A Mass Model for the Lensing Cluster SDSS J1004+4112: Constraints from the Third Time Delay

Abstract We have built a new model for the lens system SDSS J1004+4112 including the recently measured time delay of the fourth quasar image. This time delay has a strong influence on the inner mass distribution of the lensing cluster ( ρ ∝ r − α ) allowing us to determine α = 1.18 − 0.03 ( − 0.18 ) + 0.02 ( + 0.11 ) at the 68% (95%) confidence level in agreement with hydrodynamical simulations of massive galaxy clusters. We find an offset between the brightest cluster galaxy and the dark matter halo of 3.8 − 0.7 ( − 1.3 ) + 0.6 ( + 1.4 ) kpc at 68% (95%) confidence which is compatible with other galaxy cluster measurements. As an observational challenge, the estimated time delay between the leading image C and the faint ( I = 24.7) fifth image E is roughly 8 yr.