Cluster–cluster strong lensing: expectations and detection methods

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 Qm 0:3 and QL 0:7, we expect, 30 cluster–cluster strong lensing events that involve foreground X-ray luminous clusters with total mass greater than 7:5 · 1014 hÿ1 M(, or X-ray luminosity LX (2–10 keV) *8 · 10 44 hÿ2 erg sÿ1, and back-ground clusters with total mass greater than 1014 hÿ1 M(. The number expected in an open universe with Qm 0:3 is less than, 4. Because of uncertainty in j8, the root-mean-square density fluctuation in spheres of radius 8 hÿ1 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