on optical, X-ray and Sunyaev-Zel'dovich effect observations.