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Context. The gravitational lens system SDSS J1004+4112 was the first known example of a quasar lensed by a galaxy cluster. The interest in this system has been renewed following the publication of r-band light curves spanning 14.5 years and the determination of the time delays between the four brightest quasar images. Aims. We constrained the quasar accretion disk size and the fraction of the lens mass in stars using the signature of microlensing in the quasar image light curves. Methods. We built the six possible histograms of microlensing magnitude differences between the four quasar images and compared them with simulated model histograms, using a $\chi^2$ test to infer the model parameters. Results. We infer a quasar disk half-light radius of $R_{1/2}=(0.70\pm0.04)\, R_E=(6.4\pm0.4) \sqrt{M/0.3M_{\odot}}$ light-days at 2407\r{A} in the rest frame and stellar mass fractions at the quasar image positions of $\alpha_A>0.059$, $\alpha_B=0.056^{+0.021}_{-0.027}$, $\alpha_C=0.030^{+0.031}_{-0.021}$, and $\alpha_D=0.072^{+0.034}_{-0.016}$. Conclusions. The inferred disk size is broadly compatible with most previous estimates, and the stellar mass fractions are within the expected ranges for galaxy clusters. In the region where image C lies, the stellar mass fraction is compatible with a stellar contribution from the brightest cluster galaxy, galaxy cluster members, and intracluster light, but the values at images B, D, and especially A are slightly larger, possibly suggesting the presence of extra stellar components., Comment: 7 pages, 6 figures, 2 tables, A&A in press

We introduce a novel method to derive rotation curves with light-day spatial resolution of the inner regions of lensed quasars. We aim to probe the kinematics of the inner part of the broad-line region (BLR) by resolving the microlensing response - a proxy for the size of the emitting region - in the wings of the broad emission lines (BELs). Specifically, we assess the strength of the microlensing effects in the wings of the high-ionization lines Si IV and C IV across various velocity bins in five gravitationally lensed quasars: SDSS J1001+5027, SDSS J1004+4112, HE 1104$-$1805, SDSS J1206+4332, and SDSS J1339+1310. Using Bayesian methods to estimate the dimensions of the corresponding emission regions and adopting a Keplerian model as our baseline, we examine the consistency of the hypothesis of disk-like rotation. Our results reveal a monotonic, smooth increase in microlensing magnification with velocity. The deduced velocity-size relationships inferred for the various quasars and emission lines closely conform to the Keplerian model of an inclined disk. This study provides the first direct evidence of Keplerian rotation in the innermost region of quasars across a range of radial distances spanning from $\sim$5 to 20 light-days.

We aim to unveil the structure of the continuum and broad-emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1339+1310 by examining the distinct signatures of microlensing present in this system. Our study involves a comprehensive analysis of ten years (2009-2019) of photometric monitoring data and seven spectroscopic observations acquired between 2007 and 2017. This work focuses on the pronounced deformations in the BEL profiles between images A and B, alongside the chromatic changes in their adjacent continua and the striking microlensing variability observed in the $r$-band light curves. We employed a statistical model to quantify the distribution and impact of microlensing magnifications and utilized a Bayesian approach to estimate the dimensions of various emission regions within the quasar. The analysis of the $r$-band light curves reveals substantial microlensing variability in the rest-frame UV continuum, suggesting that image B is amplified relative to image A by a factor of up to six. This finding is corroborated by pronounced microlensing-induced distortions in all studied BEL profiles (Ly$\alpha$, Si IV, C IV, C III], and Mg II), especially a prominent magnification of image B's red wing. We estimated the average dimensions of the BLR to be notably smaller than usual: the region emitting the blue wings measures $R_{1/2} = 11.5 \pm 1.7$ light-days, while the red wings originate from a more compact area of $R_{1/2} = 2.9\pm0.6$ light-days. From the photometric monitoring data, we inferred that the region emitting the $r$-band is $R_{1/2} = 2.2\pm0.3$ light-days across. Furthermore, by assessing the gravitational redshift of the UV Fe III blend and combining it with the blend's microlensing-based size estimate, we calculated the central SMBH's mass to be $M_{BH} \sim2 \times 10^8 M_\odot$.

We propose and discuss a new experimental approach to measure the centroid shift induced by gravitational microlensing in the images of lensed quasars (astrometric microlensing). Our strategy is based on taking the photocenter of a region in the quasar large enough as to be insensitive to microlensing as reference to measure the centroid displacement of the continuum. In this way, single-epoch measurements of astrometric microlensing can be performed. Using numerical simulations, we show that, indeed, the centroid shift monotonically decreases as the size of the emitting region increases, and only for relatively large regions, like the broad line region (BLR), does the centroid shift become negligible. This opens interesting possibilities to study the stratification of the different emitters in the accretion disk and the BLR. We estimate the amplitude of the centroid shifts for 79 gravitationally lensed images and study more thoroughly the special cases Q2237+030 A, RXJ1131-1231 A, PG1115+080 A2 and SDSS J1004+4112 A. We propose to use spectro-astrometry to simultaneously obtain the photocenters of the continuum and of different emission line regions since, with the precision of forthcoming instruments, astrometric microlensing by $\sim 1 M_\odot$ mass microlenses may be detected in many quasar lensed images. When we consider more massive micro/millilenses, $M\gtrsim 10 M_\odot$, often proposed as the constituents of dark matter, the BLR becomes sensitive to microlensing and can no longer be used as a positional reference to measure centroid shifts. Differential microlensing between the images of a lensed quasar along several epochs should be used instead., Comment: 14 pages, 6 figures, 1 table. ApJ in press

We aim to reveal the sizes of the continuum and broad emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1004+4112 by analyzing the unique signatures of microlensing in this system. Through a comprehensive analysis of 20 spectroscopic observations acquired between 2003 and 2018, we studied the striking deformations of various BEL profiles and determined the sizes of their respective emitting regions. Our approach involves a detailed analysis of the magnitude differences in the BEL wings and their adjacent continua, and the implementation of a statistical model to quantify the distribution and impact of microlensing magnifications. To ensure a reliable baseline for no microlensing, we used the emission line cores as a reference. We then applied a Bayesian estimate to derive the size lower limits of the Ly$\alpha$, Si IV, C IV, C III], and Mg II emitting regions, as well as the sizes of the underlying continuum-emitting sources. We analyzed the outstanding microlensing-induced distortions in the line profiles of various BELs in the quasar image A, characterized by a prominent magnification of the blue part and a strong demagnification of the red part. From the statistics of microlensing magnifications and using Bayesian methods, we estimate the lower limit to the overall size of the regions emitting the BELs to be a few lt-days across, which is significantly smaller than in typically lensed quasars. The asymmetric deformations in the BELs indicate that the broad-line region is generally not spherically symmetric, and is likely confined to a plane and following the motions of the accretion disk. Additionally, the inferred continuum-emitting region sizes are larger than predictions based on standard thin-disk theory by a factor of $\sim$3.6 on average. The size-wavelength relation is consistent with that of a geometrically thin and optically thick accretion disk.

We investigate the discrepancy between the predicted size of accretion disks (ADs) in quasars and the observed sizes as deduced from gravitational microlensing studies. Specifically, we aim to understand whether the discrepancy is due to an inadequacy of current AD models or whether it can be accounted for by the contribution of diffuse broad-line region (BLR) emission to the observed continuum signal. We employed state-of-the-art emission models for quasars and high-resolution microlensing magnification maps and compared the attributes of their magnification-distribution functions to those obtained for pure Shakura-Sunyaev disk models. We tested the validity of our detailed model predictions by examining their agreement with published microlensing estimates of the half-light radius of the continuum-emitting region in a sample of lensed quasars. Our findings suggest that the steep disk temperature profiles found by microlensing studies are erroneous as the data are largely affected by the BLR, which does not obey a temperature-wavelength relation. We show with a sample of 12 lenses that the mere contribution of the BLR to the continuum signal is able to account for the deduced overestimation factors as well as the implied size-wavelength relation. Our study points to a likely solution to the AD size conundrum in lensed quasars, which is related to the interpretation of the observed signals rather than to disk physics. Our findings significantly weaken the tension between AD theory and observations, and suggest that microlensing can provide a new means to probe the hitherto poorly constrained diffuse BLR emission around accreting black holes.

Our aim is to examine the size, kinematics, and geometry of the broad-line region (BLR) in the double-lensed quasar Q 0957+561 by analyzing the impact of microlensing on various rest-frame ultraviolet broad-emission lines (BELs). We explore the influence of intrinsic variability and microlensing on the C IV, C III], and Mg II emission lines through multiple spectroscopic observations taken between April 1999 and January 2017. By utilizing the line cores as a reference for no microlensing and correcting for the long time delay between the images, we estimate the sizes of the regions emitting the broad-line wings using a Bayesian approach. Our study of the microlensing amplitudes between the lensed images of the quasar Q 0957+561 reveals differing sizes of the regions emitting the three prominent BELs C IV, C III], and Mg II. The strength of the differential microlensing indicates that the high-ionization line C IV arises from a compact inner region of the BLR with a half-light radius of $R_{1/2} \gtrsim 16.0$ lt-days, which represents a lower limit on the overall size of the BLR and is comparable to the size of the region emitting the r-band continuum in this system. A somewhat larger size of $R_{1/2}\gtrsim 44$ lt-days is obtained for the semi-forbidden line C III]. Microlensing has a weak impact on the lower-ionization line Mg II, which is emitted from a region with a half-light radius of $R_{1/2} \gtrsim 50$ lt-days. These findings suggest that the BEL regions may have distinct geometries and kinematics, with the more extended ones being spherically symmetric, and the most compact ones being nonspherical, with motions likely confined to a plane.

We report the results from a photometric reverberation mapping campaign carried out with the C18 telescope at the Wise Observatory from 2019 to 2020, targeting the active galactic nucleus (AGN) MCG 08-11-011. The monitoring was conducted on a daily basis with specially designed narrow-band filters, spanning from optical to near-infrared wavelengths ($\sim4000$ to $8000${\AA}) and avoiding prominent broad emission lines. We aim to measure inter-band continuum time lags, determine the size-wavelength relation, and estimate the host-subtracted AGN luminosity for this system. We used the point-spread function photometry to extract the continuum light curves and measure the inter-band time lags using several methods, including the interpolated cross-correlation function, the z-transformed discrete correlation function, a von Neumann estimator, JAVELIN (in spectroscopic and photometric mode), MICA, and a multivariate correlation function. We find wavelength-dependent lags, $\tau(\lambda)$, up to $\sim$7 days between the multiband light curves of MCG 08-11-011. The observed lags are larger than predictions based on standard thin-disk theory by a factor of $\sim3-7$. We discern a significantly steeper ($\tau \propto \lambda^{4.74}$) size-wavelength relation than the $\tau \propto \lambda^{4/3}$ expected for a geometrically thin and optically thick accretion disk, which may result from the contribution of diffuse continuum emission to the flux. These results are similar to those found by previous continuum reverberation mapping campaigns., Comment: arXiv admin note: text overlap with arXiv:2111.07385

We present the results of an intensive six-month optical continuum reverberation mapping campaign of the Seyfert 1 galaxy PG 2130+099 at redshift z=0.063. The ground-based photometric monitoring was conducted on a daily basis with the robotic 46cm telescope of the Wise observatory located in Israel. Specially designed narrowband filters were used to observe the central engine of the active galactic nucleus (AGN), avoiding line contamination from the broad-line region (BLR). We aim to measure inter-band continuum time lags across the optical range and determine the size-wavelength relation for this system. We used two methods, the traditional point-spread function (PSF) photometry and the recently developed proper image subtraction technique, to independently perform the extraction of the continuum light curves. The inter-band time lags are measured with several methods, including the interpolated cross-correlation function, the z-transformed discrete correlation function, a von Neumann estimator, JAVELIN (in spectroscopic mode), and MICA. PG 2130+099 displays correlated variability across the optical range, and we successfully detect significant time lags of up to 3 days between the multiband light curves. Using the flux variation gradient (FVG) method, we determined the AGN's host-galaxy-subtracted rest-frame 5100{\AA} luminosity at the time of our monitoring campaign with an uncertainty of 18%. While a continuum reprocessing model can fit the data reasonably well, our derived disk sizes are a factor of 2-6 larger than the theoretical disk sizes predicted from the AGN luminosity estimate of PG 2130+099. This result is in agreement with previous studies of AGN/quasars and suggests that the standard Shakura-Sunyaev disk theory has limitations in describing AGN accretion disks.

We aim to use signatures of microlensing induced by stars in the foreground lens galaxy to infer the size of the accretion disk in the gravitationally lensed quasar Q 0957+561. The long-term photometric monitoring of this system (which so far has provided the longest available light curves of a gravitational lens system) permits us to evaluate the impact of uncertainties on our recently developed method (controlled by the distance between the modeled and the experimental magnitude difference histograms between two lensed images), and thus to test the robustness of microlensing-based disk-size estimates. We analyzed the well-sampled 21-year GLENDAMA optical light curves of the double-lensed quasar and studied the intrinsic and extrinsic continuum variations. Using accurate measurements for the time delay between the images A and B, we modeled and removed the intrinsic quasar variability, and from the statistics of microlensing magnifications we used a Bayesian method to derive the size of the region emitting the continuum at 2558 angstroms. Analyses of the Q 0957+561 R-band light curves show a slow but systematic increase in the brightness of the B relative to the A component during the past ten years. The relatively low strength of the magnitude differences between the images indicates that the quasar has an unusually big optical accretion disk of half-light radius $R_{1/2} = 17.6 \pm 6.1 \sqrt{M/0.3M_\odot}$ lt-days.

We intend to use the impact of microlensing on the Fe III emission line blend along with a measure of its gravitational redshift to estimate the mass of the quasar's central supermassive black hole (SMBH). We fit the Fe III feature in multiple spectroscopic observations between 2008 and 2016 of the gravitationally lensed quasar Q 0957+561 with relatively high signal-to-noise ratios (at the adequate wavelength). Based on the statistics of microlensing magnifications, we used a Bayesian method to derive the size of its emitting region. The Fe III spectral feature appears systematically redshifted in all epochs of observation by a value of 17 angstroms on average. We find clear differences in the shape of the Fe III line blend between images A and B. Measuring the strength of those magnitude differences, we conclude that this blend may arise from a region of half-light radius of 15 lt-days, which is in good agreement with the accretion disk dimensions for this system. We obtain a mass for the central SMBH of (1.5 +/- 0.5) x 10^9 solar masses, consistent within uncertainties with previous mass estimates based on the virial theorem. The relatively small uncertainties in the mass determination (< 35%) make this method a compelling alternative to other existing techniques (e.g., the virial plus reverberation mapping based size) for measuring black hole masses. Combining the Fe III redshift-based method with the virial, we estimate a virial factor in the 1.2 to 1.7 range for this system.

We aim to study the structure and kinematics of the broad line region (BLR) of a sample of 27 gravitationally lensed quasars with up to five different epochs of observation. This sample is composed of ~100 spectra from the literature plus 22 unpublished spectra of 11 systems. We measure the magnitude differences in the broad emission line (BEL) wings and statistically model the distribution of microlensing magnifications to determine a maximum likelihood estimate for the sizes of the C IV, C III], and Mg II emitting regions. The BELs in lensed quasars are expected to be magnified differently owing to the different sizes of the regions from which they originate. Focusing on the most common BELs in our spectra (C IV, C III], and Mg II), we find that the low-ionization line Mg II is only weakly affected by microlensing. In contrast, the high-ionization line C IV shows strong microlensing in some cases, indicating that its emission region is more compact. Thus, the BEL profiles are deformed differently depending on the geometry and kinematics of the corresponding emitting region. We detect microlensing in either the blue or the red wing (or in both wings with different amplitudes) of C IV in more than 50% of the systems and find outstanding asymmetries in the wings of QSO 0957+561, SDSS J1004+4112, SDSS J1206+4332, and SDSS J1339+1310. This observation indicates that the BLR is, in general, not spherically symmetric and supports the existence of two regions in the BLR, one insensitive to microlensing and another that only shows up when it is magnified by microlensing.

Assuming a gravitational origin for the Fe III$\lambda\lambda$2039-2113 redshift and using microlensing based estimates of the size of the region emitting this feature, we obtain individual measurements of the virial factor, $f$, in 10 quasars. The average values for the Balmer lines, $\langle f_{H\beta}\rangle={\bf 0.43\pm 0.20}$ and $\langle f_{H\alpha}\rangle={\bf 0.50\pm 0.24}$, are in good agreement with the results of previous studies for objects with lines of comparable widths. In the case of Mg II, consistent results, $f_{Mg II} \sim {\bf 0.44}$, can be also obtained accepting a reasonable scaling for the size of the emitting region. The modeling of the cumulative histograms of individual measurements, $CDF(f)$, indicates a {relatively} high value for the ratio between isotropic and cylindrical motions, $a\sim {\bf 0.4}-0.7$. On the contrary, we find very large values of the virial factor associated to the Fe III$\lambda\lambda$2039-2113 blend, $f_{FeIII}=14.3\pm2.4$, which can be explained if this feature arises from a flattened nearly face-on structure, similar to the accretion disk., Comment: Accepted in ApJ

We use spectroscopic observations of the gravitationally lensed systems SDSS0924+0219(BC), Q1355-2257(AB), and SDSS1029+2623(BC) to analyze microlensing and dust extinction in the observed components. We detect chromatic microlensing effects in the continuum and microlensing in the broad emission line profiles of the systems SDSS0924+0219(BC), and Q1355-2257(AB). Using magnification maps to simulate microlensing and modeling the emitting region as a Gaussian intensity profile with size $r_s \propto \lambda ^p$, we obtain the probability density functions for a logarithmic size prior at $\lambda_{rest-frame}=3533$ {\AA}. In the case of SDSS0924+0219, we obtain: $r_s = 4^{+3}_{-2}$ $\sqrt{M/M_{\odot}}$ light-days (at $1 \sigma$), which is larger than the range of other estimates, and $p = 0.8 \pm 0.2$ (at $1 \sigma$), which is smaller than predicted by the thin disk theory, but still in agreement with previous results. In the case of Q1355-2257 we obtain (at $1 \sigma$): $r_s = 3.6^{+3.0}_{-1.6}$ $\sqrt{M/M_{\odot}}$ light-days, which is also larger than the theoretical prediction, and $p = 2.0 \pm 0.7$ that is in agreement with the theory within errors. SDSS1029+2326 spectra show evidence of extinction, probably produced by a galaxy in the vicinity of image C. Fitting an extinction curve to the data we estimate $\Delta E \sim 0.2$ in agreement with previous results. We found no evidence of microlensing for this system., Comment: 9 pages, 12 figures

We present new spectroscopic and polarimetric observations of the gravitational lens SDSS J1004+4112 taken with the 6m telescope of the Special Astrophysical Observatory (SAO, Russia). In order to explain the variability that is observed only in the blue wing of the C IV emission line, corresponding to image A, we analyze the spectroscopy and polarimetry of the four images of the lensed system. Spectra of the four images were taken in 2007, 2008, and 2018, and polarization was measured in the period 2014-2017. Additionally, we modeled the microlensing effect in the polarized light, assuming that the source of polarization is the equatorial scattering in the inner part of the torus. We find that a blue enhancement in the CIV line wings affects component A in all three epochs. We also find that the UV continuum of component D was amplified in the period 2007-2008, and that the red wings of CIII] and CIV appear brighter in D than in the other three components. We report significant changes in the polarization parameters of image D, which can be explained by microlensing.Our simulations of microlensing of an equatorial scattering region in the dusty torus can qualitatively explain the observed changes in the polarization degree and angle of image D. We do not detect significant variability in the polarization parameters of the other images (A, B, and C), although the averaged values of the polarization degree and angle are different for the different images. Microlensing of a broad line region model including a compact outflowing component can qualitatively explain the CIV blue wing enhancement (and variation) in component A. However, to confirmed this hypothesis, we need additional spectroscopic observation in future., Comment: accepted in the A&A, 18 paged, 15 figures

We test the recently proposed (Mediavilla et al. 2018) black hole mass scaling relationship based on the redshift {with respect to the quasar's rest frame} of the Fe III$\lambda\lambda$2039-2113 line blend. To this end, we fit this feature in the spectra of a well suited sample of quasars, observed with X-shooter at the Very Large Telescope (VLT), whose masses have been independently estimated using the virial theorem. For the quasars of this sample we consistently confirm the redshift of the Fe III$\lambda\lambda$2039-2113 blend and find that it correlates with the squared widths of H$\beta$, H$\alpha$ and Mg II, which are commonly used as a measure of $M_{BH}/R$ to determine masses from the virial theorem. The average differences between virial and Fe III$\lambda\lambda$2039-2113 redshift based masses are 0.18$\pm 0.21$ dex, 0.18$\pm 0.22$ dex and 0.14$\pm 0.21$ dex, when the full widths at half maximum (FWHM) of the H$\beta$, H$\alpha$ and MgII lines are, respectively, used. The difference is reduced to 0.10$\pm 0.16$ dex when the standard deviation, $\sigma$, of {the} MgII line is used, instead. We also study the high S/N composite quasar spectra of the Baryon Oscillation Spectroscopic Survey (BOSS), finding that the Fe III$\lambda\lambda$2039-2113 redshifts and Mg II squared widths, $FWHM_{MgII}^2$, match very well the correlation found for the individual quasar spectra observed with X-shooter. This correlation is expected if the redshift is gravitational.

We present a measurement of the accretion disk size of the quadruple lensed quasar HE 0435-1223 from well-sampled 13-yr COSMOGRAIL optical light curves. Using accurate time delays for the images A, B, C, and D, we modeled and removed the intrinsic quasar variability, and found microlensing events of amplitude up to 0.6, 0.4, and 0.5 mag in the images A, C and D respectively. From the statistics of microlensing magnifications in these images we use Bayesian methods to estimate the size of the quasar accretion disk. We have inferred the half-light radius for the accretion disk using two different methods, $R_{1/2} = 7.6_{-1.1}^{+12.0} \sqrt{M/0.3M_{\odot}}$ light-days (histogram product) and $R_{1/2} = 7.7_{-1.2}^{+7.0} \sqrt{M/0.3M_{\odot}}$ light-days ($\chi^2$ criterion). The results are self-consistent and in good agreement with the continuum size predicted by single-epoch spectroscopy and previous studies making use of narrow-band photometry of HE 0435-1223.

We find that the Fe III$\lambda\lambda$2039-2113 spectral feature in quasars appears systematically redshifted by amounts accountable under the hypothesis of gravitational redshift induced by the central supermassive black hole. Our analysis of 27 composite spectra from the BOSS survey indicates that the redshift and the broadening of the lines in the Fe III$\lambda\lambda$2039-2113 blend roughly follow the expected correlation in the weak limit of Schwarzschild geometry for virialized kinematics. Assuming that the Fe III UV redshift provides a measure of $M_{BH}\over R$ (${\Delta \lambda\over \lambda}\simeq{3\over2}{G\over c^2} {M_{BH}\over R}$) and using different estimates of the emitting region size, $R$ (either from gravitational microlensing, reverberation mapping or from the scaling of size with intrinsic quasar luminosity), we obtain masses for 10 objects which are in agreement within uncertainties with previous mass estimates based on the virial theorem. Reverberation mapping estimates of the size of the Fe III$\lambda\lambda$2039-2113 emitting region in a sample of objects would be needed to confirm the gravitational origin of the measured redshifts. Meanwhile, we present a tentative black hole mass scaling relationship based on the Fe III$\lambda\lambda$2039-2113 redshift useful to measure the black hole mass of one individual object from a single spectrum.

We study the BELs in a sample of 11 gravitationally lensed quasars with at least two epochs of observation to identify intrinsic variability and to disentangle it from microlensing. To improve our statistical significance we also include 15 systems with single-epoch spectra. MgII and CIII] emission lines are only weakly affected by microlensing, but CIV shows strong microlensing in some cases, even for regions of the line core, associated with small projected velocities. However, excluding the strongly microlensed cases, there is a strikingly good match between the red wings of the CIV and CIII] profiles. Analysis of these results supports the existence of two regions in the BLR, one that is insensitive to microlensing (of size $\gtrsim$ 50 light-days and kinematics not confined to a plane) and another that shows up only when it is magnified by microlensing (of size of a few light-days, comparable to the accretion disk). Both regions can contribute in different proportions to the emission lines of different species and, within each line profile, to different velocity bins, all of which complicates detailed studies of the BLR based on microlensing size estimates. The strength of the microlensing indicates that some spectral features that make up the pseudo-continuum, such as the shelf-like feature at {\lambda}1610 or several FeIII blends, may in part arise from an inner region of the accretion disk. In the case of FeII, microlensing is strong in some blends but not in others. This opens up interesting possibilities to study quasar accretion disk kinematics.

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.