BROAD-LINE REGION PHYSICAL CONDITIONS IN EXTREME POPULATION A QUASARS: A METHOD TO ESTIMATE CENTRAL BLACK HOLE MASS AT HIGH REDSHIFT

Boroson & Green (1992, BG92) identified a series of correlations from principal component analysis (PCA) of the correlation matrix of emission-line measures for a bright low-redshift quasar sample. The sample contained 87 PG quasars with z ∼ 0.5 (17 of them radio-loud, RL). The first PCA eigenvector (hereafter E1) identified correlations involving broad Hβ, broad Fe ii, and narrow [O iii] λλ4959, 5007 emission lines. In an effort to clarify the meaning of the E1, Sulentic et al. (2000) searched for a correlation diagram that showed maximal discrimination between the various active galaxy nucleus (AGN) subclasses. The best E1 correlation space that we could identify involved measures of (1) equivalent width (EW) of the Fe ii λ4570 blend (defined as the ratio $R_{\rm Fe\,{\textsc {ii}}}$ = W(Fe ii λ4570)/W(Hβ)) and (2) FWHM(Hβ). These were supplemented with (3) the soft X-ray photon index, Γ_soft, and the centroid line shift of high-ionization C iv λ1549. Figure 7 of Sulentic et al. (2000) shows two-dimensional projections of this four-dimensional E1 (4DE1) space: FWHM(Hβ) versus $R_{\rm Fe\,{\textsc {ii}}}$, Γ_soft versus $R_{\rm Fe\,{\textsc {ii}}}$, and FWHM(Hβ) versus Γ_soft. They supplemented the BG92 RL sample with an additional 18 sources (with comparable signal-to-noise (S/N) spectra) taken from Marziani et al. (1996), who reported W(Fe ii) measures over the range 4240–5850 Å. The range 4240–5850 Å Fe ii flux was divided by a factor ≈3.3 in order to obtain the flux in the range 4434–4684 Å that was used by BG92 (both works relied on the same Fe ii template based on I Zw 1). Sulentic et al. (2000) separated various subclasses of AGNs into two populations: Populations A and B (Pops. A and B) separated at FWHM(Hβ) = 4000 km s⁻¹. Physical drivers for the correlation were discussed in, e.g., Marziani et al. (2003) with black hole mass and Eddington ratio L/L_Edd (where L_Edd = 1.5 × 10³⁸(M/M_☉) is the Eddington luminosity) identified as the principal drivers of change along the 4DE1 sequence. Black hole mass increases from Pop. A to Pop. B, while Eddington ratio decreases from Pop. A to Pop. B.

The division into two populations is, at least, useful for highlighting major differences among Type 1 AGNs, although spectral differences among objects within the same population are still noticeable, especially for Pop. A sources (Figure 2 of Sulentic et al. 2002). This is the reason why they also divided the 4DE1 optical plane into bins of ΔFWHM(Hβ) = 4000 km s⁻¹ and $\Delta R_{\rm Fe\,{\textsc {ii}}}= 0.5$. Bins A1, A2, A3, and A4 are defined in terms of increasing $R_{\rm Fe\,{\textsc {ii}}}$, while bins B1, B1⁺, and B1⁺⁺ are defined in terms of increasing FWHM(Hβ) (see Figure 1 of Sulentic et al. 2002). Sources belonging to the same spectral type show similar spectroscopic measures and physical parameters (e.g., line profiles and UV line ratios). Systematic changes are minimized within each spectral type so that an individual quasar can be taken as representative of all sources within a given spectral bin. The binning adopted in Sulentic et al. (2002) is valid for low-z (<0.7) quasars. At higher z an adjustment must be made since no sources with FWHM(Hβ) < 3500 km s⁻¹ are found above redshift z ∼ 3 (Marziani et al. 2009).

In order to deblend and identify the principal lines, as well as to extract the core of the broad emission lines, we use the following previous results:

• 1.  
  As mentioned above, Sulentic et al. (2002) divided Pop. A and B sources into bins according to FWHM Hβ and $R_{\rm Fe\,{\textsc {ii}}}$ measures. In 2010, Zamfir et al. computed median composite Hβ spectra for each of the bins and showed that the broad Hβ profiles in composite spectra of Pop. A sources are best fit by Lorentzian functions. In Pop. B objects, on the other hand, they are best described by Gaussian profiles (see also Marziani et al. 2010). This is an empirical result clearly shown in these works. Our sources are extreme Pop. A objects (bin A3), and thus we shall use Lorentzian profiles to model the BCs.
• 2.  
  Marziani et al. (2010) analyze six sources (including I Zw 1) representative of the six most populated bins of Pops. A and B. They show that FWHM and profile shape of BCs of Si iii] λ1892, Al iii λ1860, and C iv λ1549 are similar to those of Hβ. We do not have an Hβ spectrum for SDSS J12014+0116 since there are no near-IR data for this object. However, for other high-z quasars, there are high-S/N IR spectra (Sulentic et al. 2004) that show NLSy1-like sources (defined in Section 2), with M_B = −28 and FWHM(Hβ) as much as 2000 km s⁻¹ broader than those with M_B = −22. SDSS J12014+0116 shows M_B = −29.8 with FWHM ∼ 4000 km s⁻¹, while for I Zw 1 M_B = −23.5 and FWHM ∼ 2000 km s⁻¹. With larger samples at high redshift (e.g., Marziani et al. 2009) the result that the FWHM(Hβ) can be as high as 4000 km s⁻¹ for NLSy1-like objects is confirmed. Following these results, we use a Lorentzian profile with the same width (FWHM ∼ 4000 km s⁻¹ in SDSS J12014+0116 and FWHM ∼ 2000 km s⁻¹ in I Zw 1) for all the BCs of the broad emission lines.
• 3.  
  HIL C iv λ1549 profiles show significant differences between Pop. A and B sources. In Pop. A the peak of the line is often blueshifted and the profile blue asymmetric. We model this as a strongly blueshifted (≲ − 1000 km s⁻¹) C iv λ1549 BC (hereafter labeled BLUE; Sulentic et al. 2007) plus an unshifted BC analogous to the one seen in Hβ. We assume that the profile of this blueshifted component is Gaussian as discussed in Marziani et al. (2010).
• 4.  
  In Pop. A objects, low (Si ii λ1814) and intermediate (Al iii λ1860, Si iii] λ1892) ionization lines offer the simplification of showing only the BC associated with low-ionization emission (Marziani et al. 2010).

All the above results are taken into account for modeling the lines in this paper.

After identifying the emission lines needed for our study, we isolate the broad central component in each of them using spectral decompositions as explained below. We need the line fluxes to obtain n_H and U, the rest-frame specific flux at λ = 1700 Å to compute r_BLR, and the FWHM of the BCs to estimate M_BH. We use the specfit IRAF task (Kriss 1994), which enables us to fit the continuum, emission, and absorption line components, as well as Fe ii and Fe iii contributions. We work with emission lines in the spectral range 1400–2000 Å that have been studied in great detail in both high- and low-z quasars and where identification of prominent resonance and intercombination lines is well established.

The steps we followed to accomplish identification, deblending, and measurement of lines in each object were the following:

• 1.  
  The continuum. We adopted a single power-law fit to describe it (Figure 1) using the continuum windows around 1700 and 1280 Å (see, e.g., Francis et al. 1991). Fe ii emission in these ranges is weak, leading us to assume that continuum measurement in those windows is reliable enough for our method (within the uncertainties, see Section 3.2.1).
• 2.  
  BC line widths and shifts. We assume that a single value of FWHM (last column of Table 2) is adequate to fit the BCs of all lines. BC shifts of all lines are the same and consistent with the redshift reported in the table. Due to the fact that the C iii] λ1909 emission line is mostly emitted in a different region than the rest of the broad lines (see discussion in Section 3.2.2), we do not impose the same restriction on the FWHM of C iii] λ1909.
• 3.  
  λ1900 blend. In Table 1 we summarize the properties of the strongest features expected that contribute to the λ1900 blend. Column 1 lists the ion. Column 2 lists rest-frame wavelength. Columns 3 and 4 list the ionization potential and energy levels of the transition, respectively. Column 5 gives the configuration of the levels for the transition. Columns 6 and 7 give the transition probabilities and critical densities, respectively. And in Column 8 we give some notes for each ion. Forbidden lines of Si and C are not expected to be significantly emitted in the BLR and will not be further considered.Fe iii lines are frequent and strong in the vicinity of C iii] λ1909 as seen in the SDSS template quasar spectrum (Vanden Berk et al. 2001). They appear to be strong when Al iii λ1860 is also strong (Hartig & Baldwin 1986). They are included in the photoionization simulations described below (Sigut et al. 2004). Lyα pumping enhances Fe iii λ1914.0 (UV 34; Johansson et al. 2000), and this line can be a major contributor to the blend on the red side of C iii] λ1909. The spectrum of I Zw 1 convincingly demonstrates this effect: both C iii] λ1909 and Fe iii λ1914 are needed to account for the double-peaked feature at 1910 Å that is too broad to be explained by a single line (Figure 2).⁷ We adopt the template (option B) of Vestergaard & Wilkes (2001) plus additional Fe iii λ1914, with the same profile as the other BC lines, for modeling Fe iii emission in our sources.Fe ii emission is not strong in the spectral range we studied, and the UV Fe ii template we adopt is based on a suitable cloudy simulation. Results on the λ1900 blend are not significantly affected by the assumed Fe ii contribution since it appears as a weak pseudo-continuum underlying the blend. We explore maximum and minimum contributions of Fe ii by placing the highest and lowest possible continua, as shown in Figure 1, and as explained below in Section 3.2.1. In Figure 2 we show the contribution of Fe ii. If we increase or decrease this contribution, we will see an intensity variation of the strength of the lines, with Si ii λ1814 being the most affected due its weakness (see error bands in Figure 6). We take into account these strength variations for the error estimations.Then, for both objects, we sequentially model Fe ii and Fe iii as preliminary steps. We anchor the Fe ii template to the 1785 Å feature in order to normalize it. We continue with the fit of the Si ii λ1814 and Al iii λ1860 emission lines, which are fairly unblended. The main challenge is therefore to deconvolve Si iii] λ1892, C iii] λ1909, and Fe iii λ1914, noting that we will use only the less blended line, Si iii] λ1892, for the eventual computation of diagnostic ratios.The next step is different for each object. The deblending of Si iii] λ1892, C iii] λ1909, and Fe iii λ1914 can be easily accomplished in the case of I Zw 1 because the lines are narrow. In the case of SDSS J12014+0116 the peak at λ1910 is consistent with Fe iii λ1914, indicating that Fe iii emission is dominating over C iii] λ1909. Thus, we first fit Si iii] λ1892 and Fe iii λ1914 to the observed peaks and the remaining part of the blend, as C iii] λ1909. We emphasize that in the λ1900 blend, the only two lines that are severely blended are C iii] λ1909 and Fe iii λ1914. This is more evident in the case of I Zw 1 because C iii] λ1909 and Fe iii have similar intensities. In the case of SDSS J12014+0116, C iii] λ1909 is much weaker than Fe iii λ1914 but still blended. We are not interested in the intensity of these two lines, but only in a confirmation that C iii] λ1909 is weak with respect to Si iii] λ1892. In Figure 3 we show that this is valid even for the highest possible contribution of C iii] λ1909. The residuals in Figures 2 and 3 reflect the noise. If we consider 1σ above and below zero, then we say that a line is weak when it is below 1σ. For example, in the lower right panel of Figure 2, C iii] λ1909 is below 1σ, while Si ii λ1814 is around 1.5σ.
• 4.  
  λ1550 feature. As in the case of the previous blend, we need to keep in mind the complexity of this feature. In order to fit the HIL C iv λ1549, we have to take into account that it is decomposed into a Lorentzian BC with the same width and shifts of the intermediate-ionization lines plus a blueshifted residual (assumed to be Gaussian in the specfit procedure, discussed in Section 3.1). So, in both objects, we fit first the Fe ii template with the same intensity as in the λ1900 blend. Then we fit the BC, and looking at the residuals, we fit the BLUE component. Finally, we fit the underlying weaker emission lines N iv] λ1486, Si ii λ1533, and He ii λ1640, when visible. We assume that the latter line has two components (BC and BLUE) with the same shift and width as C iv λ1549. An equivalent approach has been successfully followed by several authors (Baldwin et al. 1996; Leighly & Moore 2004; Marziani et al. 2010; Wang et al. 2011).We need to point out that in the case of I Zw 1, we observed a narrow component (NC) with a width of ∼800 km s⁻¹, close to the width of the BCs of the broad lines. The NC of C iv λ1549 is observed in several low-z quasars (also RL) and Seyfert 1 nuclei, as well as in type 2 quasars (Sulentic et al. 2007). Even if the line is collisionally excited (hence with an intensity proportional to the square of electron density), the larger volume of the narrow-line region (NLR, proportional to (R_NLR/R_BLR)³) and the absence of collisional quenching at a relatively low density (as in the case of the [O iii] λλ4959, 5007 lines) make it possible to expect a significant C iv λ1549 NC emission. We also observed that for I Zw 1, the NC of C iv λ1549 is blueshifted. This is also observed in other narrow lines (Marziani et al. 2010), in agreement with expectations for the NLR of the extreme NLSy1s. For example, [O iii] λλ4959, 5007 is blueshifted with respect to Hβ and to the systemic radial velocity of the host galaxy. In this way the analysis of the C iv λ1549 NC is fully consistent with the [O iii] λλ4959, 5007 and Hβ analysis.
• 5.  
  λ1400 blend. This blend has been one of the most enigmatic features in quasar spectra (e.g., Wills & Netzer 1979). It is known that the Si iv λ1397 doublet is blended with O iv intercombination lines (Nussbaumer & Storey 1982). In our sources the λ1400 blend is very prominent, approximately 3–4× stronger relative to C iv λ1549 than in the SDSS composite quasar spectrum (Vanden Berk et al. 2001). This is consistent with the extreme metal enrichment we found in these sources (Section 6.1.1).

We are able to obtain a reliable measurement of the Si iv λ1397 doublet, even when we cannot measure all the components of the λ1400 blend. Any O iv] λ1402 contribution to the BCs is expected to be negligible.⁸ We follow the same procedure to fit this blend as in the λ1550 blend. Note that the Si iv λ1397 low-ionization emission line shows a double-horned profile in I Zw 1 because of the large doublet separation and of the relatively narrow lines of this source. Since the peak at ≈1401 Å is somewhat broader than the peak of the individual component of Si iv λ1397, some O iv] λ1402 emission might be associated with the O iii] λ1663-emitting region. This is an additional, minority component that is needed to obtain a very good fit of the λ1400 blend.

In summary, the three following features were independently fitted (using specfit, see Figure 2):

The λ1400 blend (whose profile is very similar to the one of C iv λ1549), with BC of Si iv λ1397 (we fit the doublet with individual lines at 1402 and 1394 Å), and one blueshifted component accounting for the contribution of both Si iv λ1397 and O iv] λ1402 (+ semi-BC most probably associated with O iv] λ1402 in I Zw 1).

The λ1550 feature, with C iv λ1549 BC + BLUE + Fe ii + Si ii λ1531. We expect a contribution of He ii λ4686 with a profile similar to C iv λ1549. In SDSS J12014+0116 we can see He ii λ4686 BLUE.

The λ1900 blend considering Fe ii, Fe iii, Si ii λ1814, Al iii λ1860 (we fit the doublet with independent lines, at 1855 and 1862 Å; in Figure 2 we show only the sum), Si iii] λ1892, C iii] λ1909, and Fe iii λ1914. The latter line is assumed to be an independent additional line of unknown intensity and with the same profile as the other BCs.

All BCs of the broad emission lines are assumed to have the same width and shift, leaving only their intensity as free parameters. The HIL blends involve mainly only two components. As a result, the free parameters are reduced to the intensity of the BC lines (C iii] λ1909, Si iii] λ1892, Al iii λ1860, Si ii λ1814, C iv λ1549, and Si iv λ1397), the intensity of the Fe ii and Fe iii templates, and the width and flux of the Gaussian minor components under C iv λ1549 (N iv] λ1486, Si ii λ1533, He ii λ1640) and Si iv λ1397 (O iv] λ1402). Table 2 reports the fluxes of the BCs for intermediate- and high-ionization lines. Column 1 is the object name. Column 2 is the redshift; for I Zw 1 we adopted the one reported in Marziani et al. (2010), for the SDSS J12014+0116 object we use one reported in the SDSS database. Column 3 is the rest-frame specific flux at λ = 1700 Å. Columns 4–9 are the rest-frame line flux for the BCs only, and Column 10 is the FWHM of all the BCs.

3.2.1. Uncertainties

3.2.2. C iii] λ1909 Emission

One must work carefully with the λ1900 blend because of the close proximity of the C iii] λ1909, Fe iii λ1914, and Si iii] λ1892 emission lines. Both of our targets are extreme Pop. A sources, and one characteristic of this extreme population is that C iii] λ1909 is weak or even absent (Figure 2). Extreme Pop. A sources show the lowest C iii] λ1909/Si iii] λ1892 ratio among all quasars in the E1 sequence (Bachev et al. 2004). We can see this effect in the upper right panel of Figure 2, where we show the λ1900 blend for I Zw 1. The resolution is good enough to separate the peaks of Fe iii λ1914 and C iii] λ1909. After fitting the Fe iii template (including the Fe iii λ1914 line), we see that in order to fit the observed spectrum the intensity of the C iii] λ1909 line turns out to be comparable to Fe iii λ1914. In the right lower panel, for the SDSS J12014+0116 object, the spectrum is noisier and the peaks of the lines of C iii] λ1909 and Fe iii λ1914 are not clearly seen. However, the observed peak is at the position of Fe iii λ1914, and if we follow the same procedure to fit the Fe iii template in order to deconvolve the blend, it turns out that the contribution of the C iii] λ1909 emission line is practically insignificant. To estimate an upper limit to the C iii] λ1909 line, we remove Fe iii λ1914 (Figure 3). This estimate is C iii] λ1909 ≈ 0.5 Si iii] λ1892 for the SDSS J12014+0116 object, but the fit is poor on the red side of the blend, leaving a large residual. In order to minimize the residual, we added the maximum possible contribution of C iii] λ1909 emission line (Figure 3). We can safely conclude that C iii] λ1909/Si iii] λ1892 < 0.5 in this object. C iii] λ1909 emission line in I Zw 1 is about ≈0.6 Si iii] λ1892. The very dense region emitting the LILs should produce no C iii] λ1909 line because it is collisionally quenched; thus, any emission from this line should arise in a different region.

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Available reverberation mapping results suggest that C iii] λ1909 line is mainly emitted farther out from the central continuum source than some LILs and HILs. The results of reverberation mapping analysis are limited to a handful of low-luminosity objects and cannot be generalized in a straightforward way. However, in these low-luminosity objects C iii] λ1909 line responds to continuum changes on timescales much longer than C iv λ1549 and other HILs. This result comes from the analysis of total C iii] λ1909 + Si iii] λ1892 in NGC 3783 (Onken & Peterson 2002) and from the C iii] λ1909 of NGC 4151 (Metzroth et al. 2006) and NGC 5548. It is intriguing that the C iii] λ1909 cross-correlation delay in NGC 5548 (by far the best-studied object) is even larger than that of Hβ (32 ld versus 20 lt-day; Peterson et al. 2002; Clavel et al. 1991). For fixed density, lines of higher ionization form at higher photon flux. The C⁺⁺, Al⁺⁺, and Si⁺⁺ ionization potentials are 24, 18, and 16 eV, respectively. These comparable ionization potentials are well below the one of HILs, X^{i − 1} ≳ 50 eV. However, the much lower C iii] λ1909 critical density implies that the C iii] λ1909 line should be formed farther out than Si iii] λ1892 and Al iii λ1860 if all these lines are produced under similar ionization conditions.

We also want to point out that there are plausible physical scenarios that can give rise to C iii] λ1909 in a shielded, non-uniform environment where there gas has a range of densities at similar ionization parameter (i.e., the less dense gas is somehow shielded; Maiolino et al. 2010). Since we are considering profiles integrated over the whole unresolved emitting region, the relevant question is, however, how much will the C iii] λ1909-emitting regions contribute to the lines we are considering? The strongest C iii] λ1909 emitters along the E1 sequence (spectral type A1) typically show C iii] λ1909/Si iii] λ1892 ≈ 2.5. Kuraszkiewicz et al. (2004) more typically found C iii] λ1909/Si iii] λ1892 ≈ 5. The results of the fits indicate that C iii] λ1909 emission is very weak with respect to Si iii] λ1892 in our spectra. We obtain C iii] λ1909/Si iii] λ1892 ≈ 0.6 for I Zw 1 and C iii] λ1909/Si iii] λ1892 ≈ 0.2 for SDSS J12014+0116. Therefore, the results of our procedure (described in Section 3.2) will not be significantly affected. If the ionization parameter is log U ≲ −2.5, there will be modest HIL emission. Other intermediate-ionization lines will be little affected. The results of the fits indicate that C iii] λ1909 emission is low. We therefore neglect the effect of any C iii] λ1909-emitting gas on the intermediate- and high-ionization lines.

Our method for estimating n_H and U involves several line ratios. We discuss the product n_H · U in the following sections, and in Section 6.2 we use it to compute r_BLR. We define three groups of diagnostic ratios, which should define density, ionization parameter, and metallicity for a given continuum shape and geometry.

Line ratios such as Al iii λ1860/Si iii] λ1892 are useful diagnostics over a range of density that depends on their transition probabilities. Emission lines originating from forbidden or semi-forbidden transitions become collisionally quenched above the critical density and therefore relatively weaker than lines for which collisional effects are still negligible. The Al iii λ1860/Si iii] λ1892 ratio is well suited to sample the density range 10¹¹–10¹³ cm⁻³. This corresponds to the densest emitting regions likely associated with production of LILs like the Ca ii IR triplet (Matsuoka et al. 2008) and Fe ii (Baldwin et al. 2004).

The ratios Si ii λ1814/Si iii] λ1892 and Si iv λ1397/Si iii] λ1892 are sensitive to ionization but roughly independent of metallicity since the lines come from different ionic species of the same element. Metallicity influences thermal and ionization conditions that in turn affect these ratios. The effect is, however, second order: cloudy simulation sets for different Z indicate that, for a fivefold increase in metal content, the ratio Si iv λ1397/Si iii] λ1892 changes from ≈0.5 to 0.6.

The ratio Si iv λ1397/C iv λ1549 is mainly sensitive to the relative abundances of C and Si. The reason is that the ground and excited energy levels of these ions are very similar (the ionization potentials are close: 33.5 and 48 eV for creation of Si⁺³ and C⁺³, respectively). This implies that the dependence on continuum shape and electron temperature of the ratio of these two resonance lines is small (see also Simon & Hamann 2010).

In order to illustrate how we employ cloudy simulations to estimate where the bulk of the line emission arises, we refer to Figure 4. The left panel shows the ionic fraction as a function of geometrical depth in a slab (within a single BLR cloud) for which we choose a fixed column density⁹ (N_c = 10²⁵ cm⁻²) and density (n_H = 10^12.5 cm⁻²) exposed to a "standard" quasar continuum (the parameterization of Mathews & Ferland 1987). It is customary to consider this parameterization as standard for the ionizing continuum. However, that parameterization has been sometimes criticized and is not unique, so that we also consider as an alternative the ionizing continuum parameterization of Laor et al. (1997b). In this work, we use the term "typical continuum" to designate the average of the two, with the two continua providing two extrema in number of ionizing photons expected at a specific flux measured on the non-ionizing part of the continuum. The "typical continuum" is the one used for our computation of r_BLR (see Section 6.2).

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Computing simulations at fixed n_H and U values allows us to study how these parameters influence the diagnostic ratios we have defined. We make no assumptions about the geometry or kinematics of the BLR. The slab of gas (i.e., a single cloud) might as well involve magnetically confined clouds (Rees et al. 1989) or individual elements in an accretion disk atmosphere—provided that photoionization is the only heating mechanism.

Al⁺⁺, Fe⁺⁺, and Si⁺⁺ are intermediate-ionization lines sharing a region of dominance deep within a cloud—where the HILs also arise. It is therefore appropriate to consider intermediate-ionization line ratios between geometric depths h ∼ 10⁶–10⁸ cm (right panel of Figure 4). We prefer to show the product of the local line emissivity times the depth within the slab since the total line intensity is proportional to ∫(h)dh (in the absence of radiation transfer effects, i.e., in a cloud where lines are optically thin), and hence the product (h) · h gives a better idea of the total line emission at a distance h than simply showing (h) versus h. Figure 4 shows that C iii] λ1909 emission is expected to be orders of magnitude lower than the other lines and therefore likely undetectable.

Once we have ascertained that the computed line ratios are physically consistent (i.e., all refer to a single emitting region except the ones involving Si ii λ1814, whose intensity is significantly affected by a partially ionized zone (PIZ) emission), a multidimensional grid of cloudy simulations is needed to derive estimates for U, n_H, and metallicity from the spectral measurements (Ferland et al. 1998; Korista et al. 1997). cloudy computes population levels of the relevant ionic stages of Si, C, Al, and especially for lines emitted in the fully ionized part of a gas slab (Figure 4). Also, cloudy is expected to be especially good for predicting intermediate- and high-ionization line fluxes that are produced in the fully ionized region within the gas slab. LILs are produced in the PIZ by photoionization of hydrogen—primarily by soft X-ray photons. Since these X-ray photons create suprathermal electrons and have a relatively low cross section for photoionization, the heating processes in the PIZ are inherently non-local, making the mean escape probability formalism used by cloudy to treat radiation transfer a very rough approximation.

New simulations were needed since cloudy has undergone steady and significant improvements since the time of Korista et al. (1997). The most relevant improvement is the addition of more ionic species in the simulations, with a 371-level of the Fe⁺ ion. This will make computation of equilibrium conditions more realistic even if, in the end, we expect that predictions of line intensity ratios will not be dramatically affected: iron is singly ionized only in the PIZ (Figure 4, left panel). Other relevant improvement for our study is the post-Korista et al. (1997) update of the transition probability for Si ii λ1814 following Callegari & Trigueiros (1998) that changes the intensity of the line by a factor of ∼2 in the high-density regime of the BLR. We present the results of our simulations in Figure 5. Our results are not inconsistent with those obtained by Korista et al. (1997), for the same ranges of density and ionizing parameter: the overall behavior in the plane (U, n_H) of their Figure 3 is qualitatively consistent with the one derived from our simulations.

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Simulations assume (1) pure photoionization (see also Section 6.1) and (2) spherical symmetry in continuum emission, i.e., that the ionizing continuum incident on a slab of gas of fixed density is similar to the observed continuum (see Section 6.2.1 for caveats concerning this assumption).

The ionization state of the gas will be mainly defined by the ionization parameter:

$$\begin{equation} U = \frac{\int _{\nu _0}^{+\infty } \frac{L_\nu }{h\nu } d\nu }{4\pi n_\mathrm{H} c r^2}, \end{equation} \tag{ 1 }$$

where L_ν is the specific luminosity per unit frequency, h is the Planck constant, ν₀ is the Rydberg frequency, n_H is the hydrogen density, c is the speed of light, and r is the distance between the central source of ionizing radiation and the line-emitting region.

Simulations span the density range 7.00 ⩽ log n_H ⩽ 14.00 and −4.50 ⩽ log U ⩽ 00.00, in intervals of 0.25 assuming plane-parallel geometry. We assume the standard value of N_c = 10²³ cm⁻² (Netzer & Marziani 2010, and references therein). In Figure 5 we show the isocontours for the ratios Al iii λ1860/Si iii] λ1892, Si ii λ1814/Si iii] λ1892, Si iv λ1397/Si iii] λ1892, C iv λ1549/Al iii λ1860, C iv λ1549/Si iii] λ1892, and Si iv λ1397/C iv λ1549 derived from cloudy simulations, for solar metallicity and "standard" quasar continuum, as parameterized by Mathews & Ferland (1987, see above). We considered three chemical compositions: (1) solar metallicity; (2) constant abundance ratio Al:Si:C with Z = 5 Z_☉; (3) an overabundance of Si and Al with respect to carbon by a factor of three, again with Z = 5 Z_☉ (5 Z_☉SiAl). This last condition comes from the yields listed for Type II supernovae (Woosley & Weaver 1995). The Si overabundance is also supported by the chemical composition of the gas returned to the interstellar medium by an evolved population with a top-loaded initial mass function (IMF) simulated using starburst99 (Leitherer et al. 1999). The abundance of Al is assumed to scale with the one of Si (see also Section 6.1 on this assumption).

In this section, we compute the ratios analyzed above from the flux values and estimate the physical parameters n_H and U of the BLR, for I Zw 1 and SDSS J12014+0116. We derived these values from the emission-line measurements, reported in Table 2, and the cloudy simulations of Figure 5. Asymmetric errors due to the uncertainties described in Section 3.2.1 have been quadratically propagated following Barlow (2003, 2004).

In the left panels of Figure 6 we show the same n_H versus U plane as in Figure 5 (in right panels, we use the 5 Z_☉SiAl simulation defined above). We choose only one isocontour for each ratio, and it is the one that corresponds to the measured value. There is a convergence of the contour lines defined by several crossing points of the contour of the Al iii λ1860/Si iii] λ1892 ratio versus the contour of the other five ratios. This convergence defines the n_H and U values that point toward a low ionization plus high-density range. We use the average value of all of the crossing points to define a single n_H · U value, which is used to compute the r_BLR and the M_BH (Section 6.2).

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The uncertainties associated with a line ratio, R, broaden the lines defined by constant R to a band limited by the ratios R ± δR. In Figure 6, we show them with bands. The largest of all uncertainties is related to Si ii λ1814. This is the weakest line that we use, and thus it is the line most strongly affected by the continuum placement. The value of Si ii λ1814 intensity is probably underestimated, and if it were higher, the crossing point of Al iii λ1860/Si iii] λ1892 versus Si ii λ1814/Si iii] λ1892 would be closer to the other crossing points, marked by an arrow in Figure 6. We also stress that Si ii λ1814 is the only LIL considered in this study, and its formation is sensitive to the assumed X-ray continuum and other LIL formation issues (Dumont & Mathez 1981; Baldwin et al. 1996).

The discrepancy in the intersection point of diagnostic ratios in the plane (n_H, U) is significant for the Si iv λ1397/C iv λ1549 ratio that depends mainly on the Si abundance relative to C. The λ1400/C iv λ1549 intensity ratio has been used as a metallicity indicator also by other authors (Juarez et al. 2009; Simon & Hamann 2010). The discrepancy is less but still significant for the case when we consider the 5 Z_☉SiAl case. For this reason, we do not consider this ratio in the computation of the product of density and ionization parameter.

In similar plots made for Z = 5 Z_☉SiAl (right panels of Figure 6), the agreement of all the crossing points improves: the isocontour lines converge toward a better defined crossing point.

The high-metallicity case 5 Z_☉SiAl indicates higher U and smaller n_H with respect to the case of solar abundances, if emission-line ratios involving C iv λ1549 are considered. This reflects the increase in abundance of Si and Al relative to C with respect to solar: Si and Al lines appear stronger with respect to the C iv λ1549 line because the elements Si and Al are more abundant, and not because a lower ionization level enhances Si ii λ1814, Si iii] λ1892, and Al iii λ1860 emission with respect to C iv λ1549.

In the case of SDSS J1201+0116 we can see from Table 3 that the density is even higher than for I Zw 1, suggesting that Si iii] λ1892 is collisionally quenched to make possible a rather high Al iii λ1860/Si iii] λ1892 ratio, ≈1. The line intensity of Si iii] λ1892 is thus the result of the physical conditions of the emitting region, and in fact we measure a relatively low line intensity. The ratio Al iii λ1860/Si iii] λ1892 has a value of 0.6 for I Zw 1.

The products (n_H · U) derived from Figure 6 and reported in Table 3 are marginally different for the two sources. It is intriguing, however, that while the values of n_H and U taken separately depend significantly on metallicity, their product shows a weaker dependence: for Z = 1 Z_☉, we obtain log (n_H · U) ≈ 9.4 for I Zw 1 and 9.8 for SDSS J1201+0116. Similar results also seem to hold for a larger sample, including the objects monitored for reverberation mapping (Negrete 2011).

We also note that the log (n_H · U) values are very close to the results of several independent, previous studies summarized in Table 4.

Baldwin et al. (1996) presented a similar analysis. Their Figure 2 organizes spectra in a sequence that is roughly corresponding to E1, going from Al iii λ1860-strong sources to objects whose spectra show prominent C iii] λ1909 along with weak Al iii λ1860 (Bachev et al. 2004). The line components they isolated correspond to the ones we consider in this paper: a blueshifted feature, and a more symmetric, unshifted, and relatively NC that we call LIL-BC. They derive log n_H ≈ 12.7 and log U ≈ −2.5. A somewhat lower density and higher ionization are indicated to optimize Fe ii emission, while the Ca ii IR triplet requires conditions that are very similar to the ones derived from the intermediate-ionization lines.

We are not claiming that there is a single region that is able to account for all broad lines in all AGNs. However, a low-ionization, high-density region can account for Fe ii, Ca ii, and the intermediate-ionization line emission. This region is dominating the BC of emission lines (save weak C iii] λ1909) in the objects considered in this paper but apparently becomes less relevant along the E1 sequence (Marziani et al. 2010). The properties of the emitting BLR seem to be remarkably stable, keeping an almost constant log (n_H · U) (also seen in previous work, e.g., Wandel et al. 1999; Baldwin et al. 1995). The issue is therefore whether we can apply the physical conditions (n_H and U) we deduce to derive information of r_BLR and M_BH.

In this section we discuss other possible scenarios considering the influence of other sources of heating, besides photoionization. We again remark that, on the basis of the analysis of Section 3, the use of intermediate- and high-ionization lines takes advantage of the most robust results of photoionization computations for AGNs. The complex issue of LIL formation is mostly avoided since we do not rely on the PIZ, whose physical properties may not be adequately modeled. Nonetheless, results on density stem mainly from the Al iii λ1860 line being overstrong with respect to Si iii] λ1892. The observed Al iii λ1860/Si iii] λ1892 line ratio is inconsistent with density ∼10¹¹ cm⁻³ that would make some C iii] λ1909 emission possible. Low ionization is inferred from the intrinsic weakness of C iv λ1549 in these Pop. A sources with respect to C iv λ1549 that is observed in Pop. B objects (Sulentic et al. 2007).

While there is little doubt about the identification of the Al iii λ1860 line doublet (a resonance line with large transition probability; in several NLSy1s the doublet is resolved with ratio ∼1–1.2, suggesting large optical depth), this line could be enhanced with respect to Si iii] λ1892 by some special mechanism. We can conceive two ways of increasing Al iii λ1860 with respect to Si iii] λ1892: (1) a selective enhancement of the Al abundance with respect to Si or (2) collisional ionization due to a heating mechanism different from photoionization.

6.1.1. Anomalous Chemical Composition

6.1.2. Mechanical Heating and Fe ii Emission

In Section 5 we estimate the product n_H · U, and now we can compute the distance of the BLR (r_BLR) from the central continuum source and the black hole mass (M_BH). They are key parameters that allow us to better understand gas dynamics in the emitting region, as well as quasar phenomenology and evolution. The dependence of U on r_BLR was used to derive black hole masses assuming a plausible average value of the product n_H · U. We also use FWHM(Hβ_BC) under the assumption that the BC arises from a virialized medium (Padovani et al. 1990; Wandel et al. 1999). Equation (1) can be rewritten as

$$\begin{equation} r_{{\rm BLR}} = \left[ \frac{\int _{\nu _0}^{+\infty } \frac{L_\nu }{h\nu } d\nu }{4\pi n_\mathrm{H} U c} \right]^{1/2} \end{equation} \tag{ 2 }$$

and also as

$$\begin{equation} r_{{\rm BLR}} = \frac{1}{h^{1/2} c} (n_\mathrm{H} U)^{-1/2} \left(\int _{0}^{\lambda _{Ly}} f_\lambda \lambda d\lambda \right) ^{1/2} d_\mathrm{C}, \end{equation} \tag{ 3 }$$

where d_C is the total line-of-sight comoving distance (Hogg & Fruchter 1999):

$$\begin{equation} d_\mathrm{C} = \frac{c}{H_{0}} \zeta (z, \Omega _M, \Omega _\Lambda)= \frac{c}{H_{0}} \int _{0}^{z} \frac{dz^{\prime }}{\sqrt{\Omega _M(1+z)^3+\Omega _\Lambda }}, \end{equation} \tag{ 4 }$$

where we adopt the Hubble constant H₀ = 70 km s⁻¹ Mpc⁻¹. The function ζ has been interpolated as a function of redshift:

$$\begin{eqnarray} &&\zeta (z, \Omega _M, \Omega _\Lambda) \approx \left[1.500\left(1-e^{-\frac{z}{6.107}}\right)+0.996\left(1-e^{-\frac{z}{1.266}}\right)\right], \nonumber\\ \end{eqnarray} \tag{ 5 }$$

with Ω_M = 0.3 and $\Omega _\Lambda = 0.7$, given by Sulentic et al. (2006b).

In Equation (3), we transformed the integral from units of frequency to wavelength and rewrote the expression for r_BLR in terms of the rest-frame specific flux f_λ that can be easily derived from the observed flux, namely,

$$\begin{equation} L_{\nu } \nu ^{-1} d \nu = 4 \pi c^{-1} d_\mathrm{L}^{2} f_{\lambda } \lambda d \lambda, \end{equation} \tag{ 6 }$$

with d_L the luminosity distance that is related to d_C by the formula d_L = d_C(1 + z).

Note that

$$\begin{equation} \int _{0}^{\lambda _{Ly}} f_\lambda \lambda d\lambda = f_{\lambda 0} \cdot \tilde{Q}_\mathrm{H}, \quad \mathrm{with} \quad \tilde{Q}_\mathrm{H} = \int _{0}^{\lambda _\mathrm{Ly}} \tilde{s}_\lambda \lambda d\lambda, \end{equation} \tag{ 7 }$$

where λ₀ = 1700 Å. $\tilde{Q}_{{\rm H}}$ depends on the shape of the ionizing continuum for a given specific flux with the integral carried out from the Lyman limit to the shortest wavelengths. We use $\tilde{s}_\lambda$ to define the spectral energy distribution (SED) following Mathews & Ferland (1987) and Laor et al. (1997a) conveniently parameterized as a set of broken power laws. $\tilde{Q}_{\rm H}$ is ≈0.00963 cm Å in the case of the Laor et al. (1997a) continuum and ≈0.02181 cm Å for Mathews & Ferland (1987). We use an average value because the two SEDs give a small difference in estimated number of ionizing photons (see below).

Expressing r_BLR in units of lt-day, and scaling the variables to convenient units, Equation (3) becomes

$$\begin{equation} r_{\rm BLR} \approx 93 \left[ \frac{f_{\lambda _0,-15} \tilde{Q}_\mathrm{H,0.01}}{(n_{\mathrm H} U)_{10}} \right]^{1/2} \zeta (z, 0.3, 0.7) \;\mathrm{{\rm lt\hbox{-}day}.} \end{equation} \tag{ 8 }$$

In this equation, $f_{\lambda _0,-15}$ is the specific rest-frame flux (measured on the spectra) in units of 10⁻¹⁵ erg s¹ cm⁻² Å⁻¹, and $\tilde{Q}_{{\rm H},0.01}$ is normalized to 10⁻² cm Å. The product n_HU is normalized to 10¹⁰ cm⁻³, ζ(z, 0.3, 0.7) is derived from Equation (5), and r_BLR is now expressed in units of lt-day.

Knowing r_BLR, we can calculate the M_BH assuming virial motions of the gas

$$\begin{equation} M_\mathrm{BH} = f \frac{\Delta v^2 r_\mathrm{BLR}}{G}, \end{equation} \tag{ 9 }$$

or

$$\begin{equation} M_\mathrm{BH} = \frac{3}{4{\rm G}} f_{0.75} ({\rm FWHM})^2 r_{{\rm BLR}}, \end{equation} \tag{ 10 }$$

with the geometry term f ≈ 0.75, corresponding to f_0.75 ≈ 1.0 (Graham et al. 2011). The factor f depends on the details of the geometry, kinematics, and orientation of the BLR and is expected to be of order unity. This factor converts the measured velocity widths into an intrinsic Keplerian velocity (Peterson & Wandel 2000; Onken et al. 2004; Graham et al. 2011).

Resultant r_BLR and M_BH estimates are reported in Table 3. Errors in this table are at 2σ confidence level. They are not symmetrical around this value. They were propagated quadratically, following Barlow (2003, 2004). We consider three sources of uncertainty in the r_BLR computations.

• 1.  
  The error in the determination of n_H and U, which is described in detail in Section 5.1. We use the average value for all of the crossing points in Figure 6 to define a single n_H · U value that is used in Equation (3) to compute the r_BLR.
• 2.  
  The error derived from the shape of the ionizing continuum, which is used in the computation of the r_BLR. The two SEDs that we assumed as extreme yield a difference in ionizing photons of a factor 0.17 dex. At a 2σ confidence level this corresponds to an uncertainty in the number of ionizing photons of ±0.057 dex.
• 3.  
  Errors in the specific fluxes (at λ = 1700 Å, Column 3 of Table 2), intrinsic to the spectrophotometry. We also consider the error in the continuum placement (discussed in Section 3.2.1).

In the determination of M_BH we consider two sources of error:

• 1.  
  The combined error of the three sources of uncertainties on the r_BLR computation described above.
• 2.  
  The error on the determination of the FWHM, which is discussed at the end of Section 3.2.1.

Using our derivations for n_H and U, we obtain the r_BLR and M_BH values listed in Table 3. The last two columns give virial black hole masses following our method and using the M_BH–luminosity correlation from Vestergaard & Peterson (2006), respectively. Note that Vestergaard & Peterson (2006) used a different value for the geometry term, which is f = 1.4 (Onken et al. 2004; Woo et al. 2010), and the implication in the mass computation is that our masses are lower by a factor of two. This was taken into account, making the correction ${\rm log}(f_{{\rm ours}}/f_{V\&P}) = {\rm log}(0.75/1.4) = -0.27$. We subtract this quantity from the Vestergaard & Peterson (2006) M_BH formula used to compute the masses in Column 7 of Table 3.

The intrinsic dispersion in the Vestergaard & Peterson (2006) relation is ±0.66 dex in black hole mass at a 2σ confidence level. We are not considering here the scatter in the relation r_BLR–L derived by Bentz et al. (2009) that involves sources, where r_BLR was derived from reverberation mapping. The scatter in the r_BLR–L correlation is ≈0.2 dex in r_BLR. These r_BLR determinations are, in spite of many caveats recently summarized in Marziani & Sulentic (2012), probably the best ones available. Kaspi et al. (2007) were able to derive one point in the r_BLR–L correlation directly from reverberation mapping of a high-z (2.17) object. Additional observations will allow us to check whether the Kaspi empirical relationship holds at high redshift. At the moment we cannot rely on the mass derivation of one source only. The UV extrapolation for single-epoch virial-broadening estimates in Vestergaard & Peterson (2006) shows a much larger scatter but is the only relation that provides an M_BH suitably comparable with our result. Errors obtained with our method are a factor of ∼3 smaller than the dispersion in the Vestergaard & Peterson (2006) relation. However, the latter errors are statistical, making the comparison not very straightforward. In a forthcoming paper (C. A. Negrete et al. 2012, in preparation) we will give the results of a statistical analysis applying our method to a larger number of quasars than reported here (8 at high z and 14 at low z, belonging to both Pops. A and B). Preliminary results are given in Negrete (2011). These are all Type 1 (broader line) quasars.

6.2.1. Caveats