Time Delays in the Gravitationally Lensed Quasar H1413+117 (Cloverleaf)

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 (H ₀), the unavailability of the spectroscopic lens redshift (z_l ) in the system H1413+117 prevents a determination of H ₀ from the measured delays. In this paper, the new time-delay constraints and a concordance expansion rate (H ₀ = 70 km s^-1 Mpc^-1) 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.