# Physical Conditions in the Broad Line Region of $z\sim 3$ Quasars:
A Photoionization Method to Derive $r_{\rm BLR}$ and $M_{\rm BH}$
♣♣affiliationmark:

C. Alenka Negrete11affiliation<EMAIL_ADDRESS><EMAIL_ADDRESS>and Deborah Dultzin11affiliation:
<EMAIL_ADDRESS><EMAIL_ADDRESS>Instituto de Astonomía,
Universidad Nacional Autónoma de México, Mexico  Paola Marziani22affiliation:
<EMAIL_ADDRESS>INAF, Astronomical Observatory of Padova, Italy
Jack Sulentic33affiliation<EMAIL_ADDRESS>Instituto de Astrofísica de
Andalucía, Spain

###### Abstract

We present high S/N UV spectra for eight quasars at $z\sim 3$ obtained with
VLT/FORS. The spectra enable us to analyze in detail the strongest emission
features in the rest-frame range 1400-2000 Å of each source
(Ciii]$\lambda$1909, Siiii]$\lambda$1892, Aliii$\lambda$1860,
Siii$\lambda$1814, Civ$\lambda$1549 and Siiv$\lambda$1397). Previous work
indicates that a component of these lines is emitted in a region with well-
defined properties i.e., a high density and low ionization emitting region).
Flux ratios Aliii$\lambda$1860/ Siiii]$\lambda$1892,
Civ$\lambda$1549/Aliii$\lambda$1860, Siiv$\lambda$1397/ Siiii]$\lambda$1892,
Civ$\lambda$1549/Siiv$\lambda$1397 and Siii$\lambda$1814/ Siiii]$\lambda$1892
for this region permit us to strongly constrain electron density, ionization
parameter and metallicity through the use of diagnostic maps built from CLOUDY
simulations. Reliable estimates of the product density times ionization
parameter allow us to derive the radius of the broad line region $r_{\rm BLR}$
from the definition of the ionization parameter. The $r_{\rm BLR}$ estimate
and the assumption of virialized motions in the line emitting gas yields an
estimate for black hole mass. We compare our results with estimates obtained
from the $r_{\rm BLR}$ – luminosity correlation customarily employed to
estimate black hole masses of high redshift quasars.

galaxies: active — galaxies: high-redshift — quasars: general — quasars:
emission lines

††slugcomment: To appear in …00affiliationtext: Based on observations made
with ESO Telescopes at Paranal Observatory under programme ID 078.B-0109(A)

##  1 Introduction

###  1.1 Interpreting Quasar Spectra

Measuring relevant physical parameters from the observed broad-line spectra of
quasars is still an open challenge. Identification and intensity measurements
of the strongest emission lines has made possible a rough inference of the
typical conditions of the emitting gas since the earliest days of quasar
spectroscopy. The very first quasars of intermediate redshift discovered in
the 1960s showed a fairly high ionization spectrum, with prominent lines of
Civ$\lambda$1549, and Heii$\lambda$1640 in addition to strong Balmer lines of
the low-redshift quasars. Photoionization by the central continuum source was
considered the preeminent heating mechanism of the emitting gas. Significant
Ciii]$\lambda$1909 emission suggested electron densities ($n_{\rm e}$) in the
range $10^{9}-10^{10}$ cm-3. The observed intensity ratio
Ciii]$\lambda$1909/Civ$\lambda$1549 indicated ionization parameter (defined by
Eq. 1 later in this paper) values of the order of $10^{-1}$. This
photoionization scenario was successful in explaining at least some quasar
optical and UV spectra (see the review by Davidson and Netzer 1979 for a
synopsis). More recent work emphasized the existence of several problems with
this simple scenario. Low ionization lines (LILs), and especially Feii are too
strong to be explained by a photoionized region of moderate density and column
density (see for example Dumont and Mathez 1981; Joly 1987; Collin-Souffrin et
al. 1988; Dumont and Collin-Souffrin 1990). These authors stressed that the
LILs required a denser, low-temperature environment.

We unfortunately lack a simple well-defined diagnostic measure of physical
conditions in the broad line region. One strategy for estimating electron
density in astrophysical sources involves using two emission lines of the same
ion, and with similar energies above the ground level, but with different
radiative transition probabilities $A_{ki}$. In practice one often chooses two
lines from the same term where one forbidden/semi-forbidden transition is
associated with another that is semi-formidden/permitted in order to ensure
very different values of $A_{ki}$ (for example, [Siiii]$\lambda$1882 and
Siiii]$\lambda$1892). This technique is not straightforwardly applicable to
the broad lines of quasars, precisely because the lines are broad, suitable
candidates are too closely spaced in wavelength, and density is at least an
order of magnitudes higher than the critical density for the forbidden
transitions used in spectra of planetary nebulæ and Hii regions. In addition
the S/N and the resolution of quasar spectra are usually not very high.

Feibelman and Aller (1987) used the Ciii]$\lambda$1909/ Siiii]$\lambda$1892
ratio to study the rather high-density environment typical of symbiotic stars
($n_{\rm e}$$\sim 10^{7-10}$ cm-3). In this case we have two semi-forbidden
(intercombination) resonance lines with significantly different transition
probabilities (see Table References). The lines are emitted by two iso-
electronic species with somewhat different ionization potentials (11 eV for C+
vs. 8 eV for Si+). The ionic fraction is dependent on the relative abundance
of silicon-to-carbon (to be assumed) as well as on the ionization structure
within the emitting region (to be computed). Using lines of different ions
introduces additional potentially serious sources of uncertainty. It is
perhaps not surprising that most workers believe that $n_{\rm e}$ in the BLR
cannot be reliably estimated using quasar spectra. Strong Ciii]$\lambda$1909
emission would imply that $n_{\rm e}$ cannot be very high ($n_{\rm e}$$\sim
10^{11-13}$cm-3). Very high density was invoked to explain the rich low
ionization spectrum (especially Feii) seen in the spectra of most quasars.
Several lines in the UV spectrum of I Zw 1 point towards high density at least
for the LIL emitting zone: prominent Feii, relatively strong
Aliii$\lambda$1860, and detection of Ciii$\lambda$1176 (Baldwin et al. 1996;
Laor et al. 1997b). The region where these lines are produced cannot emit much
Ciii]$\lambda$1909\. But is Ciii]$\lambda$1909 really so strong in most
quasars? BLR conditions are certainly complex and a single emitting region is
not sufficient to explain both LILs and high ionization lines (HILs).

###  1.2 Quasar Systematics

Quasar spectra are not all alike. There are significant differences in line
intensity ratios and broad line profiles from object to object (Bachev et al.
2004; Marziani et al. 2010). More importantly, these differences can be
organized in a systematic way as has been realized since the early 1990s
(Boroson and Green 1992). Since then several authors stressed the importance
of the so-called eigenvector 1 (E1) of quasars (e.g. Gaskell et al. 1999).
Sulentic et al. (2000, 2007) expanded the E1 trends into a 4-dimensional space
involving optical, UV and X-ray measures. They also defined spectral types
along a sequence occupied by AGN in an optical plane involving Feii and FWHM
H$\beta$ parameters. Objects at extreme ends of the E1 sequence are very
different at almost all wavelengths and median spectra computed in spectral
bins within this plane emphasize systematic changes in broad line properties
(Sulentic et al. 2002, 2007). The differences have motivated the suggestion of
a possible dichotomy between Narrow Line Seyfert 1 (NLSy1s) like sources and
broader line objects that include almost all radio-loud quasars. The most
effective divider of the two quasar types appears to be at FWHM of the
H$\beta$ broad component H$\beta_{\mathrm{BC}}\approx$ 4000 km s-1 for low-to-
moderate luminosity sources (Marziani et al. 2009). This corresponds to to
Eddington ratio $L/L_{\mathrm{Edd}}\sim 0.2\pm$0.1 (Marziani et al. 2003b).

The distinction between NLSy1-like objects (hereafter Population A sources
with FWHM(H$\beta$) $\leq$ 4000 km s-1) and the rest of quasars (Population B
with FWHM(H$\beta$) $\gtrsim$ 4000 km s-1) is of special relevance here. Pop.
A sources show relatively low equivalent width lines with e.g. the
$\lambda$1900 blend $\sim$30 Å. A close analysis of the Ciii]$\lambda$1909
blend in the prototypical NLSy1 I Zw 1 shows strong Siiii]$\lambda$1892, and
Aliii$\lambda$1860 blended with rather weak Ciii]$\lambda$1909 along with
prominent Feiii(UV34)($\lambda$1895.5, $\lambda$1914.0, and $\lambda$1926.3)
and Feii blends (Laor et al. 1997b; Vestergaard and Wilkes 2001). The
Ciii]$\lambda$1909 line is apparently so weak that Feiii$\lambda$1914 may be
the most prominent feature at $\lambda\approx$ 1910Å (cf. Hartig & Baldwin
1986). This interpretation is confirmed by detailed deblending of a source
(SDSS J120144.36+011611.6) that can be considered a high luminosity analog of
I Zw 1 (§7.1).

Median composite UV spectra of low-$z$ quasars show that Aliii$\lambda$1860
and Siiii]$\lambda$1892 are more prominent in 4DE1 spectral types A2 and A3.
Bins A1, A2, A3 are defined in terms of increasing FeII$\lambda$4570 (see Fig.
1 of Sulentic et al. 2002). I Zw 1, although belonging to the extreme type A3
(Bachev et al. 2004) is not unique as a NLSy1, since the fraction of Pop. A
sources in bin A3 and A4 is $\approx$ 20 % of all Pop. A sources in the sample
of Zamfir et al. (2010). A significant number of extreme NLSy1 are not
classified as quasars in SDSS and must be collected from the galaxy catalog
(Hu et al. 2008).

###  1.3 Emission Line Diagnostics and BLR Properties

Emission lines and line ratios are used in diagnostic maps to estimate
temperatures and electronic densities in galactic and extragalactic
photoionized regions. Examples include HII-regions and galaxies with HII-
region nuclear spectra where electron densities are less than $n_{\rm
e}$$\approx 10^{4}$ cm-3. This method has been successfully applied to the
narrow line region (NLR) in AGN. Application to the broad line quasars has
yielded results that are difficult to interpret. One recent exception is the
work by Maksuoka et al. (2008) who succeeded in analyzing the partly ionized
region thought to emit most of the LILs in quasar spectra. They suggest that
Oi 8446 and the Caii triplet are emitted by dense, low ionization gas probably
located in the periphery of the BLR. If the electron density and ionization
conditions are known it is possible to derive, with additional assumptions,
the distance of the BLR emitting region from the central continuum source (as
stressed earlier also by Baldwin et al. 1996).

The physical conditions of photoionized gas can be described by electron
density $n_{\rm e}$, hydrogen column density $N_{\rm c}$, metallicity
(normalized to solar), shape of the ionizing continuum, and the ionization
parameter $U$. The latter represents the dimensionless ratio of the number of
ionizing photons and the electron density $n_{\rm e}$ or, equivalently, the
total number density of hydrogen $n_{\mathrm{H}}$, ionized and neutral.111In a
fully ionized medium $n_{\rm e}$$\approx 1.2$ $n_{\mathrm{H}}$. We prefer to
adopt the definition based on $n_{\mathrm{H}}$ because it is the one employed
in the CLOUDY computations. Both $U$ and $n_{\mathrm{H}}$ are related through
the equation

$U=\frac{\int_{\nu_{0}}^{+\infty}\frac{L_{\nu}}{h\nu}d\nu}{4\pi
n_{\mathrm{H}}cr^{2}}$ (1)

where $L_{\nu}$ is the specific luminosity per unit frequency, $h$ is the
Planck constant, $\nu_{0}$ the Rydberg frequency, $c$ the speed of light, and
$r$ can be interpreted as the distance between the central source of ionizing
radiation and the line emitting region. Note that $Un_{\mathrm{H}}c$ is the
ionizing photon flux

$\Phi(H)=\frac{Q(H)}{4\pi r^{2}}.$ (2)

If we know the product of  $n_{\mathrm{H}}$ and $U$, we can estimate the
radius $r$ of the BLR from Eq. 1. The dependence of $U$ on $r_{\rm BLR}$ was
used by Padovani & Rafanelli (1988) to derive central black hole masses
assuming a plausible average value of the product $n_{\mathrm{H}}$$\cdot U$.
The typical value of $n_{\rm e}$ was derived at that time from semiforbidden
line Ciii]$\lambda$1909 which implied that the density could not be much
higher than $n_{\rm e}$$\approx 10^{9.5}$ cm-3 (Osterbrock & Ferland 2006).
Padovani (1988) derived an average value $<U\cdot$ $n_{\rm e}$$>\approx
10^{9.8}$ from several sources where $r_{\rm BLR}$ had been determined from
reverberation mapping, and for which the number of ionizing photons could be
measured from multiwavelength observations. The average value was then used to
compute black hole masses for a much larger sample of Seyfert 1 galaxies and
low-$z$ quasars (Padovani & Rafanelli 1988; Padovani, Burg & Edelson 1989).
Wandel, Peterson & Malkan (1999) compared the results of the photoionization
method with the ones obtained through reverberation mapping, found a very good
correlation for the masses computed with the two methods, and concluded that
“both methods measure the mass of the central black hole.”

###  1.4 Outline of the paper

The importance of the product $U\cdot$$n_{\mathrm{H}}$ goes beyond knowledge
of the physical conditions in the BLR if it can lead to estimates of BLR
radius and black hole mass. This paper identifies suitable emission line
ratios that overcome some of the major problems in the analysis of emission
lines of quasars. It also defines a photoionization method that can be applied
to even the highest redshift quasars making use of high S/N near-IR
spectroscopic data. In §2 we present the spectra of 8 pilot sources obtained
with the VLT/FORS; in §3 we discuss data reduction; In §4 we describe our
method of fitting broad emission line profiles; in §5 we give a
phenomenological interpretation of the profile fits; in §6 we describe a
method for deriving BLR physical conditions and give the results of our fits;
in §7 we discuss two sources not belonging to our sample that show extreme
behavior and that are helpful to understand more common quasar spectra; in §8
we give the results for the photoionization method; in §9 we derive the radius
of the BLR (its distance from the ionizing source) and the mass of the black
hole for each quasar in our sample; in §10 we discuss our results; finally, in
§11 we summarize our results and the prospect of a more extended application
of our method. All the computations were made considering $H_{0}$ =70 km s-1
Mpc-1 and a relative energy density $\Omega_{\Lambda}=0.70$ and
$\Omega_{\mathrm{M}}=0.3$.

##  2 Observations

Data were obtained between Nov. 2006 and Jan. 2007 using the VLT2/FORS1
telescope operated in service mode. FORS1 is the visual and near UV focal
reducer and low dispersion spectrograph of the Very Large Telescope (VLT)
operated by European Southern Observatory (ESO) (Appenzeller et al. 1998). Our
VLT sample consists of 8 quasars with $z\sim 3$. In Figure 1 we show the
spectra uncorrected for redshift. Tab. 2 provides a log of observations that
is organized as follows.

Column 1: object name, Col. 2: apparent B magnitude, Col. 3 redshift, Col. 4:
line(s) used for redshift estimation: a) Oi$\lambda$1304.8, b)
Ciii]$\lambda$1909; Col. 5: absolute B magnitude, Col. 6 flux at 6 cm taken
from FIRST (Far InfraRed and Submillimetre Telescope), Col. 7: date (refers to
time at start of exposure), Col. 8: Digital Integration Time, Col. 9: number
of exposures with integration time equal to DIT, Col. 10: airmass at the
beginning of each exposure, Col. 11 $S/N$ in the continuum around 1700Å.

The observation of one of our 8 quasars, J00521-1108, yielded only a low S/N
spectrum which we retain because observed features in the blend at $\sim 1900$
Å are clear enough to fit the individual lines. Two sources, J01225+1339 and
J02287+0002, are BAL quasars. We will keep them separate because
Civ$\lambda$1549 is severely affected by absorption.

##  3 Data Reduction

Data were reduced using standard iraf tasks. All spectra were wavelength and
flux calibrated in the observed frame and then corrected for Galactic
extinction. Flux correction was applied using meteorological data provided by
ESO. The observed flux was multiplied by the inverse of the light lost
computed from the ratio seeing over slit width in arcsec. Correction to rest
frame requires estimating the redshift $z$ which is not a trivial task as
outlined below. Rest frame correction also involved scaling the specific flux
in flux per unit wavelength interval by a factor $(1+z)^{3}$. Measurements
were carried out on the rest-frame spectra. It is necessity to describe below
two important aspects of the data reduction.

###  3.1 A & B Atmospheric Bands Correction

The A or B atmospheric band falls on top of the 1900Å blend in many of the
spectra. This is an important region for this study especially because it
involves Siiii]$\lambda$1892, Aliii$\lambda$1860, and Siii$\lambda$1814\. In
order to remove these absorption features we created an A+ B band template
from standard star spectra used as specific flux calibrators. We scaled this
template to find a best fit. Fig. 1 shows the A and B absorption correction
where we make a line identification to illustrate which lines are affected. In
cases where the A or B bands overlap a weak line like Siii$\lambda$1814 the
effect is considerable and measures of Siii$\lambda$1814 should not be
considered at all or with extreme care. This happens for sources J00103-0037,
J03036-0023, and J20497-0554. In cases where one of the bands overlaps a
stronger line like Siiii]$\lambda$1892 or Aliii$\lambda$1860, the correction
was good enough to permit accurate measures.

###  3.2 Redshift Estimate

Normally one uses strong narrow emission lines to set the rest frame in a
quasar. In our case no strong narrow lines are available so we consider the
peaks of Ly$\alpha$, Civ$\lambda$1549 and Ciii]$\lambda$1909\. The Ly$\alpha$
peak is affected by absorption and Civ$\lambda$1549 is a HIL feature often
showing blueshifts and/or asymmetries (Gaskell 1982, Espey et al. 1989, Corbin
1990, Tytler & fan 1992; Marziani et al. 1996; Richards et al. 2002, Baskin &
Laor 2005; Sulentic et al. 2007). This is especially true in Pop. A sources.
Ciii]$\lambda$1909 is blended with Siiii]$\lambda$1892 and Feiii that is
especially prominent in this region and could well affect the peak. Pop. B
sources show a rather weak Fe spectrum making the Ciii]$\lambda$1909 peak a
more reliable $z$ estimator.

Our best option is to use the low ionization line Oi$\lambda$1304 whenever it
is strong. However it is blended with low ionization
Siii$\lambda$$\lambda$1304,1309 (${}^{2}P^{0}_{3/2,1/2}-^{2}S_{1/2}$). Both
Oi$\lambda$1304 and Siii$\lambda$$\lambda$1304,1309 are broad lines and in
Pop. B sources might show large redshifts or even significant blueshifts.
Simulations in the ($n_{\mathrm{H}}$, $U$) region of interest show
Oi$\lambda$1304 $\approx$ 2 Siii$\lambda$1304,1309 and this is confirmed in
the spectrum I Zw 1 where Oi$\lambda$1304 and Siii$\lambda$$\lambda$1304,1309
are resolved. The two components of the Siii$\lambda$$\lambda$1304,1309
doublet are set to the same intensity (i.e., we assume an optically thick
case). We model the blend Oi$\lambda$1304 + Siii$\lambda$$\lambda$1304,1309
with 5 Gaussians; the three components of the Oi feature are produced by Bowen
florescence mechanism, and should show ratios consistent with their transition
probabilities. Generating a model spectrum in iraf (lines broadened to 4000 km
s-1) yields a rest frame peak wavelength of 1304.8 $\pm$ 0.2 Å (in vacuum)
which we use as a reference for our VLT spectra assuming that there is no hint
of systematic BC shifts as is the case for all Pop. A sources (the majority in
our sample) and many Pop. B sources (Marziani et al. 2003a).

Examination of Fig. 2 reveals that the peak of Oi$\lambda$1304 in source
J00521-1108 is not observed clearly. We use Ciii]$\lambda$1909 to set the rest
frame in this case. There are other sources J00103-0037, J02287+0002,
J02390-0038 and J20497-0554 where the redshift estimation using both
Oi$\lambda$1304 and Ciii]$\lambda$1909 are not in good agreement. The largest
disagreement was found for J02287+0002. Redshifts obtained for the three
remaining quasars, J01225+1339, J03036-0023 and J23509-0052, were obtained
from Oi$\lambda$1304\. Fig. 3 shows the deredshifted VLT-FORS spectra for our
sample of 8 quasars.

##  4 Data Analysis

###  4.1 Methodological Considerations on Multicomponent Fits

The specfit IRAF task (Kriss 1994) allows us to fit the continuum, emission
and absorption line components, Feii and Feiii blends, etc. We fit two
spectral ranges: (1) 1450–1680 Å for analysis of Civ$\lambda$1549 and (2)
1750–2050 Å for analysis of the 1900 Å blend. Significant Feii and Feiii
emission are expected close to and underlying the 1900 Å blend. Study of the
1900 Å blend is especially difficult in quasars because the lines are broad
and the blending severe. We therefore need to take advantage of several
previous results.

###  4.2 Feii and Feiii Emission

Our approach is completely empirical and employs an Feii \+ Feiii template
taken from templates successfully used in previous works. Our Feii template is
based on a CLOUDY simulation and is not very far from the preferred model of
Bruhweiler & Verner (2008).

Feiii lines are common and strong in the vicinity of Ciii]$\lambda$1909 as is
evidenced by their presence in average LBQS (Francis et al. 1991) and SDSS
(Vanden Berk et al. 2001) spectra. They appear to be strong when
Aliii$\lambda$1860 is also strong (Hartig and Baldwin 1986). Vestergaard &
Wilkes (2001) produced an Feiii template based on the UV spectrum of I Zw 1.
Since then, Sigut et al. (2004) have modeled the Feiii BLR spectrum. See also
Verner et al. (2003) for a plot of emission around 1900 Å. Ly$\alpha$ pumping
enhances Feiii (UV 34)$\lambda$1914.0 (Johansson et al. 2000) and this line
can be a major contributor to the blend right on the red side of
Ciii]$\lambda$1909 (see Fig. 2 of Vestergaard & Wilkes). We reproduced the
option B of the empirical Feiii template of Vestergaard & Wilkes (2001),
taking advantage of the line identifications from Ekberg (1993). When detected
we can use Feii UV 191 to set a rough Feii level while the feature at 2080 Å
is helpful for a more precise estimation of the intensity of Feiii. The
continuum was fitted using the regions around 1450Å (1750 and 1960Å) that are
relatively free of Feii emission (Vanden Berk et al. 2001). We used the same
power-law to describe the continuum at both the Civ$\lambda$1549 and 1900Å
regions.

###  4.3 Line Components

We base our specfit analysis on several previous observational results. The
most important ones are as follows:

  * •

Sulentic et al. (2002) gridded the broad component of FWHM H$\beta$BC versus
$R_{\rm FeII}$=W(Feii$\lambda$4570blend)/W(H$\beta$BC) parameter plane into
bins of fixed $\Delta$ FWHM = 4000 km s-1 and $\Delta$ $R_{\rm FeII}$= 0.5.
Quasar spectra in different bins are different in many measures. As mentioned
earlier, the largest differences are found between NLSy1-like objects, Pop. A,
and broader sources of Pop. B with FWHM(H$\beta$) $\gtrsim$ 4000 km s-1. The
gridding of 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
H$\beta_{BC}<3500$ km s-1 exist above luminosity $\sim 10^{48}$ ergs s-1
(Marziani et al. 2009).

  * •

Median spectra were computed for spectral bins from the atlas of Marziani et
al. (2003a) who found that H$\beta$ can be described by a Lorentz function in
Pop. A sources and by the sum of 2 Gaussians in Pop. B sources (unshifted +
broader redshifted components) (Zamfir et al. 2010; Marziani et al. 2010).

  * •

A careful Feii subtraction reveals a blue-shifted H$\beta$ component in some
bin A3 sources (i.e. the stongest Feii emitters; Zamfir et al. 2010).

  * •

Civ$\lambda$1549 (HIL) and H$\beta$ (LIL) profiles show significant
differences in Pop. A. Large Civ$\lambda$1549 blueshifts ($\lesssim-1000$ km
s-1) are observed in Pop. A only (Sulentic et al. 2007). HIL and LIL profiles
are more similar in Pop. B sources.

  * •

We do not have H$\beta$ observations for our high-$z$ objects since there are
no near IR spectra. We use the results of Marziani et al. (2003b, 2010): they
show that the BC of Siiii]$\lambda$1892, Aliii$\lambda$1860 and
Civ$\lambda$1549 lines is similar to the one of H$\beta$, including the FWHM
and profile shape, either Gaussian or Lorentzian. The similarity helps us to
define whether an object is Population A or B in this paper.

These observational results point toward three different components in broad
line profiles (see Marziani et al. 2010) which can be described as follows:

  1. 1.

A broad component (BC) showing a roughly symmetric profile with FWHM in the
range 1000-5000 km s-1. It is consistent with the component identified by
Matsuoka et al. (2008). This broad component dominates LILs in Balmer lines of
Pop. A sources while it becomes less prominent in Pop. B. The profile is best
modeled by a Lorentzian function in Pop. A sources while Pop. B profiles are
better described by a Gaussian (Marziani et al. 2003b).

  2. 2.

A very broad component (VBC), as seen in LILs and HILs of most pop B sources
but is absent from Pop. A profiles. The VBC can be modeled as a Gaussian (FWHM
$\sim$ 10000 km s-1) often with a significant shift to the red. It can be
called a defining property of Pop. B sources (Marziani et al. 2010). This
component is clearly identified in the Civ$\lambda$1549 line of Pop. B
objects, and is also appreciable on the red side of Ciii]$\lambda$1909 of Pop.
B objects J00103-0037 and J02390-0038.

  3. 3.

A blueshifted broad component (BBC), defined as the residual emission in the
Civ$\lambda$1549 line after subtracting a scaled BC Lorentzian profile
(Marziani et al. 2010). This blueshifted component is often prominent in
Civ$\lambda$1549 and Ly$\alpha$ of Pop. A sources. It is much less intense in
radio-loud Pop. B sources (Marziani et al. 1996; Punsly 2010; Richards et al.
2010). We model this profile as a blueshifted Gaussian. The Gaussian
approximation is probably inappropriate especially if the BCC is strong: this
component is believed to be produced in a partially-obscured radial flow, not
in a virialized emitting system. In the present work we do not even try to fit
the blueshifted in the doubly ionized lines. It is quite obvious from the fits
that a possible contribution of this component would be negligible.

Baldwin et al. (1996) presented a similar analysis. Their Fig. 2 organizes
spectra in a sequence that is roughly corresponding to E1, going from
Aliii$\lambda$1860-strong sources to objects whose spectra show prominent
Ciii]$\lambda$1909 along with weak Aliii$\lambda$1860 (Bachev et al. 2004).
Two of the three line components they isolated correspond to the ones we
consider in this paper: a blue-shifted feature, and a more symmetric,
unshifted and relatively narrow component that we call LIL-BC. Less obvious is
the correspondence of a third feature, although it appears to be the
redshifted part of what we call the VBC.

Several improvements have been introduced since the paper of Baldwin et al.
1996. These improvements are expected to make our analysis easier. First, the
definition of a template of Feiii emission (Vestergaard & Wilkes 2001), along
with the possibility to model Feii in the 1400–2000 Å spectral region with
cloudy (Verner et al. 1999, 2004). The analysis of spectra along the E1
sequence allows one to see trends that make the interpretation of the emission
line blends easier (Marziani et al. 2010).

###  4.4 Expected emission from the various components

We looked for evidence of three possible components as described above: BC,
VBC and BBC only for the most intense HILs: Civ$\lambda$1549 and
Siiv$\lambda$1397\. We did not include the contributions of the BBC for the
doubly-ionized lines. In the case of Pop. A sources, we indeed assume that the
BC contains the vast majority of the light. In the case of Pop. B sources we
consider the contribution of the VBC. The Aliii$\lambda$1860 doublet shows no
evidence of either a BBC or VBC. There is no obvious BBC for
Siiii]$\lambda$1892 in the blend. There is evidence of a VBC of
Ciii]$\lambda$1909 extending on the red side of the blend, and this is taken
into account. Moreover, we expect that the Aliii$\lambda$1860 doublet is
emitted exclusively in the BC, the region where Feii is also emitted. This is
empirically confirmed by the aspect of the 1900 blend in many sources, where
we do not see any evidence of BBC nor VBC. We remark that the
Aliii$\lambda$1860 doublet is relatively unblended, and that a BBC feature as
strong as in Civ$\lambda$1549 would not easily escape visual detection.The
same is also true for Siiii]$\lambda$1892\. Several fits that included BBC in
Ciii]$\lambda$1909 yielded 0 intensity, implying a large
Civ$\lambda$1549/Ciii]$\lambda$1909 (Marziani et al. 2010). The
Siiv$\lambda$1397 + Oiv]$\lambda$1402 blend closely resembles the shape of
Civ$\lambda$1549, suggesting that BBC is relevant, especially for
Siiv$\lambda$1397 (Oiv]$\lambda$1402 is expected to give a minority
contribution to line emission at the high density derived for the BC; any
Oiv]$\lambda$1402 contribution to the BBC is not relevant to our method). BBC
is very weak or undetectable in the vast majority of the H$\beta$ profiles
analyzed in Marziani et al. 2010 (but see Zamfir et al. 2010 for several cases
of H$\beta$ BBC), while prominent in Ly$\alpha$; the Ly$\alpha$/H$\beta$ ratio
in this component is high. In summary, BBC is visually strong in Ly$\alpha$,
Civ$\lambda$1549, and Siiv$\lambda$1397\. Heii$\lambda$1640 in BBC is needed
for a self-consistent fit of the Civ$\lambda$1549+Heii$\lambda$1640 blend. The
VBC of Siiii]$\lambda$1892 is poorly constrained, but in the fits where
Ciii]$\lambda$1909 VBC is visible, we always find Siiii]$\lambda$1892 $<$
Ciii]$\lambda$1909, consistent with the high ionization level expected in the
VBC region. Some Siiv$\lambda$1397 VBC emission is assumed in the Pop. B fits.
No VBC emission is expected in Aliii$\lambda$1860 and Feii. These constraints
help also to make the fits less ambiguous.

The absence of a VBC makes the decomposition of Pop. A spectra easier. As said
earlier, the Feii intensity scale of the template (but Feii is in general
weak) is anchored to the UV 191 intensity; similarly the Feiii intensity is
set by a feature external to the 1900 Å blend (2080 Å). There is no evidence
of BBC of Aliii$\lambda$1860 and Siiii]$\lambda$1892; the Aliii$\lambda$1860
doublet profile is mostly unblended and defines the LIL-BC. The additional
complication here is the Feiii 1914 line whose intensity is affected by
Ly$\alpha$ pumping. Since the shift and FWHM are assumed the same for all
lines (and templates) in the 1900 blend, the only free parameters in addition
to shift and FWHM are the intensities of 6 components, including the two from
the templates, and Siii$\lambda$1814 and Aliii$\lambda$1860 that are not
heavily blended. The specfit analysis is especially helpful to measure in a
non-subjective way, taking all constraints into account, the two parameters
that are most affected by the blend: the intensity of Siiii]$\lambda$1892 and
Ciii]$\lambda$1909 (we repeat that any Feiii $\lambda$1914 contribution in
excess to the one of the adopted template is included in the estimated
Ciii]$\lambda$1909 intensity).

In the case of Pop B, the presence of a VBC does not really complicate the fit
as a matter of fact. The Ciii]$\lambda$1909 line undeniably shows a VBC
protruding on the red side of the 1900 blend. In any case, considering that we
can expect the VBC to be assimilable to a shifted Gaussian with FWHM $\sim
10000$km s-1, the unblended part of the Ciii]$\lambda$1909 VBC provides a
strong constraint. The Siiii]$\lambda$1892 VBC is certainly the most difficult
feature to ascertain, as it buried under Siiii]$\lambda$1892 and
Ciii]$\lambda$1909 emission. We rely on the specfit results. that indicate
negligible Siiii]$\lambda$1892 VBC.

###  4.5 Errors

We identify five sources of error from the conditions for data reduction and
methodological considerations described above:

  1. 1.

A & B atmospheric bands correction (already described in §3.1).

  2. 2.

Line profile shape, Gaussian or Lorentzian (Pop. A or B). The distinction
between Pop. A and B is based on line width with the boundary at FWHM
H$\beta\approx$ km s-1 in low luminosity quasars and around $\approx$ 5000 km
s-1 at higher luminosity such as the eight sources presented here. Most of our
quasars are unambiguously Pop. A or B because of line width and because Pop. B
sources show an H$\beta$ VBC and pop A sources a prominent Civ$\lambda$1549
BBC. In these cases only one profile shape (Gaussian or Lorentzian) was
fitted.

  3. 3.

Rest-frame determination using Oi$\lambda$1304 or Ciii]$\lambda$1909\. In some
cases the redshift estimates derived from the two lines do not agree, most
likely because of absorptions present in Oi$\lambda$1304.8 and because this is
not a very intense line. The principal impact of uncertainty in the rest frame
placement is estimation of the peak wavelength of Civ$\lambda$1549\. If the
line peak differs from $\lambda$1549Å, the BC intensity is diminished and we
infer a greater contribution from the blue (BBC) component. Similarly, for the
blend 1900Å, the rest frame shift may increase or decrease our estimate for
the strength of Ciii]$\lambda$1909 with consequent decrease or increase of the
Siiii]$\lambda$1892 contribution. This additional source of uncertainty
affects J00103-0037, J02287+0002 and J20497-0554.

  4. 4.

Feii intensity (continuum placement). Broad Feii emission can produce a
pseudo-continuum affecting our estimates of emission line intensities.
Siii$\lambda$1814 is especially affected in our spectra because it is weak.
Aliii$\lambda$1860 is similarly affected when it is weak. The effect is less
noticeable for Civ$\lambda$1549 since expected Feii emission underlying the
Civ$\lambda$1549 line is weak also for strong Feii emitters.

  5. 5.

Broad absorption lines (BALs) in quasars principally affect the blue side of
Civ$\lambda$1549\. We also find an absorption feature between
FeII$\lambda$1787 and Siii$\lambda$1814 (eg. Fig. 6). In sources J01225+1339
and J02287+0002 we can only set upper limits for line intensities (since we
fit unabsorbed components).

There are other sources of error such as small BC shifts and FWHM variations.
We assume that the BC of the Siiii]$\lambda$1892, Aliii$\lambda$1860,
Siii$\lambda$1814 and Civ$\lambda$1549 line has the same FWHM and wavelength
shift, although we allow for variations in their relative flux strengths and
adopted profile type (Lorentzian for Pop. A and Gaussian for Pop. B). For
Feiii(UV34) and Feii we slightly relax this constraint. The Feiii(UV34) and
Feii emission is not very strong and the FWHM of individual features is poorly
constrained by specfit. In the case of Ciii]$\lambda$1909 we need to consider
the possibility that the profile is narrower because there might be a
contribution from different regions: indeed, the specfit routine usually
converges toward a narrower profile if the Ciii]$\lambda$1909 width is not
constrained. The effect depends on the strength of the Feiii $\lambda$ 1914
feature.

The goal of this study is to estimate diagnostic line ratios. A posteriori, we
can say that the estimated line ratios are rather insensitive to the emission
component profile shape: assuming a Gaussian or Lorentzian profile yields the
same ratio for the strongest lines (i.e., Civ$\lambda$1549,
Siiii]$\lambda$1892, Aliii$\lambda$1860) upon which our analysis is based
(with an uncertainty of $\sim$10%). The same conclusion applies to the
redshift uncertainty. Only in the case of J02287+0002 the redshift difference
produces a significant effect due to a $\Delta z\approx 0.16$. However, we
adopt the fit based on Oi$\lambda$1304: the alternative fit produces line
ratios that are of not obvious interpretation and at variance with respect to
the other sources. The most serious sources of error remain effects of A/B
band overlap for Siii$\lambda$1814 and the presence of a BAL for
Civ$\lambda$1549.

##  5 Results of Line Component Analysis on Individual Objects

In Figures from 4 to 6 we show our best fits for the VLT sample taking into
account the considerations described in §4. The fits of Siiv$\lambda$1397 are
shown in Fig. 7 and the intensity values and equivalent widths are in Tables 3
and 5. We present here a phenomenological description of the fits. The line
profiles, intensities and line ratios usually follow the trends of Pop. A or B
sources, although in some objects there are features that are ambiguous (for
example the line shape). In these cases however, we have assigned Pop. A or B
type on the basis of the FWHM (see Cols. 5 and 6 of Table 7).

###  5.1 Pop. A Objects

  * •

J03036-0023 – We estimate for this source a FWHM(BC)$\sim$3700 km s-1 and we
use a Lorentzian function to fit the broad lines. The peak of Civ$\lambda$1549
is blueshifted and requires a strong BBC (Fig. 4(a)). The bump on the red side
of Civ$\lambda$1549 can be accounted for by Heii$\lambda$4686 BC and BBC.
There is no evidence for a red shifted component in Ciii]$\lambda$1909 (Fig.
4(b)). Aliii$\lambda$1860 is prominent. Unfortunately the blue wing of
Siii$\lambda$1814 and the red wing of Feii$\lambda$1787 are affected by A band
absorption.

  * •

J20497-0554 – This source shows FWHM(BC)$\sim$3800 km s-1. As for J03036-0023,
the Civ$\lambda$1549 line can be accounted for by an unshifted BC (assumed
Lorentzian) of a considerably contribution of a BBC (Fig. 4(c)). We see a
prominent Aliii$\lambda$1860 line and FeII$\lambda$1787 (Fig. 4(d)).
Siiii]$\lambda$1892 is affected by several narrow absorption lines; however,
it is obviously strong. The lack of a red wing on Ciii]$\lambda$1909 suggests
that no VBC is present.

  * •

J23509-0052 – This source has FWHM(BC)$\sim$3600 km s-1. Civ$\lambda$1549
shows a slight blue asymmetry with a BBC (Fig. 4(e)) required to model it. The
contribution of Feii is small and Feii$\lambda$1787 is weak (Fig. 4(f)).
Ciii]$\lambda$1909 is very strong. Aliii$\lambda$1860 is affected by A band
absorption; the profile we fit is probably an upper limit. This object could
well belong to spectral type A1 that includes Pop. A sources with the lowest
$R_{\rm FeII}$($\lower 2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}0.5$).

###  5.2 Pop. B Objects

.

  * •

J00103-0037 – This source has a FWHM(BC)$\sim$4500 kms-1. The red side of
Civ$\lambda$1549 is blended with Heii$\lambda$4686\. Fitting a BC with no
shift plus a BBC to Civ$\lambda$1549 leaves a very large residual on the red
side. A very broad redshifted component (VBC) is needed to model the spectrum
(Fig.5 (a)). The faint narrow line under Civ$\lambda$1549 can be explained as
the narrow component (NC) of Civ$\lambda$1549(see Sulentic et al. 2007). The
presence of a similar NC in Ciii]$\lambda$1909 could possible explain the
large residual seen $\sim$1900\. We specifically note the prominent
Ciii]$\lambda$1909 emission and weak (but detected) Aliii$\lambda$1860 (Fig.
5(b)). The Feii “bump” at 1787 Å(UV 191) is appreciable. Fainter Feii emission
is relatively unimportant because Feii creates a pseudo-continuum.
Siii$\lambda$1814 is compromised by A-band absorption. The blend at 1900Å
includes a Ciii]$\lambda$1909 VBC and the fit indicates Civ$\lambda$1549/
Ciii]$\lambda$1909 (VBC) $\approx$ 7 which is reasonable.

  * •

J00521-1108 – This source shows the noisiest spectrum in the sample. We fit a
FWHM(BC) $\sim$ 5300 km s-1 with Civ$\lambda$1549 requiring a large VBC to
account for the red wing. (Fig. 5(c)). Absorption features seriously affect
the Civ$\lambda$1549 profile. The profile of Ciii]$\lambda$1909 is strongly
asymmetric due to some sort of absorption on the red side. Aliii$\lambda$1860
is weak consistent with pop. B (Fig. 5(d)).

  * •

J02390-0038 – This objects has a somewhat atypical Pop. B spectrum due to a
very strong BBC in Civ$\lambda$1549 (Figure 5(e)). This source has a
FWHM(BC)$\sim$ 5400 km s-1. Consistent with pop. B we find Feii$\lambda$1787
to be weaker than Siii$\lambda$1814\. Ciii]$\lambda$1909 is flat topped and
has a very similar intensity as Siiii]$\lambda$1892\. Both Civ$\lambda$1549
and Ciii]$\lambda$1909 it show red wings indicating VBC emission. The A band
absorption lies between Siiii]$\lambda$1892 and Aliii$\lambda$1860 (Fig. 5(f))
producing a possible overestimation of Aliii$\lambda$1860.

###  5.3 BAL QSOs

  * •

J01225+1339 – Civ$\lambda$1549 is highly affected by two broad absorption
lines (Fig. 6(a)) with blueshifts of 5200 and 10800 km s-1 at peak absorption
with equivalent widths/FWHM -12Å / 3900 km s-1 and -25Å/5200 km s-1,
respectively. The blueshift of the Civ$\lambda$1549 peak leads us to suspect a
large blueshifted BBC emission component. The 1900 Å blend shows absorptions
coincident with Feii$\lambda$1787 and the blue side of Siii$\lambda$1814 which
is however unambiguously detected (Fig. 6(b)). Aliii$\lambda$1860 is prominent
which implies that this a Pop. A source. The FWHM(BC) $\sim$ 4400 km s-1 is
consistent with a high-luminosity Pop. A source. It is also possible that this
BAL QSO is an outlier like Mark 231 at low-$z$ (Sulentic et al. 2006), in
other words an extreme Pop. A object.  The Ciii]$\lambda$1909 is well fitted
with a Lorentzian profile. Broad A band atmospheric absorption lies over
Siiii]$\lambda$1892.

  * •

J02287+0002 – This object has a very complex spectrum. On one side it has a
FWHM(BC) $\approx$ 4700 km s-1 which is typical of low-luminosity Pop. B and
the lines profiles are better fitted with Gaussians. On the other side,
however, it shows features that are typical of extreme Pop. A sources:
prominent Feii$\lambda$1787, strong Aliii$\lambda$1860, no Ciii]$\lambda$1909
VBC (Fig. 6(d)). Considering that the FWHM limit between Pop. A and B is
increasing with luminosity, the FWHM(BC) is within the limit of Pop. A. The
Ciii]$\lambda$1909 line is not very flat topped but the similar intensities of
Ciii]$\lambda$1909 and Siiii]$\lambda$1892 remind the case of J02390-0038.
Also because it has a strong blue-shifted component in Civ$\lambda$1549
atypical to Pop. B objects (Fig. 6(c)).

The estimated rest frame of this quasar differs by $\sim$ 1400 km s-1 using
Oi$\lambda$1304 and Ciii]$\lambda$1909\. This is the largest discrepancy in
our sample. In order to evaluate the effect of the $z$ discrepancy we
performed two fits using both rest frames. Figs. 6(a) and (b) use the
Ciii]$\lambda$1909 restframe. In the 1900 Å blend, we found a contribution of
Siiii]$\lambda$1892 similar to Ciii]$\lambda$1909\. If we use the
Oi$\lambda$1304 inferred rest frame we show in Figs. 6(e) and (f) that
Ciii]$\lambda$1909 becomes stronger with a resultant decrease of
Siiii]$\lambda$1892\. A similar effect occurs for Civ$\lambda$1549 broad and
blue-shifted components.

The Civ$\lambda$1549 BAL shows a blueshift of 9100 km s-1at deepest
absorption, a EW of –14 Å and a FWHM of 4600 km s-1.

Summing up, we are able to assign an A/B identification to all sources in our
sample. The two BAL QSOs appear as objects of extreme Pop. A. We remind that
the identification of Ciii]$\lambda$1909 in the BAL QSOs and in sources with
strong Aliii$\lambda$1860 is debatable (Hartig and Baldwin 1986): strong Feiii
1914 could take the place of most Ciii]$\lambda$1909 emission.

##  6 Estimation of Physical Conditions in the Emitting regions

###  6.1 CLOUDY Simulations

We computed a multidimensional grid of CLOUDY (Ferland et al. 1998)
simulations, (see also Korista et al. 1997) to derive $U$ and $n_{\mathrm{H}}$
from our spectral measurements. Simulations span the density range
$7.00\leq\log$ $n_{\mathrm{H}}$$\leq 14.00$, and $-4.50\leq\log U\leq 00.00$,
in intervals of 0.25. Each simulation was computed for a fixed ionization
parameter and density assuming plane parallel geometry. The 2D grid of
simulations was repeated twice assuming $N_{\rm c}$$=10^{23}$ and $10^{24}$
cm-2. Several cases were computed also for $N_{\rm c}$= $10^{25}$cm-2.
Metallicity was assumed to be either solar or five times solar. Two
alternative input continua were used: 1) the standard AGN continuum of CLOUDY
which is equivalent to the continuum described by Mathews and Ferland (1987)
and 2) the low-$z$ quasar continuum of Laor et al. (1997a). Computed line
ratios are almost identical for fixed ($U$, $n_{\mathrm{H}}$). However the
ionizing luminosity differs by more than a factor of 2 for a fixed specific
continuum luminosity. The contour plots showing the distributions of
Ciii]$\lambda$1909/ Siiii]$\lambda$1892, Aliii$\lambda$1860/
Siiii]$\lambda$1892, Siii$\lambda$1814/ Siiii]$\lambda$1892,
Siiv$\lambda$1397/ Siiii]$\lambda$1892, Civ$\lambda$1549/Aliii$\lambda$1860and
Civ$\lambda$1549/ Siiii]$\lambda$1892 (Fig. 9) are generated from 29 $\times$
19 = 551 simulations and assume a standard set of simulations using a Mathews
and Ferland (1987) continuum, $N_{c}=10^{23}$ cm-2, and solar metallicity. The
CLOUDY 08.00 computations included a model of the Fe+ ion with 371 levels. The
UV Feii template, described in §4.2 is based on a suitable CLOUDY simulation.
Even if a relationship is very likely between the dense low ionization gas
producing our diagnostic lines and Feii emission (supported observationally)
our diagnostics do not use any Feii computation. The weak line Oi$\lambda$1304
is used only for rest frame estimation and not for diagnostic considerations.

Apart from the hypothesis of plane-parallel geometry, no inferences are made
about the actual distribution, location, and kinematics of the line emitting
gas. The assumption of constant density is crude. If gas is distributed in
clouds then magnetic confinement appears to be unnecessary to avoid cloud
dispersion from pressure imbalance or cloud shear associated with a hot
confining medium. Magnetic confinement could make density uniform within the
cloud (Rees 1987; Bottorff and Ferland 2000).

###  6.2 Intermediate Ionization Lines in the Blend at $\lambda$1900

The ratio Ciii]$\lambda$1909/ Siiii]$\lambda$1892 is density dependent because
the transition probabilities of the two lines are so different: 114 s-1 vs
12600 s-1 (see Table References). The forbidden lines at 1883Å and 1907Å have
such low transition probabilities that they are collisionally quenched at much
lower density and will not be considered. Line ratios like Ciii]$\lambda$1909/
Siiii]$\lambda$1892 are useful diagnostics in a rather narrow range of density
which depends on the transition probabilities. Above the critical density,
emission lines originating from forbidden or semi-forbidden transitions become
collisionally quenched, and hence weaker than lines for which collisional
effects are still negligible. Ciii]$\lambda$1909 is clearly unsuitable as a
diagnostic for $n_{\rm e}$$\gg 10^{11}$ cm-3, as the Ciii]$\lambda$1909/
Siiii]$\lambda$1892 $\rightarrow$ 0\. Feldman et al. (1992) gives critical
density of Siiii]$\lambda$1892 $n_{e}\sim 2\cdot 10^{11}$ cm-3.
Aliii$\lambda$1860 is a permitted transition with large transition probability
($A\sim 5\cdot 10^{8}$ s-1) and has very-high critical density (i.e., its
equivalent width goes to zero toward thermodynamic equilibrium, which occurs
at very high density, when all line emission is collisionally quenched). Our
2D array of CLOUDY simulations shows that the ratio Aliii$\lambda$1860/
Siiii]$\lambda$1892 is well suited to sample the density range
$10^{10}-10^{12.5}$ cm-3. Within this range the Siiii]$\lambda$1892 intensity
decreases smoothly by a factor 10; above the upper limit in density, the
predicted intensity of Siiii]$\lambda$1892 decreases. This corresponds to the
densest, low ionization emitting regions likely associated to the production
of Feii.

Intermediate-ionization lines such as Ciii]$\lambda$1909, Aliii$\lambda$1860,
Siiii]$\lambda$1892 and Siiv$\lambda$1397avoid the issue of collisional
ionization (invoked for the production of low-ionization species by S. Collin
and collaborators, as mentioned in the introduction).

The widely separated doublet Aliii$\lambda$1860 is expected to be produced
entirely in the fully ionized zone (Laor et al. 1997b). CLOUDY simulations
confirm this suggestion. Figure 10 (top panel) shows the ionic fraction as a
function of the geometrical depth in a cloud (or slab) of fixed column density
($N_{\rm c}$$=10^{23}$ cm-2) and density ($n_{\mathrm{H}}$$=10^{12.5}$cm-2).
As it can be seen, Al++, Fe++, and Si++ share a region of dominance deep in
the cloud, close to the end of the Strömgren sphere. Beyond, in the partially-
ionized zone (PIZ) there is, as by definition, a significant fraction of
ionized hydrogen. The dominant ionic stages of Si and Fe become Fe+ and Si+.
It is very appropriate to consider the Aliii$\lambda$1860/ Siiii]$\lambda$1892
ratio since the two lines are apparently emitted in the very same zones within
the gas slab. Available reverberation mapping results may support this
interpretation but are rather difficult to extrapolate since they are limited
to an handful of low luminosity objects. The main finding is that
Ciii]$\lambda$1909 responds to continuum changes on timescales much longer
than Civ$\lambda$1549 and other HILs. This results comes from the analysis of
total Ciii]$\lambda$1909 + Siiii]$\lambda$1892 in NGC 3783 (Onken & Peterson
2002), from the Ciii]$\lambda$1909 of NGC 4151 (Metzroth et al. 2006) and of
NGC 5548. It is intriguing that the Ciii]$\lambda$1909 cross-correlation delay
in NGC 5548 (by far the best studied object) is even larger than that of
H$\beta$ (32 ld vs. 20 ld; Peterson et al. 2002; Clavel et al. 1991). For
fixed density, lines of higher ionization form at higher photon flux. The C+,
Al+, Si+ ionization potential are 24, 18, and 16 eV respectively. These
comparable ionization potentials are well below the one of HILs,
$X^{i-1}\gtrsim$ 50 eV. However, the much lower Ciii]$\lambda$1909 critical
density implies that the Ciii]$\lambda$1909 line should be formed farther out
than Siiii]$\lambda$1892 and Aliii$\lambda$1860 if all these lines are
produced under similar ionization conditions.

###  6.3 The Siii Contribution to the UV Spectrum of Quasars

AGN have a rather rich singly-ionized silicon spectrum in the range 1000-2000
Å, due to several resonant transitions from the ground term
$3s^{2}3p^{1}{}^{2}P^{0}$ to terms associated to the $3s^{1}3p^{2}$
($\lambda$1814 and $\lambda$1304), $3s^{2}4s$ ($\lambda$1531), $3s^{2}3d$
($\lambda$1263) electronic configurations. A feature on the red side of
Ly$\alpha$, at 1263 Å is detected in several Pop. A sources like I Zw 1
(Marziani et al. 2010).

The $\lambda$1309 feature is partially blended with the Oi triplet associated
with a Bowen fluorescence mechanism from HI Ly$\beta$. The $\lambda$1309 line
is well resolved in sources like I Zw 1 with the extension of the broad
$\lambda$1309 feature suggesting significant Siii emission around
$\lambda$1309\. The $\lambda$1531 feature is blended with Civ$\lambda$1549\.
High S/N spectra of low redshift sources from HST (Laor et al. 1994) as well
as for quasars at $z\approx$ 4 (Constantin et al. 2002) indicate that the
feature is very weak in most sources.

The Siii feature at $\lambda$1814 is detected in at least four of the five
quasars studied by Laor et al. (1994). In the 6 objects used for the E1
sequence of Marziani et al. (2010), it is detected without reasonable doubt in
I Zw 1 only. However this has to do more with the poor S/N of the 1900 Å
region than of anything else; good S/N HST spectra show an unambiguous
detection in Akn 120 and Mark 509, for example. Early detection of the UV Siii
lines from IUE observations suggested collisional excitation and no relevant
fluorescence effects (as observed in type Ia supernovæ; Dumont and Mathez
1981). Fluorescence effects and recombination are revealed by optical lines
which are emitted through several cascade routes to the ground state. However,
a median spectrum of A2 quasars with S/N $\approx$ 200 (Zamfir et al. 2010)
barely detects any expected emission feature in the range 4000-6500 Å. The
prominence of the $\lambda$1814 feature may then be associated to the
relatively low temperature believed to exist in the innermost part of the line
emitting “cloud”, $T_{e}\sim 5000-8000^{\circ}$ K. We may consider the
equivalent width ($W$) ratio between the doublet lines at 1264 and at 1814 Å
both due to a ${}^{2}D_{\frac{5}{2}}\rightarrow^{2}P_{\frac{3}{2}}$
transition; in the simplest case we have:
${W_{1263}}/{W_{1814}}\approx\left({N_{\mathrm{u,1264}}}/{N_{\mathrm{u,1814}}}\right)\left({f_{1264}}/{f_{1816}}\right)\left({\lambda_{1264}}/{\lambda_{1816}}\right)^{2}\approx
0.485\frac{f_{1264}}{f_{1816}}e^{-\frac{\Delta E}{kT}}\approx 0.27$ if
$T=5000^{\circ}$, where $f$ is the oscillator strength, $N_{\mathrm{u}}$ are
the density of the upper electronic levels giving rise to the two lines, and
the energy difference between the transitions is $\Delta E\approx$ 3 eV.

###  6.4 Use of Siiv$\lambda$1397, Civ$\lambda$1549 and Siii$\lambda$1814

The same caveats mentioned for the ratio Ciii]$\lambda$1909/
Siiii]$\lambda$1892 apply to the Aliii$\lambda$1860/ Siiii]$\lambda$1892 ratio
as well. The ground term ${}^{1}S_{0}$ has energy 16 eV and 24 eV for Si+2 and
C+2 respectively. A dependence on the ionization parameter is expected, as
already mentioned. However, given the similarity in the ionization structure
of the photo-ionized slab, it is after all not surprising that the ratio
Aliii$\lambda$1860/ Siiii]$\lambda$1892 is almost insensitive to the
ionization parameter over a wide range of density. We remind that the
detection of strong Aliii$\lambda$1860 alone already suggests that we are
considering very high density emitting gas even if metallicity is super-solar.
Simulations indicate that Aliii$\lambda$1860 should increase smoothly with
density and be weakest in canonical BLR if the density is
$n_{\mathrm{H}}$$\sim 10^{9}$ cm-3 (cf. Korista et al. 1997).

The ratio Aliii$\lambda$1860/ Siiii]$\lambda$1892 is therefore diagnosing high
density gas, while the Ciii]$\lambda$1909/ Siiii]$\lambda$1892 ratio covers
the domain of $n_{\mathrm{H}}$$\sim 10^{10}$cm-3. The ratio
Aliii$\lambda$1860/ Siiii]$\lambda$1892 alone is, generally speaking,
insufficient to determine $n_{\mathrm{H}}$. A second diagnostic ratio is
needed to constrain $U$ and to unambiguously derive $n_{\mathrm{H}}$. We
consider Siii$\lambda$1814/ Siiii]$\lambda$1892, Civ$\lambda$1549/
Siiii]$\lambda$1892, Siiv$\lambda$1397/ Siiii]$\lambda$1892 as three
diagnostic ratios suitable for constraining $U$.

The Siii$\lambda$1814 doublet is conveniently placed, although weak or
undetectable in most sources. The Siii$\lambda$1814/ Siiii]$\lambda$1892 ratio
is anti-correlated with $U$ in a regular form, as our cloudy  simulations
show, especially for $\log U\lesssim-2$, and for density not much above the
critical density of Siiii]$\lambda$1892\. The behavior of the ratio
Siii$\lambda$1814/ Siiii]$\lambda$1892 resembles the distribution of
Ciii]$\lambda$1909/Civ$\lambda$1549 in the plane ($n_{\mathrm{H}}$, $U$) which
shows a very regular dependence and a smooth anti-correlation with $U$ until
the collisional quenching of Ciii]$\lambda$1909 sets on. However, the IP of
Si0 is just 8 eV. The majority of the $\lambda$1814 doublet is emitted in the
partially ionized zone (PIZ) near the hydrogen ionization front. Fig 10
(bottom panel) shows the behavior of the volume emissivity $\epsilon$ times
the geometrical depth within an emitting slab of gas as a function of the
depth itself. Since the actual line emission is proportional to $\epsilon\cdot
h$ reported in Fig. 10, the emission of the Aliii$\lambda$1860, and
Siiii]$\lambda$1892 lines is negligible in the PIZ, but the one of H$\beta$
certainly is not, and may be well dominating if $N_{\rm c}$$\gg 10^{23}$cm-2.
Significant emission in the PIZ is expected also for the Siii$\lambda$1814
doublet. However, for this latter line, total emission should not depend
strongly on column density, since the emissivity becomes very low at $N_{\rm
c}$$\gtrsim 10^{23}$cm-2. If higher $N_{\rm c}$ are considered (up to
1025cm-2), ratios including Siiii]$\lambda$1892, Aliii$\lambda$1860, and
Siii$\lambda$1814 show a very weak dependence on column density, with changes
a few percent at worst.

We attempted to isolate a Civ$\lambda$1549 and a Siiv$\lambda$1397 component
that corresponds to the Aliii$\lambda$1860 and Siiii]$\lambda$1892 lines. This
can be a small part of the total Civ$\lambda$1549 and of Siiv$\lambda$1397
emission, but there is no point to consider the whole Civ$\lambda$1549
emission when Civ$\lambda$1549 shows a large blueshift and is much broader
than H$\beta$ (Fig. 5 of Sulentic et al. 2000) and Siiii]$\lambda$1892 and
Aliii$\lambda$1860 (Fig. 2 of Marziani et al. 2010). Taking into account
various sources of ambiguity (mainly uncertainty in the quasar rest frame,
S/N, blending with HeII$\lambda$1640), the Civ$\lambda$1549 BC component we
measure with our fits is constrained within $\pm$ 50% at worst. Thus we find
significant Civ$\lambda$1549 emission from the low-ionization gas, and the
basic assumption is that its Civ$\lambda$1549 profile is the same as the
Aliii$\lambda$1860, Siiii]$\lambda$1892 lines. If one considers the emissivity
behavior, Civ$\lambda$1549 and Siiv$\lambda$1397 are obviously favored within
the fully ionized zone.

The ratio of Civ$\lambda$1549 and Siiv$\lambda$1397 over Ciii]$\lambda$1909 or
over Siiii]$\lambda$1892 increases with ionization parameter in a way that is
roughly independent on density until the collisional quenching of the semi-
forbidden lines sets on (Fig. 9). The previous considerations are helpful to
understand why the Civ$\lambda$1549 and Siiv$\lambda$1397 ratios provide clear
diagnostics of the ionization parameter and seem to be in (at least
qualitative) agreement with ratios employing lower ionization lines like
Siii$\lambda$1814/ Siiii]$\lambda$1892 that is also mainly sensitive to $U$.
The striking fact that the Civ$\lambda$1549 and Siiv$\lambda$1397 emission
confirms low-ionization supports the hypothesis that the four lines are
emitted by the same region. The ratios involving Si only have the obvious
advantage that the the determination of the physical parameters is not
dependent on metallicity; the drawback of Siiv$\lambda$1397 is that this line
is weaker and blended with Oiv]$\lambda$1402\. However, as already pointed
out, the Siiv$\lambda$1397 BC intensity should be slightly affected by
Oiv]$\lambda$1402\.

##  7 Results on two Extreme, Elucidating Cases

We analyze two extreme objects – one extreme Pop. A and one extreme Pop. B –
with the same methodology we used previously. The aim of this analysis is to
help the interpretation of the line components measured on the spectra of the
8 $z\approx$3 quasars.

###  7.1 SDSS Weak Ciii]$\lambda$1909 source: SDSS J120144.36+011611.6

Our project stems from the careful analysis of the I Zw 1 UV spectrum by Laor
et al. (1997b), and the evidence of a well-defined trend in the $\lambda$1900Å
blend along the E1 sequence (Aoki & Yoshida 1999, Wills et al. 1999, Bachev et
al. 2004, Marziani et al., 2010). The NLSy1 I Zw 1 is known to be a sort of
extremum in the E1 sequence: it shows strong Feii and Feiii, prominent
Aliii$\lambda$1860 and Siiii]$\lambda$1892 emission. It is an example of the
A3 spectral type, whose median 1900Å blend in shown in Fig. 3 of Bachev et al.
(2004). Definitely, these sources are present also at intermediate to high
redshift. We describe here the analysis of one source, SDSS
J120144.36+011611.6 (Fig. 8), which seems to be a high-redshift, high-
luminosity replica of I Zw 1, with broader lines (the FWHM limit of NLSy1s and
Pop. A sources is luminosity dependent; see Netzer & Trahktenbrot 2007 and
Marziani et al. 2009). These sources are Pop. A, and we assume that the
profile of the BC is Lorentzian. Hereafter unshifted Lorentzian part of the
line is said to be BC. Pop. A sources are also free of any VBC, making the
analysis of the blend simpler.

Several considerations can be made from Fig. 8.

##### Aliii$\lambda$1860

The lines less ambiguous to measure are the Aliii$\lambda$1860 doublet because
the two lines are less blended with other features, and they are remarkably
strong. Siiii]$\lambda$1892 is more heavily blended with Ciii]$\lambda$1909
and Feiii. However, the specfit routine allows usually a plausible
deconvolution of Siiii]$\lambda$1892, making the Aliii$\lambda$1860/
Siiii]$\lambda$1892 ratio very reliable. Feii and Feiii are obviously strong.
We can use Feii UV 191 to set roughly the level of Feii, while the feature at
2080Å is helpful to estimate intensity of Feiii.

##### Feiii

Our specfit analysis produces a very weak Ciii]$\lambda$1909 component. A
precise measurement of Ciii]$\lambda$1909 is cumbersome, since its intensity
depends on the actual Feiii emission. The strong feature at $\lambda$1914
could be dominating, and the template may seriously underestimate it (see
Vestergaard and Wilkes 2001 for several alternatives in the empirical Feiii
emission of I Zw 1). In any case the residual Ciii]$\lambda$1909 emission is
small, suggesting that the $\lambda$1900 blend, once believed to be mostly
Ciii]$\lambda$1909, is actually almost void of Ciii]$\lambda$1909 emission in
these A3-type sources.

##### Siii$\lambda$1814

The Siii$\lambda$1814 line is well visible in the spectrum of SDSS
J120144.36+011611.6 and can be used as a substitute of Civ$\lambda$1549 to
measure the ionization parameter. The ratio Siii$\lambda$1814/
Siiii]$\lambda$1892 is mainly sensitive to the ionization parameters, as it is
the ratio Civ$\lambda$1549/ Siiii]$\lambda$1892\. The ratio Siii$\lambda$1814/
Siiii]$\lambda$1892 has the considerable advantage of being weekly dependent
on metallicity. If metallicity is known (see also §8.1), the ratio
Civ$\lambda$1549/Aliii$\lambda$1860 should be in principle preferred since
Aliii$\lambda$1860 is emitted through a permitted resonance transition while
Siii$\lambda$1814 is emitted in the collisionally excited, partially-ionized
zone (PIZ).

#####  Civ$\lambda$1549

We fit Civ$\lambda$1549 with a Lorentzian component that is unshifted + a
Civ$\lambda$1549 BBC. Note that the lack of shift in Aliii$\lambda$1860 and
Siiii]$\lambda$1892 imposes a strong, determinant condition on the strength of
the Lorentzian-component in Civ$\lambda$1549\. It is important to stress that
some Civ$\lambda$1549 BC emission is expected to be present according to our
array of simulations. The ratio Civ$\lambda$1549/Aliii$\lambda$1860 is rather
modest, as we can easily see even by eye. We note in passing that the with of
BCC is $\approx 10000$ km s-1, with a peak blueshift indicatively of $-6000$km
s-1, significantly larger than the one measured on the Civ$\lambda$1549 of I
Zw 1 by Marziani et al. (2009).

##### Siiv$\lambda$1397

We fit Siiv$\lambda$1397 with a Lorentzian component that is unshifted + a BBC
(that may include Siiv$\lambda$1397 and Oiv]$\lambda$1402 contribution).
Results that are consistent with the ones of Civ$\lambda$1549\. The ratio
Siiv$\lambda$1397/ Siiii]$\lambda$1892 has the advantage that is almost
independent on metallicity. In principle, the crossing point between the
Siii$\lambda$1814/ Siiii]$\lambda$1892 and Siii$\lambda$1814/
Siiii]$\lambda$1892 can set a metallicity independent point in the
($n_{\mathrm{H}}$, $U$) plane. If the accuracy of the Siii$\lambda$1814
intensity is good then this point can be used to retrieve information on
metallicity (§8.1).

We consider the measured line ratios in the plane $U$ vs. $n_{\mathrm{H}}$
(initally assuming metallicity equal to solar), and see where they cross. We
find very high density and low ionization (Fig. 11).

####  7.1.1 Along the E1 Sequence: A More Complex Scenario

Looking at the fit solution (Fig. 8(b)), it seems that our spectrum has almost
no Ciii]$\lambda$1909\. In many ways this is not surprising. The physical
solutions in the ($U$, $n_{\mathrm{H}}$) plane of Fig. 11, points toward very
low ionization ($U\sim 10^{-3}-10^{-2}$) and high density
($n_{\mathrm{H}}$$\gtrsim 10^{12}$cm-3). At such high values of
$n_{\mathrm{H}}$ we expect that Ciii]$\lambda$1909 is collisionally quenched,
and no significant emission. The ratio Ciii]$\lambda$1909/Civ$\lambda$1549 is
expected to be just $\sim$ 10-2 in the dense LIL-BLR. Therefore we can say
that sources like SDSS and I Zw 1 are extreme because all of the
$\lambda$1900Å blend is emitted by very low ionization, dense gas.

However, as soon as we move away from spectral types A3+ along the E1
sequence, we see that the prominence of Aliii$\lambda$1860 diminishes greatly.
The emission disappears altogether at the other end of the E1 sequence, where
several lobe-dominated radio-loud sources are found. For most quasars we see
that Ciii]$\lambda$1909 is rather strong and unmistakably present. At a first
glance this complicates the interpretation of the spectrum. However, one has
to consider that Ciii]$\lambda$1909 can be emitted only by gas of much lower
$n_{\mathrm{H}}$ than that of the region where the bulk of Siiii]$\lambda$1892
and Aliii$\lambda$1860 is emitted. Our simulations show that
Aliii$\lambda$1860 intensity grows smoothly as a function of density in the
ionization parameter range of interest $-3\lesssim\log U\lesssim-1$. This
said, and considered the smooth trend we see from A3 to B1+, the most
reasonable conclusion is that a dense region emits significantly whenever
Aliii$\lambda$1860 emission is detected, although the relative prominence of
the dense BC changes along the E1 sequence: it accounts for the entire LIL
emission only in the most extreme Pop. A sources. The sequence of Fig. 3 of
Bachev et al. (2004) seems to be mainly a sequence of prominence of
Aliii$\lambda$1860+ Siiii]$\lambda$1892 vs Ciii]$\lambda$1909.

So, a very important conclusion is that a very dense, low-ionization region
exists in the wide majority of quasars. It is associated with Feii prominence,
as such gas is expected to emit a strong low-ionization spectrum. The most
extreme Feii emitters are also the most extreme Aliii$\lambda$1860 emitters;
in some cases where no Aliii$\lambda$1860 emission is measured, we also fail
to detect any Feii emission (Marziani et al. 2010). Where is this region
located? Why there are such distinctive line profiles as Lorentzian? The
second issue goes beyond the present paper; for the moment our aim is to
measure line components of Aliii$\lambda$1860, Siii$\lambda$1814,
Siiii]$\lambda$1892 and Civ$\lambda$1549 that come from this region and to
estimate its distance from the central black hole (§9).

###  7.2 The Other E1 Extremum: 3C 390.3

3C 390.3 is a lobe-dominated (LD) RL source, with very broad emission lines
and no optical Feii within detection limits (see Marziani et al. 2003, for the
criterion used). It also shows a large peak shift in its H$\beta$ profile, and
prominent narrow lines ([Oiii]$\lambda$5007, H$\beta$), but also narrow
components of Civ$\lambda$1549 and Ciii]$\lambda$1909 which are all well
separated from the broad H$\beta$ profile.

To deconvolve the blends around Ciii]$\lambda$1909 and Civ$\lambda$1549, we
assume the same emission line profiles as for H$\beta$. The H$\beta$ broad
profile can be described as the sum of a BC and a VBC. An unusual property of
the BC is its large peak blueshift (it is unusual because of the shift
amplitude: even if median spectra of Pop. B sources show a small BC redshift,
there is a pretty large scatter with both red- and blueshifted peaks observed
in individual sources; Zamfir et al. 2010). Applying in a self consistent way
the BC and VBC to the Ciii]$\lambda$1909 and Civ$\lambda$1549 blends, leads to
very interesting results as shown in Figure 8:

  * $\bullet$

Aliii$\lambda$1860 is very weak or even absent within the S/N limits;

  * $\bullet$

the Civ$\lambda$1549 profile is very similar to the one of H$\beta$: BC+VBC
accounts for more than 90% emission, with a possible, very weak contribution
of the blueshifted component which is usually dominating in Pop. A sources;

  * $\bullet$

the red wing observed in the 1900Å blend is accounted for only if there is a
strong Ciii]$\lambda$1909 VBC, Feii and Feiii emission being below the
detectability limit in this source;

  * $\bullet$

there is no evidence of a VBC in Aliii$\lambda$1860;

  * $\bullet$

the ratio Civ$\lambda$1549/Ciii]$\lambda$1909 BC is $\approx$ 10, a far cry
from the ratios observed in extreme Pop. A sources like I Zw 1 and SDSS
J120144.36+011611.6;

  * $\bullet$

even more interesting we find a Civ$\lambda$1549/Ciii]$\lambda$1909 VBC
$\approx$10, as for the BC.

We conclude that this object is fundamentally different from Pop. A sources.
The low ionization, high density BC seems to be absent. The similarity in the
Civ$\lambda$1549/Ciii]$\lambda$1909 ratios suggest that we are observing a gas
in conditions similar to the one associated to the VBC. We predict that Feii
will remain undetected or found to be weak even with S/N $\rightarrow\infty$.

In the plane ($U$, $n_{\mathrm{H}}$) of Figure 11, the line ratios converge to
a point at $\log U\approx$ -1.5, and log $n_{\mathrm{H}}$$\approx$ 10.1 (the
Siii$\lambda$1814 line cannot be measured accurately since S/N is poor). In
this case, the Ciii]$\lambda$1909/Civ$\lambda$1549 ratio also converges toward
a ($U$, $n_{\mathrm{H}}$) value consistent with the one indicated by the
Aliii$\lambda$1860/Siii$\lambda$1814\. In most other cases, this does not
happen because the Aliii$\lambda$1860 doublet is too strong to be accounted
for by gas of $n_{\mathrm{H}}$$\sim 10^{10}$cm-3 even at super-solar
metallicity. Emission occurs at pretty high ionization, in conditions that
once upon a time were thought to be standard in quasars (Davidson and Netzer
1979). This Pop. A and B difference at the extrema was already pointed out, in
a semi-quantitative way, by Sulentic et al. (2000) and Marziani et al. (2001).

It is however important not to generalize the case of 3C 390.3 to the
remaining Pop. B sources. In most of them, Aliii$\lambda$1860 is detected, and
there is evidence of strong Ciii]$\lambda$1909\. Actually Ciii]$\lambda$1909
emission seems to be appreciable in all of our VLT quasars. This means that we
are in a composite situation, where low-ionization, high-density emission is
present, along with significant VBC and other emission. The two extreme cases
help us however to understand these more complex cases.

###  7.3 The Contribution of Lower Density Gas

Once the true intensity of the BC components is retrieved, the presence of
significant Ciii]$\lambda$1909 emission complicates the analysis. As pointed
out, the photoionization solution for the BC suggests very high density, and
in this region no Ciii]$\lambda$1909 emission is expected. Whenever
Ciii]$\lambda$1909 is observed, we need to reverse the question: how much does
any Ciii]$\lambda$1909 emitting gas contributes to the lines used for
diagnostic ratios? Negligible contribution is expected to Aliii$\lambda$1860\.
However, this is not true for Civ$\lambda$1549 and Siiii]$\lambda$1892\.
Especially among Pop. A2 and A3 objects, it is not so obvious that the profile
of Ciii]$\lambda$1909 and Siiii]$\lambda$1892 is the same. It could be well
that the Ciii]$\lambda$1909 profile is narrower than the ones of
Siiii]$\lambda$1892 and Aliii$\lambda$1860 (as found for SDSS J1201+0116),
justifying the idea of Ciii]$\lambda$1909 emission from a disjoint region
(§6.2). For the BAL QSOs in our sample and Aliii$\lambda$1860-strong sources
most of what we ascribe to Ciii]$\lambda$1909 could be actually Feiii, as
suggested by Hartig and Baldwin (1986).

However, objects like the typical A1 sources show Siiii]$\lambda$1892 and
Ciii]$\lambda$1909 with similar profiles, so in the following we will assume
the worst condition, that is all Ciii]$\lambda$1909 emitting gas is
contributing to the BC lines.

To estimate the contribution of the Ciii]$\lambda$1909 emitting gas to
Siiii]$\lambda$1892 and Civ$\lambda$1549, we can consider the trends observed
along E1. Siiii]$\lambda$1892 is strong when Aliii$\lambda$1860 is strong, and
the Siiii]$\lambda$1892/ Ciii]$\lambda$1909 ratio is lower when
Ciii]$\lambda$1909 is strong, as visible in both Baldwin et al. (1996) and
Bachev et al. (2004), as well as in the present paper. The observed
Siiii]$\lambda$1892/Ciii]$\lambda$1909 ratio in the A1 median bin seems to be
as low as in Mark 335, $\approx 0.4$. Pop. B sources that often show prominent
Ciii]$\lambda$1909 also show a low Siiii]$\lambda$1892/Ciii]$\lambda$1909
ratio, as also appreciable in the median spectra of Bachev et al. (2004).
These trends suggest that most Siiii]$\lambda$1892 is emitted where
Aliii$\lambda$1860 is also emitted. As a consequence, any correction due to
gas in different physical conditions (lower density) emitting
Siiii]$\lambda$1892 is expected not to be dominant unless Ciii]$\lambda$1909
is extremely strong. The Ciii]$\lambda$1909 emitting gas should be at density
$\log n\sim\ 9$, or lower. Higher density would imply increasing
Siiii]$\lambda$1892/Ciii]$\lambda$1909 to values that would exceed the
observed ones even if the LIL-BC is not emitting any significant
Siiii]$\lambda$1892 (see Fig. 13).

####  7.3.1 Preliminary analysis of a low-$z$ sample

To set these trends on a more quantitative basis we considered the set of pre-
costar recalibrated sources, for which Ciii]$\lambda$1909 and Civ$\lambda$1549
data are publicly available (Kuraszkiewicz et al 2002, Evans & Koratkar
2004).We performed measurements (interactively with the task splot of iraf)
for about $30$ sources with the highest S/N, holding a Ciii]$\lambda$1909
blend that could be relatively easily deblended, and following the
expectations described in §4.4. The rest frame equivalent width of
Aliii$\lambda$1860 and Siiii]$\lambda$1892 are found to be highly correlated
(Fig. 12). The correlation is due to Siiii]$\lambda$1892 being stronger when
Aliii$\lambda$1860 is strong, not necessarily because Ciii]$\lambda$1909 is
strong: actually, the Siiii]$\lambda$1892/Ciii]$\lambda$1909 ratio can be low
when Ciii]$\lambda$1909 is strong, and the Aliii$\lambda$1860/
Siiii]$\lambda$1892 ratio achieves maximum values when Ciii]$\lambda$1909 is
faintest. This is consistent with the bulk of Aliii$\lambda$1860 and
Siiii]$\lambda$1892 originating in the same region. At the same time the
presence of Ciii]$\lambda$1909 lowers the Aliii$\lambda$1860/
Siiii]$\lambda$1892, Civ$\lambda$1549/ Siiii]$\lambda$1892 and
Siiv$\lambda$1397/ Siiii]$\lambda$1892 because of “excess” Siiii]$\lambda$1892
emission associated to the gas emitting Ciii]$\lambda$1909\.

####  7.3.2 The effect of low-density gas on the product ($U$$n_{\mathrm{H}}$)

We expect that any correction will increase density (increase
Aliii$\lambda$1860/ Siiii]$\lambda$1892 lowering Siiii]$\lambda$1892) and
decrease ionization parameter (lowering Civ$\lambda$1549 more than
Siiii]$\lambda$1892), but that their product will be less affected. To show
the amplitude of the effect we performed an experiment, adding to a pure,
high-density solution, contribution from moderate density gas ($\log$
$n_{\mathrm{H}}$$\sim 9-10$). The Fig. 14 shows the displacement in the
density – ionization parameter plane for several values of the
Ciii]$\lambda$1909/ Siiii]$\lambda$1892 intensity ratio. The values refer to
the Ciii]$\lambda$1909 addition over Siiii]$\lambda$1892 in the ideal case,
corresponding to observed ratios of 0.34, 0.7, 1.0, 1.1 for an addition of a
Ciii]$\lambda$1909 component whose intensity is 0.4, 1.0 ,1.5 ,2.0 the
intensity of the Siiii]$\lambda$1892 component associate to the high density
gas. As one can see from the figure, even if deviation for $U$ and
$n_{\mathrm{H}}$ taken separately are significant, deviations for the product
are by far less important. The largest change for the product is found to be
$\approx$ 0.15, if we exclude the gray dots corresponding to $\log$
$n_{\mathrm{H}}$= 10 (an unlikley case, since this would imply a correction
Siiii]$\lambda$1892/Ciii]$\lambda$1909 $>$ 1, inconsistent with what we
observe when Ciii]$\lambda$1909 is strong). Following the expected line ratios
of Fig.13 we apply a correction to the BC fluxes that is 0.4 and 1.5
Ciii]$\lambda$1909 for Siiii]$\lambda$1892 and Civ$\lambda$1549 respectively
(Figures 15, 16 and 11), corresponding to $\log U=-2$ and
$\log$$n_{\mathrm{H}}$= 9. We remark that that if $U$ is lower, the correction
will have negligible effect, while assuming a larger $U$ will lead to
Civ$\lambda$1549 flux in excess to the one observed.

To constrain the ionization parameter we can first consider that, since the
Ciii]$\lambda$1909 gas comes from a (relatively) low density region, the
contribution to Siii$\lambda$1814 is small: for $\log n\sim\ 9$ and $\log
U\approx-2$, the contribution should be $\approx 0.03$ Ciii]$\lambda$1909\.
Second, another powerful feature is the Siiv$\lambda$1397 doublet (Baldwin et
al. 1996): the Siiv$\lambda$1397 doublet is less affected by the
Ciii]$\lambda$1909 correction, the contribution from lower density gas being
estimated $\approx$ 0.25 Ciii]$\lambda$1909\. The line ratio
Siiv$\lambda$1397/Aliii$\lambda$1860 is also sensitive to ionization and less
affected by any lower density correction (provided that the relative abundance
of S and Al stays the same, as it seems to be the case).

In summary, corrected BC line intensities are computed as follows:
$I^{\mathrm{c}}$(Siii$\lambda$1814)BC = $I$(Siii$\lambda$1814)BC – 0.03
$I$(Ciii]$\lambda$1909)BC; $I^{\mathrm{c}}$( Siiii]$\lambda$1892)BC = $I$(
Siiii]$\lambda$1892)BC – 0.4 $I$(Ciii]$\lambda$1909)BC;
$I^{\mathrm{c}}$(Siiv$\lambda$1397)BC = $I$(Siiv$\lambda$1397)BC – 0.26
$I$(Ciii]$\lambda$1909)BC; $I^{\mathrm{c}}$(Civ$\lambda$1549)BC =
$I$(Civ$\lambda$1549)BC – 1.5 $I$(Ciii]$\lambda$1909)BC.

##  8 Results on the $z\approx$ 3 Quasars

To estimate $\log$$n_{\mathrm{H}}$ and $\log U$ values, we use the cloudy
contour plots of the ratios Aliii$\lambda$1860/ Siiii]$\lambda$1892,
Siii$\lambda$1814/ Siiii]$\lambda$1892, Civ$\lambda$1549/ Siiii]$\lambda$1892,
Siiv$\lambda$1397/ Siiii]$\lambda$1892 showed in Fig. 9222Note that there are
regions where the ratio values are actually undefined: close to the high $U$
limit ($\log U\gtrsim-0.3$), ratios Aliii$\lambda$1860/ Siiii]$\lambda$1892
and Siii$\lambda$1814/ Siiii]$\lambda$1892(with $n_{\mathrm{H}}$$\lesssim
10^{9}$cm-3) should not be considered.. The data points of our objects are in
regions were the ratios are well-defined. The ratios Civ$\lambda$1549/
Siiii]$\lambda$1892, Siiv$\lambda$1397/ Siiii]$\lambda$1892, and
Siii$\lambda$1814/ Siiii]$\lambda$1892 are mainly sensitive to the ionization
parameter $U$, while Aliii$\lambda$1860/ Siiii]$\lambda$1892 and
Ciii]$\lambda$1909/ Siiii]$\lambda$1892 are mainly sensitive to the electron
density. We know that Ciii]$\lambda$1909 is collisionally quenched at $\log$
$n_{\rm e}$$\gtrsim$ 10 and in the contour plot for Ciii]$\lambda$1909/
Siiii]$\lambda$1892 we see a step around this value.

We measure the BC intensity of Siiii]$\lambda$1892, Aliii$\lambda$1860,
Siii$\lambda$1814, Siiv$\lambda$1397 and Civ$\lambda$1549; with them we
compute the diagnostic ratios (for 3C390.3 we use Ciii]$\lambda$1909 in place
of Siii$\lambda$1814; however there is no object similar to 3C390.3 among the
$z\approx$ 3 quasars). We present the fluxes of the line components in Tab. 3
and the equivalent width in Tab. 5. Table 4 shows the weak lines around
Civ$\lambda$1549\. For Civ$\lambda$1549 line we show the core, blue shifted
and the very broad components. Errors are at a $2\sigma$ confidence level, and
include the sources of uncertainty described in §4.5. Errors are then
quadratically propagated according to standard practice to compute intensity
ratios and their logarithm.

From Table 3 we can derive the diagnostic ratios. As we see in Fig. 1,
Siii$\lambda$1814 is absorbed by telluric B band in J00103-0037, J03036-0023,
J20497-0554 (most affected). We will not consider Siii$\lambda$1814 to compute
$n_{\mathrm{H}}$ and $U$ on those cases. However, if we take at face value the
Siii$\lambda$1814 measure on J00103-0037 and J20497-0554, it will converge
close to the point set by the remaining two ratios. We display on a graph a
line representing the behavior of each ratio under the assumption of solar
metallicity; the ideal point where the lines representing different diagnostic
ratios cross determines the values of $\log$$n_{\mathrm{H}}$ and $\log U$.
Figs. 15 and 16 shows the contour plots were we can see that the diagnostic
ratios converge to rather well defined values. The cross point is very precise
for the objects J00103-0037, J00521-1108, J02287+0002 (using $z_{CIII}$), and
J20497-0554 ; for the remaining objects J01225+1339, J02287+0002 (using
$z_{OI}$), J02390-0038, J03036-0023, and J23509-0052 the cross point is
slightly different. We must not forget the errors involving the fits, such as
the changing of the shape profile that makes large the peak intensity if is
Lorentzian or it could be less intense if it is Gaussian; the Feii pseudo-
continuum contribution that affects principally to Siii$\lambda$1814 or the
Feiii that in some cases affects Ciii]$\lambda$1909.

In principle, the crossing point of the ratios Siiv$\lambda$1397/
Siiii]$\lambda$1892 and Siii$\lambda$1814/ Siiii]$\lambda$1892 is independent
on metallicity. Therefore, any significant disagreement between this crossing
point and the ratios based on Civ$\lambda$1549 may indicate chemical
composition different from the assumed solar one (§8.1). The difficulty here
is the large uncertainty of the Siii$\lambda$1814 line. In all contour plots
we show the $\pm 2\sigma$ interval as a shaded band. So, it is proper to
consider deviations from metallicity only in the case of 4 sources where the
crossing point excluding Siii$\lambda$1814 is outside the uncertainty band.

For the objects J00103-0037, J03036-0023 and J20497-0554 we exclude the
Siii$\lambda$1814 line from the diagnostic ratios because it is affected by
absorption. For the remaining objects, we take the average of the crossing
contour plots of $\log$(Aliii$\lambda$1860/ Siiii]$\lambda$1892) crossing with
$\log$(Civ$\lambda$1549/ Siiii]$\lambda$1892) and $\log$(Aliii$\lambda$1860/
Siiii]$\lambda$1892) crossing with $\log$(Siii$\lambda$1814/
Siiii]$\lambda$1892). For 3C390.3 we use $\log$(Ciii]$\lambda$1909/
Siiii]$\lambda$1892) instead of $\log$(Siii$\lambda$1814/
Siiii]$\lambda$1892). Table 6 summarizes the $\log n_{\mathrm{H}}$ and $\log
U$ values including their uncertainty. Since $U$ and $n_{\mathrm{H}}$ are not
independent quantities (their correlation coefficient is found to be 0.55), we
adopt the appropriate formula for the errors on the product
$U$$n_{\mathrm{H}}$ (following Bevington 1969). We present average values of
the crossing points for extreme objects of Fig. 11 and 18(d). In the SDSS
J12014+0116 case we give full weight to the Siii$\lambda$1814 measurement. The
crossing points disagree somewhat for SDSS J12014+0116. This could be due to
an underestimate of both Siii$\lambda$1814 and Civ$\lambda$1549 in the fits.
On the one hand, Siii$\lambda$1814 is clearly seen and strong but is
contaminated by Feii blend; on the other hand, Civ$\lambda$1549 is strongly
affected by the blue-shifted component and by the assumption that it is of
Gaussian shape. An increase by 30% in the measurement of the intensity of the
two line would lead to a better agreement but this is somewhat an ad-hoc
speculation. Rather, the significant difference between the crossing point of
the Siii$\lambda$1814/ Siiii]$\lambda$1892 and Siiv$\lambda$1397/
Siiii]$\lambda$1892 ratios and the other ones point toward strong metal
enrichment. We will show in §8.1 that this is probably the case.

At any rate, the convergence is toward a value of $\log U\approx-3$, lower
than for the other $z\approx$3 quasars. This is reflected in the
Civ$\lambda$1549 EW of this source, also significantly lower. It is intriguing
to note that the correction because of lower density drives the other sources
toward values of $U$ and $n_{\mathrm{H}}$ that are closer to the ones of SDSS
J12014+0116.

Table 7 reports the values of the $r_{\rm BLR}$ and the $M_{\rm BH}$ of our 8
objects and the extreme objects in the last two rows. Column 1 identifies the
quasar name; Col. 2 gives the quasar proper distance in mega parsecs [Mpc];
Cols. 3 and 4 are the continuum specific flux value at 1350Å and 1700Å
respectively, Col. 5 reports the FWHM in km s-1 for the broad components, Col.
6 is the Population designation. Cols. (7) to (10) report the logarithm of the
size of the BLR in cm obtained from: a) $1Z_{\odot}$, b) $1Z_{\odot}$ line
ratios corrected because of low density emission, c) $5Z_{\odot}$, and d)
$5Z_{\odot}$ line ratios corrected because of low density emission. Cols. (11)
-(14) list the logarithm of the black hole mass in solar masses in the same
order as for $r_{\rm BLR}$. Finally Col. (15) is $M_{\rm BH}$ computed from
Vestergaard and Peterson (2006) formula (Equation 10). We will explain in §10
how these quantities are computed.

###  8.1 Effects of Metallicity

The strength of Nv$\lambda$1240 relative to Civ$\lambda$1549 and
Heii$\lambda$1640 suggests supersolar chemical abundances (Hamann and Ferland
1993; Hamann & Ferland 1999). Chemical abundances may be well 5 to 10 times
solar (Dhanda et al. 2007), with Z $\approx$ 5$Z_{\odot}$ reputed typical of
high $z$ quasars (Ferland et al. 1996). The E1 sequence seems to be mainly a
sequence of ionization in the sense of a steady decrease in prominence of the
low-ionization BC toward Population B (Marziani et al. 2001, 2010). However,
this is not to neglect that metal-enrichment also plays a role, especially for
the most extreme Pop. A sources i.e., those in bin A3 and higher (Sulentic et
al. 2001).

The lines employed in the present study come from carbon, silicon and
aluminium; all these element can be significantly depleted from gas if dust
grains are formed (e. g., Mathis 1990). However, the emitting regions where
our lines are produced are thought too hot to contain significant amount of
dust (a definition of broad line region is right the central engine region
below the dust sublimation region: e.g., Elitzur 2009). In addition Si and Al
are expected to be produced under similar circumstances in the late stage of
evolution of massive stars (Clayton 1983, Ch. 7). We note also that the
Civ$\lambda$1549/ Siiii]$\lambda$1892 and Civ$\lambda$1549/Aliii$\lambda$1860
usually give results that are in perfect agreement in the plane
($n_{\mathrm{H}}$,$U$). These findings support our assumption that, if
metallicity variations are present, the relative abundance Al to Si remains
constant. We considered two cases for enhanced metallicity: (1) constant solar
abundance ratio Al:Si:C with $Z=5Z_{\odot}$ (5Z) ; (2) an overabundance of Si
with respect to carbon by a factor 3, again with $Z=5Z_{\odot}$ (5ZSA). This
condition comes from the yields listed by Woosley and Weaver (1995) from type
II Supernovæ. 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 simulated using Starburst
99 (Leitherer et al. 1999). The abundance of Al should scale roughly with the
one of Si. While some cases with Al scaling with C are possible from the
Woosely and Weaver (1995) yields, they are rarer than cases in which Al scales
with Si. This latter case is appropriate for the most massive progenitors.
Also, the assumption of Al scaling with C with [Si/C] = 0.477 would yield to
implausible high density and lack of convergence to a well-defined solution
for $\log$$n_{\mathrm{H}}$$\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}14$. We therefore assume in the
following that Al scales with Si in the two cases listed above.

An array of simulations as a function of ionization parameter and density was
computed assuming the conditions (1) and (2) listed in the previous paragraph.
As expected, if the solar metallicity is simply scaled by a factor (5Z) we
find that the ratio Aliii$\lambda$1860/ Siiii]$\lambda$1892 is not strongly
dependent on $Z$: the ratio increases by about 40% passing from $Z=1Z_{\odot}$
to $Z=5Z_{\odot}$, for $\log$$n_{\mathrm{H}}$$\approx 12$ and $\log
U\approx$–2. The same is true for the Siii$\lambda$1814/ Siiii]$\lambda$1892
and Siiv$\lambda$1397/ Siiii]$\lambda$1892 ratios. Since the first ratio sets
$n_{\mathrm{H}}$, and the last two $U$, the ratios mentioned in this paragraph
should be preferred because they provide $n_{\mathrm{H}}$ and $U$ values that
are weakly affected by a factor 5 change in metallicity. A posteriori we
confirm that the effect on the product $U$$n_{\mathrm{H}}$ derived also with
ratios involving Civ$\lambda$1549 is negligible in case 5Z (and it should be
even more so if a metallicity increase is $Z_{\odot}\lesssim Z\lesssim
5Z_{\odot}$).

The two extreme cases seem to be revealing also as far as metallicity is
concerned. Ratios converge to a fairly well defined point in the case of 3C
390.3 (see Fig. 11, left panel, $Z=1Z_{\odot}$ assumed). In this case there is
no major evidence of supersolar metallicity. The converse is true in the case
of SDSS J120144.36+011611.6. The ratios involving Civ$\lambda$1549 indicate a
lower ionization level, with $\log U\sim-3$. This is because C3+ changes
ionization state to C2+ for smaller ionization parameters, and so
Civ$\lambda$1549 rapidly disappears. The Civ$\lambda$1549 intensity depends
weakly on $Z$ while the Aliii$\lambda$1860 and Siiii]$\lambda$1892 lines are
more sensitive. The 5Z case yields values closer to the ones obtained from the
Si and Al line ratios, but not yet in concordance. If we pass to case 5ZSA
with a factor 3 Si overabundance, then the concordance of the line ratios is
good, especially if no correction because of low density emission is applied.
As a further confirmation we checked that the metallicity-dependent
Civ$\lambda$1549/Siiv$\lambda$1397 ratio is in very good agreement with the
crossing point of the other lines. Therefore, in this case, we have
independent measures of metallicity, $n_{\mathrm{H}}$, and $U$. The case of
even higher metallicity, say $Z\sim 10Z_{\odot}$, remains to be explored but
may not be appropriate considering the good agreement with 5ZSA.

In principle, the discrepancy in the intersection point, with
Siiii]$\lambda$1892/Civ$\lambda$1549 and Aliii$\lambda$1860/Civ$\lambda$1549
yielding lower $U$ than the Al-Si ratios, should signal a significant
enrichment in Si and Al of the BLR gas. In this case the
Siiv$\lambda$1397/Civ$\lambda$1549 ratio should be helpful, as it can be
assumed to be dependent mainly on the Si abundance relative to C. Here, more
than precisely determining the exact abundance value we are interested in
analyzing the effect of large metallicity changes on $U$, $n_{\mathrm{H}}$,
and their product. Appreciable discrepancy is visible in the contour plots of
the BAL quasar J01225+1339, J03036-0023, J20497-0554 and J23509-0052 if
$Z=Z_{\odot}$ is assumed.

In the same plots made for $Z=5Z_{\odot}$SA, the agreement becomes better (see
Fig. 18). High metallicity yields higher $U$ and smaller $n_{\mathrm{H}}$ if
emission line ratios involving Civ$\lambda$1549 are considered. This reflect
the increase in abudance of Si and Al with respect to C, and the fact the
Siii$\lambda$1814, Siiii]$\lambda$1892, Aliii$\lambda$1860 lines are emitted
at lower ionization than Civ$\lambda$1549\. In the case of sources like
J02390-0038 and J20497-0554, the discrepancy of the crossing lines might
indicate $Z_{\odot}\lesssim Z\lesssim 5Z_{\odot}$, more than the extreme
enrichment like the one assumed in 5ZSA, as also suggested by the
Civ$\lambda$1549/Siiv$\lambda$1397 ratio.

In Fig. 18 and 19 the contour plots are shown for the case 5ZSA. We consider
uncorrected and corrected line ratios as two independent cases. The halftone
bands also show the importance of accurate Siii$\lambda$1814 measurements to
infer unambiguous constrain on metallicity (and, by extension, to estimate
$n_{\mathrm{H}}$ and $U$ independently). The product $n_{\mathrm{H}}$$U$ is
however much less affected than $n_{\mathrm{H}}$ and $U$ individually (Tab.
6).

A first $r_{\rm BLR}$ and $M_{\rm BH}$ estimate can be obtained considering
only the Siii$\lambda$1814/ Siiii]$\lambda$1892 and Aliii$\lambda$1860/
Siiii]$\lambda$1892 ratios. We conclude that the effect of scaling the
metallicity up to $Z=5Z_{\odot}$ is within the uncertainty of the method, and
particularly small if the ratios Siii$\lambda$1814/ Siiii]$\lambda$1892,
Aliii$\lambda$1860/ Siiii]$\lambda$1892, and Siiv$\lambda$1397/
Siiii]$\lambda$1892 are considered to compute $n_{\mathrm{H}}$ and $U$. It is
significant if strong enrichment of Al and Si over C occurs. A more refined
approach could exploit the dependence of Aliii$\lambda$1860/Civ$\lambda$1549
(and Siiii]$\lambda$1892/Civ$\lambda$1549 and
Siiv$\lambda$1397/Civ$\lambda$1549) on $Z$ to build a 3D diagram where
$n_{\mathrm{H}}$, $U$, $Z$ along with Si-Al enrichment can be determined
independently.

###  8.2 Determining the best estimate of $n_{\mathrm{H}}$, $U$

There are two sets of line ratios for each object: one comes from the specfit
results, and the other is the one computed after correcting the specfit
results because of low density contributions. Solutions with corrected value
usually point toward very high density and low ionization, predicting
Siii$\lambda$1814 emission even twice as strong as Siiii]$\lambda$1892\.
However, increasing the metallicity for corrected ratios leads to better
agreement among lines and more reasonable $n_{\mathrm{H}}$, $U$ values, while
leaving the product fairly unaffected. Especially the assumption of Silicon -
Aluminium enrichment improves the concordance in the intriguing cases of SDSS
J12014+0116, J01225+1339, J02287+0002 (using $z_{oi}$), the extreme objects
and the two BAL QSOs in our sample. However, apart from the case of SDSS
J12014+0116, the enrichment is probably excessive. From the discussion above
the independent determination of $n_{\mathrm{H}}$ and $U$ seems possible only
if metallicity is at least roughly known. We exclude metallicity cases where
we find a sizeable disagreement in the crossing points (with the exceptions of
ratios involving Siii$\lambda$1814: the ionization level can be estimated in a
$Z$-independent way using the Siiv$\lambda$1397/Siii$\lambda$1814 and the
Siiv$\lambda$1397). We consider each individual source with line intensity
before and after correction to obtain two independent sets of product
$n_{\mathrm{H}}$$U$ values. As mentioned, changing metallicity is not
affecting the product $n_{\mathrm{H}}$$U$ as much as $n_{\mathrm{H}}$ and $U$
individually. In case of concordance of the crossing points and of high
accuracy in the Siii$\lambda$1814 ratio, $n_{\mathrm{H}}$ $U$, and $Z$ can be
considered independently determined. In Table 6 we indicate the values that
are deemed most appropriate.

##  9 A Photoionization Method to Compute the Broad Line Region Distance and
the Black Hole Mass.

The distance of the broad line region ($r_{\rm BLR}$) from the central
continuum source and the black hole mass ($M_{\rm BH}$) are key parameters
that let us understand the dynamics of the gas in the emitting region and the
quasar behavior and evolution. In this work we will use a method based on the
determination of $n_{\mathrm{H}}$ and $U$ to compute $r_{\rm BLR}$. Eq. 1 can
be rewritten as

$r_{BLR}=\left[\frac{\int_{\nu_{0}}^{+\infty}\frac{L_{\nu}}{h\nu}d\nu}{4\pi
Un_{\mathrm{H}}c}\right]^{1/2}$ (3)

and also as

$r_{BLR}=\frac{1}{h^{1/2}c}(Un_{\mathrm{H}})^{-1/2}\left(\int_{0}^{\lambda_{Ly}}f_{\lambda}\lambda
d\lambda\right)^{1/2}d_{p}$ (4)

where $h$ is the Plank constant, $c$ is the light speed, $d_{\mathrm{p}}$ is
the proper distance. The integral is carried out from the Lyman limit to the
shortest wavelengths on the rest frame specific flux $f_{\lambda}$. For the
integral we will use two Spectral Energy Distributions (SEDs): one described
by Mathews & Ferland (1987) and one by Laor et al. (1997a), also reproduced in
Fig. 20.

Eq. 4 becomes:

$r_{\rm BLR}\approx 93\cdot(Un_{\mathrm{e}})_{10}^{-\frac{1}{2}}\cdot
f_{\lambda_{0},-15}^{\frac{1}{2}}\tilde{Q}_{H,0.1}^{\frac{1}{2}}\zeta(z,0.3,0.7)~{}~{}\mathrm{ld}$
(5)

where
$\tilde{Q}_{H}=\int_{0}^{\lambda_{\mathrm{Ly}}}\tilde{n}_{\lambda}\lambda
d\lambda$, and $\zeta(z,0.3,0.7)$ is an interpolation function for
$d_{\mathrm{p}}$ as a function of redshift.

$\tilde{Q}_{H}$ is 0.00963 cmÅ in the case the continuum of Laor et al. (1997)
is considered; $\tilde{Q}_{H}\approx$0.02181 cmÅ for Mathews & Ferland (1987).
We use their average value, since the derived $U$ and $n_{\mathrm{H}}$ are not
sensitive to the two different shapes to a first approximation.333Since the
Laor et al. (1997) continuum produces a fewer ionizing photons, the same value
of $U$ is obtained at a smaller distance.

Knowing $r_{\rm BLR}$ we can calculate the $M_{\mathrm{BH}}$ assuming virial
motions of the gas

$M_{\mathrm{BH}}=f\frac{\Delta v^{2}r_{\mathrm{BLR}}}{G}.$ (6)

or,

$M_{\mathrm{BH}}=\frac{3}{4G}f_{0.75}(FWHM)^{2}r_{BLR}$ (7)

with the geometry term $f\approx 0.75$, corresponding to $f_{0.75}\approx 1.0$
(Graham et al. 2011, see also Onken et al. 2004 and Woo et al. 2010). Collin
et al. (2006) suggest that $f$ is significantly different for Pop.A and B
sources; we do not consider here their important result for the sake of
comparison with previous work (§10.2). The resulting $r_{\rm BLR}$ and $M_{\rm
BH}$ are reported in Columns 7 to 14 of Table 7. Errors are at 2$\sigma$
confidence level and have been computed propagating quadratically the major
sources of uncertainty. More precisely, in addition to the error on
$\log$($n_{\mathrm{H}}$$U$), the $r_{\rm BLR}$ determination is affected by
the uncertainty in the spectrophotometry (specific fluxes of Col. 3 of Tab.
7), and errors on the shape of the ionizing continuum. The two SEDs that we
assumed as extreme yield a difference in ionizing photons of a factor 2.2. At
a 2$\sigma$ confidence level this corresponds to an uncertainty of $\pm$0.065
in logarithm. An additional source of uncertainty affects $M_{\rm BH}$ due to
the FWHM determination. Errors on FWHM are quadratically added to the
uncertainty on $r_{\rm BLR}$ in the values reported as $\log$$M_{\rm BH}$
errors.

##  10 Discussion

###  10.1 Previous work

There have been several studies aimed at computing $r_{\rm BLR}$ and $M_{\rm
BH}$. A direct measure of $r_{\rm BLR}$ through reverberation mapping requires
an enormous amount of observational effort and has only been applied to a
relatively small number of quasars: slightly less than 50 objects with
$z\lesssim 0.4$ (Kaspi et al. 2000, 2005, Peterson et al. 2004; Bentz et al.
2010). A second way to measure $r_{\rm BLR}$ uses a less direct method. Kaspi
et al. (2000, 2005) and Bentz et al. (2009) used reverberation mapping results
to find, in an empirical way, a relationship between $r_{\rm BLR}$ and the
optical continuum luminosity at 5100Å,

$r_{\mathrm{BLR}}\propto L^{\alpha}$ (8)

with $\alpha\approx 0.52$. Vestergaard & Peterson (2006) obtained a similar
result for the optical continuum luminosity with an $\alpha\approx 0.50$ and
for the UV continuum at 1350Å, $\alpha\approx 0.53$. These relationships have
been used to compute the $r_{\rm BLR}$ not only for nearby objects, but also
for high redshift, high luminosity objects. There are other works that use
single epoch spectra and the continuum at 3000Å, obtaining an $\alpha\approx
0.47$ (McLure & Jarvis 2002).

We can rewrite Eq. 6 as

$M_{\mathrm{BH}}\propto f\frac{\mathrm{FWHM}^{2}L^{\alpha}}{G}.$ (9)

H$\beta$ is a low ionization strong line whose FWHM has been widely used to
determine the $M_{\rm BH}$ for objects mainly up to $z\lesssim 0.9$; above
this limit IR spectrometers and large telescopes are needed to cover the
redshifted line. For distant objects ($z\sim 2$), an alternative is to use
Civ$\lambda$1549, a high ionization line emitted in the UV. However, this line
should be used with caution because the line is often blueshifted. This means
that at least part of this line is likely emitted in an outflow (Sulentic et
al. 2007; Richards et al. 2010). Thus the estimation of $M_{\rm BH}$ using
FWHM(Civ$\lambda$1549) tend to be systematically higher than those using
FWHM(H$\beta$), especially for objects of Population A.

###  10.2 Comparison with Vestergaard and Peterson (2006)

Vestergaard & Peterson (2006) used the relationship $r_{\mathrm{BLR}}\propto
L^{0.53}$ to obtain the following formula that relates $M_{\rm BH}$ to the
FWHM(Civ$\lambda$1549) and the continuum luminosity at 1350Å:

$\log M_{\mathrm{BH}}(\mathrm{C\sc{\i
v}})=\log\left\\{\left[\frac{\mathrm{FWHM}(\mathrm{C\sc{\i
v}})}{1000\>\mathrm{km}\>\mathrm{s}^{-1}}\right]^{2}\left[\frac{\lambda
L_{\lambda}(1350\mathrm{\AA})}{10^{44}\>\mathrm{ergs}\>\mathrm{s}^{-1}}\right]^{0.53}\right\\}+(6.66\pm
0.01)-s_{\mathrm{f}}.$ (10)

The scale factor $s_{\mathrm{f}}\approx-0.27$ sets the masses to the $f$ value
obtained by Graham et al. (2011). In Cols. 11 and 15 of Table 7 and in Fig. 21
we compare our $M_{\rm BH}$ results with those using Eq. 10. We do not apply
corrections for radiation-pressure effects that are likely relevant especially
for objects radiating at large Eddington ratio (Netzer 2009; Netzer & Marziani
2010). The difference between this computation and the one reported in
Sulentic et al. (2007) is that in the latter work the blueshifted component
was not separated from the broad component of Civ$\lambda$1549 just to show
how larger values of FWHM(Civ$\lambda$1549) yielded $M_{\rm BH}$ much larger
than the ones derived from FWHM(H$\beta$) in Pop. A objects.

We compare the masses obtained using our photoionization method with those of
Vestergaard & Peterson (2006) in Fig. 21. We use the FWHM of the BC as an
estimator of the virial line broadening. From our results we can see that the
masses agree within less than 1$\sigma$ uncertainty in the luminosity
correlation (0.33). There is a systematic offset of 0.17$\pm$0.10 if
uncorrected ratios are used. The mass values obtained after correction for low
density gas are systematically lower. This happens because the correction
increases the product $U$$n_{\mathrm{H}}$, lowering $r_{\rm BLR}$ and hence
$M_{\rm BH}$. The $M_{\rm BH}$ obtained after corrections are within the error
bars. The systematic offset is then $0.13\pm 0.12$. It is important to
consider that the computed correction is in many ways a maximum correction.
Ciii]$\lambda$1909 emission is assumed to have the same FWHM of
Siiii]$\lambda$1892 while it could be significantly narrower; in addition part
of the Ciii]$\lambda$1909 emission could be due to Feiii $\lambda$ 1914\. In
many sources of Pop. A the correction could be ignored altogether.  The
present results indicate that the Kaspi et al. (2000) relationships can be
extended to be used in high redshift objects (or at least until z$\sim$3) if
the FWHM of the core broad line region can be well determined and measured. In
order to do this, we need:

  * $\bullet$

Spectra with S/N high enough to see the profile shape that allows
decomposition of the Civ$\lambda$1549 line, especially to separate the blue
component from the broad core;

  * $\bullet$

to follow the methodological considerations explained in §4 .

Fig. 21 should be looked at with two cautions. First, the correlation is
dominated by the luminosity dependence of $r_{\rm BLR}$, used to compute
$M_{\rm BH}$ in both cases. Second, the spread of $M_{\rm BH}$ values is
small, less than one order of magnitude (and most objects have statistically
indistinguishable masses). Our estimated error bars are however smaller
compared to the spread expected on the basis of the $r_{\rm BLR}$-$L$
correlation which is, according to Vestergaard & Peterson (2006), $\pm$0.66 at
a 2$\sigma$ confidence level. The two shaded bands of Fig. 21 limit the region
where we can expect to find data points on the basis of the $r_{\rm BLR}$-$L$
correlation. Clearly, a proper interpretation of the Civ$\lambda$1549 profile
may help to reduce the scatter. In any case, our method should provide $M_{\rm
BH}$ estimates with somewhat lower uncertainty. It is interesting to note that
SDSS J12014+0116 appear at the largest $M_{\rm BH}$, and the agreement with
the $r_{\rm BLR}$-$L$ is very good. The $r_{\rm BLR}$ value of 3C 390.3 we
obtain is fairly uncertain due to the low S/N. The size computed in the
present paper is larger than the reverberation mapping derived $r_{\rm BLR}$
for H$\beta$ and Civ$\lambda$1549, although consistent with the value derived
from Ly$\alpha$. 3C 390.3 has the unusual property of having a response time
longer in Civ$\lambda$1549 than in H$\beta$, although the large error bars do
not exclude that the two lines respond with similar time. This behavior might
be related to different physical conditions found for this object.

###  10.3 The LIL-BLR

While the existence of high density and low ionization has been invoked since
long to explain Feii emission (especially by S. Collin and collaborators, as
mentioned in the introduction), we have provided additional evidence that high
density and low ionization are indeed diagnosed from emission lines other than
Feii blends, and that conditions are the one producing most line emission in
extreme Pop. A quasars. Last but not least, both $U$ and $n_{\mathrm{H}}$ can
be observationally determined with reasonable accuracy from the diagnostic
ratios Siii$\lambda$1814/ Siiii]$\lambda$1892, Siiv$\lambda$1397/
Siiii]$\lambda$1892, Aliii$\lambda$1860/ Siiii]$\lambda$1892, and
Civ$\lambda$1549/(Aliii$\lambda$1860 or Siiii]$\lambda$1892). Metallicity can
be also constrained from the previous ratios as well as from
Civ$\lambda$1549/Siiv$\lambda$1397\. These ratios are pretty well defined,
while estimating Ciii]$\lambda$1909 and Feiii$\lambda$1914 relative
contribution is not relevant to our method (with the exceptions of sources
like 3C 390.3). This low ionization BLR (or LIL BLR) has very similar
properties to the Oi and Caii emitting region identified by Matsuoka et al.
(2008). The LIL-BLR seems to be present in the vast majority of quasars,
probably all the ones with significant Feii emission (Marziani et al. 2010).
The low values of $U$ could be a consequence of the high density rather than
of a far away location of the emitting region. The assumption of a single well
defined value of $U$ and $n_{\mathrm{H}}$ is probably an idealization even for
the LIL-BLR taken alone; however the convergence of emission line ratios
toward a well defined point, along with the ability to qualitatively explain
Feii and most H$\beta$ emission, indicate that the LIL-BLR might be a region
with a small range of low $U$ and high $n_{\mathrm{H}}$.

Do density and ionization parameter in the LIL BLR converge to a single well
defined value with a small dispersion? A tentative answer comes from the
values reported in Tab. 6. Excluding 3C390.3, the range $U$ and
$n_{\mathrm{H}}$ span is not very large (even considering changes in
metallicity): less than one order of magnitude around $\log$
$n_{\mathrm{H}}$$\sim$ 12.5, and ionization parameter $\sim-2.75$, and the
spread is not much larger than the uncertainties in the individual
measurements. The product $U\cdot$$n_{\mathrm{H}}$ seems to be fairly stable.
We have $<\log(U\cdot$$n_{\mathrm{H}}$)$>\approx 9.5$, with a sample
dispersion of 0.15 (excluding 3C 390.3). We applied the same method to 14
low-$z$ quasars (Negrete et al. 2010), and we obtain
$<\log(U\cdot$$n_{\mathrm{H}}$)$>\approx 9.7$, with a dispersion of 0.3.
Assuming $\log(U\cdot$$n_{\mathrm{H}}$) $\approx 9.6$ could be a good approach
to estimate $M_{\rm BH}$ if elaborate measurements on Civ$\lambda$1549 and
Ciii]$\lambda$1909 are not possible, and only a rough estimate of the
Siiii]$\lambda$1892 BC FWHM is available. On the other hand, there is still a
major effect of measurement errors on the uncertainty derived for
$\log(U\cdot$$n_{\mathrm{H}}$); instrumental improvements may lead to a
significant appreciation of object-by-object diversity.

The $U\cdot$$n_{\mathrm{H}}$ values reported in Table 6 are not very far from
the average value obtained by Padovani and Rafanelli (1988). This is not
surprising since the spectra at low and high $z$ seems to show the same
diversity, classified through the E1 sequence and the Pop. A/Pop. B
distinction. In other words, NLSy1-like sources whose spectrum is similar to I
Zw1 appear to be present at high redshift, meaning that the LIL-BLR remains
strong and prominent over a wide range of redshifts. A second reason is that
Padovani and Rafanelli (1988) considered H$\beta$. Emission of H$\beta$ can be
significant under a much wider range of $U$ and $n_{\mathrm{H}}$; however, the
Aliii$\lambda$1860, Mgii$\lambda$2800, Feii emitting region should be also a
strong producer of H$\beta$. This region with well-defined physical conditions
is expected to be the emitter of the core of H$\beta$, i.e., the part of the
line responding more strongly to continuum changes.

####  10.3.1 Verification on EW and Line Luminosity

Considering that we have very low ionization parameter values, a legitimate
question is whether we have a sufficient number of photons to explain the EW
and luminosity of the emission lines. We made a preliminary check of
consistency for the EW from CLOUDY simulations. A second, a-posteriori test
was to consider the predicted line luminosity assuming the actual luminosity
of the quasar, the density and the distance $r_{\rm BLR}$ derived from our
method, and spherical geometry.

A remarkable property common to all spectra is the low EW of the emission
lines. The extreme source SDSS J120144.36+011611.6 has total
$W$(Civ$\lambda$1549) $\approx$ 19 Å, which becomes $\approx$ 7 Å if only the
LIL component is considered. The whole 1900 Å blend has $W\approx$ 20 Å; the
individual EWs of Siiii]$\lambda$1892 and Aliii$\lambda$1860 are just a few Å.
Similar considerations apply to the other high-$z$ quasars, especially for
Pop. A sources. In this case we have $W$(Civ$\lambda$1549)$\approx 20-30$ Å,
the equivalent width of the whole 1900 Å $30-40$Å including the uncertain
contribution of Feiii and Ciii]$\lambda$1909\. This has the important
implication that the ionization parameter cannot be very large. From our
simulations, we deduce that the LIL-BLR $\log U$ is always $\lesssim-2.0$. On
the other hand, toward the low $U$, high density limit emission lines tend to
disappear altogether. The predicted EWs become too low to account for the
observed EW with a covering factor $f_{\mathrm{c}}\lesssim 0.5$ if $\log
U\lesssim-3$. The values obtained after correction $\log U\approx-3.25$ are
still possible within the condition of $f_{\mathrm{c}}\lesssim 0.5$ since the
Civ$\lambda$1549 EW is greatly diminished. Cases of very low $U$ are rather
indicative of strong metal enhancement than of extremely low ionization level
(see §8.1). If we take $\log$ $n_{\mathrm{H}}$$\approx$12.5, $\log U=-2.75$,
the predicted equivalent width of is $W$(Civ$\lambda$1549)$\approx$37 Å for a
covering factor 0.5, close to the largest values observed in our quasars.
However, The Civ$\lambda$1549 EW of SDSS J12014+0116 can be accounted for by
the values of $\log U\approx-3.00$ and $\log$ $n_{\mathrm{H}}$$\sim$ 12.75 –
12.50.

If we model the BLR with a spherical geometry where the emitting gas covers a
fraction $f_{\mathrm{c}}$ of the continuum, CLOUDY computations confirm that
the line luminosity can be accounted for. The luminosity at 1700 Å of
J00103-0037 is $\log\lambda L_{\lambda}\approx$ 46.6; the predicted luminosity
of Civ$\lambda$1549 is $\log L$(Civ$\lambda$1549) $\approx$ 44.5, under the
assumption of $Z=Z_{\odot}$, $f_{\mathrm{c}}=0.1$, and Mathews & Ferland
continuum shape. The observed Civ$\lambda$1549 line luminosity of J00103-0037,
$\approx 9\cdot 10^{44}$ ergs s-1, is obtained with $f_{\mathrm{c}}\approx
0.3$.

####  10.3.2 Analogy with $\eta$ Carinæ

The physical conditions we envisage for the BC of quasars find a
correspondence in the so-called Weigelt blobs of $\eta$ Carinæ, located in the
equatorial plane of the system, perpendicular to the symmetry axis of the
bipolar lobes forming the homunculus nebula (cf. Marziani et al. 2010). Unlike
the gas of the bipolar lobes, predominantly shock heated, the Weigelt blobs
are believed to be dense gas photoionized by the radiation associated to the
central, massive star and to a possible companion (e.g., Johansson et al.
2000; Davidson 2005). The spectrum of the Weigelt blobs shows very weak
Ciii]$\lambda$1909 along with a prominent line at $\lambda$1914, ascribed to
the $z^{7}P_{3}^{0}\rightarrow a^{7}S_{3}$ Feiii transition. The line appears
very strong because the upper level is populated by Ly$\alpha$ fluorescence.
This very same process is expected to be present also in quasars. Indeed, in I
Zw 1, where lines are narrow, and in SDSS J120144.36+011611.6 the peak
emission at around 1914 Å is actually visible. The amount of Ly$\alpha$
pumping to the upper level (z${}^{7}P^{\mathrm{o}}_{3}$) of the UV 34 cannot
be estimated through the standard edition of CLOUDY (the relevant levels of
the UV 34 multiplets of Fe+2 ion are not included). Additional photoionization
computations including a suitable Fe+2 model and line transfer should be
considered. This is beyond the aim of the present study; we can conclude in a
qualitative fashion that the spectrum of the $\eta$ Carinæ blobs supports a
view of the low-ionization part of the BLR that is not conventional: very high
density gas, at very low ionization.

##  11 Conclusions

In this paper we presented new observations of eight high redshift quasars.
The spectra were meant to provide high S/N, moderate resolution data on which
the Civ$\lambda$1549, Siiii]$\lambda$1892, Aliii$\lambda$1860, and
Siii$\lambda$1814 emission line profiles could be accurately analyzed. Line
profile fits allowed us to isolate a specific component whose intensity ratios
were used to derive consistent values for electron density and ionization
parameter. This line component (LIL BC) seems to be emitted predominantly by
low ionization, high density gas in the majority of quasars studied thus far
by us.

These results permitted us to compute the product $n_{\mathrm{H}}$$\cdot U$
and hence the size of the Broad Line Region and the central black hole mass.
The method described in this paper rests on the assumption of photoionization
as the mechanism of gas heating; on the assumption of isotropic luminosity,
and on line ratios predicted by cloudy simulations. The photoionization method
explored in this paper offers an estimate of $r_{\rm BLR}$ for each quasar,
with some advantages on the $r_{\rm BLR}$ valued derived from the luminosity-
size correlation. The luminosity correlation suffers from large scatter and is
simply extrapolated to very high luminosity without any support since there
are, unfortunately, no conclusive results on reverberation of high luminosity
quasars even if heroic efforts are underway (e.g., Trevese et al. 2007, Botti
et al. 2010). We found that the black hole masses derived from the computed
$r_{\rm BLR}$ and from the virial assumption are in good agreement with the
ones derived from the luminosity-size relationship. Actually, Fig. 21 suggests
that we might have reduced the errors of the $M_{\rm BH}$ by a factor of two
with respect to the expectation from the Vestergaard & Peterson (2006)
relationship.

We repeat that our $M_{\rm BH}$ and $r_{\rm BLR}$ results are based on the
product $n_{\mathrm{H}}$$\cdot U$ and not on values of $n_{\mathrm{H}}$ and of
$U$ taken separately. It seems that this product converges to two typical
ranges of values, one of them associated to low-ionization, high density gas
(the LIL-BLR). For our $n_{\mathrm{H}}$ and $U$ determinations we do not use
ratio Ciii]$\lambda$1909/ Siiii]$\lambda$1892 except for 3C 390.3. As we
discussed in §7.2, this ratio should not be considered at high density because
Ciii]$\lambda$1909 is collisionally quenced if $n_{\mathrm{H}}$ $\gtrsim
10^{10}$ cm-3. Ciii]$\lambda$1909 is produced in conditions that are very
different from the ones we found for the LIL-BLR. While the method can be
applied to most quasars, the application seems to be especially
straightforward to quasars whose spectrum is like SDSS J120144.36+011611.6 (if
high metallicity is properly taken into account) or, at the other end,
3C390.3. In the first case we have dominance by the LIL-BLR, in the second
case the LIL-BLR seems to be completely absent and physical conditions look
radically different: high ionization and moderate density. An inspection of
SDSS spectra covering both the 1900 Å blend and Civ$\lambda$1549 (up to
$z\approx 3.5$) shows that SDSS J120144.36+011611.6 has many replicas at high
redshift, accounting for at least a few percent of all quasars. These high-
metallicity objects should be the first candidates to expand black hole mass
computations to high redshift without relying on the $r_{\rm BLR}$ \- $L$
correlation.

To apply the photoionization method in the most effective way, determining
$n_{\mathrm{H}}$ and $U$ with the lowest uncertainty, spectral data should be
of moderate resolution ($\lambda/\Delta\lambda\sim 1000$) as well as of high
S/N. If the Siii$\lambda$1814 line can be measured in an accurate way, it
would be possible to derive independent estimates of $U$, $n_{\mathrm{H}}$,
and $Z/Z_{\odot}$ in most quasars.

Especially the most extreme (in terms of Aliii$\lambda$1860 strength) objects
in bin A3 and A2 hold the promise to make possible an independent estimate of
$n_{\mathrm{H}}$, $U$, and metallicity. Clearly, objects in bin A1 resembling
their median spectrum are not well suited for an application of the method.
Also, any source with Ciii]$\lambda$1909/ Siiii]$\lambda$1892$>$ 1 is subject
to a large correction. In light of the many uncertainty, an average value of
the product $Un$ (obtained from the objects of the other spectral types) could
be considered.  Pop. B objects should not avoided entirely, especially
whenever Siiii]$\lambda$1892 $\;\buildrel>\over{\sim}\;$ Ciii]$\lambda$1909
after VBC removal.

The present exploratory analysis emphasized several sources of uncertainty.
However, the parameter needed for $r_{\rm BLR}$ and $M_{\rm BH}$ computation,
the product $U$$n_{\mathrm{H}}$, seems to be fairly stable and well-defined.
Even with an error of a 0.3 in logarithm, the square root will be subject to a
0.15 uncertainty in logarithm, much lower than the uncertainty associated with
the $r_{\rm BLR}$luminosity correlation. The large intrinsic spread of the
correlation at low luminosity, its uncertain extrapolation at very high
luminosity make preferable a one-by-one determination based on physical
properties of an emitting region that remains similar to itself.

A. Negrete and D.Dultzin acknowledge support form grant IN111610-3 PAPIIT,
DGAPA UNAM. Funding for the SDSS and SDSS-II has been provided by the Alfred
P. Sloan Foundation, the Participating Institutions, the National Science
Foundation, the U.S. Department of Energy, the National Aeronautics and Space
Administration, the Japanese Monbukagakusho, the Max Planck Society, and the
Higher Education Funding Council for England. The SDSS Web Site is
http://www.sdss.org. The SDSS is managed by the Astrophysical Research
Consortium for the Participating Institutions listed at the SDSS Web Site.

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Table 1: Line Components in the $\lambda$1900 blend.

Ion | $\lambda$ | $X$ | $E_{l}-E_{u}$ | Transition | $A_{ki}$ | $n_{\mathrm{c}}$ | Note
---|---|---|---|---|---|---|---
| Å | eV | eV |  | s-1 | cm-3 |
Si II | 1808.00 | 8.15 | 0.000 - 6.857 | ${}^{2}D^{o}_{3/2}\rightarrow{}^{2}P_{1/2}$ | $2.54\cdot 10^{6}$ |  $\cdots$ | 1
Si II | 1816.92 | 8.15 | 0.036 - 6.859 | ${}^{2}D^{o}_{5/2}\rightarrow{}^{2}P_{3/2}$ | $2.65\cdot 10^{6}$ |  $\cdots$ | 1
Al III | 1854.716 | 18.83 | 0.000 - 6.685 | ${}^{2}P^{o}_{3/2}\rightarrow{}^{2}S_{1/2}$ | $5.40\cdot 10^{8}$ |  $\cdots$ | 1
Al III | 1862.790 | 18.83 | 0.000 - 6.656 | ${}^{2}P^{o}_{1/2}\rightarrow{}^{2}S_{1/2}$ | $5.33\cdot 10^{8}$ |  $\cdots$ | 1
| 1882.7 | 16.34 | 0.000 - 6.585 | ${}^{3}P^{o}_{2}\rightarrow{}^{1}S_{0}$ | 0.012 | $6.4\cdot 10^{4}$ | 1,2,3
Si III] | 1892.03 | 16.34 | 0.000 - 6.553 | ${}^{3}P^{o}_{1}\rightarrow{}^{1}S_{0}$ | 16700 | $2.1\cdot 10^{11}$ | 1,4,5
| 1906.7 | 24.38 | 0.000 - 6.502 | ${}^{3}P^{o}_{2}\rightarrow{}^{1}S_{0}$ | 0.0052 | $7.7\cdot 10^{4}$ | 1,2,6
C III] | 1908.734 | 24.38 | 0.000 - 6.495 | ${}^{3}P^{o}_{1}\rightarrow{}^{1}S_{0}$ | 114 | $1.4\cdot 10^{10}$ | 1,2,4,5
Fe III | 1914.066 | 16.18 | 3.727 - 10.200 | $z^{7}P^{o}_{3}\rightarrow a^{7}S_{3}$ | $6.6\cdot 10^{8}$ |  $\cdots$ | 7

Note. — All wavelengths are in vacuum. (1) Ralchenko, Yu., Kramida, A.E.,
Reader, J., and NIST ASD Team (2008). NIST Atomic Spectra Database (version
3.1.5). Available at: http://physics.nist.gov/asd3. 2: Feibelman & Aller
(1987). 3: $n_{\mathrm{c}}$ computed following Shaw & Dufour (1995). 4: Morton
(1991). 5: Feldman (1992). 6: Zheng (1988). 7: Wavelength and $A_{ki}$ from
Ekberg (1993), energy levels from Edlén and Swings (1942).

Table 2: Basic Properties of Sources and Log of Observations.

Object name | $\rm m_{B}$ | $z$ | Line | $M_{\mathrm{B}}$ | Flux 6cm (mJy) | Date | DIT | Nexp | Airmass | S/N
---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
J00103-0037 | 18.39 | 3.1546 | 1 | -25.68 | 0.40 | 2006-11-08 | 1139 | 3 | 1.16, 1.13, 1.11 | 60
J00521-1108 | 18.70 | 3.2364 | 2 | -25.39 | 0.43 | 2007-01-01 | 1199 | 3 | 1.15, 1.21, 1.29 | 41
J01225+1339 | 18.24 | 3.0511 | 1 | -25.80 | * | 2006-11-08 | 1259 | 2 | 1.36, 1.32 | 92
J02287+0002 | 18.20 | 2.7282 | 1 | -25.72 | 0.35 | 2006-12-16 | 1259 | 2 | 1.10, 1.12 | 67
J02390-0038 | 18.68 | 3.0675 | 1 | -25.36 | 0.43 | 2006-11-07 | 1199 | 3 | 1.35, 1.46, 1.60 | 57
J03036-0023 | 17.65 | 3.2319 | 1 | -26.44 | 0.34 | 2006-12-16 | 1259 | 2 | 1.11, 1.14 | 88
J20497-0554 | 18.29 | 3.1979 | 1 | -25.79 | * | 2006-11-04 | 1259 | 2 | 1.52, 1.70 | 54
J23509-0052 | 18.67 | 3.0305 | 1 | -25.36 | 0.41 | 2006-11-07 | 1199 | 3 | 1.10, 1.11, 1.14 | 62

**footnotetext: Not in FIRST

Table 3: Line Fluxes a

|  Ciii]$\lambda$1909 |  |  |  |  Civ$\lambda$1549 |  | Siiv$\lambda$1397
---|---|---|---|---|---|---|---