11institutetext: National Institute for Astrophysics (INAF), Astronomical
Observatory of Padova, IT-35122 Padova, Italy
11email<EMAIL_ADDRESS><EMAIL_ADDRESS>22institutetext:
Dipartimento di Fisica e Astronomia, Università di Padova, Vicolo dell’
Osservatorio 3, IT-35122 Padova, Italy
22email<EMAIL_ADDRESS>33institutetext: Laboratório Nacional de
Astrofísica, MCTI, R. dos Estados Unidos 154, Nações, CEP 37504-364, Itajubá,
Brazil
33email<EMAIL_ADDRESS>44institutetext: School of Physics and Astronomy, Tel
Aviv University, Tel Aviv, 69978, Israel
44email<EMAIL_ADDRESS>55institutetext: Instituto de Astrofísica
de Andalucía (IAA-CSIC), Glorieta de Astronomía s/n, 38038 Granada, Spain
55email<EMAIL_ADDRESS><EMAIL_ADDRESS>66institutetext: Center for Theoretical
Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
66email<EMAIL_ADDRESS>
# Chemical abundances along the quasar main sequence

A. Floris 1122 P. Marziani 11 S. Panda CNPq Fellow33 M. Sniegowska 44
M. D’Onofrio 22 A. Deconto-Machado 55 A. del Olmo 55 B. Czerny 66

(Received ; accepted )

###### Abstract

Context. The 4D eigenvector 1 (E1) sequence has emerged as a powerful tool for
organizing the observational and physical characteristics of type-1 active
galactic nuclei (AGNs).

Aims. In this study, we present a comprehensive analysis of the metallicity of
the broad line region gas, incorporating both new data and previously
published findings, to assess the presence of any trend along the sequence.

Methods. We perform a multi-component analysis on the strongest UV and optical
emission lines, compute $\sim 10$ diagnostic ratios, and compare them with the
prediction of CLOUDY photoionization simulations, identifying a
photoionization solution closest to the data.

Results. Our investigation reveals a consistent pattern along the optical
plane of the E1. We observe a systematic progression in metallicity, ranging
from sub-solar values to metallicity levels several times higher than solar
values

Conclusions. These findings underscore the role of metallicity as a
fundamental correlate of the 4DE1/main sequence. Extreme values of
metallicity, at least several tens solar, are confirmed in low-$z$ AGNs
radiating at a high Eddington ratio, although the origin of the extreme
enrichment remains open to debate.

###### Key Words.:

Active Galactic Nuclei, Spectroscopy, Metals

##  1 Introduction

In recent years the 4DE1 (4 Dimensional Eigenvector 1) correlation space,
initially defined in Boroson & Green (1992); Sulentic et al. (2000b), has
proved to be a crucial tool for unraveling the spectral properties of type 1
Active Galactic Nuclei (AGN, e.g., Panda et al. 2019b; Panda & Śniegowska
2022; Fu et al. 2022; Wang et al. 2022; Nagoshi & Iwamuro 2022, among the most
recent works), even at the highest redshifts (e.g., Yang et al., 2023;
Loiacono et al., 2024). The optical plane, referred to as the Main Sequence
(MS) of quasars (Marziani et al., 2001, 2010; Shen & Ho, 2014) is the
parameter space defined by $R_{\rm FeII}$ (the ratio between the intensity of
the Feii emission at $\lambda 4570$ to H$\beta$) and the FWHM(H$\beta$)
(Gaskell, 1985; Boroson & Green, 1992). The MS allows for the definition of
two main populations of quasars occupying different regions of this parameter
space (Sulentic et al., 2000a, 2011):

  * •

Population A found below 4000 km s-1 of FWHM(H$\beta$),

  * •

Population B found above 4000 km s-1 of FWHM(H$\beta$).

A subpopulation of Population A AGNs, characterized by a $R_{\rm
FeII}$$\;\buildrel>\over{\sim}\;$1, is the Extreme Population A (xA),
associated with extreme-accreting AGNs (Marziani & Sulentic, 2014; Du et al.,
2016; Panda & Marziani, 2023). These populations exhibit different spectral
features associated with an array of physical conditions in the Broad Line
Region (BLR) of these objects (Fraix-Burnet et al., 2017; Marziani et al.,
2018b; Panda et al., 2019b).

Several parameters vary along the MS (see e.g., Sulentic et al., 2011; Fraix-
Burnet et al., 2017; Panda, 2021a, for summaries). Trends involve parameters
associated with line-formation, such as the ionization parameter $U$, which
has been shown to gradually increase moving from xA to Population B objects
(Sulentic et al., 2000b; Marziani et al., 2010). The gas density $n_{\rm H}$
seems to follow an inverse trend to $U$, with xA objects associated with much
higher densities than Population B objects (Marziani et al., 2001; Matsuoka et
al., 2008; Negrete et al., 2012; Martínez-Aldama et al., 2015; Panda et al.,
2018). Notably, $R_{\rm FeII}$ is believed to be primarily driven by the
Eddington ratio $L/L_{\mathrm{Edd}}$ (Boroson & Green, 1992; Marziani et al.,
2001; Sun & Shen, 2015; D’Onofrio et al., 2021). The position of objects along
the MS is thus connected to the radiation emitted by the AGN continuum source,
itself connected to the rate of accretion of matter onto the SMBH.

The FWHM(H$\beta$) is strongly affected by the viewing angle even if the
objects considered in the Eigenvector sequence are all type 1 AGNs. There is
increasing evidence that the low-ionization lines (LILs) are emitted in a
flattened configuration in correspondence of the accretion disk (e.g., Decarli
et al., 2011; Mejía-Restrepo et al., 2018; Negrete et al., 2018; Panda,
2021b), as suggested since long (Collin-Souffrin et al., 1988). The effect of
the viewing angle on the line width (roughly proportional to $\sin\theta$,
where $\theta$ is the angle between the line of sight and the accretion disk
axis) is compounded with the effect of the supermassive black hole (SMBH) mass
that is weak but becomes significant if AGNs in luminosity ranges of several
orders of magnitudes are considered (Marziani et al., 2018a). If no correction
for viewing angle is applied, the Population B objects, by definition with
larger FWHM, are characterized by systematically more massive SMBHs than their
Population A counterparts (Marziani et al., 2003b).

The role of the chemical content of the BLR is, however, not yet completely
understood in the process of line formation. Previous studies like Śniegowska
et al. (2021) and Garnica et al. (2022), focused on the metal content of xA
quasars and determined high metallicity $Z$ in the BLR of these objects,
reaching extreme values. High $Z$ is a potential explanation for the observed
trends of density and ionization parameter, as resonant scattering becomes
more efficient when metals are more abundant (e.g., Murray et al., 1995).
Additionally, various studies have indicated the systematic enrichment of the
BLR of AGNs compared to their host galaxies, nearly always reaching super-
solar values (e.g., Hamann & Ferland, 1999; Nagao et al., 2006; Xu et al.,
2018; Maiolino & Mannucci, 2019, and references therein). High $Z$ values have
been confirmed through independent techniques, such as iron emission and
absorption features detected in the nuclear region (Jiang et al., 2018;
Maiolino & Mannucci, 2019). Some proposed explanations include selective
enrichment of the circumnuclear region of the AGN (Śniegowska et al., 2021).
Metallicities around solar are possible for xA sources only under the most
extreme conditions (Temple et al., 2021). In addition, there is still the
possibility that the adopted empirical and photoionization models are
inadequate.

Recent works suggest that enrichment may not occur for the BLR gas of all
AGNs: toward the opposite extreme of the sequence, estimation of metallicity
indicate solar (for radio-quiet Population B) or sub-solar (for radio-loud
Population B; Punsly et al. 2018; Marziani et al. 2022). Previous studies
involved a few objects and samples in different redshift and luminosity
domains (; ; ), focusing on specific spectral bins or populations of the MS.
It is necessary to understand what happens between the extremes of the MS,
attempting to uncover any trend in metallicity along the MS that could help
unveil possible mechanisms behind the evolution of quasars and their host
galaxies: evidence of blueshifts (Zamanov et al., 2002; Komossa et al., 2008;
Boroson, 2005; Aoki et al., 2005; Zhang et al., 2011; Negrete et al., 2018) in
the lines of the spectra of most AGNs hints at the possibility that outflows
could chemically enrich the gas found in the Interstellar Medium (ISM) or even
the Intergalactic Medium (IGM) (Choi et al., 2024; Sabhlok et al., 2024).
Indeed, Harrison et al. (2014) pointed out the far-reaching impact of such
outflows beyond the BLR of these objects, suggesting an interplay between the
enriched material produced in the regions close to the active nucleus and
expelled over time in the direction of the host galaxy.

In this work, we present the systematic study of the metallicity of a sample
of objects covering most spectral types along the MS at low redshift (Section
2). Section 3 describes the methodology and techniques used. Results for the
objects of the sample are provided in Section 4. In Section 5 we address the
potential issues of our methodology. The discussion of the results in Section
6 focuses on the correlation of the metallicity of objects with accretion
parameters and the possible enrichment mechanisms that may explain our
results. The conclusions are summarized in Section 7.

##  2 Sample

Table 1: Basic sample properties

Common Name | IAU Code | $z$ | FWHM(H$\beta$) | RFeII | Spectral type | $R_{\mathrm{K}}$ | UV | Optical
---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
Mrk 335 | J00063+2012 | 0.0256 | $2209\pm 220$ | $0.21\pm 0.04$ | A1 | 0.42 | COS | M03
TXS 0042+101 | J00449+1026 | 0.587 | $7279\pm 728$ | $0.04\pm 0.06$ | B1/RL | 197.37 | FOS | J91
I Zw 1 | J00535+1241 | 0.061 | $1506\pm 151$ | $1.83\pm 0.28$ | A4 | 0.40 | FOS, COS | M03
Fairall 9 | J01237$-$5848 | 0.046 | $5958\pm 596$ | $0.43\pm 0.08$ | B1 | 0.92 | FOS, COS | M03
PHL 1092 | J01399+0619 | 0.3965 | $2494\pm 249$ | $1.76\pm 0.39$ | A4 | 0.42 | STIS, M20 | M20
Ark 120 | J05161$-$0008 | 0.033 | $5863\pm 586$ | $0.49\pm 0.04$ | B1 | 0.30 | FOS | M03
Mrk 110 | J09252+5217 | 0.036 | $2048\pm 205$ | $0.19\pm 0.04$ | A1 | 2.18 | COS | M03
Ton 28 | J10040+2855 | 0.329 | $2398\pm 240$ | $1.04\pm 0.18$ | A3 | $<0.40$ | FOS | M03
NGC 3783 | J11390$-$3744 | 0.009 | $3514\pm 351$ | $0.20\pm 0.04$ | B1 | 0.30 | FOS, COS | M03
LB 2522 | J13012+5902 | 0.472 | $3999\pm 400$ | $1.30\pm 0.32$ | A3 | $<0.25$ | FOS | M03
LEDA 51016 | J14170+4456 | 0.114 | $2720\pm 272$ | $1.01\pm 0.16$ | A3 | 0.17 | FOS, COS | M03
Mrk 478 | J14421+3526 | 0.077 | $1322\pm 132$ | $1.04\pm 0.10$ | A3 | 0.20 | FOS | M03
Mrk 509 | J20441$-$1043 | 0.035 | $3309\pm 331$ | $0.02\pm 0.02$ | A1 | 0.35 | COS | M03
Ark 564 | J22426+2943 | 0.025 | $1011\pm 101$ | $0.67\pm 0.22$ | A2 | 0.88 | FOS, COS | M03

111(1) Object common name. (2) IAU coordinate name. (3) Redshift. (4) FWHM of
H$\beta$, in units of km s-1. (5) $R_{\rm FeII}$= Feii$\lambda$4570/H$\beta$
measured in this work. (6) Spectral type. (7) Kellerman ratio, from NED, or
from the following sources: Wang et al. (2023a) for Mrk 110, Järvelä et al.
(2022) for Ark 564; Capetti et al. (2021), Baldi et al. (2022) and Kellermann
et al. (1994), for Ton 28, LB 2522 and LEDA 51016 respectively. (8) HST camera
used for collecting UV spectra of the object, using the abbreviation FOS for
the Faint Object Spectrograph, and COS for the Cosmic Origins Spectrograph.
(9) Optical data source, using the abbreviations M03, M20 and J91 for the
papers Marziani et al. (2003a), Marinello et al. (2020), Jackson & Browne
(1991), respectively.

###  2.1 Sample definition

The sample of objects used in this work was selected based on a few criteria:

  1. 1.

Availability of ground observations in the optical wavelength range of objects
below a redshift $z$ of 0.8, where H$\beta$ can be observed.

  2. 2.

Availability of archival UV data from HST covering the $\lambda$1300-2100 Å
rest-frame range of the object.

  3. 3.

Requirement of Radio Quiet (RQ) objects, except for TXS 0042+101 that is Radio
Loud (RL), to study the properties of the BLR without the influence of a
collimated jet (Baker et al., 1994; Punsly et al., 2018; Gaur et al., 2019).

Table 1 reports the main observational parameters, in the following order:
common name, IAU coordinate name, adopted redshift, the H$\beta$ FWHM, the
FeII-to-H$\beta$ intensity ratio $R_{\rm FeII}$, with Feii emission integrated
over the $\lambda 4434$-$4684$ Å range, and H$\beta$ measured on the full
broad profile; spectral type (ST) based on H$\beta$ FWHM and $R_{\rm FeII}$,
and the Kellerman’s ratio (Kellermann et al., 1989), necessary to distinguish
RQ from RL objects, defined as

${\rm R}_{K}=\frac{f_{\text{Radio}}}{f_{B}},$ (1)

using data from the NED database. Here, $f_{\text{Radio}}$ is the specific
flux at a wavelength of $\lambda=6$ cm (5 GHz) and $f_{B}$ is the specific
flux at $\lambda=4400$ Å (680 THz) in the $B$ band. When the NED data was not
available, the flux density used in the calculation was obtained from other
works. The last two columns summarize the UV and optical data sources for each
object.

Most objects that satisfied these selection criteria were included in the
sample of objects in Marziani et al. (2003a). The spectra of two objects, PHL
1092 and TXS 0042+101, which are found in more extreme regions of the MS, were
obtained from Marinello et al. (2020) and Jackson & Browne (1991),
respectively, with the latter being digitized from Jackson & Browne (1991) due
to the unavailability of the original spectrum.

Figure 1 describes the distribution of the objects of the sample in bolometric
luminosity (ad computed in Section 6.2) and $z$, confronting them with average
values from the samples used in the works of Śniegowska et al. (2021), Garnica
et al. (2022) and Marziani et al. (2023) (hereafter referred to as S21, G22,
M23, respectively).

Figure 1: Stacked histograms depicting the distribution of sample objects in
$\log(L_{\rm bol})$ and $z$, categorized by the respective population.
Assigned colors correspond to the legend, while vertical lines denote average
values from the objects used in the referenced works S21, G22 and M23.

##  3 Methodology

###  3.1 Subdivision of spectral types

An advantage of the MS/E1 approach is the possibility of defining spectral
types along the optical plane of the sequence with simple selection criteria
(Sulentic et al., 2002; Shen & Ho, 2014; Panda & Śniegowska, 2022). The
expectation is that the effect of systematic trends along the sequence is
minimized in each spectral type, so that an average spectrum of the sources in
each bin is representative of all or most of the individual sources, not only
phenomenologically, but also in terms of physical properties. This has been
shown to be the case (Sulentic et al., 2002; Bachev et al., 2004; Marziani et
al., 2010), even with some limitations (Marziani et al., 2001, 2018b, 2018a;
Panda et al., 2019b), as the 2D optical E1/MS is not a simple 1D trend (Wildy
et al., 2019; Martínez-Aldama et al., 2021), but rather the projection of a
trend in a 4D space (Sulentic et al., 2000b).

In this paper we follow the naming convention and the subdivision of Sulentic
et al. (2002) in regular steps of $\delta$$R_{\rm FeII}$=0.5 (increasing
numerals with increasing $R_{\rm FeII}$), and $\delta$FWHM H$\beta$= 4000 km
s-1(A, B, and afterward B+, B++, etc.).

###  3.2 Emission line interpretation and empirical modelling

In this work, we adopt an interpretation of the emission line profiles of
Type-I AGNs based on three main components:

  * •

Broad Component (BC): A virialized component that constitutes the bulk of the
line profiles of the main emission lines. It follows a Lorentzian profile in
Population A objects, and a Gaussian profile in Population B objects (Marziani
et al., 2010). It is a distinctive component of Type-I AGN line profiles,
identifying the BLR of these objects.

  * •

Blueshifted Component (BLUE): A blue-shifted outflow component present in the
lines of almost all AGNs, affecting broad and narrow lines (Bachev et al.,
2004; Zamanov et al., 2002). It is typically modeled by a skewed Gaussian that
exhibits an asymmetry towards the blue (Zhang et al., 2011). This component is
predominant in xA objects that are characterized by strong winds, being mainly
present in High Ionization Lines (HILs) like Civ, that require high column
density and density of the gas, as well as low $U$ in the BLR (Negrete et al.,
2012, 2013).

  * •

Very Broad Component (VBC): A virialized component with larger FWHM compared
to the BC, as it models regions of the BLR that are closer to the SMBH (a Very
Broad Line Region (VBLR), Peterson & Ferland, 1986; Sulentic et al., 2000c;
Snedden & Gaskell, 2007). It is a component exclusive of Population B objects
that are modeled with a Gaussian that is redshifted by several km s-1 to the
rest-frame wavelength of the emission line. It is a simplification introduced
to account for the gradients more properly modeled in the ”Locally optimally
emitting clouds” (LOCs) scheme (Baldwin et al., 1995) that accounts for the
stratification of properties in the BLR assuming that there is a gradual
gradient of variation of properties in the BLR that follows a power-law.

An additional component that can be encountered is the Narrow Component (NC)
which is, however, not associated with the BLR and thus modeled with narrow
lines and disregarded for the estimation of the metallicity of the gas in the
BLR.

###  3.3 Multi-component fitting technique

Our sample was analyzed using the specfit (Kriss, 1994) task from IRAF,
inspecting the regions of our spectra centered on the Siiv+Oiv]$\lambda 1400$,
Civ$\lambda 1549$, Ciii]$\lambda 1909$ (hereafter, Siiv+Oiv], Civ, Ciii],
respectively) and H$\beta$ lines. The laboratory vacuum wavelengths of these
lines, as well as all other lines measured during the analysis are from Vanden
Berk et al. (2001). The specfit task runs on the Space Telescope Science Data
Analysis System (STSDAS) contrib package of IRAF, which was developed by the
National Optical Astronomy Observatory (NOAO) in Tucson, Arizona (Tody, 1986,
1993).

Specfit allows users to interactively fit a wide range of emission and
absorption lines on the continuum model of the input spectrum. To achieve
this, it employs input ASCII files created using the dbcreate task, containing
the necessary functions to model various components of the spectrum. Gaussian
and Lorentzian functions, widely used in multi-component fitting, are each
described by values of line intensity, central wavelength, FWHM, and asymmetry
parameter.

In addition to the standard functions provided, specfit allows the use of
user-provided functions. In particular, we utilized the usercont and userline
functions to model the complex Feiii (found in the UV range) and Feii (found
also in optical ranges) emissions respectively.

The specfit multi-component fitting procedure is interactive, based on the
input file described in the previous paragraphs. The initial parameter values
in the input file serve as starting guesses for modeling the components. Each
parameter can be refined using a minimization fit provided by the routine.
When the algorithm converges successfully, it provides the best-fit parameters
that minimize the $\chi^{2}$ between the model and observed data, resulting in
an optimal solution. This fitting is carried out with two different algorithms
(out of the five available in specfit):

  * •

Marquardt is based on the Levenberg-Marquardt (LM) algorithm, which
iteratively minimizes the $\chi^{2}$ using the Jacobian matrix. This matrix
contains the partial derivatives of the model function fitting the data to
each fit parameter. The algorithm combines a combination of gradient descent
and Gauss-Newton methods, adjusting the step size at each iteration. It takes
larger steps when the fitting improves, and smaller steps when it does not.

  * •

The downhill Simplex algorithm utilizes an iterative method for fitting, and
adjusting values for user-provided components starting from initial guesses
and constraints. It iteratively improves the solution toward the minimum
$\chi^{2}$ with operations on an N-dimensional (the number of free parameters)
simplex (Press et al., 1992). Unlike the Levenberg-Marquardt method, the
simplex algorithm requires only function evaluations and no derivatives. Even
if it is not efficient in terms of iteration number, it is very robust and
never causes the specfit task to crash.

We start by fitting the continuum emission in the wavelength range with a
power-law function, carefully selecting regions of the spectrum unaffected by
the presence of emission or absorption lines. The flux values of the continuum
at various reference wavelengths are provided in Table 2.

In the optical wavelength range, we incorporate a Feii template to correct for
Feii contamination, which can act as a pseudo-continuum on the modeled
spectrum, particularly problematic in objects with strong Feii emission. Our
Feii template is derived from a European Southern Observatory (ESO) spectrum
of I Zw 1 (Marziani et al., 2009, 2010, 2021). To address Feiii contamination,
prevalent in the $\lambda$1800-2100 Å wavelength range, we utilize a template
from Vestergaard & Wilkes (2001), based on the Feiii emission of I Zw 1. In
cases where the Feiii emission is strong, and there is evidence of a stronger
feature at 1914 Å to the template, we model the 1914 Å feature with a Gaussian
profile, even if it is severely blended with Ciii]. This step is typically
necessary for xA objects.

When fitting emission lines, we allow them to vary while imposing the NC of
lines to remain fixed at the rest frame of the object. Additionally, we ensure
that the FWHM of Siiv+Oiv] is similar to those measured for Civ and H$\beta$
(Marziani et al., 2010). This is because lines associated with the virialized
component of H$\beta$, Ciii], Civ, and Siiv+Oiv] are produced in approximately
the same regions. By the same token, BLUE and VBC widths and asymmetries are
also made consistent in the fit.

All measurements reported in the tables along the paper and those employed for
the metallicity computations have been corrected for galactic extinction for
each object using the equations of Cardelli et al. (1989).

Table 2: Flux and uncertainty measurements

Object name |  $\lambda$1300-1450Å |  $\lambda$1450-2100Å | Optical range | $A(V)$
---|---|---|---|---
| $f_{\lambda 1350}$ | ${\rm RMS}_{\rm SiIV}$ | $f_{\lambda 1700}$ | ${\rm RMS}_{\rm CIV}$ | ${\rm RMS}_{\rm CIII]}$ | $f_{\lambda 5100}$ | ${\rm RMS}_{\rm opt}$ |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
Mrk 335 | 22.11 | 0.65 | 14.83 | 0.70 | 1.30 | 5.25 | 0.12 | 0.096
TXS 0042+101 | 0.17 | 0.05 | 0.15 | 0.04 | 0.03 | 0.08 | 0.01 | 0.186
I Zw 1 | 10.15 | 0.38 | 16.43 | 0.70 | 0.37 | 6.65 | 0.12 | 0.176
Fairall 9 | 35.19 | 0.91 | 26.36 | 1.63 | 1.19 | 2.72 | 0.09 | 0.071
PHL 1092 | 3.40 | 0.08 | 2.77 | 0.06 | 0.07 | 0.28 | 0.01 | 0.110
Ark 120 | 33.13 | 2.32 | 13.81 | 1.00 | 0.88 | 9.67 | 0.15 | 0.349
Mrk 110 | 24.01 | 1.57 | 16.02 | 1.74 | … | 0.76 | 0.03 | 0.034
Ton 28 | 10.36 | 3.11 | 7.98 | 1.38 | 1.25 | 1.92 | 0.04 | 0.060
NGC 3783 | 79.16 | 2.05 | 63.26 | 2.84 | 2.09 | 10.36 | 0.20 | 0.332
LB 2522 | 6.25 | 2.08 | 5.89 | 1.67 | 1.27 | 0.54 | 0.02 | 0.022
LEDA 51016 | 8.90 | 0.24 | 7.22 | 0.45 | 0.26 | 0.79 | 0.02 | 0.024
Mrk 478 | 36.23 | 2.06 | 26.93 | 0.93 | 0.52 | 2.00 | 0.02 | 0.039
Mrk 509 | 84.18 | 1.71 | 73.99 | 2.10 | 1.91 | 8.87 | 0.31 | 0.157
Ark 564 | 6.86 | 0.52 | 6.06 | 0.84 | 0.27 | 0.75 | 0.04 | 0.166
222(1) Object common name. (2), (4), (7) Specific flux of the continuum
emission measured at 1350 Å, 1700 Å and 5100 Å, respectively, and measured in
units of $10^{-15}$ erg s-1 cm-2 ${\rm\AA}^{-1}$. (3), (5), (6), (8) RMS of
the flux associated with the continuum emission, measured in units of
$10^{-15}$ erg s-1 cm-2 ${\rm\AA}^{-1}$, in the ranges of the various lines
inspected in this work. (9) Absorption parameter in the V band obtained from
the NED database.

###  3.4 Estimation of uncertainties

The placement of the continuum is one of the main sources of uncertainty in
measuring emission-line intensities. In particular, the continuum placement
strongly influences extended features such as the Feiii and emissions in the
UV range, and the Feii emission in the H$\beta$ range.

The uncertainty associated with continuum placement was estimated as follows
(cf. Śniegowska et al., 2021): initially, the intensity of the continuum was
measured using IRAF in each range where the best fit was conducted, yielding
the Root Mean Square (RMS) of the flux (measured in units of $10^{-15}$ erg
s-1 cm-2 ${\rm\AA}^{-1}$), as shown in Table 2. Subsequently, the intensity of
each line was measured by fixing the continuum’s intensity at both maximum and
minimum values, by adding or subtracting the RMS, to obtain the line’s
intensity at its minimum and maximum, respectively. When the continuum is
higher (lower), the line intensity decreases (increases), compensating for the
flux change, resulting in lower (upper) limits that are asymmetric and
represent the range of emission line intensities.

To handle these uncertainties, we assume that the error distribution follows a
triangular distribution (D’Agostini, 2003). This simplifies error computation
and is the preferred method for dealing with asymmetric uncertainties. For
each line measurement, the variance $\sigma^{2}(X)$ of any parameter $X$ is
calculated using the formula for the triangular distribution:

$\sigma^{2}(X)=\frac{\Delta^{2}x_{+}+\Delta^{2}x_{-}+\Delta x_{+}+\Delta
x_{-}}{18}$ (2)

where $\Delta x_{+}$ and $\Delta x_{-}$ represent the differences between
measurements with the maximum and best continuum, and with the best and
minimum continuum, respectively. Finally, errors in spectral diagnostic ratios
were calculated using standard error propagation formulas.

###  3.5 CLOUDY photoionization simulations

To constrain the properties of the gas in the BLR, we conducted
photoionization simulations using the CLOUDY spectral synthesis code (Ferland
et al., 2017). CLOUDY is a C++ code that models the ionization, chemical, and
thermal state of the material that may be exposed to an external radiation
field or other sources of heating. It predicts observables, including emission
and absorption spectra, by solving the statistical and thermal equilibrium
equations for many chemical species, including ions. The code accounts for
collisional excitations, and radiative processes, and treats radiation
transfer through an escape probability formalism.

Photoionization simulations require input parameters that define ionization
and level populations, along with electron temperature and optical thickness
as a function of the geometrical depth within the emitting gas cloud. The
assumed geometry is open and plane-parallel, representing a cloud of emitting
gas as a slab exposed to a radiation field only on one side. The input
parameters for a complete computation of the gas state, used to predict
emission line intensities, include:

  1. 1.

The ionization parameter $U$, defined by the equation:

$U=\frac{\int_{\nu_{0}}^{\infty}\frac{L_{\nu}}{h\nu}\,d\nu}{4\pi r_{\rm
BLR}^{2}cn_{\rm H}}=\frac{Q({\rm H})}{4\pi r_{\rm BLR}^{2}cn_{\rm H}},$ (3)

where $Q({\rm H})$ is the number of ionizing photons, $r_{\rm BLR}$ is the
distance between the continuum source and the line emitting gas. It provides
the ratio between the Hydrogen-ionizing photons and the Hydrogen number
density.

  2. 2.

Gas Hydrogen number density $n_{\rm H}$ [cm-3].

  3. 3.

Metallicity $Z$, to solar metallicity $Z_{\odot}$, defined as $\log
Z=\log[\frac{Z}{H}]-\log[\frac{Z}{H}]_{\odot}$, where $[\frac{Z}{H}]$ and
$[\frac{Z}{H}]_{\odot}$ are the ratio of the measured number density of metals
to Hydrogen, and the same quantity for the Sun, respectively.

  4. 4.

Spectral energy distribution (SED) of the quasar.

  5. 5.

Column density $N_{\rm c}$.

  6. 6.

Micro-turbulence parameter.

This resulting six-dimensional parameter space is not typically fully
explored, and in our case, we examined trends using arrays of simulations that
were organized as follows: 3 different SEDs, one for each of the following
cases: Pop. B RQ, a SED for Population A sources (Mathews & Ferland, 1987) and
one for xA quasars (Ferland et al., 2020). $Z$ was assumed to scale as solar
($Z_{\odot}$), with 12 values ranging between $0.01$ and 1000 $Z_{\odot}$ for
Pop. A and xA sources, and 14 values between $0.001$ and 20 $Z_{\odot}$ for
Pop. B. The micro-turbulence parameter was set to 0 km s-1. This is negligible
for resonance UV lines as outlined in Śniegowska et al. (2021) but is expected
to lead to an under-prediction of Feii emission (Sigut & Pradhan, 2003;
Bruhweiler & Verner, 2008; Panda et al., 2018, 2019a; Śniegowska et al., 2021;
Panda, 2021b). For each metallicity value, we considered an array of
simulations covering the $n_{H}$ and $U$ parameter plane in the range
$7\leq\log n_{\rm H}\leq 14$ cm-3, $-4.5\leq\log U\leq 1$ for Pop. A (667
simulations), and $7\leq\log n_{\rm H}\leq 13$ cm-3, $-3\leq\log U\leq 1$ for
Pop. B (425 simulations).

The separation of the three components (BC, VBC, BLUE) can be heuristically
associated with three different regions expected to be in different physical
conditions, BLR, VBLR, BLUE (see also the scheme in Fig. 2 Deconto-Machado et
al. 2023). A source of uncertainty comes from the fact that photoionization
computations are carried out under the assumption of single-zone emission,
albeit separately for each of the three regions. While this assumption seems a
good one for the BLR of extreme Population A, where density and ionization
tend toward limiting values (Marziani et al., 2001; Panda et al., 2019b;
Panda, 2021b), this might not be the case for Pop. B sources (Korista & Goad,
2000), or less-extreme Population A.

###  3.6 Diagnostic ratios

Diagnostic ratios of lines provide constraints on the ionization, metallicity,
and density of the emitting gas in the BLR. The following diagnostic ratios
were used for computing the metallicity of our low $z$ quasar sample.

  1. 1.

(SiIV+OIV])/CIV: widely used as a metallicity indicator (Nagao et al., 2006;
Shin et al., 2013). An excellent explanation of why this ratio is a reliable
metallicity indicator is provided by Huang et al. (2023).

  2. 2.

(SiIV+OIV])/HeII: sensitive to metallicity, assuming that He abundance
relative to Hydrogen is constant. The OIV] line has a critical density $n_{\rm
c}$$\sim$ 1011 cm-3 (Marziani et al., 2020), making this diagnostic ratio
affected by density.

  3. 3.

CIV/HeII: diagnostic ratio sensitive to metallicity, again assuming constant
He abundance relative to Hydrogen. The reasons why the Siiv+Oiv]/ and Civ/ are
very reliable metallicity indicators are similar. First, there is the linear
increase of the abundance of Si and C to He with increasing $Z$. In the Civ/
case, the ionization potentials of C2+ and He+ are almost coincident; however,
the main difference is that is a recombination line and the Civ is due to
collisional excitation (Marziani et al., 2020; Śniegowska et al., 2021). As
the metallicity $Z$ increases, the electron temperature $T_{\mathrm{e}}$
decreases (e.g., Pagel et al., 1979) and hence metal lines excitation is
disfavored. Conversely, the lower $T_{\mathrm{e}}$ increases the rate of He++
recombination, reinforcing the increase of the ratios with $Z$. The ratio Civ/
has been used (Shin et al., 2013; Sulentic et al., 2014) despite of the
weakness. However, with high S/N and resolution measurements from FOS and
especially COS, we can accurately estimate the line intensity of , previously
very difficult to assess, and self-consistently deblend it from the much
stronger Civ emission.

  4. 4.

CIV/H$\beta$. Unlike all other ratios employed in this work, the Civ/H$\beta$
ratio is subject to major observational uncertainty in the photometric
precision of the optical data, and lack of concurrent optical and UV
observations. The depth of absorption features close to the rest frame in the
Civ profile is difficult to assess and may significantly lower the
Civ/H$\beta$ (one of the most serious cases could be PHL 1092, Table 10). The
diagnostic value of the Civ/H$\beta$ ratio is primarily due to its strong
dependence on the ionization parameter. Fig. 2 shows the behavior of the
Civ/H$\beta$ intensity ratio in the plane $\log Z$, $\log U$: the isophotal
contours are almost parallel to the $Z$ axis.

In the presence of a very low Civ/H$\beta$ ($\sim 1)$ ratio, the $U$ must be
very low, with $\log U\lesssim-2.5$. At higher ionization parameters
$-1\lesssim\log U\lesssim 0$, and moderate density, the Civ emission to the
Balmer line is optimized at relatively low values of $Z$. At higher $Z$
($\gtrsim 10Z_{\odot}$), for the same $U$, the electron temperature is
significantly lowered, decreasing the collisional excitation rate, and
therefore lowering the line emission. There are two implications relevant to
this work: a very weak Civ requires very low $U$, with the lowest Civ
prominence obtained for low $Z$ (Fig. 2). Conversely, for $\log U\sim-1\div
0$, where Civ is efficiently produced, Civ/H$\beta$ $\gtrsim 10$ can be
achieved for $\log Z\sim-2$, for density $\log$$n_{\mathrm{H}}$$\sim 11\div
13$.

  5. 5.

AlIII/CIV: a diagnostic ratio sensitive to the ionization parameter. This is
because it relates lines of elements with different ionization potentials. It
is potentially useful to constrain the effect of feedback from supernovæ since
Aliii is overproduced in the explosion of type Ibc supernovae to the Civ solar
abundances (Chieffi & Limongi, 2013). This diagnostic ratio may tend to bias
the estimated $Z$ toward higher values.

  6. 6.

AlIII/SiIII]: a diagnostic ratio sensitive to density, since it involves an
intercombination line with a well-defined critical density: $n_{\rm c}$$\sim$
1011 cm-3 for Siiii] (Negrete et al., 2013). If the ratio Aliii/Siiii] is $\gg
1$, the resulting density will be much greater than the critical density.
Historically, diagnostic ratios employing Aliii have rarely been used, since
the measurement of the intensity of Aliii was quite uncertain, but with high-
quality COS and FOS spectra, we have been able to measure it accurately.

  7. 7.

SiIII]/CIII]: a diagnostic ratio sensitive to density, similar to Aliii/Siiii]
but around lower values, $n_{\rm c}$$\sim$ 1010 cm-3 for Ciii] (Hamann et al.,
2002). As the ratio described above, if Siiii]/Ciii] is $\gg 1$, the resulting
density will be much greater than the critical density of Ciii] as well, and
is a very powerful density estimator, constraining density very well. The
inclusion of strong Ciii] may however bias the ($U$, $n_{\mathrm{H}}$, $Z$)
solution toward lower densities. The issue is analyzed in Section 5.

  8. 8.

CIII]/CIV: it is a diagnostic ratio sensitive to the ionization parameter as
it compares the intensity of different ionization degrees of the same atomic
species. However, since Ciii] is an intercombination line, it is also
sensitive to density. For xA sources the ratio Ciii]/Civ is subject to higher
uncertainties due to Feiii contamination, making it difficult to measure the
intensity of Ciii] accurately. However, since xA Ciii] is weakest along the MS
(Bachev et al., 2004; Aoki & Yoshida, 1999), a fairly high-density solution is
anyway suggested despite the uncertainties.

  9. 9.

FeII/H$\beta$: it is a diagnostic ratio sensitive to metallicity, as it
involves a metal and Hydrogen. However, this diagnostic ratio is also
sensitive to the density, ionization parameter, and column density of the
line-emitting gas (Verner et al., 1999, 2004; Bruhweiler & Verner, 2008; Panda
et al., 2018, 2019b; Panda, 2021b). High Feii/H$\beta$ is only possible if
conditions of low ionization, high density ($n_{\rm H}$$\gtrsim 10^{11}$ cm-3)
and large column density ($N_{\rm c}$ $\gtrsim 10^{23}$ cm-2) are satisfied
(Panda et al., 2018, 2019b; Panda, 2021b). The ratio Feii/H$\beta$ is
relatively easy to measure with good precision ($\sim 0.1$ at 1$\sigma$
confidence level). However, the mean escape probability formalism is known to
perform poorly in the prediction of the emission line strength for gas
irradiated by strong X-ray sources (e.g., Dumont et al., 2003, and references
therein). In the case of this particular ratio, there is therefore
considerable uncertainty associated with the photoionization computations.

  10. 10.

HeIIopt/H$\beta$: it is a diagnostic ratio sensitive to the ionization
parameter. Assuming the abundance of He relative to Hydrogen is constant, it
is the ratio between two species with very different ionization potential:
Heii$\lambda$4686 requires $\sim 50$ eV to be ionized, while Hydrogen requires
$\sim 10$ eV. The Heii$\lambda$4686/H$\beta$ ratio is relatively insignificant
in the $Z$ estimates.

These diagnostic ratios are used differently depending on the quasar
population. Notably, not all components are present in all objects. Although
most objects can be modeled assuming a BLUE component for HILs, it is not
always present for LILs. By the same token, the VBC appears only in Population
B sources. Population A objects allow reliable estimation only of physical
parameters associated with the BC. Population B quasars allow for the
estimation of physical parameters of gas located in the VBLR and BLR, while xA
quasars allow for the estimation of the properties of the BLUE and BC. In this
study, we exclusively examined the BLUE of PHL 1092, since it was the only
object with a sufficient number of diagnostic ratios enabling an accurate
constraint of its physical conditions.

The solution for the single-zone model, represented by a single point in the
3D space ($n_{\mathrm{H}}$, $U$, $Z$) is determined by minimizing the
$\chi^{2}$ computed from the difference between the observed line ratios and
the predicted line ratios across the entire 3D space (Marziani et al., 2024),
applying the following relation:

$\chi^{2}_{\rm kc}(n_{\rm H},U,Z)=\sum_{\rm i}\left(\frac{R_{\rm kci}-R_{\rm
kci,mod}(n_{\rm H},U,Z)}{\delta R_{\rm kci}}\right)^{2},$ (4)

with $R_{\rm kc}$ identifying the diagnostic ratio considered for the object
and component, and $\delta R_{\rm kc}$ identifying the error associated with
each component. The ”mod” subscript identifies the value of the specific
diagnostic ratio predicted by the CLOUDY simulations for each value in the 3D
grid of the ($n_{\mathrm{H}}$, $U$, $Z$) parameter space.

Figure 2: Behavior of the diagnostic ratio Civ/H$\beta$ (shown in logarithmic
scale) as a function of ionization parameter $U$ and metallicity $Z$, for four
values of Hydrogen density, $\log$ $n_{\mathrm{H}}$= 7,9,11,13 [cm-3], using
the Mathews & Ferland (1987) Population A SED.

###  3.7 FeII and AlIII Upper limits

CLOUDY photoionization simulations have previously hinted at the possibility
of a contribution to the intensity of Aliii and Feii emission from the VBC for
Pop. B Quasars and from the BLUE for xA Quasars (Zhou et al., 2023). This
possibility was thus investigated by damping the intensity of Aliii emission
obtained from the multi-component fitting of our spectra, adding a Gaussian
component to the fit with the same blueshift (redshift) for xA Quasars (for
Population B quasars) correspondent to the shift between the H$\beta$ BC and
the H$\beta$ BLUE (H$\beta$ VBC), and the same FWHM as the BLUE (VBC). After
including this additional component the $\chi^{2}$ associated with the fit was
calculated for varying intensity values of the Gaussian line. As a result,
regions associated with 1$\sigma$, 2$\sigma$, and 3$\sigma$ compatibility were
drawn in the plots shown in Figure 3. The same procedure was applied to the
Feii emission in the optical wavelength range, with the difference that
instead of adding a Gaussian component, the additional Feii emission was
modeled from the ESO Feii template (Marziani et al., 2009, 2010). The results
of this computation were then added to the known diagnostic ratios associated
with the VBC or the BLUE of our objects, by using the 1$\sigma$ upper limit as
the diagnostic ratio.

Figure 3: Left: Plot of the $\chi^{2}/\chi^{2}_{\rm min}$ distribution as a
function of the relative intensity of the FeIIBC of PHL 1092 with respect to
the specfit retrieved intensity, versus the relative intensity of the FeIIBLUE
with respect to the original intensity of FeIIBC. Middle: Same, but for the
AlIIIVBC emission of Fairall 9. Right: Same, but for the FeIIVBC emission of
Fairall 9.

##  4 Results

###  4.1 Results on individual sources

Table 3: Siiv+Oiv] blend line measurements.

Object name | Siiv+Oiv]
---|---
| BLUE | BC | VBC
(1) | (2) | (3) | (4)
Mrk 335 | $85.2\pm 25.4$ | $634.9\pm 74.6$ | …
Mrk 110 | … | $706.3\pm 104.9$ | …
Mrk 509 | $251.7\pm 98.9$ | $1859\pm 300$ | …
Ark 564 | $11.5\pm 10.5$ | $115.5\pm 24.5$ | …
Mrk 478 | $6.9\pm 22.8$ | $541\pm 122$ | …
Ton 28 | $63.5\pm 40.7$ | $200\pm 139$ | …
LB 2522 | $146\pm 67$ | $76.9\pm 113.5$ | …
LEDA 51016 | $34.3\pm 12.2$ | $305\pm 35$ | …
I Zw 1 | $104.9\pm 22.8$ | $481\pm 56$ | …
PHL 1092 | $27.1\pm 5.6$ | $7.31\pm 3.55$ | …
Fairall 9 | $108\pm 26$ | $363\pm 32$ | $390\pm 70$
Ark 120 | $220\pm 114$ | $881\pm 155$ | $501\pm 188$
NGC 3783 | $404\pm 141$ | $1013\pm 159$ | $539\pm 145$
TXS 0042+101 | $0.6\pm 1.1$ | $3.4\pm 1.7$ | $3.5\pm 3.3$
333(1) Object common name. (2) Intensity of the line associated with the BLUE,
with associated errors, measured in units of $10^{-15}$ erg s-1 cm-2. (3)
Intensity of the line associated with the BC, with associated errors, measured
in units of $10^{-15}$ erg s-1 cm-2. (4) Intensity of the line associated with
the VBC, with associated errors, measured in units of $10^{-15}$ erg s-1 cm-2.

Table 4: Civ and line measurements.

Object name |  Civ |
---|---|---
| BLUE | BC | VBC | BLUE | BC | VBC
(1) | (2) | (3) | (4) | (5) | (6) | (7)
Mrk 335 | $24.9\pm 16.9$ | $3943\pm 274$ | … | $153\pm 33$ | $454\pm 77$ | …
Mrk 110 | $68.2\pm 40.2$ | $5526\pm 427$ | … | … | $413\pm 99$ | …
Mrk 509 | $266\pm 130$ | $11100\pm 994$ | … | $394\pm 154$ | $1096\pm 300$ | …
Ark 564 | $29.5\pm 21.5$ | $409\pm 54$ | … | $42.1\pm 24.9$ | $140\pm 30$ | …
Mrk 478 | $213\pm 30$ | $820\pm 100$ | … | $124\pm 25$ | $102\pm 35$ | …
Ton 28 | $203\pm 65$ | $221\pm 88$ | … | $63.9\pm 46.5$ | $36.4\pm 62.7$ | …
LB 2522 | $201\pm 83$ | $87.6\pm 99.2$ | … | $53.5\pm 59.8$ | $31.8\pm 95.1$ | …
LEDA 51016 | $151\pm 25$ | $446\pm 67$ | … | $58.4\pm 17.1$ | $42.5\pm 25.0$ | …
I Zw 1 | $987\pm 97$ | $678\pm 96$ | … | $197\pm 47$ | $143\pm 45$ | …
PHL 1092 | $26.2\pm 4.4$ | $5.23\pm 2.84$ | … | $3.17\pm 2.06$ | $0.56\pm 2.23$ | …
Fairall 9 | $448\pm 84$ | $2354\pm 185$ | $1772\pm 295$ | $14.7\pm 33.2$ | $172\pm 59$ | $127\pm 86$
Ark 120 | $1500\pm 155$ | $2500\pm 169$ | $1002\pm 154$ | … | $150\pm 48$ | $401\pm 107$
NGC 3783 | $2318\pm 282$ | $8720\pm 534$ | $6119\pm 867$ | $85.6\pm 86.0$ | $794\pm 175$ | $2180\pm 570$
TXS 0042+101 | $5.0\pm 1.6$ | $18.7\pm 2.8$ | $33.0\pm 6.9$ | … | $1.5\pm 1.1$ | $7.5\pm 4.2$

444(1) Object common name. (2),(5) Intensity of the line associated with the
BLUE, with associated errors, measured in units of $10^{-15}$ erg s-1 cm-2.
(3),(6) Intensity of the line associated with the BC, with associated errors,
measured in units of $10^{-15}$ erg s-1 cm-2. (4),(7) Intensity of the line
associated with the VBC, with associated errors, measured in units of
$10^{-15}$ erg s-1 cm-2.

Table 5: $\lambda 1900$ blend line measurements.

Object name | AlIII | SiIII] | CIII]
---|---|---|---
| BLUE | BC | BLUE | BC | BLUE | BC | VBC
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
Mrk 335 | … | $42.5\pm 45.9$ | … | $186\pm 68$ | … | $705\pm 125$ | …
Mrk 110 | … | … | … | … | … | … | …
Mrk 509 | … | $441\pm 210$ | … | $916\pm 277$ | … | $2034\pm 401$ | …
Ark 564 | … | $14.6\pm 7.4$ | … | $36.5\pm 10.5$ | … | $231\pm 25$ | …
Mrk 478 | … | $101\pm 26$ | … | $217\pm 38$ | … | $298\pm 46$ | …
Ton 28 | … | $135\pm 81$ | … | $84.8\pm 74.3$ | … | $51.2\pm 51.8$ | …
LB 2522 | … | $60.2\pm 87.4$ | … | $13.1\pm 89.4$ | … | $85.7\pm 92.0$ | …
LEDA 51016 | … | $30.9\pm 14.6$ | … | $93.9\pm 23.0$ | … | $94.0\pm 23.1$ | …
I Zw 1 | … | $153\pm 34$ | … | $270\pm 46$ | … | $162\pm 35$ | …
PHL 1092 | $3.9\pm 1.6$ | $9.6\pm 4.1$ | $4.1\pm 1.7$ | $9.7\pm 4.2$ | $3.3\pm 1.5$ | $1.2\pm 3.9$ | …
Fairall 9 | … | $137\pm 43$ | … | $440\pm 70$ | … | $294\pm 59$ | $189\pm 51$
Ark 120 | … | $116\pm 51$ | … | $396\pm 82$ | … | $457\pm 77$ | $301\pm 93$
NGC 3783 | … | $499\pm 151$ | … | $661\pm 170$ | … | $1160\pm 201$ | $1024\pm 344$
TXS 0042+101 | … | $2.1\pm 1.1$ | … | $2.3\pm 1.2$ | … | $5.4\pm 1.5$ | $6.0\pm 3.0$
555(1) Object common name. (2),(4),(6) Intensity of the line associated with
the BLUE, with associated errors, measured in units of $10^{-15}$ erg s-1
cm-2. (3),(5),(7) Intensity of the line associated with the BC, with
associated errors, measured in units of $10^{-15}$ erg s-1 cm-2. (8) Intensity
of the line associated with the VBC, with associated errors, measured in units
of $10^{-15}$ erg s-1 cm-2.

Table 6: Optical line measurements.

Object name | HeII$\lambda 4686$ | H$\beta$ | FeII
---|---|---|---
| BC | VBC | BLUE | BC | VBC | BC
(1) | (2) | (3) | (4) | (5) | (6) | (7)
Mrk 335 | $199\pm 46$ | … | … | $669\pm 72$ | … | $139\pm 25$
Mrk 110 | $24.1\pm 4.3$ |  | … | $147\pm 16$ | … | $29.2\pm 5.6$
Mrk 509 | $447\pm 92$ | … | … | $1877\pm 230$ | … | $38.6\pm 28.7$
Ark 564 | $10.2\pm 3.7$ | … | … | $36.5\pm 6.4$ | … | $24.3\pm 6.8$
Mrk 478 | $5.35\pm 0.99$ | … | $6.15\pm 1.53$ | $157\pm 12$ | … | $169\pm 10$
Ton 28 | … | … | … | $124\pm 17$ | … | $129\pm 12$
LB 2522 | … | … | … | $35.3\pm 7.8$ | … | $45.7\pm 5.3$
LEDA 51016 | … | … | $8.1\pm 1.6$ | $58.7\pm 8.3$ | … | $67.4\pm 6.4$
I Zw 1 | … | … | $29.2\pm 6.2$ | $298\pm 40$ | … | $599\pm 50$
PHL 1092 | … | … | $2.3\pm 0.7$ | $12.7\pm 2.7$ | … | $26.2\pm 3.0$
Fairall 9 | … | … | … | $187.0\pm 20.7$ | $239\pm 42$ | $184\pm 24$
Ark 120 | … | $154\pm 39$ | $261\pm 26$ | $809\pm 56$ | $991\pm 103$ | $1160\pm 86$
NGC 3783 | … | $231\pm 55$ | … | $1142\pm 73$ | $521\pm 112$ | $332\pm 56$
TXS 0042+101 | … | … | … | $3.1\pm 1.1$ | $8.8\pm 4.0$ | $0.5\pm 0.7$
666(1) Object common name. (2),(5),(7) Intensity of the line associated with
the BC, with associated errors, measured in units of $10^{-15}$ erg s-1 cm-2.
(3),(6) Intensity of the line associated with the VBC, with associated errors,
measured in units of $10^{-15}$ erg s-1 cm-2. (4) Intensity of the line
associated with the BLUE, with associated errors, measured in units of
$10^{-15}$ erg s-1 cm-2.

Table 7: Diagnostic intensity ratios

Object | Component | $\frac{{\rm CIV}}{{\rm HeII}_{\rm UV}}$ | $\frac{{\rm CIV}}{\rm H\beta}$ | $\frac{\rm SiIV+OIV]}{{\rm CIV}}$ | $\frac{\rm SiIV+OIV]}{{\rm HeII}_{\rm UV}}$ | $\frac{{\rm AlIII}}{{\rm CIV}}$ | $\frac{{\rm AlIII}}{{\rm SiIII]}}$ | $\frac{{\rm SiIII]}}{{\rm CIII]}}$ | $\frac{\rm FeII}{{\rm H}\beta}$ | $\frac{{\rm HeII}_{\rm opt}}{\rm H\beta}$ | $\frac{{\rm CIII]}}{{\rm CIV}}$
---|---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
Mrk 335 | BC | $8.69\pm 1.60$ | — | $0.16\pm 0.02$ | $1.40\pm 0.29$ | $0.01\pm 0.01$ | $0.23\pm 0.26$ | $0.26\pm 0.11$ | $0.21\pm 0.04$ | $0.30\pm 0.08$ | $0.18\pm 0.03$
Mrk 110 | BC | $13.39\pm 3.37$ | — | $0.13\pm 0.02$ | $1.71\pm 0.48$ | — | — | — | $0.20\pm 0.04$ | $0.16\pm 0.03$ | —
Mrk 509 | BC | $10.16\pm 2.93$ | — | $0.17\pm 0.03$ | $1.70\pm 0.54$ | $0.04\pm 0.02$ | $0.48\pm 0.27$ | $0.45\pm 0.16$ | $0.02\pm 0.02$ | $0.24\pm 0.06$ | $0.18\pm 0.04$
Ark 564 | BC | $2.91\pm 0.74$ | $11.19\pm 2.45$ | $0.28\pm 0.07$ | $0.82\pm 0.25$ | $0.04\pm 0.02$ | $0.40\pm 0.23$ | $0.16\pm 0.05$ | $0.67\pm 0.22$ | $0.28\pm 0.11$ | $0.57\pm 0.10$
Mrk 478 | BC | $8.04\pm 2.94$ | $5.21\pm 0.75$ | $0.66\pm 0.17$ | $5.31\pm 2.18$ | $0.12\pm 0.03$ | $0.46\pm 0.14$ | $0.73\pm 0.17$ | $1.08\pm 0.11$ | $0.03\pm 0.01$ | $0.36\pm 0.07$
Ton 28 | BC | $6.08\pm 10.72$ | — | $0.90\pm 0.72$ | $5.47\pm 10.15$ | $0.61\pm 0.44$ | $1.59\pm 1.69$ | $1.66\pm 2.22$ | $1.04\pm 0.18$ | — | $0.23\pm 0.25$
LB 2522 | BC | $2.75^{+8.79}_{-2.75}$ | — | $1.78^{+2.40}_{-1.78}$ | $4.91^{+15.08}_{-4.91}$ | $0.69^{+1.27}_{-0.69}$ | $4.59^{+32.04}_{-4.59}$ | $0.15^{+1.06}_{-0.15}$ | $1.30\pm 0.32$ | — | $0.98^{+1.53}_{-0.98}$
LEDA 51016 | BC | $10.50\pm 6.37$ | — | $0.68\pm 0.13$ | $7.17\pm 4.30$ | $0.07\pm 0.03$ | $0.33\pm 0.18$ | $1.00\pm 0.35$ | $1.15\pm 0.19$ | — | $0.21\pm 0.06$
I Zw 1 | BC | $4.73\pm 1.63$ | — | $0.71\pm 0.13$ | $3.36\pm 1.12$ | $0.23\pm 0.06$ | $0.57\pm 0.16$ | $1.66\pm 0.46$ | $2.01\pm 0.32$ | — | $0.24\pm 0.06$
PHL 1092 | BC | $9.27^{+36.94}_{-9.27}$ | — | $1.40\pm 1.02$ | $12.97^{+51.60}_{-12.97}$ | $1.84\pm 1.27$ | $0.99\pm 0.60$ | $7.84^{+24.72}_{-7.84}$ | $2.07\pm 0.49$ | — | $0.24^{+0.75}_{-0.24}$
| BLUE | $8.26\pm 5.56$ | — | $1.04\pm 0.27$ | $8.55\pm 5.84$ | $0.15\pm 0.07$ | $0.96\pm 0.56$ | $1.24\pm 0.76$ | $\leq 1.28$ | — | $0.13\pm 0.06$
Fairall 9 | BC | $13.69\pm 4.80$ | $12.60\pm 1.71$ | $0.15\pm 0.02$ | $2.11\pm 0.75$ | $0.06\pm 0.02$ | $0.31\pm 0.11$ | $1.49\pm 0.38$ | $0.98\pm 0.17$ | — | $0.12\pm 0.03$
| VBC | $13.92\pm 9.73$ | $7.41\pm 1.79$ | $0.17\pm 0.03$ | $3.06\pm 2.15$ | $\leq 0.02$ | — | — | $\leq 0.15$ | — | $0.11\pm 0.03$
Ark 120 | BC | $16.66\pm 5.41$ | — | $0.35\pm 0.07$ | $5.87\pm 2.13$ | $0.05\pm 0.02$ | $0.29\pm 0.14$ | $0.87\pm 0.23$ | $0.84\pm 0.08$ | — | $0.18\pm 0.03$
| VBC | $2.50\pm 0.77$ | — | $0.50\pm 0.20$ | $1.25\pm 0.58$ | $\leq 0.05$ | — | — | $\leq 0.17$ | $0.16\pm 0.04$ | $0.30\pm 0.10$
NGC 3783 | BC | $10.99\pm 2.51$ | $7.64\pm 0.68$ | $0.12\pm 0.02$ | $1.28\pm 0.34$ | $0.06\pm 0.02$ | $0.75\pm 0.30$ | $0.57\pm 0.18$ | $0.29\pm 0.05$ | — | $0.13\pm 0.02$
| VBC | $2.80\pm 0.83$ | $11.74\pm 3.02$ | $0.06\pm 0.02$ | $0.25\pm 0.09$ | $\leq 0.03$ | — | — | $\leq 0.67$ | $0.44\pm 0.14$ | $0.12\pm 0.04$
TXS 0042+101 | BC | $12.56\pm 9.78$ | $6.01\pm 2.24$ | $0.18\pm 0.09$ | $2.29\pm 2.07$ | $0.11\pm 0.07$ | $0.90\pm 0.66$ | $0.43\pm 0.24$ | $0.16\pm 0.24$ | — | $0.29\pm 0.09$
| VBC | $4.40\pm 2.63$ | $3.75\pm 1.89$ | $0.19\pm 0.18$ | $0.46\pm 0.51$ | $\leq 0.05$ | — | — | $\leq 0.20$ | — | $0.32\pm 0.17$

777(1) Object common name. (2) Component considered for the estimation of
metallicity. (3)-(12) Diagnostic ratios used for the estimation of
metallicity, with the associated error. —: not used or not available. Upper
limits for some diagnostic ratios as described in Section 3.7 are shown.

Tables 3, 4, 5, 6 report the intensity of each different line component for
the objects of the sample measured from the multi-component fitting, with
associated errors, for the four spectral ranges that have been fit separately,
namely the Siiv+Oiv], Civ+, Aliii+Siiii]+Ciii], H$\beta$+Feii. The fits are
shown in the Figures of Appendix A, and the projections of the ($U$,
$n_{\mathrm{H}}$, $Z$) parameter space in Appendix B. Table 7 summarizes the
diagnostic intensity ratios used for the estimation of the physical
parameters, while estimates for the metallicity and physical conditions in the
BLR for our sample are shown in Table 8. Here follow considerations on the
results obtained for each of the individual sources:

  * •

Mrk 335 is a Population A object. It has been a target of several
reverberation mapping campaigns in the optical (Peterson et al., 2004): Grier
et al. (2012) obtain 13.9 $\pm$ 0.9 days for H$\beta$. The resulting $M_{\rm
BH}$ is $(2.6\pm 0.8)\times 10^{7}$ M⊙, for a luminosity $\approx 7.7\cdot
10^{44}$ erg s-1. Mrk 335 is therefore considered a Population A source
radiating at a modest Eddington ratio
($L_{\mathrm{bol}}/L_{\mathrm{Edd}}$$\lesssim 0.2$). (although see Mastroserio
et al., 2020). Its BLR was spatially resolved in the infrared, obtaining an
upper limit for its size of 0.155 pc (GRAVITY Collaboration et al., 2020). The
source might presently be close to its lowest state (Grupe et al., 2018),
although there has been a recent upturn (Komossa et al., 2020). Both Civ and
H$\beta$ do not reveal any significant blueshifted excess to the Lorentzian
profile (cf. van Groningen, 1987), implying a very weak wind component.

The estimation of the physical conditions in the BLR yielded a result
characterized by subsolar metallicity and very low density. The low
metallicity reported in the paper is a lower limit since the result is likely
due to the lack of CLOUDY simulations with 0.2 $Z_{\odot}$ or 0.5 $Z_{\odot}$
(the $Z$ of Mrk 110 and 509, with similar spectra, is around solar).
Additionally, the gas density value is the lowest in the sample
($\log$$n_{\mathrm{H}}$ $\sim 8$ cm-3). A low-density value is supported by
very strong Ciii] emission and a very low Aliii/Ciii] ratio. Interestingly,
the [O iii]$\lambda\lambda$4959,5007 doublet can be fit by a narrow component
with a semi-broad component with a width similar to the one of H$\beta$BC. The
estimated BLR density is higher than the critical density of [O
iii]$\lambda\lambda$4959,5007. However, some [O iii]$\lambda\lambda$4959,5007
emission is predicted by CLOUDY simulations to be $\sim 0.05$ the one of
H$\beta$ in the BLR. Considering the low BLR $n_{\mathrm{H}}$, a radial
stratification of $n_{\mathrm{H}}$ (Baldwin et al., 1995) may facilitate [O
iii]$\lambda\lambda$4959,5007 emission.

  * •

Mrk 110 is a Population A object of spectral type A1 that, not surprisingly,
exhibits spectral features remarkably similar to Mrk 335. A peculiarity is the
presence of a weak asymmetry towards the red in the profiles of both Civ and
H$\beta$. The asymmetry was modeled adding a faint redshifted component
affecting Civ intensity by about 20%, with no significant effect on the
H$\beta$ flux. A redshifted asymmetry had been already detected in the Balmer,
Hei, and Heii$\lambda$4686 lines and has been interpreted as due to
gravitational redshift (Kollatschny, 2004; Müller & Wold, 2006; Gavrilović et
al., 2007). Consistently, the BLR of Mrk 110 appears to be compact:
$\tau\approx 20-30$ ld (Peterson et al., 1998; Kollatschny et al., 2001; Li et
al., 2013). If the $M_{\rm BH}$$\approx 2\cdot 10^{7}$ M⊙ derived by
Kollatschny et al. is corrected for a viewing angle $\theta\approx
30^{\circ{}}$ the central mass could reach $\sim 10^{8}$. A photoionization
solution following the locally optimized cloud model indicates emission from
the BLR region starting at $\log r\approx 15.3$ (Juráňová et al., 2024),
implying an inner radius $\sim 100$ gravitational radii. Gravitational and
transverse shifts could then explain the shift amplitude of the additional
components of Civ and H$\beta$ included in the fit ($\approx 4500$ km s-1). If
this interpretation is correct, the compact BLR and an overmassive black hole
compared to other A1 sources could be at the origin of the redshifted excess
(Gavrilović et al., 2007; Marziani, 2023).

The Civ/H$\beta$ $\sim 37$ was deemed inappropriate and thus excluded from the
measurement of the metallicity. Indeed, similar measurements of the intensity
of the lines from Juráňová et al. (2024) returned a value of $\sim 13$, much
more appropriate, indicating a light loss in our optical spectrum as a
possible cause of the mismatch. The solution obtained is very well-constrained
around solar metallicity (Fig. 15, Tab. 8).

  * •

Mrk 509 is a Population A1 object, with very weak or absent Feii lines in its
optical spectrum. It has been monitored in the optical, UV, and X-ray domain
(Kriss et al., 2019), and more recently in IR (Mitchell et al., 2024). Any
blueshifted excess is barely visible in Siiv+Oiv] and , and very faint in both
Civ and H$\beta$, although spectropolarimetry reveals the presence of an
accretion disk wind (Lira et al., 2021). H$\beta$ reverberation mapping yields
a time delay of $\approx$ 79.6${}^{+6.1}_{-5.4}$ ld (Bentz et al., 2013; Du et
al., 2015), and a mass $\sim 2\cdot 10^{8}$ M⊙ (Yu et al., 2020).
Additionally, its BLR was recently spatially resolved in the infrared,
revealing an upper limit to its size of 0.249 pc (GRAVITY Collaboration et
al., 2020).

Measurement of the intensity of its lines, especially Civ and Siiv+Oiv], has
been affected by the presence of many absorption lines. However, the measured
line ratios constrain very well $Z$, $U$, and $n_{\rm H}$, yielding about
solar metallicity, a value that could be considered typical of spectral type
A1.

  * •

Ark 564 is a Population A object belonging to the A2 spectral bin of the MS.
Long-term monitoring of the object has been performed over time in the optical
range (Shapovalova et al., 2012), yielding a rather short time delay between
continuum and H$\beta$ variation, around $6.7\pm 10$ days. There is evidence
of an excess emission on the blue side of the of Civ and and a high-
ionization, the relativistic wind has been detected in the X-ray domain via
the discovery of lines of highly ionized oxygen shifted by $\sim 0.1c$ (Gupta
et al., 2013). These properties are fairly typical of A2 sources with quite
strong Feii emission and higher $L/L_{\mathrm{Edd}}$ compared to the objects
of spectral type A1.

The ionization parameter is consistent with $\log U\sim-1$. and the presence
of strong Ciii] emission drives the solution toward low-density values $\log$
$n_{\mathrm{H}}$$\sim 7$, as in the case of Mrk 335. Repeating the estimation
of the physical parameters without the use of the diagnostic ratios including
Ciii] returned a somewhat different scenario, with higher density ($\log
n_{\rm H}\sim 11$) and solar metallicity, in better agreement with the
reverberation delay (see the discussion in Section 6.4). The rather high
$\chi^{2}$ value (Tab. 8) is due to the contributions of the Civ/ and
Ciii]/Civ, which are in turn due mainly to the small uncertainties associated
with these two ratios, rather than to a disagreement between the observed and
the predicted value from the minimum $\chi^{2}$ solution (Civ/ $\approx$ 4.3
vs. 2.9, and Ciii]/Civ $\approx$ 0.87 vs. 0.57 predicted vs. observed). The
result obtained for the metallicity, 5 $Z_{\odot}$ is thus stable, also
compared to other Population A objects. A detached 1$\sigma$ region (Fig. 15)
would imply a slightly lower $Z$ and a significantly higher $n_{\mathrm{H}}$
($\log n_{\mathrm{H}}\sim 10$ [cm-3]).

  * •

Mrk 478 is a Population A object, a NLSy1 with prominent but not extreme Feii
emission. A very recent study indicates an H$\beta$ lag of $\approx 45-55$
days to continuum changes (Woo et al., 2024). Not unlike Ark 564, Mrk 478
could be regarded as a bridge between the A1 and xA spectral types, since it
exhibits some spectral characteristics that are typical of both. Its $R_{\rm
FeII}$ $\sim$ 1 makes Mrk 478 a borderline source (Marziani et al., 2010, see
also Table 7). The high $Z$ value obtained, along with $U$ and $n_{\rm H}$ are
plausible given our measurements. A relevant question is what drives the
metallicity to a value that is higher by a factor of 10 to an object that is
not so dissimilar in the optical spectral range to Ark 564? As a matter of
fact, Civ/, Siiv+Oiv]/Civ and Siiv+Oiv]/, all $Z$ indicators, are $\approx
2.8$, 2.4, and 6.5 times higher in Mrk 478. The Siiv+Oiv]/Civ close to unity
requires, under the physical conditions of the BLR, very high
$Z\sim\mathcal{O}(100)$ (Śniegowska et al., 2021; Garnica et al., 2022). The
high $\chi^{2}$ (actually the highest of the sample) is due to the
Feii/H$\beta$ ratio: the predicted value is too low, by a factor of 3. As in
the case of Ark 564, the high intensity of Ciii] measurement returns a lower
density of the gas compared to that obtained for other xA sources. The
relatively low density and high ionization are not conducive to strong Feii
emission, but the observed prominence of Feii is certainly consistent with a
high metallicity solution.

  * •

Ton 28 Even if the $R_{\rm FeII}$ is not as high, Ton 28 shares several
extreme properties with I Zw 1, such as extreme blueshifts in both Civ and [O
iii]$\lambda\lambda$4959,5007 (Zamanov et al., 2002). Estimates of the time-
lag $\tau$ between continuum variations and H$\beta$ response are dependent on
the method applied for the cross-correlation analysis; the Javelin-based (Zu
et al., 2011) estimate is $c\tau\approx 48.2^{+3.3}_{-3.1}$ ld, larger than
the CCF centroid $c\tau\approx 37.3_{-6.0}^{+6.9}$ ld (Li et al., 2021),
consistent with a previous estimate affected by a large uncertainty
($32.2_{-4.2}^{+43.5}$ ld, Du et al., 2018). Velocity-resolved reverberation
maps of H$\beta$ reveal a signature of Keplerian disk-like motion (Li et al.,
2021). Spectro-polarimetric observations indicate a large H$\alpha$ line width
in polarized light ($\approx 4220$ km s-1) compared to the width in natural
light ($\approx 1770$ km s-1, Capetti et al. 2021), implying an almost face-on
view ($\theta\approx 15^{\circ{}}$, Śniegowska et al., 2023). Despite the
lower S/N to other sources used in this work, the results obtained during the
estimation of physical parameters are well constrained and suggest a solution
of $\approx 50Z_{\odot}$, with high density.

  * •

LB 2522 $\equiv$ PG 1259+593 represents a typical xA object in our sample
(Negrete et al., 2018), belonging to the A3 spectral type. LB 2522 has been
subject to a reverberation study in the MIR wavelength range (Lyu et al.,
2019) that yields a delay time in the W2
band888https://www.astro.ucla.edu/~wright/WISE/passbands.html of $\tau\approx
794$ days. These values set an upper limit for $r_{\mathrm{BLR}}$, with the
delay time of the H$\beta$ emission being estimated around $\tau=225\pm 75$
days (Du, private communication).

Although it is one of the most luminous objects of the sample, due to its
large distance its FOS spectra are subject to more noise ($S/N\approx 5$) than
other sources studied in this work. Nevertheless, the line intensity yielded a
fairly precise measurement of the physical parameters of the BLR, with a
metallicity of about 20 $Z_{\odot}$ and an average density of the gas (Tab. 8,
Fig. 17).

  * •

LEDA 51016 $\equiv$ PG 1415+451 is a typical xA object, exhibiting a very
strong Feii emission in the optical wavelength range, and a prominent
blueshifted component in Civ, appreciable also in H$\beta$ (Fig. 12). Optical
monitoring for reverberation mapping yields a time delay of H$\beta$ to
continuum at 5100 Å of $\tau\approx 30.0_{-4.6}^{+5.4}$ days (Hu et al.,
2021), to be compared with $\tau\approx 433$ days in the MIR (Lyu et al.,
2019).

The COS and FOS spectra of LEDA 51016 appear with very high S/N, and the
results are consistent with other xA sources of the sample, including well-
constrained supersolar metallicity ($\log Z\approx 1.3^{+0.4}_{-0.3}$) and
relatively high gas density. In this case, as for the prototypical source I Zw
1, the low ionization, high-density solution retrieved by Negrete et al.
(2012) is possible within the 1$\sigma$ uncertainty range (Tab. 8, Fig. 16).

  * •

I Zw 1 is a narrow-line Seyfert 1 galaxy with a strong Feii emission
(Phillips, 1978). Emission lines are narrow, with H$\beta$ FWHM estimates in
the range between 1100–1500 km s-1. The line narrowness has made I Zw 1 an
ideal source for the extraction of a template of Feii emission in the optical
(Boroson & Green, 1992; Laor et al., 1997; Marziani et al., 2009), IR (Garcia-
Rissmann et al., 2012), and UV (Vestergaard & Wilkes, 2001) domains. The
source has been hailed as a prototype for Population A (Sulentic et al.,
2000a) and, more recently, for extreme Population A (Marziani & Sulentic,
2014), due to its strong Feii, weak Ciii], high Siiv+Oiv]/Civ ratio, and weak
Civ equivalent width. I Zw 1 has been monitored for reverberation mapping: the
rest-frame delay for H$\beta$ is $\tau\approx 37.2^{+4.9}_{-4.6}$ days (Huang
et al., 2019). More recently, the amplitude of flux variation has been so
small to make it is impossible to estimate a time lag for H$\beta$ (U et al.,
2022).

Previous studies focused on the physical conditions in the virialized BLR of I
Zw 1 suggested a low ionization solution, with high density (Marziani et al.,
2010; Panda, 2021b) and a possible metallicity enhancement (Negrete et al.,
2012). The estimation of the physical parameters in this work leads to a
solution of $\approx 20Z_{\odot}$, with medium-high density.

  * •

PHL 1092 has been hailed as one of the strongest Feii emitters ever discovered
(Marinello et al., 2020; Panda et al., 2020; Martínez-Aldama et al., 2021, and
references therein). Our measurements confirm the extremely strong $R_{\rm
FeII}$$\approx 1.75$ placing PHL 1092 in the spectral type A4, where only
$\approx$3% of optically selected quasars are found (Marziani et al., 2013).
The measurements of line intensities and FWHM for the BC and BLUE in both the
optical and UV ranges are consistent with those reported in Marinello et al.
(2020) (the slightly higher value of $R_{\rm FeII}$ reported by these authors
is due to their removal of the BLUE of H$\beta$). The extreme attributes of
this object are highlighted by its distinction as the sole source in the
sample displaying a BLUE in the $\lambda 1900$ blend, a rare occurrence even
among xA objects (Marziani et al., 2022; Buendia-Rios et al., 2023).

The metallicity estimated for this source ($Z\sim 1000Z_{\odot}$) is
apparently out of scale, higher than the highest estimates for xA quasars at
high luminosity, seldom exceeding $Z\sim 100Z_{\odot}$ (Garnica et al., 2022).
However, this result aligns with the low ionization, high-density solution of
xA sources (Negrete et al., 2012): low Civ, high Aliii/Siiii], high
Siiv+Oiv]/Heii$\lambda$4686 prominent Feii, and very low Ciii]/Siiii] imply
low $U$, high $n_{\mathrm{H}}$, and high $Z$. The inordinately high value of
the $Z$ is driven by the Siiv+Oiv]/Civ $\gtrsim 1$, which excludes $Z$ values
only a few times above solar. In the case of PHL 1092, the
Civ/Heii$\lambda$4686 and Civ/H$\beta$ ratios are highly uncertain, in part
because of absorptions. The ionization parameter $\sim 10^{-3}$ accounts for
the weak Civ: the Civ BC equivalent width is just $\lesssim 2\AA$, with a
Civ/H$\beta$ ratio $\sim 1$. The $W$ Civ BC+BLUE $\approx 8\AA$, qualifies PHL
1092 among the weak-lined quasars (WLQ; Diamond-Stanic et al. 2009; Shemmer et
al. 2010; Shemmer & Lieber 2015), that are xA sources by the wide majority
(Marziani et al., 2016; Martínez-Aldama et al., 2018).

A major difficulty is introduced by the large errors associated with most
measured ratios (Tab. 7). Most ratios should be considered upper limits. In
addition, the out-of-scale value $Z\sim 1000Z_{\odot}$, is greatly reduced to
$\sim 50$ $Z_{\odot}$ if a microturbulence $\approx$ 10 km s-1 is introduced
in the computations which act as a metallicity controller (see Panda, 2021b,
for an in-depth analysis).

Therefore, the metallicity estimated for the BLUE ($Z\sim 50Z_{\odot}$) could
provide a representative lower limit for this object, since it accounts for
most of the observed flux in the HILs. BLUE and the BC revision with
turbulence will still place the source on par with the highest $Z$ estimates
in the sample.

  * •

Fairall 9 is a prototypical Population B source, with its spectrum almost
coinciding with the composite spectrum of Population B objects (Jiang et al.,
2021, M23). Reverberation mapping of the object has been performed in the past
both in the optical, yielding a well-defined delay $\tau\approx
17.4^{+3.2}_{-4.3}$ days (Bentz et al., 2013). Dust-reverberation mapping
yielded a delay in the W1 and W2 maps $\approx$ 250 days in the W1 band at
$3.4\mu$m, and between $\approx 280$ and $\approx 370$ days for the W2 band at
4.6 $\mu$m (Chen et al., 2023). The Fairall 9 H$\beta$ red wing extends up to
$\sim 18,000$ km s-1, beyond [O iii]$\lambda\lambda$4959,5007 (Fig. 13). This
is not uncommon among Pop. B sources. The only peculiarity is the occurrence
of a plateau on the red side of H$\beta$ NC, leaving a faint semi-broad
residual at $v_{\mathrm{r}}\approx 2500$ km s-1. Analogous features are seen
in Pop. B objects, albeit rarely. One case in point is Ark 120, discussed
below. A spectropolarimetric analysis of Fairall 9 (Jiang et al., 2021)
suggested the presence of a warped geometry of the accretion disk, but it is
not obvious if the residual feature detected in natural light might be
connected to the warped disk.

The estimations of the metallicity of the BC and VBC return about 2
$Z_{\odot}$ for the BC, and 1 $Z_{\odot}$ for the VBC, consistent within the
uncertainties (Fig. 17). The $1\sigma$ confidence range of $Z$ for the BC is
rather broad ranging from -1 to 0.7. The ionization parameter is constrained
within an order of magnitude, and the $n_{\mathrm{H}}$ is only within 4 orders
of magnitude. The VBC parameters appear better constrained. The wide range of
confidence intervals might be the indication of radial stratification in the
BLR gas emitting the BC. The VBC, as associated with gas in the innermost
region, may have intrinsically better-defined physical parameters.

  * •

Ark 120 stands out as the most peculiar object in the sample. The main
peculiarity is its unusual double-peaked H$\beta$ profile, which was modeled
in this work using a BC and two satellite components, one blueshifted and the
other redshifted, roughly symmetrically displaced by $\pm 2000$ km s-1. This
profile is not unique, and likely hints toward some reproducible structure or
dynamical process within the BLR (Marziani et al., 1992; Korista, 1992;
Korista et al., 1997). Even after extensive monitoring, the nature of its
double-peaked profile has not been completely understood, although periodic
variations have been suggested (Li et al., 2019). Fairall 9 might undergo a
similar phenomenon. Ark 120 exhibits a rather strong Feii emission for a
Population B object ($R_{\rm FeII}$ = 0.84, see Table 7), likely originating
in a region further from the one in which originates H$\beta$, which exhibits
a time delay of $\tau=57.3\pm 23.0$ days (Kuehn et al., 2008).

The presence of a mismatch between the UV and optical fluxes after correcting
the flux for galactic extinction indicates the presence of a stronger
extinction than expected. This leads to an underestimation of the Civ/H$\beta$
ratio, which reduces the resulting metallicity. We therefore excluded the
Civ/H$\beta$ diagnostic ratio during the computation. Once excluded from the
inordinately low Civ/H$\beta$, the $Z$ solution converges to a well-defined
metallicity value. The moderate Siiv+Oiv]/Civ ratio indicates abundances at
least solar or a few times above solar. The value obtained ($Z\sim
10Z_{\odot}$) for the BC is consistent with the one for the VBC ($Z\sim
5Z_{\odot}$). This is in the case that the satellite lines are included in the
total flux of the BC. Removing them, and using only the central core of the
H$\beta$ profile (Fig. 14) would imply an $R_{\rm FeII}$$\approx 1.5$ that is
out-of-scale to the other line ratios.

  * •

NGC 3783 is the closest object of the sample, located at a redshift, z =
0.009. It is a well-known object, extensively monitored for reverberation
mapping, with an H$\beta$-emitting region having a median radius delay $r_{\rm
median}=10.07^{+1.10}_{-1.21}$ lt-day (Bentz et al., 2021). Lira et al. (2021)
performed a spectropolarimetric study of the object, revealing evidence of a
nuclear wind whose presence is also revealed by the excess of the blue side of
Civ and Siiv+Oiv] (Fig. 14), most likely due to outflowing gas. The BLR of NGC
3783 was spatially resolved in the infrared, obtaining an upper limit for its
size of 0.110 pc (GRAVITY Collaboration et al., 2020). The spectrum of this
object almost coincides with the composite spectrum obtained for the RQ
Population B.

Confronting the diagnostic ratios of the analyzed spectra with the CLOUDY
simulations, the BC is associated with a slightly sub-solar metallicity, with
the VBC having a compatible result of solar metallicity. The ionization
parameter gradient obtained for the BC and VBC of this object is consistent
with a more ionized VBC, being closer to the ionizing source.

  * •

TXS 0042+101 is the farthest object of the sample. We measured $z\approx$
0.587, in agreement with Tang et al. (2012). It is the only RL object of the
sample. Like many other RL sources, it is well studied in the radio wavelength
range, with its FRII radio morphology described in Hutchings et al. (1998).
Optical observations are poor. The VBC is relatively prominent, allowing for
an independent $Z$ estimate, even if the S/N is among the worst in the sample.

The $Z$ results are reliable, with sub-solar metallicity for the BC and VBC,
consistent among each other, and with a low minimum $\chi^{2}$. The spectrum
of TXS 0042+101 and its derived properties are consistent with the median
composite of RL quasars in the B1 spectral type (M23).

###  4.2 The trend along the MS

Figure 4 depicts the MS representation of our sample, alongside representative
values from S21, G22 and M23. The main result is that the highest-metallicity
objects are clustered in the xA region of the MS. Conversely, all other
objects with solar or subsolar metallicity are situated in the left portion of
the MS, demonstrating a gradient of metallicity that peaks in the xA segment
of the MS and gradually decreases towards RL Population B sources - an
outstanding result confirming the theoretical predictions from Panda et al.
(2019b). At one extreme, TXS 0042+101 comes close to the RL template of M23,
with subsolar $Z$, with $\log Z\sim-0.3$ and $\sim-1.0$, respectively. For the
sources of ST A1 and B1 with stronger Feii we encounter $Z$ around solar,
which become supersolar for $R_{\rm FeII}$$\gtrsim$ 0.5. An important result
is that these sources are at low-$z$, and reach $Z$ comparable to the samples
of S21 and Garnica2022 that are high $z$, and associated with quasars of very
high $M_{\rm BH}$ and extreme luminosity. Conversely, xA sources of the
present sample are AGNs of moderate luminosity, Narrow Line Seyfert 1s
(NLSy1s) with $M_{\rm BH}$$\lesssim 10^{8}$ M⊙. Since the high-$z$ objects are
extreme radiators at high Eddington ratio
$L_{\mathrm{bol}}/L_{\mathrm{Edd}}$$\sim 1$, as are the xA of our sample, the
enrichment phenomenon appears to be independent of cosmic epoch and from black
hole mass, at least up to cosmic ages $\sim 3$ Gyr after the Big Bang.

The mechanisms that could explain the high $Z$ values and the presence of a
gradient of metallicity will be briefly discussed in Section 6.5.

Figure 4: MS representation of our sample. Every object is placed according to
its RFeII and FWHM(H$\beta$). Greater metallicity $Z$ is expressed with
increasing marker sizes and different colors. Objects with sub-solar
metallicity are marked in red, objects with $1\ Z_{\odot}\leq Z\leq 2\
Z_{\odot}$ in orange, objects with $2\ Z_{\odot}<Z\leq 10\ Z_{\odot}$ are
marked in gold, objects with $10\ Z_{\odot}<Z\leq 50\ Z_{\odot}$ are marked in
blue, and objects with metallicity greater than 50 $Z_{\odot}$ are marked in
indigo. Sources from this work are shown in circles. Squares are used as
reference values for the objects in S21, G22, and M23. The latter with two
squares, one for RL sources, and the other for RQ sources. Table 8:
Metallicity and physical parameter estimates along the Quasar MS

Object | SED | Component | Minimum $\chi^{2}$ | $\log U$ | $\Delta\log U$ | $\log Z$ | $\Delta\log Z$ | $\log n_{\rm H}$ | $\Delta\log n_{\rm H}$
---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  | [$Z_{\odot}$] | [$Z_{\odot}$] | [cm-3] | [cm-3]
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
Mrk 335 | A | BC | $12.68$ | $-1.75$ |  $-1.75$ \- $-1.50$ | $-1.00$ |  $-1.00$ \- $-1.00$ | $7.75$ |  $7.00$ \- $8.75$
Mrk 110 | A | BC | $0.67$ | $-0.50$ |  $-0.75$ \- $-0.50$ | $0.30$ |  $0.30$ \- $0.30$ | $8.50$ |  $8.50$ \- $8.75$
Mrk 509 | A | BC | $8.81$ | $-0.75$ |  $-1.00$ \- $-0.50$ | $0.00$ |  $0.00$ \- $0.00$ | $10.00$ |  $9.75$ \- $10.25$
Ark 564 | A | BC | $32.26$ | $-1.25$ |  $-1.75$ \- $-0.25$ | $0.70$ |  $0.30$ \- $1.00$ | $7.00^{\rm a}$ |  $7.00$ \- $10.00$
Mrk 478 | xA | BC | $84.01$ | $-0.75$ |  $-2.75$ \- $0.00$ | $1.70$ |  $1.70$ \- $2.30$ | $9.75$ |  $7.00$ \- $10.25$
Ton 28 | xA | BC | $1.40$ | $-0.50$ |  $-1.00$ \- $-0.50$ | $1.70$ |  $1.30$ \- $1.70$ | $11.25$ |  $11.00$ \- $13.25$
I Zw 1 | xA | BC | $36.73$ | $-0.75$ |  $-1.75$ \- $-0.50$ | $1.30$ |  $1.00$ \- $1.30$ | $10.75$ |  $10.25$ \- $11.75$
LB 2522 | xA | BC | $1.15$ | $-0.75$ |  $-1.00$ \- $0.00$ | $1.30$ |  $1.00$ \- $2.30$ | $11.75$ |  $11.25$ \- $14.00$
LEDA 51016 | xA | BC | $24.23$ | $-1.00$ |  $-2.50$ \- $-0.75$ | $1.30$ |  $1.00$ \- $1.70$ | $10.50$ |  $10.00$ \- $11.50$
PHL 1092 | xA | BC | $1.42$ | $-3.25$ |  $-3.25$ \- $-3.00$ | $3.00$ |  $3.00$ \- $3.00$ | $12.00$ |  $11.75$ \- $12.00$
| xA | BLUE | $2.20$ | $-0.25$ |  $-0.75$ \- $-0.25$ | $1.70$ |  $1.30$ \- $1.70$ | $11.50$ |  $11.25$ \- $12.50$
Fairall 9 | B | BC | $34.17$ | $-1.75$ |  $-2.00$ \- $-1.00$ | $0.30$ |  $-1.00$ \- $0.70$ | $10.50$ |  $7.00$ \- $11.00$
| B | VBC | $1.76$ | $-2.00$ |  $-2.00$ \- $-1.75$ | $0.00$ |  $-0.30$ \- $0.00$ | $10.50$ |  $10.00$ \- $10.50$
Ark 120 | B | BC | $32.26$ | $-1.25$ |  $-1.75$ \- $-1.00$ | $1.00$ |  $-0.70$ \- $1.30$ | $11.00$ |  $7.00$ \- $11.50$
| B | VBC | $5.38$ | $-2.00$ |  $-2.25$ \- $-1.50$ | $-1.30$ |  $-1.70$ \- $-1.00$ | $9.00$ |  $7.00$ \- $9.75$
NGC 3783 | B | BC | $30.96$ | $-1.75$ |  $-1.75$ \- $-1.50$ | $-0.30$ |  $-1.30$ \- $0.00$ | $9.75$ |  $7.00$ \- $10.00$
| B | VBC | $9.67$ | $0.00$ |  $-2.00$ \- $0.25$ | $0.30$ |  $-1.70$ \- $0.30$ | $7.25$ |  $7.00$ \- $11.75$
TXS 0042+101 | B | BC | $5.12$ | $-2.00$ |  $-2.00$ \- $-1.00$ | $-0.30$ |  $-1.30$ \- $0.70$ | $9.75$ |  $7.00$ \- $10.00$
| B | VBC | $0.60$ | $-2.00$ |  $-2.00$ \- $-2.00$ | $-1.30$ |  $-1.30$ \- $-1.00$ | $9.00$ |  $8.50$ \- $9.50$

999(1) Object common name. (2) SED used for the computation, with A using the
SED from Mathews & Ferland (1987), xA using the xA SED computed from PHL 1092,
and B using the Population B SED. (3) Component measured. (4) Minimum
$\chi^{2}$ associated with the object and the component. (5) Decimal logarithm
of the ionization parameter $U$ associated to the minimum $\chi^{2}$. (6)
Logarithmic interval associated to the variation of the ionization parameter
$U$. (7) Decimal logarithm of the metallicity $Z$ associated to the minimum
$\chi^{2}$. (8) Logarithmic interval associated to the variation of the
metallicity $Z$. (9) Decimal logarithm of the Hydrogen density $n_{\rm H}$
associated to the minimum $\chi^{2}$. (10) Logarithmic interval associated to
the variation of the Hydrogen density $n_{\rm H}$. a: A significantly higher
$n_{\mathrm{H}}$ ($\log n_{\mathrm{H}}\sim 11$ [cm-3]) was obtained removing
the diagnostic ratios connected to Ciii] (see text on Ark 564 in Section 4.1).

##  5 Validation

In the following sections, we will discuss the limits of our technique and the
tests that we used to address these limits.

###  5.1 Statistical errors

The minimum $\chi^{2}$ criterion and the $F$-test are not suited to estimate
the influence of statistical errors. In this respect, bootstrap repetition of
the $Z$, $n_{\mathrm{H}}$ and $U$ estimate allows for deviation from a perfect
solution (i.e., from the diagnostic ratio values predicted by a definite model
$Z$, $n_{\mathrm{H}}$ and $U$) permit to assess how large the relative
uncertainties in the intensity ratios can be until the correct solution in
terms of metallicity is lost. Bootstrap simulations were carried out assuming
random variations following a Gaussian distribution with $\sigma$
corresponding to several fractional uncertainties. In practice, each
replication assigned new values for the ratios, following Gaussian deviates
with dispersion corresponding to the fractional uncertainty. Fig. 5 shows that
the $Z$ information is preserved for statistical errors up to $\approx 0.45$
for the somewhat idealized case of 10 diagnostic ratios having a constant
fractional uncertainty, assuming diagnostic ratios from simulated cases with
metallicity ranging from $\log Z=0.3$ to 1.7, that could be fairly typical for
Pop. A and xA. The statistical uncertainties do not affect the $Z$ estimates
up to 0.3 – 0.35 fractional errors. Increasing the statistical uncertainties
by 50% for ratios Civ/ and Siiv+Oiv]/, because of the faintness of , lowers
the highest uncertainty preserving the $Z$ value by 0.05 (i.e., from 35% to
30%). The statistical errors tend to lower $Z$ (as well as $U$ and
$n_{\mathrm{H}}$, not shown). Therefore, statistical fluctuations are unlikely
to induce systematically higher values of the metallicity to the ones derived
from the model and to account for the very high $Z$ deduced for the extreme
Population A sources. More relevant to the analysis of the result is the
possibility of systematic discrepancies in emission line ratios to the
expectation of a photoionization solution.

Figure 5: Median $Z$ values for 200 replications of the intensity ratios
deviating from the ones predicted by four models as a function of fractional
uncertainties.

###  5.2 Alternative $\chi^{2}$ evaluations

Could the technique employed for the $\chi^{2}$ estimate be at the origin of
the out-of-scale $Z$ of PHL 1092, and of the very high values ($Z\lesssim
100$) encountered among xA sources? The $\chi^{2}$ expression of Eq. 4 is
weighting the contribution of each measurement on the inverse of the
uncertainty squared. This is expected to be effective in increasing the
likelihood of the solution, but at the same time is giving minimum weight to
“bad” data that have large uncertainty. Several ratios in Table 7 are between
two detected lines, but have an uncertainty larger than the reported value. We
therefore considered two alternatives to the $\chi^{2}$ technique whose
results are reported in Table 8, and those are shown in Table 9.

Instead of dividing each addendum by the error squared, the addenda could be
divided by the value expected from the simulation for each ($U$,
$n_{\mathrm{H}}$, $Z$) grid element (different for each $U$, $n_{\mathrm{H}}$,
$Z$), or by the observed ratios that are constant. Especially this last option
offers a valid alternative to the conventional $\chi^{2}$ because it
effectively quantifies the relative difference between any model and the
observed set of ratios. Each ratio will have a weight independent from its
associated uncertainty. If this exercise is carried out, the minimum
$\chi^{2}$ solutions confirm the high $Z$ values for both LB 2522 and PHL
1092. The $Z$ derived for PHL 1092 BLUE is even increased to 20 – 50
$Z_{\odot}$. Therefore, the metallicity estimates at high $Z$ do not appear
strongly sensitive to the different choices of $\chi^{2}$ that we have
considered.

Table 9: Different normalization for $\chi^{2}$ computation

Object | SED | Component | Minimum $\chi^{2}$ | $\log U$ | $\Delta\log U$ | $\log Z$ | $\Delta\log Z$ | $\log n_{\rm H}$ | $\Delta\log n_{\rm H}$
---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  | [$Z_{\odot}$] | [$Z_{\odot}$] | [cm-3] | [cm-3]
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
Normalization over expected value
LB 2522 | xA | BC | $19.62$ | $-3.50$ |  $-3.50$ \- $0.75$ | $3.00$ |  $1.70$ \- $3.00$ | $14.00$ |  $10.75$ \- $14.00$
PHL 1092 | xA | BC | $45.33$ | $-0.75$ |  $-2.75$ \- $-0.50$ | $3.00$ |  $1.70$ \- $3.00$ | $14.00$ |  $12.50$ \- $14.00$
| xA | BLUE | $1.93$ | $-0.25$ |  $-1.00$ \- $0.50$ | $1.70$ |  $1.70$ \- $2.70$ | $12.50$ |  $11.25$ \- $13.75$
Normalization over observed value
LB 2522 | xA | BC | $4.97$ | $0.00$ |  $-2.50$ \- $1.00$ | $1.70$ |  $-2.00$ \- $2.00$ | $7.00$ |  $7.00$ \- $11.25$
PHL 1092 | xA | BC | $2.78$ | $-3.25$ |  $-3.25$ \- $-3.00$ | $2.70$ |  $1.70$ \- $3.00$ | $11.50$ |  $11.00$ \- $12.00$
| xA | BLUE | $5.79$ | $-2.50$ |  $-2.75$ \- $1.00$ | $-2.00$ |  $-1.00$ \- $0.30$ | $10.25$ |  $7.00$ \- $14.00$

101010(1) Object common name. (2) Adopted SED, with nomenclature used in Table
8. (3) Component measured. (4) Minimum $\chi^{2}$ associated with the object
and the component. (5) Decimal logarithm of the ionization parameter $U$
associated to the minimum $\chi^{2}$. (6) Logarithmic interval associated with
the variation of the ionization parameter $U$. (7) Decimal logarithm of the
metallicity $Z$ associated to the minimum $\chi^{2}$. (8) Logarithmic interval
associated with the variation of the metallicity $Z$. (9) Decimal logarithm of
the Hydrogen density $n_{\rm H}$ associated to the minimum $\chi^{2}$. (10)
Logarithmic interval associated with the variation of the Hydrogen density
$n_{\rm H}$.

###  5.3 Influence of optical/UV mismatch

As discussed in Section 4.1, several sources are affected by an optical/UV
flux mismatch, likely originated by observations conducted at different
moments using both ground-based and space-based observatories. Optical
observations are susceptible to uncontrollable light loss, significantly
impacting the reliability of diagnostic ratios based on both optical and UV
lines. However, diagnostic ratios dependent on lines found at similar
wavelengths are less susceptible to this issue, as the intrinsic variability
of the quasar should similarly affect them. The most likely candidate for this
problem is the Civ/H$\beta$ ratio, as it is the sole diagnostic ratio
involving a UV and an optical line.

Indeed, when estimating the physical parameters associated with the BLR of our
sample of quasars, the Civ/H$\beta$ ratio often disrupted the computation,
returning combinations of $U$, $Z$ and $n_{\rm H}$ that were not compatible
with our previous assumptions, or solutions strongly incompatible with any of
the CLOUDY simulations used in this work: very low Civ/H$\beta$ values are
possible for low $U$, for most $Z$s (Fig. 2). The values of Civ/H$\beta$ along
with the $\log U$ and $\log Z$ results obtained from the calculation are shown
in Table 10. It is important to note that the Civ/H$\beta$ ratio was excluded
in most calculations (Table 7). The primary observation from Table 10 is that
the Civ/H$\beta$ value follows a clear pattern, steadily decreasing towards
the most extreme xA sources. This pattern has been observed in other works,
and is a peculiar feature of xA quasars (Sulentic et al., 2017; Vietri et al.,
2018), exhibiting the bulk of their Civ emission in the BLUE. However, despite
being a physical result, inappropriate estimation of this ratio due to the
aforementioned problems strongly affects the measurements of $Z$ and $U$,
rendering the estimation incorrect. The Civ/H$\beta$ ratio, being particularly
sensitive to $U$, loses its dependence on metallicity (represented in Figure
2), returning a solution that is not physical, distorting the results
associated with other diagnostic ratios.

Table 10: CIV/H$\beta$ results

Object name | CIV/H$\beta$ | $\log U_{\rm CIV/H\beta}$ | $\log Z_{\rm CIV/H\beta}$ | $\log U_{\rm no\ CIV/H\beta}$ | $\log Z_{\rm no\ CIV/H\beta}$
---|---|---|---|---|---
|  |  | [$Z_{\odot}$] |  | [$Z_{\odot}$]
(1) | (2) | (3) | (4) | (5) | (6)
Mrk 335 | $5.89\pm 0.76$ | $-1.75$ | $-1.00$ | $-1.75$ | $-1.00$
Mrk 110 | $37.71\pm 4.98$ | $-1.25$ | $0.00$ | $-0.50$ | $0.30$
Mrk 509 | $5.93\pm 0.90$ | $-1.75$ | $-1.00$ | $-0.75$ | $0.00$
Ark 564 | $11.19\pm 2.45$ | $-1.25$ | $0.70$ | $-1.25$ | $0.70$
Mrk 478 | $5.21\pm 0.75$ | $-0.75$ | $1.70$ | $-0.75$ | $1.70$
Ton 28 | $1.78\pm 0.75$ | $-3.00$ | $2.30$ | $-0.50$ | $1.70$
I Zw 1 | $2.28\pm 0.44$ | $-2.75$ | $0.30$ | $-0.75$ | $1.30$
LB 2522 | $2.48\pm 2.87$ | $-3.50$ | $3.00$ | $-0.75$ | $1.30$
LEDA 51016 | $7.60\pm 1.56$ | $-0.75$ | $1.30$ | $-1.00$ | $1.30$
PHL 1092 | $0.41\pm 0.24$ | $-3.50$ | $2.70$ | $-3.25$ | $3.00$
Fairall 9 | $12.60\pm 1.71$ | $-1.75$ | $0.30$ | $-1.75$ | $0.30$
Ark 120 | $3.09\pm 0.30$ | $-2.50$ | $-0.30$ | $-1.25$ | $1.00$
NGC 3783 | $7.64\pm 0.68$ | $-1.75$ | $-0.30$ | $-1.50$ | $-0.70$
TXS 0042+101 | $6.01\pm 2.24$ | $-2.00$ | $-0.30$ | $-1.00$ | $0.70$
111111(1) Object common name. (2) Civ/H$\beta$ ratio obtained from the multi-
component fitting. (3) $\log U$ associated to the minimum $\chi^{2}$ between
the observations and CLOUDY simulations including the Civ/H$\beta$ ratio. (4)
$\log Z$ associated to the minimum $\chi^{2}$ between the observations and
CLOUDY simulations including the Civ/H$\beta$ ratio. (5) $\log U$ associated
to the minimum $\chi^{2}$ between the observations and CLOUDY simulations
excluding the Civ/H$\beta$ ratio. (6) $\log Z$ associated to the minimum
$\chi^{2}$ between the observations and CLOUDY simulations excluding the
Civ/H$\beta$ ratio.

###  5.4 Influence of SED

The choice of the SED used for the photoionization simulations is expected to
significantly influence the results obtained during the estimation of physical
parameters in the BLR, as it dictates the luminosity of the central source.
Population A and B sources typically display distinct spectral features,
leading to remarkably different SEDs (see Figure 1 in Panda et al., 2019b).
However, the distinction between Population A and xA sources is less clear-
cut, particularly between the A2 and A3 spectral bins, as observed in some
objects in our sample that exhibit borderline features. Furthermore, the
Population A SED has been used in other works (Marziani et al., 2024), since
the xA SED employed in this work has often been considered too extreme for
many Population A objects. To address this issue, we recalculated the
$\chi^{2}$ using the Population A SED for xA sources, keeping track of the
systematic changes encountered (as summarized in Table 11). Additionally, in
Figure 6, we illustrate the positions occupied by the results for both SEDs in
the $\log U$ \- $\log Z$ parameter space.

Table 11: Metallicity and physical parameter estimates using Pop.A SED

Object | SED | Component | Minimum $\chi^{2}$ | $\log U$ | $\Delta\log U$ | $\log Z$ | $\Delta\log Z$ | $\log n_{\rm H}$ | $\Delta\log n_{\rm H}$
---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  | [$Z_{\odot}$] | [$Z_{\odot}$] | [cm-3] | [cm-3]
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
Mrk 335 | A | BC | $12.68$ | $-1.75$ |  $-1.75$ \- $-1.50$ | $-1.00$ |  $-1.00$ \- $-1.00$ | $7.75$ |  $7.00$ \- $8.75$
Mrk 110 | A | BC | $0.67$ | $-0.50$ |  $-0.75$ \- $-0.50$ | $0.30$ |  $0.30$ \- $0.30$ | $8.50$ |  $8.50$ \- $8.75$
Mrk 509 | A | BC | $8.81$ | $-0.75$ |  $-1.00$ \- $-0.50$ | $0.00$ |  $0.00$ \- $0.00$ | $10.00$ |  $9.75$ \- $10.25$
Ark 564 | A | BC | $32.26$ | $-1.25$ |  $-1.75$ \- $-0.25$ | $0.70$ |  $0.30$ \- $1.00$ | $7.00$ |  $7.00$ \- $10.00$
Mrk 478 | A | BC | $68.22$ | $-1.75$ |  $-2.25$ \- $-1.00$ | $1.70$ |  $1.30$ \- $2.00$ | $10.25$ |  $9.75$ \- $10.75$
Ton 28 | A | BC | $1.05$ | $-0.75$ |  $-1.75$ \- $-0.75$ | $1.30$ |  $1.30$ \- $1.30$ | $11.25$ |  $11.25$ \- $13.50$
LB 2522 | A | BC | $1.11$ | $-0.75$ |  $-1.25$ \- $0.00$ | $1.30$ |  $1.00$ \- $2.30$ | $12.50$ |  $11.25$ \- $14.00$
LEDA 51016 | A | BC | $21.47$ | $-1.25$ |  $-1.25$ \- $-0.75$ | $1.00$ |  $0.70$ \- $1.30$ | $11.25$ |  $10.25$ \- $11.50$
I Zw 1 | A | BC | $30.84$ | $-1.50$ |  $-2.25$ \- $-0.75$ | $1.30$ |  $0.70$ \- $1.30$ | $11.50$ |  $10.50$ \- $12.00$
PHL 1092 | A | BC | $1.97$ | $-3.00$ |  $-3.25$ \- $0.00$ | $3.00$ |  $1.30$ \- $3.00$ | $11.75$ |  $10.75$ \- $12.50$
| A | BLUE | $2.28$ | $-0.75$ |  $-1.25$ \- $-0.50$ | $1.00$ |  $1.00$ \- $1.30$ | $11.75$ |  $11.25$ \- $12.25$

121212(1) Object common name. (2) Adopted SED, with nomenclature used in Table
8. (3) Component measured. (4) Minimum $\chi^{2}$ associated with the object
and the component. (5) Decimal logarithm of the ionization parameter $U$
associated to the minimum $\chi^{2}$. (6) Logarithmic interval associated with
the variation of the ionization parameter $U$. (7) Decimal logarithm of the
metallicity $Z$ associated to the minimum $\chi^{2}$. (8) Logarithmic interval
associated with the variation of the metallicity $Z$. (9) Decimal logarithm of
the Hydrogen density $n_{\rm H}$ associated to the minimum $\chi^{2}$. (10)
Logarithmic interval associated with the variation of the Hydrogen density
$n_{\rm H}$.

The primary outcome of this test was a systematic decrease of the minimum
$\chi^{2}$ obtained for all xA objects with the exception of PHL 1092 (which
served as the basis for the xA SED). Furthermore, the solutions consistently
indicate higher densities, typically moving upward by an order of magnitude or
less. However, no significant changes to metallicity or $U$ have been
observed, as depicted in Figure 6. Nonetheless, the parameter distributions
obtained using the xA SED are generally more constrained.

Figure 6: Two-dimensional parameter space of $\log Z$ \- $\log U$ illustrating
the physical conditions of the gas surrounding xA sources with different SEDs.
In each plot the minimum $\chi^{2}$ computed between measured diagnostic
ratios and CLOUDY simulations is shown with dots: green for the Mathews &
Ferland (1987) SED and blue for the xA SED. The orange region corresponds to
the 1$\sigma$ accuracy range for the Mathews & Ferland (1987) SED, and the
blue region for the xA SED.

###  5.5 Micro-turbulence and highest $Z$ values

Figure 7: Behavior of the diagnostic ratio Civ/ (magenta), Civ/H$\beta$
(blue), $R_{\rm FeII}$(green) in logarithmic scale vs microturbulence velocity
in km s-1. Left: using the solution for I Zw 1 (squares) and PHL 1092
(circles); right: using a low-ionization, high-density solution appropriate
for xA sources (see text for details), with three different $Z$ values: 200
$Z_{\odot}$ (circles), 100 $Z_{\odot}$ (squares), 50 $Z_{\odot}$ (triangles).

Micro-turbulence is believed to increase the efficiency of metal line
production. This is especially true for Feii blends (Verner et al., 1999,
2004; Bruhweiler & Verner, 2008; Panda et al., 2018), as micro-turbulence is
expected to increase Feii self-fluorescence and fluorescent excitation due to
continuum and strong emission lines. CLOUDY simulations were carried out
starting from the ($U$, $n_{\mathrm{H}}$, $Z$) values of I Zw 1 and PHL 1092.
The left panel of Fig. 7, where the key intensity ratios Civ/, Civ/H$\beta$,
and $R_{\rm FeII}$ are shown as a function of the microturbulent velocity. A
microturbulent velocity $v_{\mathrm{turn}}=\sqrt{kT/m}\approx 10$ km s-1
corresponds to the thermal broadening of lines emitted by gas at the electron
temperature of the BLR, $T\sim 10000$ K. The effect of microturbulence passing
from 0 to 10 km s-1 is a net increase in $R_{\rm FeII}$ for PHL 1092, while
the effect is less clear for I Zw 1. The right panel of Fig. 7 shows the
trends for the same ratios, starting from low ionization, and high-density
solutions, for three very high $Z$ values, namely 50, 100, and 200
$Z_{\odot}$. The effect on $R_{\rm FeII}$ is remarkable in all of the three
cases. The increase in the emission efficiency of Feii features implies that
less iron is needed to produce the same line luminosity.

We recomputed the array of simulations for the Mathews & Ferland (1987) SED in
the range $7\leq\log$$n_{\mathrm{H}}$ $\leq 14$, $-3.5\leq\log U\leq 0$, and
for 10 values of $Z$ between 1 and 1000 $Z_{\odot}$. The results for PHL 1092
indicate a greatly reduced value of the metallicity, $\log Z\approx
1.7^{+0.6}_{-0.4}$[Z⊙]. The inclusion of turbulence aligns the estimate of the
out-of-scale measurement to more likely values $Z\lesssim$ 100 $Z_{\odot}$.
Most sources with $Z\geq 10Z_{\odot}$ have their $Z$ estimates unchanged or
reduced by a factor $\approx 2$ as was first suggested in Panda (2021b). It is
interesting to note that this reduction seems to occur only for the highest
values of $Z$, while for lower metallicity around solar, the effect of
turbulence is not obvious.

###  5.6 Stratification

Evidence indicates trends for various parameters along the Quasar MS.
Specifically, in the case of Population B, there is observable evidence of a
radial stratification of properties within the BLR (Baldwin et al., 1995;
Korista et al., 1997). As previously mentioned, this region is modeled by
distinguishing between a BC and a VBC. However, it is not certain whether the
assumption of constant physical parameters within the BLR is entirely accurate
for Population A. On the one hand, the physical parameters appear to be
associated with a much smaller uncertainty range in Pop. A than in Pop. B
(compare Figures 15, 16, 17 vs 18, 19). On the other hand, several Pop. A
sources show prominent Ciii] that may bias the photoionization solution toward
lower $n_{\mathrm{H}}$. To test whether the estimates of $Z$ are stable to
this potential bias, we repeated the $Z$ estimates removing the diagnostic
ratios involving Ciii] for Mrk 335 and Ark 564, the objects which exhibit the
lowest $n_{\mathrm{H}}$. The computation yielded different results for the two
objects: Mrk 335 retained a very low density ($\log$ $n_{\mathrm{H}}$$\approx
7.5$ [cm-3]), confirming the presence of low-density gas in its BLR, also
supported by the fitting of a semi-broad component of [O
iii]$\lambda\lambda$4959,5007, as described in Section 4.1. Ark 564, instead,
returned a higher density solution, with $\log$$n_{\mathrm{H}}$$\approx 11$
[cm-3], suggesting that the absorption feature affecting Ciii] led to an
overestimation of its line intensity.

Figure 8 displays the trend of $Z$ along the MS by analyzing the average value
of $Z$ across specific spectral types, averaging all the values obtained with
the methods that most affect the determination. The trend in metallicity is
evident from this figure, with a dip in metallicity for the A1 spectral type
being influenced by the selection of objects in our sample. In the A1 spectral
type, the average RFeII is lower than that measured for the adjacent bins: A1
sources are associated with lower RFeII than typically measured in that
spectral type, thus contributing to lower estimations of $Z$. Additionally,
the absence of CLOUDY simulations with $\log Z=-0.3,-0.7$ for Population A
objects contributed to an underestimation of $Z$. Nevertheless, the trend in
metallicity proceeds quite steadily from Population B RL quasars to xA
quasars.

Figure 8: Diagram illustrating the trend of $Z$ across different spectral
types, with the reference values for each spectral type obtained as the
geometric mean of all the measurements assumed for all the objects belonging
to a specific spectral type, including our method, the use of the Civ/H$\beta$
ratio, and the presence of microturbulence for all sources belonging to the
A2, A3, and A4 spectral types. Confidence intervals are obtained as the
standard deviation of our results. The number of objects contributing to each
spectral type is shown in green, along with the average RFeII of the sources
considered. Two reference points (in red) are shown describing the RL and RQ
Population B sources studied in M23.

##  6 Discussion

###  6.1 A recipe to compute BLR metal content

Summarizing the procedure followed in this paper, we can define a recipe with
several steps that could be easily applicable to larger samples of quasars:

  1. 1.

identification of the spectral type and radio loudness, or at least if an
object belongs to Pop. B, Pop. A or extreme Pop. A. Note that RL xA AGN are
extremely rare in Population A at low-$z$ (Ganci et al., 2019);

  2. 2.

consideration of a maximum number of ratios for each component, avoiding
ratios between two faint components;

  3. 3.

multi-component fitting, to separate individual components associated with
different associated physical conditions (Section 3.2);

  4. 4.

computation of the minimum $\chi^{2}$ between our measurements and the results
obtained from CLOUDY photoionization simulations to cover the parameter space
in terms of SED, $Z$, $n_{\mathrm{H}}$, $U$ and microturbulence parameter.
Ideally, SEDs should be different for at least Pop. B RQ and RL, Pop. A and
xA. Microturbulence parameter could be 0 or 10 km s-1;

  5. 5.

definition of $1\sigma$ confidence ranges via an F-test with the appropriate
number of degrees of freedom.

In Section 5.3 we discussed that the presence of an optical-UV flux mismatch
was a major obstacle encountered during this procedure. The effect of this
mismatch, which plays a crucial role in nullifying the information of the
Civ/H$\beta$ diagnostic ratio, mostly affects objects with non-contemporary
observations. However, the Civ/H$\beta$ ratio is extremely effective for
constraining $U$, so relinquishing this ratio has a negative impact on the
accuracy of the measurement of the physical conditions in the BLR. We thus
propose that the Civ/H$\beta$ ratio should be used with the highest confidence
in the case of contemporary observations in the UV and optical range. In this
case, the diagnostic ratio has a positive effect on the measurement and should
help retrieve well-constrained results.

The Feii/H$\beta$ ratio has often yielded discrepant information with respect
to Civ/H$\beta$. Indeed, this ratio is not typically predicted to be very high
for the SEDs employed in this work. This raises the possibility that the
optical ratios could be problematic for the estimation of the physical
parameters, and should thus be excluded from the computation.

###  6.2 Estimation of accretion parameters

The bolometric luminosity ($L_{\rm bol}$) of the AGNs of the sample is
estimated using the relation

$L_{\rm bol}=4\pi[\lambda\cdot
f_{\lambda}](5100\AA)d^{2}_{\mathrm{P}}=L(5100\AA)k_{\rm bol},$ (5)

where $d_{\mathrm{P}}$ is the luminosity distance divided by (1+$z$). In this
paper, the values of the cosmological parameters are adopted as follows:
$H_{0}$ =70 km s-1 Mpc-1, $\Omega_{\mathrm{M}}$=0.3, $\Omega_{\Lambda}$=0.7.
The bolometric correction factor $k_{\rm bol}$ is calculated using the formula
from Netzer (2019):

$k_{\rm bol}=40\times\left(\frac{L(5100\AA)}{10^{42}\ {\rm erg}\ {\rm
s}^{-1}}\right)^{-0.2},$ (6)

while $L(5100\AA)$ is the luminosity of the quasar at 5100 Å. The mass of the
black hole ($M_{\rm BH}$) is estimated using the relation:

$\begin{split}\log(M_{\rm BH}/M_{\odot})=0.83\log({\rm FWHM}({\rm
H}\beta))+0.45\log(l_{44})+\\\ -0.35\log({\rm
R}_{\mathrm{FeII}})+5.22,\end{split}$ (7)

with $l_{44}=L(5100\AA)/10^{44}{\rm erg\ s}^{-1}$ obtained from Du & Wang
(2019). The formula in Equation 7 is the Vestergaard & Peterson (2006)
relation with two changes: (1) a correction on the FWHM following Mejía-
Restrepo et al. (2018), and (2) the inclusion of the dependence of the BLR
radius on $R_{\rm FeII}$ (Du & Wang, 2019). In practice, Eq. 7 rectifies the
mass estimations for extreme accretors while keeping the results unchanged for
other objects.

The Eddington ratio is estimated using the formula $L_{\rm bol}/L_{\rm Edd}$,
with the Eddington luminosity $L_{\rm Edd}$ obtained as follows:

$L_{\rm Edd}=1.5\times 10^{38}{\rm erg}\ {\rm s}^{-1}\frac{M_{\rm
BH}}{M_{\odot}}.$ (8)

The derived properties of the sample are shown in Table 12.

Table 12: Derived properties of the sample

Object Name | $\log(L_{\mathrm{bol}})$ | $\log(M_{\mathrm{BH}})$ | $L/L_{\mathrm{Edd}}$
---|---|---|---
| [erg s-1] | [M⊙] |
(1) | (2) | (3) | (4)
Mrk 335 | $44.95\pm 0.03$ | $7.78\pm 0.05$ | $0.10\pm 0.01$
Mrk 110 | $44.46\pm 0.03$ | $7.48\pm 0.05$ | $0.06\pm 0.01$
Mrk 509 | $45.34\pm 0.03$ | $8.21\pm 0.16$ | $0.09\pm 0.03$
Ark 564 | $44.25\pm 0.03$ | $6.94\pm 0.06$ | $0.14\pm 0.02$
Mrk 478 | $45.32\pm 0.03$ | $7.51\pm 0.04$ | $0.43\pm 0.05$
Ton 28 | $46.26\pm 0.03$ | $8.26\pm 0.05$ | $0.67\pm 0.10$
I Zw 1 | $45.62\pm 0.03$ | $7.45\pm 0.05$ | $0.98\pm 0.12$
LB 2522 | $46.03\pm 0.03$ | $8.22\pm 0.06$ | $0.43\pm 0.07$
LEDA 51016 | $45.26\pm 0.03$ | $7.75\pm 0.05$ | $0.22\pm 0.02$
PHL 1092 | $45.72\pm 0.03$ | $7.71\pm 0.05$ | $0.67\pm 0.12$
Fairall 9 | $45.08\pm 0.03$ | $8.14\pm 0.05$ | $0.06\pm 0.01$
Ark 120 | $45.40\pm 0.03$ | $8.29\pm 0.04$ | $0.09\pm 0.01$
NGC 3783 | $44.52\pm 0.03$ | $7.71\pm 0.05$ | $0.04\pm 0.01$
TXS 0042+101 | $45.53\pm 0.03$ | $8.60\pm 0.23$ | $0.06\pm 0.04$
131313(1) Object common name. (2) Bolometric luminosity. (3) Mass of the SMBH
at the center of the galaxy. (4) Eddington ratio associated with accretion
onto the SMBH.

###  6.3 Correlation with accretion parameters

We investigated the correlation of accretion parameters with metallicity and
the RFeII parameter that defines the MS. Utilizing the SLOPES FORTRAN code
outlined in Feigelson & Babu (1992), we calculated the Pearson’s correlation
coefficient $r_{\rm P}$ between the quantities. Subsequently, we determined
the probability $P$ of a spurious correlation, computed using the
complementary error function
erfc$(x)=\frac{2}{\sqrt{\pi}}\int_{x}^{\infty}e^{-t^{2}}\,dt$, where $x$ is
defined as $x=\sqrt{\frac{N}{2}}|r_{\rm P}|$ with $N$ representing the number
of objects (Press et al., 1986).

The correlation analysis (Figure 9) yielded interesting results. The
parameters correlating more strongly are RFeII and $\log(L/L_{\rm Edd})$, with
$r_{\rm P}=0.925$. This result reinforces the hypothesis that the Eddington
ratio is the physical parameter behind the RFeII, serving as the primary
driver of the MS, as found by several works (Marziani et al., 2001; Sun &
Shen, 2015; Du et al., 2016; Panda et al., 2019b; Panda & Marziani, 2023, see
also the synopsis in D’Onofrio et al. 2021). Additionally, very robust
correlations were also observed in this sample between RFeII and $\log Z$, and
between $\log(L/L_{\rm Edd})$ and $\log Z$, confirming once again that
extreme-accreting sources are characterized by high metallicities (Martínez-
Aldama et al., 2018; Śniegowska et al., 2021; Garnica et al., 2022). Moreover,
the correlation in this work is extended to most spectral types along the MS,
also including Population B sources, rather than being limited exclusively to
xA sources as in Śniegowska et al. (2021) and Garnica et al. (2022). The
presence of such strong correlations is not trivial, as these quantities were
derived independently and using different procedures.

Our results confirm the earlier finding concerning low-$z$ PG quasars that the
BLR gas $Z$ correlates with Eddington ratio while $Z$ shows much weaker
correlation with $M_{\rm BH}$ (Shin et al., 2013). Typical values of the
Siiv+Oiv]/Civ and /Civ at low redshifts suggested values around solar or a few
times solar. The range covered by the two diagnostic ratios were found
consistent with those measured for a sample of intermediate redshift quasars
of luminosity comparable to the one of luminous AGN at low-$z$ (Sulentic et
al., 2014). The trend with $L_{\mathrm{bol}}/L_{\mathrm{Edd}}$ is due to the
inclusion of Population B, and spectral type A1 that are radiating at lower
Eddington ratio with respect to xA sources. The absence of a clear trend at
intermediate-$z$ corresponding to the cosmic noon with a maximum of nuclear
activity and star formation (e.g., Madau & Dickinson, 2014; Florez et al.,
2020; Förster Schreiber & Wuyts, 2020), and the large $Z$ estimated for
quasars at that cosmic epoch, might be just the result of a selection effect
disfavoring the lowest $L_{\mathrm{bol}}/L_{\mathrm{Edd}}$ for any given
$M_{\rm BH}$ (Sulentic et al., 2014).

The three remaining correlations depicted in Figure 9 were not found to be
statistically significant. The absence of a significant correlation between
$\log Z$ and $\log M_{\rm BH}$ was particularly puzzling, as these quantities
have been found to correlate in other works (Xu et al., 2018; Maiolino &
Mannucci, 2019), and larger SMBHs were found to be the ones with the highest
metallicity, since their stronger gravitational potential is able to trap the
more metallic matter in their virialized region.

Figure 9: Figures showing correlation between various accretion parameters
with $\log Z$ and RFeII. Points are displayed using the same color-coding as
in Figure 4 with their errorbars. When the correlation is considered
significant ($r_{\rm P}\gtrsim 0.7$, corresponding to a confidence level of
$\approx 0.01$), the correlation line is shown, with its defining parameters
intercept ($A$) and slope ($B$) shown with their respective errors. For each
correlation are also shown the Pearson correlation coefficient $r_{\rm P}$
from the SLOPES program (Feigelson & Babu, 1992) and the probability $P$ of a
spurious correlation.

###  6.4 Comparison between the photoionization and reverberation solutions
for $r_{\mathrm{BLR}}$

The computation of physical parameters in the BLR, coupled with Equation 3 for
the ionization parameter, yields an independent measurement of
$r_{\mathrm{BLR}}$, which could be compared with the results obtained from
H$\beta$ reverberation mapping for our sources (cf. Wandel, 2000; Negrete et
al., 2013). The reverberation $r_{\mathrm{BLR}}$ or time delays are reported
whenever available in the presentation of the individual objects of the
sample. The $r_{\mathrm{BLR}}$ estimations are compared in Figure 10. The two
independent estimations yield similar results for most sources of our sample,
within a factor $\sim 3$ (Vestergaard & Peterson, 2006; Negrete et al., 2013;
Panda, 2022).

Three estimations of the BLR radius using the physical parameters obtained
from our spectral measurements yield results incompatible with the
reverberation mapping estimation: Mrk 335, Mrk 110 and Ark 564 (Fig. 10). This
discrepancy arises from the estimations returning a low-density solution, thus
likely overestimating the extent of the H$\beta$-emitting region. The Ciii]
intensity of Ark 564 might be overestimated because of the correction needed
to account for heavy absorption close to the line rest-frame (Fig. 11).
Removing the Ciii] diagnostic ratios, moves the data point for this source in
agreement with the H$\beta$ reverberation mapping estimate. However, in the
other two cases, the intensity of Ciii] and the presence of other spectral
features suggested the presence of low-density gas in the BLR, a
stratification of properties that may be consistent with the presence of an
extended BLR. This seems to be especially true for Mrk 110, where the redward
asymmetry of a faint VBC might require an innermost radius of $\sim 100$
gravitational radii.

Nevertheless, the bulk of the measurements confirm the physical conditions
obtained from the estimation associated with CLOUDY photoionization
simulations, providing an independent measurement of the $r_{\mathrm{BLR}}$.

Figure 10: Top: Scatter plot showing the comparison of $r_{\mathrm{BLR}}$
estimated with reverberation mapping ($r_{\rm BLR,RM}$), and using CLOUDY
photoionization simulations ($r_{\rm BLR,\Phi}$), in the logarithmic plane.
Points are displayed using the same color-coding as in Figure 4, with their
respective errorbars. The dotted-dashed line describes the position of objects
for which the two independent determinations coincide. The values of $r_{\rm
BLR,\Phi}$ for objects whose determinations do not coincide with $r_{\rm
BLR,RM}$ by a margin are shown in the upper-right quadrant of the figure
(expressed in pc), connected to their representative points through an arrow.
An alternative result of the determination of physical parameters is shown for
Ark 564 with a square, obtained removing the diagnostic ratios employing
Ciii]. Bottom: Plot showing the difference between the two estimations. The
horizontal dotted-dashed line describes the position of objects for which the
two independent determinations coincide. The dotted line connects the two
different determinations for Ark 564 described above.

###  6.5 Enrichment mechanisms along the quasar MS

The results obtained from the estimation of metallicity in the BLR of our
sources suggest the presence of different enrichment mechanisms acting in the
different objects of our sample, giving rise to the solar or subsolar
metallicity that we observe in Population A and B sources, and the highest
metallicity that we observe in extreme accretors. Matteucci & Padovani (1993)
discussed the possibility of metal enrichment in quasars, and predicted that
the gas can reach solar abundances in less than $10^{8}$ years after star
formation starts for a Salpeter-like Initial Mass Function (IMF). There are
thus many possible mechanisms explaining the metal abundances observed in
Population A and Population B quasars. We have, however, observed a remarkable
number of objects displaying supersolar metallicity, with the totality of xA
sources exhibiting $Z\gtrsim 10Z_{\odot}$.

One of the primary proposals to explain this phenomenon is the possibility of
star formation in the vicinity of the active nucleus, starting from the models
developed by Artymowicz et al. (1993) and Collin & Zahn (1999). In this
context, Wang et al. (2009) predicted the presence of highly enriched BLRs in
quasars, with $Z$ up to 100 $Z_{\odot}$, suggesting the possibility of star
formation in the vicinity of the accretion disk of the central nucleus as a
means of chemical enrichment. The SMBH could then trap these metals in the
region due to its gravitational potential. A similar mechanism involves
Accretion Modified Stars (AMS): a stellar population characterized by stars
accreting material from the disk and rapidly attaining high masses,
subsequently exploding as supernovae and further enriching the surrounding
material (Wang et al., 2021; Cantiello et al., 2021; Wang et al., 2023b). In
our sample, I Zw 1 and PHL 1092 display blueshifts that dominate the emission
of their HILs, particularly Civ. The presence of strong winds originating from
the high-accretion phase experienced by these objects produce outflows capable
of escaping the BLR and enriching the surrounding regions (Vietri et al.,
2016, 2018, M23).

Furthermore, there is a lack of redshift evolution of the metallicity of
quasars (Juarez et al., 2009; Fan & Wu, 2023, and references therein).
Metallicity in the BLRs is higher than in the NLRs, suggesting that the
chemical enrichment occurs in-situ, near the molecular torus (Collin & Zahn,
1999). A top-heavy IMF can explain the observed metal abundances, that could
produce a strong metal enrichment in a short timescale ($\tau<10^{9}$ yr, even
though accretion-modified stars could be longer living than isolated stars,
see Chen & Lin 2024). An additional line of evidence supporting an in-situ
enrichment is provided by the strong similarity observed between the objects
in our sample, and those found in high-redshift samples (Bañados et al., 2016;
D’Odorico et al., 2023), since at high redshift there is no time to produce
the extreme amounts of metals observed (Xu et al., 2018).

The similarity between low-$z$ quasars accreting at a high rate and most
intermediate-to-high $z$ quasars (Sulentic et al., 2000a) has been interpreted
as a selection effect (Sulentic et al., 2014). In flux-limited surveys, for a
given mass, the only observable objects are those of higher luminosity or,
equivalently, higher Eddington ratio. Therefore, the presence of a high
percentage of high-accretors at high redshift should not be interpreted as
them being the only quasars present at high redshift. Low-luminosity quasars
observed at low redshifts, such as NGC 3783 in our sample, are yet
unobservable at intermediate-to-high redshifts. If, as our results suggest,
$Z$ is correlated with $L_{\mathrm{bol}}/L_{\mathrm{Edd}}$, a population of
quasars with metallicity around solar might be present up to $z\approx 4$, as
indeed found from a small sample of deep observations of very faint quasars
(Sulentic et al., 2014).

The morphological types of the objects of the sample were retrieved from the
NED extragalactic database and other works (McKernan et al., 2010; Khorunzhev
et al., 2012; Kim et al., 2017; Zhao et al., 2021; Kim et al., 2021). The
sample is however too small to reach even a tentative conclusion. A reliable
analysis of the non-ionizing part of the SED (especially radio, FIR, and MIR
emission) that may yield information on the circumnuclear of host star-
formation properties is deferred to an eventual work.

##  7 Conclusions

We analyzed a sample of 14 Type-I AGNs distributed along the MS of quasars. We
carried out a multi-component fitting, as described in Section 3, to measure
the intensity of major emission lines in the $\lambda 1300$ \- $\lambda 2100$
and optical wavelength ranges, and confronted the results from approximately
10 diagnostic ratios with those obtained through CLOUDY photoionization
simulations, constraining the physical parameters that describe the BLRs of
these sources. The outcomes of our analysis can be summarized as follows:

  * •

We identified a strong trend in metallicity along the MS, exhibiting an
increasing gradient of metallicity from Population B quasars (with subsolar or
solar metallicity) to xA sources (with supersolar metallicity
$Z>10Z_{\odot}$). The hypothesis regarding $Z$ as one of the principal
correlates of the MS (Panda et al., 2019b; Marziani et al., 2024) is
confirmed.

  * •

We proposed a “recipe” to estimate the metal content in the BLR, utilizing
approximately 10 diagnostic ratios sensitive to $Z$, $U$, and $n_{\rm H}$. We
recommend employing the Civ/H$\beta$ ratio only in the case of UV and optical
spectra acquired simultaneously, as it was identified as a major source of
error in this work.

  * •

We confirmed metallicity values of several tens of the solar metallicity,
among sources classified as xA that are consistent on average with the values
reported for the highly accreting quasars of Śniegowska et al. (2021); Garnica
et al. (2022).

  * •

The highest $Z$ objects, might be significantly affected by the introduction
of micro-turbulence, at the level expected for the line thermal broadening
($\sim$ 10 km s-1).

The main caveats concerning the $Z$ estimates are related to the precision of
the measurements (ideally, relative uncertainties should be less than $\sim
30$ %), the lack of contemporaneity of optical and UV observations, and the
simplification introduced by the single zone approximation in the
photoionization modeling, even if the separation between BLR, VBLR and
outflowing component takes into account major physical differences. In this
respect, we plan to implement a locally optimized emitting cloud scheme
(Baldwin et al., 1995). The application of the scheme to higher $z$ would
require photoionization computations employing SEDs appropriate for sources at
high luminosity (Duras et al., 2020; Krawczyk et al., 2013). However,
estimations of metallicity at very high redshifts (e.g., Rojas-Ruiz et al.,
2024, at $z\approx 7.24$) are now becoming possible from the combination of
NIR and MIR observations and may offer an important constraint on the early
evolution of the supermassive black holes and their host galaxies (e.g.,
Cattaneo et al., 2009).

###### Acknowledgements.

We thank Pu Du, Jian-Min Wang and Chen Hu for providing us with the tentative
value of the time-delay of H$\beta$ for PG 1259+593. SP acknowledges the
financial support of the _Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq)_ Fellowships 300936/2023-0 and 301628/2024-6. The authors
would like to thank Dr. Jaime Perea for his useful comments and for his help
and generous allocation of computing time on hypercat and idilico at IAA
(CSIC). A.d.O. acknowledges financial support from the Spanish MCIU through
project PID2022-140871NB-C21 by “ERDF A way of making Europe” and the Severo
Ochoa grant CEX2021- 515001131-S funded by MCIN/AEI/10.13039/501100011033.

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