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

TL;DR

This study measures the first time delays in the quadruple quasar H1413+117 using optical monitoring, enabling improved lens modeling and an estimate of the lens galaxy's redshift, demonstrating gravitational lensing's potential to infer distant galaxy properties.

Contribution

First measurement of time delays in H1413+117, leading to improved lens modeling and estimation of the lens galaxy's redshift using gravitational lensing techniques.

Findings

Measured time delays: -17, -20, and 23 days with uncertainties.

Estimated lens galaxy redshift: approximately 1.88.

Enhanced lens model accuracy based on new delay constraints.

Abstract

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 \sim 15 mmag. We then use the observed (intrinsic) variations of \sim 50-100 mmag to measure the three time delays for the lens system for the first time (1\sigma confidence intervals): \Delta \tau_{AB} = -17 +/- 3, \Delta \tau_{AC} = -20 +/- 4, and \Delta \tau_{AD} = 23 +/- 4 days (\Delta \tau_{ij} = \tau_j - \tau_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 1\sigma 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.