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

TL;DR

This paper presents a new mass model for the lensing cluster SDSS J1004+4112, constrained by the third time delay measurement, revealing insights into the cluster's inner mass distribution and galaxy-dark matter offset.

Contribution

The study introduces a model incorporating the third time delay, providing refined constraints on the cluster's density profile and galaxy-dark matter offset.

Findings

Determined the inner mass density slope as α=1.18 with confidence intervals.

Measured an offset of 3.8 kpc between BCG and dark matter halo.

Estimated an 8-year time delay between specific images.

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 ($\rho \propto r^{-\alpha}$) allowing us to determine $\alpha=1.18^{+0.02(+0.11)}_{-0.03(-0.18)}$ at the 68% (95%) confidence level in agreement with hydrodynamical simulations of massive galaxy clusters. We find an offset between the brightest cluster galaxy (BCG) and the dark matter halo of $3.8^{+0.6(+1.4)}_{-0.7(-1.3)}$ 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.