The Mass Distribution of SDSS J1004+4112 Revisited

We present a strong lens analysis of SDSS J1004+4112, a unique quasar lens produced by a massive cluster of galaxies at z = 0. 68, using newly developed software for gravitational lensing. We find that our parametric mass model well reproduces all observations, including the positions of quasar images as well as those of multiply imaged galaxies with measured spectroscopic redshifts, time delays between quasar images, and the positions of faint central images. The predicted large total magnification of 70 suggests that the lens system is indeed a useful site for studying the fine structure of a distant quasar and its host galaxy. The dark halo component is found to be unimodal, centered on the brightest cluster galaxy and the Chandra X-ray surface brightness profile. In addition, the orientation of the halo component is quite consistent with those of the brightest cluster galaxy and member galaxy distribution, implying that the lensing cluster is a relaxed system. The radial profile of the best-fit mass model is in good agreement with a mass profile inferred from the X-ray observation. While the inner radial slope of the dark halo component is consistent with being -1, a clear dependence of the predicted A–D time delay on the slope indicates that an additional time-delay measurement will improve constraints on the mass model.