Observations and Theoretical Implications of the Large-Separation Lensed Quasar SDSS J1004+4112

We study the recently discovered gravitational lens SDSS J1004+4112, the first quasar lensed by a cluster of galaxies. It consists of four images with a maximum separation of 14.″62. The system was selected from the photometric data of the Sloan Digital Sky Survey (SDSS) and has been confirmed as a lensed quasar at z = 1.734 on the basis of deep imaging and spectroscopic follow-up observations. We present color-magnitude relations for galaxies near the lens plus spectroscopy of three central cluster members, which unambiguously confirm that a cluster at z = 0.68 is responsible for the large image separation. We find a wide range of lens models consistent with the data, and despite considerable diversity they suggest four general conclusions: (1) the brightest cluster galaxy and the center of the cluster potential well appear to be offset by several kiloparsecs; (2) the cluster mass distribution must be elongated in the north-south direction, which is consistent with the observed distribution of cluster galaxies; (3) the inference of a large tidal shear (~0.2) suggests significant substructure in the cluster; and (4) enormous uncertainty in the predicted time delays between the images means that measuring the delays would greatly improve constraints on the models. We also compute the probability of such large-separation lensing in the SDSS quasar sample on the basis of the cold dark matter model. The lack of large-separation lenses in previous surveys and the discovery of one in SDSS together imply a mass fluctuation normalization σ8 = 1.0 (95% confidence) if cluster dark matter halos have an inner density profile ρ ∝ r-1.5. Shallower profiles would require higher values of σ8. Although the statistical conclusion might be somewhat dependent on the degree of the complexity of the lens potential, the discovery of SDSS J1004+4112 is consistent with the predictions of the abundance of cluster-scale halos in the cold dark matter scenario.