| Abstract | The quadruple quasar H1413+117 (zs = 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): ∆τ AB = -17 ± 3, ∆τ AC = -20 ± 4, and ∆τ AD = 23 ± 4 days (∆τ 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 (zl ) 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 zl . Our 1σ estimate zl = 1.88+0.09 -0.11 is an example of how to infer the redshift of very distant galaxies via gravitational lensing. |
