High Metal Content of Highly Accreting Quasars

Qualitatively, extreme Population A objects show prominent Al iii and weak or absent C iii] emission lines. In general, they show low emission-line equivalent widths (≈$\tfrac{1}{2}$ of them meet the W(C iv) ≲ 10 Å and qualify as weak-lined quasars following Diamond-Stanic et al. 2009) ⁸ and a spectrum that is easily recognizable even by a visual inspection, also because of the "trapezoidal" shape of the C iv profile and the intensity of the λ1400 blend, comparable to the one of C iv (Martinez-Aldama et al. 2018b).

xA sources were selected according to the criteria given in Section 1, using line measurements automatically obtained by the splot task with a cursor script within the IRAF data reduction package. We focus on the spectral range from ≈1200 to 2100 Å, where (1) UV lines used for xA identification are present and (2) the strongest emission features helpful for metallicity diagnostics are also located. The Lyα + N v blend is usually too heavily compromised by absorptions, which make it impossible to reconstruct the emission components especially for Lyα. We will make some consideration on the mean strength of the N v with respect to C iv and He ii λ1640 (Section 5.3), but we will not consider N v as a diagnostic. We selected SDSS DR12 ⁹ spectra in the redshift range 2.15 < z < 2.40, relatively bright (r < 19) to ensure moderate to high S/N in the continua (in all cases S/N ≳ 5 in the continuum, and the wide majority with S/N ≳ 10), and of low decl. δ < 10. The redshift range was chosen to allow for the possibility of H β coverage in the H band by eventual near-IR spectroscopic observations. The DR12 sample selected with these criteria is ≈500 sources strong. xA sources were selected out of this sample with an automated procedure, inspected to avoid broad absorption lines, and further vetted for obtaining a small pilot sample of ∼10 sources. A larger sample of xA sources will be considered in a subsequent work (K. Garnica et al. 2021, in preparation). The final selection includes 13 sources. With the adopted selection criteria in flux and redshift, we expect a small dispersion in the accretion parameters (especially luminosity; Section 5.2). Indeed, the selected sources are rather homogeneous in terms of spectral appearance, with a few sources included in our sample that, however, show borderline criteria. They will be considered in Section 4.1.1 in terms of their individual U, n_H.

Table 1 provides basic information for the 13 sources of our sample: SDSS name, redshift from the SDSS, the difference between our redshift estimation using Al iii (described in 3.1) and the SDSS redshift δ z = z − z_SDSS, the g-band magnitude provided by Adelman-McCarthy et al. (2008), the g − r color index, the rest-frame-specific continuum flux at 1700 and 1350 Å measured on the rest frame, and the S/N at 1450 Å. All other sources were covered by FIRST (Becker et al. 1995) but undetected. Considering that the typical rms scatter of FIRST radio maps is ≈0.15 Jy, as well as the typical fluxes in the g band, we have upper limits ≲5 in the radio-to-optical ratio, qualifying the sample sources as radio-quiet. Distances were computed using the formula provided by Sulentic et al. (2006, their Equation (B.5)), and ΛCDM cosmology (Ω_Λ = 0.7, Ω_M = 0.3, H₀ = 70 km s⁻¹ Mpc⁻¹). The bolometric luminosity is ∼10⁴⁷ erg s⁻¹, assuming a bolometric correction B.C.₁₃₅₀ = 3.5 (Richards et al. 2006). The sample rms is just ≈0.2 dex: all sources are in a narrow range of distances and have observed fluxes within a factor of ≈2 from their average. This is, in principle, an advantage for the estimation of the physical parameters such as L/L_Edd, considering the large uncertainty and serious biases associated with the estimation of M_BH from UV high-ionization lines. Accretion parameters will be discussed in Section 5.2.

The estimate of the quasar systemic redshift in the UV is not trivial, as there are no low-ionization narrow lines available in the spectral range (Vanden Berk et al. 2001). In practice, one can resort to the broad LIL. Negrete et al. (2014) and Martínez-Aldama et al. (2018a) consider the Si ii λ1263 and O i λ1302 lines to obtain a first estimate. A readjustment is then made from the wavelength of the Al iii doublet, which is found, in almost all cases, to have a consistent redshift. To determine the Al iii shift, those authors used multicomponent fits with all the lines in the region of the blend λ1900 included. The peak of Al iii is clearly visible in the spectra of our sample, since in high accretors emission of Al iii is strong with respect to the other lines in the blend at 1900 Å. We decided to use only this method for redshift estimation (in Table 1), and to measure the peak, we use single Gaussian fitting from the splot task of the Al iii doublet and/or of the Si iii] line, depending on which feature is sharper. The obtained values are usually ≥ z_SDSS (Table 1). This is not a surprise, as z_SDSS is based on lines that are mainly blueshifted in xA sources and hence is a systematic underestimation of the unbiased redshift.

Line ratios are sensitive to different parameters. In the UV range, four groups of diagnostic ratios are defined in the literature (e.g., Negrete et al. 2012; Martinez-Aldama et al. 2018b):

• 1.  
  C iv/Si iv + O iv] and C iv/He ii have been widely applied as metallicity indicators (e.g., Shin et al. 2013). In principle, C iv/He ii and Si iv/He ii should be sensitive to C and Si abundance because the He abundance relative to hydrogen can be considered constant. The ionization potentials of C²⁺ and He⁺ are similar. The main difference is that the He ii line is a recombination line, equivalent to H i Hα, and the regions where they are formed are not coincident (see Figure 4).
• 2.  
  Ratios involving N v, N v/C iv, and N v/He ii have been also widely used in past work, after it was noted that the N v line was stronger than expected in a photoionization scenario (e.g., Osmer & Smith 1976). A selective enhancement of nitrogen (Shields 1976) is expected owing to secondary production of N by massive and intermediate-mass stars, yielding [N/H] ∝ Z² (Vila-Costas & Edmunds 1993; Izotov & Thuan 1999). This process might be especially important at the high metallicities inferred for the quasar BLR. Therefore, estimates based on N v may differ in a systematic way from estimates based on other metal lines (e.g., Matsuoka et al. 2011). In the present sample of quasars, contamination by narrow and semibroad absorption is severe, and even if we model precisely the high-ionization lines, it might be impossible to reconstruct the unabsorbed profile of the red wing of Lyα. In addition, S/N is not sufficient to allow for a careful measurement of N iv] λ1486 and N iii] λ1750 lines. We defer the systematic analysis of nitrogen lines to a subsequent work, while discussing the consistency of the N v measures in a high-Z scenario (Section 5.3).
• 3.  
  The ratios Al iii/Si iii] and Si iii]/C iii] are sensitive to density, as the ratios involve intercombination lines with a well-defined critical density (n_c ∼ 10¹⁰ cm⁻³ for C iii], Hamann et al. 2002; n_c ∼ 10¹¹ cm⁻³ for Si iii], Negrete et al. 2010).
• 4.  
  Si iii]/Si iv, Si ii λ1814/Si iii], and Si ii λ1814/Si iv are sensitive to the ionization parameters and insensitive to Z, as they are different ionic species of the same element.

Other intensity ratios entail a dependence on metallicity Z, but also on ionization parameter U and density n_H (Marziani et al. 2020).

The comparison between LILs and HILs has provided insightful information over a broad range of redshift and luminosity (Corbin & Boroson 1996; Marziani et al. 1996, 2010; Shen 2016; Bisogni et al. 2017; Sulentic et al. 2017; Vietri et al. 2018). An LIL BLR appears to remain basically virialized (Marziani et al. 2009; Sulentic et al. 2017), as the H β profile remains (almost) symmetric and unshifted with respect to rest frame even if C iv blueshifts can reach several thousands of kilometers per second. In Population A, the lines have been decomposed into two components:

• 1.  
  The BC, also known as the intermediate component, the core component, or the central BC following various authors (e.g., Brotherton et al. 1994; Popović et al. 2002; Kovačević-Dojčinović et al. 2015; Adhikari et al. 2016). The BC is modeled by a symmetric and unshifted profile (Lorentzian for Population A; Véron-Cetty et al. 2001; Sulentic et al. 2002; Zhou et al. 2006) and is believed to be associated with a virialized BLR subsystem.
• 2.  
  The blueshifted component (BLUE). A strong blue excess in Population A C iv profiles is obvious, as in some C iv profiles—like the one of the xA prototype I Zw 1 or high-luminosity quasars—BLUE dominates the total emission-line flux (Marziani et al. 1996; Leighly & Moore 2004; Sulentic et al. 2017). For BLUE, there is no evidence of a regular profile, and the fit attempts to empirically reproduce the observed excess emission. BLUE is detected in an LIL such as H β at a very low level and is not strongly affecting FWHM measurements (Negrete et al. 2018).

3.3.1. Broad Component

3.3.2. BLUE Component

We analyze 13 objects using the specfit task from IRAF (Kriss 1994). The use of the χ² minimization is aimed at providing a heuristic separation between the BC and the blue component (BLUE) of the emission lines. After redshift correction following the method described in Section 3.1, for each source of our sample we perform a detailed modeling using various components as described below, including computation of asymmetric errors (Section 3.4.1). As mentioned in Section 3.2, in our analysis we consider five diagnostic ratios for the BC, C iv/λ1400, C iv/He ii λ1640, Al iii/He ii λ1640, λ1400/He ii λ1640, and λ1400/Al iii, and three for the BLUE, C iv/λ1400, C iv/He ii λ1640, and λ1400/He ii λ1640. The C iv/He ii λ1640 is used with care, as it may yield poor constraints. In addition, it is important to stress that, of the five ratios measured on the BC, only three (the ones dividing by the intensity of He ii λ1640 BC) are independent. We compare the fit results with arrays of CLOUDY (Ferland et al. 2013) simulations for various metallicities and physical conditions (Section 3.5).

For each source we perform the multicomponent fitting in three ranges described below. The best fit is identified by the model with the lowest χ², i.e., with a minimized difference between the observed and the model spectrum. Following the data analysis by Negrete et al. (2012), we use the following components:

The continuum.—This was modeled as a power law, and we use the line-free windows around 1300 and 1700 Å (two small ranges where there are no strong emission lines) to scale it. If needed, we divide the continuum into three parts (corresponding to the three regions mentioned below). Assumed continua are shown in the figures of Appendix A.

Fe ii emission.—This usually does not contribute significantly in the studied spectral ranges. We consider the Fe ii template that is based on CLOUDY simulations of Brühweiler & Verner (2008) when necessary. In practice, the contamination by the blended Fe ii emission yielding a pseudo-continuum is negligible. Some Fe ii emission lines were detectable in only a few objects and around ≈1715 Å, at 1785 Å, and at 2020 Å. In these cases, we model them using single Gaussians.

Fe iii emission.—This affects more the λ1900 region and seems to be strong when Al iii λ1860 is strong as well (Hartig & Baldwin 1986). To model these lines, we use the template of Vestergaard & Wilkes (2001).

Region 1300–1450 Å.—This is dominated by the Si iv + O iv] high-ionization blend with strong blueshifted component. Fainter lines such as Si ii λ1306, O i λ1304, and C ii λ1335 are also detectable. For the broad and blueshifted components we use the same model as in the case of C iv and He ii λ1640. This spectral range is often strongly affected by absorption.

Region 1450–1700 Å.—This is dominated by the C iv emission line, which we model as fixed in the rest-frame wavelength Lorentzian profile representing the BC, and two blueshifted asymmetric Gaussian profiles vary freely. The same model is used for He ii λ1640.

Region 1700–2200 Å is dominated by Al iii, Si iii], and Fe iii intermediate-ionization lines. We model Al iii and Si iii] using Lorentzian profiles, following Negrete et al. (2012). C iii] emission is also included in the fit, although the dominant contribution around 1900 Å is to be ascribed to Fe iii (Martínez-Aldama et al. 2018a and references therein). We use the template of Vestergaard & Wilkes (2001) to model Fe iii emission. No BLUE is ascribed to these intermediate-ionization lines.

Absorption lines.—These are modeled by Gaussians and included whenever necessary to obtain a good fit.

The fits to the observed spectral ranges are shown in the figures of Appendix A.

3.4.1. Error Estimation on Line Fluxes

The choice of the continuum placement is the main source of uncertainty in the measurement of the emission-line intensities. The fits in Appendix A show that, in the majority of cases, the FWHMs of the Al iii and Si iii] lines (assumed equal) satisfy the condition FWHM(Al iii) ∼ FWHM(C iv _BC ∼ FWHM(Si iv _BC). Figure 1 shows the best-fit, maximum, and minimum placement of the continuum, which we choose empirically. With this approach the continua of Figure 1 should provide the continuum uncertainty at a ±3σ confidence.

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The continuum placement strongly affects the measurement of an extended feature such as the Fe iii blends and the He ii λ1640 emission. Figure 1 makes it evident that errors on fluxes are asymmetric. The thick line shows the continuum best fit and the thinner minimum and maximum plausible continua. Even if the minimum and maximum are displaced by the same difference in the intensity with respect to the best-fit continuum, assuming the minimum continuum would yield an increase in line flux larger than the flux decrease assuming the maximum continuum level. In other words, a symmetric uncertainty in the continuum-specific flux translates into an asymmetric uncertainty in the line fluxes. To manage asymmetric uncertainties, we assume that the distribution of errors follows the triangular distribution (D' Agostini 2003). This method assumes linear decreasing on either side of maximum of the distribution (which is the best fit in our case) to the values obtained for maximum and minimum contributions of the continuum. We motivate using the triangular error distribution as a relatively easy analytical method to deal with asymmetric errors. For each line measurement we calculate the variance using the following formula for the triangular distribution:

$$\begin{eqnarray}&&{\sigma }^{2}(X)=\frac{{{\rm{\Delta }}}^{2}{x}_{+}+{{\rm{\Delta }}}^{2}{x}_{-}+{\rm{\Delta }}{x}_{+}+{\rm{\Delta }}{x}_{-}}{18},\end{eqnarray} \tag{ 1 }$$

where Δx₊ and Δx₋ are differences between measurement with maximum and best continuum and measurement with best and minimum continuum, respectively. To analyze the error of diagnostic ratios, we propagate uncertainties using standard formulas of error propagation.

To interpret our fitting results, we compare the line intensity ratio for BC and BLUE with the ones predicted by CLOUDY 13.05 and 17.02 simulations (Ferland et al. 2013, 2017). ¹⁰ An array of simulations is used as reference for comparison with the observed line intensity ratios. It was computed under the assumption that (1) column density is N_c = 10²³ cm⁻²; (2) the continuum is represented by the model continuum of Mathews & Ferland (1987), which is believed to be appropriate for Population A quasars; and (3) microturbulence is negligible. The simulation arrays cover the hydrogen density range $7.00\leqslant \mathrm{log}({n}_{{\rm{H}}})\leqslant 14.00$ and the ionization parameter −4.5 ≤ $\mathrm{log}(U)$ ≤ 1.00, in intervals of 0.25 dex. They are repeated for values of metallicities in a range encompassing five orders of magnitude: 0.01, 0.1, 1, 2, 5, 10, 20, 50, 100, 200, 500, and 1000 Z_⊙. Extremely high metallicity Z ≳ 100 Z_⊙ is considered physically unrealistic (Z ≈ 100 Z_⊙ implies that more than half of the gas mass is made up by metals!), unless the enrichment is provided in situ within the disk (Cantiello et al. 2020). The behavior of diagnostic line ratios as a function of U and n_H for selected values of Z is shown in Figure 17 of Appendix B.

3.5.1. Basic Interpretation

The line emissivity _coll (ergs cm⁻³ s⁻¹) of a collisionally excited line emitted from an element X in its ith ionization stage has a strong temperature dependence. In the high-density limit

$$\begin{eqnarray}\begin{array}{rcl}{\epsilon }_{{{\rm{X}}}^{i},\mathrm{coll}}\ & = & \ {n}_{{{\rm{X}}}^{i},{\rm{l}}}\beta {A}_{{{\rm{X}}}^{i},\mathrm{ul}}h{\nu }_{0}\,\displaystyle \frac{{g}_{{{\rm{X}}}^{i},{\rm{l}}}}{{g}_{{{\rm{X}}}^{i},{\rm{u}}}}\,\exp \left(-\displaystyle \frac{h{\nu }_{0}}{{{kT}}_{{\rm{e}}}}\right)\\ & \propto & {n}_{{{\rm{X}}}^{i},{\rm{l}}}\exp \left(-\displaystyle \frac{h{\nu }_{0}}{{{kT}}_{{\rm{e}}}}\right)\end{array}\end{eqnarray} \tag{ 2 }$$

the line is said to be "thermalized," as its strength depends only on the atomic level population and not on the transition strength (Hamann & Ferland 1999). β is the photon escape probability, and ${A}_{{{\rm{X}}}^{i},\mathrm{ul}}$ is the spontaneous decay coefficient. At low densities we have

$$\begin{eqnarray}&&{\epsilon }_{{{\rm{X}}}^{i},\mathrm{coll}}={n}_{{{\rm{X}}}^{i},{\rm{l}}}{n}_{{\rm{e}}}{q}_{{{\rm{X}}}^{i},\mathrm{lu}}h{\nu }_{0}\ \propto {n}_{{{\rm{X}}}^{i}}^{2}{T}_{{\rm{e}}}^{-1/2}\,\exp \left(-\displaystyle \frac{h{\nu }_{0}}{{{kT}}_{{\rm{e}}}}\right).\end{eqnarray} \tag{ 3 }$$

The recombination lines considered in our analysis are H β and He ii λ1640, for which the emissivity (with an approximate dependence of radiative recombination coefficient α on electron temperature; Osterbrock & Ferland 2006) becomes

$$\begin{eqnarray}&&{\epsilon }_{{{\rm{Y}}}^{j},\mathrm{rec}}={n}_{{{\rm{Y}}}^{j}}\,{n}_{{\rm{e}}}\,\alpha \,h{\nu }_{0}\ \propto {n}_{{{\rm{Y}}}^{j}}^{2}{T}_{{\rm{e}}}^{-1}\ \ \ \ ,\end{eqnarray} \tag{ 4 }$$

and ${n}_{{{\rm{Y}}}^{j}}$ is the number density of the parent ion.

Under these simplifying, illustrative assumptions we can write

$$\begin{eqnarray}&&\displaystyle \frac{{\epsilon }_{{{\rm{X}}}^{i},\mathrm{coll}}}{{\epsilon }_{{{\rm{Y}}}^{j},\mathrm{rec}}}\propto {\left(\displaystyle \frac{{n}_{{{\rm{X}}}^{i}}}{{n}_{{{\rm{Y}}}^{j}}}\right)}^{2}{T}_{{\rm{e}}}^{\displaystyle \frac{1}{2}}\exp \left(-\displaystyle \frac{h{\nu }_{0}}{{{kT}}_{{\rm{e}}}}\right)\end{eqnarray} \tag{ 5 }$$

for the low-density case and

$$\begin{eqnarray}&&\displaystyle \frac{{\epsilon }_{{{\rm{X}}}^{i},\mathrm{coll}}}{{\epsilon }_{{{\rm{Y}}}^{j},\mathrm{rec}}}\propto \displaystyle \frac{{n}_{{{\rm{X}}}^{i}}}{{n}_{{{\rm{Y}}}^{j}}^{2}}{T}_{{\rm{e}}}\exp \left(-\displaystyle \frac{h{\nu }_{0}}{{{kT}}_{{\rm{e}}}}\right)\end{eqnarray} \tag{ 6 }$$

for the high-density case.

Similarly, for the ratio of two collisionally excited lines at frequencies ν₀ and ν₁,

$$\begin{eqnarray}&&\frac{{\epsilon }_{{{\rm{X}}}^{i},\mathrm{coll}}}{{\epsilon }_{{{\rm{Y}}}^{j},\mathrm{coll}}}\propto {\left(\frac{{n}_{{{\rm{X}}}^{i}}}{{n}_{{{\rm{Y}}}^{j}}}\right)}^{\kappa }\exp \left(-\frac{h({\nu }_{0}-{\nu }_{1})}{{{kT}}_{{\rm{e}}}}\right),\end{eqnarray} \tag{ 7 }$$

where κ = 1 and 2 in the high- and low-density case, respectively.

Connecting the relative chemical abundance to the line emissivity ratios in the previous equation requires the reconstruction of the ionic stage distribution for each element, i.e., the computation of the ionic equilibrium, as well as the consideration of the extension of the emitting region within the gas clouds, i.e., that the line emission is not cospatial, and possible differences in optical depth effects. This is achieved by the CLOUDY simulations. However, we can see that the main variable parameter for a given relative emissivity is T_e. In other words, electron temperature is the main parameter connected to metallicity. This is especially true for a fixed physical condition (U, n_H, N_c = 10²³, spectral energy distribution (SED) given). This is most likely the case for xA sources: the spectral similarity implies that the scatter in physical properties is modest. We further investigate this issue in Section 4.3.

The electron temperature is also the dominating factor affecting the strength of the He ii λ1640 line, for a given density. The He ii Lyα line at 304 Å ionizes hydrogen atoms and other ionic species with ionization potential up to 3 ryd. Being absorbed by different ionic species, He ii λ1640 Lyα cannot sustain a population of excited electrons at the level n = 2 of He ii λ1640. This is markedly different from hydrogen Lyα, which in case B is assumed to scatter many times and to sustain a population of hydrogen atoms at level n = 2. The He ii line is therefore produced almost only by recombination, and no collisional excitation from level n = 2 or radiative transfer effects are expected, unlike the case of the hydrogen Balmer lines (Marziani et al. 2020). The prediction of the He ii line is relatively simple once the electron temperature and the density are known by assumption or computation. The additional advantage in the use of He ii is that there is no significant enhancement of the He abundance over the entire lifetime of the universe (Peimbert et al. 2001; Peimbert 2008). The normalization to the He ii line flux of the flux of metal lines should yield robust Z estimates. This is shown by the isophotal contours of Appendix B (Figure 17), tracing the behavior of the diagnostic ratios as a function of Z and U: the (Si iv + O iv])/He ii and Al iii/He ii ratios monotonically increase with Z over a large range of U; for C iv/He ii λ1640 the behavior is monotonic at low U, but more complex at $\mathrm{log}U\sim -1-0$. Ratios involving pairs of metal lines yield more complex trends in the plane Z–U. At low n_H, the C iv/Al iii ratio is a good Z estimator, although of limited usefulness since Al iii is weak; at high n_H, its sensitivity is greatly reduced (Appendix B, Figure 17). The C iv/(Si iv + O iv]) does not appear to be especially sensitive to Z. The diagnostic ratios change as a function of Z, although the behavior as a function of n_H and U is roughly preserved (Appendix B, Figure 18).

One of the main results of previous investigations is the systematic differences in ionization between BLUE and BC (Marziani et al. 2010; Negrete et al. 2012; Sulentic et al. 2017). Previous inferences suggest very low ionization (U ∼ 10^−2.5), also because of the relatively low C iv/H β ratio for the BC emitting part of the BLR, and high density. A robust lower limit to density n_H ∼10^11.5 cm⁻³ has been obtained from the analysis of the Ca ii triplet emission (Matsuoka et al. 2007; Panda et al. 2020a). Less constrained are the physical conditions for BLUE emission. Apart from C iv/H β ≫ 1 and Lyα/H β and C iv/C iii] also ≫1, few constraints exist on density and column density. This result hardly comes as a surprise considering the difference in dynamical status associated with the two components. It is expected that the BC is emitted in a region of high column density $\mathrm{log}$ N_c ≳ 23 [cm⁻²], not last because radiation forces are proportional to the inverse of N_c (Netzer & Marziani 2010, see also Ferland et al. 2009). More explicitly, the equation of motion for a gas cloud under the combined effect of gravitation and radiation forces contains an acceleration term due to radiation that is inversely proportional to N_c. The high-N_c region is expected to be relatively stable (at rest frame, with no sign of systematic, large shifts in Population A) and presumably devoid of low-density gas (considering the weakness of C iii]; Negrete et al. 2012). The same cannot be assumed for BLUE. BLUE is associated with a high radial velocity outflow, probably with the outflowing streams creating BAL features when intercepted by the line of sight (e.g., Elvis 2000).

Here we consider $\mathrm{log}U=-2.5$, $\mathrm{log}$ n_H = 12 (−2.5, 12), and $\mathrm{log}U=0,\mathrm{log}$ n_H = 9 (0, 9) as representative of the low- and high-ionization emitting gas. Figure 2 illustrates the behavior of the C iv/H β, He ii λ1640/H β, and C iv/He ii λ1640 in the high- and low-ionization cases as a function of metallicity. The C iv intensity with respect to H β has a steep drop around Z ≳ 1 Z_⊙, after a steady increase for subsolar Z. The He ii λ1640/H β ratio decreases steadily, with a steepening at around solar value. Physically, this behavior is due to the high value of the ionization parameter (assumed constant), while the electron temperature decreases with metallicity, implying a much lower collisional excitation rate for C iv production. The dominant effect for the He ii λ1640 decrease is likely the "ionization competition" between C iv and He ii λ1640 parent ionic species (Hamann & Ferland 1999). As a consequence, the ratio C iv/He ii λ1640 has a nonmonotonic behavior with a local maximum around solar metallicity. At low ionization and high density, the behavior is more regular, as the steady increase in C iv/H β is followed by a saturation to a maximum C iv/H β. The He ii λ1640/H β ratio is constant up to solar and steadily decreases above solar, where the ionization competition with triply ionized carbon sets on. The result is a smooth, steady increase in the C iv/He ii λ1640 ratio.

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Figure 3 shows the behavior of the other intensity ratios used as metallicity diagnostics, for BLUE and BC. Si iv + O iv]/C iv and Si iv + O iv]/He ii λ1640 saturate above 100 Z_⊙. Only around Z ∼ 10 Z_⊙ are values C iv/Si iv + O iv] ≲ 1 possible, but the behavior is not monotonic and the ratio rises again at Z ≳ 30 Z_⊙, with the unpleasant consequence that a ratio C iv/Si iv + O iv] ≈ 1.6 might imply 10 Z_⊙ as well as 1000 Z_⊙. The ratios usable for the BC also show regular behavior. The C iv/Al iii ratio remains almost constant up Z ∼ 0.1 Z_⊙, and then starts a regular decrease with increasing Z, due to the decrease of T_e with Z (C iv is affected more strongly than Al iii). Interestingly, Al iii/He ii λ1640 shows the opposite trend, due to the steady decrease of the He ii λ1640 prominence with Z. Especially of interest is, however, the behavior of ratio Al iii/He ii λ1640 that shows a monotonic, very linear behavior in the log-log diagram. As for the high-ionization case, values (Si iv + O iv])/C iv ≳ 1 are possible only at very high metallicity, although the nonmonotonic behavior (around the minimum at Z ≈ 200 Z_⊙) complicates the interpretation of the observed emission-line ratios.

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The ionization structure within the slab remains self-similar over a wide metallicity range, with the same systematic differences between the high- and low-ionization case (Figure 4), consistent with the assumption of a constant ionization parameter. As expected, the electron temperature decreases with metallicity, and the transition between the fully and partially ionized zone (FIZ and PIZ) occurs at smaller depth. In addition, close to the illuminated side of the cloud the electron temperature remains almost constant; the gas starts becoming colder before the transition from FIZ to PIZ. The depth at which T_e starts decreasing is well defined, and its value becomes lower with increasing Z (Figure 4). The effect is present for both the low- and high-ionization case, although it is more pronounced for the high-ionization case. Figure 5 shows how an increase in metallicity is affecting the T_e in the line-emitting cloud. Figure 5 reports the behavior of T_e at the illuminated face of the cloud (τ ∼ 0) and at maximum τ (corresponding to N_c = 10²³ cm⁻², the side facing the observer) for the high- and low-ionization case. The T_e monotonically decreases as a function of metallicity. The difference between the two cloud faces is almost constant for the low-ionization case, with $\delta \mathrm{log}{T}_{{\rm{e}}}\approx 0.5$ dex, while it increases for the high-ionization case, reaching $\delta \mathrm{log}{T}_{{\rm{e}}}\approx 0.75$ dex at the highest Z value considered, 10³ Z_⊙.

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The observational results of our analysis involve the measurements of the intensity of the line BC and BLUE component separately. The rest-frame spectra with the continuum placements and the fits to the blends of the spectra are shown in Appendix A. Table 2 reports the measurement for the λ1900 blend. The columns list the SDSS identification code, the FWHM (in units of km s⁻¹) and equivalent width and flux of Al iii (the sum of the doublet lines, in units of Å and 10⁻¹⁴ erg s⁻¹ cm⁻², respectively), FWHM and flux of C iii], and flux of Si iii] (its FWHM is assumed equal to the one of the single Al iii lines). Similarly, Table 3 reports the parameter of the C iv blend: equivalent width, FWHM and flux of the C iv BC, the flux of the C iv blueshifted component, and the fluxes of the BC and BLUE of He ii λ1640. FWHM values are reported, but especially values ≳5000 km s⁻¹ should be considered as highly uncertain. There is the concrete possibility of an additional broadening (∼10% of the observed FWHM) associated with nonvirial motions for the Al iii line (A. del Olmo et al. 2021, in preparation). The fluxes of the BC and of BLUE of Si iv and O iv] are reported in Table 4. Intensity ratios with uncertainties are reported in Table 5. The last row lists the median values of the ratios with their semi-interquartile ranges (SIQR).

4.1.1. Identification of xA Sources and of "Intruders"

Figure 6 shows that the majority of sources meet both UV selection criteria and should be considered xA quasars. The median value of the Al iii/Si iii] (last row of Table 5) implies that the Al iii is strong relative to Si iii]. Also, Si iii] is stronger than C iii]. Both selection criteria are satisfied by the median ratios. Only one source (SDSS J084525.84+072222.3 ) shows C iii]/Si iii] significantly larger than 1. This quasar is, however, confirmed as an xA by the very large Al iii/Si iii], by the blueshift of C iv, and by the prominent λ1400 blend comparable to the C iv emission. The lines in the spectrum of SDSS J084525.84+072222.3 are broad, and any C iii] emission is heavily blended with Fe iii emission. The C iii] value should be considered an upper limit. Three outlying/borderline data points (in orange) in Figure 6 have ratio C iii]/Si iii] ∼ 1, and Al iii/Si iii] consistent with the selection criteria within the uncertainties, but other criteria support their classification as xA. The borderline sources will be further discussed in Section 4.3. In conclusion, all 13 sources of the present sample save one should be considered bona fide xA sources.

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It is intriguing that the intensity ratios C iii]/Si iii] and Al iii/Si iii] are apparently anticorrelated in Figure 6, if we exclude the two outlying points. Excluding the two outlying data points, the Spearman rank correlation coefficient is ρ ≈ 0.8, which implies a 4σ significance for a correlation, but the correlation coefficient between the two ratios for the full sample is much lower. Given the small number of sources, a larger sample is needed to confirm the trend.

4.1.2. BC Intensity Ratios

Figure 7 shows the distribution of diagnostic intensity ratios C iv/He ii λ1640, Si iv/He ii λ1640, and Al iii/He ii λ1640 for the BC. The bottom panels of Figure 7 show the results for individual sources.

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The vertical lines identify the median values, ${\mu }_{\tfrac{1}{2}}$(C iv/He ii λ1640) ≈ 4.03, ${\mu }_{\tfrac{1}{2}}$(Al iii/He ii λ1640) ≈ 4.31, ${\mu }_{\tfrac{1}{2}}$(Si iv/He ii λ1640) ≈ 6.39. The higher value for Si iv/He ii λ1640 than for C iv/He ii λ1640 implies ${\mu }_{\tfrac{1}{2}}$(C iv/Si iv) ≈ 0.69, a value that is predicted by CLOUDY for very low values of the ionization parameter (Appendix B). The C iv/Al iii ratio is also constraining: the CLOUDY simulations indicate high Z and low ionization.

The distribution of the data points is relatively well behaved, with individual ratios showing small scatter around their median values. In the histogram, we see a tail made by three to five objects, suggesting systematically higher values. In particular, at least two objects (SDSS J102606.67+011459.0 and SDSS J085856.00+015219.4 ) show systematically higher ratios, with C iv/He ii λ1640 ≈ 10, and Al iii/He ii λ1640 ≈ 4. Both of them show extreme C iv blueshifts, and SDSS J102606.67+011459.0 shows the highest Al iii/Si iii] ratio in the sample.

Since the three ratios are, for fixed physical conditions, proportional to metallicity, we expect an overall consistency in their behavior, i.e., if one ratio is higher than the median for one object, also the other intensity ratios should be also higher. The lower diagrams are helpful to identify sources for which only one intensity ratio deviates significantly from the rest of the sample. A case in point is SDSS J082936.30+080140.6, whose ratio Al iii/He ii λ1640 ≈ 8 is one of the highest values, but whose C iv/He ii λ1640 and Si iv/He ii λ1640 are slightly below the median values. The fits of Appendix A show that this object is indeed extreme in Al iii emission. The C iv and λ1400 blends are dominated by the BLUE excess, and an estimate of the C iv and Si iv BC is very difficult, as it accounts for a small fraction of the line emission. The He ii λ1640 emission is almost undetectable, especially in correspondence with the rest frame. SDSS J082936.30+080140.6, along with other sources with high Al iii/He ii λ1640 or Si iv/He ii λ1640 ratios, may indicate selective enhancement of aluminum or silicon (see also Section 5.7).

4.1.3. BLUE Intensity Ratios

Similar considerations apply to the blue intensity ratios. We see systematic trends in Figure 8 that imply consistency of the ratios for most sources, although the uncertainties are larger, especially for C iv/He ii λ1640. The ratio C iv/(Si iv + O iv]) values are systematically higher than for the BC, while the C iv/He ii λ1640 is slightly higher (median BLUE 5.8 vs. median BC 4.38). The ratio (Si iv + O iv])/He ii λ1640 is much lower than for the BC (median BLUE 2.09 vs. median BC 6.27). The difference might be in part explained by the difficulty of deblending Si iv from O iv], and by the frequent occurrence of absorptions affecting the blue side of the blend. Both factors may conspire to depress BLUE. The bottom panels of Figure 8 are again helpful to identify sources for which intensity ratios deviate significantly from the rest of the sample. SDSS J102606.67+011459.0 shows a strong enhancement of C iv/He ii λ1640 and Si iv + O iv], confirming the trend seen in its BC.

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4.1.4. Correlation between Diagnostic Ratios

Figure 9 shows a matrix of correlation coefficients for all diagnostic ratios that we considered in this work. The 2σ confidence level of significance for the Spearman's rank correlation coefficient for 13 objects is achieved at ρ ≈ 0.54. The highest degree of correlation is found between the ratios C iv/He ii λ1640 and C iv/Si iv (0.87) and between C iv/He ii λ1640 and Si iv/He ii λ1640 (0.81). A milder degree of correlation is found between Al iii/He ii λ1640 and C iv/He ii λ1640 (0.23) and Si iv/He ii λ1640 (0.44). These results imply that Si iv and C iv are likely affected in a related way by a single parameter. The main parameter is expected to be T_e, and hence Z (Section 3.5.1). The Al iii (normalized to the He ii λ1640 flux) line shows much lower values of the correlation coefficient. The Al iii line has a different dependence on U, n_H, and optical depth variations. The prominence of C iii] with respect to Si iii] decreases with Si iv/He ii λ1640 BLUE, C iv/He ii λ1640, and Si iv/He ii λ1640 BLUE and increases with C iv/Si iv + O iv]. Apparently the C iii]/Si iii] ratio is strongly affected by an increase in metallicity and more in general by ratios that are indicative of "extremeness" in our sample. For BLUE, the two main independent Z estimators are correlated (ρ ≈ 0.68).

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4.2.1. Fixed (U, n_H)

We propagated the diagnostic intensity ratios measured on the BC and BLUE components with their lower and upper uncertainties following the relation between ratios and Z in Figure 2, for the fixed physical conditions assumed in the low- and high-ionization region. The results are reported in Tables 6 and 7 for the BC and for the blueshifted component, respectively. The last row reports the median values of the individual sources' Z estimates with the sample SIQR. The distributions are shown in Figures 10 and 11, along with a graphical presentation of each source and its associated uncertainties.

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Table 6. Metallicity ($\mathrm{log}Z$) of the BC Assuming Fixed U, n_H

SDSS JCODE	C iv/He ii λ1640	Si iv/He ii λ1640	Al iii/He ii λ1640
J010657.94−085500.1	1.16${}_{-0.33}^{+0.26}$	1.85${}_{-0.20}^{+0.20}$	1.7${}_{-0.15}^{+0.16}$
J085856.00+015219.4	2.22${}_{-0.35}^{+0.36}$	2.41${}_{-0.36}^{+0.59}$	2.2${}_{-0.29}^{+0.31}$
J082936.30+080140.6	0.63${}_{-0.65}^{+0.36}$	1.89${}_{-0.15}^{+0.16}$	2.36${}_{-0.09}^{+0.10}$
J084525.84+072222.3	1.41${}_{-0.16}^{+0.14}$	2.31${}_{-0.11}^{+0.11}$	2.07${}_{-0.09}^{+0.10}$
J084719.12+094323.4	1.50${}_{-0.23}^{+0.20}$	1.99 ${}_{-0.19}^{+0.21}$	1.91${}_{-0.17}^{+0.17}$
J092641.41+013506.6	1.27${}_{-0.29}^{+0.24}$	2.12${}_{-0.12}^{+0.12}$	1.59${}_{-0.10}^{+0.11}$
J094637.83−012411.5	1.80${}_{-0.14}^{+0.15}$	2.29${}_{-0.15}^{+0.16}$	1.44${}_{-0.13}^{+0.12}$
J102421.32+024520.2	1.16${}_{-0.12}^{+0.11}$	1.77${}_{-0.08}^{+0.09}$	1.74${}_{-0.06}^{+0.07}$
J102606.67+011459.0	1.82${}_{-0.32}^{+0.30}$	2.49${}_{-0.32}^{+0.51}$	2.38${}_{-0.26}^{+0.27}$
J114557.84+080029.0	1.12${}_{-0.27}^{+0.22}$	1.96${}_{-0.18}^{+0.19}$	1.92${}_{-0.15}^{+0.15}$
J150959.16+074450.1	0.19${}_{-0.47}^{+0.49}$	1.76${}_{-0.07}^{+0.06}$	1.69${}_{-0.06}^{+0.05}$
J151929.45+072328.7	1.18${}_{-0.09}^{+0.08}$	1.97${}_{-0.09}^{+0.08}$	1.98${}_{-0.05}^{+0.05}$
J211651.48+044123.7	2.11${}_{-0.04}^{+0.04}$	2.39${}_{-0.06}^{+0.06}$	1.9${}_{-0.06}^{+0.06}$
Median	1.27 ± 0.32	1.99 ± 0.21	1.91 ± 0.18

Note. Column (1): SDSS identification. Columns (2), (3), and (4): metallicity values for C iv/He ii λ1640, Si iv + O iv]/He ii λ1640, and Al iii/He ii λ1640 with uncertainties.

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Table 7. Metallicity ($\mathrm{log}Z$) of BLUE Assuming Fixed U, n_H

SDSS JCODE	Si iv + O iv]/He ii λ1640	C iv/Si iv + O iv]	C iv/He ii λ1640
J010657.94−085500.1	1.00${}_{-0.16}^{+0.12}$	0.88${}_{-0.12}^{+0.14}$	1.34${}_{-1.99}^{+0.34}$
J085856.00+015219.4	1.26${}_{-0.13}^{+0.20}$	1.12${}_{-0.21}^{+0.23}$	1.55${}_{-2.05}^{+0.35}$
J082936.30+080140.6	1.10${}_{-0.16}^{+0.14}$	1.03${}_{-0.19}^{+0.16}$	1.33${}_{-2.14}^{+0.41}$
J084525.84+072222.3	0.62${}_{-0.19}^{+0.20}$	0.63${}_{-0.09}^{+0.09}$	1.13${}_{-2.07}^{+0.50}$
J084719.12+094323.4	0.72${}_{-0.24}^{+0.27}$	0.68${}_{-0.15}^{+0.21}$	1.22${}_{-2.32}^{+0.59}$
J092641.41+013506.6	0.93${}_{-0.14}^{+0.11}$	0.99${}_{-0.16}^{+0.14}$	−0.56${}_{-0.46}^{+1.93}$
J094637.83−012411.5	0.74${}_{-0.18}^{+0.20}$	0.98${}_{-0.22}^{+0.20}$	−0.99${}_{-1.06}^{+2.16}$
J102421.32+024520.2	0.73${}_{-0.20}^{+0.24}$	0.78${}_{-0.14}^{+0.19}$	−0.52${}_{-0.65}^{+2.10}$
J102606.67+011459.0	1.02${}_{-0.12}^{+0.11}$	0.73${}_{-0.10}^{+0.12}$	1.67${}_{-0.31}^{+0.24}$
J114557.84+080029.0	0.89${}_{-0.22}^{+0.19}$	0.87${}_{-0.20}^{+0.25}$	0.99${}_{-2.12}^{+0.70}$
J150959.16+074450.1	1.07${}_{-0.21}^{+0.18}$	1.01${}_{-0.23}^{+0.22}$	1.28${}_{-2.28}^{+0.52}$
J151929.45+072328.7	0.79${}_{-0.06}^{+0.07}$	0.78${}_{-0.11}^{+0.13}$	1.02${}_{-0.59}^{+0.40}$
J211651.48+044123.7	-0.57${}_{-0.43}^{+0.81}$	0.66${}_{-0.05}^{+0.06}$	−1.46${}_{-0.23}^{+0.27}$
Medians	0.89 ± 0.15	0.87 ± 0.13	1.13 ± 0.92

Note. Column (1): SDSS identification. Columns (2), (3), and (4): metallicity values for Si iv + O iv]/He ii λ1640, C iv/Si iv + O iv], and C iv/He ii λ1640 with uncertainties.

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Tables 6 and 7 permit us to quantify the systematic differences that are apparent in Figures 10 and 11. The agreement between the various estimators is good on average (the medians scatter around $\mathrm{log}Z\approx 1$ by less than 0.2 dex). However, there are systematic differences between the Z obtained from the various diagnostic ratios. Si iv and Al iii over He ii λ1640 apparently overestimate the Z by a factor of 2 with respect to C iv/He ii λ1640. The out-of-scale values of C iv/Si iv and C iv/Al iii may suggest that metallicity scaling according to solar proportion may not be strictly correct (Section 5.6). In the case of BLUE, several estimates from C iv/He ii λ1640 strongly deviate from the ones obtained with the other ratios, due to the nonmonotonic behavior of the relation between Z and C iv/He ii λ1640, right in the range of metallicity that is expected. Figure 17 shows that the nonmonotonic behavior as a function of Z occurs for −1 ≲ $\mathrm{log}U$ ≲ 0, assuming $\mathrm{log}$ n_H = 9.

The median values of all three ratios consistently suggest high metallicity with a firm lower limit Z ≈ 5, and in the range 10 Z_⊙ ≲ Z ≲ 100 Z_⊙, with typical values between 20 and 50 Z_⊙. There is apparently a systematic difference between BC and BLUE, in the sense that Z derived from the BC is systematically higher than Z from BLUE. The difference is small in the case of C iv/He ii λ1640 but is significant in the case of (Si iv + O iv])/He ii λ1640, where Z from BLUE are a factor of 10 lower. We have stressed earlier that there are often absorptions affecting the BLUE of Si iv + O iv]/He ii λ1640. Absorptions and the blending with C ii λ1332 and Si iv BC lines make it difficult to properly define the continuum underlying the λ1400 blend at negative radial velocities. We think that the Si iv + O iv] BLUE intensity estimate is more of a lower limit. Another explanation might be related to the assumption of a constant density and U for all sources. While there are observational constraints supporting this condition for the BC (Panda et al. 2018, 2019, 2020b), there are no strong clues to the BLUE properties, save a high-ionization degree.

Table 8 reports the Z estimates for the BC, BLUE, and a combination of BC and BLUE for each individual object. The values reported are the median values of the individual objects' estimates from the different ratios. Here the Z value for each object is computed by vetting the ratios according to concordance. If the discordance is not due to a physical origin, but rather to instrumental problems (e.g., contamination by absorption lines, nonlinear dependence on Z of some ratios), a proper strategy is to use estimators such as the median that eliminate discordant values even for small sample sizes (n ≥ 3). Measuring medians and SIQR is an efficient way to deal with the measurements of large samples of objects. All estimates $\mathrm{log}Z\lesssim 0$ were excluded, as either the product of heavy absorptions (Si iv + O iv]/He ii λ1640) or the product of difficulties in relating the ratio (C iv/He ii λ1640) to Z; apart from J211651.48+044123.7, the upper uncertainty of the negative estimates is so large that Z is actually unconstrained. The difference between BLUE and BC is even more evident: the median (last row) indicates a factor of ≈6 difference between BLUE and BC. The BC suggests a median Z ≈ 60 Z_⊙, while the BLUE Z ≈ 10 Z_⊙. The assumption that the wind and disk component have the same Z in each object is a reasonable one, with the caveats mentioned in Section 5.6. Therefore, the two estimates, for BLUE and BC, could be considered two independent estimators of Z. If the two estimates are combined for each individual object, 10 Z_⊙ ≲ Z ≲ 100 Z_⊙, with a median value of Z ≈ 20 Z_⊙.

There is a good agreement between the Z median estimates from the BC and BLUE of C iv, $\mathrm{log}Z\approx 1.27$ versus $\mathrm{log}Z\approx 1.13$, respectively (Tables 6 and 7). Ignoring Si iv+O iv] and Al iii, the Z ≈ 20 Z_⊙ value derived for the C iv BC is not affected by a possible enhancement of [Si/C] and [Al/C] with respect to the solar values. If the carbon abundance is used as a reference, the BC Z estimate from Al iii and Si iv could point toward a selective enhancement of Si and Al with respect to C.

The disagreement between BLUE and BC Z estimates rests on the blueshifted component of Si iv + O iv]. The disagreement between the Z estimates from ratios involving Si iv+O iv] BC and BLUE might be explained if one considers that the measurement of the Si iv+O iv] BLUE is most problematic and the Si iv+O iv] intensity might be systematically underestimated.

We computed the χ² in the following form, to identify the value of the metallicity for median values of the diagnostic ratios and for the diagnostic ratios of individual objects relaxing the assumption of fixed density and ionization parameters. For each object k, and for each component c, we can write

$$\begin{eqnarray}&&{\chi }_{\mathrm{kc}}^{2}({n}_{{\rm{H}}},U,Z)=\sum _{{\rm{i}}}{w}_{\mathrm{ci}}{\left(\frac{{R}_{\mathrm{kci}}-{R}_{\mathrm{kci},\mathrm{mod}}({n}_{{\rm{H}}},U,Z)}{\delta {R}_{\mathrm{kci}}}\right)}^{2},\end{eqnarray} \tag{ 8 }$$

where the summation is done over the available diagnostic ratios, and the χ² is computed with respect to the results of the CLOUDY simulations as a function of U, n_H, and Z (subscript "mod"). Weights w_ci = 1 were assigned to C iv/He ii λ1640, Si iv/He ii λ1640, and Al iii/He ii λ1640; w_ci = 0 or 0.5 was assigned to C iv/Al iii and C iv/Si iv. For BLUE, the three diagnostic ratios were all assigned w_ci = 1. The Z estimates for the BC are based on the three ratios involving He ii λ1640 normalization.

To gain a global, bird's-eye view of the Z dependence on the physical parameters, Figure 12 shows the 3D space U, n_H, Z. Each point in this space corresponds to an element of the grid of CLOUDY in the parameter space and is consistent with the minimum χ² within the uncertainties at 1σ confidence level. The case shown in the panels of Figure 12 is the one with the median values of the sample objects.

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The distribution of the data points is constrained in a relatively narrow range of U, n_H, Z, at very high density, low ionization, and high metallicity. Within the limit in U, n_H, the distribution of Z is flat and thin, around Z ∼ 50–100 Z_⊙. This implies that, for a change of the U and n_H within the limits allowed by the data, the estimate of Z is stable and independent of U and n_H. Table 8 reports the individual Z estimates and the SIQR for the sources in the sample (the last row is the median).

The allowed parameter space volume for BLUE is by far less constrained. The right panel of Figure 12 shows the parameter space for the Z estimates from the three BLUE intensity ratios. The condition on the χ² distribution is the same as used for the BC, namely, that the data points all satisfy the condition ${\chi }^{2}\leqslant {\chi }_{\min }^{2}+1$. A similar shape is obtained if we consider the condition that all three ratios agree with the ones predicted by the model within 1σ. The spread in ionization and density is very large, although the concentration of data points is higher in the case of low n_H ($\mathrm{log}$ n_H ∼ 8–9 [cm⁻³]) and high ionization ($\mathrm{log}U\sim 0$). At any rate the spread of the data points indicates that solutions at low ionization and high density are also possible. The results for individual sources tend to disfavor this scenario for the wide majority of the objects, but the properties of the gas emitting the BLUE component are less constrained than the ones of the gas emitting the BC. What is missing for BLUE is especially a firm diagnostic of density that in the case of BC is provided mainly by the ratio Al iii/He ii λ1640. Results on Z are, however, as stable as for the BC, even if the dispersion is larger, and suggest values in the range 10 Z_⊙ ≲ Z ≲ 50 Z_⊙.

Summing up, all meaningful estimators converge toward high Z values, definitely supersolar, with Z ≳ 10 Z_⊙. Ratios C iv/Si iv significantly less than <1 are predicted in the parameter space. Si iv/He ii λ1640 seems to give the largest estimates of Z. Also, the high Al iii/C iv requires high values of Z. A conclusion has to be tentative, considering the possible systematic errors affecting the estimates of the C iv and Si iv intensities: for C iv, the BC in the most extreme cases is often buried under an overwhelming BLUE; a fit is not providing a reliable estimate of the BC (by far the fainter component) but provides a reliable BLUE intensity; for Si iv we may overestimate the intensity due to "cancellation" of the BLUE by absorptions. This said, the present data are consistent with the possibility of a selective enhancement of Al and Si, as already considered by Negrete et al. (2012). This issue will be briefly discussed in Section 5.

At any rate, the absence of correlation between BLUE and BC parameters (Figure 9), the difference in the diagnostic ratios and differences in inferred Z, and the results for individual sources described below justify the approach followed in the paper to maintain a separation between BLUE and BC. The meaning of possible systematic differences between the BC and BLUE is further discussed in Section 5.

4.4.1. Individual Sources

BC.—The best n_H, U, and Z for each object have been obtained by minimizing the χ² as defined in Equation (8), and they are reported in Table 9. The ${\chi }_{\min }^{2}$ values are listed in the second column of Table 9. At the side of each value there is the uncertainty range for each parameter defined from volume in the parameter space satisfying the condition ${\chi }^{2}\approx {\chi }_{\min }^{2}+1$. ¹¹ In other words, the choice of the best physical conditions was obtained by minimizing the sum of the deviations between the model predictions and the observer diagnostic ratios. The last two rows list the minimum χ² values for the median (with the SIQR of the sample from Table 5) and for the median of the values reported for individual sources in Table 9. The obtained values of Z cover the range 5 Z_⊙ ≲ Z ≲ 100 Z_⊙, with 9 out of 13 sources with 50 Z_⊙ ≲ Z ≲ 100 Z_⊙, and medians of intensity ratios yielding Z ∼ 50 Z_⊙. There is some spread in the ionization parameter values, −4 ≲ U ≲ −1, but in most cases U indicates low or very low ionization level. The hydrogen density is very high: in only a few cases $\mathrm{log}$ n_H ∼ 10–11, and in several cases n_H reaches 10¹⁴ cm⁻³. The median values from the ratios are $\mathrm{log}U=-2.25$, $\mathrm{log}$ n_H = 13.75 (with a range 12.5–14), therefore validating the original assumption of $\mathrm{log}U=-2.5$, $\mathrm{log}$ n_H = 12 for a fixed physical condition. The results for individual sources confirm the scenario of Figure 12 for the wide majority of the sample sources. The higher n_H values are consistent with recent inferences for the low-ionization BLR derived from Temple et al. (2020), based on the Fe iii UV emission, which is especially prominent in the UV spectra of xA quasars (Martínez-Aldama et al. 2018a). It is interesting to note that two of the borderline objects (Al iii/Si iii] ≈ 0.5, C iii]/Si iii] ≈ 1) show higher values of the ionization parameter ($\mathrm{log}U$ ≈ −1.0 to −1.5).

Table 9.  Z, U, n_H of Individual Sources and Median Derived from the BC

SDSS JCODE	${\chi }_{\min }^{2}$	$\mathrm{log}Z$ (Z⊙)	$\delta \mathrm{log}Z$ (Z⊙)	$\mathrm{log}U$	$\delta \mathrm{log}U$	$\mathrm{log}$ nH	$\delta \mathrm{log}$ nH
(1)	(2)	(3)	(4)	(5)	(6)	(7)
J010657.94−085500.1	2.6894	1.7	0.7–1.7	−2.00	−2.75 to −1.25	13.50	12.00–14.00
J082936.30+080140.6	6.6414	1.3	0.7–2.7	−4.00	−4.00 to −3.50	14.00	12.75–14.00
J084525.84+072222.3	13.700	1.7	1.0–3.0	−1.75	−3.75 to −0.25	14.00	12.00–14.00
J084719.12+094323.4	1.7004	1.7	1.0–2.0	−2.25	−2.50 to −1.50	13.75	12.50–14.00
J085856.00+015219.4	0.0012	2.0	1.7–2.7	−2.25	−3.00 to −1.75	12.50	12.00–14.00
J092641.41+013506.6	1.7982	1.7	1.7–2.0	−1.50	−1.75 to −1.00	14.00	13.50–14.00
J094637.83−012411.5	0.3253	1.7	1.7–2.3	−1.00	−1.25 to −0.75	12.25	11.75–14.00
J102421.32+024520.2	15.819	1.7	1.3–2.0	−2.25	−3.00 to −1.50	13.50	12.75–14.00
J102606.67+011459.0	1.5020	2.0	1.7–2.3	−1.75	−2.50 to −0.75	14.00	12.50–14.00
J114557.84+080029.0	6.6174	0.7	0.7–2.0	−3.75	−3.75 to −1.25	14.00	12.25–14.00
J150959.16+074450.1	45.287	1.3	0.5–2.0	−1.75	−0.50 to −3.50	13.75	12.25–14.00
J151929.45+072328.7	29.220	0.7	0.3–3.0	−3.75	−4.00 to −2.75	14.00	11.00–14.00
J211651.48+044123.7	1.4476	2.0	1.7–2.0	−2.00	−2.00 to −0.75	12.25	10.75–12.25
${\mu }_{\tfrac{1}{2}}$(Ratios)	1.9914	1.7	0.7–2.0	−2.25	−2.75 to −1.25	13.75	12.50–14.00
${\mu }_{\tfrac{1}{2}}$(Objects)	⋯	1.7	1.5–1.9	−2.00	−2.25 to −1.75	13.75	13.50–14.00

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Large (≫1) values of ${\chi }_{\min }^{2}$ are associated with cases in which the BC components of Al iii and/or of Si iv are strong with respect to the BC of C iv, and are further increased by small uncertainty ranges (which are more likely to occur if a line is strong). Intensity ratios C iv/Al iii ≲ 1 and C iv/Si iv ≲ 1 are reproduced by photoionization simulations in conditions of very low ionization. The ratio C iv/Al iii tends to decrease with increasing Z, although the trend is shallow at the lower ionization levels appropriate for the BC emission (Appendix B). However, high values of the Al iii and Si iv + O iv] over He ii ratios induced by overabundances could bias the U and lower its values.

BLUE.—The inferences are less clear from BLUE (Table 10, organized like Table 9). In most cases, the permitted volume in the 3D parameter space for individual sources covers a broad range in U and n_H as for the median (Figure 12). Figure 12 shows that there is a strip of χ² values statistically consistent with the minimum χ² that crosses the full domain of the parameter space. Along this strip of permitted values n_H and U are linearly dependent, with $\mathrm{log}U\approx -0.5\cdot {n}_{{\rm{H}}}+4$ for the median composite ratios. In most sources the U value implies a high degree of ionization, −1 ≲ $\mathrm{log}U$ ≲ 0, but in three cases (e.g., SDSS J150959.16+074450.1) there is apparently a low-ionization solution with U comparable to that of the low-ionization BLR. The medians are $\mathrm{log}$ n_H ∼ 7.75, $\mathrm{log}\,U$ ∼ −0.5, close to the values that we assumed for the fixed (U, n_H) approach. The results on metallicity suggest in most cases Z ≳ 20 Z_⊙. However, within 1 SIQR from the minimum χ², Z values up to 30 are also possible.

Table 10.  Z, U, n_H of Individual Sources and Median Derived from BLUE

SDSS JCODE	${\chi }_{\min }^{2}$	$\mathrm{log}Z$ (Z⊙)	$\delta \mathrm{log}Z$ (Z⊙)	$\mathrm{log}U$	$\delta \mathrm{log}U$	$\mathrm{log}$ nH	$\delta \mathrm{log}$ nH
(1)	(2)	(3)	(4)	(5)	(6)	(7)
J010657.94−085500.1	0.00985	1.70	0.70–1.7	0.75	−1.5–0.75	7.75	7.50–9.75
J082936.30+080140.6	0.01506	1.30	1.00–1.70	−0.25	−2.0 to −0.00	8.00	7.75–12.25
J084525.84+072222.3	0.00143	1.0	0.00–2.30	−1.50	−2.50 to −1.25	7.25	7.00–11.25
J084719.12+094323.4	0.00097	1.00	0.00–3.00	−2.24	−2.50–0.75	8.75	7.50–11.50
J085856.00+015219.4	0.00305	1.70	1.0–2.00	0.50	−1.75–0.50	8.25	7.00–11.75
J102606.67+011459.0	0.00111	0.70	0.70–3.00	−1.00	−2.50 to −0.5	9.25	8.25–11.25
J114557.84+080029.0	0.00164	1.30	0.30–1.70	−2.50	−2.50–0.25	11.50	7.25–12.50
J150959.16+074450.1	0.00288	1.30	0.30–2.00	−2.00	−2.75–0.75	11.75	7.00–13.75
J151929.45+072328.7	0.00032	0.30	0.30–1.30	−0.50	−0.75–0.25	10.00	7.75–10.25
${\mu }_{\tfrac{1}{2}}$(Ratios)	0.07336	1.30	1.0–1.30	−0.50	−0.50 to −0.50	7.75	7.75–8.00
${\mu }_{\tfrac{1}{2}}$(Objects)	⋯	1.30	1.15–1.45	−1.00	−0.125 to −1.875	8.75	7.75–9.75

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Z values from BLUE are systematically lower than those from the BC. The medians differ by a factor of 2. However, a Welch t-test (Welch 1947) fails to detect a significant difference between the average values of the metallicity for the two components: t ≈ 0.86 for 5 degrees of freedom (computed using the Welch-Satterthwaite equation) implies a significance of just 80%. Three cases in which the disagreement is large, more than a factor of 5, namely, J084525.84+072222.3, J084719.12+094323.4, and J102606.67+011459.0, are apparently not strongly affected by absorption lines, but the constraints from Tables 10 and 9 are poor, implying that also for BLUE the Z could be much higher. Therefore, we cannot substantiate any claim of a systematic difference between BLUE and BC Z estimates.

The Z, U, n_H parameter space occupation of xA quasars.—In summary, the low-ionization BLR of xA sources seems to be consistently characterized by low ionization, extremely high density, and very high metallicity, under the assumption that Z scales with the solar chemical composition. Diagnostics on BLUE is less constraining, and measurements are more difficult. The zero-order results are, however, consistent again with high metallicity Z ≳ 5 Z_⊙.

The 3D distribution in Figure 12 indicates that, although there might be a large range of uncertainty in the U and n_H especially for BLUE, the Z values tend to remain constrained within a narrow strip around a well-defined Z, parallel to the U, n_H plane. In other words, Z estimates should be stable, as they are not strongly dependent on the assumed physical parameters.

Comparing the individual Z estimates for fixed and free n_H and U (Cols. (2) of Tables 6 and 9) for the BC, the agreement is good, with a median difference of 0.22 and an SIQR of 0.15, with the fixed n_H and U being therefore a factor of ≈1.65 higher than the one derived assuming a free n_H and U. Two sources (J151929.45+072328.7 and J114557.84+080029.0) show a large disagreement, in the sense that the Z values leaving U and n_H free are much lower. These Z estimates are, however, highly uncertain, with a shallow χ² distribution around the minimum especially for J151929.45+072328.7. For this object the maximum metallicity covered by the simulations Z = 1000 Z_⊙ is still consistent within the uncertainties.

The determination of the metal content of the broad-line-emitting region of xA quasars was made possible by the following procedure:

• 1.  
  The estimation of an accurate redshift. Even if all lines are affected by significant blueshifts that reduce the values of measured redshift, in the absence of information from the H β spectral range the Al iii and the λ1900 blend can be used as proxies of proper redshift estimators. The blueshifts are the smallest in the intermediate-ionization lines at λ1900 (A. del Olmo et al. 2021, in preparation).
• 2.  
  The separation of the BC and BLUE, for C iv and the λ1400 blend. The line width of the individual components of the Al iii doublet can be used as a template BC. The component BLUE is defined as the excess emission on the blue side of the BC.
• 3.  
  A first estimate of metallicity can be obtained from the assumption that the low-ionization BLR associated with the BC and wind/outflow component associated with BLUE can be described by similar physical conditions in different objects. Several diagnostic ratios can be associated with the intensity ratios predicted by an array of photoionization simulations, namely,

  • (a)  
    for the BC: Al iii/He ii λ1640, C iv/He ii λ1640, Si iv/He ii λ1640, assuming ($\mathrm{log}U$, $\mathrm{log}$ n_H) = (−2.5, 12) or ($\mathrm{log}U$, $\mathrm{log}$ n_H) = (−2.5, 13);
  • (b)  
    for the BLUE: C iv/He ii λ1640, Si iv + O iv]/He ii λ1640, C iv/Si iv + O iv] assuming ($\mathrm{log}U$, $\mathrm{log}$ n_H) = (0, 9).
• 4.  
  Estimates can be refined for individual sources relaxing the constant ($\mathrm{log}U$, $\mathrm{log}$ n_H) assumptions. Tight constraints can be obtained for the BC. The BLUE is more problematic, because of both observational difficulties and the absence of unambiguous diagnostics.

Our method relies on ratios involving He ii λ1640 that have not been much considered in previous literature. In addition, we have considered fixed SED, turbulence (equal to 0), and column density in the simulations (N_c = 10²³) as fixed. The role of turbulence is further discussed in Section 5.5 and is found to be not relevant, unlike in the case of Fe ii emission in the optical spectral range, where effects of self- and Lyα-fluorescence are important (e.g., Verner et al. 1999; Panda et al. 2018), while the N_c effect is most likely negligible.

Extension of the method to the full Population A is a likely possibility, since we do not expect a very strong effect of the SED on the metallicity estimate, as long as the SED has a prominent big blue bump, as seems to be case for Population A. The role of SED is likely important if the method has to be extended to sources of Population B along the main sequence. At least two SED cases should be considered, if the aim is to apply the method presented in this paper to a large sample of quasars.

Intensity ratios involving He ii λ1640 are difficult to measure in the xA spectra but may be more accessible for Population B spectra. Ferland et al. (2020) have shown significant differences in the SED as a function of L/L_Edd, with a much flatter SED at low L/L_Edd. The extension to Population B would therefore require a new dedicated array of simulations.

The bolometric luminosity has been computed assuming a flat ΛCDM cosmological model with Ω_Λ = 0.7, Ω_m = 0.3, and H₀ = 70 km s⁻¹ Mpc⁻¹. Following Marziani & Sulentic (2014), we decided to use Al iii as a virial broadening estimator for computing the M_BH. Our estimates adopt two different scaling laws: the scaling laws of Vestergaard & Peterson (2006) for C iv, and a second, unpublished one based on Al iii (A. del Olmo et al. 2021, in preparation). Eddington ratios have been obtained using the Eddington luminosity L_Edd ≈ 1.3 × 10³⁸(M_BH/M_⊙) erg s⁻¹. The luminosity range of the sample is very limited, less than a factor of 3, $46.8\lesssim \mathrm{log}L\lesssim 47.3$, in line with the requirement of similar redshift and high flux values. Correspondingly, the M_BH and the Eddington ratio are constrained in the range $8.8\lesssim \mathrm{log}$ M_BH ≲ 9.5 and −0.55 ≲ $\mathrm{log}$ L/L_Edd ≲ 0.18, respectively. The M_BH sample dispersion is small, with $\mathrm{log}$ M_BH ∼ 9.4 ± 0.2 [M_⊙]. The scatter in M_BH and L/L_Edd is reduced to ≈0.1 dex if we exclude one object with the lowest M_BH and highest L/L_Edd. Applying a small correction (10%) to the FWHM to account for an excess broadening in Al iii due to nonvirial motions will decrease the M_BH by 0.1 dex (as found by Negrete et al. 2018 for H β) and increase L/L_Edd correspondingly. If this correction is applied, the median L/L_Edd is ≈0.6. Using the C iv BC FWHM as a virial broadening estimator further decreases the M_BH median estimate by 0.1 dex. The accretion parameters are consistent with extreme quasars of Population A at high mass and luminosity; they are mainly at the low-L/L_Edd end of sample 3 (based on M_BH estimates from Al iii) of Marziani & Sulentic (2014). The small dispersion in physical properties of the present sample (0.2 dex) focuses the analysis on properties that may differ for fixed accretion parameters, and fixed ratio of radiation and gravitation forces, perhaps related to different enrichment histories.

5.2.1. Correlation between Diagnostic Ratios and AGN Physical Properties

Considering the small dispersion in M_BH, L/L_Edd, and bolometric luminosity, it is hardly surprising that none of the ratios utilized in this paper are significantly correlated with the accretion parameter. The highest degree of correlation is seen between L/L_Edd and C iv/Al iii, but still below the minimum ρ needed for a statistically significant correlation.

In Figure 13 we present the correlation between metallicity and diagnostic ratios, along with log of bolometric luminosity, log of black hole mass, and log of Eddington ratio, for BC and BLUE. The strongest correlations between Z_BC and intensity ratios are with Si iv/He ii λ1640 (0.75) and Al iii/He ii λ1640 (0.77). For Z_BLUE, Si iv/He ii λ1640 (BLUE components) correlates strongly (0.99). Z_BLUE correlates with physical parameters, whereas Z_BC rather anticorrelates with them, but not at a statistically significant level. Considering the limited range in luminosity and M_BH and the small sample size, these trends should be confirmed.

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The metallicity values we derive are very high among quasars analyzed with similar techniques (e.g., Nagao et al. 2006b; Shin et al. 2013; Sulentic et al. 2014): as mentioned, typical values for high-z quasars are around 5 Z_⊙. This value could be taken as a reference over a broad range of redshift, and also for the sample considered in the present paper, as there is no evidence of metallicity evolution in the BLR up to z ≈ 7.5 (e.g., Nagao et al. 2006b; Juarez et al. 2009; Xu et al. 2012; Onoue et al. 2020). This is in line with the results of Negrete et al. (2012), who found very similar intensity ratios for the prototypical NLSy1 and xA source I Zw 1, of relatively low luminosity at low z, and a luminous xA object at redshift z ≈ 3.23. Even if these authors did not derive Z from their data, the I Zw 1 intensity ratios reported in their paper indicate very high metallicity, consistent with the values derived for the present sample.

More than inferences on the global enhancement of Z in the host galaxies, the absence of evolution points toward a circumnuclear source of metal enrichment, ultimately associated with a starburst (e.g., Collin & Zahn 1999a; Xu et al. 2012).

A detailed comparison with previous work on the dependence of Z on accretion parameters is hampered by two difficulties: (1) Before comparing the intensity ratios of this paper, we should consider that other authors do not distinguish between BLUE and BC when computing the ratios. This has the unfortunate implication that in some cases, such as Al iii/C iv, the ratio is taken between lines emitted predominantly in different regions (virialized and wind), presumably in very different physical conditions. Not distinguishing between BC and BLUE yields C iv/Al iii ∼ 10 ≫ 1. (2) Methods of M_BH estimate differ. For example, Matsuoka et al. (2011) use the Vestergaard & Peterson (2006) scaling laws without any correction to the line width of C iv. This might easily imply overestimates of the M_BH by factors of 5–10 (Sulentic et al. 2007). The analysis by Shemmer et al. (2004) instead used H β from optical and IR observations to compute M_BH and to examine the dependence of metallicity on accretion parameters. These authors found the strongest dependence on Eddington ratio (with respect to luminosity and mass) over 6 orders of magnitude in luminosity, suggesting that luminosity and black hole mass are less relevant (as also found, e.g., by Shin et al. 2013).

As was stressed in several works (e.g., Wang et al. 2012a; Sulentic et al. 2014), the intensity of the N v line is difficult to estimate owing to blending with Lyα and strongly affected by absorption. We model Lyα and N v using the same criteria as in Si iv modeling. However, in this work, we give only a qualitative judgment of N v strength for our sample, because of large uncertainties due to the effect mentioned above. For sources in the highest metallicity range obtained from ratios from BC, the N v BC intensity is slightly higher than or comparable to Lyα BC. Blue components dominate both lines. We notice also significantly higher intensity of the blue component in comparison to the broad one in Si iv and C iv blends. An example of source of this type is shown in the upper half of Figure 14. On the contrary, sources with the lowest metallicities obtained from BC intensity ratios show the Lyα BC intensity higher than in N v, and the BC is stronger than BLUE. We see the same behavior of strong BC in the Si iv and C iv ranges. An example of sources of this type is shown in the lower half of Figure 14. Shin et al. (2013) compared Si iv + O iv] and N v fluxes and found strong, significant correlation between them (ρ = 0.75). The N v over He ii λ1640 or H β should be a strong tracer of Z, as it is sensitive to secondary Z production and hence proportional to Z² (Hamann & Ferland 1999). Therefore, we conclude that the N v emission is extremely strong and consistent with very high metal content. A much more thorough investigation of the quasar absorption/emission system is needed to include N v as a Z estimator. This is deferred to further work.

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The column density assumed in the present paper is $\mathrm{log}$ N_c = 23 [cm⁻²]. With this value the emitting clouds in the low-ionization conditions remain optically thick to the Lyman continuum for most of the geometrical depth of the cloud. Even if the value $\mathrm{log}$ N_c = 23 may appear as a lower limit for the low-ionization BLR, as higher values are required to explain low-ionization emission such as Ca ii and Fe ii (Panda 2020; Panda et al. 2020a), the emission of the intermediate- and high-ionized region is confined within the fully ionized part of the line-emitting gas, whose extension is already much less than the geometrical depth of the gas slab for $\mathrm{log}$ N_c = 23. Therefore, we expect no or a negligible effect from an increase in the column density for the low-ionization part of the BLR.

For BLUE, the situation is radically different, and we have no actual strong constraints on column density. Most emission may come from a clumpy outflow (Matthews 2016 and references therein), and therefore assuming a constant N_c may not be appropriate. Considering the poor constraint that we are able to obtain, we leave the issue to an eventual investigation.

The results presented in this work refer to the case in which there is no significant microturbulence included in the CLOUDY computations. Figure 15 shows that at low ionization the effect is relatively modest, and that in the high-ionization case appropriate for BLUE the effect is very modest. Less obvious is the behavior at low ionization for R_{Fe ii} : it shows an increase for t = 10 km s⁻¹, but then it has a surprising drop at a larger value of the microturbulence. While the increase can be explained by an increase of the transitions for which fluorescence is possible, the decrease is not of obvious interpretation. It has been, however, confirmed by the independent set of simulations of Panda et al. (2018, 2019).

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Metals are expected to be preferentially accelerated by resonance scattering (e.g., Proga 2007b; Risaliti & Elvis 2010). In principle, for a sufficiently large photon flux, the acceleration of metals by radiation pressure might become larger than the Coulomb friction, therefore causing a decoupling of the metals with respect to their parent plasma (Baskin & Laor 2012). This possibility has been explored in the context of the BALs, and broad absorption and emission components are expected to be related (Elvis 2000; Xu et al. 2020). The ionization parameter values are, however, several orders of magnitudes higher than the ones derived for the BLUE emission component. In addition, our Z estimates for the BLUE suggest, if anything, values lower than or equal to those for the BC, whose Z might be related more to the original chemical composition of the gas in the accretion material. However, we ascribe the systematic differences between BC and BLUE as uncertainties in the method and measurement, so that Z from BLUE and BC should be considered intrinsically equal.

Considering that the most metal-rich stars, galaxies, and molecular clouds in the universe do not exceed Z ≈ 5 Z_⊙ (Maiolino & Mannucci 2019), circumnuclear star formation is needed for the chemical enrichment of the BLR gas (e.g., Collin & Zahn 1999a, 1999b; Wang et al. 2011, 2012b). Star formation may occur in the self-gravitating, outer part of the disk. An alternative possibility is that a massive star could be formed inside the disk by accretion of disk gas (Cantiello et al. 2020).

An implication of the scenarios involving circumnuclear or even nuclear star formation is that there could be an alteration of the relative abundance of elements with respect to the standard solar composition (Anders & Grevesse 1989; Grevesse & Sauval 1998). Support for this hypothesis is provided by the extreme C iv/Si iv and C iv/Al iii that may hint at a selective enhancement of Al with respect to C. As suggested by Negrete et al. (2012), core-collapse supernovæ with very massive progenitors could be at the origin of a selective enhancement. Supernovae with progenitors of masses between 15 and 40 M_⊙ have selective enhancement in their yields of Al and Si by factors of ≈100 and 10 relative to hydrogen with respect to solar (Chieffi & Limongi 2013). Since carbon is also increased by a factor of ∼10 with respect to solar, the [Al/C] is expected to be a factor of ∼10 larger than the solar value in supernova ejecta. The case for silicon is less clear, as the enhancement is of the same order of magnitude as the one expected for carbon. Pollution of gas by supernovæ may therefore lead to an estimate of the Z higher than the actual one, if solar relative abundances are assumed. This possibility will be explored in an eventual work (K. Garnica et al. 2021, in preparation).

Metallicity and the outflow prominence of quasars were found to be highly correlated (Wang et al. 2012a; Shin et al. 2017). The implication of these results is that xA sources, which show the highest blueshifts (Sulentic et al. 2017; Martinez-Aldama et al. 2018a, 2018b; Vietri et al. 2018), should also be the most metal-rich. The xA sources should be at the top of the Z outflow parameter correlation of Wang et al. (2012a), if Z ≳ 10 Z_⊙.

There is evidence of a metallicity correlation between the BLR and NLR (Du et al. 2014), as expected if the outflows on spatial scales of kiloparsecs are originating in a disk wind. Zamanov et al. (2002) derived very small spatial scales at low luminosity. This provides additional support to the idea that xA sources, which at low z phenomenologically appear as Fe ii-strong NLSy1s, are relatively young sources. Their low [O iii] λ5007 equivalent width implied young age more than orientation effects (Risaliti et al. 2011; Bisogni et al. 2017). The z ≈ 2 quasars of the present sample are radiating at relatively high L/L_Edd, although there are no examples of the extremes of xA sources showing blueshifted emission in Al iii as prominent as the one of C iv (e.g., Martínez-Aldama et al. 2017). There is no evidence of heavy obscuration. They are certainly out of the obscured early evolution stage in which the accreting black hole is enveloped by gas and dust (see the sketch in D'Onofrio & Marziani 2018). The W C iv distribution covers the upper half of the one of Martínez-Aldama et al. (2018a). There are no weak-lined quasars following Diamond-Stanic et al. (2009). The xA sources of the present sample may have reached a sort of stable equilibrium between gravitation and radiation forces made perhaps possible by the development by an optically thick, geometrically thick accretion disk, and by its anisotropic radiation properties (e.g., Abramowicz et al. 1988; Szuszkiewicz et al. 1996; Sa̧dowski et al. 2014).

The median value of the peak displacement of the BLUE component is ≈3500 km s⁻¹, and the centroid at half-maximum is shifted by 5000 km s⁻¹. The extreme blueshifts in the metal lines imply outflows that may not remain bound to the potential well of the black hole and of the inner bulge of the host galaxies (e.g., Marziani et al. 2016b and references therein). The high metal content of the outflows, estimated by the present work to be in the range of 10–50 Z_⊙, implies that these sources are likely to be a major source of metal enrichment of the interstellar gas of the host galaxy and of the intergalactic medium. Using a standard estimate for the mass outflow rate $\dot{M}$ (Marziani et al. 2016b), $\dot{M}\,\approx 15{L}_{{\rm{C}}\mathrm{IV},45}{v}_{5000}{r}_{1\,\mathrm{pc}}^{-1}{n}_{9}^{-1}\,{M}_{\odot }$ yr⁻¹, we obtain an outflow rate of $\dot{M}\approx 20\,{M}_{\odot }$ yr⁻¹, assuming median values for the sources of our sample: median outflow velocity from the peak of BLUE ≈ −3500 km s⁻¹, a median luminosity of the C iv BLUE (corrected because of Galactic extinction) of 4.2 × 10⁴⁴ erg s⁻¹, a median radius 5.9 × 10¹⁷ cm from the Kaspi et al. (2007) radius−luminosity correlation for C iv, and n₉ = 1. For a duty cycle of ∼10⁸ yr, the expelled mass of heavily enriched gas could be ∼10⁹ M_⊙.