The Rewards of Patience: An 822 Day Time Delay in the Gravitational Lens SDSS J1004+4112

We present 107 new epochs of optical monitoring data for the four brightest images of the gravitational lens SDSS J1004+4112 observed between 2006 October and 2007 June. Combining this data with the previously obtained light curves, we determine the time delays between images A, B, and C. We confirm our previous measurement, that B leads A by Δ τ_BA = 40.6 +/- 1.8 days, and find that image C leads image A by Δ τ_CA = 821.6 +/- 2.1 days. The lower limit on the remaining delay is that image D lags image A by Δ τ_AD > 1250 days. Based on the microlensing of images A and B, we estimate that the accretion disk size at a rest wavelength of 2300 Å is 10^{14.8 +/- 0.3} cm for a disk inclination of {cos} i=\frac{1}{2}, which is consistent with the microlensing disk size-black hole mass correlation function given our estimate of the black hole mass from the Mg II line width of log M_BH/M_⊙ = 8.4 +/- 0.2. The long delays allow us to fill in the seasonal gaps and assemble a continuous, densely sampled light curve spanning 5.7 yr whose variability implies a structure function with a logarithmic slope of β = 0.52 +/- 0.02. As C is the leading image, sharp features in the C light curve can be intensively studied 2.3 yr later in the A/B pair, potentially allowing detailed reverberation mapping studies of a quasar at minimal cost.