# Virial Black Hole Mass Estimates of Quasars in the XQ-100 Legacy Survey

Samuel Lai,1 ID Christopher A. Onken,1,2 ID Christian Wolf,1,2 ID Fuyan Bian,3
ID Guido Cupani,4,5 ID Sebastian Lopez4 ID and Valentina D’Odorico,5,6,7 ID
1Research School of Astronomy and Astrophysics, Australian National
University, Canberra, ACT 2611, Australia
2Centre for Gravitational Astrophysics, Research Schools of Physics, and
Astronomy and Astrophysics, Australian National University, Canberra, ACT
2601, Australia
3European Southern Observatory, Alonso de Córdova 3107, Casilla 19001,
Vitacura, Santiago 19, Chile
4Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago,
Chile
5INAF – Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34143
Trieste, Italy
6IFPU–Institute for Fundamental Physics of the Universe, via Beirut 2, I-34151
Trieste, Italy
7Scuola Normale Superiore, Piazza dei Cavalieri, I-56126 Pisa, Italy
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The black hole (BH) mass and luminosity are key factors in determining how a
quasar interacts with its environment. In this study, we utilise data from the
European Southern Observatory Large Programme XQ-100, a high-quality sample of
100 X-shooter spectra of the most luminous quasars in the redshift range
$3.5<z<4.5$, and measure the properties of three prominent optical and
ultraviolet broad emission-lines present in the wide wavelength coverage of
X-shooter: C iv, Mg ii, and H$\beta$. The line properties of all three broad
lines are used for virial estimates of the BH mass and their resulting mass
estimates for this sample are tightly correlated. The BH mass range is
$\log{(\rm{M_{BH}}/\rm{M_{\odot}})}=8.6-10.3$ with bolometric luminosities
estimated from the 3000 Å continuum in the range
$\log{(\rm{L_{bol}}/\rm{erg\,s^{-1}})}=46.7-48.0$. Robustly determined
properties of these quasars enable a variety of follow-up research in quasar
astrophysics, from chemical abundance and evolution in the broad-line region
to radiatively driven quasar outflows.

###### keywords:

galaxies: active – galaxies: high-redshift – quasars: emission lines

††pubyear: 2022††pagerange: Virial Black Hole Mass Estimates of Quasars in the
XQ-100 Legacy Survey–B

##  1 Introduction

Hundreds of thousands of quasar (QSO) sources have now been confirmed through
massive surveys (e.g., Flesch, 2015; Yao et al., 2019; Lyke et al., 2020) up
to a redshift of $z=7.642$ (Wang et al., 2021). Despite the abundance of
sources, high-quality echelle spectroscopy is available for only a few
thousand unique QSOs, of which only a fraction contain data in the near-
infrared (NIR). As the redshift increases, more of the rest-frame ultraviolet
(UV) and optical atomic transitions shift into the infrared, which renders NIR
observations invaluable for QSO emission and absorption-line studies.

The European Southern Observatory Large Programme ”Quasars and their
absorption lines: a legacy survey of the high-redshift universe with
VLT/X-shooter" (hereafter referred to as XQ-100, PI: S. López, programme
number 189.A-0424) is a publicly available and high-quality sample of echelle
spectra from 100 luminous QSOs in the redshift range $3.5<z<4.5$ (López et
al., 2016). The simultaneous full spectral coverage is from 315 nm to 2500 nm
with resolving power $R\sim 5400-8900$ and median signal-to-noise ratio (SNR)
of 24, measured across the whole spectrum and entire sample of 100 QSOs. Prior
to XQ-100, the largest NIR spectroscopic survey, conducted using the FIRE
spectrograph at Magellan, was comprised of 50 QSOs at $2<z<5$ (Matejek &
Simcoe, 2012) with a median SNR per-pixel of 13 across the entire QSO sample.
The XQ-100 survey with its high SNR and broad spectral coverage provides a
unique and statistically significant sample to study the rest-frame UV and
optical spectral properties of 100 high-redshift QSOs.

Among the scientific themes of the XQ-100 programme is the study of galactic
absorption. Sub-damped (subDLA) or damped Ly $\alpha$ systems (DLA; Wolfe et
al., 2005) are used to determine the cosmic density of neutral gas as they are
the main reservoirs for neutral gas in the Universe (e.g., Prochaska & Wolfe,
2009; Noterdaeme et al., 2012; Sánchez-Ramírez et al., 2016; Berg et al.,
2019). The same systems can be used to probe metal abundances of QSO hosts by
tracing gaseous absorbers along QSO sightlines (Berg et al., 2016, 2021).
Similarly, intrinsic narrow absorption lines (NALs) in XQR-30 data are probes
of the physical conditions of the QSO immediate environment and energetics of
its outflow (Perrotta et al., 2016), where absorption-line diagnostics
indicate metallicity, absorber covering fraction, and ionisation structure
(Perrotta et al., 2018). In addition, the XQ-100 spectra also addresses
cosmological questions through independent constraints of the Ly $\alpha$
forest power spectrum at high redshift (Iršič et al., 2017; Yèche et al.,
2017).

The study of active galactic nuclei (AGN) properties is also one of the
scientific themes from the XQ-100 programme. The high-quality spectra can be
used for accurate measurements of $z>3.5$ black hole masses using line
profiles of rest-frame UV C iv, Mg ii, or rest-frame optical H$\beta$
emission-lines and the continuum luminosity (e.g., McLure & Dunlop, 2004;
Greene & Ho, 2005; Vestergaard & Peterson, 2006; Vestergaard & Osmer, 2009).
Flux ratios of emission-lines in the rest-frame UV, such as N v/C iv or (Si
iv+O iv)/C iv, provide estimates of the metallicity in the QSO broad-line
region (BLR), which probes the chemical enrichment history in high-redshift
galactic nuclear regions (e.g., Hamann & Ferland, 1999; Hamann et al., 2002;
Nagao et al., 2006; Wang et al., 2012; Xu et al., 2018; Wang et al., 2022; Lai
et al., 2022). In the local universe, black hole masses and galactic bulge
masses are strongly correlated (the $\rm{M}_{\rm{BH}}-\rm{M}_{\rm{bulge}}$
relation; Marconi & Hunt, 2003; Häring & Rix, 2004; Greene et al., 2010),
indicating that host galaxies and their central supermassive black holes co-
evolve. Determining the black hole masses of high-redshift QSOs is valuable
for studies that aim to investigate how properties of host galaxies and their
black holes came to be strongly coupled (e.g., Croton et al., 2006; McConnell
& Ma, 2013; Terrazas et al., 2020).

In this study, we estimate the black hole masses of every source in XQ-100
using single-epoch virial estimates based on the prominent broad C
iv$\lambda$1549Å, Mg ii$\lambda$2799Å, and H$\beta$$\lambda$4863Å lines. We
measure emission-line properties utilising the high SNR, resolving power, and
wide spectral coverage of the X-shooter data to tightly constrain the observed
spectral profiles. This study produces a large catalogue of bright QSOs with
robustly measured emission-line properties, black hole masses, and luminosity
estimates at high-redshift ($z>3.5$).

The content of this paper is organised as follows: in Section 2, we describe
the XQ-100 data and their further processing. In Section 3, we present our
approach to modelling prominent emission-lines in the observed spectra. In
Section 4, we describe virial mass estimates based on the measured line
properties. In Section 5, we discuss measurements of the emission-lines, black
hole mass, and QSO luminosity. We compare the different virial mass estimates
against each other and contextualise our results with large low-redshift
samples. We summarize and conclude in Section 6. Throughout the paper, we
adopt a flat $\Lambda$CDM cosmology with H${}_{0}=70$ km s-1 Mpc-1 and
$\left(\Omega_{\rm m},\Omega_{\Lambda}\right)=\left(0.3,0.7\right)$. All
referenced wavelengths of emission-lines are measured in vacuum.

##  2 XQ-100 Sample Data and Processing

Targets in the XQ-100 sample were initially selected from the NASA/IPAC
Extragalactic Database (NED) with declinations $\delta<+15^{\circ}$ and
redshifts $z>3.5$. An additional twelve targets were obtained from the
literature with declination $+15^{\circ}<\delta<+30^{\circ}$. Deliberate steps
were taken to avoid targets with known broad absorption features and to avoid
intrinsic colour selection bias. A full description of the target selection
process can be found in López et al. (2016).

###  2.1 Sample Description and Data Reduction

The targets span the redshifts from $z=3.508$ to $z=4.716$ (López et al.,
2016), although all but four are within the redshift range $3.5<z<4.5$. The
sample is biased towards bright sources, covering a magnitude range in Gaia
DR3 GRP band (Gaia Collaboration et al., 2021) of 16.78 to 19.00 Vegamag.
Observations were carried out between 2012 April 1, and 2014 March 26 by the
X-shooter instrument (Vernet et al., 2011) on the Very Large Telescope (VLT)
using all three spectroscopic arms: UVB (300$-$559.5 nm), VIS (559.5$-$1024
nm), and NIR (1024$-$2480 nm). The wide wavelength coverage ensures that the C
iv and Mg ii emission-lines are always observed within the VIS and NIR arms
for the range of redshifts in the sample. Additional information on the
requested observing conditions and instrumental setup is available in López et
al. (2016). We briefly summarise the reduction and processing procedures
behind the XQ-100 data products, as described in López et al. (2016).

Extraction of XQ-100 spectra was performed using an IDL-based custom pipeline
(Becker et al., 2012). The strategy of the custom pipeline follows techniques
described in Kelson (2003). Flux calibration uses response curves generated
from observations of spectro-photometric standard stars, observed close in
time to the science frames (López et al., 2016), where a fiducial response
curve was used if the temporally closest standard star observation was not
optimal. Newer versions of this pipeline have been used in other QSO studies,
such as XQR-30 (D’Odorico et al., 2023). While XQ-100 data from all three
spectrograph arms are available, for the present study, we consider only the
VIS and NIR arms, because they contain all emission-lines of interest. The
velocity resolution chosen to rebin the spectra are 11 km s-1 and 19 km s-1
for the VIS and NIR arms, respectively.

The absolute flux calibration is a crucial step in determining the luminosity
of the QSO continuum. A comparison between XQ-100 and Sloan Digital Sky Survey
(SDSS; York et al., 2000) spectra showed a systematic underestimation of flux
for the X-shooter spectra due to slit losses. However, the slit losses appear
to be roughly achromatic, such that the spectral shape is correctly
reconstructed, but the flux calibration should be taken as order-of-magnitude
estimates (López et al., 2016). Thus, we describe our independent calibration
of the XQ-100 spectra to observed photometry in Section 2.2.

Telluric absorption features appear prominently in both the VIS and NIR arms.
Corrections to the spectra are derived using model transmission spectra based
on the ESO SKYCALC Cerro Paranal Advanced Sky Model, version 1.3.5 (Noll et
al., 2012; Jones et al., 2013), which are applied to individual-epoch spectra
of all XQ-100 QSOs. After extraction and telluric correction, the median per-
pixel SNR for the whole QSO sample are 33, 25, and 43, measured at rest-frame
wavelengths 1700, 3000, and 3600 Å, respectively (López et al., 2016),
computed in $\pm 10$Å windows.

The processed XQ-100 data products, including reduced spectra and telluric
models, are publicly available through the ESO Science Archive Facility.
However, the spliced spectra and the multi-epoch averaged spectra are not
telluric corrected.

###  2.2 Data Post-Processing

We obtain individual VIS and NIR single-epoch frames from the ESO Science
Archive Facility for all XQ-100 sources and apply the following post-
processing procedure:

  1. 1.

We use the respective telluric model included in each frame to obtain the
telluric-corrected spectra and use the emission redshift to transform the
spectra into the rest-frame.

  2. 2.

We identify pixels for which the per-pixel SNR is 5 or below and mask them
from further processing and modelling.

  3. 3.

We apply a mask by sigma-clipping with a 3$\sigma$-threshold along a box width
of 40 pixels to remove some of the narrow absorption features and noise above
3$\sigma$. The absorption features are not desired when modelling the
intrinsic profile of the broad emission-lines and the sigma-clipped spectrum
also helps constrain the continuum. While this procedure alone will not remove
the base of absorption troughs, we follow the procedure in Shen et al. (2011),
which defines our single-epoch virial mass calibration of Mg ii. In Section
3.2, we describe an additional mask buffer window to remove the base of
absorption features embedded in the C iv line profile, but this is not applied
throughout the entire spectrum.

  4. 4.

We crossmatch the XQ-100 sample with UKIRT Infrared Deep Sky Survey (UKIDSS;
Lawrence et al., 2007) DR11, UKIRT Hemisphere Survey (UHS; Dye et al., 2018)
DR1, VISTA Hemisphere Survey (VHS; McMahon et al., 2013) DR6, VISTA Kilo-
degree Infrared Galaxy Survey (VIKING; Edge et al., 2013) DR5, and Two Micron
All-Sky Survey (2MASS; Skrutskie et al., 2006) to obtain near-infrared J-band
photometry. We also crossmatch all targets with the SkyMapper Southern Survey
(SMSS; Onken et al., 2019) DR3, Panoramic Survey Telescope and Rapid Response
System (Pan-STARRS; Chambers et al., 2016) DR1, Sloan Digital Sky Survey
(SDSS; York et al., 2000) DR16, and Dark Energy Sky Survey (DES; Abbott et
al., 2021) DR2 to obtain optical i-band photometry. We obtain the transmission
profile of the broadband filters using the SVO Filter Profile Service (Rodrigo
& Solano, 2020) and integrate the observed-frame spectra across the profile,
obtaining a flux ratio between the photometry and spectrum with an associated
uncertainty, which is used to calibrate the observed spectra to the
photometry. There is one target, SDSS J004219.74$-$102009.4, for which no
publicly available J-band photometry was found in the above surveys. In this
case, we scale the flux of the NIR arm to match the flux of the VIS arm within
the overlapping wavelength coverage. The magnitudes used for calibration are
provided in the online supplementary table. We note that the median correction
required to match the spectrum to photometry is a 42% flux increase with an
error of 2–3%, which is higher than the $\sim$ 30% flux underestimation on
X-shooter’s part compared to SDSS spectra estimated in López et al. (2016). As
the photometry is taken from a separate epoch from the spectroscopic data, the
additional uncertainty from the photometric calibration is insignificant
compared to QSO variability, which we quantify and discuss in Section 5.1.

  5. 5.

We standardise the rest-frame wavelength domain for all of the spectra. Every
spectrum is resampled using a flux-conserving algorithm (SPECTRES; Carnall,
2017) into rest-frame bins with a common velocity dispersion of 50 km s-1. The
resampling calculation and error propagation are described in detail in
Carnall (2017). Then the VIS and NIR arms are spliced together without
rescaling, using the inverse variance weighted mean flux for the superposition
between arms. In a few cases, we observe a discontinuity between the VIS and
NIR arms, located between 1860Å to 2275Å for the redshift range of our sample.
The median flux difference between arms as measured in the overlapping region
is 0.6%, albeit with a large standard deviation of 24%. However, we emphasise
that the data in the overlapping region between arms are naturally at the edge
of the wavelength coverage of each arm and is particularly noisy, so the flux
difference measured in this fashion can be exaggerated. Nevertheless, we flag
all targets with higher than 25% flux difference between the VIS and NIR arms
in the supplementary table under the column “NIR_VIS_Flag”. We rely on the
flux calibration in each respective arm and only use data within one arm at a
time to fit the QSO continuum. Thus, the flux discontinuity between arms does
not affect our continuum or emission-line models.

  6. 6.

If there are repeated observations of a single source, we make use of all the
available data and stack the resampled telluric-corrected spectra together,
using the mean weighted by the inverse variance to define the value at each 50
km s-1 velocity bin and propagate the uncertainty. Because of the calibration
in step (iv), the flux density at each velocity bin between repeated
observations are in good agreement. The temporal separation between repeated
observations range from 10 days to 1.5 years. However, we are interested in
the average spectrum in order to determine representative properties of the
black hole mass and luminosity. Prior to rescaling the flux level of the
spectra to photometry, the median flux difference between exposures measured
at every velocity bin is 7.3% with a standard deviation of 7.6%. After
rescaling, our flux level is more consistent, measured at 2.3% with a standard
deviation of 0.6%. We also quantify the uncertainty from QSO variability in
Section 5.1.

  7. 7.

We use $R_{\rm{v}}=3.1$ and the Schlegel, Finkbeiner & Davis (SFD; Schlegel et
al., 1998) extinction map to apply a correction for the Milky Way extinction
in the observed frame. However, the normalisation of the colour excess based
on the SDSS footprint and fits to the blue tip of the stellar locus suggests
that SFD systematically over-predicts $E(B-V)$ by 14%. (Schlafly et al., 2010)
Thus, we apply a 14% re-calibration factor to the colour excess, such that
$E(B-V)=0.86\times E(B-V)_{\rm{SFD}}$ (Schlafly & Finkbeiner, 2011).

After the post-processing procedure, the median SNR per 50 km s-1 for the
whole QSO sample measured at rest-frame 1700, 3000, and 3600 Å is 76, 52, and
74, respectively, measured from the median SNR within $\pm 10$Å windows. Much
of the increase in signal originates from the SNR floor and consolidating the
flux from its native resolution into the rest frame 50 km s-1 grid.

For the wavelength range redder than rest-frame 3600 Å, a similar post-
processing procedure is applied, but the sigma-clip mask of step (iii) is
omitted to preserve narrow emission-line features of H$\beta$ and [O iii]. Due
to the redshift range of this sample, only a subset of sources contains the
H$\beta$ line within the X-shooter coverage. We visually inspect the data to
ensure that the H$\beta$ line is distinguishable from the additional noise of
the thermal background and second-order contamination at edge of the NIR arm
wavelength coverage. We also ensure that the H$\beta$ line is observed with
sufficient SNR (> 10 per resolution element), which produces a sub-sample of
21 QSOs, where the median 50 km s-1 SNR across all 21 QSOs is 13. In this
case, the SNR of each QSO is measured from the median SNR between 5090$-$5110
Å.

##  3 Spectral Modelling

Our objective in this study is to measure the properties of the following QSO
broad emission-lines: C iv$\lambda$1549Å, Mg ii$\lambda$2799Å, and
H$\beta$$\lambda$4863Å. In the XQ-100 sample, both C iv and Mg ii can be
located in all spectra, while H$\beta$ is observable only in lower redshift
targets with sufficient signal. In this section, we describe our approach
towards modelling emission-lines, using a publicly available code
(PyQSpecFit111https://github.com/samlaihei/PyQSpecFit; Lai, 2023) designed
specifically for modelling QSO spectral lines.

###  3.1 Continuum Modelling

Although a continuum model is provided as part of the XQ-100 data products, we
elect to use our own continuum model due to how sensitive the broad emission-
line models are to the local continuum. Our model follows similar studies
(e.g., Wang et al., 2009) in that the underlying continuum is built from two
components: a power-law continuum and Fe ii template, simultaneously fit to
selected pseudo-continuum-modelled wavelength regions. We briefly comment on
the Balmer continuum later in this section and quantify its effect in Appendix
A. All components of the pseudo-continuum are used in measuring the Mg ii and
H$\beta$ emission-lines, but the flux contribution from the Fe ii continuum is
less significant in the wavelength region of C iv. Thus, we only use a power-
law to constrain the continuum in the vicinity of the C iv line.

The power-law continuum is defined by the following function normalised at
rest-frame 3000 Å,

$F_{\rm{pl}}(\lambda;F_{\rm{0}},\gamma)=F_{\rm{pl,0}}\left(\frac{\lambda}{3000\mbox{\AA}}\right)^{\gamma}\,,$
(1)

where $F_{\rm{pl,0}}$ and $\gamma$ are the normalization and power-law slope,
respectively.

The Fe ii continuum is of considerable importance to the Mg ii and H$\beta$
models, as both lines are sensitive to the features of the Fe ii contribution
underneath the emission-line. To eliminate the Fe ii emission when strong, we
convolve the Fe ii model with a Gaussian broadening kernel $G(\lambda,\sigma)$
of standard deviation $\sigma$ in order to match the variety of features
observed in our spectra. The Gaussian broadening follows,

$F_{\rm{Fe}}(\lambda;\zeta_{\rm{0}},\delta,\sigma)=\zeta_{\rm{0}}\,F_{\rm{template}}|_{\lambda(1+\delta)}\circledast
G(\lambda,\sigma)\,,$ (2)

where the free parameters of the Fe ii contribution include the flux scaling
factor denoted by $\zeta_{\rm{0}}$, the standard deviation of the broadening
kernel $\sigma$, and a small multiplicative wavelength shift $\delta$.
Furthermore, we consider a variety of empirical and semi-empirical Fe ii
emission templates: Vestergaard & Wilkes (2001, VW01) and Mejía-Restrepo et
al. (2016, M16) cover the rest-frame UV while Boroson & Green (1992, BG92) and
Park et al. (2022, P22) cover the rest-frame optical. Bruhweiler & Verner
(2008, BV08) and Tsuzuki et al. (2006, T06) cover both regions. We use a VW01
template spliced with the Salviander et al. (2007) template, which
extrapolates underneath the Mg ii line from rest-frame 2200$-$3090Å.
Furthermore, the wavelength range 3090$-$3500Å is augmented with the T06
template (Shen & Liu, 2012). This version of VW01 is also used in other QSO
modelling codes such as PyQSOFit (Guo et al., 2018). We find the typical value
of the Gaussian broadening dispersion $\sigma$ to be 1600 km s-1 in the rest-
frame UV and 1300 km s-1 in the rest-frame optical.

In this work, we are not concerned with the specific properties of the Fe ii
emission, and thus we will not discuss the physical interpretation of the
dispersion and velocity shifts of the Fe ii emission. The Fe ii pseudo-
continuum is used solely as an approximation to remove iron emission when
significant in the spectra. Figure 1 shows the spectrum of J110352$+$100403
close to the Mg ii region with the four UV Fe ii templates models overplotted
along with the resulting emission-line models in a separate panel. Properties
of the Mg ii line model depend sensitively on the assumed Fe ii model. In the
extreme case of SDSS J093556.91$+$002255.6, differences in the Fe ii model
alone are responsible for shifting the measured full-width half-maximum (FWHM)
in a range from 3700 to 5200 km s-1. Similarly, the H$\beta$ line model is
also sensitive to the optical Fe ii model. In Section 3.2, we discuss how the
differences in measured line properties resulting from various Fe ii models
inform the measurement uncertainty.

Figure 1: Example model of the Mg ii emission feature of J110352$+$100403 with
the combined pseudo-continuum from the power-law, Balmer, and Fe ii
components. The line models differ from one another by the applied Fe ii
template as indicated in the legend. The resulting continuum for each template
is plotted in solid lines in the top panel and the continuum-subtracted line
profile model is plotted in the bottom panel. In this example, the Mg ii FWHM
between models with different Fe ii templates ranges from 4000 to 4400 km s-1.

The full pseudo-continuum is the sum of all contributing components, which is
uniquely defined by 5 free parameters. All components of the continuum are fit
simultaneously to selected pseudo-continuum windows close to the emission-line
of interest. For each emission feature, the local underlying continuum is fit
separately. We do not fit a “global" continuum across the the spectral range
from C iv to H$\beta$ in order to avoid biases due to deviations from a single
power-law model, such as dust reddening (e.g., Richards et al., 2003) and host
galaxy contributions (e.g., Vanden Berk et al., 2001). Outside irregular
circumstances, such as a discontinuity in the flux-calibrated spectrum between
the VIS and NIR arms, the pseudo-continuum modelling windows are selected
from: 1275–1290Å, 1348–1353Å, 1445–1455Å, 1687–1697Å, 1973–1983Å, 2200–2750Å,
2820–3300Å, 3500–3800Å, 4200–4230Å, and 4435–4700Å with occasional $\pm 30$Å
deviations to suit specific features of the spectra, avoid telluric regions,
or to accommodate the properties of particular emission or absorption
features.

The Balmer continuum is also often included in the pseudo-continuum model when
modelling QSO spectra, but it is not always well-constrained and is degenerate
with the power-law and Fe ii continuum (e.g., Wang et al., 2009; Shen & Liu,
2012), such that the Balmer contribution is not considered for the underlying
continuum in some other QSO studies (e.g., Shen et al., 2011). For the XQ-100
sample, we find that the Balmer continuum properties are not well-constrained
and the broad emission-line decomposition is not strongly affected by either
the inclusion or exclusion of the Balmer continuum. Therefore, in the
following sections, we present our results without the Balmer continuum, but
we quantify the effect of its inclusion in Appendix A.

###  3.2 Line Modelling

Broad emission-line profiles exhibit a wide range of properties and
complexities from asymmetries to multiple peaks and plateaus, making single
Gaussian models unsuitable. Instead, many QSO spectral modelling studies use a
multiple Gaussian approach to fit each emission feature (e.g., Greene & Ho,
2005; Shen et al., 2011; Rakshit et al., 2020). Following these studies, we
fit each broad emission-line with multiple $(N_{\rm{gauss}})$ symmetric
Gaussian functions having $3\times N_{\rm{gauss}}$ free parameters, to obtain
smooth realisations of the observed line profile. Similar to Rakshit et al.
(2020), we choose $N_{\rm{gauss}}$ = (3, 4, 4) for C iv, Mg ii, and H$\beta$,
respectively. The 4 Gaussian components of the Mg ii and H$\beta$ lines are
divided into 3 broad and 1 narrow component. For high luminosity QSOs, such as
the targets in the XQ-100 sample, [O iii] lines with FWHMs exceeding 1000 km
s-1 are more common (e.g. Shen & Liu, 2012; Coatman et al., 2019), so we adopt
a FWHM upper threshold of 1200 km s-1 for the H$\beta$ narrow lines. The Mg ii
narrow lines are often ambiguous and poorly constrained. Thus, we further
constrain the upper FWHM threshold for Mg ii to 1000 km s-1, ensuring that the
modelled components are indeed narrow. To measure the broad-line properties of
each line, we subtract the narrow-line contribution from the total line
profile, using only the 3 broad components to model the emission-line.

The adjoining [O iii] lines can present a challenge for modelling the redder
wing of the H$\beta$ line profile, but they are also useful to constrain the
width of the narrow H$\beta$ component. However, these adjoining lines are
infrequently detected in the XQ-100 spectra with J133254$+$005250 presented in
Figure 2 as one of the only two cases with detectable [O iii], alongside
J101818$+$054822\. Without the presence of the [O iii] lines, the
decomposition of the total H$\beta$ line profile into its broad and narrow
emission may not be unique.

While all broad emission-line profiles are affected by embedded narrow
absorption features, the effect that they have on the resulting model is more
significant for C iv. In order to obtain more appropriate models of the
intrinsic C iv broad emission profile, we apply an additional 2500 km s-1 box-
width sigma-clip mask with a 3$\sigma$-threshold. Every contiguous masked
region has a masked buffer window of 3 pixels, equivalent to 150 km s-1,
applied on each end. Most broad C iv emission profiles can be fit
automatically, but some QSOs contain features which are visually inspected and
masked.

If not accounted for, neighbouring lines can influence the measurement of the
intrinsic C iv broad-line properties. In order to disentangle the C iv line
model from its neighbours, we simultaneously model the broad Si
iv$\lambda$1398Å, O iv$\lambda$1402Å, N iv]$\lambda$1486Å, He
ii$\lambda$1640Å, and [O iii]$\lambda$1663Å lines, using one broad component
or one broad and one narrow component to constrain each neighbouring line. We
find that the C iv line properties are not sensitive to whether narrow
features, if present, in adjacent lines are modelled as a separate component.
The neighbouring lines are only modelled in order to account for their
influence on the C iv line properties. As such, we do not tabulate properties
of the neighbouring lines in our catalogue.

For both Mg ii and H$\beta$, the final emission-line properties, tabulated in
Table 3, are determined as the average of properties measured from the
resulting line models, created by applying in turn each of the four Fe ii
templates. We consider two primary sources of uncertainty in the measurement
of emission-line and continuum properties. One source is the uncertainty from
the various Fe ii emission templates and another is the measurement
uncertainty. We estimate the uncertainty from the Fe ii template by
independently modelling each spectrum with four models; VW01, T06, BV08, and
M16 at UV wavelengths and BG92, T06, P22, and BV08 at optical wavelengths.
Then we measure the line properties for a given model and quote the standard
deviation. We also estimate the measurement uncertainty using a Monte Carlo
approach by creating 50 synthetic spectra for individual target (e.g., Shen et
al., 2011), where the flux at each pixel is resampled from a symmetric
distribution with a standard deviation equivalent to the pixel flux error. We
assume that the noise in the spectrum follows a normal distribution. After
modelling all of the synthetic spectra independently and varying the Fe ii
template, the final measurement uncertainty is determined from these two
sources added in quadrature. Each of the two sources contributes roughly
equivalent uncertainty to emission-line FWHM, but the choice of Fe ii emission
template dominates the variance in the measured continuum luminosity.

For the C iv line properties, we use only the Monte Carlo uncertainty
estimated by modelling 50 synthetic spectra. In this case, we do not consider
the uncertainty from modelling different Fe ii templates, because the Fe ii
emission is weak in this wavelength region and it is not used to define the
continuum. The different realisations of the resampled spectra and their
resulting line models help to capture degeneracies in the way that flux can be
distributed between C iv and its neighbouring lines, propagating that
degeneracy into the uncertainty of the line properties.

We provide a data quality flag, indicated by “Quality_Flag”, for each
emission-line model which is used to identify where the median SNR per 50 km
s-1 resolution element of the data within the emission-line modeling region is
below 20. We manually flag additional targets with the Mg ii data quality flag
to indicate poor quality fits or that significant residual telluric features
are evident in the spectrum. As there are no targets below the SNR threshold
for the data quality flag for C iv, we instead use the flag to indicate where
we have manually adjusted the fit, by choosing more appropriate continuum
windows or manually masking absorption features. Additionally, we flag
targets, using “Hbeta_Truncation_Flag”, for which the red wings of the
H$\beta$ profile is clearly truncated by the edge of X-shooter’s NIR arm
wavelength coverage, which would reduce the reliability of the line model.
However, we do not exclude flagged targets from further analysis and
contextualisation of the XQ-100 sample in Section 5.

Figure 2 shows samples of emission-line models of SDSS J092041.76$+$072544.0
and J133254$+$005250, which are both lower redshift for our sample and contain
the H$\beta$ emission feature. Models of C iv, Mg ii, and H$\beta$ are
presented. In this figure, both Mg ii and H$\beta$ models use an underlying
T06 Fe ii template. Examples of all line models of C iv, Mg ii, and H$\beta$,
showing the emission-line models in greater detail, are provided as online
supplementary material, where models of Mg ii and H$\beta$ are separated by Fe
ii template. Due to the lack of a continuum redward of H$\beta$, we can only
use the blue side to constrain the continuum.

---
Figure 2: Example models of the C iv, Mg ii, and H$\beta$ emission-lines from
SDSS J092041.76$+$072544.0 and J133254$+$005250\. The spectroscopic data are
plotted in black, its error spectrum in grey, and the power-law continuum is
in orange. The error spectrum is shifted vertically such that the bottom of
the panel represents zero flux error. The combined pseudo-continuum which
includes a power-law and the Tsuzuki et al. (2006) Fe ii template is plotted
in blue. The red lines indicate the total line profile and the dashed lines
are the multiple Gaussian decomposition. We show the narrow-line model with
the green dotted line and in the C iv panel, green highlights the line models
of neighbouring lines. The residuals are shown normalized by the flux error,
$\sigma$, in order to represent the quantity minimised by the line-modelling
algorithm, (data-model)/error. We represent $\pm 3\sigma$ in the residual
panel with the dashed lines and we also show the result of the automated
sigma-clipping in the C iv residual, where masked features remain in blue
rather than red or green. Telluric absorption windows are denoted by the solid
grey bar in the residual panel. These figures are available for all targets in
the online supplementary material.

##  4 Single-Epoch Virial Mass Estimate

We measure the black hole mass from single-epoch spectroscopic data using the
virial estimate, which is a method routinely applied to QSO spectra (e.g.,
Vestergaard, 2002; McLure & Jarvis, 2002; McLure & Dunlop, 2004; Greene & Ho,
2005; Vestergaard & Peterson, 2006). The model assumes that the motion of gas
around the black hole is virialized and its dynamics are dominated by the
central gravitational field. The velocity-broadened line profile measures the
gas velocity and the nuclear continuum luminosity is used as a proxy for the
radius of the BLR. The radius-luminosity ($R$-$L$) relationship is an
empirical correlation derived from reverberation mapping experiments which
tightly links the radius of the BLR to the continuum luminosity (e.g., Kaspi
et al., 2000, 2005; Bentz et al., 2006; Bentz et al., 2013). Common emission-
lines used to estimate gas velocity include H$\beta$, C iv, and Mg ii, but the
H$\beta$ line is redshifted out of the X-shooter NIR coverage at $z\gtrsim 4$.
Instead, the Mg ii emission-line profile is found to generally be correlated
with H$\beta$ and can be used as its substitute in single-epoch virial black
hole mass estimates (e.g., Salviander et al., 2007; Shen et al., 2008; Wang et
al., 2009; Shen & Liu, 2012). Additionally, there are indications that the Mg
ii-based estimator is more reliable for QSOs with large (> 4000 km s-1)
H$\beta$ FWHM (see Marziani et al., 2013). The following equation describes
the single-epoch virial mass estimate,

$\left(\frac{M_{\rm{BH,vir}}}{M_{\odot}}\right)=10^{\rm{a}}\left[\frac{\lambda
L_{\lambda}}{10^{44}\,\rm{erg\,s^{-1}}}\right]^{b}\left[\frac{\rm{FWHM_{\rm{line}}}}{1000\,\rm{km\,s^{-1}}}\right]^{2}\,,$
(3)

where $\lambda L_{\lambda}$ is the monochromatic luminosity of the QSO
continuum, which we measure from the power-law continuum model, and FWHMline
is the measured line full-width half-maximum of the total broad line profile.
We opt to use the FWHM for the virial mass estimate instead of the line
dispersion, i.e., the second moment of the line profile. Although the
dispersion is well-defined for arbitrary line profiles and may have advantages
over the FWHM (e.g., Fromerth & Melia, 2000; Peterson et al., 2004; Collin et
al., 2006; Rafiee & Hall, 2011; Dalla Bontà et al., 2020), in practice, the
line dispersion is sensitive to the wings of the line profile, which are
naturally low in flux and can often be difficult to constrain independently
from noise due to the accretion disk and Fe ii continuum. We determine all
line properties, including the FWHM of Mg ii and H$\beta$, as the average of
the measurements obtained from spectral decomposition using each of the all
four Fe ii templates. We further quantify the deviation of the measured black
hole mass using each template in Appendix B.

The exponents (a, b) in Equation 3 depend on the choice of line and luminosity
and are empirically calibrated by reverberation mapping experiments. For the
Mg ii line and a monochromatic luminosity at rest-frame 3000 Å, (a, b) are
calibrated to the values (6.86, 0.5) in Vestergaard & Osmer (2009) and (6.74,
0.62) in Shen et al. (2011). On average, the differences between these
different calibrations are 0.1 dex, but virial mass estimators show an
instrinsic scatter of $\sim 0.3$ dex around their reverberation mapping
counterparts (Dalla Bontà et al., 2020), while the reverberation-based
estimates exhibit an intrinsic scatter of $\sim 0.4$ dex around the $M_{\rm
BH}-\sigma_{*}$ relation (Bennert et al., 2021), meaning the virial mass
estimates could have errors as large as $\sim 0.5$ dex. We adopt 0.5 dex as
our single-epoch virial black hole mass uncertainty in this study. In this
study, we use the Mg ii-based calibration from Shen et al. (2011), which is
anchored to a high-luminosity subset of local reverberation mapping
determinations from H$\beta$, making it better suited to the XQ-100 sources.
Other broad emission-lines present in our spectra can be used to obtain virial
estimates of the black hole mass as well. Compared with the Mg ii line, the C
iv line is more likely to be affected by non-virial motions, such as the
radiatively driven outflows (e.g., Proga et al., 2000; Saturni et al., 2018),
making it potentially a biased black hole mass estimator (e.g., Baskin & Laor,
2005; Sulentic et al., 2007; Shen et al., 2008). We provide a measure of the C
iv blueshift, a signature of outflowing emission (Richards et al., 2011), in
order to quantify how much the C iv-based black hole masses may be biased by
non-virial components. The velocity shifts of C iv are measured relative to
the systemic redshifts from López et al. (2016).

Table 1 presents the virial relations and specific calibrations used in this
study for determining the black hole mass using C iv, Mg ii, and H$\beta$
emission-lines. Using the 3000 Å luminosity, we also estimate the bolometric
luminosity by adopting a fixed bolometric correction factor of 5.15, which can
lead to errors as large as 50%, or $\sim$0.3 dex, for individual QSOs
(Richards et al., 2006).

The typical final measurement uncertainties are $\sim$240 km s-1 for the Mg ii
FWHM and 0.01 dex for the 3000 Å monochromatic luminosity, resulting in an
average of 0.06 dex uncertainty in the Mg ii black hole mass estimate.
Similarly for H$\beta$, the average uncertainty is $\sim$640 km s-1 for the
FWHM and 0.02 dex for the 5100 Å luminosity, resulting in 0.12 dex mean
uncertainty in $M_{\rm{BH}}$. Therefore, the measurement uncertainty for both
estimates are well below the errors of the virial mass estimator. Without the
additional uncertainties introduced by the multiple Fe ii templates, the mean
final measurement uncertainty in C iv FWHM is $\sim$130 km s-1 with negligible
uncertainty in the 1450Å luminosity. The typical black hole mass uncertainty
from the C iv virial estimator is thus 0.02 dex. However, line asymmetries and
contribution from QSO outflows or disk winds should imply a greater
uncertainty of C iv-based black hole masses.

Table 1:  Virial relations used in this study (see Equation 3) Emission-line | Luminosity | a | b | Ref
---|---|---|---|---
C iv | 1450 Å | 6.66 | 0.53 | 1
Mg ii | 3000 Å | 6.74 | 0.62 | 2
H$\beta$ | 5100 Å | 6.91 | 0.50 | 1
1 Vestergaard & Peterson (2006) 2 Shen et al. (2011)

##  5 Results and Discussion

For each of the 3 broad emission-lines (C iv, Mg ii, and H$\beta$) used for
virial black hole mass estimates in this study, we measure 6 properties of the
broad line profile, described in Table 2. The FWHM of each line is used in the
virial mass estimate. The line dispersion, Sigma, is the second moment of the
line profile. We also measure the Blueshift, equivalent width (EW), and
wavelength of the line profile peak (pWavelength). The blueshift is measured
from the median wavelength bisecting the total flux of the line profile, and
can be a useful indicator of QSO orientation, particularly with the C iv line
(e.g., Richards et al., 2002; Yong et al., 2020). We measure the integrated
line luminosity (iLuminosity) from the reconstructed broad emission-line
profile. Ratios of the integrated luminosity may be used for chemical
abundance estimates (e.g., Hamann & Ferland, 1999; Hamann et al., 2002; Nagao
et al., 2006), while the EWs may be used in studies of the Baldwin effect
(e.g., Baldwin, 1977; Patiño Álvarez et al., 2016). We present a sample of
measured emission-line properties for 5 selected QSOs in Table 3, while the
full table is available as online supplementary material.

Table 2:  Description of measured properties for each broad emission-line. Suffix | Description | Units
---|---|---
FWHM | Full-width half-maximum of profile | km s-1
Sigma | Second moment of profile | km s-1
Blueshift | Defined by the flux-bisecting wavelength | km s-1
EW | Equivalent width in rest-frame | Å
pWavelength | Peak wavelength | Å
iLuminosity | Integrated log luminosity | erg s-1

###  5.1 QSO Variability

Ever since the identification of the first QSOs, it has been recognized that
QSOs are intrinsically variable (Matthews & Sandage, 1963). Variations of QSO
brightness occur on a large range of timescales from hours to years, where
short timescales are typically associated with higher energy X-ray flux and
longer timescales to the disk emission (Edelson et al., 2015; Lira et al.,
2015). Models of QSO variability focus on its stochastic origin, comparing the
ensemble variability structure function (SF) to damped random walk (DRW)
models (e.g., Kelly et al., 2009; MacLeod et al., 2010; Kozłowski, 2016;
Suberlak et al., 2021).

Many studies have shown that the amplitude of QSO variability is anti-
correlated with the QSO luminosity, with little apparent dependence on the
redshift (e.g., Vanden Berk et al., 2004; MacLeod et al., 2010; Kozłowski,
2016; Caplar et al., 2017). For a high-redshift and high-luminosity sample,
such as XQ-100, the long-term asymptotic variability amplitude (SF∞) is
measured to be low, from 0.1 mag (e.g., MacLeod et al., 2010; Suberlak et al.,
2021) to 0.25 mag (e.g., Kozłowski, 2016), where these studies made use of
SDSS Stripe 82 (Jiang et al., 2014), an equatorial region imaged repeatedly
during 2005, 2006, and 2007.

In this study, our sample of XQ-100 QSOs is flux calibrated to photometry
observed at a separate epoch, thus our results are susceptible to QSO
variability. In order to constrain variability in the XQ-100 sample, we
crossmatch all sources with the Pan-STARRS DR2 detections table (Flewelling et
al., 2020), removing all cases for which the number of multi-epoch i-band
detections is less than 5. This results in a nearly complete sample of 82
QSOs, each with up to 33 independent i-band detections across a period of 3-5
years from 2009-2015. Models of QSO variability characteristic timescales
typically find a best-fit parameter of a few hundred days for supermassive
black holes in the rest-frame (e.g., MacLeod et al., 2010; Burke et al., 2021;
Suberlak et al., 2021), so the Pan-STARRS detections cover little more than
one rest-frame characteristic timescale. For this analysis, we estimate the
observed variability amplitude using the structure function,
SF${}_{\rm{obs}}(\Delta t)$ = $\rm{rms}\left[m(t)-m(t+\Delta t)\right]$, where
rms is the root-mean-square deviation. We calculate SF${}_{\rm{obs}}(\Delta
t_{\rm{obs}})$ from the ensemble of 82 QSOs with multi-epoch photometric
measurements by considering the distribution of $\Delta m$, the measured
magnitude difference, for each pair of measurements separated by a time-lag,
$\Delta t_{\rm{obs}}\sim$ 2, 3, or 4 years in the observed frame.

Using Pan-STARRS DR2 i-band detections, we find the ensemble variability
amplitude of the XQ-100 sample to be SF${}_{\rm{obs}}(\Delta t_{\rm{obs}})$ =
(0.125, 0.132, 0.150) mag for observed frame $\Delta t_{\rm{obs}}\sim$ (2, 3,
4) years, which is consistent with a luminous QSO asymptotic long-term
variability of SF${}_{\infty}<0.20$ (MacLeod et al., 2010; Kozłowski, 2016).
The photometric calibrations we have used span an even wider timeframe
relative to the spectroscopic observations taken between 2012–2014. Therefore,
we assume the asymptotic variability as our uncertainty in the overall flux
normalisation for each spectrum. A 0.20 mag variability amplitude between the
X-shooter and photometric observation would manifest as $<0.1$ dex uncertainty
in the measured luminosities. As a consequence, we expect a black hole mass
uncertainty up to $\sim$0.05 dex may be present from variability.

###  5.2 XQ-100 Sample Properties

We now examine the black hole mass estimates from the C iv, Mg ii, and
H$\beta$-based virial estimators and contextualise the results. For both the
H$\beta$ and Mg ii lines, we subtract the narrow component to obtain the pure
broad emission profile (e.g., Kovačević-Dojčinović et al., 2017) and measure
the broad-line properties. Figure 3 compares the three mass estimates to each
other. As we do not exclude any flagged targets from further analysis and
contextualisation, the C iv and Mg ii comparison contains all 100 QSOs in the
sample and the comparisons to H$\beta$ are limited to 21 measurements. All
three panels show data dispersed around the 1:1 relation denoted by the black
dashed line, where the total sample variance is smaller than the adopted 0.5
dex uncertainty of the virial mass relation, which is shown for scale on the
top-left of each plot. The mean differences and the standard deviation between
black hole mass estimates are
$\log\left(\rm{M_{Mg\,\textsc{ii}}}/\rm{M_{C\,\textsc{iv}}}\right)=-0.05\pm
0.34$,
$\log\left(\rm{M_{H\textsc{$\beta$}}}/\rm{M_{C\,\textsc{iv}}}\right)=-0.12\pm
0.36$, and
$\log\left(\rm{M_{Mg\,\textsc{ii}}}/\rm{M_{H\textsc{$\beta$}}}\right)=0.06\pm
0.22$. In the online supplementary table, we provide an averaged black hole
mass estimate from all measured lines and determine a “Mbh_Flag” for when the
averaged masses differ from the Mg ii-based masses by more than 0.3 dex.
Throughout the XQ-100 sample, 8% of QSOs are flagged in this way, and only one
(SDSSJ1042$+$1957) has a H$\beta$ virial mass estimate to shed light on the
discrepancy between C iv and Mg ii-based masses. For SDSSJ1042$+$1957, the
H$\beta$-based mass estimate is much more consistent with C iv than Mg ii. The
reason may be that the emission-lines are relatively narrow (FWHM$\sim$2000 km
s-1) compared to the rest of the sample, and only the Mg ii line models
consistently contain a narrow component.

Although the mass measurement for the XQ-100 sample relies on an extrapolation
of the well-determined and lower luminosity H$\beta$ reverberation mapping
$R$-$L$ relation (e.g., Bentz et al., 2013), we find all three virial
estimators to remain consistent with each other within the measurement
uncertainties in the high luminosity regime. This shows that the relative
physical geometry of the three line-emitting regions does not change
significantly with luminosity. Additionally, there are minimal systematic
differences between our models to individual emission-lines and this increases
our confidence in the resulting mass estimate.

In the case of outliers such as SDSSJ1202–0054, where
M${}_{\rm{H\textsc{$\beta$}}}\sim 9.8$ and M${}_{\rm{C\,\textsc{iv}}}\sim
9.0$, or the inverse scenario for J1320299–052335, where
M${}_{\rm{H\textsc{$\beta$}}}\sim 9.2$ and M${}_{\rm{C\,\textsc{iv}}}\sim
9.8$, their H$\beta$ profiles are truncated and broad components are not well
constrained. We present SDSSJ1202–0054 in additional detail in Appendix B.
Other outliers, such as SDSS J074711.15$+$273903.3 which exhibits a > 1 dex
mass difference between different lines, are characterised by relatively poor
data quality in the wavelength regions surrounding the Mg ii line, resulting
in weaker constraints on the Fe ii continuum model and a narrower emission-
line FWHM. Residual telluric features from an insufficient telluric correction
can corrupt the continuum model. Additionally, for targets with $3.8\lesssim
z\lesssim 4.2$, the Mg ii line overlaps with a wide H2O telluric absorption
band at 1.4 $\mu$m which deteriorates the quality of its detection.

Figure 3: Comparison of virial black hole masses based on Mg ii, C iv, and
H$\beta$ relations in Table 1. The blue shaded contours represent the two-
dimensional continuous probability density distribution calculated with a
kernel density estimator (Waskom, 2021). Each subsequent contour level marks
density iso-proportions increasing by an additional 10% up to 90% enclosed.
The red error bars plotted on the top left of each plot show the extent of the
0.5 dex uncertainty, which is a conservative estimate of the uncertainty
inherent in the virial mass estimation method. Comparisons between all three
virial mass estimates are scatted around the 1:1 relation, indicated by the
black dashed line. The mean and standard deviation listed in the top-left of
each panel are based on the residual from the mass measure on the y-axis
subtracted by the mass measure on the x-axis.

We compare the distribution of black hole masses and bolometric luminosities
in XQ-100 to the SDSS DR7 QSO catalogue from Shen et al. (2011) in Figure 4,
using mean masses from at least two virial mass estimates to represent the
XQ-100 sample. The QSOs in the SDSS DR7 catalogue cover $0.06<z<5.47$ in
redshift and their black hole masses are primarily based on the Mg ii
emission-line with the same virial mass calibration we have used, but
$\sim$40% of the sample utilise either C iv or H$\beta$ with calibrations from
Vestergaard & Peterson (2006). The median black hole mass and bolometric
luminosity for the SDSS DR7 QSO catalogue is
$\log{(\rm{M_{BH}}/\rm{M_{\odot}})}=9.0^{+0.5}_{-0.6}$ and
$\log{(\rm{L_{bol}}/\rm{erg\,s^{-1}})}=46.4^{+0.5}_{-0.7}$, where the
asymmetric dispersion is set by the 16% and 84% percentile.

We also identify the sub-sample of the SDSS DR7 QSO catalogue consisting of
3127 QSOs within the $3.5<z<4.5$ redshift range of the XQ-100 sample. Relative
to the full catalogue of 104746 objects, the sub-sample has higher median
black hole mass and luminosity with
$\log{(\rm{M_{BH}}/\rm{M_{\odot}})}=9.3^{+0.5}_{-0.8}$ and
$\log{(\rm{L_{bol}}/\rm{erg\,s^{-1}})}=47.0^{+0.3}_{-0.3}$. The XQ-100 sample
is more tightly distributed at the high-mass and high-luminosity tail of the
redshift-selected SDSS DR7 QSO sub-sample with
$\log{(\rm{M_{BH}}/\rm{M_{\odot}})}=9.6^{+0.3}_{-0.4}$ and
$\log{(\rm{L_{bol}}/\rm{erg\,s^{-1}})}=47.5^{+0.2}_{-0.2}$. A sub-sample (27%)
of the XQ-100 sample exhibits mildly super-Eddington accretion rates. We also
plot J2157$-$3602, one of the most luminous known QSO (Onken et al., 2020),
which is at a comparable redshift ($z=4.692$), with a black hole mass of
$\log{(\rm{M_{BH}}/\rm{M_{\odot}})}=10.33$ and bolometric luminosity
$\log{(\rm{L_{bol}}/\rm{erg\,s^{-1}})}=48.4$, measured with the same approach
used here (Lai et al., 2023). The full range of XQ-100 QSO properties is
measured to span $\log{(\rm{M_{BH}}/\rm{M_{\odot}})}=8.6-10.3$ in black hole
mass and $\log{(\rm{L_{bol}}/\rm{erg\,s^{-1}})}=46.7-48.0$ in bolometric
luminosity, where over 85% of the sample lies within
$\log(\rm{M_{BH}}/\rm{M_{\odot}})=9-10$ and
$\log{(\rm{L_{bol}}/\rm{erg\,s^{-1}})}=47-48$.

We find that 55 of the targets have C iv measurements in the Shen et al.
(2011) catalogue, which has also produced C iv-based virial mass estimates
using the same Vestergaard & Peterson (2006) calibration. The mean and
standard deviation of differences between the mass estimates from our work and
from Shen et al. (2011) is
$\log(\rm{M_{\rm{C\,\textsc{iv}}}}/\rm{M_{\rm{Shen}}})=-0.07\pm 0.18$ using
the C iv-based mass from our sample and
$\log(\rm{M_{\rm{avg}}}/\rm{M_{\rm{Shen}}})=-0.12\pm 0.24$ using the mean
mass, which is a small systematic adjustment towards lower masses on average.
We find no significant correlations between these mass differences and other
measurable line properties.

Figure 4: Distribution of XQ-100 black hole masses and luminosities compared to the SDSS DR7 QSO catalogue from Shen et al. (2011). The mean virial black hole mass measurements of XQ-100 are shown in purple and the SDSS DR7 data points are shown in blue. The contours delineate iso-proportions in the continuous probability distribution of the higher redshift SDSS sub-sample calculated with a kernel density estimator (Waskom, 2021). Each contour encloses an additional 10% up to a 50% threshold. The black hole mass and bolometric luminosity histograms of the XQ-100 sample are normalised to the same area. Compared to the SDSS DR7 QSO catalogue, the XQ-100 sample occupies the high mass and high luminosity tail. The orange point is J2157$-$3602 ($z=4.692$), one of the most luminous known QSOs (Onken et al., 2020). Table 3:  Measured emission-line properties of Mg ii, C iv, and H$\beta$ and continuum measurements for a selected sample of QSOs. Refer to Table 2 for the entry explanations. The reported uncertainties are sourced from the measurement and do not include the additional error of the virial mass method or QSO variability. The full table containing details for all XQ-100 QSOs is available as online supplementary material. | Units | HB89 0000-263 | PMN J0100-2708 | BRI 0241-0146 | J112634-012436 | J1401+0244
---|---|---|---|---|---|---
OBJECT |  | HB89 0000-263 | PMN J0100-2708 | BRI 0241-0146 | J112634-012436 | J1401+0244
RA |  | 00:03:22.79 | 01:00:12.47 | 02:44:01.83 | 11:26:34.42 | 14:01:46.52
Dec |  | -26:03:19.40 | -27:08:52.10 | -01:34:06.30 | -01:24:38.00 | 02:44:37.70
redshift |  | 4.125 | 3.546 | 4.055 | 3.765 | 4.408
Source_i |  | SkyMapper | SkyMapper | SkyMapper | SkyMapper | SkyMapper
imag | mag | 17.075 $\pm$ 0.006 | 18.928 $\pm$ 0.026 | 18.099 $\pm$ 0.028 | 19.038 $\pm$ 0.071 | 18.395 $\pm$ 0.014
Source_J |  | VHS | VIKINGDR5 | VHS | UKIDSS | UKIDSS
Jmag | mag | 16.023 $\pm$ 0.008 | 17.590 $\pm$ 0.011 | 16.916 $\pm$ 0.015 | 18.053 $\pm$ 0.038 | 17.419 $\pm$ 0.032
CIV_FWHM | km s-1 | 5275 $\pm$ 34 | 6103 $\pm$ 228 | 8387 $\pm$ 418 | 5746 $\pm$ 64 | 6048 $\pm$ 195
CIV_Sigma | km s-1 | 3820 $\pm$ 91 | 2888 $\pm$ 367 | 3568 $\pm$ 229 | 3662 $\pm$ 134 | 3888 $\pm$ 276
CIV_Blueshift | km s-1 | 1206 $\pm$ 45 | 1618 $\pm$ 110 | 1833 $\pm$ 228 | 2191 $\pm$ 44 | 821 $\pm$ 97
CIV_EW | Å | 27.370 $\pm$ 0.270 | 23.930 $\pm$ 1.060 | 23.310 $\pm$ 1.100 | 23.270 $\pm$ 0.490 | 39.040 $\pm$ 0.450
CIV_pWavelength | Å | 1543.380 $\pm$ 0.140 | 1540.830 $\pm$ 0.510 | 1540.860 $\pm$ 0.740 | 1539.290 $\pm$ 0.670 | 1545.790 $\pm$ 0.770
CIV_iLuminosity | erg s-1 | 45.754 $\pm$ 0.004 | 44.833 $\pm$ 0.019 | 45.256 $\pm$ 0.021 | 44.819 $\pm$ 0.008 | 45.430 $\pm$ 0.005
CIV_PL_slope |  | -1.622 $\pm$ 0.008 | -1.352 $\pm$ 0.020 | -1.525 $\pm$ 0.016 | -1.340 $\pm$ 0.025 | -1.374 $\pm$ 0.008
MgII_FWHM | km s-1 | 3396 $\pm$ 111 | 3599 $\pm$ 238 | 6378 $\pm$ 537 | 4574 $\pm$ 288 | 4319 $\pm$ 313
MgII_Sigma | km s-1 | 3379 $\pm$ 113 | 2810 $\pm$ 297 | 3488 $\pm$ 386 | 3761 $\pm$ 75 | 3410 $\pm$ 245
MgII_Blueshift | km s-1 | 217 $\pm$ 71 | 434 $\pm$ 171 | -239 $\pm$ 100 | -57 $\pm$ 132 | -289 $\pm$ 103
MgII_EW | Å | 21.620 $\pm$ 1.670 | 28.940 $\pm$ 3.150 | 40.640 $\pm$ 3.270 | 36.500 $\pm$ 2.280 | 37.360 $\pm$ 2.110
MgII_pWavelength | Å | 2798.540 $\pm$ 2.310 | 2792.860 $\pm$ 0.990 | 2808.220 $\pm$ 4.840 | 2794.430 $\pm$ 0.650 | 2804.110 $\pm$ 0.450
MgII_iLuminosity | erg s-1 | 45.210 $\pm$ 0.039 | 44.502 $\pm$ 0.059 | 45.083 $\pm$ 0.038 | 44.502 $\pm$ 0.028 | 44.961 $\pm$ 0.032
MgII_PL_slope |  | -1.339 $\pm$ 0.087 | -1.145 $\pm$ 0.023 | -1.519 $\pm$ 0.140 | -1.685 $\pm$ 0.087 | -1.400 $\pm$ 0.155
Hbeta_FWHM | km s-1 |  | 5308 $\pm$ 924 |  |  |
Hbeta_Sigma | km s-1 |  | 3864 $\pm$ 637 |  |  |
Hbeta_Blueshift | km s-1 |  | -634 $\pm$ 330 |  |  |
Hbeta_EW | Å |  | 86.440 $\pm$ 25.040 |  |  |
Hbeta_pWavelength | Å |  | 4856.340 $\pm$ 4.640 |  |  |
Hbeta_iLuminosity | erg s-1 |  | 44.494 $\pm$ 0.099 |  |  |
Hbeta_PL_slope |  |  | -2.426 $\pm$ 0.395 |  |  |
log_L1450 | erg s-1 | 47.522 $\pm$ 0.001 | 46.651 $\pm$ 0.001 | 47.090 $\pm$ 0.001 | 46.647 $\pm$ 0.001 | 47.038 $\pm$ 0.001
log_L3000 | erg s-1 | 47.312 $\pm$ 0.018 | 46.486 $\pm$ 0.021 | 46.907 $\pm$ 0.023 | 46.369 $\pm$ 0.013 | 46.824 $\pm$ 0.019
log_L5100 | erg s-1 |  | 46.240 $\pm$ 0.057 |  |  |
logMBH_CIV | M⊙ | 9.971 $\pm$ 0.006 | 9.636 $\pm$ 0.032 | 10.145 $\pm$ 0.043 | 9.582 $\pm$ 0.010 | 9.833 $\pm$ 0.028
CIV_Quality_Flag |  | 1 |  |  |  |
logMBH_MgII | M⊙ | 9.855 $\pm$ 0.030 | 9.394 $\pm$ 0.059 | 10.152 $\pm$ 0.074 | 9.529 $\pm$ 0.055 | 9.762 $\pm$ 0.064
MgII_Quality_Flag |  |  |  | 1 |  |
logMBH_Hbeta | M⊙ |  | 9.480 $\pm$ 0.154 |  |  |
Hbeta_Quality_Flag |  |  | 1 |  |  |
logMBH_avg | M⊙ | 9.913 $\pm$ 0.015 | 9.503 $\pm$ 0.056 | 10.148 $\pm$ 0.043 | 9.556 $\pm$ 0.028 | 9.797 $\pm$ 0.035
Mbh_Flag |  |  |  |  |  |
NIR_VIS_Flag |  |  |  |  |  |
Hbeta_Truncation_Flag |  |  | 1 |  |  |

##  6 Summary and Conclusion

Infrared echelle spectroscopic observations of high-redshift QSOs provide an
opportunity to investigate their optical and ultraviolet atomic transitions.
The XQ-100 legacy survey provides a high-quality sample of 100 QSOs in the
redshift range of $z=3.5-4.5$ with high SNR, wide spectroscopic coverage
between its three observation arms, and moderate resolving power.

In this study, we examine rest-frame UV and optical broad-emission-lines from
all 100 QSOs in the XQ-100 legacy survey. We measure properties of the C iv,
Mg ii, and H$\beta$ emission-lines as well as the QSO continuum to estimate
QSO luminosities and black hole masses through virial relations. The main
results of this study are as follows:

  * •

We measure the C iv and Mg ii line for all 100 QSOs and the H$\beta$ line for
21 QSOs, using multiple templates to estimate the underlying Fe ii emission.
The virial mass estimate is based on the measured FWHM of all three broad
emission-lines and the continuum luminosity measured near each respective
emission-line at 1450, 3000, and 5100 Å. We provide an averaged black hole
mass estimate from all measured emission-lines for each QSO in the online
supplementary table${}^{\ref{github_footnote}}$ and determine the black hole
masses of the XQ-100 sample to be
$\log{(\rm{M_{BH}}/\rm{M_{\odot}})}=8.6-10.3$. A comparison of mass
measurements between the Mg ii virial mass estimate and the C iv and H$\beta$
virial estimates show a mean difference and standard deviation of $-0.05\pm
0.34$ dex and $0.06\pm 0.22$ dex, respectively, which are both well below the
0.5 dex uncertainty of the virial estimate. There is a general consistency
between the mass estimates derived from the C iv, Mg ii, and H$\beta$ broad
emission lines. Using a fixed 5.15 bolometric correction factor applied to the
3000 Å continuum luminosity, we estimate the bolometric luminosity range of
the XQ-100 sample to be $\log{(\rm{L_{bol}}/\rm{erg\,s^{-1}})}=46.7-48.0$.

  * •

Compared to the SDSS DR7 QSO catalogue, QSOs in the XQ-100 legacy survey
occupy the high-mass and high-luminosity tail of the distribution. A sizable
sub-sample consisting of 27% of the XQ-100 QSOs are accreting at mildly super-
Eddington rates.

  * •

For each broad emission-line from C iv, Mg ii, and H$\beta$, we measure 6
properties from the broad line profile and release the full set of
measurements as online supplementary material. The measured properties of each
line include the full-width half maximum (FWHM), line dispersion, blueshift,
equivalent width (EW), wavelength of the peak line profile, and integrated
luminosity. We also release example figures of all line models in the sample
as online material222also available at https://github.com/samlaihei/XQ-100 .

Characterising basic properties of the XQ-100 QSOs enables a variety of
follow-up research in QSO astrophysics, from chemical enrichment history using
emission-line diagnostics to black hole orientation and QSO outflows. As a
sample of some of the most luminous QSOs in redshift $3.5<z<4.5$, the XQ-100
targets are among most massive, rapidly accreting black holes in the early
universe and likely harbour the most massive and active host galaxies as well.
These targets can potentially be used to further investigate the relationship
between black holes and their host galaxies in the high redshift universe.

## Acknowledgements

We thank the anonymous referee for their constructive comments and suggestions
which have improved this manuscript. We also thank the authors of Vestergaard
& Wilkes (2001), Tsuzuki et al. (2006), Bruhweiler & Verner (2008), Mejía-
Restrepo et al. (2016), Boroson & Green (1992), and Park et al. (2022) for
producing and sharing their Fe ii emission templates.

S.L. is grateful to the Research School of Astronomy & Astrophysics at
Australian National University for funding his Ph.D. studentship.

CAO was supported by the Australian Research Council (ARC) through Discovery
Project DP190100252.

This paper is based on observations made with ESO Telescopes at the La Silla
Paranal Observatory under programme ID 189.A-0424.

The national facility capability for SkyMapper has been funded through ARC
LIEF grant LE130100104 from the Australian Research Council, awarded to the
University of Sydney, the Australian National University, Swinburne University
of Technology, the University of Queensland, the University of Western
Australia, the University of Melbourne, Curtin University of Technology,
Monash University and the Australian Astronomical Observatory. SkyMapper is
owned and operated by The Australian National University’s Research School of
Astronomy and Astrophysics. The survey data were processed and provided by the
SkyMapper Team at ANU. The SkyMapper node of the All-Sky Virtual Observatory
(ASVO) is hosted at the National Computational Infrastructure (NCI).
Development and support of the SkyMapper node of the ASVO has been funded in
part by Astronomy Australia Limited (AAL) and the Australian Government
through the Commonwealth’s Education Investment Fund (EIF) and National
Collaborative Research Infrastructure Strategy (NCRIS), particularly the
National eResearch Collaboration Tools and Resources (NeCTAR) and the
Australian National Data Service Projects (ANDS).

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
made possible through contributions by the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society
and its participating institutes, the Max Planck Institute for Astronomy,
Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
Garching, The Johns Hopkins University, Durham University, the University of
Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

The VISTA Hemisphere Survey data products served at Astro Data Lab are based
on observations collected at the European Organisation for Astronomical
Research in the Southern Hemisphere under ESO programme 179.A-2010, and/or
data products created thereof.

This work is based in part on data obtained as part of the UKIRT Infrared Deep
Sky Survey and the UKIRT Hemisphere Survey.

This publication has made use of data from the VIKING survey from VISTA at the
ESO Paranal Observatory, programme ID 179.A-2004. Data processing has been
contributed by the VISTA Data Flow System at CASU, Cambridge and WFAU,
Edinburgh.

This publication makes use of data products from the Two Micron All Sky
Survey, which is a joint project of the University of Massachusetts and the
Infrared Processing and Analysis Center/California Institute of Technology,
funded by the National Aeronautics and Space Administration and the National
Science Foundation.

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. The Participating Institutions are the American
Museum of Natural History, Astrophysical Institute Potsdam, University of
Basel, University of Cambridge, Case Western Reserve University, University of
Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the
Japan Participation Group, Johns Hopkins University, the Joint Institute for
Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and
Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences
(LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for
Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico
State University, Ohio State University, University of Pittsburgh, University
of Portsmouth, Princeton University, the United States Naval Observatory, and
the University of Washington.

This project used public archival data from the Dark Energy Survey (DES).
Funding for the DES Projects has been provided by the U.S. Department of
Energy, the U.S. National Science Foundation, the Ministry of Science and
Education of Spain, the Science and Technology Facilities Council of the
United Kingdom, the Higher Education Funding Council for England, the National
Center for Supercomputing Applications at the University of Illinois at
Urbana-Champaign, the Kavli Institute of Cosmological Physics at the
University of Chicago, the Center for Cosmology and Astro-Particle Physics at
the Ohio State University, the Mitchell Institute for Fundamental Physics and
Astronomy at Texas A&M University, Financiadora de Estudos e Projetos,
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro,
Conselho Nacional de Desenvolvimento Científico e Tecnológico and the
Ministério da Ciência, Tecnologia e Inovação, the Deutsche
Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy
Survey.

The Collaborating Institutions are Argonne National Laboratory, the University
of California at Santa Cruz, the University of Cambridge, Centro de
Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the
University of Chicago, University College London, the DES-Brazil Consortium,
the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH)
Zürich, Fermi National Accelerator Laboratory, the University of Illinois at
Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the
Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory,
the Ludwig-Maximilians Universität München and the associated Excellence
Cluster Universe, the University of Michigan, the National Optical Astronomy
Observatory, the University of Nottingham, The Ohio State University, the
OzDES Membership Consortium, the University of Pennsylvania, the University of
Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the
University of Sussex, and Texas A&M University.

Based in part on observations at Cerro Tololo Inter-American Observatory,
National Optical Astronomy Observatory, which is operated by the Association
of Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation.

Software packages used in this study include Numpy (van der Walt et al.,
2011), Scipy (Virtanen et al., 2020), Astropy (Astropy Collaboration et al.,
2013), Specutils (Earl et al., 2022), Matplotlib (Hunter, 2007), and seaborn
(Waskom, 2021).

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author. The post-processed spectra, supplementary table, and
figures can be downloaded from a GitHub repository:
https://github.com/samlaihei/XQ-100.

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##  Appendix A Significance of the Balmer Continuum

In Section 3.1, we discussed our pseudo-continuum model which includes two
components: a power-law and Fe ii flux. The Balmer continuum is also often
considered as part of a QSO pseudo-continuum model. However, we found that for
the sources in our XQ-100 sample, the broad emission-line models are not
strongly affected by either the inclusion or exclusion of the Balmer
continuum. We refer to similar studies of QSO spectra and use the following
model for the Balmer continuum (e.g., Grandi, 1982; Dietrich et al., 2002;
Wang et al., 2009; Kovačević et al., 2014):

$\displaystyle
F_{\rm{Bal}}(\lambda;F_{\rm{0}},T_{\rm{e}},\tau_{\lambda})=F_{\rm{Bal,0}}\,B_{\lambda}(\lambda,T_{\rm{e}})(1-e^{-\tau_{\lambda}});$
$\displaystyle\lambda\leq\lambda_{\rm{BE}}\,,$ (4)

where $F_{\rm{Bal,0}}$ is the normalisation, $B_{\lambda}(\lambda,T_{\rm{e}})$
is the Planck blackbody with uniform electron temperature $T_{\rm{e}}$, and
$\tau_{\lambda}$ is the optical depth. This Balmer continuum is defined at
wavelengths shorter than the Balmer edge at rest-frame
$\lambda_{\rm{BE}}\equiv 3646$ Å. Here, we quantify the difference in our
results by including the Balmer continuum in Table 4, which measures the
effect in the resulting Mg ii model properties. From the entire sample of 100
QSOs, we quantify the effect in terms of the mean residual and its standard
deviation. The change in each line property resulting from pseudocontinuum
models with the Balmer continuum is typically no larger than 1%. With
reference to the mean uncertainties of the measured emission-line properties
in our sample, the inclusion of the Balmer continuum has a statistically
insignificant effect on all measured Mg ii line properties and there is no
observable systematic bias to emission-line models by removing the Balmer
continuum from our pseudocontinuum model. However, the absence of the Balmer
model can affect the slope of the power-law continuum and amplitude of the Fe
ii models.

Table 4:  Mean difference and standard deviation in the measured line properties of the Mg ii line between including and excluding the Balmer continuum flux contribution. Refer to Table 2 for a description of each line property. The monochromatic luminosity at 3000Å, L3000, has units of erg s-1 and is represented on a log-scale as with the integrated line luminosity, iLuminosity. For comparison, we show the mean value measured in the XQ-100 sample for each line property and the mean uncertainty. Mg ii Property | Balmer Residual | Sample Mean
---|---|---
FWHM |  $54\pm 189$ |  $3633\pm 237$
Sigma |  $16\pm 146$ |  $2821\pm 286$
Blueshift |  $7\pm 45$ |  $-240\pm 99$
EW |  $0.2\pm 1.0$ |  $30\pm 2$
pWavelength |  $-0.10\pm 0.58$ |  $2803\pm 1$
iLuminosity |  $0.00\pm 0.01$ |  $44.78\pm 0.04$
L3000 |  $0.00\pm 0.01$ |  $46.78\pm 0.01$

##  Appendix B Black hole mass comparisons

In this section, we discuss outliers between black hole masses determined from
different emission-lines and variations in mass measurements between different
assumptions for the Fe ii model. Among those with a greater than $0.3$ dex
difference between the Mg ii-based single-epoch virial mass estimate and the
averaged mass from all measured emission-lines as flagged by the “Mbh_Flag”,
we focus on two targets with the highest mass discrepancy that are not flagged
by any quality flags, PSS J0121$+$0347 and BR J0714–6455, with
$\log\left(\rm{M_{mean}}/\rm{M_{Mg\,\textsc{ii}}}\right)$ = $-0.36$ and
$0.31$, respectively. As another example, we show SDSSJ1202–0054, which was
identified as an outlier in Section 5.2 due to greater than 0.5 dex difference
between the H$\beta$ and C iv-based black hole masses.

In Figure 5, we present example emission-line models of C iv and Mg ii for the
“Mbh_Flag” outliers PSS J0121$+$0347 and BR J0714–6455. In the case of PSS
J0121$+$0347, the C iv line profile is sharply peaked. As seen from the
residual on both sides of the peak, the intrinsic line profile is possibly
broader than the model suggests, but complexities of the line near its peak
could not be adequately modeled by three Gaussian components. The narrowest C
iv component has a FWHM of $\sim$540 km s-1. Although some studies argue in
favour of narrow-line subtraction for C iv (Baskin & Laor, 2005), we do not
make this consideration in this study.

For BR J0714–6455, the C iv line profile may be broadened by non-virial
components, as evidenced by the strong asymmetry present in both C iv and the
Si iv$+$O iv complex. The relative velocity shift between the two lines is
$\Delta v(\rm{C\,\textsc{iv}-Mg\,\textsc{ii}})\sim 3300$ km s-1, which is in
the top 10% highest relative velocity shifts measured in our sample. The mean
mass discrepancy and its standard deviation for targets with $\Delta
v(\rm{C\,\textsc{iv}-Mg\,\textsc{ii}})>3000$ km s-1 is
$\log\left(\rm{M_{C\,\textsc{iv}}}/\rm{M_{Mg\,\textsc{ii}}}\right)=0.25\pm
0.14$. At lower velocity shifts, this discrepancy is
$\log\left(\rm{M_{C\,\textsc{iv}}}/\rm{M_{Mg\,\textsc{ii}}}\right)=0.01\pm
0.14$, indicating the potential for outflows to preferentially bias the C iv
line profile and resulting mass measurements relative to other lines.

In Figure 6, we present example emission-line models of all three broad lines
for SDSSJ1202–0054, one of the outliers identified due to the discrepancy
between C iv and H$\beta$-based virial mass estimates,
$\log\left(\rm{M_{C\,\textsc{iv}}}/\rm{M_{H\textsc{$\beta$}}}\right)\approx-0.8$.
Similar to PSS J0121$+$0347, the C iv line model is sharply peaked with FWHM
$\sim$1750 km s-1 for the narrowest C iv component. However, the H$\beta$ line
profile is truncated and its broad component is poorly constrained. For this
target, the Mg ii virial mass estimate is intermediate between the H$\beta$
and C iv-based estimates.

---
Figure 5: Example models of the C iv and Mg ii emission-lines from PSS
J0121$+$0347 and BR J0714–6455, outliers identified by the “Mbh_Flag” which
indicates when the Mg ii-based virial mass estimate differs from the mean mass
estimated from all measured emission-lines by over 0.3 dex. Refer to Figure 2
for a description of the plotted elements. Figure 6: Example models of the C
iv, Mg ii, and H$\beta$ emission-lines from SDSSJ1202–0054, an outlier
identified by a discrepancy in the C iv and H$\beta$-based virial mass
estimates,
$\log\left(\rm{M_{C\,\textsc{iv}}}/\rm{M_{H\textsc{$\beta$}}}\right)\approx-0.8$.
Refer to Figure 2 for a description of the plotted elements.

From Section 3, we discussed how properties of the Mg ii and H$\beta$
emission-line models are sensitive to the choice of Fe ii template. In this
study, our reported line properties are averaged over measurements based on
applying spectral decomposition with four different UV and optical Fe ii
templates. However, we note that one should always be careful about systematic
effects introduced by the choice of templates, particularly if the template is
different from the one used in the virial mass calibration (e.g., Woo et al.,
2018; Schindler et al., 2020). For instance, Mg ii line models obtained using
the VW01 template to model the underlying Fe ii emission has been shown to be
biased towards broader line profiles, resulting in higher black hole mass
estimates (e.g., Schindler et al., 2020).

In Figure 7, we compare black hole mass, $\log{(\rm{M_{BH}}/\rm{M_{\odot}})}$,
measurement pairs between Mg ii and H$\beta$-based single-epoch virial
estimates. We split the panels by the Fe ii template, resulting in a $4\times
4$ grid of panels for the four UV templates and four optical templates,
described in Section 3.1, used to constrain the pseudo-continuum model in the
vicinity of each emission-line. We show the mean residual,
$\log\left(\rm{M_{Mg\,\textsc{ii}}}/\rm{M_{H\textsc{$\beta$}}}\right)$, and
its standard deviation on the top left corner of each panel. The majority of
single-epoch virial mass calibrations are based on Mg ii and H$\beta$
emission-line models obtained using the original VW01 and BG92 templates
(e.g., McLure & Dunlop, 2004; Vestergaard & Peterson, 2006), so combination of
these two templates may be expected to present the tightest relationship.
However, it is not apparent in this comparison that those measurements are
more consistent than the results from any other pair of templates. Thus in our
study, we report the line properties from averaging measurements of resulting
line models based on applying spectral decomposition with each Fe ii template.

In order to examine the black hole mass estimate deviation caused by each
individual Fe ii template from the measured average, we present Figures 8 and
9, which compare measurements of H$\beta$ and Mg ii against their respective
mean black hole mass estimates. In each panel, the residual,
$\log\left(\rm{M_{line}}/\rm{M_{mean}}\right)$, is plotted with its mean shown
on the top left along with its standard deviation. From Figure 8, we observe
that all templates of the underlying Fe ii emission result in statistically
similar black hole mass estimates, albeit with a fairly large scatter in this
high-redshift sample due to the lower SNR of the spectrum around H$\beta$ and
often truncated line profile. In Figure 9, we observe the effect seen in
Schindler et al. (2020) that the VW01 template tends to result in higher FWHM
and overestimated black hole masses compared to other templates. However, at
approximately $1\sigma$, we note that the effect is fairly insignificant with
respect to the scatter, likely because our VW01 template is a modified version
of the original template from Vestergaard & Wilkes (2001), as elaborated upon
in Section 3.1. With these comparisons, it is reasonable to assume that, at
least for black hole mass estimates, all of the Fe ii templates tested in this
study have similar effects on the resulting line properties and there are
minimal observable systematics between them.

Figure 7: Black hole mass comparison,
$\log\left(\rm{M_{BH}}/\rm{M_{\odot}}\right)$, between different Fe ii
templates models for both Mg ii and H$\beta$. The top left value displays the
mean residual,
$\log\left(\rm{M_{Mg\,\textsc{ii}}}/\rm{M_{H\textsc{$\beta$}}}\right)$, and
standard deviation between mass measurements. The Fe ii templates are labelled
along the axes. The blue shaded contours represent the two-dimensional
continuous probability density distribution calculated with a kernel density
estimator (Waskom, 2021). Each subsequent contour level marks density iso-
proportions increasing by an additional 10% up to 90% enclosed. Figure 8:
Black hole mass comparison,
$\log\left(\rm{M_{H\textsc{$\beta$}}}/\rm{M_{mean}}\right)$, between different
Fe ii templates models for H$\beta$, compared to the average H$\beta$-based
mass estimate. The top left value displays the mean residual and its standard
deviation between mass measurements. The Fe ii template is identified in the
top-right corner of each panel. The blue shaded contours represent the two-
dimensional continuous probability density distribution calculated with a
kernel density estimator (Waskom, 2021). Each subsequent contour level marks
density iso-proportions increasing by an additional 10% up to 90% enclosed.
Figure 9: Black hole mass comparison,
$\log\left(\rm{M_{Mg\,\textsc{ii}}}/\rm{M_{mean}}\right)$, between different
Fe ii templates models for Mg ii, compared to the average Mg ii-based mass
estimate. The top left value displays the mean residual and its standard
deviation between mass measurements. The Fe ii template is identified in the
top-right corner of each panel. The blue shaded contours represent the two-
dimensional continuous probability density distribution calculated with a
kernel density estimator (Waskom, 2021). Each subsequent contour level marks
density iso-proportions increasing by an additional 10% up to 90% enclosed.