Black Hole Mass estimation in quasars

Active galactic nuclei at : Ii. Black Hole Mass estimation by means of broad emission lines

J. E. Mejia-Restrepo,, B. Trakhtenbrot, P. Lira, H. Netzer, D. M. Capellupo
Departamento de Astronomía, Universidad de Chile, Camino el Observatorio 1515, Santiago, Chile
Institute for Astronomy, Dept. of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland
School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada
Email: jemejia@das.uchile.clZwicky postdoctoral fellow
Abstract

This is the second in a series of papers aiming to test how the mass (), accretion rate () and spin () of super massive black holes (SMBHs) determine the observed properties of type-I active galactic nuclei (AGN). Our project utilizes a sample of 39 unobscured AGN at observed by VLT/X-shooter, selected to map a large range in  and  and covers the most prominent UV-optical (broad) emission lines, including H, H, Mg ii, and C iv. This paper focuses on single-epoch, “virial”  determinations from broad emission lines and examines the implications of different continuum modeling approaches in line width measurements. We find that using a local  power-law continuum instead of a physically-motivated thin disk continuum leads to only slight underestimation of the FWHM of the lines and the associated . However, the line dispersion  and associated  are strongly affected by the continuum placement and provides less reliable mass estimates than FWHM-based methods. Our analysis shows that H, H and Mg ii can be safely used for virial  estimation. The C iv line, on the other hand, is not reliable in the majority of the cases, this may indicate that the gas emitting this line is not virialized. While H and H show very similar line widths, the mean FWHM(Mg ii) is about 30% narrower than FWHM(H). We confirm several recent suggestions to improve the accuracy in C iv-based mass estimates, relying on other UV emission lines. Such improvements do not reduce the scatter between C iv-based and Balmer-line-based mass estimates.

keywords:
galaxies: active quasars:general quasars:supermassive black holes quasars: emission lines
volume: in press

1 Introduction

The mass () of Super Massive Black Holes (SMBHs), along with the SMBH spin () and accretion rate (), are the fundamental parameters that drive the physical, geometric and kinematic properties of the SMBH environment (e.g. Kaspi et al., 2005; Slone & Netzer, 2012; Capellupo et al., 2015).  is also known to be correlated with several properties of the host galaxy, suggesting a so-called “co-evolutionary” scenario for the SMBH and stellar component of the host (e.g. Ferrarese & Merritt, 2000; Häring & Rix, 2004; Gültekin et al., 2009; Xiao et al., 2011). Therefore, accurate and precise determinations of , across cosmic epochs, are crucial for our understanding of SMBH physics and evolution.

For un-obscured, type-I actively growing SMBHs (active galactic nuclei - AGN),  can be estimated from single epoch spectra of several broad emission lines. The method, which was used for many large samples of AGN across cosmic epochs (e.g., Croom et al., 2004; McLure & Dunlop, 2004; Onken et al., 2004; Fine et al., 2006; Shen et al., 2008; Rafiee & Hall, 2011; Trakhtenbrot & Netzer, 2012), is based on a combination of two basic ingredients (Vestergaard, 2002; Peterson et al., 2004). First, reverberation mapping (RM) experiments provide an empirical relation between the BLR size and the AGN continuum luminosity (, with ; see Kaspi et al. 2000, 2005; Bentz et al. 2009; Bentz et al. 2013, and references therein). Second, the gas in the broad line region (BLR) is assumed to be virialized (as suggested by several empirical studies, e.g., Peterson & Wandel, 1999; Onken et al., 2004) . After taking the line width of the BLR lines as a natural estimation of the virial velocity of the gas in the BLR (), one may obtain the mass from the virial relation:

(1)

where and is a general geometrical function which correct for the unknown structure and inclination to the line of sight. can be determined experimentally by requiring RM- estimations to be consistent, on average, with those predicted from the -bulge stellar velocity dispersion (-) relation of local galaxies where  have been dynamically estimated (e.g. Onken et al., 2004; Woo et al., 2010; Graham et al., 2011; Graham, 2015; Woo et al., 2015). In this paper, we assume , which is appropriate for the FWHM  estimates (Woo et al., 2015). However, in addition to the still large uncentainty in this value (50%), can also be different for different lines and could even depend on luminosity and/or line properties (e.g. equivalent widths, line offsets FWHM Shen, 2013).

Among the RM-based relations, the most reliable one is the relation, which is the only one based on a large number of sources, with . Thus, the  determination based on other lines and luminosities at other wavelengths needs to be re-calibrated to match  measurements based on H and . Particularly, C iv, hereafter C iv, (e.g. Vestergaard & Peterson, 2006; Park et al., 2013), Mg ii, hereafter Mg ii, (e.g. McLure & Jarvis, 2002; Vestergaard & Osmer, 2009; Wang et al., 2009; Trakhtenbrot et al., 2011; Shen & Liu, 2012; Trakhtenbrot & Netzer, 2012) and H (e.g. Greene & Ho, 2005; Xiao et al., 2011; Shen & Liu, 2012) have been re-calibrated accordingly, and are widely used lines to determine  at high redshifts.

Earlier  recalibrations based on Mg ii and H have showed good agreement and low scatter with H-based  calibration (Greene & Ho, 2005; Xiao et al., 2011; Trakhtenbrot & Netzer, 2012). However,  recalibrations using the C iv line are more problematic, compared with those based on lower-ionization lines. First, the correlation between the widths of C iv and the other lines was shown to be weak, or indeed insignificant, and to present a large scatter, in many AGN samples (e.g., Baskin & Laor, 2005; Netzer et al., 2007; Shang et al., 2007; Shen et al., 2008; Fine et al., 2010; Ho et al., 2012; Shen & Liu, 2012; Tilton & Shull, 2013). Moreover, about 40% of the objects have , in contrast to the expectations from RM experiments and the virial assumption, that suggest (see detailed discussion in TN12, and additional samples in Ho et al. (2012); Shen & Liu (2012); Tilton & Shull (2013)). Second, significant blueshifts of the entire C iv profile (i.e., not necessarily a specific sub-component of the line), reaching several 1000s km s, are ubiquitously measured in the vast majority of AGN (Richards et al., 2002; Baskin & Laor, 2005; Shang et al., 2007; Richards et al., 2011; Trakhtenbrot & Netzer, 2012). Some of these findings were explained either by a disc outflow wind (e.g. Gaskell, 1982; Sulentic et al., 2007; Richards et al., 2011) or, alternatively, by scattering off an in-falling medium in the innermost C iv-emitting regions, which would produce the C iv blueshifts (e.g. Kallman & Krolik, 1986; Goosmann & Gaskell, 2007; Gaskell, 2009; Gaskell & Goosmann, 2013). Finally, the detailed re-analysis of the RM data for C iv performed by Denney (2012) found that the (narrowest) core of the broad C iv line does not reverberate in response to continuum variability. This implies that the outermost C iv emitting regions may not be virialized, either. All this leads to the conclusion that the simplified models and prescriptions discussed above may be incorrect, or at least incomplete, for some lines.

The  determination is also subjected to several uncertainties, related to the limitations of spectral analysis, and/or the need to make several assumptions regarding the universality of some AGN properties. The former includes the blending of neighboring emission and/or absorption features; incorrect determination of the continuum emission (Shang et al., 2007, hereafter S07); poor statistics due to non-homogeneous or small nature of the sample under study (e.g. Ho et al., 2012); poor data quality (e.g., Denney et al., 2013; Tilton & Shull, 2013); and measurements obtained from non-simultaneous data (see e.g. Shen & Liu, 2012; Marziani et al., 2013a). The latter, somewhat more fundamental uncertainties, include non virial gas motion; the orientation of the (generally non-spherical) BLR with respect to the line-of-sight (Runnoe et al., 2014; Shen & Ho, 2014; Brotherton et al., 2015); and the extrapolation of the relations to luminosities which are well beyond the range probed by RM experiments.

There have been many efforts to improve single-epoch  determinations, addressing some of the aforementioned limitations (e.g. Greene & Ho, 2005; Vestergaard & Peterson, 2006; Fine et al., 2008; Wang et al., 2009; Fine et al., 2010; Xiao et al., 2011; Shen & Liu, 2012; Trakhtenbrot & Netzer, 2012; Marziani et al., 2013a; Park et al., 2013; Runnoe et al., 2013; Brotherton et al., 2015; Zuo et al., 2015). Trakhtenbrot & Netzer (2012, hereafter TN12) combined Sloan digital sky survey archival data (SDSS; Abazajian et al., 2009) with smaller surveys and samples to improve earlier Mg ii-based  prescriptions (e.g., McLure & Jarvis, 2002; McLure & Dunlop, 2004; Wang et al., 2009), by assuming virialization of the Mg ii emitting clouds. As mentioned above, the TN12 study emphasized the fact that a large fraction of AGN show . Marziani et al. (2013a) (hereafter M13) also used SDSS data to perform an Eigenvector 1 analysis (Boroson & Green, 1992), and to separate the population into “population A” () and “population B” () sources. They suggested that H- and Mg ii-based  estimates in population B sources could be systematically overestimated due to a red-shifted, extremely broad emission component. The study ofShen & Liu (2012) combined SDSS optical observations of high-z objects (1.5z2.2) with follow up FIRE-IR observations, which allowed them to compare and recalibrate the C iv, Mg ii, H and H  relations as well as contrast them with previous calibrations. While they found that FWHM(Mg ii) correlates well with the Balmer lines, the FWHM(C iv) does not show such correlations and is not a reliable viral mass estimator. The Shen & Liu (2012) results are however subjected to low quality SDSS data, non homogeneous sample selection and non simultaneous observations. Ho et al. (2012) obtained simultaneous UV, optical and infrared X-Shooter spectra for 7 objects at , resulting in similar conclusions regarding the usability of Mg ii-based  estimates, and the limitations associated with C iv.

The studies of (Denney et al., 2013, hereafter D13) and Tilton & Shull (2013) claimed that in spectra of limited S/N and/or spectral resolution, FWHM(C iv) measurements are underestimating the “real” line widths, in objects with strong intrinsic absorption features that cannot be deblended from the emission lines. This would partially explains the TN12 finding that about 40% of the objects shows FWHM(C iv)FWHM(H). However, objects with no evidence of absorption features, and yet “intrinsic” line widths with FWHM(C iv)FWHM(H) are known to exist (e.g., Corbin & Boroson, 1996). After correcting for intrinsic C iv absorption, D13 claimed that although FWHM(C iv) still does not correlate well with FWHM(H), (C iv) shows a strong correlation with (H) and can safely be used for C iv based  determinations. Based on these results, (Park et al., 2013) obtained high quality data in 39 out of 45 objects of the RM experiments campaign and improved the Vestergaard & Peterson (2006) C iv-based  estimator based on the (C iv). Both D13 and (Park et al., 2013) used non homogeneous and multi-epoch samples that could affect their results. In addition,  measurements are highly dependent on the continuum determination method (see discussion in (Peterson et al., 2004)).

Recently, Runnoe et al. (2013) (hereafter R13) and Brotherton et al. (2015) used a sample of 85 low-redshift () and low-luminosity () AGN with quasi-simultaneous UV and optical spectra to propose a method to rehabilitate C iv for  determination, based on a correlation that they found between the Si iv+O iv]C iv line peak intensity ratio and the HC iv FWHM ratio. This allowed these authors to predict FWHM(H) from measurements of the Si iv+O iv] emission. These studies suggested that this correlation may be driven by the so-called Eigenvector 1.

In this work, we use X-shooter high-quality observations that combines simultaneous UV, optical and infrared spectroscopy of a unique sample of AGN at z1.55, selected by both their  and Eddington ratio,  as described in Capellupo et al. (2015) (hereafter paper I). Selecting objects at this redshift allows simultaneous observations of H, H, Mg ii and C iv which is optimal for comparing the various mass determination methods. In Paper I, we showed that the accretion-disk continuum of most of the objects (25 out of 30) can be successfully modeled by a geometrically thin, optically thick Shakura-Sunyaev accretion disks (Shakura & Sunyaev, 1973, hereafter SS73) . The models were taken from Slone & Netzer (2012) who include several improvements upon the SS73 model, such as GR effects and a detailed treatment of the Comptonization in the disc atmosphere. Paper I shows that most earlier attempts to fit accretion disk (AD) spectra to AGNs failed because of the limited wavelength coverage and/or non-simultaneous observations. The continuation of this work, that includes 9 more sources and a more comprehensive analysis, is described in Capellupo et al. (2016, in prep.), hereafter Paper III) which is published in this volume.

The purpose of the present paper is to evaluate BH mass measurements based on different emission lines, as derived from our unique sample of X-shooter spectra. We also aim to provide to the community  correction factors that do not depend on the exact shape of the underlying continuum. The paper is structured as follows. In section 2 we describe the sample. In section 3 we first introduce the local  and global  thin disk continuum approaches and describe the fitting procedures we follow to model the continuum, emission lines, iron pseudo continuum and Balmer continuum. In section 4 we present and discuss the main results and in section 5 we list the main conclusions of our work. Throughout this paper we assume a flat CDM  cosmology with the following values for the cosmological parameters: , and .

Figure 1:  vs  using the values we obtained in this paper. Green stars and magenta diamonds represent the broad absorption line quasars (BALQSO) and the broad-Mg ii respectively (as defined in §4.3.4) . The magenta dashed vertical line represents 0.2.
Figure 2: Signal to noise ratios (S/N) measured at the peaks of each of the main broad emission lines (left), and over the corresponding nearby continuum bands (right), plotted against optical brightness, . The black dashed lines represent, from bottom top, S/N equal to 3, 5, 10 and 20.

2 Sample, Data and Analysis

The analysis presented in this paper is based on a sample of luminous, type-I AGN in a narrow redshift range around , for which we have obtained high signal to noise () single epoch spectroscopic observations using the X-Shooter instrument on the Very Large Telescope. The 39 sources span a range in brightness of . The sample selection, data acquisition and reduction for the 30 brightest sources were described in detail in paper I, and information about 9 other sources, obtained in ESO program 092.B-0613, is provided in Paper III. Here we only briefly highlight a few essential aspects.

The sample has been selected from the seventh data release of the SDSS (Abazajian et al., 2009) to homogeneously map the parameter space of  and . For the purposes of target selection, these quantities were initially obtained by spectral fitting of the Mg ii broad emission line in the SDSS spectra as part of the large compilation described in TN12. In Figure. 1 we show  vs  using updated values calculated in this paper based on the H broad emission line and following the procedure that we describe in section 4.4.

At the chosen redshift range of the sample, X-Shooter covers the rest-frame wavelength from about 1200Å to 9200Å. This broad spectral coverage has allowed us, after correction for Galactic extinction, to successfully model and constrain the observed Spectral Energy distributions (SEDs). As shown in Papers I and III, we obtain satisfactory thin AD model fits to 37 sources, 6 of which require an intrinsic reddening correction for a satisfactory fit. The wide wavelength coverage, together with the homogeneous selection of the sample in the plane, enables us to test the performance of the single epoch black hole mass estimators for the H, H, Mg ii and C iv lines and estimate the systemic bias induced when the physical SED is unknown.

In Figure 2 we show the the signal to noise ratios () for our X-Shooter spectra, measured at the peaks of each of the main emission lines under study, as well as at the corresponding continuum bands, as a function of . We note that, even in the spectral region which overlaps with the available SDSS spectra, the X-Shooter data provide a significant improvement in terms of and spectral resolution (see an example in Fig. 12, described in appendix §A). All the sources have fairly high () at the peaks of the Mg ii and C iv lines and the adjacent continuum bands. However, this is not the case for H and H. The continuum bands adjacent to H are much noisier. Most of the objects have , and for those with , the ratio is below 10. Nevertheless, we are able to obtain reliable H line measurement because most objects have fairly high at their H line peak (34 out of 39 object have and all of them have ). Moreover, the relevant continuum bands around H have low levels of contamination from iron or other, unresolved spectral features. Consequently, even a moderate continuum (i.e., 3) is enough to have reliable H fits. There are however 4 objects where and their line measurements, especially their FWHM(H) are somewhat uncertain.

Unfortunately, the H line measurements are more problematic. In addition to the fact that H is the weakest of the lines of interest, we can also see from Fig. 2 that the relevant continuum band in 21 out of 39 objects have , and 14 of them are actually below . Near infrared (NIR) telluric absorption is another issue that could also crucially affect H line measurements. The spectral regions with known low atmospheric transmission in the NIR, between Å and between 13000Å to 15000Å typically translate to rest-frame bands at 4200-4500Å and 5300-5800Å at the redshift of the sample. These bands are known to show strong iron emission which are suppressed by such telluric absorption (see the example spectrum in Fig. 3 around 4400 and 5500Å). The combined effect of the telluric absorption and the limited achieved for the fainter sources severely affects the correct modeling of their iron emission around H. This, in turn, significantly increases the measurement uncertainties related to H, ultimately making H measurements of faint objects less reliable.

Fortunately, the H line shows very similar profiles to H (e.g. Greene & Ho, 2005) which is in accordance with the expected radial ionization stratification of the BLR (Kaspi et al., 2000). Based on these results, we can probe several aspects related to the H line using the more reliable H measurements.

3 Spectral Decomposition

In this section we describe the analysis procedures we used to model the X-Shooter spectra and to obtain continuum and line emission measurements. We discuss separately the analysis of emission corresponding to the continuum, the blended iron features, and the emission line components. All the spectral modeling is done by employing the Levenberg-Marquardt algorithm for minimization, using the python based spectroscopic analysis package pyspeckit (Ginsburg & Mirocha, 2011). The fitting is preformed in the rest frame, after shifting the spectra using the improved SDSS redshifts provided by Hewett & Wild (2010). We chose to use these redshifts, instead of using the O iii]  line observed within the X-Shooter data, because of the limited quality of the relevant data and modeling of the H-O iii]  spectral region (see §2) and the weak or absent O iii]  emission in many of our sources.

3.1 Continuum Emission

We adopt here two different approaches to account for the continuum emission of the AGN,which we refer to as the local  and global  (thin disk) continuum approaches. The local  continuum attempts to account for the usual approximation of the continuum emission by a single power law when the observed spectrum is limited to a narrow wavelength range. The global  thin disk continuum, on the other hand, corresponds to the more physically-motivated AD model, that was obtained through a Bayesian analysis taking advantage of our wide spectral wavelength coverage (see paper I). A comparison of the measurements obtained with both approaches will allow us to quantify the possible bias imposed by ignoring the real SED shape, when wide-enough wavelength coverage is not available.

Figure 3: The rest-frame X-Shooter spectrum (top) and main emission line complexes (bottom), over the three X-Shooter bands (UV:left, Optical:middle, Infrared:right), for the source J0143-0056 and the corresponding line fitting using the global  thin disk continuum approach. The observed spectrum is shown in black. The best-fitting continuum is shown in gray. The blue lines represent the additional best-fit iron emission. The red lines represent the additional best-fit models for the emission lines. For the sake of comparison we show the SDSS of the source in cyan.
Figure 4: An example spectrum and spectral decomposition of one of the sources in our sample, J0143-0056 using the local  approach. The top panel presents the rest-frame X-Shooter spectrum and the overall decomposition. The solid black solid line corresponds to the “thin disk” continuum, while the dashed black line illustrates the addition of the Balmer continuum. We highlight the spectral regions surrounding the most prominent broad emission lines (from left to right: C iv in red, Mg ii in green, H in blue, and H in magenta). The bottom panels show in detail the highlighted regions of the top panel as well as the individual local  continuum determinations. Continuum fitting is in gray. Continuum plus iron emission fitting is in blue. Continuum plus, iron plus line fitting in red. Observed spectrum is in black.

3.1.1 Local continuum approach and Biases

The local  continuum approach consists of separately fitting the continuum emission surrounding each of the lines of interest. For every source in the sample, each of these continua is approximated by a single power law, which connects neighboring spectral windows known to have little line contamination. Our specific choice of such line-free continuum bands rely on several similar works (S07,TN12), and are listed in Table   1.

Line Complex ——— Continuum windows ———-
Si iv+O iv] 1340-1360Å 1420-1460Å
C iv 1420-1460Å 1680-1720Å
C iii] 1680-1720Å 1960-2020Å
Mg ii 2650-2670Å 3030-3070Å
H 4670-4730Å 5080-5120Å
H 6150-6250Å 6950-7150Å
Table 1: Spectral pseudo-continuum windows used for our line fitting procedure under the local  continuum approach. For each object, we manually adjusted the continuum bands, using the listed wavelength ranges as a reference.

The most important bias in the local  approach is that it commonly uses non real continuum windows that are affected by either (1) weak line emission flux such as the continuum window at 1700Å that is used for C iv line fitting, (2) iron continuum emission that affects continuum windows around 2600Å and 3000Å, as well as those around 4650Å and 5100Å that are respectively used for Mg ii and H line fitting and finally, (3) the Balmer continuum (BC) emission, at Å, which can significantly affect Mg ii measurements, and to a lesser extent even C iv measurements. All these biases are in the direction of an overestimation of the continuum emission when the local  approach is used which will translate into FWHM and line flux underestimation.

An additional bias comes from the shape of the SED, particularly at the turn over of most spectra at around 1000-1500Å (exact wavelengths depend on BM mass, spin and accretion rate, see Papers I and III). The simple power-law approximation to the SED does not remain valid over this range and may lead to measurement biases of the line profile properties of C iv and Si iv+O iv]   (hereafter Si iv+O iv]). In this paper we use our AD SED fittings to quantify these biases.

3.1.2 Thin Disk continuum approach

The global  AD approach is based on the best fits from the thin-accretion-disk continuum models obtained for each of the sources in Papers I and III. For the analysis in this paper we do not consider the two objects with no satisfactory fits to the thin disk continuum model.

As explained in paper I and III, the SEDs of the AD models used in this work are determined by , the accretion rate (), the spin () and the inclination of the disc with respect to the line-of-sight (). We adopted a Bayesian procedure to fit the thin AD model spectra to the observed X-shooter SEDs.  and  were taken as priors with Gaussian distributions centered on the observed values, obtained from H and  measurements (following the procedures described in this paper), and with standard deviations of 0.3 and 0.2 dex, respectively.

Within the global  continuum approach we also consider the BC emission that peaks near the Balmer edge (3647Å) and gradually decreases towards shorter wavelengths. The Balmer continuum model we used is based on calculations of the photo-ionization code ION (Netzer, 2006) with an H-atom containing 40 levels, solar abundances, hydrogen density of , column density of and ionization parameter of . The exact shape is insensitive to the exact value of these parameters and the normalization is done by direct fits to the observations.

An additional contribution to the continuum emission is due to starlight, mostly at wavelengths longer than about 6000Å. For our AGN sample such a contribution is marginal in 32 out of 39 objects and does not severely affect the continuum level and shape of the AGN SED as discussed in paper I and III ( 3% at 6200Å ). For the 7 fainter objects we used the method described in paper III which assumes a template from an 11 Gyr old stellar population to model the host galaxy emission. The scale factor of the template is determined from the ratio of the measured and the median value of the distribution of the 29 brightest objects, as discussed in paper III. The host galaxy contribution is subtracted before the thin disk continuum fitting for those objects which require this correction. We find that in this sub-sample the host galaxy contribution is between 6% and 50% at 6200Å and smaller than 3% at 3000Å. We also tested several stellar populations in the age range from 1 to 11 Gyr, but we find no significant changes in the corrected spectrum (see paper III for details).

Finally, combining the X-Shooter spectra obtained by three different arms (UV, Optical and NIR) may introduce additional uncertainties. As explained in Paper I, in most cases, the overlap and connection between the VIS and UVB arms are satisfactory, with no need for further adjustments but this is not the case for the VIS-NIR joint, as can be seen for J0043 in Fig. 3. For several objects, the slope of the VIS arm was adjusted based on comparison to SDSS (see Paper I for more details). We therefore allow our fitting to rescale the global  continuum up to 10% in each of the regions covered by each arm (1200-2200Å, 2200-4000Å, 4000-9000Å) to take into account the arm calibration uncertainties.

3.2 Blended iron lines

For an adequate modeling of H and Mg ii line profiles it is crucial to first subtract the iron line emission, originating from a large number of blended features of Fe ii and Fe iii. Generally, this is done by choosing the best-fit broadened, shifted and scaled empirical iron line template. We constrain line center shifts to be smaller than 1000 km s and broadening is constrained to the range 1000-20000 km s. For the optical region around H (4000-7000Å) we used the iron template from Boroson & Green (1992). For the UV region around Mg ii (1700-3647Å) we initially used the Tsuzuki et al. (2006) template (hereafter T06). However, the fits obtained using this template was not satisfactory, mainly due to an over-estimation of the continuum emission. We therefore built a new iron template (see Apppendix B and figure 13) based on the spectrum of I Zw 1 reported by T06, which is a composite of their UV (HST) observation and the optical (KPNO) observation reported by Laor et al. (1997).

One of the main differences between the local  and global  approaches is that under the local  approach different scaling factors for the UV iron template at each side of the Mg ii line are required in order to guarantee an acceptable match to the observed spectrum. The scale factor in the red side of Mg ii is found to be always larger than the one for the blue side, but by no more than 10%. This type of correction is not needed in the global  approach, when the complete continuum model (AD+BC) is considered. Given that under the local  approach the BC cannot be accounted for directly and that the BC is monotonically increasing from 2200 to 3647Å, we suspect that the larger scale factor in the red side of Mg ii might be due to the BC and not to intrinsic changes in iron line emission.

3.3 Emission Line Measurements

For the emission line modeling we have followed a procedure similar to the one described in TN12 (see their appendix C) and Shang et al. (2007) In short, after removing the continuum emission (following either the local  or global  approaches) and the iron template, we model the prominent broad emission lines with two broad Gaussian components. We allow for a range of line widths and shifts for each component, where the FWHM ranges between 1000 km s and 10000 km sand the line shifts are limited to for the H, H and Mg ii lines, while for the C iv line we allowed blue-shifts of up to -3000 km s. These different choices are motivated by the findings of several earlier studies (e.g., Vestergaard & Peterson (2006), S07, R13, Park et al. (2013)). In the case of doublet lines (C iv and Mg ii), we used 4 Gaussians, forcing the two broad and two narrower components to have the same profiles and intensity, and the theoretical wavelength separation. We fixed the Mg ii and C iv doublet intensity ratios to 1:1, suitable for optically thick line emission. For each of the H, H and C iv lines we have also included a third Gaussian component when needed to account for the additional emission originating from the narrow line region (NLR). Each of these narrow components are modeled by a single Gaussian profile, their FWHM is constrained not to exceed 1300 km s, and their line centers are tied to each other, with shifts of 400km s, at most. We chose not to include a narrow component in the modeling of the Mg ii and C iv lines (as in, e.g., Wills et al., 1993; Sulentic et al., 2007), since we found no significant difference in the Mg ii measurements (or fit quality) when trying to include it.111For example, for C iv we find that a narrow component typically contributes , and at most , of the total line luminosity. For other, weaker emission lines (including He ii1640, N iv1718, Si iii]1892) we used only a single Gaussian component. These lines are not necessary for the purpose of the present work except for limiting the continuum placement. More accurate modeling of these lines will be a topic of the fourth paper in this series.

All the Gaussian components we used are symmetric and defined by three parameters: peak flux density, FWHM, and central wavelength. We have made several simple, physically motivated simplifying assumptions, in order to minimize the number of free parameters: the Gaussian components of lines of the same species were forced to share an identical width; we have also tied together the relative shifts in the central wavelengths of some lines, based on their laboratory wavelengths; and assume line-intensity ratios for some lines based on their statistical weights (See Appendix  D and Table 9 for further details on the different emission line parameters, their assumed ranges, inter-connections and delimitation of the emission line regions). Our line fitting procedure runs separately on each of the main emission line regions, while all the lines in each line region are fitted simultaneously.

Generally, the global  (see Figure 3) and local  (see Figure 4) continuum approaches follow the same line fitting procedures in terms of the number of components per emission line and the way they are tied together. One important difference is that in the global  approach, the C iii] and C iv line regions are considered a single region and are therefore fitted simultaneously. The reason for this is that under the local  approach we take as continuum windows the region around 1700Å  following the same procedure of previous works (e.g., S07, TN12, and references therein). However, this region is usually contaminated by weak emission lines like N iv1718, and consequently the thin disk continuum fit does not allow us to fit C iv and C iii] independently.

In order to account for possible uncertainties in our spectral measurements, we performed 100 Monte-Carlo realizations for each of the spectra. In each of these realizations, the flux density at each spectral pixel was altered from the observed value by a random, normally distributed value, assuming the corresponding level of noise (i.e., using the noise spectrum). From these sets of best-fit models we extracted, for each emission line, the line width FWHM, the velocity dispersion (; following Peterson et al. (2004)), integrated luminosity (), rest-frame equivalent width (EW), the luminosity at the peak of the fitted profile () as well as its corresponding wavelength () and the offset of the line center (relative to the laboratory wavelength; ). The line offsets were calculated using the flux-weighted central wavelength of the broad line profile:

(2)

where is the flux density of the broad line profile at ; is the integrated broad line flux, ; is the laboratory wavelength of the line; and is the speed of light.

The best-fit values for all these parameters were taken from the medians of the parameter distribution, and the corresponding uncertainties were estimated from the central 68%  percentiles. This “re-sampling” approach for the estimation of measurement-related uncertainties was used in several recent studies of spectral decomposition of AGN UV-optical spectra (e.g., Shen & Liu, 2012). Based on our experience, such errors reflect the true uncertainties related to measuring emission line profiles, while those provided by the (statistical) spectral fitting procedure itself tend to underestimate the “real” uncertainties.

The measured parameters, and uncertainties, for the most prominent emission lines under the local  approach are summarized in Tables 2 and 3 .  The data is also available at http://www.das.uchile.cl/~jemejia/big_table_mass_paper.tar.gz which contains the plain text tables with these quantities in the local  and global  approaches as well as the FWHMs and s that we measured using the archival SDSS spectroscopy that covers both the C iv and Mg ii lines.

Object —————————— ————–————– ————————————-————————————-
name 1450 3000 5100 6200 H Si iv+O iv] C iv C iii] C iv Mg ii H H
J1152+0702 46.81 0.01 46.55 0.01 46.11 0.01 46.17 0.01 44.8 0.01 43.15 0.02 43.43 0.01 42.94 0.16 -2452.68 104.71 -97.53 101.35 1042.62 148.83 -79.15 70.63
J0155-1023 46.62 0.01 46.41 0.01 46.13 0.01 46.07 0.01 44.87 0.01 43.17 0.01 43.29 0.01 42.88 0.07 -2294.86 123.19 -139.62 75.73 510.34 86.22 -172.03 90.25
J0303+0027 46.53 0.01 46.36 0.01 46.03 0.01 45.99 0.01 44.79 0.02 43.01 0.02 43.21 0.01 42.49 0.27 -484.41 61.98 157.4 123.36 1094.57 53.3 -386.05 193.83
J1158-0322 46.52 0.01 46.35 0.01 46.08 0.01 45.99 0.01 44.82 0.01 43.02 0.03 43.22 0.01 42.83 0.05 -1775.53 40.87 -4.04 66.53 -1067.76 168.86 -534.82 64.61
J0043+0114 46.46 0.01 46.26 0.01 45.93 0.01 45.89 0.01 44.68 0.01 42.9 0.03 43.11 0.01 42.87 0.06 -2823.52 102.51 -340.23 67.91 -583.57 94.8 -330.63 51.76
J0209-0947 46.56 0.01 46.38 0.01 46.09 0.01 46.01 0.01 44.86 0.01 43.05 0.01 43.47 0.01 42.95 0.03 -1534.54 19.99 -109.47 74.22 668.06 296.98 -328.73 105.64
J0842+0151 46.39 0.01 46.21 0.01 45.79 0.04 45.78 0.02 44.74 0.02 42.97 0.05 43.24 0.01 42.81 0.08 -2393.53 53.53 -249.3 65.66 488.33 346.79 -545.4 222.08
J1002+0331 46.55 0.01 46.29 0.01 45.99 0.01 45.97 0.01 44.83 0.01 42.02 0.39 43.34 0.03 43.27 0.02 -1425.91 67.7 -224.11 84.88 771.98 121.85 127.18 72.02
J0323-0029 46.51 0.01 46.27 0.01 45.95 0.01 45.92 0.01 44.81 0.01 43.03 0.02 43.37 0.01 43.14 0.02 278.52 85.01 -477.62 92.79 674.22 97.41 -141.79 107.94
J0152-0839 46.31 0.01 46.11 0.01 45.83 0.01 45.69 0.01 44.56 0.01 42.7 0.02 43.02 0.01 42.57 0.09 -2152.61 48.73 -245.03 100.87 -523.93 142.87 -512.4 104.87
J0941+0443 46.27 0.01 46.08 0.01 45.79 0.02 45.74 0.01 44.68 0.01 42.73 0.02 43.11 0.01 42.6 0.09 306.62 92.72 -27.67 138.44 -174.21 401.45 -191.83 45.64
J0148+0003 46.4 0.01 46.38 0.01 46.11 0.02 46.07 0.01 44.97 0.01 42.85 0.07 43.05 0.08 42.92 0.06 -933.05 104.45 -60.68 95.14 799.06 63.93 -360.83 64.41
J0934+0005 46.15 0.01 45.92 0.01 45.68 0.01 45.62 0.01 44.43 0.01 42.7 0.02 42.77 0.02 42.62 0.06 -2156.93 71.57 -155.35 80.23 556.3 140.5 -449.29 174.13
J0019-1053 45.89 0.01 45.78 0.01 45.4 0.01 45.39 0.01 44.26 0.01 42.33 0.03 42.79 0.01 42.35 0.09 -571.41 38.73 269.01 71.92 789.89 108.23 725.37 59.2
J0850+0022 45.8 0.01 45.73 0.01 45.52 0.01 45.48 0.01 44.14 0.01 42.8 0.02 42.85 0.02 42.53 0.12 -2754.99 225.22 -41.26 125.73 316.41 196.98 -1044.97 142.74
J0404-0446 45.9 0.01 45.72 0.01 45.62 0.03 45.46 0.02 43.92 0.05 42.79 0.02 42.71 0.01 42.51 0.12 -3440.87 99.7 -214.1 86.61 -435.09 451.73 -560.96 145.65
J1052+0236 45.78 0.01 45.7 0.02 45.44 0.02 45.39 0.02 44.21 0.03 42.14 0.14 42.59 0.06 42.07 0.07 -70.84 116.54 263.36 147.25 1059.5 215.22 475.95 166.7
J0223-0007 45.86 0.01 45.67 0.01 45.32 0.06 45.28 0.05 44.19 0.04 42.4 0.02 42.7 0.01 42.36 0.03 -1568.3 56.19 7.56 99.2 -481.33 692.18 -404.17 271.04
J0240-0758 45.89 0.01 45.76 0.01 45.43 0.02 45.36 0.01 44.32 0.01 42.51 0.02 42.98 0.01 42.53 0.03 -293.37 33.52 185.33 57.24 478.62 212.48 710.93 26.89
J0136-0015 45.80 0.01 45.64 0.01 45.28 0.03 45.2 0.01 44.12 0.02 42.48 0.13 42.59 0.01 42.33 0.04 -2756.36 79.89 -318.27 89.48 656.58 232.12 -648.21 114.67
J0213-1003 46.2 0.01 45.93 0.01 45.64 0.02 45.58 0.01 44.39 0.01 42.98 0.05 42.98 0.01 42.65 0.04 -1739.83 261.66 -27.74 144.11 -360.87 278.85 -666.62 72.89
J0341-0037 45.73 0.01 45.56 0.01 45.3 0.03 45.22 0.03 44.12 0.03 42.39 0.02 42.6 0.01 42.33 0.03 -2330.08 129.88 -222.25 102.02 -840.53 688.41 -536.48 261.4
J0143-0056 45.72 0.01 45.52 0.01 45.18 0.02 45.1 0.04 43.99 0.04 42.35 0.03 42.73 0.01 42.24 0.06 -524.69 40.00 264.87 77.58 396.95 199.42 587.99 149.68
J0927+0004 45.74 0.01 45.51 0.01 45.18 0.02 45.18 0.01 44.04 0.02 42.33 0.03 42.71 0.01 42.17 0.09 486.01 220.26 72.03 72.29 1010.25 278.06 345.72 94.13
J0213-0036 45.64 0.01 45.46 0.01 45.15 0.02 45.12 0.02 44.11 0.01 42.29 0.05 42.86 0.01 42.29 0.04 -643.71 19.59 137.23 103.97 174.78 261.3 27.18 206.44
J1050+0207 45.61 0.01 45.43 0.02 45.12 0.06 44.94 0.03 43.89 0.03 41.89 0.07 42.36 0.03 41.92 0.07 -591.26 218.74 443.37 152.79 122.92 566.2 526.65 337.22
J0948+0137 45.43 0.01 45.3 0.02 45.03 0.04 45.02 0.05 43.96 0.03 42.09 0.11 42.53 0.02 42.13 0.08 -961.26 106.85 176.82 190.95 -62. 414.8 -424.22 354.05
J0042+0008 45.42 0.01 45.21 0.01 44.87 0.05 44.76 0.03 43.67 0.04 41.95 0.2 42.21 0.08 41.81 0.02 -1683.76 138.32 -312.02 99.56 697.42 205.71 26.51 160.33
J1013+0245 45.38 0.01 45.18 0.02 45.08 0.04 45.01 0.03 43.59 0.05 42.03 0.07 42.19 0.01 41.95 0.09 -1110.04 244.02 -113.76 240.13 -1167.31 1020.54 -197.79 213.94
J1021-0027 44.96 0.02 44.97 0.01 44.78 0.05 44.89 0.02 43.88 0.01 42.02 0.04 42.35 0.25 41.83 0.01 206.99 527.72 -219.52 49.35 1100.26 105.14 -925.29 101.62
J0038-0019 45.1 0.01 44.97 0.01 44.78 0.04 44.81 0.02 43.45 0.02 41.51 0.12 42.21 0.05 41.65 0.04 51.63 92.82 18.95 162.72 -647.1 338.03 445.16 83.86
J0912-0040 45.11 0.01 44.93 0.01 44.71 0.12 44.73 0.05 43.44 0.04 41.67 0.14 42.17 0.38 41.58 0.09 -1396.33 110.18 -79.1 162.0 600.7 567.47 -116.43 117.77
J1048-0019 45.09 0.02 44.88 0.01 44.57 0.08 44.32 1.9 43.2 0.25 41.69 0.1 42.22 0.21 41.53 0.06 -322.86 79.87 -190.12 165.63 241.99 335.73 270.64 155.81
J1045-0047 44.92 0.03 44.79 0.02 44.31 0.06 44.43 0.05 43.37 0.03 41.14 0.37 42.02 0.23 41.36 0.07 -990.37 115.71 -37.63 155.99 -158.89 564.79 66.88 89.9
J0042-0011 44.87 0.02 44.77 0.01 44.63 0.07 44.47 0.05 43.06 0.04 41.62 0.09 41.92 0.17 41.37 0.02 -2104.9 83.54 -341.65 209.76 327.91 322.67 -169.64 73.31
J1046+0025 44.97 0.01 44.7 0.02 44.42 0.1 44.41 0.1 42.48 0.12 41.66 0.09 42.07 0.34 41.43 0.05 -1255.21 69.88 -791.01 175.69 -801.5 452.36 -1299.09 125.12
J0930-0018 44.81 0.02 44.66 0.02 44.36 0.97 44.11 0.11 42.95 0.26 41.4 0.25 41.98 0.28 41.38 0.03 -1115.71 371.44 -878.01 115.31 -1023.75 423.79 -996.61 147.11
J1108+0141 46.53 0.01 46.47 0.01 46.2 0.01 46.09 0.01 44.82 0.01 43.1 0.03 42.95 0.02 42.93 0.06 -523.43 73.63 -729.27 47.84 1298.13 19.36 -354.62 45.75
J1005+0245 45.96 0.01 46.05 0.01 45.87 0.01 45.89 0.01 44.74 0.01 42.57 0.13 42.75 0.04 42.79 0.03 -1202.56 828.92 11.81 79.42 1257.99 96.71 126.41 100.23
Table 2: Monochromatic continuum luminosities (), line peak luminosity densities () and line offsets (), under local  approach 
Object ————————–————————– ————————–————————– ——————–——————–
name C iv Mg ii H H C iv Mg ii H H C iv Mg ii H
J1152+0702 6573.17 133.06 3202.24 135.98 4729.64 270.58 4283.31 240.51 3870.09 351.63 2165.29 179.2 4611.16 79.61 3186.29 246.89 9.65 0.02 9.47 0.04 9.44 0.06 9.48 0.05 9.32 0.06
J0155-1023 6581.92 92.02 3468.25 66.93 5458.28 139.76 4785.95 115.95 5553.35 131.83 2113.16 129.33 2601.71 50.29 4010.01 147.36 9.54 0.01 9.46 0.02 9.58 0.03 9.51 0.02 9.46 0.03
J0303+0027 5913.74 185.57 4790.24 136.5 7342.45 165.96 6229.92 99.96 3856.09 381.76 2519.43 219.8 3883.75 61.91 4897.97 308.97 9.39 0.03 9.7 0.03 9.77 0.02 9.69 0.02 9.64 0.02
J1158-0322 4836.3 72.18 3375.87 132.76 5192.01 408.19 4854.6 169.2 2678.57 52.06 1900.87 106.72 4516.99 348.21 4114.39 261.77 9.21 0.01 9.39 0.04 9.5 0.08 9.47 0.03 9.44 0.04
J0043+0114 7323.78 120.88 3379.59 93.25 4057.87 492.7 3227.27 123.33 3928.23 0.0 2508.89 204.13 5328.8 93.02 3633.45 83.24 9.54 0.02 9.34 0.03 9.19 0.12 9.06 0.04 9.01 0.04
J0209-0947 5032.08 56.01 2900.08 64.16 5124.13 278.41 4722.6 176.26 4030.67 60.19 2298.9 145.81 4313.91 330.76 3973.72 146.8 9.26 0.01 9.28 0.02 9.5 0.06 9.46 0.04 9.44 0.04
J0842+0151 6524.91 109.83 3951.92 128.07 5231.26 563.34 4955.88 55.58 3625.84 233.43 2044.7 165.81 4408.65 196.49 5900.66 136.71 9.39 0.02 9.45 0.03 9.32 0.12 9.36 0.02 9.42 0.02
J1002+0331 5017.31 439.6 2563.88 69.75 5464.7 596.11 4738.24 81.6 2445.63 42.2 1854.53 235.07 4000.48 125.61 3315.12 276.48 9.26 0.08 9.12 0.03 9.49 0.11 9.44 0.02 9.43 0.02
J0323-0029 5189.8 68.08 1889.87 69.24 2990.6 446.07 3127.0 668.27 3283.82 57.48 3206.57 47.72 3441.97 173.99 2955.2 188.82 9.26 0.01 8.84 0.04 8.94 0.14 9.05 0.22 9.05 0.21
J0152-0839 6481.41 69.84 3116.09 158.2 4306.36 340.16 4813.74 164.25 3754.43 348.65 2110.44 186.45 3871.83 228.1 5716.66 259.13 9.34 0.01 9.18 0.05 9.18 0.08 9.28 0.03 9.29 0.04
J0941+0443 7721.23 63.08 4218.07 286.42 6151.72 308.41 6520.48 120.97 3811.46 34.47 2948.63 94.8 3823.26 430.01 4161.47 141.57 9.46 0.01 9.42 0.07 9.46 0.06 9.58 0.02 9.62 0.02
J0148+0003 6662.44 1461.18 4542.74 183.5 6474.99 340.44 5411.48 67.74 3844.55 258.27 2278.39 233.47 3458.09 114.54 4510.4 185.17 9.42 0.22 9.67 0.04 9.72 0.06 9.62 0.01 9.62 0.01
J0934+0005 6536.46 282.31 2806.89 57.93 2880.02 144.81 2694.27 163.45 2702.42 0.0 1635.09 235.95 2573.13 254.74 2995.19 596.9 9.25 0.04 8.98 0.02 8.73 0.05 8.73 0.06 8.71 0.06
J0019-1053 5219.79 89.76 4425.79 76.59 5708.5 376.28 5908.82 506.23 3484.23 195.22 2818.44 115.48 2849.73 479.65 4694.24 467.45 8.9 0.02 9.28 0.02 9.15 0.07 9.27 0.09 9.3 0.08
J0850+0022 6115.68 272.63 2415.05 123.67 3503.46 960.02 3763.47 419.19 2905.3 123.92 1749.98 437.53 4858.84 322.37 3435.86 135.78 8.98 0.04 8.73 0.05 8.8 0.29 8.93 0.11 8.84 0.11
J0404-0446 4341.32 304.12 1965.55 50.96 2788.42 1363.96 2731.63 140.01 1841.37 99.93 1666.83 264.0 867.64 230.43 6567.38 769.42 8.74 0.06 8.54 0.03 8.66 0.6 8.64 0.06 8.43 0.08
J1052+0236 9627.85 852.07 5412.1 422.04 10110.01 1132.0 8117.99 338.71 5192.56 272.53 2701.9 339.79 5726.97 567.53 4513.15 408.93 9.37 0.08 9.41 0.08 9.66 0.11 9.54 0.05 9.55 0.05
J0223-0007 5239.8 174.63 3077.91 80.99 3416.23 549.13 5009.03 271.49 3500.23 374.37 2425.53 288.24 5199.39 403.63 5461.09 1392.14 8.88 0.03 8.9 0.03 8.65 0.19 9.05 0.08 9.12 0.07
J0240-0758 5858.64 135.99 2827.82 94.14 3542.36 445.25 4189.8 158.88 3013.8 32.58 2184.61 133.16 5569.2 275.57 4136.64 445.19 9.0 0.02 8.88 0.03 8.75 0.13 8.95 0.04 9.03 0.04
J0136-0015 7051.94 114.59 3553.55 86.89 2730.93 1000.53 3467.62 276.33 4489.88 434.54 2248.54 192.31 3648.03 195.22 5068.74 586.32 9.1 0.02 9.01 0.03 8.43 0.42 8.68 0.08 8.76 0.08
J0213-1003 5093.2 167.27 2741.59 251.38 3392.86 279.21 4054.31 192.65 3523.3 932.25 1939.26 287.79 4174.0 871.34 4579.36 117.79 9.06 0.03 8.96 0.09 8.85 0.08 9.06 0.05 9.05 0.05
J0341-0037 5246.89 130.51 2571.38 106.3 3218.83 2612.53 3405.73 610.87 3982.5 398.66 1901.38 277.54 3567.48 736.67 4447.75 907.79 8.8 0.02 8.68 0.04 8.58 1.47 8.68 0.19 8.74 0.19
J0143-0056 3890.11 76.91 2856.85 107.36 5509.54 1371.7 3894.47 570.51 3277.0 107.64 1400.35 212.49 1876.82 121.42 4417.88 1204.3 8.54 0.02 8.75 0.04 8.97 0.26 8.72 0.16 8.78 0.16
J0927+0004 8307.68 152.96 5663.93 202.87 7418.97 915.99 6255.58 148.7 4555.5 291.75 2477.82 189.86 4265.65 355.71 4497.04 557.7 9.21 0.02 9.34 0.04 9.23 0.13 9.18 0.03 9.23 0.03
J0213-0036 4063.84 101.99 3462.69 155.4 5697.36 1018.59 4458.74 171.6 2719.59 41.51 1811.81 159.25 2680.4 569.02 4997.53 672.0 8.53 0.02 8.88 0.05 8.98 0.19 8.85 0.04 8.97 0.04
J1050+0207 7608.29 816.82 4888.94 762.65 5204.91 1493.81 5402.67 504.92 4416.38 210.67 2409.78 196.71 2442.51 345.5 5260.54 706.67 9.06 0.1 9.15 0.16 8.88 0.33 8.9 0.1 9.01 0.1
J0948+0137 5115.62 251.64 3363.61 331.15 3766.11 728.57 3880.89 392.36 3292.57 178.85 1997.33 367.65 3373.17 769.02 2879.06 1025.66 8.6 0.05 8.75 0.1 8.54 0.21 8.67 0.13 8.77 0.11
J0042+0008 5362.14 347.78 2943.94 120.79 4020.34 345.5 3607.54 160.39 4970.52 292.54 1843.64 224.51 4028.2 473.32 5323.33 540.12 8.64 0.06 8.58 0.04 8.5 0.11 8.44 0.06 8.54 0.06
J1013+0245 8990.08 304.21 4603.49 709.46 8395.63 1030.61 7716.39 872.62 5124.06 469.07 2678.99 213.54 6546.57 3016.95 3037.51 291.49 9.07 0.04 8.95 0.16 9.27 0.14 9.25 0.12 9.15 0.14
J1021-0027 4912.88 628.93 3260.01 159.14 9085.38 1675.61 8817.56 719.31 2790.07 342.82 2409.75 157.98 5060.65 525.81 4593.35 183.54 8.29 0.13 8.52 0.05 9.15 0.21 9.29 0.09 9.43 0.08
J0038-0019 4332.98 333.19 2656.77 189.51 3557.91 284.34 3303.65 118.2 3397.61 353.28 2036.88 227.39 5494.81 663.5 2146.07 272.75 8.26 0.08 8.35 0.07 8.33 0.1 8.39 0.04 8.34 0.04
J0912-0040 4884.79 331.59 3859.93 251.59 5803.7 3022.45 4746.34 227.74 3198.91 193.24 2002.02 195.75 2164.52 213.84 2015.46 581.81 8.37 0.07 8.65 0.07 8.71 0.73 8.66 0.07 8.65 0.07
J1048-0019 4755.88 649.8 2901.43 155.43 2278.84 350.3 2966.74 1312.75 3167.81 288.13 2260.65 203.08 967.48 372.04 1261.05 249.41 8.34 0.14 8.37 0.06 7.81 0.2 7.99 0.136 8.11 0.71
J1045-0047 6027.95 520.11 2832.87 308.37 9706.63 3147.47 4724.3 403.71 3841.54 183.51 2202.59 227.6 6403.41 1425.91 2820.17 151.58 8.44 0.1 8.29 0.11 8.9 0.38 8.46 0.11 8.6 0.1
J0042-0011 4197.93 217.44 1829.42 210.0 1578.09 122.63 1489.82 95.27 2929.25 161.1 1097.93 599.1 1701.43 475.43 1177.48 165.01 8.1 0.06 7.9 0.11 7.52 0.12 7.49 0.09 7.42 0.08
J1046+0025 3971.3 481.38 3210.69 164.83 4319.81 1113.03 3382.7 584.84 2915.58 146.4 2207.23 226.84 1013.97 984.74 1003.89 196.21 8.11 0.12 8.35 0.06 8.26 0.33 8.16 0.24 7.81 0.24
J0930-0018 6704.04 856.67 5058.85 416.66 7035.13 796.99 6079.72 7366.64 4590.25 423.08 3059.34 415.94 842.29 247.30 1508.94 1415.15 8.47 0.13 8.72 0.09 8.65 0.496 8.48 0.106 8.59 0.134
J1108+0141 7468.9 410.2 2601.39 91.7 4093.15 591.92 4750.88 63.75 3350.98 125.47 2830.93 118.89 3947.92 434.39 4184.72 134.75 9.59 0.05 9.24 0.04 9.37 0.14 9.52 0.01 9.42 0.02
J1005+0245 6095.34 1550.64 2475.74 144.98 3878.66 3284.9 5050.79 198.95 4574.16 821.83 1745.09 154.14 4291.27 196.04 4053.76 188.6 9.07 0.26 8.94 0.06 9.11 1.64 9.45 0.04 9.44 0.04
   measurements obtained through FWHM(H) and .
   measurements obtained through FWHM(H) and .
Table 3: Broad line widths and corresponding mass estimates, under the local  approach 
Figure 5: Comparison of various line and continuum properties measured under the two general assumptions of local  (horizontal axis) and global  (vertical axis) SEDs. Top-Left panel: (blue stars), (cyan triangles),  (yellow triangles),  (green squares) and  (red dots). The colored solid lines are the best linear fits to the corresponding data. Top-Right panel: FWHM(H) (top-left), FWHM(H) (top-right), FWHM(Mg ii) (bottom-left) and FWHM(C iv) (bottom-right) lines measurements. Bottom-left panel: Same as Top-Right panel but comparing s instead of FWHMs (note the much larger scatter in this case). Bottom-right panel:  comparison between local  and global  approaches. In the top-right and bottom-right panels black dashed lines represents the median offset between global  and local  measurements. In all panels the black solid diagonal line represents the 1:1 relation. Points have been color-coded in gray scale by S/N where darker colors correspond to larger S/N.
Line
(dex) (dex) (dex) (dex)
H
H
Mg ii
C iv
Table 4: Median induced offsets when the local approach is used instead of the global  approach.

4 Results and Discussion

4.1 Local versus global continuum measurements

In this subsection we compare the local  and global  continuum approaches in order to quantify the possible biases that are introduced when the real underlying shape of the continuum cannot be accurately established. As we will describe below in detail, our main conclusion is that local  continuum measurements of FWHMs, continuum luminosities and, consequently, black hole masses present very small but systematic offsets with respect to the corresponding global  continuum measurements.

4.1.1 Continuum biases

In figure 5 we present the comparison between  and  (top-left panel) for different chosen wavelengths. We generally find small but systematic offsets between quantities derived via the local  versus global   approach. We find that the , ,  and  median offsets () are typically small ( dex, see Table 4 for details). These offset are consistent with a very subtle overestimation of the continuum emission when the local  approach is adopted (see Fig. 4 for a particular example).

4.1.2 Line width biases

The systematic continuum overestimation that we found coming from adopting the local  instead of the global  approach will naturally lead to systematical FWHM underestimation as can be also seen in Figure 5 (top-right panel). Indeed, all the relevant line width measurements present small median offsets ( ) smaller than dex as can be seen in Table. 4. As mentioned in §2 the measurements of FWHM(H) are more challenging for low S/N and/or objects where most iron emission is suppressed by telluric absorption. This explains the outliers and large uncertainties for some objects in the FWHM(H)-FWHM(H) plot. Except for these few outliers, the FWHM measurements of all the emission lines are proportional to, and systematically but slightly smaller than the FWHM measurements.

When we perform the same analysis on the velocity dispersion  (see the bottom-left panel in Fig. 5) we find a large scatter ( dex) and usually weak, if any, correlations () between the local  and global  measurements in H, Mg ii and C iv. On the other hand, the H line shows a much tighter correlation (, ) but the scatter is still very large ( dex). These results indicate a strong and perhaps non-linear dependency between the measured  and the level of its local continuum. As a result -based determinations of  may be unreliable for data of limited spectral coverage. In particular, such estimates may suffer from higher systematic uncertainties compared to those based on FWHM.

4.1.3 Black hole mass biases

In §§4.4 we will describe in detail the methods that we follow for  calibration using the local  and global  approaches. The form of the virial mass estimator (see Eqn. 1) indicates that biases in  determinations are mainly driven by the (small) line width biases. This is not the case for the continuum luminosity since one can, in principle, re-calibrate the relations to use either one of the local  or global  measured continuum luminosities, thus completely eliminating the systematic biases.

After following the procedure described in §§4.4 and the strict virial assumption () we found that the  median offsets () are in very good agreement with our predictions, as can be seen in the bottom-right panel of Figure 5 and are smaller than 0.04 dex (see Table 4). From the values listed in Table 4 and from a visual inspection of Fig. 5 one can conclude that H, Mg ii, and C iv are consistent (within the scatter) with being independent of . H is again a bit more complicated, due to the difficulties we mentioned above. However, after removing the low-quality outliers we eventually find H to be consistent with being independent of . Among all the lines considered here, we find Mg ii to be the one showing the smallest biases when following the local  approach . This is somewhat surprising, given the several important spectral features (BC, FeII lines) that are influencing this spectral region.

4.1.4 Line luminosity biases

Line luminosities are more sensitive to continuum placement than the other quantities we examined. Indeed, we found line luminosity median offsets () of dex , dex, dex and dex for C iv, Mg ii, H and H, respectively. Furthermore, we find that the large scatter that is generally found in , , and is due to the fact that these quantities are anti-correlated with continuum luminosity. In particular, the relations between these line luminosity biases and  show correlation coefficients of -0.38, -0.44, -0.65 for C iv, Mg ii, H and H, respectively. This implies that using the local approach to estimate line luminosities generally leads to an underestimation of the latter, and its effect is larger for low luminosity objects (up to 0.14 dex, or 38%, in the case of C iv).

In summary, the impact of using the local  approach to estimate the local luminosities, lines widths and black hole masses when the global  continuum is unknown is found to be small ( dex). However, the impact using the local  approach to estimate line luminosities is found be luminosity dependent, being stronger for low luminosity objects. The median values of , , , and that we found are summarized in Table 4. Based on the general good agreement between local  and global  measurements and in order to provide the community with strategies more applicable to observations with limited wavelength coverage, in the analysis that follows is based only on the local  measurements, unless otherwise stated.

tf

Figure 6: local  H line luminosity (blue),  (cyan)  (green) and  (red) vs . The color solid lines represent the best linear fits to the corresponding data. Black solid line represents the 1:1 relation.
Figure 7: FWHMs (top-panels) and s (bottom-panels) of the C iv (left) and Mg ii (center) profiles found with low quality SDSS data versus those measured in our high quality X-Shooter using the local  continuum approach. The right panels shows C iv vs Mg ii line widths measured with SDSS data. Red solid line shows the 1:1 relation and red dashed line represents . Red dots represent objects with noticeable absorption features while yellow dots are objects with SDSS incomplete profiles. It can be seen that C iv profiles with strong absorption features artificially populate the zone where .

4.2 Luminosity Correlations

Figure 6 presents a comparison between  and the luminosity indicators most commonly used in the context of  estimates. The best-fit parameters of all the correlations can be found in Table 5. These relations provide us with the links necessary to connect each luminosity indicator and , through the relation obtained from reverberation mapping experiments (Kaspi et al., 2000, 2005; Bentz et al., 2009; Bentz et al., 2013). For the purposes of the present work, we use the same calibration as in TN12, which is appropriate for sources with :

(3)

As shown in Fig. 6 the - relation shows a larger scatter than those involving UV continuum luminosities (- and -). This may therefore contribute to an increased uncertainty in -based determinations of . This is not surprising, given the expected range of conditions in the BLR. Consequently, we also investigate use of  as an alternative to . As can be seen in Fig. 6 (cyan inverted triangles) the - relation shows an even smaller scatter than  and . This is particularly the case for objects with , where host galaxy contribution is negligible.

- and - luminosity correlations are supra-linear, in the sense of showing and (see first column of Table 5 and note that ). This has been noted earlier by Vanden Berk et al. (2004) but is in contrast to Shen & Liu (2012) who found consistency with in the sample of high luminosity quasars ().

While there are various correlations with  and  (measured from H) that can, perhaps, explain these differences, it is important to note that our sample is by no means complete. It was chosen to sample the high-L z1.55 AGN population by giving equal weight to a group of sources with the same  and  (see paper I). Hence, the relationship found here should be checked in a larger and complete sample that represents the entire AGN population.

vs vs vs
A A A
L(H) 1.04 4.73 1.09 3.59 0.94 1.32
0.98 1.23 0.94 1.57 0.96 1.28
1 1 0.89 1.61 1.15 0.60
0.92 0.67 0.91 0.77 1.01 0.88
0.88 0.56 0.87 0.64 1.02 0.87
Table 5: Best fit power law parameters to the following relations:  ,  , .
Figure 8: FWHM (top) and (bottom) comparisons between different lines in the local continuum approach as indicated in the inserts of each panel (line1 vs line2). The black solid lines represents the 1:1 relation. The black dashed line represents . The yellow dashed line represents after rescaling the FWHM of each line to FWHM(H) using the median value of . Red dashed lines represent previous scaling relations (FWHM(H) vs FWHM(Mg ii) from TN12, and FWHM(H) vs FWHM(H) from Greene & Ho (2005)). Blue dashed lines represent the best fit after assuming FWHM(H)FWHM(H)FWHM(Mg ii)FWHM(C iv). Points are color-coded in gray scale by the S/N of the continuum bands around H where darker colors translates into larger S/N. Broad absorption lines quasars (BALQSO, green stars) and the broad-Mg ii objects (magenta diamonds, see §4.3.4) are the main sources of discrepancies of the C iv and Mg ii FWHMs when compared to the H and H FWHMs.

4.3 Line widths and line offsets

4.3.1 Comparison with SDSS data

At the redshift range of our sample, the archival SDSS spectroscopy covers both the C iv and Mg ii lines in 29 out of 39 objects.222For the remaining 10 objects, the only archival spectroscopy available is from the 2SLAQ survey, which is of limited and is not flux calibrated. In Figure. 12 we show an example of the SDSS and X-Shooter spectra in the overlapping region. Comparing SDSS and X-shooter data allow us to test the effects of having only survey-grade data, with limited S/N and spectral resolution, on the measurement of line widths. To this end, we used our C iv and Mg ii fitting code for the lower quality archival SDSS DR7 spectra. In Fig. 7 we compare the FWHM (top-panels) and  (bottom-panels) values of the C iv and Mg ii lines obtained from the SDSS data, with those obtained from our higher quality spectra under the local  approach.  We also show the Spearman correlation coefficients and corresponding -values in each panel.

We find that SDSS-based FWHM(C iv) for objects with absorption features which are unresolved in the SDSS data (4 out of 29 objects, red symbols), or those with partially-observed profiles because of the limited SDSS wavelength coverage (5 out of 29, yellow symbols) result in FWHM measurements which are systematically different from those obtained from the higher quality data. Specifically, while unresolved absorption features are likely to result in a systematic underestimation of FWHM(C iv), by about , incomplete profiles are likely to lead to a systematic overestimation of FWHM(C iv), by about . This result was found in previous works (e.g. Denney et al., 2013; Park et al., 2013; Tilton & Shull, 2013) and could explain, to some extent, the over-population of narrow C iv objects that is reported in TN12. The Mg ii line does not generally show strong absorption features. Indeed, we find that the SDSS-based FWHM(Mg ii) measurements are generally consistent with our higher quality FWHM(Mg ii) measurements with the exception of five objects. Of these 5 objects, three have very low S/N, one has an incomplete profile, and one shows signs of absorption.

Looking into the corresponding comparison with  (bottom panels of Fig. 7), we generally find that sources with absorption features or incomplete profiles do not stand out from the “normal” population. The entire sample shows considerable scatter when comparing the SDSS and X-Shooter line measurements and show less signifcant correlations than the FWHM(top panels of Fig. 7). For , we find the SDSS measurements to be systematically broader than our estimations, and the scatter is larger than the one in the FWHM comparison. For , there is a large dispersion (0.2 dex) between SDSS and X-Shooter measurements, that could be caused by the high sensitivity of  measurements to continuum placement.

We conclude that the usage of  to measure line width in data of limited quality introduces significant scatter. For such data, the use of FWHM is preferred, especially for the Mg ii line. In addition, the absorption features often seen in the C iv line necessitate the use of high-quality spectra, in order to resolve and properly account for these features, even if one uses FWHM instead of .

————————-H————————- ————————-Mg ii————————- ————————-C iv————————-
——-All objects —– —-No Broad-Mg ii ——-All Objects —– —-No Broad-Mg ii ——-All Objects —– —-No Broad-Mg ii 
line1 Q scatter Q scatter Q scatter Q scatter Q scatter Q scatter
H 0.13 0.08 0.69 0.13 0.07 0.81 -0.12 0.14 0.48 -0.11 0.10 0.72
Mg ii -0.13 0.08 0.69 -0.13 0.07 0.81 -0.26 0.10 0.50 -0.25 0.10 0.55
H 0.03 0.07 0.81 0.04 0.07 0.77 0.15 0.10 0.69 0.16 0.08 0.88 -0.10 0.17 0.31 -0.09 0.13 0.44
Table 6: Line width ratios and correlations.
For each pair of lines, we list median values and scatter of and the Spearman correlation coefficients between and . We tabulate these quantities for both the complete sample (under the local  approach ), and after excluding the five broad-Mg ii and the two BALQSO.

4.3.2 Line Offsets

We measured the line offsets with respect to the laboratory wavelengths of H, H and Mg ii. Their absolute values () are found to be (within the 16% and 84% percentiles) smaller than 600 km s, 550 km s and 250 km s respectively.

Many of the observed C iv lines show large negative velocity offsets () suggesting non virial equilibrium of the C iv emitting clouds. This has been noted in numerous earlier publications, (e.g. Shang et al., 2007; Wang et al., 2009; Shen & Liu, 2012; Trakhtenbrot & Netzer, 2012; Runnoe et al., 2013; Brotherton et al., 2015). Moreover, the C iv velocity offsets are anti-correlated with  (, ), i.e., higher  will translate into bluer line centers (e.g. Marziani et al., 2006; Sulentic et al., 2007). We also find that the much smaller velocity offsets of the Mg ii lines are also anti-correlated with  (, ) which is also in agreement with Marziani et al. (2013b). We repeated the analysis using the normalized accretion rate () taken from the best-fit AD models (to be presented in paper III; see paper I for details). We find that our measured , too, is anti-correlated with C iv velocity offsets (, ), however the analogous correlation with Mg ii velocity offsets becomes insignificant (). These results suggest that  is playing an important role in the line offsets of the C iv profile, while Mg ii velocity offsets may involve additional parameters. As explained earlier, the way we selected our sample makes it difficult to make strong statements regarding the entire population of AGN. When the same analysis is done with the Balmer lines, we find no correlation between neither  nor and the Balmer line velocity offsets ( and , for H and H, respectively). We further confirm earlier results (e.g., Corbin, 1990; Richards et al., 2011) of a significant anti-correlation between the C iv blueshifts and the C iv line strength, EW(C iv) (, ), but not with EW(Mg ii) (,).

Several studies investigated the possibility that broad emission lines are gravitationally red-shifted by few hundred to few thousand km s (e.g. Netzer, 1977; Zheng & Sulentic, 1990; Popovic et al., 1995; Müller & Wold, 2006; Tremaine et al., 2014). This effect is enhanced in very broad emission line components () that are formed close to the BH. In this work we made no attempt to include this in the modeling of the line profiles since we are mainly after the line FWHM which is insensitive to such small variations. We verified, however, that line offset due to this effect are smaller than the general uncertainty and scatter associated with our measurements of the line center velocity. We come back to this issue in paper IV (Mejia-Restrepo et al, in preparation).

4.3.3 Line width correlations

Figure 8 presents a comparison between the widths of some of the broad emission lines in our X-shooter observations, in terms of FWHM (top panel) and line dispersion (; bottom panel). For reference, we also illustrate the 1:1 relation (black solid line), and a constant scaling of (black dashed line). The latter scaling is motivated by the typical ratio of the corresponding BLR sizes for H and C iv, as measured in RM experiments, and under the virialized BLR assumption (see detailed discussion in TN12). We have plotted in yellow a dashed line that represents to account for the median FWHM ratio between FWHM(H) and the FWHM of H and Mg ii. Finally, we have color coded the points in gray scale by the S/N of the continuum bands around H where darker colors translates into higher S/N. In Figures 14 and 15 of the Appendix C we show the normalized H, H, Mg ii and C iv observed line profiles in velocity space to provide the reader with a direct visual comparison of the most prominent emission lines. The large error bars in the H line widths are due to the low signal to noise and the difficulty of constraining the iron emission around H, because of the telluric absorption (see §2).

We generally find very good agreement between the FWHMs of H and H (Fig. 8 top-left panel). On average, FWHM(H) is broader than FWHM(H) by 0.03 dex (see blue dashed line in Fig. 8), with a scatter of about 0.08 dex. This result is in good agreement with several previous studies, as well as with the scaling relation reported in Greene & Ho (2005) (see red dashed line in Fig. 8).

We also find that objects with () show FWHM(H) slightly narrower than the median trend (i.e. below the blue dashed line in Fig. 8) by about 0.04 dex (10%). These objects are however fainter and their values are less accurate because of the difficulties with H measurements. This results is in agreement with Denney et al. (2009) where they found that the estimated FWHM(H) in low quality data () is not reliable.

From Fig. 8 we can also see that there are significant correlations between the FWHMs of: 1) H and Mg ii (scatter of dex), 2) H and Mg ii ( dex) and 3) H and H ( dex) in agreement with several previous works (e.g. Greene & Ho, 2005; Shang et al., 2007; Wang et al., 2009; Shen & Liu, 2012; Trakhtenbrot & Netzer, 2012; Marziani et al., 2013a). Also, FWHM(Mg ii) is proportional to and narrower than FWHM(H) by 0.16 dex (30%), with a scatter of about 0.08 dex and no dependence on FWHM(H). There are however some outliers in these general trends: The two BALQSOs (green dots in Fig. 8) and 5 objects that show and have high  (, hereafter broad-Mg iiobjects, magenta diamonds in Fig. 8). These 7 objects and their implications in the FWHM(Mg ii)-Balmer lines correlations are further discussed in §4.3.4.

From the discussion above it is reasonable to assume that the emissivity weighted Mg ii region is more distant from the central BH than the corresponding regions for the H and H lines. On the other hand, both Balmer lines seem to come from the same part of the BLR. As a consequence and based on the FWHM linear correlation among H,H and Mg ii, assuming virialization of H would reasonably imply virialization of Mg ii and H.

The correlations of FWHM(C iv) with the measured FWHM of the other lines are weaker, occasionally insignificant (i.e. P0.01) and non-linear: 1) H (, P, dex), 2) H (insignificant, P) and 3)Mg ii (, P, dex). This would mean that FWHM(C iv) is not linearly proportional to the FWHM of H, H and Mg ii. For example, . Moreover, when combining the results of the RM experiments (e.g. Kaspi et al., 2007) with the virial assumption, it is expected that the C iv line would be broader than H, by a factor of about . 333The scaling factor is somewhat luminosity dependent. See TN12 for a discussion of this issue. In contrast, the vast majority of sources in our sample (35/39; 90%) show and one third of the sources have FWHM(H)FWHM(C iv). These results indicate either a non-virialized C iv emission region, or a very different ionization structure for objects with low and high FWHM(H).

Finally, when we compare the velocity dispersion () between the lines of interest (bottom panels of Fig. 8) we only find one significant correlation between FWHM(Mg ii) and FWHM(C iv) (, P) in the local  approach. However, even this correlation does not hold under the global  approach (). Due to the fact that the correlations between the FWHM of different lines are much tighter than the  correlations (under both continuum approaches), and the fact that  is strongly affected by flux in the line wings, we choose to use the FWHM to estimate  in the analysis that follows.

4.3.4 Broad-Mg ii and BALQSO objects

As discussed in §4.3 we found that Mg ii profiles are generally and systematically narrower than H and H profiles. However, the top right and top center panels of Fig. 8 show that around and () there are a handful of objects (magenta diamonds) that show and were noted earlier as “broad-Mg ii objects”.

Marziani et al. (2013b) and Marziani et al. (2013a) presented a thorough Eigen-vector 1 analysis of the Mg ii and H profiles following Sulentic et al. (2002) from an SDSS selected sample of 680 quasars. Their classification is based on the location of type-I AGN in the -FWHM(H) plane where . They claimed that the so called “Broad-Mg ii objects” belong to the extreme population A category (A3 and A4 according the their classification, see Fig. 8 in Marziani et al. (2013a)) and represents about 10% of the total population of high luminosity AGN. These extreme population A objects have narrow H profiles () and the highest values. They are also among the objects with the highest Eddington ratios and largest velocity offsets. Unfortunately, our difficulties to properly measure the Fe ii emission around H do not allow us to measure and test their assumptions. can however compare their  estimates to our H-based  estimates by applying a bolometric correction as described in TN12. As can be seen in Figure. 1 all these objects occupy the top 20 percentile of the  distribution in our sample () in agreement with Marziani et al. (2013a). The Broad-Mg ii objects in our sample also show relatively large C iv and Mg ii velocity blue-shifts (top 20%, , ) which is also in agreement with Marziani et al. (2013a). We note however that broad-Mg ii objects are not the only ones that meet the mentioned conditions.

As can be seen in Figure 8, the BALQSOs in our sample show exactly the opposite behavior. They show narrower Mg ii profiles than usual. Unfortunately, it is impossible to draw any conclusion based on only two sources.

In Table 6 we present the median values and corresponding scatter of Q as well as the Spearman correlation coefficient between the FWHM of the listed lines under two cases: a) including all objects in the analysis and b) excluding the broad-Mg ii and the BALQSOs from the analysis. It can be seen in Table 6 and Fig. 8 that after removing these outliers the FWHM correlations becomes tighter (i.e. increases) and the Q factors remain almost unchanged. We emphasize that this result is also true for FWHM(C iv)while the correlations between FWHM(C iv) and the FWHM of the Balmer lines approach to linearity after removing such 7 objects. Consequently, for the following  analysis we exclude both the 5 Broad-Mg ii objects and the two BALQSOs.

Figure 9: Comparisons between different  estimates that are derived from different lines as indicated in the inserts of each panel. The black solid line represents the 1:1 relation. H values were derived using . The dashed black line represents the best fit to previous black hole mass estimators. Points are color-coded in gray scale by the S/N of the continuum bands around H where darker colors translates into larger S/N. BALQSO and the broad-Mg ii objects (see §4.3.4) are the labeled by green stars and magenta diamonds respectively.

4.4 Black Hole Mass estimators

In this subsection we present the procedure we use to obtain, and compare, different  estimates using the different line and continuum measurements. Our starting point, and the basis for all the following correlations, is the sub-sample of 32 AGN obtained by removing from the original sample 5 sources showing large discrepancy between FWHM(H) and FWHM(Mg ii) (see §4.3.4) and the two BALQSOs in the sample. A major aim is to find a practical strategy that will allow the identification of sources that are not suitable for accurate mass determination based on single line and continuum measurement.

4.4.1 relation and H

Most present-day single epoch mass measurements are based on the - relation, established through RM experiments (see §1 and Eq.3). In this case is a local  estimation of the continuum and  is obtained from the time lag of the response of the H line to (optical) continuum variations. This lag is assumed to properly represent the emissivity weighted radius of the broad H line.  is obtained from equation 1 where both and are obtained using local continuum measurements. These values can be used to obtain the "local" BH mass estimate, . We can then use the expressions derived in §4.2, and the various biases between the local  and global   and FWHM, to derive a global  expression for .

We start by using the local  expression obtained by TN12. This expression is most appropriate for our intermediate and high luminosity AGN:

(4)

Obtaining the equivalent global  expression is not trivial since we need first to find a relation between  measured from RM and and not simply use the recipe that connects local measurements. However, we do not know for the objects targeted by RM campaigns and we have to rely on the scaling relation between and that we find in this work (see table 5). Substituting in Eq. 3 we get:

(5)

It is important to note that we have simply re-scaled the empirical vs relation to a vs relation that is adjusted to predict the same  measurements. Consequently, we do not expect any systematic bias in  measurements coming from intrinsic - biases. The bias between and are simply the results of the intrinsic differences between the and (see §4.1). The small  biases that we found are shown in the bottom right set of panels in Figure 5.

—————–Local—————– —————–global—————– —————–Local—————–
scatter scatter scatter
(dex) (dex) (dex)
FWHM(H), 6.779 0.650 0.16 6.958 0.569 0.19 6.845 0.650 0.16
FWHM(H), 6.842 0.634 0.16 7.062 0.524 0.22 6.891 0.634 0.16
FWHM(H), 7.072 0.563 0.18 7.373 0.514 0.23 7.389 0.563 0.18
FWHM(H), 6.721 0.650 0.00 6.864 0.568 0.00 6.740 0.650 0.00
FWHM(Mg ii), 6.906 0.609 0.25 6.955 0.599 0.29 6.925 0.609 0.25
FWHM(C iv), 6.331 0.599 0.33 6.349 0.588 0.38 6.353 0.599 0.33
Table 7: Virial BH mass calibrations of Equation 1 () based on different line width and luminosity combinations for 32/39 objects in our sample, calibrated against the H virial mass calibration given in Equation. 4.  calibration based on local  measurements.  calibration based on global  measurements. local   calibrations corrected for the small systematic offsets that we found with respect to global  . Note that the values in this table are valid for L in units of erg s and FWHM in units of km s