A Time Delay for the Cluster-Lensed Quasar SDSS J1004+4112

We present 426 epochs of optical monitoring data spanning 1000 days from 2003 December to 2006 June for the gravitationally lensed quasar SDSS J1004+4112. The time delay between the A and B images is Δt_BA=38.4+/-2.0 days (Δχ²=4) in the expected sense that B leads A and the overall time ordering is C-B-A-D-E. The measured delay invalidates all published models. The models probably failed because they neglected the perturbations from cluster member galaxies. Models including the galaxies can fit the data well, but conclusions about the cluster mass distribution should await the measurement of the longer, and less substructure sensitive, delays of the C and D images. For these images, a delay of Δt_CB~=681+/-15 days is plausible but requires confirmation, while delays of Δt_CB>560 days and Δt_AD>800 days are required. We clearly detect microlensing of the A/B images, with the delay-corrected flux ratios changing from m_B-m_A=0.44+/-0.01 mag in the first season to 0.29+/-0.01 mag in the second season and 0.32+/-0.01 mag in the third season.