Size of the accretion disk in the gravitationally lensed quasar SDSS J1004+4112 from the statistics of microlensing magnifications

We present eight monitoring seasons of the four brightest images of the gravitational lens SDSS J1004+4112 observed between December 2003 and October 2010. Using measured time delays for the images A, B and C and the model predicted time delay for image D we have removed the intrinsic quasar variability, finding microlensing events of about 0.5 and 0.7 mag of amplitude in the images C and D. From the statistics of microlensing amplitudes in images A, C, and D, we have inferred the half-light radius (at {lambda} rest = 2407 {AA}) for the accretion disk using two different methods, $R_{1/2}=8.7^{+18.5}_{-5.5} sqrt{M/0.3 M_odot}$ (histograms product) and $R_{1/2} = 4.2^{+3.2}_{-2.2} sqrt{M/0.3 M_odot}$ light-days ($chi^2$). The results are in agreement within uncertainties with the size predicted from the black hole mass in SDSS J1004+4112 using the thin disk theory.