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 reds hift and number distributions of clusters using a Press-Schechter analysis, and model the foreground lensing clusters as singular isothermal spheres. If Omega(m), = 0.3 and Omega(Lambda) = 0.7, we expect similar to 30 cluster -cluster strong lensing events that involve foreground X-ray luminous clust ers with total mass greater than 7.5 x 10(14) h(-1) M., or X-ray luminosity L-X (2-10 keV) greater than or similar to 8 x 10(44) h(-2) erg s(-1), and background clusters with total mass greater than 10(14) h(-1) Mo. The numbe r expected in an open universe with Omega(m) = 0.3 is less than similar to 4. Because of uncertainty in sigma(8) the root-mean-square density fluctuat ion in spheres of radius 8 h(-1) Mpc, the exact number of such lensing even ts is uncertain by a factor of about 5. We examine methods to detect cluste r-cluster lensing events based on optical, X-ray and Sunyaev-Zel'dovich eff ect observations.