Left panel: lensing optical depth, τ_d, based on NFW haloes following the differential mass function of Sheth & Tormen (2002), together with the actual data and best fit of the CARS source redshift distribution, n(z_s). Right panel: redshift distribution of the expected number density of arcs, Γ_d, based on the best fit of the sources’ redshift distribution. Note that the best fit of the source distribution used in this model overestimates the actual counts, which drop for z> 1.3 and vanish at z ≈ 2, thus suppressing the high-redshift tail of Γ_d. The vertical line marks the redshift limit of the observable sources.