Black Hole masses for 14 gravitational lensed quasars

—-ABSTRACT Aims. We estimate black hole masses (M BH ) for 14 gravitationally lensed quasars using the Balmer lines along with estimates based on MgII and CIV emission lines for four and two of them, respectively. We compare with results obtained for other lensed quasars. Methods. We use spectroscopic data from the Large Binocular Telescope (LBT), Magellan and the Very Large Telescope (VLT) to measure the FWHM of the broad emission lines. Combined with the bolometric luminosity measured from the spectra energy distribution, we estimate M BH including uncertainties from microlensing and variability. Results. We obtain M BH using the single-epoch method from the H α and / or H β broad emission lines for 14 lensed quasars, including the first estimates for QJ0158 − 4325, HE0512 − 3329 and WFI2026 − 4536. The masses are typical of non-lensed quasars of similar luminosity, and the implied Eddington ratios are typical. We have increased the sample of lenses with estimates of M BH by 60%.


Introduction
Supermassive black holes (SMBHs) are thought to be a key ingredient in galaxy formation and evolution, particularly since the discovery that the central SMBH mass (M BH ) has a tight correlation with the stellar luminosity and velocity dispersion (Kormendy & Richstone 1995;Ferrarese & Merritt 2000;Tremaine et al. 2002;Marconi & Hunt 2003;Kormendy & Ho 2013;Zubovas & King 2019) of the spheroidal components of their host galaxies.To understand this link, we need to study the evolution of the SMBH, their hosts and their environments, particularly during the phases with significant accretion rates when the active galactic nucleus (AGN) is releasing large amounts of energy (see, e.g., Di Matteo et al. 2005;Croton et al. 2006;Hopkins et al. 2008).Reliably measuring M BH is fundamental to understanding this connection.In the unified model of AGN (Antonucci 1993;Urry & Padovani 1995), the accretion disk continuum emission illuminates nearby gas to produce the broad emission lines (BELs) in the spectra.Continuum variability drives a delayed change in the BEL fluxes and line profiles.Reverberation mapping (RM, Peterson 1993;Netzer & Peterson 1997 and therein) measures this delay to determine the size of the BEL region (Wandel et al. 1999;Kaspi et al. 2000;Peterson et al. 2004;Bentz et al. 2009), which can then be used to estimate M BH given the line widths and local calibrations.Even locally, RM is challenging because it requires repeated spectroscopic observations over months (Peterson et al. 2004;Bentz et al. 2009;Barth et al. 2015;Grier et al. 2017Grier et al. , 2019;;Du et al. 2016;Lira et al. 2018), and the required monitoring periods increase for more luminous quasars or, due to time dilation, higher redshift quasars (Lira et al. 2018).Initially, RM studies were largely limited to individual studies of local, lower luminosity quasars, but the samples have recently expanded to higher luminosities and redshifts by using multi-fiber spectrographs to monitor hundreds of AGN simultaneously (Malik et al. 2023;Shen et al. 2023;Yu et al. 2023).Nonetheless, current RM samples have only ∼ 10 2 AGN, and it will be a long process to reach ∼ 10 3 AGN.Fortunately, RM revealed a correlation between the BLR distance from the BH and the optical continuum luminosity, known as the size-luminosity (R-L) relation (Kaspi et al. 2005;Bentz et al. 2006;Zu et al. 2011).This relationship combined with the virial theorem allows us to estimate M BH using a single spectrum, a procedure known as the single-epoch (SE) method (e.g.McLure & Dunlop 2004;Vestergaard & Peterson 2006;Shen et al. 2011;Shen & Liu 2012).The SE method was developed and calibrated using the Hβ width (e.g.Vestergaard 2004;Xiao et al. 2011;Shen & Liu 2012).For higher redshift systems (z > 0.9), Hβ is shifted into the Near Infrared (NIR), making it difficult to observe large samples from the ground due to the bright sky emission.One solution is to instead use the MgII or CIV lines (McLure & Jarvis 2002;Vestergaard 2002) to study z > 0.9 systems in the optical (e.g.McGill et al. 2008;Park et al. 2013Park et al. , 2015;;Coatman et al. 2017;Woo et al. 2018).However, this approach present several drawbacks: 1) these UV lines lack a local calibration because they cannot be observed from the ground, 2) their indirect calibrations are restricted to high-luminosity objects (Mejía-Restrepo et al. 2016), 3) MgII may have a small but significant dependence on the Eddington ratio of the AGN and might not be reliable in objects with FWHM(MgII)⩾ 6000 km/s (Marziani et al. 2013), and 4) there are concerns regarding CIV because its width could be affected by winds of ejected disk material (Assef et al. 2011;Coatman et al. 2016;Mejía-Restrepo et al. 2018) and microlensing in the case of lensed QSOs (Fian et al. 2018a).The CIV emission line is more asymmetric than the Balmer lines and MgII, and its width is not well correlated with those of Hβ and MgII (e.g., Baskin & Laor 2005;Shen et al. 2008), but early studies showed a strong correlation between the width of Hα, Hβ and MgII (see Greene & Ho 2005;Shen et al. 2008;Wang et al. 2009;Shen & Liu 2012).Hence, it is reasonable to argue that the virial mass estimator based on the Balmer lines is the most reliable one.The Hβ emission line is typically preferred (due to its wavelength and lack of blended emission lines), and Hα is also known to work well (Greene & Ho 2005;Netzer & Trakhtenbrot 2007;Xiao et al. 2011).Many studies have estimated M BH using the SE method for large samples of quasars (e.g.McLure & Jarvis 2002;McLure & Dunlop 2004;Vestergaard & Peterson 2006;Shen 2013;Peterson 2014;Mejía-Restrepo et al. 2016;Shen et al. 2019), and it has also been used to estimate M BH for samples of lensed AGNs.Gravitational lenses allow us to investigate the inner structure of lensed quasars (see, e.g., Kochanek 2004;Morgan et al. 2010).Peng et al. (2006) was the first to estimate the M BH of 31 gravitationally lensed AGNs.They applied the virial technique using the CIV (22 systems), MgII (19 systems) and Hβ (two systems) emission line widths and the continuum luminosities λL λ at 1300, 3000 and 5100 Å, respectively.Seven of the systems have estimates obtained from two different emission lines.Greene et al. (2010) obtained M BH for 11 systems using Hα and Hβ (nine have both).Their goal was to search for systematic biases in the Peng et al. (2006) M BH estimates due to the use of the CIV emission line.Even though the masses presented by Greene et al. (2010) are more robust (they used spectra with higher S/N), they conclude that there is no evidence for a systematic bias between the lines used by Peng et al. (2006) and the Balmer lines, despite the large scatter.Assef et al. 2011 searched for possible biases between M BH estimates based on the Hα, Hβ and CIV broad emission lines, improving the sample with new observations and adding missing luminosity estimates at λ = 5100 Å .They selected 12 lensed quasars from the CfA-Arizona Space TElescope LEns Survey (CASTLES 1 , Falco et al. 2001) with high quality CIV spectra and published NIR spectra of the Balmer lines.The FWHM were obtained using broad and narrow Gaussian components and the continuum luminosity at 5100 Å was estimated using the AGN spectral energy distribution (SED) template of Assef et al. (2010).They conclude that the M BH inferred from CIV using the line dispersion (σ l ) shows a systematic offset with 1 https://lweb.cfa.harvard.edu/castles/respect to the estimate using the FWHM.However, Assef et al. (2011) compared the M BH estimated using CIV and the Balmer lines and found no significant offset.Sluse et al. (2012), in a study of microlensing in a sample of 17 lensed quasars, obtained M BH using the CIV (5 systems), MgII (12 systems) and Hβ emission lines (2 systems), where two objects have estimates from two different emission lines and four had published values from Peng et al. (2006) and Assef et al. (2011).
There have been no new M BH estimates for lensed quasars in the last decade.In general, recent publications refer to the M BH mentioned above (e.g.Ding et al. 2017b;Guerras et al. 2020;Ding et al. 2021;Hutsemékers & Sluse 2021), and only 14 of the 2222 known lensed quasars have M BH measurements based on the Hα and/or Hβ lines.In this work, we increase the sample of Balmer lines M BH estimates for lensed AGNs from 14 to 23 sources.Even though the majority of the objects in our sample (with the exception of WFI2026−4536 and HE0512−3329) have BH mass estimates (Peng et al. 2006;Assef et al. 2011;Sluse et al. 2012;Ding et al. 2017b), only two of them (SDSS1138+0314 and HE1104−1805) were obtained using Hα or Hβ.Most are based on the CIV and/or MgII broad emission lines.We also include three quasars with no previous M BH estimates.
This paper is structured as follows.In Sect. 2 we present the systems and data reduction for the three different instruments used in this work (VLT/X-shooter, LBT/LUCI and Magellan/MMIRS).Section 3 describes the method for obtaining M BH and the factors that could contribute to its uncertainties.Our results are presented in section 4, analyzing the systems and comparing with the large samples of non-lensed AGNs.Finally, our conclusions are presented in section 5. Throughout the text we assume a ΛCDM cosmology with Ω Λ = 0.7, Ω M = 0.3 and H O = 70 kms −1 Mpc −1 .

Observations and Data Reduction
We present observations for three systems with the X-shooter instrument (Vernet et al. 2011) and one observation with the FOcal Reducer/low dispersion Spectrograph 2 (FORS2, Rupprecht & Böhnhardt 2000) at the Very Large Telescope (VLT).In addition, we include 21 spectroscopic observations taken in 2012 for 14 lensed quasars with the Large Binocular Telescope (LBT) and the LUCI spectograph (Seifert et al. 2003) or the Magellan telescope and the MMT and Magellan Infrared Spectrograph (MMIRS;McLeod et al. 2012).Table 1 summarizes the main observational characteristics for the observing runs, the image(s) observed for each lensed quasar and the orientation of the slit.Data reduction for each instrument is described below.

X-shooter
LBQS1333+0113, QJ0158−4325 and Q1355−2257 were observed with X-shooter between August of 2019 and April of 2021 (ESO proposal ID 103.B − 0566(A); PI: A. Melo).We used two Observing Blocks (OBs) for each system with a slit width of 1 ′′ .0 × 11 ′′ for the UVB band (resolution of R = 5400) and 1 ′′ . 2 × 11 ′′ for VIS and NIR arm (R = 6500 and 4300 respectively).In the first OB, four exposures were taken in the NIR arm (600s each) and two exposures in the VIS and UVB arm (600s each), with a nodding of 3 ′′ per frame and a readout mode (UVB and VIS) of 100k/1pt/hg.The second OB had the same configuration as the first one, but the NIR data was taken with two exposures instead of four.The slit was centered on the brightest image of the lensed quasar and the position angle was chosen to include the second brightest image.We used the atmospheric dispersion corrector (ADC) to correct for differential atmospheric refraction.SDSS1226−0006 was observed in 2013, with slit width of 1 ′′ .6 × 11 ′′ for the UVB band, 1 ′′ .5 × 11 ′′ for VIS and 0 ′′ .9 × 11 ′′ NIR arm.The data were reduced using the ESO pipeline EsoReflex (Freudling et al. 2013) along with Principal Component Analysis (PCA; Deeming 1964;Bujarrabal et al. 1981;Francis & Wills 1999) for the sky emission subtraction.We briefly summarize the steps here (more details can be found in Melo et al. 2021).First, X-shooter pipeline version 3.5.0 of EsoReflex was used to reduce each individual OB (flat field, dark current, wavelength calibration, among others) without correction for nodding and without subtracting the sky background.We used PCA for the sky emission correction in the NIR on each individual frame.First, we masked outliers (such as bad pixels) using σ−clipping and replace them with a value from a bicubic interpolation of the surrounding pixels.We calculated a sky median as a function of wavelength, subtract it from each frame and collapse the two dimensional (2D) spectra along the wavelength axis to select an uncontaminated spatial region for the sky emission.We chose the PCA-basis as the region of threshold equal to 3 of the median above the background (see Fig. 2 of Melo et al. 2021).Finally, we constructed a model of the sky emission in the selected spatial region as our PCA eigenvector basis and subtracted it from the frame.
Flux calibration is done by using equation 3 of the X-shooter Pipeline User Manual 3 with the response curve from the Xshooter pipeline based on a standard star observed the same night as the target.
3 https://ftp.eso.org/pub/dfs/pipelines/instruments/xshooter/xshoo-pipeline-manual-3.5.3.pdf We used molecfit (Smette et al. 2015;Kausch et al. 2015) for the telluric correction of each spectrum and employed the best fit to each spectrum row by row.Finally, the spectra were median combined using the parameters from the header for the stacking.The uncertainties were estimated as the median absolute deviation.
For the VIS and UVB reduction, we used a median of each sky region as the model of the sky brightness, but otherwise followed the same steps used for the NIR.
Data reduction was performed using IRAF packages along with IDL task xtellcor_general from Vacca et al. (2003) for the telluric absorption correction.The detailed reduction is described in Assef et al. 2011, but we present a summary of the steps here.For each exposure, a two-dimensional wavelength calibration was performed using the sky emission lines, and a combined median sky frame was built.This sky frame was used to remove the sky before extracting the spectra.The telluric absorption correction was made using xtellcor_general.

MMIRS
Seven lensed systems were observed using MMIRS on 2012 April 6 and 7 using the long-slit data spanning H/K bands (1.25-2.4µm).Two images of the lensed quasar were positioned in a Article number, page 3 of 15 slit of 0 ′′ .8 wide with a pixel scale of 0 ′′ .20124 .The spectra were taken with nodding to control for the sky background.
Data reductions were carried out with the instrument pipeline (Chilingarian et al. 2015) and IRAF5 tasks.The code mmfixall, provided by the MMIRS instrument scientific team, was used to collapse the information contained in the multi-extension files.The remaining procedures were performed in IRAF and consisted of dark correction, sky subtraction, 1D spectra extraction, wavelength calibration and telluric correction.The 1D spectra was extracted using the apall task with apertures of ± 3 − 4 pixels.Flux calibration was carried out using xtellcor_general for telluric absorption corrections.

FORS2
Only SDSS1226−0006 was observed using FORS2 on February of 2010.Data reduction was performed using IRAF and standard procedure consisting of bias subtraction and flat fielding, including the rejection of cosmic rays.The spectra were extracted using the apall task, setting two apertures and fixing the centroid of each quasar spectra.

Method
As discussed earlier, the SE method combines the BLR line width and size determined from the luminosity to estimate where R BLR is the distance from the SMBH to the BLR, ∆v is the virial velocity of the BLR, G is the gravitational constant and f is the virial factor that depends on the unkown kinematics, structure, inclination and distribution of the BLR (Peterson et al. 2004 and references therein).Since the emission lines may originate under different conditions, the f parameter may differ between them (Shen 2013), which in turn gives rise to one of the main uncertainties in measuring M BH .The virial factor has been estimated (e.g, Collin et al. 2006;Woo et al. 2015;Mediavilla et al. 2020) from different emission lines.In this paper we assume f = 1 following the observational constraint given by Woo et al. (2015), which is in agreement with the nonweighted average ⟨ f ⟩ = 0.99 ± 0.08 given by Mediavilla & Jiménez-Vicente (2021).Thanks to the known correlation between the luminosity of the AGN and the size of the BEL (e.g.Kaspi et al. 2000Kaspi et al. , 2005;;Bentz et 1 for the LUCIFER and MMIRS data, and in ?? for QJ0158−4325, LBQS1333−0113, Q1355−2257 and SDSS1226−0006, respectively.In the cases using two broad emission lines, the FWHM was calculated from the combined profile after removing the NLR components.We carried out a Monte Carlo simulation consisting of 1000 simulated spectra randomnly adding the estimated spectral noise to obtain a 95% confidence uncertainty estimate.

Luminosity measurements
We follow Assef et al. (2011) and estimate the monochromatic luminosity of each quasar using the broad band spectral energy distribution (SED) of the brightest image (A) using the fluxes from CASTLES and other sources in the literature (see Table 3).This method was preferred over using the continuum obtained from the spectra due to several factors affecting the LUCIFER and MMIRS data (e.g.low S/N (3-18), unresolved images in the slit, seeing conditions varying between the target and the standard star) and because of the chromatic microlensing detected in the continuum of the four systems observed with X-shooter and FORS2 (Melo et al. in prep.).To demagnify the fluxes, we use the magnification estimated from a lens model (Table 2).We chose photometric data that were obtained close in time to our observations to minimize differences in the amount of microlensing or a large intrinsic variation that coupled with the time delay could mimic chromatic microlensing.If light curves were available, we included the variability amplitude as part of the flux uncertainties.For instance, Giannini et al. (2017) demonstrated that HE0047−1756 varied by ∼0.2-0.3 over a five-year period, and WFI2033−4723 varies by 0.5 mag in four years.The system HE0435−1223 varied ∼0.4 mag (Ricci et al. 2011) and more recently, Bonvin et al. (2017) presented 13-year light curves, with a variability ambplitude of ∼ 0.7 mag.

Uncertainties
We need to consider multiple factors that could contribute to the uncertainties in M BH .For example, the BEL of one of the images could be microlensed (e.  that even if we have a FWHM difference between the images of > 5 sigma, the impact on M BH is negligible compared with other sources of errors (see below for an specific example).
Another contribution to the uncertainties is the blending of the images in some of the MMIRS spectra.To see how much this could affect the M BH , we compare the FWHM we find from fitting the blended image A+B spectrum of LBQS1333+0113 as compared to the separate spectra of the two images (see Fig. 6).For Hα the FWHM of the combined spectrum is 4746.39 ± 109.89 km/s compared to 4608.55 ± 69.73 km/s for image A and 4754.73 ± 23.66 km/s for image B. These differences translate in estimated masses of log 10 ( M BH /M ⊙ ) = 9.16 ± 0.59, 9.13 ± 0.54, and 9.16 ± 0.48 which are much smaller than the other sources of error and thus unimportant for the BH mass estimate.A similar result is obtained for the MgII line.Another factor contributing to the error is the monochromatic luminosity uncertainty.This has several systematic uncertainties: the systematic errors of the instrument, the magnification of the image given by the lens model, the flux calibration and intrinsic variability.To account for the intrinsic AGN variability, we add the observed variability as a contribution to the error in the monochromatic luminosity (section 3.2).Although the uncertainties in the luminosity are large, the M BH estimate scales as L 1/2 , making it less sensitive to these errors compared to the FWHM because the M BH ∝ FWHM 2 is so much stronger.

Results
Using the FWHM from the models of the emission lines and the monochromatic luminosity obtained from the SEDs, we measure M BH following equation 2. The results are shown in Table 4 along with their respective errors.Two systems have previous Hα log 10 (M BH /M ⊙ ) (Assef et al. 2011): HE1104−1805 (9.05 ± 0.23) and SDSS1138+0314 (8.22 ± 0.22), respectively.Our estimate for HE1104−1805 is in agreement given its error (8.87 ± 0.70) The systems in which the M BH differ for both lines (FBQ0951+2635,B1422+231 and Q2237+030) were obtained by different authors using different methods (Assef et al. 2011;Sluse et al. 2012) and different epochs.
The left panel of Figure 8 shows the distribution in M BH and L bol for our systems along with estimates from the literature for 34 lensed quasars (Peng et al. 2006;Greene et al. 2010;Assef et al. 2011;Sluse et al. 2012;Melo et al. 2021).the same range of masses as the lensed and non-lensed AGNs (Figure 8).In particular, we were able to obtain estimates for the lower luminosity systems QJ0158−4325, SDSS0924+0219, HE0512−3329 and HE0047−1756 (from 10 44 to 10 46.5 ).The systems QJ0158−4325 and SDSS0924+0219 have the lowest luminosities (log 10 ( L re f ) < 44.60 L ⊙ ), and the latter has the lowest M BH , log 10 ( M BH /M ⊙ ) = 7.43 ± 0.05 (this is the average of the Hα and Hβ estimates).We separately examine the three systems observed with X- We can also estimate the unlensed size of the quasar accretion disk, r s (equation 3 of Mosquera & Kochanek 2011) using our M BH estimates and assuming a thin disk model (Shakura & Sunyaev 1973).The details of the parameters used are in Melo et al. (2021) and the size estimates are shown in table 4. SDSS0924+0219 has the smallest accretion disk size (mean value between Hα and Hβ emission line of r s = 10 14.78±2.62cm, an error in dex of 5.99.These spectra had very low signal-tonoise (∼5.9 and ∼3.9 in Hα and Hβ lines, respectively).The mean value for the systems QJ0158−4325, SDSS1226−0006, LBQS1333+0113 and Q1355−2257 (all emission lines from both images excluding CIV are 10 15.28±1.28cm, 10 15.39±0.89cm and 10 15.84±1.13cm, respectively.

Conclusions
We estimated M BH using the broad Balmer emission lines of 14 lensed quasars measured using four different spectographs (LUCI, MMIRS, X-shooter and FORS2).After reducing and extracting the spectra corresponding to each image, the FWHM of the broad emission lines were estimated with the standard deviation of the model line profile after subtracting the narrow line components.The monochromatic luminosities were estimated using the de-magnified SED of the brightest image, taking into account the variability (if any) in the uncertainty budget.Three systems observed with X-shooter (QJ0158−4325, LBQS13333+0113, and Q1355−2257) were analyzed in detail because they have multiple M BH estimates using different emission lines.A decade after the initial black hole mass measurements for gravitational lens systems (Peng et al. 2006;Greene et al. 2010;Assef et al. 2011;Sluse et al. 2012), this work ex-pands the sample from 14 to 23 mass estimates.The M BH measurements of lensed quasars based on the Balmer lines show a lower dispersion (RMS ∼ 0.45 dex) in M BH at fixed bolometric luminosity, which is also true of non-lensed quasars (Shen et al. 2019).Including the MgII estimates increases the dispersion (RMS ∼ 0.65 dex), confirming that the Balmer lines are more reliable.An even larger dispersion is observed too when including the MgII lens M BH estimates from the literature.The recent discovery of new gravitational lens systems (Lemon et al. 2023)

Fig. 1 :Fig. 1 :
Fig. 1: Gaussian fits to the Hα and Hβ lines of the lensed systems.The red line is the best fit, the black lines are the different components of each region (emission and absorption), the green line is the Fe template and the blue line is the continuum fit.The 1-sigma errors are shown by the blue regions and the model residuals are shown below each spectrum.Article number, page 5 of 15

Fig. 2 :Fig. 3 :
Fig. 2: Gaussian fits to the A and B image broad emission lines of QJ0158-4325.The red line is the best fit, the black lines are the different components of each region (emission and absorption), the green line is the Fe template and the blue line is the continuum fit.The 1-sigma errors are shown by the blue regions and the model residuals are shown below each spectrum.Article number, page 8 of 15

Fig. 4 :Fig. 5 :Fig. 6 :Fig. 7 :
Fig. 4: Gaussian fits to the A and B image broad emission lines of Q1355-2257.The red line is the best fit, the black lines are the different components of each region (emission and absorption), the green line is the Fe template and the blue line is the continuum fit.The 1-sigma errors are shown by the blue regions and the model residuals are shown below each spectrum.Article number, page 10 of 15 These are the first M BH estimates for the systems QJ0158−4325, HE0512−3329 and WFI2026−4536.We also calculated M BH using the MgII emission line for the systems QJ0158−4325, SDSS1226−0006, LBQS13333+0113 and Q1355−2257.We compared the new M BH Balmer line to previous MgII M BH estimates for HE0047−1756, HE0435−1223, SDSS0924+0219, SDSS1226−0006, LBQS1333+0113, Q1355−2257 and WFI2033−4723.The mass estimates are well correlated, with the exception of three lensed quasars (FBQ0951+2635, B1422+231 and Q2237+030) where the Balmer masses were not derived here.The new Balmer M BH span the same range of masses estimates as non-lensed quasars with the systems QJ0158−4325, SDSS0924+0219, HE0512−3329, and HE0047−1756 being the lowest luminosities.The masses of the lensed quasars imply low Eddington ratios (∼0.1), in agreement with the results of Shen et al. (2019) from single-epoch black hole masses of SDSS quasars.

Table 1
Mejía-Restrepo et al. (2016)are the calibrated parameters fromMejía-Restrepo et al. (2018)for the Hα, Hβ, MgII and CIV lines, respectively, and the luminosities are those at 5100Å (L 5100 ) for Hα and Hβ, 3000Å (L 3000 ) for MgII, and 1450Å (L 1450 ) for CIV.We modeled the emission line profiles after removing the continuum and an iron line template, followingMejía-Restrepo et al. (2016).We use a maximum of two Gaussian broad components and a single narrow line component for each emission line.In addition to the narrow and broad components of the principal emission lines (Hα, Hβ, CIV and MgII), we added four extra components in the Hα profile for the [N II] and [S II] narrow-line doublets, two for the [O III] NLR doublet in the Hβ profile plus one to the He II broad emission line.We masked regions with telluric absorption problems, bad seeing and poor S/N that could affect our fit.The best final fit is shown as a red line in Figure al. 2009), and assuming viral equilibrium, we estimate the mass as log(M BH /M ⊙ ) = log(K) + α log

Table 2 :
Magnification values used for demagnifying the flux and their references.

Table 4 :
Hα and Hβ Mass estimates of the observed images.