Time delays in the gravitationally lensed quasar H1413+117 (Cloverleaf)

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): ΔτAB = −17 ± 3, ΔτAC = −20 ± 4, and ΔτAD = 23 ± 4 days (Δτij = τj − τi; 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 (zl) 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−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.