2010ApJ...708..995G

The quadruple quasar H1413+117 (z_s= 2.56) has been monitored with the 2.0 m Liverpool Telescope in the r Sloan band from 2008 February to July. This optical follow-up leads to accurate light curves of the four quasar images (A-D), which are defined by 33 epochs of observation and an average photometric error of ∼15 mmag. We then use the observed (intrinsic) variations of ∼50-100 mmag to measure the three time delays for the lens system for the first time (1σ confidence intervals): Δτ_AB= -17 ±3, Δτ_AC= -20±4, and Δτ_AD= 23±4 days (Δτ_ ij_= τ_j- τ_i; B and C are leading, while D is trailing). Although time delays for lens systems are often used to obtain the Hubble constant (H₀), the unavailability of the spectroscopic lens redshift (z_l ) in the system H1413+117 prevents a determination of H₀ from the measured delays. In this paper, the new time-delay constraints and a concordance expansion rate (H₀= 70 km/s/Mpc) allow us to improve the lens model and to estimate the previously unknown z_l. Our 1σ estimate z_l= 1.88^+0.09 _–0.11 is an example of how to infer the redshift of very distant galaxies via gravitational lensing.