COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses: XIII. Time delays and 9-yr optical monitoring of the lensed quasar RX J1131-1231

We present the results from 9 years of optically monitoring the gravitationally lensed z=0.658 quasar RX J1131-1231. The R band light curves of the 4 individual images of the quasar are obtained using deconvolution photometry, for a total of 707 epochs. Several sharp quasar variability features strongly constrain the time delays between the quasar images. Using three different numerical techniques, we measure these delays for all possible pairs of quasar images, while always processing the 4 light curves simultaneously. For all three methods, the delays between the 3 close images A, B and C are compatible with being 0, while we measure the delay of image D to be 91 days, with a fractional uncertainty of 1.5% (1 sigma), including systematic errors. Our analysis of random and systematic errors accounts in a realistic way for the observed quasar variability, fluctuating microlensing magnification over a broad range of temporal scales, noise properties, and seasonal gaps. Finally, we find that our time delay measurement methods yield compatible results when applied to subsets of the data.