Virial Black Hole Masses for Active Galactic Nuclei behind the Magellanic Clouds

We use the spectroscopic data collected by the Magellanic Quasars Survey (MQS) and the photometric V- and I-band data from the Optical Gravitational Lensing Experiment (OGLE) to measure the physical parameters for active galactic nuclei (AGNs) located behind the Magellanic Clouds. The flux-uncalibrated MQS spectra were obtained with the 4 m Anglo-Australian Telescope and the AAOmega spectroscope (R = 1300) in a typical ∼1.5 hr visit. They span a spectral range of 3700–8500 Å and have signal-to-noise ratios in a range of 3–300. We report the discovery and observational properties of 161 AGNs in this footprint, which expands the total number of spectroscopically confirmed AGNs by MQS to 919. After the conversion of the OGLE mean magnitudes to the monochromatic luminosities at 5100, 3000, and 1350 Å, we were able to reliably measure the black hole masses for 165 out of 919 AGNs. The remaining physical parameters we provide are the bolometric luminosities and the Eddington ratios. A fraction of these AGNs have been observed by the OGLE survey since 1997 (all of them since 2001), enabling studies of correlations between the variability and physical parameters of these AGNs.


Introduction
The black hole (BH) mass, M BH , in active galactic nuclei (AGNs) is the single most important physical parameter determining most of their properties.It influences the sizes of accretion disks, their innermost stable orbits, temperature profiles, or the spectral energy distribution shapes and luminosities.That is why the BH mass is the primary parameter sought in AGNs.
Early reverberation mapping campaigns have enabled the first measurements of the BH masses (e.g., Netzer & Peterson 1997;Gebhardt et al. 2000;Kaspi et al. 2000).These campaigns determined simultaneously the distance R to the broad-line region (BLR) clouds, the time delay τ between the continuum variability and the responding emission lines (R = cτ), and the velocity v of the BLR clouds.In principle, these two parameters are sufficient to determine the mass, as M BH ∝ Rv 2 .Kaspi et al. (2000) realized that the BLR radius R is tightly correlated with the continuum luminosity L, as R ∝ L 0.7 , which is known as the radius-luminosity relation for AGNs.The relation was soon improved to yield R ∝ L 0.5 (Bentz et al. 2006(Bentz et al. , 2009(Bentz et al. , 2013)).Combining the radiusluminosity relation with the equation for the BH mass, we end up with a simple prescription for the measurement of the BH mass, as M BH ∝ L 0.5 v 2 .Since both the luminosity L and the velocity v can be simultaneously measured from a single AGN spectrum, it is straightforward nowadays to determine AGN BH masses for massive spectroscopic surveys with hundreds of thousands of AGN spectra (Shen et al. 2011;Rakshit et al. 2020;Wu & Shen 2022), albeit with the typical uncertainty of 0.4 dex.
In this paper, we measure the physical parameters (virial BH masses, luminosities) for AGNs discovered behind the Magellanic Clouds by the Magellanic Quasars Survey (MQS; Kozłowski et al. 2011Kozłowski et al. , 2012Kozłowski et al. , 2013)).These two nearby galaxies have been the primary target for microlensing and variability surveys since the early 1990s, so 100 million sources, which can be resolved from Earth, now have two-to-three-decadelong photometric light curves.A combination of the photometric variability and physical parameters for AGNs is a way to improve our understanding of these objects (e.g., Kelly et al. 2009;Kozłowski 2016;Simm et al. 2016;Burke et al. 2021;Suberlak et al. 2021).
In Section 2, we present both photometric and spectroscopic data used in our analyses.In Section 3, we elaborate on the methods used to calculate both monochromatic and bolometric luminosities, the methodology of fitting the AGN spectra, and the measurement of basic spectroscopic parameters, in particular the FWHM of broad emission lines.This section concludes with the methodology and calculation of the BH masses for our AGNs, along with the corresponding Eddington ratios.The results are presented in Section 4 and discussed in Section 5.The paper is summarized in Section 6.

Data
In this paper, we analyze spectra for AGNs discovered behind the Magellanic Clouds and obtained by MQS Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.(Kozłowski et al. 2011(Kozłowski et al. , 2012(Kozłowski et al. , 2013)).The ∼4000 spectroscopically observed AGN candidates were selected based on their mid-IR and optical colors, optical variability in the OGLE-III survey, and the X-ray flux.They were observed with the 4 m Anglo-Australian Telescope (AAT) equipped with the AAOmega spectroscope, producing a resolution of R ≈ 1300 inside a spectral range of 3700-8800 Å in the 580V (blue channel) and 385R (red channel) gratings.Most observations were 1.5 hr long (3 × 30 minutes), producing a signal-to-noise ratio (S/N) of 3-300 with a median of about 40 for I < 19.5 mag sources (Kozłowski et al. 2011).The spectra were reduced with the AAOmega 2DFDR routines (Taylor et al. 1996).Kozłowski et al. (2013) reported the discovery of 758 AGNs.
We have reinspected all the MQS spectra in this analysis and identified 161 additional AGNs, albeit faint (Table A1).This makes the sample of analyzed spectra contain a total of 919 AGNs.
We also use the V-and I-band light curves from the Optical Gravitational Lensing Experiment (OGLE; Udalski et al. 1997Udalski et al. , 2008Udalski et al. , 2015) ) to calculate both the monochromatic and bolometric AGN luminosities.The data have been collected since 1997 with the 1.3 m Warsaw Telescope located in Las Campanas Observatory, Chile.
A detailed methodology for analyzing both spectra and photometric data is presented in the next section.

Methods
In this section, we provide details of the AGN monochromatic and bolometric luminosity calculation from the OGLE photometry, spectral fitting, and estimation of the BH masses and Eddington luminosities.

Estimating the AGN Monochromatic Luminosities from Photometry
The primary objective of MQS was to find and confirm as many AGNs behind the Magellanic Clouds as possible, to measure proper motions of the Magellanic Clouds (e.g., Zivick et al. 2018), and to enable future AGN variability studies.
The spectroscopic AAT observations were taken in suboptimal weather conditions and without the flux calibration procedure (unnecessary for finding redshifts).Therefore, we are unable to measure the monochromatic (and so bolometric) fluxes directly from these spectra.Kozłowski (2015), however, provides a method to estimate the monochromatic fluxes from broadband optical and IR photometry with a typical 0.1 dex uncertainty in a redshift range of 0.1 < z < 4.9.Because most AGNs are variable sources, to estimate the weighted mean photometric magnitudes (obtained in the flux space), we use the long-term OGLE data in the V-and I-band filters, spanning up to 26 yr.We then correct the mean observed magnitudes for the extinction using the reddening maps of the LMC and SMC from red clump stars (Skowron et al. 2021) Skowron et al. (2021) maps provide the median reddening to the red clump stars, which can be interpreted as the extinction to the center of their distribution in the LMC/SMC, we double the extinction correction to mimic the lines of sight extending all the way though these galaxies.We also calculate the k-corrections by using the composite Sloan Digital Sky Survey (SDSS) AGN spectrum (Vanden Berk et al. 2001) and OGLE V and I filters (Udalski et al. 2015).Finally, we calculate the absolute V and I magnitudes for each AGN assuming a standard ΛCDM cosmological model with (Ω Λ , Ω M , Ω k ) = (0.72, 0.28, 0.0) and H 0 = 70 km s −1 Mpc −1 to calculate the distance modulus (DM).They are provided in Table A2.
We then follow the prescription of Kozłowski (2015) to calculate L 5100 , L 3000 , and L 1350 monochromatic fluxes (twice: one from the V-band mean magnitude and one from the I-band mean magnitude).For each monochromatic flux, we calculate the mean from V and I, and the final fluxes are provided in Table A2.

Spectral Fitting with PYQSOFIT
We use PYQSOFIT for spectral decomposition (Guo et al. 2018) of all of our MQS AGN spectra.We correct the spectra to the rest frame and correct for Galactic extinction using the extinction curve of Cardelli et al. (1989) and the reddening map of Skowron et al. (2021).We then perform a host galaxy decomposition using galaxy eigenspectra from Yip et al. (2004a), as well as quasar eigenspectra from Yip et al. (2004b) implemented in the PYQSOFIT code.If more than half of the pixels from the resulting host galaxy fit are negative, then the host galaxy and quasar eigenspectra fit are not applied.
We then fit the power-law, UV/optical Fe II, and Balmer continuum models utilizing the continuum fitting windows as described in Guo et al. (2018) and Rakshit et al. (2020).The optical Fe II emission template spans 3686-7484 Å, from Boroson & Green (1992), while the UV Fe II template spans 1000-3500 Å, adopted from Vestergaard & Wilkes (2001), Tsuzuki et al. (2006), andSalviander et al. (2007).PYQSOFIT fits these empirical Fe II templates using a normalization, broadening, and wavelength shift.Next, we perform emissionline fits, using Gaussian profiles as described in Shen et al. (2019) and Rakshit et al. (2020).Depending on redshift and spectral coverage, we fit the following emission lines: Hα λ6564.6 broad and narrow, [N II] λλ6549, 6585, [S II] λλ6718, 6732, Hβ λ4861 broad and narrow, [O III] λλ5007, 4959, Mg II λ2800 broad and narrow, and C IV λ1549 broad and narrow.In addition, we also fitted the C III] λ1909 and Lyα 12166 broad and narrow components but restricted our analysis and results in this work to the sources with fits in the Hα, Hβ, Mg II, and C IV broad emission lines.We run all of these fits using Monte Carlo simulation based on the actual observed spectral error array, which in turn yields an error array for all our decomposition fits.An example spectral decomposition is shown in Figure 1. 7 The host galaxy fits used in PYQSOFIT are limited to rest-frame wavelengths between 3450 and 8000 Å. Due to this limitation, to fit the Mg II line complex, we follow the prescription of Green et al. (2022) but make a conditional execution of host decomposition in the same run, i.e., if z < 0.25, then the host contribution is included.Otherwise, the host contribution is not accounted for.In our fitting routine using PyQSOFit, we fit the spectrum over the whole wavelength range, although for this work we only use the measurements of the FWHMs of the broad emission lines (Hβ, Mg II, and C IV).These profiles are fitted within narrow wavelength windows (∼100-150 Å, e.g., as shown in the bottom panels of Figure 1) after the power-law continuum and host contribution are removed, leaving only the emission-line profiles to be fitted, and the effect from the absolute spectrophotometric calibration is minimal.This primarily affects the estimation of the continuum luminosities, and therefore we make use of the OGLE photometry-derived monochromatic luminosities throughout this work.We report the FWHMs for the Hβ, Mg II, and C IV emission lines for our sources in Table A3.

Estimating Black Hole Mass and Eddington Ratios
To calculate the bolometric luminosity (L bol ), we follow the prescription of Richards et al. (2006), Shen et al. (2011), andRakshit et al. (2020), where the AGN monochromatic luminosity is scaled by a bolometric correction factor to estimate the L bol :

⎧ ⎨ ⎩
Next, the BH mass (M BH ) can be estimated using the virial relation from the single-epoch spectrum for which continuum monochromatic luminosity (here derived from photometry) and line width measurements are available using the following relation: where A and B are the constants empirically calibrated from prior studies.Following the prescription of Subsequently, we estimate the Eddington ratio (λ Edd ), i.e., the ratio of the L bol to the Eddington luminosity 8 (L Edd ).The derived L bol , M BH , and λ Edd for the sources in our sample are reported in Table A4.We do not account for the error on the constant term (A) while estimating the uncertainties on the BH masses (Section 3.4).

Error Budget
In this subsection, we discuss the error budget for the BH mass and luminosity measurements.
The BH mass equation (Equation ( 1)) contains four variables (A, B, L λ , and FWHM).While the uncertainties for A and B typically are not reported, the usual dispersion of this relation is 0.3-0.4dex (e.g., VP06).This means that a single measurement of the BH mass has an uncertainty of about 0.4 dex.
The BH mass, via Equation (1), also depends on FWHM, which is estimated along with its uncertainty by PyQSOfit from fitting the broad emission lines, and the monochromatic luminosity.The uncertainty of the latter is estimated as a  (Guo et al. 2018) for a quasar spectrum (MQS J045538.57-690455.1)without significant host galaxy contribution.In each panel, we show the MQS data (black), power-law continuum (yellow), Fe II pseudocontinuum (in addition to the power-law continuum; light green), broad emission lines (red), narrow emission lines (dark green), and the total best-fit qso model (blue), which is the sum of continuum and emission lines.The host galaxy contribution is shown in magenta, while the host-subtracted data are shown with a continuous gray line, and the sum of the host and qso model is shown in pink.Top panel: the rest-frame central wavelengths for prominent emission lines are shown using the dashed vertical lines.The sky coordinates (in degrees) and the redshift for the sources are quoted in the title of the figure.Bottom panels: a zoomed-in version of individual line complexes.The residuals are shown in dotted gray in each panel.
combination of two factors: (1) the uncertainty of the conversion of the broadband magnitudes to the monochromatic luminosities, which is typically of the order of 0.1 dex, and (2) the uncertainty of the mean broadband magnitude.The latter depends not only on the photometric quality of the survey but also on the data length and number of points, as AGNs are variable sources.The longer the light curve and the larger the number of photometric points, the closer the mean estimation is to the true mean.The contribution of this uncertainty to the total uncertainty is 0.004 dex.

Luminosity Distribution as a Function of Redshift
In Figure 2, we demonstrate the dependence of the monochromatic luminosity on the redshift for the sources in our sample.The luminosities are derived from the photometry as described in Section 3.1.We highlight three cases of monochromatic luminosities: (a) at 5100 Å, (b) at 3000 Å, and (c) at 1350 Å, which are in the vicinity of the prominent broad emission lines, i.e., Hβ, Mg II, and C IV, respectively.The properties (median and the 16th and 84th percentiles) for the respective joint distributions presented in Figure 2 are reported in Table 1.
To facilitate the comparison of the sources and their luminosities across redshift, we estimate the bolometric luminosities (using the prescription outlined in Section 3.3).Figure 3 demonstrates the bolometric luminosity (L bol ) as a function of redshift for all of the sources in our sample.The sources are colored based on the monochromatic luminosity used to estimate the respective L bol values.We see a clear increase in the net L bol with increasing redshift extending up to z ∼3.5, where the bottom envelope is due to the limiting magnitude of the SDSS or MQS/OGLE surveys.
We overlay a filtered version of the SDSS DR14 QSO sample (Rakshit et al. 2020) on this distribution to compare the two distributions.The filtering of the sources is made by using the quality flags associated with the M BH and L bol estimations from Rakshit et al. (2020).They use QUAL flag = 0 to identify sources with reliable M BH and L bol estimations.We have chosen to use the two flags simultaneously to avoid confusion later when discussing the M BH measurements from SDSS and our sample.The original SDSS DR14 QSO sample contains 526,265 sources, of which, after filtering, we are left with 449,863.We note here that before filtering the sample of sources in the SDSS many erroneous estimates were reported for the L bol and M BH with significantly large uncertainties.The filtering allowed us to remove sources with such measurements and limit ourselves to estimates with higher reliability.To highlight the large differences due to the filtering, we report the median, minimum, and maximum values for the redshift, L bol , and M BH distributions for the original and filtered SDSS samples in Table 2.In Figure 3, we show the filtered SDSS sample using contours.We use nine levels for the contour map that correspond to the isodensity lines encompassing 90% of  Note.The median and 16th and 84th percentile values are represented in respective panels in Figure 2 and are truncated to three decimal digits.the SDSS AGNs (the outermost contour) and decreasing inward by 10%.We note that some of the sources in our sample (28) lie outside the lowest contour line, which is the consequence of differences in the surveys' setups.We see an overall agreement between the two distributions with a clear increase in the L bol with increasing redshift.Additionally, we note that sources in our sample have relatively higher L bol values as compared to the peak of the SDSS distribution irrespective of the monochromatic luminosity used to estimate the L bol values.This can be attributed to the shallower depth of the OGLE survey as compared to SDSS.

Black Hole Mass and Eddington Ratio Distributions
In Figure 4, we demonstrate the M BH -M BH planes estimated using the pairs of emission lines, i.e., (Hα, Hβ), (Hβ, Mg II), and (Mg II, C IV), respectively.We have 10 sources with simultaneously reliable Hα-based and Hβ-based M BH measurements in our sample.Similarly, we have eight sources with reliable Hβbased and Mg II-based M BH measurements and three sources with reliable Mg II-based and C IV-based M BH measurements.Overall, we find a good agreement between the masses estimated using FWHM from different emission lines and monochromatic luminosities, which are depicted using the line of unity (dashed line) in each panel of Figure 4.The scatter in the panels of Figure 4 can be attributed to either the relative offsets in the FWHM values between the lines, the monochromatic luminosities differences, or the uncertainty in the relations (i.e., mostly due to the constant term (B) associated with the monochromatic luminosity) used to derive the M BH .We note, however, that we do not account for the error on the constant term (A; see Equation (1)) while estimating the uncertainties on the BH masses.
Similarly to Figure 3, in Figure 4 we overlay the contours from the filtered SDSS sample.The SDSS catalog provides the M BH mass measurements obtained using the Hβ, Mg II, and C IV emission lines and respective monochromatic continuum luminosities (no Hα).Hence, we only show these contour maps for the middle (Hβ-based M BH vs. Mg II-based M BH ) and right (Mg IIbased M BH versus C IV-based M BH ) panels.Contrary to the contour maps in Figure 3, we truncate the contours at 67% and above for the probability mass for the respective distributions for better visualization of the comparison between the two samples.We notice that all the measurements from our sample, including the uncertainties, lie within the threshold of the filtered SDSS sample.
In Figure 5, we present the Eddington ratio (λ Edd )-M BH plane occupied by the sources in our sample.The sources are colored based on the respective emission lines and monochromatic continuum luminosities incorporated to estimate the λ Edd and M BH .We notice that the distribution shifts toward higher BH masses and higher Eddington ratios as we move from (Hβ, 5100 Å) subsamples to (Mg II, 3000 Å) and (C IV, 1350 Å) subsamples.This trend is also quantified in Table 3, where we see that the ranges covered by the Hβ-based M BH and λ Edd are the widest, while the Mg II-based sample is more concentrated at a slightly larger M BH range but covers a subset of the range in the Eddington ratio relative to the Hβ-based subsample.Finally, the C IV−based sample only contains seven sources, much smaller than the other two subsamples (we have 70 and 97 sources for the Hβ-based and Mg II-based subsamples, respectively), and occupies a region with the highest λ Edd , even going above the Eddington limit.However, the M BH range is relatively modest as compared to the other two subsamples.Similar to the previous analyses, we overlay the corresponding contour maps from the filtered SDSS sample for the respective subsamples.In this figure, the contour maps show the full range of the distribution from the filtered SDSS sample without any threshold cuts.We notice that the sources from both our sample and the SDSS sample occupy roughly the same region in the λ Edd -M BH plane.However, there are a few sources from the Hβ subsample from our sample that have slightly lower Eddington ratio values as compared to their SDSS counterparts.We note in passing that the masses derived using the C IV region and Mg II region are comparable for our MQS quasar sample.This similarity between the M BH estimates is also noted in the M BH distributions derived from the SDSS DR14 sample (see Figure 6).We consider the sources where the quality flag for the M BH is 0, i.e., the mass measurements are reliable.We independently show the masses estimated from the Hβ, Mg II, and C IV regions that use the formalisms from Vestergaard & Peterson (2006), Vestergaard & Osmer (2009), and Vestergaard & Peterson (2006), respectively.The median values for each subsample are shown using dashed lines, and the region between the 16th and 84th percentiles is shown using shaded colors per subsample.For Mg II-(green) and C IV-based (blue) subsamples, we find that the distributions behave similarly, i.e., the respective medians are comparable (8.74 vs. 8.71), and the regions bounded by the 16th and 84th percentiles also overlap.The overall similarity in M BH using different broad emission lines has been noted in other studies (Assef et al. 2011;Kozłowski 2017b).We note, however, that the mass measurements can be affected by the choice of methodology (see, e.g., Mejía-Restrepo et al. 2018;Dalla Bontà et al. 2020).

Optical Plane of the Eigenvector 1
Understanding the diversity in spectral properties within AGNs poses a significant challenge.To this end, the work by Boroson & Green (1992) holds paramount importance for two key reasons.First, it represents one of the pioneering contributions in AGN research employing principal component analysis (PCA) to unravel the interrelation between observed quasar properties.This analysis delves into the main sequence of quasars, employing eigenvectors, notably Eigenvector 1.This particular eigenvector reveals an intriguing anticorrelation between the equivalent width (EW) of the optical Fe II blend (spanning 4434-4684 Å) and the peak intensity of the forbidden line [O III] λ5007.Second, this study also establishes a connection between the FWHM of the broad Hβ emission and this eigenvector.This linkage, specifically between the FWHM of the broad Hβ line and the strength of the Fe II blend (expressed as EW(Fe II) relative to the EW of the broad component of Hβ, or R Fe II ), has evolved into the well- Note.The median, minimum, and maximum values are truncated to three decimal digits.The filtered sample is prepared using the QUAL flag = 0 for the L bol and M BH simultaneously.The numbers in parentheses denote the sources in each sample.
established "quasar main sequence."This sequence, illustrated in the left panel of Figure 7, is primarily influenced by the Eddington ratio, among other physical properties, as documented in subsequent studies (e.g., Sulentic et al. 2000;Shen & Ho 2014;Marziani et al. 2018;Panda et al. 2018Panda et al. , 2019aPanda et al. , 2019b)).Furthermore, an additional classification system based on the width of the Hβ emission-line profile in AGN spectra has been introduced, distinguishing between Population A and Population B. Population A encompasses local narrow-line Seyfert 1 galaxies (NLS1s) and more massive high accretors, primarily identified as radio-quiet sources (e.g., Marziani & Sulentic 2014), with FWHM (Hβ)  4000 km s −1 .Notably, Population A sources often exhibit a Hβ profile with a Lorentzian-like shape (e.g., Sulentic et al. 2002;Zamfir et al. 2010).In contrast, Population B sources, characterized by broader Hβ profiles (4000 km s −1 ), are predominantly associated with "jetted" characteristics (e.g., Padovani et al. 2017).These sources tend to exhibit Gaussianshaped Hβ profiles, and for those with even higher FWHMs, disklike double Gaussian profiles are observed in Balmer lines.The choice of the FWHM cutoff at 4000 km s −1 was proposed by Sulentic et al. (2000) and Marziani et al. (2018), who observed more pronounced changes in AGN properties beyond this line width threshold.Subsequent studies have shown that the two populations form a continuous link and share a connection (Fraix-Burnet et al. 2017;Berton et al. 2020).The morphology of the emission-line profiles and the characteristics of the continuum are    intricately linked to the central engine, specifically the BH mass, accretion rate, BH spin, and viewing angle from a distant observer (Czerny et al. 2017;Marziani et al. 2018;Panda et al. 2018Panda et al. , 2019b;;Panda 2021b).
In our sample, to check the location of the sources on the Eigenvector 1 sequence, we first filtered the sources where the relative uncertainties on the R Fe II and the FWHM(Hβ) were below a certain threshold.We assume this limit to be 20% to keep reasonable measurements and avoid sources where these values could be unreliable or affected by low-S/N spectral quality.This limits the total number of sources to 41/58, where 58 was the source count where we have a nonzero measurement for the R Fe II and FWHM(Hβ).We tabulate the salient properties of this limited sample of 41 sources in Table 4.In the right panel of Figure 7, we demonstrate the optical plane of the Eigenvector 1 sequence for our sources.These sources are color-coded by their respective λ Edd values.To facilitate the comparison between our sample and the filtered SDSS sample, we overlay the SDSS sample using contour maps.We find remarkable agreement between the two samples.Some of the sources from our sample do have slightly larger FWHM(Hβ) and/or larger R Fe II estimates.We note, however, that the exact extent of the filtered and limited SDSS sample considered here does have a wider coverage (please see the lower half of Table 4), although these sources constitute a minor fraction of the total sample considered here.
We highlight the spectra of three of our sources in Figure 8.These three sources are marked with bull's-eye symbols in Figure 7 and were chosen to demonstrate the variety in R Fe II measurements we have in our sample.The spectra have been binned for better visualization.We can see that, going from the source with one of the lowest R Fe II measurements (spectrum in red) toward the source with one of the highest values for R Fe II (spectrum in blue), there is a substantial change in the Fe II bump feature and the weakening of the Hβ emission.This further demonstrates the efficacy of the quasar main-sequence analysis and its potential to categorize a diverse population of type 1 AGNs.

Discussion
Measuring the physical parameters of AGNs appears to be a straightforward task nowadays, as a single spectrum for an AGN is typically necessary to measure the monochromatic and bolometric luminosities, the BH mass, and the Eddington ratio.The prime example, where such measurements were reported for 526,265 AGNs, is the SDSS DR14 QSO catalog by Rakshit et al. (2020); the SDSS DR16 version contains 750,414 AGNs (Wu & Shen 2022).
While the BH mass sets the size of an accretion disk, the key to our understanding of the physical processes within the disk .The vertical blue line marks the limit for R Fe II = 1 separating the weak and strong Fe II emitters (or xA sources).Right panel: the optical plane for the MQS sources.Similar to the left panel, the horizontal dashed and dotted lines represent the 4000 and 2000 km s −1 thresholds, respectively, while the dashed vertical line marks the R Fe II = 1 limit.The sources are colored based on their Eddington ratios (in the log scale).Here we demonstrate the sources where both the FWHM(Hβ) and R Fe II are of high quality, i.e., corresponding errors are within 20% of the estimated values.The sources from the SDSS DR14 QSO sample are shown using contours where a similar quality filtering is adopted.Spectra for the three sources marked with the bull's-eyes are shown in Figure 8. Note.The median, minimum, and maximum values are truncated to three decimal digits.The numbers in parentheses denote the sources in each sample.may be ciphered in the observed AGN variability patterns.
Several theoretical variability timescales are predicted: the dynamical one, which is the time it takes the matter to orbit the BH (t = GM r dyn 3 ); the thermal timescale (τ th = α −1 τ dyn ); or the viscous timescale (τ vis = τ th (r/h) 2 ).Here M is the BH mass, r is the radial size of the disk, α is the viscosity, and h is the disk height (e.g., Czerny 2004;Kelly et al. 2009).
In Kelly et al. (2009), authors analyze ∼7.5 yr long MACHO light curves for 15 AGNs and model them with the damped random walk model.The resulting AGN variability timescales in that article are comparable to the rest-frame light-curve lengths, which likely means that they are unreliable (Kozłowski 2017a;Sánchez et al. 2017;Burke et al. 2021;Suberlak et al. 2021).Kozłowski (2017a) showed that timescales derived for the ∼9000 SDSS AGNs having 8 yr long light curves are also unreliable.
Because an AGN light-curve length is the most important parameter that influences the reliability of the intrinsic timescale measurement (Kozłowski 2017a(Kozłowski , 2021)), a quest for the longest possible length has begun.For example, Suberlak et al. (2021) used the Pan-STARRS1 data to extend the SDSS Stripe 82 quasar light curves to 15 yr.A similar approach was used in Burke et al. (2021), where the authors used 20 yr long photometric light curves for SDSS Stripe 82 quasars.
The OGLE survey has surveyed the sky since 1992 and the Magellanic Clouds since 1997.There exist AGN light curves from OGLE spanning 26 yr, and they are continuously growing.By providing the physical parameters for these sources, this article sets a pathway to the forthcoming studies on the relations between the physical AGN parameters and variability parameters.

Summary
In this paper, we reanalyzed ∼4000 spectra from MQS.In addition to the already-reported 758 AGNs in Kozłowski et al. (2013), we discovered 161 new AGNs, albeit very faint, so the total number of the MQS AGNs increases to 919.
The spectra for these 919 AGNs were fit with the PYQSOFIT code to measure the FWHM (and EW) for the broad lines common in AGNs: Hα, Hβ, Mg II, and C IV, but also the EW of the Fe II blend (reported as the ratio to the EW Hβ; R Fe II ).
Since the spectra were flux-uncalibrated (by design), we used empirical conversions of the broadband extinctioncorrected V-and I-band mean OGLE magnitudes to the monochromatic luminosities from Kozłowski (2015).For all the sources, we also calculated the bolometric luminosities, kcorrections, DMs, and absolute magnitudes.
By combining the broad-line FWHM with the monochromatic luminosities, we calculated the BH masses for 165 AGNs, where the spectra had adequate quality to do so.Whenever two BH mass measurements were simultaneously available from a single spectrum (Hα-Hβ, Hβ-Mg II, or Mg II-C IV), we checked whether the two masses stayed in agreement, which was the case.
We also demonstrate the optical plane of the Eigenvector 1, or the quasar main sequence for the subsample (41/165) of our sources with reliable measurements of the FWHM(Hβ) and the strength of the optical Fe II emission, i.e., R Fe II .There is an overall agreement with the SDSS-based main-sequence diagram where we notice a discernible trend-increasing Eddington ratio with an increase/decrease in the R Fe II /FWHM(Hβ), along the main sequence as found in earlier works (Sun & Shen 2015;Marziani et al. 2018;Panda et al. 2019bPanda et al. , 2020;;Zajaček et al. 2024).The sources with R Fe II  1 will be especially interesting to follow up in the optical and near-infrared spectral regions to characterize their variable nature and evaluate the strength of other low-ionization lines, e.g., Ca II triplet (emitting at λλ8498, 8542, and 8662) and OI λ8446, which are efficient proxies to reveal the physical conditions of the low-ionization line-emitting region in such AGNs (Martínez-Aldama et al. 2015;Marinello et al. 2016Marinello et al. , 2020;;Martínez-Aldama et al. 2021a, 2021b;Panda 2021aPanda , 2021c)).Such targets have also been found to be of to standardize the BLR radius-luminosity relation, which can allow us to employ quasars as standardizable distance indicators (Du & Wang 2019;Martínez-Aldama et al. 2019;Panda & Marziani 2023;Panda et al. 2023).
The physical parameters of those AGNs, such as the BH mass, the Eddington luminosity, or the bolometric luminosity, will be invaluable for future AGN variability studies.The OGLE survey alone has collected for some of these sources 26 yr long light curves (up to 19 yr long rest frame) in I band and slightly shorter Vband light curves that will be demonstrated in a forthcoming work.

Figure 1 .
Figure1.Exemplary fit using PYQSOFIT(Guo et al. 2018) for a quasar spectrum (MQS J045538.57-690455.1)without significant host galaxy contribution.In each panel, we show the MQS data (black), power-law continuum (yellow), Fe II pseudocontinuum (in addition to the power-law continuum; light green), broad emission lines (red), narrow emission lines (dark green), and the total best-fit qso model (blue), which is the sum of continuum and emission lines.The host galaxy contribution is shown in magenta, while the host-subtracted data are shown with a continuous gray line, and the sum of the host and qso model is shown in pink.Top panel: the rest-frame central wavelengths for prominent emission lines are shown using the dashed vertical lines.The sky coordinates (in degrees) and the redshift for the sources are quoted in the title of the figure.Bottom panels: a zoomed-in version of individual line complexes.The residuals are shown in dotted gray in each panel.

Figure 2 .
Figure 2. AGN luminosity at 5100 Å (left panel), 3000 Å (middle panel), and 1350 Å (right panel) derived from the OGLE photometry as a function of redshift.The respective marginal distributions are shown per panel.The medians are marked with dashed lines, and the shaded regions mark the region between 16th and 84th percentiles of the distributions in each of the marginal distributions.

Figure 3 .
Figure3.Bolometric luminosity as a function of redshift for the sources in our sample.The sources are colored by the AGN monochromatic luminosity used to estimate the bolometric luminosity.The sources from the SDSS DR14 QSO sample are shown using contours where the fiducial L bol are reported with the QUAL flag = 0. We show nine levels for the contour map, which correspond to the isodensity of the SDSS sources, with the outermost contour encompassing 90% of the sources and decreasing inward by 10%.

Figure 4 .
Figure 4. Comparison of the BH mass estimates for sources where both Hα and Hβ FWHMs are simultaneously available (left), for sources where both Hβ and Mg II FWHMs are simultaneously available (middle), and for sources where both Mg II and C IV are simultaneously available in a spectrum (right).In each panel, the dotted black line represents the 1-to-1 line shown for reference.The sources from the SDSS DR14 QSO sample are shown using contours where the Hβ-, Mg II-, and C IVbased BH masses are reported (no Hα).For the SDSS sample, we filter the sources based on the fiducial L bol and M BH with the QUAL flags = 0.The largest contour represents 67% of the total number of the SDSS AGNs.

Figure 5 .
Figure 5. BH masses vs. Eddington ratios for the sources in our sample.The sources are colored based on the monochromatic luminosity-emission-line pairs.The sources from the SDSS DR14 QSO sample are shown using contours where the Hβ-(in pink), Mg II-(in light green), and C IV-based (in light blue) BH masses are considered.The SDSS sources are filtered based on the adopted fiducial L bol and M BH with the QUAL flags = 0. We do not show the uncertainties associated with the M BH and λ Edd for the MQS AGNs for clarity.

Figure 6 .
Figure 6.M BH distributions from the cleaned SDSS DR14 QSO sample (Rakshit et al. 2020).The Hβ-(red), Mg II-(green), and C IV-based (blue) masses are shown in this histogram.The respective median values are shown using dashed lines of identical colors, while the shaded regions mark regions bounded by the 16th and 84th percentiles for the respective distributions.

Figure 7 .
Figure 7. Left panel: schematic diagram of the optical plane of Eigenvector 1. Abridged version from Panda et al. (2020).The horizontal line denotes the threshold in FWHM(Hβ) at 4000 km s −1 that separates the Population A and Population B sources.The "classical" NLS1s are located below FWHM(Hβ) 2000 km s −1 (dotteddashed line).The vertical blue line marks the limit for R Fe II = 1 separating the weak and strong Fe II emitters (or xA sources).Right panel: the optical plane for the MQS sources.Similar to the left panel, the horizontal dashed and dotted lines represent the 4000 and 2000 km s −1 thresholds, respectively, while the dashed vertical line marks the R Fe II = 1 limit.The sources are colored based on their Eddington ratios (in the log scale).Here we demonstrate the sources where both the FWHM(Hβ) and R Fe II are of high quality, i.e., corresponding errors are within 20% of the estimated values.The sources from the SDSS DR14 QSO sample are shown using contours where a similar quality filtering is adopted.Spectra for the three sources marked with the bull's-eyes are shown in Figure 8.

Table 1
Properties of the Monochromatic Luminosity and Redshift Distributions

Table 2
Properties from the SDSS DR14 QSO Sample (Original versus Filtered Sample)

Table 3
Properties from the λ Edd -M BH Distribution for Our Sample

Table 4
Properties of the Sample Presented in the Quasar Main-sequence Diagram in The Astrophysical Journal Supplement Series, 272:11 (15pp), 2024 May Panda et al.