Microlensing in Spectra of Multiply Lensed QSO

# Measuring Microlensing using Spectra of Multiply Lensed Quasars

V. Motta Departamento de Física y Astronomía, Universidad de Valparaíso, Avda. Gran Bretaña 1111, Playa Ancha, Valparaíso 2360102, Chile E. Mediavilla Instituto de Astrofísica de Canarias, Avda. Vía Láctea s/n, La Laguna, Tenerife 38200, Spain Departamento de Astrofísica, Universidad de La Laguna, La Laguna, Tenerife 38205, Spain E. Falco Whipple Observatory, Smithsonian Institution, 670 Mt. Hopkins Road, P.O. Box 97, Amado, Arizona 85645, USA J.A. Muñoz Departamento de Astronomía y Astrofísica, Universidad de Valencia, 46100-Burjassot, Valencia, Spain
###### Abstract

We report on a program of spectroscopic observations of gravitationally-lensed QSOs with multiple images. We seek to establish whether microlensing is occurring in each QSO image using only single-epoch observations. We calculate flux ratios for the cores of emission lines in image pairs to set a baseline for no microlensing. The offset of the continuum flux ratios relative to this baseline yields the microlensing magnification free from extinction, as extinction affects the continuum and the lines equally. When we find chromatic microlensing, we attempt to constrain the size of the QSO accretion disk. SDSSJ1004+4112 and HE1104-1805 show chromatic microlensing with amplitudes and mag, respectively. Modeling the accretion disk with a Gaussian source () of size and using magnification maps to simulate microlensing we find ) and for SDSS1004+4112, and ) and for HE1104-1805. For SDSSJ1029+2623 we find strong chromaticity of mag in the continuum flux ratio, which probably arises from microlensing although not all the available data fit within this explanation. For Q0957+561 we measure B-A magnitude differences of 0.4 mag, much greater than the 0.05 mag amplitude usually inferred from lightcurve variability. It may substantially modify the current interpretations of microlensing in this system, likely favoring the hypothesis of smaller sources and/or larger microdeflectors. For HS0818+1227, our data yield posible evidence of microlensing.

gravitational lensing: strong - gravitational lensing: micro - accretion disks - quasars: individual: HS0818+1227, Q0957+561, SDSS1004+4112, SDSS1029+2623, HE1104-1805

## 1 Introduction

Gravitational lenses are a powerful tool to study not only the structure of the lensed quasar but also the composition of the lens galaxy (Schneider et al., 1992; Kochanek, 2004; Wambsganss, 2006). Simple lens models are usually sufficient to reproduce the positions of lensed QSO images, but they can fail to reproduce the optical fluxes of these images. The so-called flux ratio anomalies are thought to be produced by small-scale structures in the gravitational potential of lens galaxies (Witt et al., 1995; Mao & Schneider, 1998; Chiba, 2002; Metcalf & Madeau, 2001; Dalal & Kochanek, 2002; Schechter & Wambsganss, 2002; Keeton, 2002; Bradac et al., 2002; Metcalf & Zao, 2002; Moustakas & Metcalf, 2003). These structures are either dark matter subhalos or stars and the effects they produce are referred to as millilensing and microlensing respectively.

A substructure is able to produce a flux anomaly if the radius of its Einstein ring is large compared to the emitting region. Since the sizes of the quasar continuum emitting regions depend on the wavelength, microlensing by stars in a lens galaxy will yield a wavelength-dependent magnification of the continuum (Wambsganss & Paczyński, 1991; Wisotzki et al., 1995; Mosquera, Muñoz & Mediavilla, 2009; Mediavilla et al., 2011) that can be strong for the UV and the optical but is negligible for the IR. Microlensing could also affect the high ionization broad emission lines (BEL) that are expected to arise from the inner part of the broad-line region (BLR). Specifically, microlensing would affect the broad wings of the profiles of the high ionization lines that correspond to high velocity emitters, leaving unchanged the core (Popović et al., 2001; Abajas et al., 2002; Richards et al., 2004; Lewis & Ibata, 2004; Gómez-Álvarez et al., 2006). Low ionization BEL and narrow emission lines (NEL) arise from considerably larger regions and are supposed to be insensitive to microlensing (Abajas et al., 2002) although the low ionization BEL of some low-luminosity lensed AGNs may be slightly affected by microlensing.

Observational studies aimed at measuring the microlensing effect in lensed QSOs usually consist of broadband observations repeated over extended periods, longer than the time delays for image pairs (Woźniak et al., 2000; Oscoz et al., 2001; Colley et al., 2002; Schechter et al., 2003; Fohlmeister et al., 2008), leading to several years of monitoring.

On the other hand, most of the microlensing searches using optical imaging have been concentrated on quadruple lenses because the effect of substructure is more important at high magnification (Witt et al., 1995; Schechter & Wambsganss, 2002; Pooley et al., 2007). They provide enough constraints to fit the simplest singular isothermal (SIS) model (Schechter & Wambsganss, 2002; Kochanek & Dalal, 2004) and find the flux anomalies. Double lenses, however, do not provide enough constraints to produce such a model unless the fluxes are used as additional constraints. In these cases, the flux ratio of emission lines (Wisotzki et al., 1993; Mediavilla et al., 2009, 2011) or in the infrared (Agol et al., 2007) has been used assuming that the emission regions are larger than the microlensing source and dust extinction is negligible.

In the present paper, we use spectra of lensed quasars as an alternative approach to photometric monitoring, to study microlensing in quadruple or double lenses. For each pair of images of a lensed quasar ( and ), we base our analysis on the measurement of the offsets of the flux ratio of the core of the emission lines compared to the flux ratio of the continuum . This analysis allows us to distinguish between microlensing and dust extinction without assuming a model for the lensed system (see Mediavilla et al., 2011, and references therein). In this way, a single-epoch spectroscopic observation can suffice –through the measurement of microlensing– to estimate physical parameters of interest of the lens galaxy (like the fraction of mass in compact objects, Mediavilla et al. 2009) or of the unresolved quasar source (like the size or the radial temperature profile).

In section 2 we present the data for 5 gravitationally-lensed quasars with multiple images for which we have obtained low-resolution spectra with signal-to-noise greater than 40. The systems, HS0818+1227, Q0957+561, SDSS1004+4112, SDSS1029+2623, and HE1104-1805, were selected because the separations between the images were larger than 3. Section 3 is devoted to present the data analysis methodology. We discuss our results in §4 and give some concluding remarks in section §5.

## 2 Observations and data reduction

Microlensing detection using spectra of lensed QSOs has stringent requirements. First of all, we need high signal-to-noise ratio in the spectra () and sufficient spectral resolution ( km s) to resolve the shape of the line profiles. Second, we need to obtain simultaneous, spatially-separated spectra of pairs of lensed QSO images to compare their continuum and emission lines at different wavelengths, which requires good seeing conditions (). These requirements are achieved using 6-8 m class telescopes under good seeing conditions.

We observed the sample on 11 and 12 January 2008 with the Blue Channel spectrograph on the MMT. Table 1 shows the log of observations. We also observed HE1104-1805 on 07 April 2008 with the FORS2 spectrograph at the Very Large Telescope (VLT). Our ground-based observations were acquired under excellent atmospheric conditions (Table 1). For Q0957+561, we used archival data111archive data were obtained at the Space Telescope Science Institute, operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555 obtained with the STIS spectrograph on the Hubble Space Telescope (HST). Components and were observed with HST at different epochs to account for time delay variations in the continuum spectra (see Table 1). A detailed description of these observations and the spectrum analysis can be found in Hutchings (2003).

We performed the data reduction with IRAF222IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation tasks. These included bias subtraction, flat fielding, extraction of 1-D spectra and wavelength calibration. As we are currently interested only in flux ratios (i.e. magnitude difference ), we did not flux-calibrate our data. Cosmic-ray rejection was carried out in those cases where we had at least three exposures. The data obtained from the HST archive are already fully reduced.

In spite of the careful data reduction process, some systematic errors can affect our measurements. We discuss these in the following paragraphs.

### 2.1 Spectrum Cross-Contamination

To avoid cross-contamination between the spectra of lensed QSO image pairs we selected pairs with separation much wider than the average seeing (), which was larger in turn than our typical seeing. Our pairs have separations ranging from to as shown in Table 1; we estimate that cross-contamination is negligible in our observations.

### 2.2 Long-Slit Losses

To obtain simultaneous pairs of spectra with a single slit, we did not observe our targets at the parallactic angle; in each case we used the position angle defined by the two components. In these ground-based observations, we lost a small amount of the blue part of the spectra because part of the blue quasar light may fall outside the slit. Our airmass range was ; we used a slit width. We used a program developed by E. Marchetti at ESO to calculate the differential atmospheric refraction (DAR) for each given wavelength and airmass. The atmospheric parameters (temperature, humidity, and pressure) we used are C, %, mbar for VLT and C, %, mbar for MMT. The focus for FORS2 is set at 5000 Å  which is our reference wavelength to calculate the displacement due to DAR. We estimated the relative loss in the flux of each pair of images at 3500 Å  and 8000 Å, and at 4500 Å  and 9500 Å  for the MMT and VLT data respectively. We found relative losses of % in all MMT spectra; for the VLT spectra, we found losses of % due to an error in the position angle used in the observations. Considering the separation between pairs of images ( to ), the losses are nearly identical for both spectra in each case, and as we are concerned with flux ratio changes with wavelength, those losses do not affect our results.

## 3 Data Analysis Methods and Uncertainties

### 3.1 Continuum microlensing measurement

The method we use to untangle microlensing and extinction is based on the measurement of the offsets between the continuum and the emission line flux ratios (see, e.g., Vanderriest, 1990; Motta et al., 2002; Wucknitz et al., 2003; Wisotzki et al., 2003; Mediavilla et al., 2009, 2011; Sluse et al., 2011). The multicomponent nature of quasar emission-lines imply that the emission-line spectra are produced over a wide range of distances from the central continuum (see e.g. Sulentic et al., 2000). According to Marziani et al. (2010) the low ionization lines (LIL) and the core of the high ionization lines (HIL) will be dominated by a component (FWHM ) that corresponds to the region of reverberation mapping typically large enough as to be insensitive to microlensing by solar mass objects. The broad wings of the emission lines (FWHM ), however, could arise from the inner parts of the BLR and may be microlensed. For this reason, we prefer to use exclusively the line cores (dominated by the NLR and the outer regions of the BLR) as reference to set the baseline for no microlensing. To compute the core flux without attempting an analytical decomposition into several components (Marziani et al., 2010), we have used a narrow band decomposition similar to that used by Sluse et al. (2011). Specifically, we define as core flux the continuum subtracted flux integrated in a relatively narrow velocity interval (from 25 to 90 Å depending on the line profile shape for the different sources) centered on the peak of the line. To accommodate the varying widths of the lines, the continuum estimate for each line requires windows with varying width as indicated below for each lens system.

For each component and each emission line we used DIPSO (Howarth, 2004) in STARLINK444Support provided by the Starlink Project which is run by CCLRC on behalf of PPARC. to fit a function to the continuum on either side of the emission line, given a total wavelength range (, ). The task also gives the error coefficients (, ) in the continuum fitting. This error is largest in the bluest and reddest ends of the continuum, because it is affected by the response of the CCD. The flux under the continuum is then obtained as the integral below the fitted function , i.e. . The error in the flux is estimated as .

The emission line flux is obtained by integrating the emission line profiles in each continuum-subtracted emission line using DIPSO. As commented above, we have separated the line core from the wings which could be affected by microlensing. The error in the narrow emission line is estimated as the error in the continuum fitting. In those cases in which the emission line is affected by absorption lines, a narrower integration window was chosen (10 to 15 Å in the case of SDSS1029+2623). In most of the cases in which these absorptions are mild, they can be successfully avoided. However, when the absorptions are broad and affect the central part of the emission lines (e.g. SDSS1029+2623) the measurements have correspondingly larger uncertainties.

### 3.2 Impact of microlensing in the BEL

Nemiroff (1988) and Schneider & Wambsganss (1990) suggested that, depending on the structure of the BLR, microlensing could modify the broad line profiles. Abajas et al. (2002) have estimated which gravitational lens systems are more likely to show BLR changes due to microlensing. Some examples of these variations in the BLR have been presented by Filippenko (1989); Chartas et al. (2002, 2004); Richards et al. (2004); Gómez-Álvarez et al. (2006); Sluse et al. (2011) in the cases of MG0414+0534, H1413+117, SDSS1004+4112, and Q2237+0305.

Superposition of the spectra for each image pair (see Figures 1, 6, 7, 11, 13, and 16) shows excellent matches between the emission lines profiles of HE1104-1805, SDSS1029+2623, Q0957+561 and HS0818+1227. Significant microlensing of BELs is detected only in the wings of one of the systems, SDSS1004+4112 (see §4.1). A slight enhancement of the red wings that may be tentatively related to microlensing has been also detected in HE1104-1805 (see §4.2). Thus, the impact of microlensing on the BEL looks negligible except in SDSS1004+4112. The excellent matches between the emission line profiles for each image pair imply that, except for fluctuations due to absorptions or noise, the choice of the size of the line core has no impact on the results. To show this explicitly, we have compared the A-B magnitudes (averaged on all the lines for each system) computed using only the line core or the whole line (as estimated from the factor used to match the line profiles). We find differences of =0.02, 0.03, 0.01, and 0.06 for HE1104, SDSS1029, QSO0957, and HE0818, respectively. Thus, we find that for all the systems except SDSS1004+4112 the A-B emission line ratios do not significantly depend on the choice of the core width. In any case, we have used the core of the emission lines exclusively to estimate the emission line flux ratios (see section 3.1).

### 3.3 Estimate of accretion disk parameters

For those cases in which chromatic microlensing is detected, we can study the structure of the accretion disk in the lensed quasar by estimating its size and temperature profile. We model the accretion disk as a Gaussian, , with radius variable with wavelength, . To estimate the probability of reproducing the measured microlensing magnifications we have randomly placed a Gaussian source on microlensing magnification maps of Einstein Radii squared ( pixels) for SDSS1004+4112 and Einstein Radii squared ( pixels) for HE1104-1805 computed for each image using the Inverse Polygon Mapping method (Mediavilla et al., 2006). The convergence () and shear () for each image are selected from available models in the literature (see e.g. Kochanek et al., 2006; Mediavilla et al., 2009). We take for the fraction of mass in compact objects, a reasonable value according to current estimates (see e.g. Schechter & Wambsganss, 2002; Mediavilla et al., 2009; Pooley et al., 2009). We consider microlenses. Following a Bayesian approach as in Mediavilla et al. (2011), we estimate the probability of and conditioned on the measured microlensing magnifications for both uniform and logarithmic priors on . We have considered these two priors to analyze the sensitivity of our study to the treatment of the size prior (see Morgan et al., 2010; Mediavilla et al., 2011). We consider a range of 1 to 15 light-days () for and a range of 0 to 3 for . In §4 we will apply this method to SDSS1004+4112 and HE1104-1805. The results for and are given with errors.

### 3.4 Dust extinction fitting

Each lensed QSO image follows a different path through the lens galaxy, encountering different amounts of dust and gas that produce differential extinction. Falco et al. (1999) measured the mean differential extinction, , in 23 lens galaxies using HST broad-band filters. This extinction can affect not only the continuum flux ratio but also the emission-line fluxes (Motta et al., 2002; Mediavilla et al., 2005, 2009, 2011). Thus, considering that the cores of the emission lines are affected neither by microlensing nor by intrinsic variability, measuring the emission lines flux ratio in several wavelengths provides us with a method to determine the existence of dust extinction in the system. We fitted the extinction curve to the magnitude difference in emission lines for images 1 and 2 using the equation (Falco et al., 1999; Muñoz et al., 2004)

 m1(λ)−m2(λ)=−2.5log(M1M2)+(E1−E2)RV(λ1+zL),

where is the constant magnification ratio, is the extinction difference, and is the extinction curve in the lens rest frame. We minimized per number of degree of freedom (). In the majority of the systems (except Q0957+561) we have only a few narrow emission lines in the optical part of the spectra. We make our estimates with the Cardelli, Clayton, & Mathis (1989) extinction curve of the Milky Way (i.e. we fixed the parameter ) at the redshift of the lens galaxy. As is standard and to facilitate comparison of our results with those of other authors, magnitude differences are shown as a function of inverse wavelength in microns in the lens galaxy rest frame.

### 3.5 Contamination from other sources of chromaticity

There are two effects, intrinsic variability and contamination by the lens galaxy, that can produce chromatic variations in the flux of lensed QSOs and, hence, mimic microlensing.

The continuum flux variation in QSOs is a well-know effect that does not significantly affect the NEL fluxes (Peterson, 1993). Intrinsic continuum variability combined with the time delay between images can produce a change in the flux ratios between images that can be wavelength dependent, thus inducing changes in the chromaticity. These changes should be avoided if possible or at least estimated. In two of the objects, Q0957+561 and HE1104-1805 we can use data taken at two different epochs separated by the time delay to avoid the problem of intrinsic variability.

In all the objects, we can estimate the effects of intrinsic variability (following Yonehara, Hirashita & Richter, 2008) using the structure function inferred from the SDSS imaging data of quasars (Vanden Berk et al., 2004; Ivezić et al., 2004). We will consider the less favorable case; an intrinsic magnitude of for the quasar (Yonehara, Hirashita & Richter, 2008), the bluest photometric band to measure variability and the two bands with the largest separation in wavelength to estimate the chromaticity variation. In the case of SDSS1004+4112A,B with a measured time-delay of about 40 days, the expected intrinsic variability is mag and the chromaticity change is mag. For HE1104-1805 with a measured time delay of about 150 days and for HS0818+1227 with a comparable theoretical delay, variability of mag and chromaticity change mag are predicted. Finally, for the largest separation systems, Q0957+561 and SDSS1029+2623, variability of mag and chromaticity change of mag are expected. Thus, changes in chromaticity, that are most significant to study the quasar structure, are rather small.

The expected values of the intrinsic variability are in reasonable agreement with the analysis of lightcurves for Q0957+561 (Goicoechea et al., 2008; Goicoechea, 2002; Ovaldsen et al., 2003a, b), SDSS1004+4112 (Fohlmeister et al., 2008) and HE1104-1805 (Poindexter et al., 2007). In the case of HE1104-1805, Poindexter et al. (2007) specifically studied the effect of intrinsic variability on flux ratios finding a global displacement of 0.1 mag in magnitude differences due to the time delay without apparent changes in chromaticity in the optical (from the J to B photometric bands).

In summary, we used photometry corrected for known time delays to avoid the effects induced by intrinsic variability in Q0957+561 and HE1104-1805. These effects are within the uncertainties for SDSS1004+4112 and, likely, for HS0818+1227 (although we lack on a measured time delay for this object). Finally, SDSS1029+2623 can potentially have relatively strong effects ( mag change in chromaticity) induced by intrinsic variability.

On the other hand, in the cases of HS0818+1227 and Q0957+561 the lens galaxy is bright and very close to one of the components on the sky ( and respectively) and some of the spectra may suffer contamination from the continuum of the lens galaxy. This continuum contamination is stronger at longer wavelengths, but it does not affect the emission line fluxes. In these two cases, to avoid the continuum flux contamination we have considered the broad-band flux ratio obtained by CASTLES555CfA-Arizona Space Telescope LEns Survey, Kochanek, C.S., Falco, E.E., Impey, C., Lehar, J., McLeod, B., Rix H.-W., http://www.cfa.harvard.edu/glensdata/ using HST imaging, in which the lens galaxy was modeled and subtracted.

## 4 Results

### 4.1 Sdss1004+4112

SDSS1004+4112 is a five-image lens system at discovered by Inada et al. (2003) with distances between components ranging from to . The lens is a cluster at (Oguri et al., 2004; Inada et al., 2008), which has also been studied in X-rays (Ota et al., 2006). This system has known CIV broad-line profile variations (Richards et al., 2004) that are argued to arise either from microlensing (Richards et al., 2004; Gómez-Álvarez et al., 2006; Abajas et al., 2007) or due to small line-of-sight differences through the quasar absorbing outflows (Green, 2006). Recently, Fohlmeister et al. (2008) have measured a time delay of days for images and , and days for and , detecting microlensing variability with an amplitude of the order of  mag between and (Fohlmeister et al., 2008).

Comparing the and spectra taken with the MMT we notice an enhancement in the blue wing and a decrement in the red wing of the CIV and SIV emission lines (Figure 1). Ly and CIII] emission lines show smaller differences. Hence, our results are consistent with Richards et al. (2004); Gómez-Álvarez et al. (2006) and Lamer et al. (2006) although the amplitude of the enhancement of the blue wing is smaller than that observed previously. This can be appreciated in Figure 2 where the and CIV emission line profiles taken in 2004 with the Keck telescope are presented (data kindly provided by G.T. Richards). While the component and the red part of the A component are basically the same in both epochs, the blue wing enhancement of component is significantly smaller in 2008. This variability is the kind of gradual change in the line profile expected from microlensing. According to §3.1, in what follows we will use the cores of the emission lines to compute flux ratios avoiding the effects of microlensing in the blue wings.

magnitude differences in the continuum and in the emission lines estimated from our spectra or obtained from the literature are shown in Figure 3 (see also Tables 2 and 3). The magnitude differences corresponding to the emission lines show no trend with wavelength (within uncertainties) and are distributed around  mag supporting the absence of dust extinction and defining the baseline for no microlensing magnification. In 2004 the continuum difference curve obtained from the spectra matched within errors the zero microlensing baseline defined from the low ionization emission lines. With small offsets the broad-band based continuum data from Oguri et al. (2004) and Inada et al. (2003, 2005) also match the baseline for no microlensing. This lack of microlensing evidence in the continuum in 2004 (as the counterpart of the blue wing enhancements) was considered a serious drawback to interpret the enhancements in terms of microlensing (Gómez-Álvarez et al., 2006).

On the contrary, our continuum difference measurements (see Figure 3) based on spectra taken in 2008, strongly depart from the zero microlensing baseline with an increasing trend towards the blue that would include the X-ray measurements obtained by Ota et al. (2006). The magnitude difference in the continuum is consistent with CASTLES broad-band data.

The A-B continuum differences corrected for the time delay measured by Fohlmeister et al. (2008) change in the sequence:  mag (2003-04),  mag (2004-05),  mag (2005-06), and  mag (2006-07). The lowest value,  mag, is close to the mean magnitude difference in the emission lines,  mag, likely indicating that at this epoch (2003-04) the system showed little microlensing.

Figure 4 shows a linear fit to the continuum data and the average of the emission line data. The magnitude difference variation in the continuum data (with a slope of ) implies differences with respect to the emission lines of and  mag at 7680 and 3320 Å  respectively. Our results are consistent with the trend indicated by the X-ray continuum data (Ota et al., 2006). In summary, our data indicate negligible dust extinction and evidence of chromatic microlensing affecting the continuum. These results and the variability detected in the emission line profile give strong support to the hypothesis of microlensing to explain the enhancement in the blue wings.

The structure of the accretion disk was studied using the procedure explained in section 3.3. We used the values (, ) and (, ) taken from Mediavilla et al. (2009) to obtain the magnification maps for the and images respectively. Applying this procedure to microlensing measurements at three different wavelengths corresponding to our MMT data (see Table 4), we obtained the 2D probability density functions (pdfs) shown in Figure 5 for both linear and logarithmic grids in . From these distributions we obtain estimates ) and for the linear prior and ) and for the logarithmic prior. Although the value of is consistent within uncertainties with the thin disk theory it is interesting to mention the trend in this and in other objects to have (see Mediavilla et al., 2011; Blackburne et al., 2011). The microlensing estimate for the size also exceeds substantially the estimate obtained from thin-disk theory (, Mosquera & Kochanek, 2011).

To study the impact of intrinsic variability in these results, we can compare the A-B difference we measured using the emission lines or the continuum at 12500Å (see Table 4), where microlensing and dust extinction should be less significant. We find a difference between both measurements (which is a conservative upper bound to continuum variability) of 0.08 mag, for an insignificant impact on the estimate of and .

### 4.2 He1104-1805

HE1104-1805 was discovered by Wisotzki et al. (1993); it consists of two lensed images and separated by at . The lens galaxy was detected by Courbin et al. (1998) at . Image is from the main lens galaxy. Variability in the continuum was detected in spectra taken by Wisotzki et al. (1995) (optical), Courbin et al. (1998) (near infrared), and Chartas et al. (2009) (X-ray). Poindexter et al. (2007) monitored the system between 2003 and 2006, concluding that the magnitude difference in the optical bands has changed from , when the lens was discovered, to in their optical data (2006). These authors also provide a time delay estimation of (1 ) days.

The data obtained with the MMT and VLT show that the emission line profiles of both images, A and B, are very similar, although some slight but interesting differences can be found in the broad components of CIV and SiIV (Figures 6 and 7). Ly is only seen in our MMT spectra. The profile of the MgII emission line is asymmetric both in and . CIII] presents heavy absorption lines both in the BEL and NEL. In the higher SNR data obtained from VLT it is clearly seen that the spectrum shows several absorption lines, none of them present in the spectrum. The profiles of CIV and SiIV emission lines show a slight enhancement in the red wing of compared to those of both in MMT and VLT data. These wing enhancements present only in high ionization lines might be evidence of microlensing.

Figure 8 (see also Table 5) presents the magnitude differences in the continuum and in the emission lines. We have also included data from the literature (Table 2). The mean B-A magnitude difference ( mag) corresponding to the emission lines obtained from MMT and VLT spectra is consistent with the values derived by Wisotzki et al. (1995) ( mag) and Courbin et al. (2000) ( mag). These values are also in agreement with the value estimated from infrared data  mag (Poindexter et al., 2007). These results confirm that the cores of the emission lines are not affected by microlensing and that little extinction is present.

The magnitude differences in the continuum obtained from the MMT and VLT spectra show a slope that is in agreement with optical broad-band data obtained in 2006 (Poindexter et al., 2007)666As we cannot correct our data for time delay, we have considered both the time-delay corrected and uncorrected optical data obtained by Poindexter et al. (2007) (magenta pentagons). Notice also that the lens galaxy continuum is very faint, so it cannot contaminate our spectra.. Broad-band data obtained several years before (Falco et al., 1999; Lehár et al., 2000; Courbin et al., 2000; Schechter et al., 2003) are all consistent (slope ) but are very different from our own recent data and that obtained by Poindexter et al. (2007).

Linear fits to the magnitude differences of continua are shown in Figure 9. The slope for the magnitude differences in the emission lines and the IR data is which is consistent with no extinction and it is in good agreement with results obtained from near-infrared spectra by Courbin et al. (2000) () and those found by Falco et al. (1999) () using broadband data. The continuum data from the literature are fitted in two separate sets: 1992-1994 data with a slope of and the more recent data from Poindexter et al. (2007) with a slope of . The slope of the linear fit to our 2008 continuum data (MMT+VLT), , is thus in good agreement with the slope of corresponding to the 2006 data of Poindexter et al. (2007), but remarkably different from the value corresponding to 1992-1994 broadband data . Thus, microlensing in HE1104-1805 has induced an extreme change in continuum slope that needs explanation. The chromaticity during the 1992-1994 epoch with an increasing amplitude towards the blue leads to an straightforward interpretation in terms of the magnification of the dominant component . To explain the slope of the continuum corresponding to 2006-2008 epoch (under common assumptions about the unresolved source structure) we need to combine chromatic microlensing in both and . For instance, we can consider the combination of two events of magnification in both and with a progressive increase in the strength of the event from 1994 to 2008. This is only a qualitative example and simulations are needed to consistently reproduce microlensing chromaticity in each of the two epochs.

Following the procedure described in section 3.3 we have used the detected microlensing chromaticity to study the structure of the accretion disk in HE1104-1805. We have done this for three sets of data: our VLT continuum data from 2008, the Poindexter et al. (2007) data corrected for time delay and the average of the data from Courbin et al. (1998), Falco et al. (1999), Lehár et al. (2000), and Schechter et al. (2003) that consistently follow a common trend with wavelength. In Table 6 we present the microlensing measurements for each dataset. To compute the microlensing maps we have used the following projected densities and shears for each lens image (, ) and (, ) according to Mediavilla et al. (2009)

The resulting pdfs are plotted in Figure 10, and the expected values and uncertainties in Table 7. The pdfs corresponding to the MMT/VLT (Fig.10a) and to the Poindexter et al. (2008) data (Fig.10c) are not as concentrated near the maximum of the pdf as in the case of the broad-band data (Fig 10b). These pdfs may present a secondary maximum (perhaps due to the complexity of the microlensing phenomenon corresponding to this epoch) and, individually considered, are not very conclusive. However, the product pdf strongly increases the concentration of the probability near the maximum and the significance of the estimates: ), for the linear prior and ), for the logarithmic prior. Our estimates correspond to one half light radius at the central wavelength of B filter, ). This value is in good agreement with the results obtained by Muñoz et al. (2011) with HST data and by Poindexter et al. (2008) from photometric monitoring. The values of are, however, considerably smaller.

The microlensing-based size estimates are significantly larger than those inferred from the black-hole mass or from the observed I-band flux (see Poindexter et al., 2008).

### 4.3 Sdss1029+2623

SDSS1029+2623 was discovered by Inada et al. (2006); it consists of two images and separated by at and a cluster lens galaxies at . Recently Oguri et al. (2008) found a third image from and several complex absorption systems in the emission lines.

Although the emission line profiles are similar for and (Figure 11), there are several groups of absorption line systems affecting Ly and CIV that are associated with MgI/MgII/FeII absorption systems, as found by Oguri et al. (2008). There are also self-absorption systems associated with Ly, SiIV, and CIV lines that are present in both components but with significant differences. In spite of this we have attempted to determine flux ratios by defining suitable integration windows to avoid the absorptions. In the case of CIII], the emission line profiles are almost identical in both components and show no absorption lines. Thus, the results derived from CIII] should be more reliable than the results inferred from the other lines.

The magnitude differences obtained from our data (continuum and emission lines) compared to those obtained by Inada et al. (2006) and Oguri et al. (2008) are shown in Figure 12 (Table 8). Our continuum flux ratio agrees well with the data corresponding to the and broadband filters from Oguri et al. (2008) that were taken with the Keck at the same epoch. However, there is a difference of mag with the data taken at other epochs. This is explained by variability in the continuum between 2007 and 2008 (another peculiar feature is that the measurement in the band (Inada et al., 2006) is mag above all the other broad-band measurements). In principle the variability could be attributed to microlensing or intrinsic variability of the quasar continuum combined with a time lag between both components. However, the strong chromaticity of the continuum flux ratio (of about 0.4 mag) that exceeds the mag global offset between continuum flux ratios at different epochs excludes the explanation based on intrinsic continuum variability. Dust extinction, on the other hand, cannot explain the chromaticity for the flux ratio inferred from radio observations agrees with the flux ratio of the bluest continuum contrary to the expectations under this hypothesis. Thus, microlensing is the more likely explanation and is supported by the agreement of the flux ratios inferred from three of the lines, CIV, SiIV, and Ly with the radio flux ratio. However, the flux ratio inferred from the other emission line, CIII] which presents the smoothest line profile, shows a large offset with respect to the baseline defined by the radio data that disagrees with the microlensing hypothesis. Under the hypothesis of chromatic microlensing we could follow the same steps as in the case of SDSS1004+4112 to estimate the size and temperature profile of the quasar source in SDSS1029+2623. However, lens modeling in this system is complex (see e.g. Kratzer et al., 2011) and we defer this study to future work.

### 4.4 Q0957+561

The first known gravitational lens was discovered by Walsh, Carswell, & Weymann (1979); it has been studied in great detail. It consists of two images and with separation . The source QSO is at and the main lens galaxy is at and is part of a poor cluster of galaxies. Comparison between and emission lines (Figure 13) do not show significant differences between the emission line profiles of CIV, CIII] and MgII. This limits the possible impact of microlensing on the broad component of the emission lines. To quantify this impact we have compared the flux ratios of the wings and the core of the CIV emission line (that has the highest S/N ratio) finding differences 10%. In any case we have computed flux ratios from the cores of the lines.

Figure 14 (see also Table 9) shows the magnitude differences in the continuum and in the emission lines for Q0957+561. This figure also includes other data from the literature and a re-analysis of HST/STIS data by Goicoechea et al. (2005b). Averaging the radio data from Conner et al. (1992) at , Gorenstein et al. (1988) at , and Haschick et al. (1981) at , the magnitude difference uncontaminated by the lens galaxy continuum and free from dust extinction is obtained,  mag. The magnitude differences corresponding to the emission lines follow a decreasing trend towards the blue compatible with extinction. A linear fit to the emission line magnitude differences (see Figure 15) has a slope of and a dispersion of 0.09 mag. This dispersion is reasonable taking into account the intrinsic difficulty and the inhomogeneity of the data analysis procedures followed by the different authors especially regarding the criteria used to select the continuum. Towards the red this linear fit is fully consistent with the radio measurements, confirming that the emission lines are not significantly affected by microlensing.

In Figure 15 we also present an extinction curve fit to the emission line magnitude differences (both from the literature and from our own measurements). The best-fit parameters (obtained fixing the dust redshift to the lens redshift) were: and () The data are also compatible with an extinction curve similar to the Milky Way (, ). It is remarkable that the fitting to the narrow emission lines is in agreement with other data obtained from the continuum (Falco et al., 1999). However our results are not in agreement with the values and found by Goicoechea et al. (2005b).

The continuum data also show a decreasing trend towards the blue with a slightly steeper slope ( for CASTLES and for HST/STIS). In fact, the same extinction curve fitted to the emission line data with a shift of fits well the continuum flux ratios from CASTLES and HST/STIS (notice that these continuum flux ratios obtained from HST data are not affected by lens galaxy contamination). This global shift between the continuum and the baseline of no microlensing magnification defined by the emission lines imply that the continuum is experimenting microlensing of and allows us to re-examine the microlensing history in Q0957+561 based in this result. The differential magnitude lightcurve of Q0957+561 (Pelt et al., 1998; Oscoz et al., 2002) can be described as an event of 0.25 mag taking place from 1981 to 1986 and a quiet phase of mean value  mag with fluctuations of less than 0.05 mag from 1987 to 1999 (Oscoz et al. 2002). Previous attempts to model the observed microlensing through simulations have not used the emission line flux ratios as microlensing zeropoint. These studies have either accepted any zeropoint for microlensing magnification, modeling microlensing variability of less than 0.05 mag with respect to an unrestricted zeropoint value (e.g. Refsdal et al., 2000), or implicitly supposed that the zeropoint was placed at the mean value of the quiet phase ( mag) modeling a microlensing amplitude of less than 0.05 mag (e.g. Wambsganss et al., 2000). However, considering the zeropoint defined by the emission line flux ratios the correct procedure will be to model fluctuations of 0.05 mag with respect to a mean microlensing amplitude of .

Although detailed microlensing simulations should be made to estimate physical parameters from the source and/or the microlenses, it seems that under this new perspective the likelihood of smaller sources (or bigger microdeflectors) will increase.

On the other hand, there is an offset of mag between the magnitude differences in the continuum obtained with the MMT and those obtained with HST/STIS (data obtained at different epochs to correct for time delay). This difference between MMT and HST/STIS data might be explained by (i) intrinsic variability (ii) a microlensing amplitude change, and (iii) continuum contamination by the lens galaxy. We plan to examine available photometric monitoring of Q0957+561 covering 2008 (phased by the lag associated with component ) to ascertain the origin of this offset.

If we compare the slopes of the linear fits corresponding to emission lines and continua (CASTLES plus HST/STIS data) we found that the offsets at MgII and at OVI wavelengths have a difference of  mag, these may be due to a wavelength dependence of microlensing (chromatic microlensing). This estimate is, however, greatly affected by the uncertainties in the determination of the emission line flux ratios.

In summary, for Q0957+561 our results indicate that: (i) there is no significant variation in the broad component of the emission line profiles, (ii) there is dust extinction affecting the emission lines and the continuum produced by dust likely at the same redshift as the lens galaxy and (iii) there is microlensing with amplitude affecting the continuum.

### 4.5 Hs0818+1227

HS0818+1227 was discovered by Hagen & Reimers (2000); it consists of two lensed images , separated by , with and . Image in this case is mag fainter than . We scaled the continuum-subtracted spectrum to match the emission line peaks in A (Figure 16). The and emission line profiles are very similar to each other and do not show significant differences in the BLR.

Figure 17 shows the magnitude differences we calculated from the continuum (solid black squares) and from the cores of the emission-lines (solid black triangles) integrating our MMT spectra. The magnitude differences corresponding to the narrow emission lines (Table 10) will define a zero microlensing baseline of  mag. The average of CASTLES broadband data ( mag) shows an offset of 0.22 mag with respect to this baseline. Note, however that the significance of this offset is dominated by the F555W data taken by CASTLES. According to section 3.5, part of this offset (0.1 mag) may arise from intrinsic variability.

Our continuum data agree with Hagen & Reimers (2000), but do not match CASTLES (Table 2), especially in the reddest part. This discrepancy is due to the lens galaxy continuum. We estimate, using the integrated broad-band magnitudes obtained by CASTLES for the lens galaxy, that the contamination is % of the lens galaxy flux.

Considering the emission lines, our results indicate negligible dust extinction and posible evidence of microlensing.

## 5 Conclusions

The method we use in this paper allows us to separate microlensing from dust extinction without a theoretical model for the lens system. We have demonstrated the method for the most complicated cases: doubly-imaged quasars.

We tested the hypothesis that the cores of the emission lines do not vary with time by comparing our own magnitude differences in the emission lines with values from the literature that were obtained at different epochs, including values corrected for measured time-delays, and we conclude that they are nearly constant in time. Thus, except in cases where extinction is significant, the magnitude differences in the emission line cores are reliable estimators of the intrinsic magnitude differences unaffected by microlensing.

Following Yonehara, Hirashita & Richter (2008) we have estimated the impact of time delays in our microlensing measurements for our objects. In the worst case scenario (Q0957+561, SDSS1004+4142, and SDSS1029+2623) a time delay can introduce variabilities mag and chromaticities mag. The measurements we obtain for those objects are at least twice the estimated values. Although more data are needed for confirmation, it appears that time-delay induced variability has a modest impact.

Differences in the wings of the CIV and SiIV broad emission line profiles are found in and images of SDSS1004+4112, as detected previously by Richards et al. (2004), but the enhancement in the blue wing is smaller than observed in 2004. In HE1104-1805 we also have detected a slight enhancement in the red wings of CIV and SiIV in image with respect to image .

The average microlensing magnification free from extinction was obtained as the difference in magnitudes between the emission lines and the continuum. The latter was obtained directly from the spectra in those cases where there is no contamination by the lens galaxy (all systems except HS0818+1227 and Q0957+561), otherwise we used HST continuum data free from lens galaxy contamination available in the literature. Significant chromatic microlensing was detected in SDSS1004+4112, SDSS1029+2623, and HE1104-1805.

Below is a summary of the results for each system:

1. We detected a blue wing enhancement in the high ionization lines of SDSS1004+4112 that are qualitatively similar to the effect described by previous authors but of smaller amplitude. We have also detected strong chromatic variability in the continuum. The presence of variability in both lines and continuum supports the hypothesis of microlensing to explain the blue wing enhancements in the lines. Our data indicate negligible dust extinction. We infer an accretion disk size of at Å and a wavelength dependence of the size with exponent .

2. In HE1104-1805 we find no extinction but we detected chromatic microlensing with large variations between two epochs that change the sign of the continuum slope. We estimate at Å and . This size is greater than those inferred from the thin disk theory and either the intrinsic flux or the central black hole mass by Poindexter et al. (2008). However, our results agree with recent values presented in Muñoz et al. (2011) and The value of we obtain is significantly smaller than the 4/3 value predicted by the standard model. Similar discrepancies have been found in other objects (Poindexter et al., 2008; Floyd et al., 2009; Morgan et al., 2010; Blackburne et al., 2011; Mediavilla et al., 2011; Muñoz et al., 2011).

3. SDSS1029+2623 is affected by strong chromaticity of about 0.4 mag that can be explained neither by dust extinction nor by intrinsic variability. Chromatic microlensing is the most probable explanation although not all the available data fit well within this hypothesis.

4. A Cardelli, Clayton, & Mathis (1989) extinction law with and () can be used to fit, within uncertainties, both the continuum and the emission line flux ratios in Q0957+561. There is a global offset between the continuum and emission line magnitude differences that implies a microlensing amplitude of  mag. There are marginal indications of chromatic microlensing.

5. We detect evidence of microlensing but not extinction (within uncertainties) in HS0818+1227.

We thank the anonymous referee for thoughtful suggestions. We thank G.T. Richards for kindly providing us the Keck spectra of SDSS1004+4112, and N. Inada for kindly confirming us the infrared measurements for SDSS1029+2623. V.M. gratefully acknowledges support from FONDECYT through grants 1090673 and 1120741. E.M. and J.A.M are supported by the Spanish Ministerio de Educación y Ciencias through the grants AYA2007-67342-C03-01/03 and AYA2010-21741-C03/02. J.A.M. is also supported by the Generalitat Valenciana with the grant PROMETEO/2009/64. This research has made use of NASA’s Astrophysics Data System. Facilities: MMT (Blue-Channel), HST (STIS), VLT (FORS2).

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