Microlensing Analysis for the gravitational lens systems SDSS0924+0219, Q1355-2257, and SDSS1029+2623
K. Rojas, V. Motta, E. Mediavilla, J. JimÉnez-Vicente, E. Falco, C. Fian
DD RAFT VERSION F EBRUARY
7, 2020Typeset using L A TEX twocolumn style in AASTeX61
MICROLENSING ANALYSIS FOR THE GRAVITATIONAL LENS SYSTEMS SDSS0924+0219, Q1355-2257, ANDSDSS1029+2623
K. R
OJAS ,
1, 2
V. M
OTTA , E. M
EDIAVILLA ,
3, 4
J. J
IMÉNEZ -V ICENTE ,
5, 6
E. F
ALCO , AND
C. F
IAN
3, 41
Institute of Physics, Laboratoire d’Astrophysique, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, CH-1290 Versoix, Switzerland Instituto de Física y Astronomía, Universidad de Valparaíso, Avda. Gran Bretaña 1111, Valparaíso, Chile Instituto de Astrofísica de Canarias, Avda. Vía Láctea s/n, La Laguna, Tenerife 38200, Spain Departamento de Astrofísica de Canarias, Universidad de La Laguna, Avda. Vía Láctea s/n, La Laguna, Tenerife 38200, Spain Departamento de Física Teórica y del Cosmos, Universidad de Granada, Campus de Fuentenueva, E-18071 Granada, Spain Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain Whipple Observatory, Smithsonian Institution, 670 Mt. Hopkins Road, PO Box 6369, Amado, AZ 85645, USA
ABSTRACTWe use spectroscopic observations of the gravitationally lensed systems SDSS0924+0219(BC), Q1355-2257(AB), andSDSS1029+2623(BC) to analyze microlensing and dust extinction in the observed components. We detect chromatic microlens-ing effects in the continuum and microlensing in the broad emission line profiles of the systems SDSS0924+0219(BC), andQ1355-2257(AB). Using magnification maps to simulate microlensing and modeling the emitting region as a Gaussian intensityprofile with size r s ∝ λ p , we obtain the probability density functions for a logarithmic size prior at λ rest − f rame = 3533 Å. In thecase of SDSS0924+0219, we obtain: r s = 4 + − (cid:112) M / M (cid:12) light-days (at 1 σ ), which is larger than the range of other estimates, and p = 0 . ± . σ ), which is smaller than predicted by the thin disk theory, but still in agreement with previous results. In thecase of Q1355-2257 we obtain (at 1 σ ): r s = 3 . + . − . (cid:112) M / M (cid:12) light-days, which is also larger than the theoretical prediction, and p = 2 . ± . ∆ E ∼ . Keywords: gravitational lensing: micro, galaxies: quasars: individual (SDSS0924+0219, Q1355-2257,SDSS1029+2623) R
OJAS ET AL . INTRODUCTIONThe study of the inner structure of distant quasars (QSOs)is a big challenge, because this region is small and it is notresolvable with current observational facilities. As a conse-quence, theories of accretion disks, which predicted accre-tion disk sizes and their radial temperature profile (Shakura& Sunyaev 1973), still need to be proven. Indirect obser-vational evidence, such as reverberation mapping (Wanderset al. 1997; Collier et al. 1998; Edelson et al. 2015) or mi-crolensing (Moustakas & Metcalf 2003; Anguita et al. 2008;Bate et al. 2008; Floyd et al. 2009; Sluse et al. 2012; Mottaet al. 2012; Guerras et al. 2013; Jiménez-Vicente et al. 2014;Rojas et al. 2014; Mediavilla et al. 2015; Motta et al. 2017),have found that accretion disks are larger than predicted bytheory. Both techniques require long monitoring campaignsin multiple wavelength bands, but microlensing can also bestudied using single-epoch spectra, which is an advantagewith regard to observing time.Microlensing by stars in the lens galaxy causes flux varia-tions in QSO lensed images (Chang & Refsdal 1979; Wamb-sganss 2006). This effect is size sensitive, producing largemagnifications of sources with angular size comparable to (orsmaller than) the microlens Einstein radius. The flux of largerregions, like the Narrow Line Region (NLR), is expected tobe insensitive to microlensing, while inner regions, such asthe accretion disk and the inner parts of the Broad Line Re-gion (BLR), can be affected by microlensing. Theoreticalwork by Shakura & Sunyaev (1973) shows that the size ofthe accretion disk (r s ) varies with wavelength ( r s ∝ λ p ). Thisvariation produces a chromatic microlensing effect (Wamb-sganss & Paczynski 1991; Wisotzki et al. 1995; Mosqueraet al. 2009; Mediavilla et al. 2011) because the magnifica-tion will be different depending on the wavelength (region ofthe disk), i.e. the flux variation is stronger for shorter wave-lengths and almost negligible in the infrared (IR).However, there are other reasons for chromatic variationssuch as QSO intrinsic variability coupled with time delaysbetween images and dust extinction. Following Yoneharaet al. (2008), for a pair of images with small separation(<2.0”), a time delay of ∼
40 days produces a chromatic-ity change <0.03 mag. Then, the effect of chromaticity dueto intrinsic variability is negligible for the objects presentedin this work. On the other hand, dust extinction affects bothcontinuum and emission lines. Then, the chromatic variationtrend will be seen in all measurements. For these reasons,special care is required to distinguish among microlensing,chromaticity, and differential dust extinction along the pathtowards each image through the lens galaxy.In this paper we present single-epoch spectra for the lensedquasars SDSS0924+0219, Q1355-2257, and SDSS1029+2623to search for perturbations produced by microlensing, chro-matic microlensing and/or dust extinction. In the cases of chromatic microlensing detection, the measurements will beused to improve the statistical analysis of quasar accretiondisk sizes as shown in previous studies (Jiménez-Vicenteet al. 2014, 2015a,b). In Section 2 we present the data andreduction technique used. We explain the methods appliedto perform the different analysis in Section 3. In Section 4we discuss our results, and the conclusions are presented inSection 5. OBSERVATIONS AND DATA REDUCTIONWe obtained VLT/FORS2 spectra for SDSS0924+0219and Q1355-2257 in 2008/04/02 (P.I. V. Motta, 381.A-0508),with a seeing of 0.8”. We used the grism 300V, with res-olution of 11.0 Å pixel − , and the blocking filter GG435.The wavelength range of the spectra is 2946-9645 Å. Theposition angle of the slit (in degrees E to N) was chosen toobserve simultaneously two images of the quasar: 42 o to ob-serve C and B for SDSS0924+0219, and -72 o to observe Aand B for Q1355-2257. The exposure times are: 10 × ×
540 s for Q1355-2257, withan average airmass of 1.1”. In the case of Q1355-2257, weadditionally used the deconvolved spectra from Sluse et al.(2012) provided by the VizieR catalog (Ochsenbein et al.2000).The data reduction was performed with IRAF tasks and in-cluded bias subtraction, flat normalization, and wavelengthcalibration. The flux calibration was not applied since weare only interested in flux ratios. The spectra extraction, inthe case of Q1355-2257, was made by fitting a Gaussian toeach component through each wavelength bin, because theseparation between the components is 1.03” and the spectraoverlap. In the case of SDSS 0924+0219, the separation isalso small (1 . for FORS2 instrument. We choose the template ofan elliptical galaxy spectrum (Kochanek et al. 1999) at red-shift 0.39 with magnitude V=21 mag. The sky conditions andinstrument setup were selected to match those of our obser-vation. Figures showing the wavelength calibrated and ex-tracted spectra are in Appendix A Based on data obtained with the VizieR catalog access tool, CDS, Stras-bourg, France. AST E X 6.1 T
EMPLATE .These were taken in 2003 with the Hubble Space Tele-scope (HST) in three different bands (F160W, F555W, andF814W). Additionally, we used data from the literature forSDSS0924+0219 (Inada et al. 2003; Pooley et al. 2007;Floyd et al. 2009; Blackburne et al. 2011), and Q1355-2257(Morgan et al. 2003; Sluse et al. 2012).SDSS J1029+2623 spectra were taken with the LRIS-ADCat Keck and reduced spectra were kindly provided by M.Oguri. The details related to the observation and data re-duction are explained in Oguri et al. (2008). METHODTo distinguish between microlensing, chromatic mi-crolensing and extinction we compare the magnitude dif-ference in the continuum under the emission lines withthe magnitude difference in the emission line cores, ∆ m =( m B − m A ) cont − ( m B − m A ) core (e.g., see Mediavilla et al. 2009,2011; Rojas et al. 2014; Motta et al. 2017). We perform thisanalysis using a set of python packages . The continuumis obtained by fitting a straight line to regions selected atboth sides of each emission line. Then, the continuum issubtracted, and we integrate the emission line in a relativelynarrow interval (between 20 to 60 Å, depending on the lineshape) around the peak (hereafter: core of the line). For thoseemission lines with absorption around the core (e.g. CIV inSDSS1029+2623) a much narrower interval was selected(20-25 Å). The uncertainty in the continuum is the fit rootmean square (rms) error, and for the lines it is the rms errorin the determination of the total flux added in quadrature,which is assumed to be the same as the continuum.If ( m B − m A ) core does not present any change with wave-length, we use the mean of all values as a no-microlensingbaseline. Thus, if ( m B − m A ) cont (cid:54) = ( m B − m A ) core (i.e. ∆ m (cid:54) = 0)it means there is microlensing. Furthermore, if these | ∆ m | values change with wavelength, being larger at blue than atred wavelengths, tentatively the system exhibits chromaticmicrolensing.For each pair of images, we compare the profiles of theemission lines after the continuum substraction to search formicrolensing in the Broad Line Region (BLR). If we finddifferences between the profiles, we integrate the line usingwindows of 25-30 Å (in the rest frame) for both the red andblue wings. The magnitude difference between the lines isused to estimate the size of the BLR (Guerras et al. 2013;Motta et al. 2017).For those systems with no lens model available in the lit-erature, we calculate our own by using a Singular Isothermal https://github.com/Krojas/QSO_microlensing Ellipsoid (SIE) in
Lensmodel (Keeton 2001). We employ theastrometry available in CASTLES and the measured flux ra-tios of the emission line cores. The model provides the con-vergence and shear at the position of each image ( κ A , γ A , κ B , γ B ), which are used to compute magnification maps applyingthe Inverse Polygon Mapping method (Mediavilla et al. 2006,2011). We considered microlenses of 1 M (cid:12) and assumed amass fraction in stars α = 0.1 (Mediavilla et al. 2009; Pooleyet al. 2009). The size for each map is 15 ×
15 Einstein radii(5000 × ).To estimate the size of the accretion disk and its tempera-ture profile from the microlensing data, we follow a Bayesianprocedure (see, e.g. Mediavilla et al. 2011). Mortonsonet al. (2005) have shown that the magnification statistics ofmicrolensing are dependent on the half light radius of thesource, but are quite insensitive to the specific radial profileof the source. We have used a Gaussian intensity profile I(R) ∝ exp(-R /2r s ), where r s is the accretion disk size and p is re-lated to the temperature profile of the disk (p=1/ β ). This pro-file is computationally convenient, for which r / =1.18r s (be-ing r s the sigma of the Gaussian). For a thin disk, (Shakura &Sunyaev 1973), p=4/3. To estimate the likelihood of repro-ducing the measured microlensing amplitudes we randomlyplace Gaussian sources with different sizes and profile slopeson the magnification maps, using a logarithmic prior on r s .All the estimations were obtained at λ rest − f rame = 3533Å.We expect that the cores of the emission lines are not af-fected by microlensing, but we could find differences in ( m B − m A ) core with wavelength produced by extinction from differ-ent amounts of dust and gas in the lens galaxy. Using theCardelli et al. (1989) extinction law, we fit the data using theequation: m ( λ ) − m ( λ ) = − . M / M ) + ( ∆ E ) R v ( λ/ + z L ) (Falco et al. 1999), where ∆ M = M / M is the magnifi-cation ratio, ∆ E = E − E is the differential extinction and R v is the parametrized extinction law. We considered two cases:one where we left R v as a free parameter, and a second onewith a fixed R v = 3 . RESULTS4.1.
SDSS0924+0219
This quadruple system was discovered by Inada et al.(2003) who found a quasar redshift of z S =1.52. The lensis an elliptical galaxy at z L =0.39 (Ofek et al. 2006). Wepresent VLT spectra (see Figure 1) for the C and B compo-nents which are separated by 1.52". The line profiles showdifferences in the line wings likely produced by microlens-ing in the red wing of CIII], but a single measurement is notenough to study the BLR structure. The blue wings of CIII]and MgII and the red wing of MgII are probably affected byunderlying lines like FeII. R OJAS ET AL . Wavelength [ Å ] F l u x [ A r b i t r a r y ] CIII
Wavelength [ Å ] F l u x [ A r b i t r a r y ] MgII
Figure 1.
CIII] and MgII emission lines profiles without the con-tinuum for SDSS0924+0219. In black the A component and in bluethe B component multiplied by a factor of 1.38 (CIII]) and 1.33(MgII) respectively.
We calculate the magnitude differences for the cores of theemission lines and the continua ( ∆ m ) for the spectra (Fig-ure 2 and Table 2) and compared them with values from theliterature. CASTLES and Keeton et al. (2006) values are inagreement with our measurements and with the IR values,meaning that there is no microlensing effect in that epoch(2003). We take as no-microlensing baseline the medianvalue of the cores of the lines, HST broad-band, and Kee-ton et al. (2006) data: 0 . ± .
04 mag. In our data we find ∆ m up to 0.34 mag at λ ∼ .
25 magat λ . ± .
17 mag.As the probability density function for each data set isan independent measurement of r s and p, we calculate theirproduct (see Figure 3). This distribution gives a size for the Wavelength [ Å ] m C - m B ( m a g ) Continuum-This workLines-This workCASTLESInada et al. (2003)Floyd et al. (2009)Pooley et al. (2007)Blackburne et al. (2011)Keeton et al. (2006)
Figure 2.
Magnitude differences m C - m B as a function of wavelengthfor SDSS0924+0219. Red triangles are the emission line cores andthe red squares are the continuum calculated from VLT spectra.Orange squares are the photometric data presented by Inada et al.(2003) for the bands: ugri. Green squares are the broad band con-tinuum from CASTLES. Blue squares are Keeton et al. (2006) mea-surements for HST bands F555W and F816W. Purple squares arethe relative photometry for the bands u’g’r’i’z’JHK s in Blackburneet al. (2011). The black square is an X-ray measurement in the 0.5-8 keV band given by (Pooley et al. 2007). Light blue squares arephotometric data of Floyd et al. (2009) for the bands: HJYz’i’r’g’.The black dotted line is the median among the measurements of theline cores, CASTLES data and Keeton et al. (2006) bands, and theshaded area around is the linear fit standard deviation. The coloreddotted lines represent the best linear fit for each set of points, thecolor shaded region represent the error in the linear fit associatedwith magnitude difference. Table 2.
SDSS0924+0219 Magnitude differencesRegion λ (Å) Window a (Å) m C - m B (mag)Continuum 4818 4543-5174 0 . ± . . ± . . ± . . ± . . ± . a Integration window. accretion disk of r s = 4 + − (cid:112) M / M (cid:12) light-days at λ s / light-days) (cid:112) M / M (cid:12) )= 1 . ± .
5) and a value for the thermal profile p = 0 . ± . σ . From the thin disk theory, we expect r s = 0 . (cid:112) M / M (cid:12) light-days, assuming a black hole mass of 2 . × M (cid:12) (Mor-gan et al. 2006), an Eddington ratio of L / L E = 0 . η = 0 .
1. This predicted size is significantlyAST E X 6.1 T
EMPLATE Table 3.
SDSS0924+0219 Chromatic MicrolensingData λ (Å) ∆ m (mag)Inada et al. (2003) 3545.0 -0.31 ± ± ± ± ± ± ± ± ± smaller than our measurement, but is in agreement with otherestimates: 0.07 44 light-days (cid:112) M / M (cid:12) (Mos-quera & Kochanek 2011), r s , λ = 0 . + . − . (cid:112) M / M (cid:12) light-days (MacLeod et al. 2015). On the other hand Blackburneet al. (2011) calculated r s , λ = 1 . + . − . (cid:112) M / M (cid:12) light-days, and Floyd et al. (2009) r s , λ = 4 . (cid:112) M / M (cid:12) light-days(for all data presented in) which are in agreement with ourestimation. With respect to the temperature index Floydet al. (2009) estimate p=0.75 using only Magellan data, and0 . < p < 17 using all their data set, and MacLeod et al.(2015) estimated p = 2 . ± . 17. Our result is in agreementwith Floyd et al. (2009) and also with the average slope foundby Jiménez-Vicente et al. (2014) (p = 0.8) using a sample of8 systems. 4.2. Q1355-2257 Discovered by Morgan et al. (2003) using HST data, it is adouble lensed quasar with an image separation of 1.23". Theredshift of the quasar is z S =1.37 (Morgan et al. 2003) and theredshift for the lens is z L =0.70 (Eigenbrod et al. 2006).We present VLT spectra for both images of the quasar(AB), and also a re-analysis of the deconvolved data (see Ap-pendix A) presented by Sluse et al. (2012). The line profilesfor both data sets (Figure 4) show small differences in thewings but are likely produced by microlensing.The magnitude differences for the core of the emissionlines and the continua below are shown in Figure 5 and Table4. Comparing our results for the deconvolved data and thevalues published in Sluse et al. (2012) we notice a discrep-ancy between both results of -0.06 mag for the continuumand +0.08 mag for the lines. This could be explained due to Figure 3. Combined probability density function forSDSS0924+0219 using a logarithmic size prior for the differ-ent ∆ m values. Contours correspond to 0.5 σ , 1 σ , 1.5 σ , and 2 σ respectively. The black solid line shows the value for p predictedby Shakura & Sunyaev (1973). The light blue star represent themeasurements presented by Floyd et al. (2009). The purple starshow the accretion disk size measure by Blackburne et al. (2011),the value of the temperature profile have been shift -0.02 forvisualization purposes. The red star represents the average sizeand temperature for the sample analyzed by Jiménez-Vicente et al.(2014). Wavelength [ Å ] F l u x [ A r b i t r a r y ] CIII] Wavelength [ Å ] F l u x [ A r b i t r a r y ] CIII] Wavelength [ Å ] F l u x [ A r b i t r a r y ] MgII Wavelength [ Å ] F l u x [ A r b i t r a r y ] MgII Figure 4. CIII] and MgII emission line profiles without the contin-uum for Q1355-2257. This work (left panel) and our re-analysis ofSluse et al. (2012) spectra (right panel). Shown in black is the Acomponent and in blue is the B component multiplied by a factorof 3.3 (CIII]), and 3.1 (MgII) for our data and 3.3 (CIII]), and 3.2(MgII] for deconvolved data. differences in the method to analyze the data. In the men-tioned publication, they fitted Gaussian profiles for the NLRand BLR while we integrate restrictive windows around thecore of the emission line to avoid taking into account fluxaffected by microlensing coming from of the BLR. We ob-tained a no microlensing baseline of 1.24 ± OJAS ET AL .lating the median among the emission lines cores from ourdata, the results published by Sluse et al. (2012) and the oneobtained with our method.In general, there is a difference of at least 0.3 mag be-tween the baseline and continuum from our data, Sluse et al.(2012) deconvolved spectra, and Morgan et al. (2003) data,corroborating the presence of microlensing. We found ev-idence of chromatic microlensing for wavelengths greaterthan λ > Wavelength [ Å ] m B - m A ( m a g ) Continuum-This workLines-This workContinuum-DeconvolvedLines-DeconcolvedCASTLESMorgan et al. (2003)Sluse et al. (2012) Figure 5. Magnitude differences m B - m A as a function of wavelengthfor Q1355-2257. Triangles are the emission line cores without thecontinuum, and squares are the integrated continuum under the linecores. Red symbols are the measurements obtained from our VLTspectra. Orange symbols are the results obtained using the decon-volved data of Sluse et al. (2012), while the purple symbols are theestimation presented by the authors, with error bars smaller than thesymbols. Green squares are the continua obtained from CASTLES.Light blue squares are the data for the g, r, i, and z bands in Morganet al. (2003). The black dotted line is the median of the emissionlines, and the grey shaded area represents the standard deviation.The colored dotted lines are the best linear fit to our spectra plusdeconvolved (red) and Morgan data sets between λ − λ To explain the increase of ∆ m > . 42 for wavelength be-yond λ ∆ m = − . 14. The introduction of galaxyflux produces the opposite effect by moving the m B − m A dif-ference in the direction of the lines instead of the contin-uum. Another alternative is contamination by the quasar hostgalaxy, considering that HST data show a ring in the bandswith anomalous flux.We used the data between λ − λ Table 4. Q1355-2257 Magnitude differencesRegion λ (Å) Window a (Å) m C - m B (mag)ContinuumOur data 4521 4400-4764 1.73 ± ± ± ± ± ± ± ± a integration window. Table 5. Q1355-2257 Chromatic-MicrolensingData λ (Å) ∆ m (mag)Our + Deconvolved dataset 4400 0.53 ± ± ± ± ± ± section 3, we modeled the system using Lensmodel (Keeton2001) to obtain the parameters to compute the magnificationmaps. We obtained the convergence and the shear for eachimage: κ A = 0 . γ A = 0 . κ B = 1 . γ B = 1 . 08. These val-ues are consistent with those obtained by Sluse et al. (2012).We obtained the probability density functions of r s and pusing a logarithmic prior for the size for each data set. Asboth calculations are independent we performed the productof these results to obtain the probability distribution functionin Figure 6. We found that the size and temperature pro-file of the accretion disk is: r s = 3 . + . − . (cid:112) M / M (cid:12) light-days(ln ((r s / light-days) (cid:112) M / M (cid:12) ) = 1 . ± . ± σ . This is the first estimation of the size and p using mi-crolensing for this system. If we compare our results withthose expected from the theory we find that the size is largerthan the theoretical value r s − theory = 0 . (cid:112) M / M (cid:12) light-daysassuming p=4/3, a M BH = 1 . × M (cid:12) (Sluse et al. 2012),AST E X 6.1 T EMPLATE L / L E = 0 . η = 0 . 1. The value for p is in agreement, within errors, withthe proposed by Shakura & Sunyaev (1973). Considering theresults obtained for other systems using this technique (Rojaset al. 2014; Jiménez-Vicente et al. 2015b; Motta et al. 2017),our results confirm that the size of the accretion disk is largerthan predicted. Figure 6. Probability density function using a logarithmic size priorfor the chromatic microlensing measurements in Q1355-2257. Con-tours correspond to 0.5 σ , 1 σ , 1.5 σ , and 2 σ respectively. The blacksolid line shows the value for p by Shakura & Sunyaev (1973). SDSS1029+2623 For this system the source is at z s =2.197. It was discov-ered by Inada et al. (2006). It was thought to be a doublesystem with a large separation between A and B (22.5"), butOguri et al. (2008) discovered a third component separated1.8" from the B component. The large separation betweenA and B occurs because the lens is a cluster of galaxies atz l =0.58 (Oguri et al. 2008).We present our own analysis for the spectra in Oguri et al.(2008). The line profiles (Figure 7) show strong absorptionin the case of Ly α and CIV. For that reason, we used smallwindows to integrate the line flux, and in the case of CIV, wesplit the analysis into two windows (Table 6).The differences between the core of the emission line andthe adjacent continuum are negligible (Figure 8), which is ev-idence of no microlensing effect in the spectra at that epoch(December 2007). The broad band fluxes presented in Oguriet al. (2008) where taken in November 2006 (B), May 2007(VRI), and January 2008 (g, and R) respectively. The B bandfollows the trend of the spectroscopic data, but the rest of thebands show an offset of ∼ . Wavelength [ Å ] F l u x [ e r g s c m Å ] 1e 16 Ly Wavelength [ Å ] F l u x [ e r g s c m Å ] 1e 17 CIII] Wavelength [ Å ] F l u x [ e r g s c m Å ] 1e 16 CIV Wavelength [ Å ] F l u x [ e r g s c m Å ] 1e 17 MgII Figure 7. Ly α , CIII], CIV, and MgII emission lines profiles with-out the continuum for SDSS1029+2623. In black wre show the Acomponent and in blue the B component multiplied by a factor of6.0 (Ly α and CIII]), 4.5 (CIV), and 3.3 (MgII]. Table 6. SDSS1029+2623 Magnitude DifferencesRegion λ (Å) Window a (Å) m C - m B (mag)Continuum 3905 3640-4250 2.09 ± ± ± ± ± α ± ± ± ± ± a integration window. range of the V,R,I,g, and R bands. However, the integrationshows the same trend as the measurements in the spectra. Apossible explanation is flux loss in the spectra (e.g. ∼ 10% inB component), producing a displacement in the data.Figure 8 shows that the magnitude differences for bothlines and the continua increase towards blue wavelengths,which could be explained by dust extinction produced bya galaxy in the vicinity of the C component (Oguri et al.2013). The possibility of extinction was previously analyzedby Oguri et al. (2008), obtaining ∆ E ∼ v =3.1, and Ota et al. (2012), giving ∆ E ∼ l = 0.584. R OJAS ET AL .We used the spectroscopic data to perform a new extinctionanalysis under the assumptions that the absorber is the galaxyin the vicinity of component C. Considering the absence ofmicrolensing, we combine both the emission line and thecontinuum magnitude differences to fit an extinction curveat the redshift of the lens. We present two cases, for the firstone we left R v as a free parameter and for the second onewe fixed R V = 3 . 1, which corresponds to the average valuefor our galaxy. The best fit parameters for the first case are: ∆ M = 1 . ± . ∆ E = 0.22 ± R V = 3.24 ± χ = 39.93, degree of freedom = 11). For the second case thebest fit parameters are: ∆ M = 1 . ± . 01, and ∆ E = 0.20 ± χ = 205.5, degree of freedom = 12). In both caseswe obtain similar results for the extinction in agreement withprevious results by Oguri et al. (2008) and Ota et al. (2012). lens rest frame [ m ] m C - m B ( m a g ) Continuum-This workLines-This workgR bands (Oguri et al. 2008)BVR bands (Oguri et al. 2008)extinction curve (R v free)extinction curve (R v =3.1) Figure 8. Magnitude differences m C − m B as a function of wave-length for SDSS1029+2623. The wavelength axis is plot in the lensrest frame for a better interpretation of the extinction curve. Thetriangles are the values for the emission line cores without contin-uum and the squares are the continuum integration from the spectraor band, depending on the data set. Red and orange symbols aremeasurements from the spectra. Data from Oguri et al. (2008) areplotted in light blue (bands g and R, taken in 2008 with the Kecktelescope) and in purple (bands, B, V, R, and I, taken in 2006-2007with the UH88 telescope). The black (green) dashed line is the ex-tinction curve fitted to the spectroscopic data using all the param-eters free (fixing R v = 3.1), the grey (light green) shaded regionrepresents the error associated with the magnitude difference.5. CONCLUSIONSWe used spectroscopic data of the lensed quasars: SDSS0924+0219(BC), Q1355-2257 (AB), and SDSS1029+2623 (BC) tostudy their flux anomalies. We obtained the following re-sults:1. Comparing the magnitude differences of the coresof the emission lines with those of the continua wefound chromatic microlensing in SDSS0924+0219,and Q1355-2257. We estimate the accretion disk at λ rest − f rame = 3533Å size and temperature pro-file. Although the CIII] and MgII line profiles ofSDSS0924+0219 and Q1355-2257 present slight dif-ferences in the wings, only those in the red wing ofCIII] in SDSS0924+0219 are large enough to be likelydue to microlensing in the BLR, but only one epoch isnot enough to constrain the size of this region. In thecase of SDSS1029+2623 we found evidence of extinc-tion, produced by a galaxy near C and no evidence ofmicrolensing.2. In the case of SDSS0924+0219 we obtain r s , λ = 4 + − (cid:112) M / M (cid:12) light-days and p = 0 . ± . 2. The size is inagreement with those of Floyd et al. (2009) and Black-burne et al. (2011). The estimation for p is significantlysmaller than the value expected from the theory, but inagreement with the average value found by Jiménez-Vicente et al. (2014) in a sample of 8 lensed quasars.3. Q1355-2257 shows chromatic microlensing which al-lows us to estimate r s , λ = 3 . + . − . (cid:112) M / M (cid:12) light-days and p = 2 . ± . 7. This is the first estimate of theaccretion disk size and temperature profile for this sys-tem. Comparing with theory we found that the size islarger than, and p is in agreement within errors withpredictions.4. For SDSS1029+2623 we fitted an extinction curve tothe data assuming that the galaxy acting as absorberis at the redshift of the cluster. We study two cases,one with R V as a free parameter and other where wefixed R V = 3 . 1. In both cases we obtained a value forthe extinction around ∆ E = 0.2 that is in agreementwith previous estimations (Oguri et al. 2008; Ota et al.2012).The authors are grateful to M. Oguri for kindly providingthe spectra of SDSS1029+2623. K.R. acknowledge supportfrom PhD fellowship FIB-UV 2015/2016, Becas de Doctor-ado Nacional CONICYT 2017, LSSTC Data Science Fel-lowship Program, her time as a Fellow has benefited thiswork, and support from the Swiss National Science Founda-tion (SNSF). 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Deconvolved spectra for Q1355-2257 presented in Sluse et al. (2012). The data was observed with VLT/FORS1 in 2005. In blackthe A component and in blue the B component. AST E X 6.1 T EMPLATE Wavelength [ Å ] F l u x [ e r g s c m Å ] 1e 16 SDSS1029+2623