1999MNRAS.305L..11C

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 Ο_m=0.3 and Ο_Λ =0.7, we expect ∼ 30 cluster–cluster strong lensing events that involve foreground X-ray luminous clusters with total mass greater than 7.5x10¹⁴ h^–1 M_sun, or X-ray luminosity L_X (2–10 keV) ≥ 8x10⁴⁴ h^–2erg.s^–1, and background clusters with total mass greater than 10¹⁴ h^–1 M_sun. The number expected in an open universe with Ο_m = 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.