# BASS XXV: DR2 Broad-line Based Black Hole Mass Estimates and Biases from
Obscuration

Julian E. Mejía-Restrepo European Southern Observatory, Casilla 19001,
Santiago 19, Chile  Benny Trakhtenbrot School of Physics and Astronomy, Tel
Aviv University, Tel Aviv 69978, Israel  Michael J. Koss Eureka Scientific,
2452 Delmer Street Suite 100, Oakland, CA 94602-3017, USA  Space Science
Institute, 4750 Walnut Street, Suite 205, Boulder, Colorado 80301, USA
Kyuseok Oh Korea Astronomy & Space Science institute, 776, Daedeokdae-ro,
Yuseong-gu, Daejeon 34055, Republic of Korea  Department of Astronomy, Kyoto
University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan  JSPS
Fellow  Jakob den Brok Argelander-Institut fur Astronomie, Universität Bonn,
Auf dem Hügel 71, D-53121 Bonn, Germany  Daniel Stern Jet Propulsion
Laboratory, California Institute of Technology, 4800 Oak Grove Drive, MS
169-224, Pasadena, CA 91109, USA  Meredith C. Powell Kavli Institute of
Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall,
Stanford, CA 94305, USA  Federica Ricci Instituto de Astrofísica and Centro de
Astroingeniería, Facultad de Física, Pontificia Universidad Católica de Chile,
Casilla 306, Santiago 22, Chile  Dipartimento di Fisica e Astronomia,
Universitá di Bologna, via Piero Gobetti 93/2, I-40129 Bologna, Italy  INAF -
Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti,
93/3, I40129 Bologna, Italy.  Turgay Caglar Leiden Observatory, PO Box 9513,
2300 RA, Leiden, The Netherlands  Claudio Ricci Núcleo de Astronomía de la
Facultad de Ingeniería, Universidad Diego Portales, Av. Ejército Libertador
441, Santiago 22, Chile  Kavli Institute for Astronomy and Astrophysics,
Peking University, Beijing 100871, People’s Republic of China  Franz E. Bauer
Instituto de Astrofísica and Centro de Astroingeniería, Facultad de Física,
Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
Millennium Institute of Astrophysics (MAS), Nuncio Monseñor Sótero Sanz 100,
Providencia, Santiago, Chile  Space Science Institute, 4750 Walnut Street,
Suite 205, Boulder, CO 80301, USA  Ezequiel Treister Instituto de Astrofísica,
Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306,
Santiago 22, Chile  Fiona A. Harrison  Cahill Center for Astronomy and
Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA  C.
M. Urry Yale Center for Astronomy & Astrophysics, Physics Department, Yale
University, PO BOX 201820, New Haven, CT 06520-8120, USA  Tonima Tasnim Ananna
Department of Physics & Astronomy, Dartmouth College, 6127 Wilder Laboratory,
Hanover, NH 03755, USA  Daniel Asmus Department of Physics & Astronomy,
University of Southampton, SO17 1BJ, Hampshire, Southampton, United Kingdom
Roberto J. Assef Núcleo de Astronomía de la Facultad de Ingeniería y Ciencias,
Universidad Diego Portales, Av. Ejército Libertador 441, Santiago 8370191,
Chile  Rudolf E. Bär Institute for Particle Physics and Astrophysics, ETH
Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland  Patricia S.
Bessiere Instituto de Astrofísica and Centro de Astroingeniería, Facultad de
Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22,
Chile  Instituto de Astrofísica de Canarias (IAC), C/Ví a Láctea, s/n,
E-38205, La Laguna, Tenerife, Spain  Leonard Burtscher Leiden Observatory, PO
Box 9513, 2300 RA, Leiden, the Netherlands  Kohei Ichikawa Frontier Research
Institute for Interdisciplinary Sciences, Tohoku University, Sendai 980-8578,
Japan  Darshan Kakkad European Southern Observatory, Casilla 19001, Santiago
19, Chile  Department of Physics, University of Oxford, Denys Wilkinson
Building, Keble Road, Oxford, OX1 3RH, UK  Nikita Kamraj Cahill Center for
Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA
91125, USA  Richard Mushotzky Department of Astronomy, University of Maryland,
College Park, MD 20742, USA  George C. Privon National Radio Astronomy
Observatory, 520 Edgemont Rd, Charlottesville, VA 22903, USA  Department of
Astronomy, University of Florida, 211 Bryant Space Sciences Center,
Gainesville, FL 32611, USA  Alejandra F. Rojas Centro de Astronomia (CITEVA),
Universidad de Antofagasta, Avenida Angamos 601, Antofagasta, Chile  Eleonora
Sani European Southern Observatory, Casilla 19001, Santiago 19, Chile  Kevin
Schawinski Modulos AG, Technoparkstrasse 1, CH-8005 Zurich, Switzerland
Sylvain Veilleux Department of Astronomy, University of Maryland, College
Park, MD 20742, USA

(Received March 31, 2021; Accepted TBD)

###### Abstract

We present measurements of broad emission lines and virial estimates of
supermassive black hole masses ($M_{\rm BH}$) for a large sample of ultra-hard
X-ray selected active galactic nuclei (AGNs) as part of the second data
release of the BAT AGN Spectroscopic Survey (BASS/DR2). Our catalog includes
$M_{\rm BH}$ estimates for a total 689 AGNs, determined from the H$\alpha$,
H$\beta$, Mg ii $\lambda 2798$, and/or C iv $\lambda 1549$ broad emission
lines. The core sample includes a total of 512 AGNs drawn from the 70-month
Swift/BAT all-sky catalog. We also provide measurements for 177 additional
AGNs that are drawn from deeper Swift/BAT survey data. We study the links
between $M_{\rm BH}$ estimates and line-of-sight obscuration measured from
X-ray spectral analysis. We find that broad H$\alpha$ emission lines in
obscured AGNs ($\log(N_{\rm H}/{\rm cm}^{-2})>22.0$) are on average a factor
of $8.0_{-2.4}^{+4.1}$ weaker, relative to ultra-hard X-ray emission, and
about $35_{-12}^{\leavevmode\nobreak\ +7}$% narrower than in unobscured
sources (i.e., $\log(N_{\rm H}/{\rm cm}^{-2})<21.5$). This indicates that the
innermost part of the broad-line region is preferentially absorbed.
Consequently, current single-epoch $M_{\rm BH}$ prescriptions result in
severely underestimated ($>$1 dex) masses for Type 1.9 sources (AGNs with
broad H$\alpha$ but no broad H$\beta$) and/or sources with $\log(N_{\rm
H}/{\rm cm}^{-2})\gtrsim 22.0$. We provide simple multiplicative corrections
for the observed luminosity and width of the broad H$\alpha$ component
($L[{\rm b}{\text{H}}\alpha]$ and FWHM[bH$\alpha$]) in such sources to account
for this effect, and to (partially) remedy $M_{\rm BH}$ estimates for Type 1.9
objects. As key ingredient of BASS/DR2, our work provides the community with
the data needed to further study powerful AGNs in the low-redshift Universe.

Active galactic nuclei (16), Surveys (1671), Catalogs (205), Supermassive
black holes (1663), X-ray surveys (1824), M-sigma relation (2026), Seyfert
galaxies(1447)

††journal: ApJS††facilities: Keck:I (LRIS), Magellan:Clay, Hale (Doublespec),
NuSTAR, Swift (XRT and BAT), VLT:Kueyen (X-Shooter), VLT:Antu (FORS2), SOAR
(Goodman)††software: AstroPy (Astropy Collaboration et al., 2013; Price-Whelan
et al., 2018), Matplotlib (Hunter, 2007), NumPy (Harris et al., 2020)

##  1 Introduction

Accurate estimates of super-massive black hole (SMBH) masses ($M_{\rm BH}$) in
Active Galactic Nuclei (AGNs) are critical to understand SMBH demographics and
growth, and their apparent co-evolution with their host galaxies (e.g.,
Ferrarese & Merritt, 2000; Kormendy & Ho, 2013). This requires large, highly
complete surveys of AGNs (and SMBHs in general), as well as a detailed
characterization of the different sources of uncertainties involved in the
currently available methods to estimate $M_{\rm BH}$.

In unobscured AGN, $M_{\rm BH}$ is commonly determined through the so-called
“single epoch” (SE), or “virial” black hole mass estimation method, which uses
detailed spectral measurements probing the broad emission line region (BLR;
see, e.g., works by Greene & Ho 2005; Wang et al. 2009; Trakhtenbrot & Netzer
2012; Shen & Liu 2012; Mejía-Restrepo et al. 2016, or reviews by Shen 2013;
Peterson 2014). This method is based on (1) the assumption of virialized
motion of the BLR gas and (2) empirical relations between the accretion-
related continuum luminosity and the BLR size. These latter relations are
calibrated in reverberation mapping (RM) experiments, and take the general
form $R_{\rm BLR}\propto L_{\lambda}^{\alpha}$, where $L_{\lambda}$ is the
monochromatic luminosity at a particular wavelength $\lambda$ (e.g., Kaspi et
al., 2000, 2005; Bentz et al., 2009; Park et al., 2012; Bentz et al., 2013).
Under these assumptions, the width of the broad-emission-line profiles, such
as the full width at half maximum (FWHM), can be used as a proxy for the
virial velocity of the BLR clouds, $v_{\rm BLR}$. $M_{\rm BH}$ can thus be
expressed as:

$M_{\rm BH}=G^{-1}R_{\text{BLR}}\,v_{\text{BLR}}^{2}\propto
f\,L_{\lambda}^{\alpha}\,{\text{FWHM}}^{2}.$ (1)

Here $G$ is the gravitational constant and $f$ is a geometrical factor that
accounts for the unknown structure and inclination of the BLR with respect to
the line of sight. The $R_{\rm
BLR}\left({\text{H}}\beta\right)-L_{\lambda}(5100\,{\rm\AA})$ relation is the
only $R_{\rm BLR}-L_{\lambda}$ relation that has been established for a large
number of AGN covering a broad luminosity range, $10^{43}\lesssim
L_{5100}/{\text{erg\,s}}^{-1}\lesssim 10^{47}$ (Bentz et al., 2013; Bentz &
Katz, 2015). Consequently, it has been used to calibrate several other SE
$M_{\rm BH}$ prescriptions, using other emission lines and/or continuum bands
(e.g., McLure & Jarvis, 2002; Greene & Ho, 2005; Trakhtenbrot & Netzer, 2012).

Single-epoch mass prescriptions have allowed the estimation of $M_{\rm BH}$
for tens of thousands of AGNs in large spectroscopic surveys (e.g. Shen et
al., 2008; Kozłowski, 2017), and have thus allowed probing of the evolution of
the active SMBH population (e.g., Greene & Ho, 2007; Vestergaard & Osmer,
2009a; Schulze & Wisotzki, 2010; Trakhtenbrot & Netzer, 2012; Kelly & Shen,
2013; Schulze et al., 2015) and of the links between SMBHs and their hosts
(e.g., Jahnke et al., 2009; Decarli et al., 2010; Merloni et al., 2010;
Bongiorno et al., 2014; Suh et al., 2020) – out to the highest accessible
redshifts (e.g., Mazzucchelli et al., 2017; Shen et al., 2019). Most of these
studies, and particularly those dedicated to the largest samples and/or the
highest-redshift ones (i.e., $z>3$), had to be based on surveys of luminous,
unobscured and optically-selected AGN (e.g., SDSS quasars).

Despite these significant achievements, the SE approach should be used with
care as it is subject to several significant (systematic) uncertainties that,
in principle, may total to 0.4 dex in $M_{\rm BH}$, or even more (e.g., Shen,
2013; Pancoast et al., 2014a; Peterson, 2014). Below, we briefly describe the
most critical uncertainties relevant to the current work. A major source of
uncertainty stems from the need to assume a structural geometrical factor,
$f$. The common approach is to deduce a universal $f$ by requiring that RM-
based BH masses match those expected from the relation between $M_{\rm BH}$
and the stellar velocity dispersion ($\sigma_{*}$) found in local galaxies
(Onken et al., 2004; Graham, 2016; Woo et al., 2015; Batiste et al., 2017).
Some studies, however, have put forward the idea that the BLR may have a disk-
like structure, at least in some AGN (e.g., Eracleous & Halpern, 1994; Grier
et al., 2013; Pancoast et al., 2014b; Mejía-Restrepo et al., 2018a, and
references therein). Such a distribution of gas would introduce a bias to the
SE $M_{\rm BH}$ determination, as the (unknown) inclination angle of the BLR
disk with respect to the line of sight, for each AGN, limits the ability to
measure the true virial velocity. In particular, BH masses would be
overestimated (underestimated) at larger (smaller) inclination angles (e.g.
Collin et al., 2006; Shen & Ho, 2014; Mejía-Restrepo et al., 2018a).

Another important bias comes from the possible presence of winds, which could
potentially affect the (observed) BLR gas dynamics. Indeed, several studies
have shown that high ionization lines such as C iv $\lambda 1549$, commonly
used to estimate $M_{\rm BH}$ at $z\gtrsim 2$, show highly blue-shifted
profiles (by up to 8000 km s-1; e.g., Marziani et al., 2015; Vietri et al.,
2020, and references therein), and thus their line widths are known to be
poorer tracers of the virial velocity of the BLR gas, compared to other lines
(e.g., Richards et al., 2011; Coatman et al., 2016; Mejía-Restrepo et al.,
2018b). In the case of the Mg ii $\lambda 2798$ line, several studies have
shown that the innermost, highest-velocity gas is affected by fountain-like
winds and the global virial assumption is likely no longer valid for systems
with ${\text{FWHM}}\gtrsim 6000\,{\rm km\,s}^{-1}$ (e.g., Trakhtenbrot &
Netzer, 2012; Marziani et al., 2013; Popović et al., 2019).

Unlike the aforementioned biases, the partial obscuration of the broad line
emitting region and its potential effect on $M_{\rm BH}$ estimates remains
poorly understood. Gaskell & Harrington (2018) proposed that compact,
outflowing dusty clumps driven by radiation pressure may partially block the
BLR emission. Such partial obscuration may explain the lack of correlation
between disk and BLR line variabilities occasionally reported in RM campaigns
(e.g., Goad et al., 1999; Cackett et al., 2015; Goad et al., 2016).
Preliminary observational evidence for this comes from the recent study of
Caglar et al. (2020), who identified a systematic offset of roughly $-0.6$ dex
between the broad-H$\alpha$ based $M_{\rm BH}$ estimates and those based on
the stellar velocity dispersion in 19 hard X-ray selected AGN drawn from the
volume-complete LLAMA sample (Davies et al., 2015), including both unobscured
and partially-obscured systems (as deduced from the relative strength of broad
H$\beta$). Further support for the idea that this discrepancy could be
(partially) attributed to dust obscuration comes from the fact that the
discrepancy is found to be more dramatic in systems that completely lack broad
H$\beta$ emission (Type 1.9 AGNs; see also Goodrich, 1989, 1990; Ricci et al.,
2017d).

One way to overcome these complications is to focus on the (rest-frame) near-
infrared (NIR) regime, which is at least 10 times less sensitive to extinction
than the optical. Ricci et al. (2017c) have provided SE $M_{\rm BH}$
prescriptions that rely on several broad NIR lines (Pa$\alpha$, Pa$\beta$ and
He i $\lambda 1.083$ µm), and on the hard X-ray continuum luminosity (in
either the 2-10 keV and/or the 14-195 keV regime) as BLR probes. In addition
to the advantages in overcoming obscuration, the use of the hard X-ray
luminosity allows measurement of $M_{\rm BH}$ even in low luminosity systems,
where host contamination significantly affects optical AGN continuum
estimates. One further advantage of this method is that it can even be applied
to some Type 2 AGNs – the so-called hidden BLR Type 2s, where broad lines are
detected in the NIR regime while the optical spectrum shows only narrow
H$\beta$ and/or H$\alpha$ (see e.g., Veilleux et al., 1997b, a, 1999; Riffel
et al., 2006; Lamperti et al., 2017; Onori et al., 2017; Brok et al., 2022).
However, calibrating this method requires larger datasets of high signal-to-
noise NIR spectra in order to improve the reliability of the method and better
characterize the obscuration effects in Type 2 AGNs.

In order to further investigate all these issues, one has to obtain high
quality optical-NIR spectroscopy of broad AGN emission lines and robust,
independent line-of-sight obscuration measures for a large AGN sample that is
unbiased with regard to obscuration. The BAT AGN Spectroscopic Survey (BASS)
has been collecting and analyzing optical and NIR spectroscopy, X-ray spectral
observations, and other multi-wavelength data for bright AGNs selected in the
ultra-hard X-rays (14-195 keV) by the Swift/BAT mission. The first data
release of BASS (DR1; Koss et al., 2017; Lamperti et al., 2017; Ricci et al.,
2017a) has already provided $M_{\rm BH}$ estimates for hundreds of AGNs, over
a wide range of obscuration, drawn from the 70-month catalog of Swift/BAT
(Baumgartner et al., 2013). This highly complete and rich collection of multi-
wavelength data has already been used in several studies that examined the
links between AGN physics, structure and various emission components, and
specifically to investigate topics where obscuration and/or orientation may
play a key role (e.g., Ricci et al., 2017b; Shimizu et al., 2018; Bär et al.,
2019; Rojas et al., 2020).

In this paper we present broad emission line measurements as part of the
second data release of the BAT AGN Spectroscopic Survey (BASS/DR2), including
the analysis of hundreds of new spectra and improved estimates of the black
hole masses of hundreds of AGN, thus greatly improving and expanding on the
first data release described in Koss et al. (2017). We then combine these new
measurements with the rich BASS/DR2 multi-wavelength dataset to explore the
effect of dust obscuration on single-epoch $M_{\rm BH}$ estimates from optical
broad emission lines. Other BASS/DR2 studies present extensive NIR
spectroscopy and use it to address complementary issues (Brok et al., 2022;
Ricci et al., 2022). Throughout this work, we adopt $\Omega_{\rm M}=0.3$,
$\Omega_{\Lambda}=0.7$, and $H_{0}=70\,{\rm km\,s}^{-1}\,{\rm Mpc}^{-1}$.

##  2 Data Content and Analysis

###  2.1 Overview of Survey, Sample and Data Content

The ultimate goal of BASS is to complement the largest available sample of
Swift/BAT, hard X-ray selected AGNs with optical spectroscopy and ancillary
multi-wavelength data using dedicated observations and archival data, to
complete the first large survey (${\gtrsim}1000$ sources) of the most powerful
accreting SMBHs in the low-redshift Universe. This work is part of a series of
papers devoted to the 2nd Data Release (DR2) of BASS. In particular, this
paper presents detailed spectral measurements of the broad-line AGN, with
either a broad H$\beta$ or H$\alpha$ line (i.e., ${\text{FWHM}}>1000\,{\rm
km\,s}^{-1}$), as well as a smaller subset of higher-redshift sources with Mg
ii and C iv broad emission lines. Koss et al. (2022a) provides an overview of
BASS DR2, while Koss et al. (2022b) provides a detailed account of the
BASS/DR2 AGN catalog and main observational data, in particular the optical
spectroscopy which is used here. Other key BASS DR2 papers include Koss et al.
(2022c), where we present the velocity dispersion measurements for (obscured)
BASS sources; Oh et al. (2022), where we focus on spectral measurements for
narrow-line AGN and host light decomposition; and Brok et al. (2022) and Ricci
et al. (2022), where we present extensive NIR spectroscopic observations, and
analyze (broad) hydrogen and high-ionization (coronal) emission lines. The
broad line measurements and related $M_{\rm BH}$ (and $L/L_{\rm Edd}$)
estimates presented herein are used in Ananna et al. 2022 to determine the BH
mass and Eddington ratio distribution functions among essentially all BASS/DR2
AGNs.

BASS/DR1 used mostly archival telescope data (see e.g. Fig 1 in Koss et al.,
2017) for 641 BAT AGNs, including $>$250 spectra from the SDSS and 6dF
surveys. In this DR2 paper we provide a complete sample of black hole mass
estimates from optical broad emission lines for 512 AGNs with such lines in
the 70-month Swift/BAT survey (Baumgartner et al., 2013). As part of our
efforts towards DR2, we obtained new spectroscopy for many AGNs that did not
have reliable black hole mass determination in DR1. This includes (1) AGNs
that did not have sufficient data (or data quality) to yield a black hole mass
measurement, including cases where the DR1 archival spectra were not properly
flux-calibrated (e.g., 6dF/2dF spectra; Jones et al., 2009); (2) Type 1.9 AGNs
that were lacking a sufficiently high quality spectrum to derive their BH
masses, i.e. either a high-quality spectrum of their broad H$\alpha$ lines or
a spectrum that enables a robust velocity dispersion measurement; and (3) any
DR1 AGN with only a broad H$\beta$ line measurement, where H$\alpha$ coverage
was missing.

The new BASS/DR2 spectroscopic observations were carried out with a variety of
facilities and instruments, as detailed in the main DR2 Catalog and Data paper
(Koss et al., 2022b). Here we note that the large majority of new spectra were
obtained with either the Double Beam Spectrograph (DBSP) mounted on the Hale 5
m telescope at Palomar observatory (Oke & Gunn 1982; $>$400 AGNs, mainly
northern targets); the X-Shooter spectrograph at the Very Large Telescope
(Vernet et al. 2011; $>$200 sources, mainly southern); or the Goodman
spectrograph mounted on the SOAR telescope at Cerro Pachon (Clemens et al.
2004; $>$150 sources, also southern). More details on the facilities used, the
spectroscopic setups and spectral resolutions, the observations, and the
reduction procedures, can be found in Koss et al. (2022b).

The DR2 also includes  publicly available optical spectroscopy from the SDSS
($\sim$150 sources; drawn from SDSS DR16, Ahumada et al. 2020), and a small
number of additional archival spectra, obtained as part of follow-up
observations of ROSAT sources (Grupe et al., 1998, 1999). Finally, it includes
spectra from recent studies of newly identified BAT AGNs (see Rojas et al.,
2017).

In a non-negligible number of cases, the extensive data collecting process
resulted in multiple optical spectra of the same source. In such cases we
select for each AGN the single best spectrum for broad-line based $M_{\rm BH}$
measurements, and use it in the present analysis (i.e., in Sections 3 and 4).
This selection is done by considering the signal-to-noise ratio, spectral
resolution and quality of our spectral fits (see Section 2.3 below). Following
this selection, our dataset consists of a total of 559 unique AGNs with at
least one useful optical spectrum. These 559 AGNs cover the redshift range
$z\sim 0-4$, with the vast majority ($>$90%) being at $z\lesssim 0.5$.

All BASS DR2 spectra used here have sufficient spectral resolution to robustly
measure the broad emission lines that are at the heart of the present paper.
As noted, the main DR2 Catalog and Data paper (Koss et al., 2022b) provides
ample details about the new, the previously-obtained (DR1), and the archival
spectra used throughout BASS DR2.

As mentioned above, the BASS/DR2 sample is fundamentally based on AGNs
identified through the 70-month Swift/BAT catalog. However, the broad line
measurements described in the present study were also carried out on the
optical spectra of 207 additional AGNs, which were acquired as part of the on-
going BASS efforts to follow up on the increasingly deeper (and larger)
content of the Swift/BAT all-sky survey (e.g., Oh et al., 2018). While we
provide these measurements, we stress that this “bonus” sample is neither
complete nor final: it does not represent any sort of flux- or volume-complete
subset of deeper BAT data, and it is possible that future BASS follow-up
observations and analysis could reveal significant changes to the
determinations of optical counterparts, their redshifts, their AGN nature,
and/or any other property. Apart from providing the relevant spectral
measurements, we ignore this bonus sample throughout the rest of this paper.
In particular, we do not include the bonus sample measurements when further
discussing the BASS broad-line AGN statistics, measurements or implications
for any of the analyses we present (unless explicitly mentioned otherwise).  A
summary of the number of $M_{\rm BH}$ estimations from the H$\alpha$,
H$\beta$, Mg ii and C iv Broad Emission lines is presented in Table 1

The data reduction and analysis for the DR2 has maintained the same uniform
approach described in the initial DR1 paper (Koss et al., 2017). All the
spectra were processed using standard tasks (in IRAF or comparable reduction
frameworks) for cosmic ray removal, 1d spectral extraction, and wavelength and
flux calibrations. The spectra were flux calibrated using standard stars,
which were typically observed twice per night, whenever possible. In the DR2,
we have also implemented the use of the molecfit software (Smette et al.,
2015) to correct spectral regions affected by telluric absorption (e.g. H2O,
CO2, CH4 and O2), based on nightly weather data (Koss et al., 2022a, b).

###  2.2 Continuum and Line Emission Modeling

For each of the 559 broad-line emitting sources in BASS with optical
spectroscopy of either one of the H$\alpha$, H$\beta$, Mg ii $\lambda 2798$
and/or C iv $\lambda 1549$ broad emission lines, we fitted the spectral
complexes around these lines following the established and well-tested
procedures initially presented in Trakhtenbrot & Netzer (2012) and further
developed in Mejía-Restrepo et al. (2016), where more details can be found.

We note that the spectral modeling of narrow-line (i.e., Type 2) AGNs in
BASS/DR2, and generally host galaxy decomposition and narrow line emission
(including beyond the spectral regions considered here), was carried out
independently, using a different fitting procedure, and is described in a
dedicated BASS/DR2 paper (Oh et al., 2022). In Section 3 we show a few basic
properties of the BASS/DR2 Type 2 AGN population, based on this independent
spectral analysis, which is however not used in any other part of the present
study.

The broad line fitting procedures use the PySpecKit Python package (Ginsburg &
Mirocha, 2011) to measure broad emission line properties. In brief, each
spectrum is first corrected for Milky-Way (foreground) dust extinction, using
the Schlegel et al. (1998) maps and the Cardelli et al. (1989) extinction law
(with $R_{\rm V}=3.1$). Next, the continuum emission is modeled with a (local)
power law, fitted to certain continuum-dominated bands around the emission
line complex of interest (see Table 1 in Mejía-Restrepo et al. 2016). After
subtracting the continuum emission we proceed with the emission line modeling
as follows. Narrow line components, including the [O iii]
$\lambda\lambda$4959,5007, [N ii] $\lambda\lambda$6548,6584, and [S ii]
$\lambda\lambda$6717,6731 lines, as well as the narrow components of the
H$\alpha$ and H$\beta$ lines, are modeled with a single Gaussian profile,
each, except for rare cases where a visual inspection of the residuals
motivated us to use an additional Gaussian. The widths and relative (velocity)
shifts of these (primary) narrow profiles are tied to each other, to avoid
over-fitting in heavily blended line complexes such as the H$\alpha$ spectral
complex. The profiles of the most prominent broad lines (H$\alpha$, H$\beta$,
Mg ii and C iv) are modeled using two broad Gaussian components (each), while
weaker emission lines are modeled with a single broad Gaussian (including He
ii $\lambda$1640, N iv $\lambda$1718, Si iii] $\lambda$1892). We emphasize
that the two broad Gaussian components are used only in order to account for
the total broad emission line profiles, and we do not consider any physical
interpretation to the two separate components. This choice is based on
previous works, which showed that two broad Gaussian components provide a good
compromise between the number of free parameters (i.e., 6) and the achieved
goodness of fit (Shang et al., 2007; Trakhtenbrot & Netzer, 2012; Mejía-
Restrepo et al., 2016, e.g.,). All broad emission features are restricted to
have ${\text{FWHM}}>1000\,{\rm km\,s}^{-1}$ and to be broader than the narrow
emission features (including of the same transition; see above). We allow the
central wavelength of each Gaussian component to be shifted by up to 1500 km
s-1 relative to the laboratory central wavelength of the transition. The blue-
shift of the C iv and He ii $\lambda$1640 components is allowed to be larger,
up to 5000 km s-1, in agreement with what is observed in other large AGN
samples (e.g., Shang et al., 2007; Runnoe et al., 2014; Coatman et al., 2017).
We verified that yet larger shifts are neither observed in our sample nor
required in our modeling of the spectra. When fitting the H$\beta$, Mg ii and
C iv spectral complexes, we also account for (heavily blended) Fe ii and Fe
iii using the iron template described in Mejía-Restrepo et al. (2016),
broadened and shifted separately for each source. Since the Mg ii spectral
complex was modeled using a relatively narrow, “local” part of the spectrum
($\sim$2600–3000 Å), we did not include a designated model for the Balmer
continuum. In our modeling approach, the Balmer continuum is assumed to be
blended with the underlying disk continuum, forming the “local” continuum
emission (see Mejía-Restrepo et al. 2016 for a detailed discussion).

From each fitted emission line profile we extract (1) the shift of the line
centroid, i.e. the flux-weighted average center of the line emission, and (2)
the shift of the line peak – providing two probes of $\Delta v$; (3) the total
line luminosity; and (4) the line width, in terms of FWHM. From the latter we
subtract in quadrature the instrumental spectral resolution, according to the
observational setup (i.e., in velocity space; see Koss et al. 2022a and Koss
et al. 2022b). Whenever the resolution-corrected FWHMs of narrow lines fall
below the corresponding instrumental resolution, we regard the emission line
FWHMs as upper limits, and report the (velocity-equivalent) instrumental
resolution in our catalog (see descriptions of Tables 5-8). We note that even
in these cases (affecting 26 sources with H$\beta$ measurements and 69 sources
with H$\alpha$ measurements), the narrow lines still provide the best way to
decompose the complex key broad emission line profiles, and tease out the
broad emission line widths, which are crucial for BH mass estimates.

Together with the line profile properties, we also computed the monochromatic
continuum luminosities at several narrow wavelength bands,
$L_{\lambda}\equiv\lambda\ L\left(\lambda\right)$, to be used for the
estimation of $M_{\rm BH}$. In particular, we measured $L_{1450}$, $L_{3000}$,
$L_{5100}$ and $L_{6200}$ for $M_{\rm BH}$ estimates using C iv, Mg ii,
H$\beta$ and H$\alpha$, respectively (see, e.g., Greene & Ho, 2005;
Vestergaard & Peterson, 2006; Wang et al., 2009; Mejía-Restrepo et al., 2016).

Uncertainties on all spectral measurements were derived by a resampling
procedure. Each observed spectrum was used to generate 100 mock spectra, based
on its noise (variance). Each of these mock spectra were then fit using our
spectral decomposition procedures. For each measured quantity, of each AGN,
the 16th and 84th percentiles of the corresponding distribution of
measurements were then used to determine the corresponding uncertainty.

All spectral fits were visually inspected by at least three independent,
experienced team members (J. M.-R., B. T., and M. K.). In the cases where the
fits were inadequate, we have adjusted some of the parameters of the fitting
procedure and re-fitted the data. These manual adjustments typically involved
the continuum placement and/or the limits to the widths and/or shifts of
emission line components. We note that these minor numerical adjustments did
not contradict the physical motivation and/or meaning of the emission
components (e.g., broad Gaussian components always remained broader than the
narrow ones, etc.).

We ultimately visually inspected all the final (adjusted) spectral fits, used
them to derive the spectral measurements we rely upon throughout the rest of
the paper and catalog (as well as the related uncertainties, using our re-
sampling procedure), and assigned them spectral fit quality flags, which we
describe immediately below.

###  2.3 Model Fit Quality

We visually inspected all the (final) spectral fits and assigned a quality
flag ($f_{\rm Q}$) representing the quality of each fit (i.e., each spectral
complex for each source), ranging from 1 to 3. $f_{\rm Q}=1$ marks good
quality fits, with randomly distributed residuals, providing the most reliable
line measurements we can hope to achieve within the scope of a large effort
like BASS. $f_{\rm Q}=2$ is used to mark good/acceptable fits, that may show
slight systematic residuals and that could be slightly improved with further,
less-trivial manual adjustments; however $f_{\rm Q}=2$ fits can still be used
to provide reliable broad line measurements. In such cases we preferred not to
further adjust the fits, as this may make our fitting procedure too
heterogeneous. Finally, $f_{\rm Q}=3$ marks those spectral fits that have
failed, and/or data that exhibit very low signal-to-noise or otherwise severe
issues. In such cases, our (reasonable) attempts to manually adjust the
spectral fitting procedure could not result in an acceptable fit. We exclude
all such $f_{\rm Q}=3$ fits from both the BASS/DR2 catalog and any of the
analysis that follows. We further discuss these problematic fits in Section
2.3.1 below.

Examples of spectra and best-fit models representing the three $f_{\rm Q}$
classes are shown in Appendix A and Fig 13. By examining the results of the
“useful” fits (i.e., with $f_{\rm Q}=1$ and 2), we estimate that the minimum
rest-frame equivalent width (rEW) needed to achieve such high-quality fits for
the H$\alpha$, H$\beta$, Mg ii and C iv lines are ${\rm EW}=10$, 3, 9, and 10
Å, respectively.111Given the highly heterogeneous nature of the BASS/DR2
spectroscopic observations and data, we prefer to report the lowest EWs (i.e.
physically weakest lines) we can measure, instead of reporting a more generic
$S/N$ criterion.

Out of the initial 515 and 433 unique objects with available spectra of the
broad H$\alpha$ and/or H$\beta$ lines (respectively), after retaining only
fits with $f_{\rm Q}=1$ and $2$, we end up with 457 unique AGNs with useful
measurements of the broad H$\alpha$ line, of which 341 and 77 unique objects
have $f_{\rm Q}=1$ and 2, (respectively); and 381 AGNs with useful
measurements of the broad H$\beta$ line, of which 245 and 118 unique objects
have $f_{\rm Q}=1$ and 2 (respectively). The remaining useful measurements
come from sources with with acceptable fits but large errors ($f_{\rm Q}=2.5$;
see Section 2.3.1 below). Also, there are 348 AGNs for which we have useful
measurements of both the H$\beta$ and H$\alpha$ broad emission line. In total,
we have 485 unique AGNs with useful measurements of either the H$\alpha$
and/or H$\beta$ broad emission lines. For higher-redshift sources ($z\gtrsim
0.7$), essentially all of which are classified as beamed AGNs, only the Mg ii
and/or the C iv lines are available in our optical spectroscopy. From the
initial 41 and 32 spectra with broad Mg ii and C iv lines (respectively), we
obtained 28 and 22 useful measurements of the Mg ii and C iv broad emission
line complexes (respectively). These are further split to 15 and 13 fits with
$f_{\rm Q}=1$, and 13 and 9 fits with $f_{\rm Q}=2$ (in each case, for Mg ii
and C iv, respectively). There are 6 objects with useful measurements in both
Mg ii and C iv. Our data-set thus consists of 43 unique AGNs with either Mg ii
and/or C iv broad lines measurements  out of which 27 do not have
complementary H$\alpha$ and/or H$\beta$ broad line measurements. Therefore, we
end up with a total of 512 objects ( $485$, from H$\alpha$ and H$\beta$, plus
27, from Mg ii and C iv) with black hole mass estimations from Broad emission
lines.

Table 1:  Summary of good and acceptable $M_{\rm BH}$ estimations from different Broad emission lines (see section 2.3). Bonus 105m objects correspond to additional sources drawn from deeper-than-70-month DR2 Swift/BAT survey data.  Subset | H$\alpha$ | H$\beta$ | Mg ii | C iv | Total Objectsb
---|---|---|---|---|---
70m non beamed | 434 | 343 | 3 | 0 | 445
70m beamed | 23 | 38 | 25 | 22 | 67
Total 70m | 457 | 381 | 28 | 22 | 512
Bonus 105ma | 140 | 109 | 17 | 5 | 177
Total Objects | 597 | 490 | 45 | 27 | 689

####  2.3.1 Problematic Fits

After our visual inspection of the spectral fits (including those that
required minor adjustments), we have a total of 29 objects with failed fits
($f_{\rm Q}=3$) of the broad H$\alpha$ line, 32 in the case of H$\beta$, 13 in
the case of Mg ii, and 10 in the case of C iv. There is a variety of reasons
for such failed fits, including a low signal-to-noise ratio ($S/N$), imperfect
correction of telluric features associated with certain redshift ranges,
incomplete profiles due to the specific source redshift and observation setup,
and/or difficulties in data reduction. Table 2 summarizes the breakdown of the
failed fits according to these (and other) categories, and below we further
discuss some of the main ones.

Among the 15 objects with low $S/N$ over the H$\alpha$ complex, 4 are
classified as Type 1.9 AGNs, that is sources which show broad H$\alpha$ but no
broad H$\beta$ line emission (see Section 3.1 for more details). This may
result from significant obscuration by dust, dimming even the H$\alpha$
emission, and making even prominent emission lines like H$\alpha$ harder to
detect and model. There are also two beamed (“BZQ”) AGNs whose H$\alpha$ line
is difficult to detect due to their relatively high redshift. The remaining
systems with low $S/N$ are bona-fide broad-line (Type 1) AGNs whose spectra
have not been re-observed since DR1, despite their apparent low $S/N$ in that
initial data release. The higher number of objects with low $S/N$ in the
H$\beta$ line, 18, is not surprising as H$\beta$ is weaker than H$\alpha$ by
at least a factor of $\sim$3, and thus requires a higher overall $S/N$,
particularly given the need to properly model the blended iron emission
complex. These low $S/N$ sources will likely be re-observed in future BASS
spectroscopy and analyzed as part of a future DR.

For one source (BAT ID 1204, a.k.a. RBS 2043), the Mg ii emission line is
considerably narrower ($\approx$1200 km s-1) than what is seen in quasars,
while the H$\beta$ line is narrower still, consistent with an NLR origin. The
Mg ii width leads to a BH mass estimate (see Section 2.4 below) that is much
lower than what is deduced from stellar velocity dispersion ($\log\left[M_{\rm
BH}/M_{\odot}\right]\simeq 7.4$ vs. 9.6; Koss et al. 2022c). Our broad line
catalog thus reports the basic measurements for the Mg ii spectral complex,
but not the associated BH mass.

There is a single object with unclear presence of BLR features (in H$\beta$;
BAT ID 349, a.k.a. UGC 3601), that is with the data in hand we could not
robustly determine whether there is a broad emission component. We note that,
in principle, in extreme cases one could also expect a mis-identification of
blended narrow H$\alpha$ and [N ii] lines as a broad and weak H$\alpha$
profile.  We have not identified such questionable broad H$\alpha$ profiles
among our BASS/DR2 AGNs. At any rate, if such ambiguous cases indeed have
broad Balmer emission lines (that is, they originate from the BLR), their
measurement would require sufficiently high $S/N$ and line EW, as well as more
detailed analysis (see, e.g., Oh et al. 2015 for detailed examples and
discussion).

In addition to the failed fits (i.e., $f_{\rm Q}=3$), our inspection of the
fitting results uncovered another subset of 43 spectral fits for which the
resampling technique resulted in exceptionally large (fractional)
uncertainties on the H$\alpha$ (39), H$\beta$ (18), and C iv (0) line widths,
$\Delta[{\text{FWHM}}({\text{H}}\alpha)]/{\text{FWHM}}({\text{H}}\alpha)\geq
50\%$,  and/or large systemic offsets of the narrow line. However, our visual
inspection suggests the fits are acceptable. Upon closer inspection, it seems
that in these cases the contrast between the broad emission line and the
adjacent continuum emission is relatively low, which led a significant
fraction of the re-sampled (mock) spectra to be fitted by extremely broad
profiles (i.e., FWHM[H$\alpha$] $>10,000\,{\rm km\,s}^{-1}$). Since the best-
fit parameters appear to represent the observed spectra well, we do not
downgrade the quality flags of such fits to $f_{\rm Q}=3$, and instead mark
these 43 cases with a dedicated flag, $f_{\rm Q}=2.5$.

We finally note that any physical interpretation of the line (velocity) shifts
reported in our catalog should be done with care, as these naturally depend on
the precise redshifts used for our spectral analysis. Specifically, any
interpretation of narrow emission line shifts should consider the fact that
our redshifts are, themselves, based on narrow emission lines (i.e., [O iii]
$\lambda 5007$; Koss et al. 2022b). The two sources in our catalogs that have
extremely large shifts listed ($>$1000 km s-1; BAT IDs 334 & 1332) are also
marked as $f_{\rm Q}=2.5$.

To summarize, users of our catalog who prefer to have the largest possible
sample of reliable fits of the broad H$\alpha$ line, and of derived
quantities, can use the default quality cut $f_{\rm Q}<3$. More cautious
analyses may however prefer to impose the stricter $f_{\rm Q}\leq 2$ cut. We
indeed adopt this stricter cut for all of the analyses presented below.

Table 2: Breakdown of failed and/or problematic spectral fits Reason for failure | H$\alpha$ | H$\beta$ | Mg ii | C iv | Total Spectra
---|---|---|---|---|---
Low $S/N$ | 15 | 18 | 8 | 4 | 45
Tellurics | 7 | 0 | 1 | 0 | 8
Unclear BLR | 0 | 1 | 0 | 0 | 1
Mismatched NLR | 2 | 0 | 0 | 0 | 2
Incomplete profile | 3 | 1 | 0 | 2 | 6
Reduction issueaa Apart from providing the relevant spectral measurements, we ignore this bonus sample throughout the rest of this paper. | 2 | 9 | 4 | 2 | 17
FeII fit issue | 0 | 2 | 0 | 0 | 2
Absorption featuresbb Since there are objects with simultaneous $M_{\rm BH}$ estimations from different broad emission lines (e.g. H$\alpha$-H$\beta$, H$\beta$-Mg ii and Mg ii-C iv), the total number objects is smaller than the sum of available $M_{\rm BH}$ measurements from the different emission lines. | 0 | 1 | 0 | 2 | 3
Double-peak broad lines | 29 | 20 | 0 | 0 | 49
Total Failed fits | 58 | 52 | 13 | 10 | 133

In addition to the failed fits described above, we also excluded from our main
catalog and analysis objects with indications of double-peaked broad emission
lines where the SE black hole mass estimation approach is not applicable, and
their physical origin is still debated. The proposed origins include the
accretion disk, dual BLR in a binary SMBH system, bipolar outflows, and/or
flares or spiral arms in the accretion disk (see,e.g., Veilleux & Zheng, 1991;
Zheng et al., 1991; Eracleous & Halpern, 1994; Jovanović et al., 2010;
Storchi-Bergmann et al., 2017; Ricci & Steiner, 2019, and references therein).
Out of our initial sample of broad-lined Swift/BAT AGNs, we find a total of 29
candidate double-peaked systems, comprising 29 and 20 sources with double-
peaked H$\alpha$ and H$\beta$, respectively (20 sources have double-peaked
profiles in both Balmer lines). We provide basic information regarding these
double-peaked sources in Table 4.

###  2.4 Black hole Mass and Eddington Ratio Estimates

Black hole masses are estimated using the H$\alpha$, H$\beta$, Mg ii, and C iv
emission line measurements, according to their availability for each source.
In all our estimates, we assume a common (and universal) virial factor of
$f=1$.222This virial factor is appropriate for $M_{\rm BH}$ prescriptions that
depend on the FWHM of the respective emission line, and corresponds to
$f_{\sigma}=5.5$ if one uses line velocity dispersion instead. This value is
appropriate for $M_{\rm BH}$ estimates that rely on the FWHM of broad emission
lines as the BLR velocity tracer, and is further motivated by the
observationally-derived mean value from Woo et al. (2015), where RM-based
$M_{\rm BH}$ estimates were matched, on average, to the corresponding
expectations from the $M_{\rm BH}$-$\sigma_{\star}$ relation. Woo et al.
(2015) found an uncertainty on the mean value of $f$ of about 30%.

For the H$\alpha$ line, we used the specific prescription calibrated in Greene
& Ho (2005), and in particular their Eq. 6. We note, however, that their
calibration assumed $f=0.75$ (corresponding to a spherical BLR distribution).
Our choice of $f=1$ therefore requires adjusting the Greene & Ho (2005)
calibration by $\times 4/3$ (or $+$0.125 dex). Our H$\alpha$-based
prescription for $M_{\rm BH}$ is thus

$M_{\rm BH}({\text{H}}\alpha)=\\\ 2.67\times 10^{6}\left(\frac{L[{\rm
b}{\text{H}}\alpha]}{10^{42}\,{\text{erg\,s}}^{-1}}\right)^{0.55}\,\left(\frac{{\rm
FWHM}[{\rm b}{\text{H}}\alpha]}{10^{3}\,{\rm
km\,s}^{-1}}\right)^{2.06}\,M_{\odot}\,.$ (2)

We note that this prescription was calibrated to best match H$\beta$-related
(RM) measurements, and it does not strictly follow the virial assumption, in
the sense that the exponent of the velocity term is 2.06 (and not 2.00). In
the case of H$\beta$, we used the calibration presented in Trakhtenbrot &
Netzer (2012) while in the case of Mg ii and C iv we followed Mejía-Restrepo
et al. (2016). A summary of the specific calibrations that we adopted can be
found in Table 3.

Table 3: Parameters of virial BH mass prescriptions

Observables | $\log{K}$ | $\alpha$ | $\beta$
---|---|---|---
FWHM(H$\alpha$), $L\left({\rm b}{\text{H}}\alpha\right)$ | 7.526 | 0.55 | 2.06
FWHM(H$\beta$), $L_{5100}$ | 6.721 | 0.65 | 2.00
FWHM(Mg ii), $L_{\rm 3000}$ | 6.906 | 0.61 | 2.00
FWHM(C iv),$L_{\rm 1450}$ | 6.331 | 0.60 | 2.00

Note. — The mass prescriptions are of the form $M_{\rm BH}=K\,\,(\lambda
L_{\lambda})^{\alpha}\,\,{\text{FWHM}}^{\beta}$, with $\lambda L_{\lambda}$ in
units of $10^{44}\,{\text{erg\,s}}^{-1}$, FWHM in units of 1000 km s-1, and
$M_{\rm BH}$ in units of $M_{\odot}$.

While not essential for the main findings of the present study, we use two key
properties of broad-line AGNs to provide context in Section 3: their
bolometric luminosities, $L_{\rm bol}$, and Eddington ratios, $L/L_{\rm
Edd}\equiv L_{\rm bol}/(1.5\times 10^{38}M_{\rm BH})$. This scaling assumes
$L_{\rm bol}$ in units of erg s-1, $M_{\rm BH}$ in units of $M_{\odot}$, and
solar composition gas. For $L_{\rm bol}$ estimates, we rely on the intrinsic,
absorption-corrected X-ray luminosities in the $2-10$ keV regime, $L_{\rm
int}(2-10\,{\text{keV}})$, as determined through the elaborate spectral
decomposition of the entire X-ray SEDs, discussed in detail in Ricci et al.
(2017a). We then assume a simple, universal bolometric correction of
$\kappa_{2-10\,{\text{keV}}}\equiv L_{\rm bol}/L_{\rm
int}(2-10\,{\text{keV}})=20$, which is a typical value for luminous AGNs
(e.g., Marconi et al., 2004; Vasudevan et al., 2009). There are many other
bolometric corrections suggested in the literature, including those defined at
other spectral regimes (e.g., Richards et al., 2006; Runnoe et al., 2012;
Trakhtenbrot & Netzer, 2012), luminosity-dependent corrections (e.g., Marconi
et al., 2004; Trakhtenbrot & Netzer, 2012; Duras et al., 2020), $L/L_{\rm
Edd}$-dependent ones (e.g., Vasudevan et al., 2009), and/or those motivated by
accretion disc models (e.g., Netzer, 2019). To exemplify how these various
prescriptions may affect the simple $L/L_{\rm Edd}$ estimates we use here, we
note that given the range of $L_{\rm int}(2-10\,{\text{keV}})$ for our broad-
line sources, the luminosity-dependent prescription of Marconi et al. (2004)
would suggest $\kappa_{2-10\,{\text{keV}}}\sim 10-70$.

The publicly available DR2 catalogs provide many measurements that can be used
for alternative determinations of $L_{\rm bol}$ (and thus of $L/L_{\rm Edd}$),
and in particular rest-frame optical monochromatic continuum luminosities
($L_{5100}$) and broad H$\alpha$ line luminosities ($L\left({\rm
b}{\text{H}}\alpha\right)$; both included in this catalog333 The luminosities
measured in the optical regime are corrected for galactic extinction.), as
well as X-ray continuum luminosities ($L_{2-10\,{\text{keV}}}$ and
$L_{14-150\,{\text{keV}}}$). Indeed, other BASS (DR2) publications may use
different choices for the determination of $L_{\rm bol}$ and $L/L_{\rm Edd}$,
as best suits their science goals.

We finally stress that neither the $M_{\rm BH}$ nor the $L_{\rm bol}$
prescriptions we use were calibrated using, are meant to be applied on, beamed
AGNs. In such sources the continuum X-ray, UV and optical luminosities may be
boosted, and thus both $M_{\rm BH}$ and $L_{\rm bol}$ may be significantly
overestimated. We describe the identification of beamed sources among our
sample of BASS/DR2 broad-line AGNs in Section 3.1.

##  3 The BASS/DR2 Broad Line catalog

In this Section we present the BASS/DR2 broad emission line catalog and some
key characteristics of the broad line AGN demographics in BASS.

Our detailed spectral measurements, their uncertainties, and select derived
quantities, are provided in electronic form herein, and
online.444http://www.bass-survey.com/data.html Tables 5, 6, 7 and 8 (in
Appendix D) describe the content of the BASS/DR2 broad-line catalogs for the
H$\alpha$, H$\beta$, Mg ii, and C iv spectral regions (respectively), for the
BASS/DR2 AGNs with adequate spectral fit quality ($f_{\rm Q}<3$). We also
provide, in a separate set of tables with identical format, spectral
measurements for the 177 AGNs from the “bonus” sample (i.e., sources drawn
from deeper-than-70-month Swift/BAT survey data), which had adequate spectral
fit quality (i.e., $f_{\rm Q}\leq 2$).

In Appendix B we provide a detailed comparison of line width and BH mass
measurements derived in BASS/DR2 and DR1 for those broad-line AGNs that are
part of both DRs. Fig. 14 summarizes these comparisons graphically,
highlighting that our DR2 spectral measurements are, overall, in excellent
agreement with DR1 measurements.

###  3.1 Demographics of Optical AGN Emission Line Classes

Here we further refine the classification of broad line AGNs in BASS/DR2, with
coverage of both H$\beta$ and H$\alpha$, based on the presence and (relative)
strength of the broad components of these emission lines (e.g., Osterbrock,
1981). Specifically, we follow the quantitative approach outlined in Winkler
(1992) to classify our sources into AGN sub-classes (Type 1, 1.2, 1.5, 1.8,
1.9 and 2) using the observed flux ratio of the broad H$\beta$ to the [O iii]
emission lines, $L\left({\rm b}{\text{H}}\beta\right)/L\left(\left[{\rm
O}\,\textsc{iii}\right]\right)$, as follows:

  * •

Sy1 if $L\left({\rm b}{\text{H}}\beta\right)/L\left(\left[{\rm
O}\,\textsc{iii}\right]\right)>5.0$;

  * •

Sy1.2 if $2.0<L\left({\rm b}{\text{H}}\beta\right)/L\left(\left[{\rm
O}\,\textsc{iii}\right]\right)<5.0$;

  * •

Sy1.5 if $1/3<L\left({\rm b}{\text{H}}\beta\right)/L\left(\left[{\rm
O}\,\textsc{iii}\right]\right)<2.0$;

  * •

Sy1.8 if $L\left({\rm b}{\text{H}}\beta\right)/L\left(\left[{\rm
O}\,\textsc{iii}\right]\right)<1/3$; broad component visible in H$\alpha$ and
H$\beta$;

  * •

Sy1.9 if there is a broad component visible in H$\alpha$ but not in H$\beta$.

  * •

Sy2 if no broad components are visible.

Throughout the rest of this work, we refer to “Type 1.x” AGNs simply as
“Sy1.x” sources. This “Sy” nomenclature is used here for the sake of
simplicity and consistency with previous work, despite the fact that most of
our BASS/DR2 AGNs may not be considered as “Seyfert galaxies” given their high
(X-ray) luminosities.

We acknowledge that this classification scheme practically depends on source
distance (or redshift), as it combines aperture-limited measurements of the
compact, unresolved BLR (broad Balmer lines) and of the extended, host-wide [O
iii] emission. Thus, for any given slit width and/or angular extraction
aperture, and a given (intrinsic) $L\left({\rm
b}{\text{H}}\beta\right)/L\left(\left[{\rm O}\,\textsc{iii}\right]\right)$,
the measured [O iii] flux would increase, and thus the $L\left({\rm
b}{\text{H}}\beta\right)/L\left(\left[{\rm O}\,\textsc{iii}\right]\right)$
ratio would decrease, with increasing source distance (redshift). This may
systematically shift the classification of sources towards weaker broad
components, or more specifically shift the classification of a source from,
e.g., Sy1 to Sy1.2 or from Sy1.2 to Sy1.5. We stress, however, that the
present study focuses on the comparison between Type 1.9 AGNs (Sy1.9s) and the
combined group of Type 1, 1.2 and 1.5 AGNs (Sy1-1.5s). Consequently, this
caveat does not affect our key results. Additionally, whenever we present
separate results for Sy1, Sy1.2 and Sy1.5 sources, we verify that the quoted
statistics of each AGN Type sub-sample (i.e., medians and/or means) are  not
statistically different from each other. More generally, the interested reader
is encouraged to use the tabulated slit/aperture widths of all BASS/DR2
optical spectra, and the distances to all AGNs, to address this caveat in any
future study that relies on BASS data (details are available in Koss et al.
2022b).

A previous BASS study by Shimizu et al. (2018) investigated Sy1.9 sources in
BASS/DR1 and showed that Sy1.9s with high column densities, i.e., $\log(N_{\rm
H}/{\rm cm}^{-2})>22$ and especially galaxies with $\log(N_{\rm H}/{\rm
cm}^{-2})\gtrsim 23$, have optical spectra that may be contaminated by line
emission from outflowing gas. Such systems have broad H$\alpha$ lines that are
relatively narrow, and that are blueshifted with respect to the NLR emission,
as well as outflow signatures in their [O iii] profiles. That study was based
on ad-hoc emission line diagnostics which were motivated by spatially-resolved
(IFU) data for certain exemplary systems, and further noted that with higher
resolution spectroscopy, these mis-classified outflowing systems would be easy
to identify. The superior BASS/DR2 data we use here, with hundreds of new
VLT/X-Shooter spectra, indeed allows us to more directly rule out the
possibility that outflows dominate the key emission line complexes considered
in the present study, and to be more confident in our classification of
(high-$N_{\rm H}$) Sy1.9s in BASS/DR2. We thus proceed with our analysis of
all BASS/DR2 AGNs, including Sy1.9s, according to the respective criteria
listed above. We defer the identification of (weak) outflow signatures in such
sources to a future study.

In addition to the AGN sub-classification, we also mark the 67 beamed AGNs,
comprised of high-$z$ systems and “candidate” beamed sources, with a dedicated
flag (BZQ). These are blazars or flat spectrum radio quasars, where Doppler
boosting may significantly amplify the non-thermal emission, including the
hard X-rays. This classification was done based on commonly-used techniques
(e.g., intense radio emission, a flat radio spectrum, dramatic variability),
combined with cross-matching to Fermi data products and multi-wavelength
broad-band SED fitting (e.g., Oh et al., 2018; Paliya et al., 2019). The
BASS/DR2 Data & Catalog paper (Koss et al., 2022b) provides further
information on the classification of these sources, particularly those not
identified as beamed AGNs in BASS/DR1 (see Paliya et al. 2019 and Marcotulli
et al., in prep). This identification of beamed AGNs eventually included all
AGNs with (reliable) measurements of the Mg ii and/or C iv broad emission
lines (i.e., $z\gtrsim 0.43$ and $\gtrsim 3.67$ respectively). There are also
22 (candidate) beamed systems among the lower-$z$ sources, where our optical
spectra cover the spectral complexes of H$\beta$ and/or H$\alpha$. Our catalog
provides all the available spectral measurements, and derived properties
(including AGN Type sub-classes when possible), regardless of any evidence for
beaming. We note that continuum and line measurements for such sources should
be used with caution, while line ratios may be more robust.

Figure 1: The distribution of BASS/DR2 AGNs in terms of various AGN Type sub-
classes. We show the percentages and total numbers of Sy1 (blue), Sy1.2
(orange), Sy1.5 (green), Sy1.9 (red), Sy2 (purple) and BZQ (magenta) sources.
See text for classification details. Figure 2: The distribution of BASS/DR2
AGNs among AGN Type sub-classes in bins of ultra-hard X-ray luminosity ($\log
L_{14-150\,{\text{keV}}}$), as indicated in each panel. Higher (lower)
luminosity AGNs tend to preferentially belong to the Sy1-1.2 (Sy1.9-2)
classes. Figure 3: The fraction of BASS/DR2 AGNs of various AGN Type sub-
classes as a function of ultra-hard X-ray luminosity ($\log
L_{14-150\,{\text{keV}}}$). The various symbols and lines trace AGNs belonging
to the Sy1-1.5 (blue), Sy1.9 (red), and Sy2 (purple) sub-classes.

In Figure 1 we show the composition of our BASS/DR2 sample of broad line AGNs
in terms of the fraction and total number of sources belonging to each of the
aforementioned AGN Type sub-classes (Sy1.0, 1.2, 1.5, 1.9, and BZQ).  We do
not identify any Sy1.8 sources among our BASS/DR2 AGNs. For completeness, we
also include narrow-line BASS/DR2 AGNs (Sy2s), which are not part of the
present catalog and are instead presented in other BASS/DR2 papers (Koss et
al., 2022a, b; Oh et al., 2022).

In Figures 2 and 3 we further illustrate how the fractions of AGNs in each of
the AGN sub-classes varies with (ultra-hard) X-ray luminosity. At low
luminosities ($L_{\rm 14-150\,{\text{keV}}}<10^{43}\,{\text{erg\,s}}^{-1}$)
the population is mostly dominated by Sy2 and Sy1.9 sources; however, as the
X-ray luminosity increases the relative fraction of Sy1-1.5 sources increases,
while the fraction of Sy1.9s and Sy2s decreases. This trend is in agreement
with several previous studies (e.g., Lawrence, 1991; Maiolino et al., 2007;
Merloni et al., 2014; Oh et al., 2015; Ricci et al., 2017b; Ichikawa et al.,
2019), which suggest that the typical dust covering factor in AGNs decreases
as the radiative power of the accretion disk increases. Earlier studies
attributed this trend to the “receding torus” scenario, where the increasing
(UV) disk emission sublimates dust at increasingly larger (inner) radii of the
dusty torus. A previous BASS study by Ricci et al. (2017b) conclusively showed
that the underlying trend is in fact that the fraction of unobscured sources
increases with increasing $L/L_{\rm Edd}$ (and not $L$). The dearth of
high-$L/L_{\rm Edd}$, high-$N_{\rm H}$ AGNs is commonly interpreted as
evidence for the amount of obscuring material, and indeed the degree of
obscuration, to be driven by radiation pressure exerted by the central engine
on the (inner) obscuring torodial structure (e.g., Fabian et al., 2009; Ricci
et al., 2017b; Ishibashi et al., 2018, and references therein). Revisiting the
distribution of BASS/DR2 AGNs in the $L/L_{\rm Edd}-N_{\rm H}$ plane, and the
relevant physical scenarios, is beyond the scope of the present study, and
will be addressed in a forthcoming BASS publication (see however the results
of the companion BASS/DR2 paper by Ananna et al. 2022).

We note that selection effects may also play a role in the trends seen in
Figs. 2 and 3. For instance, as the accretion disk luminosity decreases, the
contrast of AGN with respect to the host galaxy also decreases. In the context
of BASS optical spectroscopy, the $S/N$ required to robustly detect broad
emission lines would become unrealistically large, and our analysis may thus
favor the classification of low-luminosity AGNs as Sy2 and Sy1.9 sources, over
the Sy1-1.5 sub-classes.

###  3.2 Comparison of H$\alpha$ and H$\beta$ Line Width and $M_{\rm BH}$
Measurements

Figure 4: H$\beta$ versus H$\alpha$ FWHMs (left) and black hole masses (right)
in BASS/DR2. Black solid crosses represent the median error bars associated to
the FWHM and $M_{\rm BH}$ estimates. The relation we find between
FWHM(H$\alpha$) and FWHM(H$\beta$) (black dotted line) is broadly consistent
with the relation derived in Greene & Ho (2005, red dotted line), which
supports our use of their H$\alpha$-based $M_{\rm BH}$ prescription. The black
solid line represents the 1:1 relation.

In Figure 4 we compare the FWHM measurements (left panel) and $M_{\rm BH}$
estimates (right panel) associated with the broad H$\beta$ and H$\alpha$
emission lines. Our FWHM(H$\alpha$) and FWHM(H$\beta$) measurements are
generally in good agreement with the relation derived by Greene & Ho (2005,
see the red dash-dotted line). A formal fit to our set of FWHM measurements,
derived using the emcee Markov Chain Monte Carlo (MCMC) sampler (Foreman-
Mackey et al., 2013), yields the best-fit relation

$\log{\text{FWHM}}\left({\text{H}}\beta\right)=(0.98\pm
0.05)\log{\text{FWHM}}({\text{H}}\alpha)+(0.16^{+0.19}_{-0.17})\,,$ (3)

where FWHMs are given in km s-1, and the quoted uncertainties represent 95%
confidence intervals. A fit using the BCES(Y$|$X) method (Akritas & Bershady,
1996) provides an indistinguishable best-fit relation.

The right panel of Figure 4 shows that our H$\beta$\- and H$\alpha$-based
$M_{\rm BH}$ estimates are indeed in excellent agreement, with a median offset
of merely 0.03 dex, and a scatter of 0.25 dex. This scatter is mostly driven
by the scatter between FWHM(H$\alpha$) and FWHM(H$\beta$), which is found to
be 0.11 dex, which is expected to yield a scatter in $M_{\rm BH}$ of 0.23 dex.
This agreement between H$\beta$\- and H$\alpha$-based $M_{\rm BH}$ estimates
further justifies our choice to use the not-strictly-virial H$\alpha$-based
$M_{\rm BH}$ prescription, derived by Greene & Ho (2005). We stress again that
the excellent agreement between the two kinds of mass estimates is reached
only after considering a virial factor of $f_{{\text{FWHM}}}=1$ for both the
H$\alpha$ and H$\beta$ mass prescriptions. This is justified as the two lines
are expected to be formed in a similar circumnuclear region and consequently
should have the same geometrical factor.

###  3.3 Black hole Mass and Eddington Ratio Distributions

Figure 5: The luminosities, BH masses, and Eddington ratios of BASS/DR2 broad
line AGNs. Top: The distribution of BASS/DR2 AGNs in the $L/L_{\rm Edd}-M_{\rm
BH}$ plane. Our AGNs are further split by AGN Type (left panel) and by
redshift range (right panel). Bottom: cumulative distributions of $L_{\rm
bol}$ (left), $M_{\rm BH}$ (center) and $L/L_{\rm Edd}$ (right). The $M_{\rm
BH}$ of Sy1.9 sources are likely underestimated, and their $L/L_{\rm Edd}$ are
thus over-estimated (see text for discussion). The small arrows in the top
panels indicate the direction of a simple, uniform correction towards the true
$M_{\rm BH}$ and $L/L_{\rm Edd}$ of Sy1.9s (see §4.5 for more detailed
discussion of mass corrections). The $L_{\rm bol}$ and $L/L_{\rm Edd}$ of
beamed AGNs may be significantly over-estimated due to jet emission and/or
relativistic boosting.

In Figure 5 we show the distribution of broad-line BASS/DR2 AGNs in the
$M_{\rm BH}-L/L_{\rm Edd}$ plane, with sources further divided either by AGN
sub-class (top-left) or by redshift regime (top-right). We also show the
cumulative distributions of $L_{\rm bol}$ (bottom-left), $M_{\rm BH}$ (bottom-
center) and $L/L_{\rm Edd}$ (bottom-right). In this analysis we include all
AGNs for which reliable estimates of $M_{\rm BH}$ (and thus of $L/L_{\rm
Edd}$) are derived from broad emission lines, that is Type 1-1.9 AGNs, and
beamed sources (BZQ).

Figure 5 clearly demonstrates the wide range in both $M_{\rm BH}$ and
$L/L_{\rm Edd}$ that is sampled by BASS/DR2 AGNs. First, unbeamed AGNs where
both broad H$\beta$ and H$\alpha$ lines are robustly detected (Sy1-1.5s
hereafter) cover $6\lesssim\log(M_{\rm BH}/M_{\odot})\lesssim 10$ and
$-3\lesssim\log L/L_{\rm Edd}\lesssim 1$. This is comparable to the
distribution reported in BASS/DR1 (see Fig. 16 in Koss et al. 2017).555For a
few sources, BASS/DR1 measurements indicated exceptionally low $L/L_{\rm Edd}$
(i.e., $\log L/L_{\rm Edd}\lesssim-4$). The higher quality DR2 data and
measurements have corrected these outliers. Compared with other wide-field AGN
surveys in the local Universe where SE mass estimates were used (e.g., Greene
& Ho, 2007; Vestergaard & Osmer, 2009b; Schulze & Wisotzki, 2010), BASS
naturally includes the most luminous, rarest AGNs accessible, powered by the
most massive and/or highest-$L/L_{\rm Edd}$ BHs.

Second, beamed AGNs in BASS/DR2, which preferentially reside at higher
redshifts, appear to have higher $L_{\rm bol}$, $M_{\rm BH}$, and $L/L_{\rm
Edd}$, covering $8\lesssim\log(M_{\rm BH}/M_{\odot})\lesssim 10$ and,
importantly, $-1\lesssim\log L/L_{\rm Edd}\lesssim 2$ and
$46\lesssim\log(L_{\rm bol}/{\text{erg\,s}}^{-1})\lesssim 49$. Although this
may be partially attributed to the higher redshifts of the beamed sources
(given the flux-limited nature of the Swift/BAT all-sky survey), we stress
again that in such systems $L_{14-150\,{\text{keV}}}$ is most likely over-
estimated, as their X-ray emission is affected by jets, and is boosted by
relativistic effects. This propagates to an over-estimated $L_{\rm bol}$ and
thus $L/L_{\rm Edd}$.

Finally, a large fraction of (unbeamed) Sy1.9 sources show lower masses,
$\log(M_{\rm BH}/M_{\odot})\lesssim 7$, and higher Eddington ratios, $\log
L/L_{\rm Edd}\gtrsim-1$, compared to Sy1-1.5 sources, while covering a similar
luminosity range. This difference, however, likely highlights a bias among
this class. As we show in the next Section, the H$\alpha$-based masses of
Sy1.9s are underestimated, and their $L/L_{\rm Edd}$ are thus overestimated,
likely due to the suppression of broad H$\alpha$ emission, which we argue is
linked to (partial) obscuration of the BLR by dust. The small arrows added to
each Sy1.9 in the top panels of Fig. 5 demonstrate how a simple (uniform)
correction for this bias would be reflected in the $M_{\rm BH}-L/L_{\rm Edd}$
plane,  with increasing $M_{\rm BH}$ and accordingly decreasing $L/L_{\rm
Edd}\propto L/M_{\rm BH}$. In Section 4.5 we provide a set of simple $M_{\rm
BH}$ corrections for Sy1.9 sources.

##  4 Reduced broad Balmer line emission and obscuration in BASS/DR2 AGNs

In what follows, we examine in detail the properties of the broad Balmer
emission lines in our BASS/DR2 sample of broad-line AGNs. We particularly
focus on those sources where only H$\alpha$, but not H$\beta$ broad line
emission is identified - i.e., Type 1.9 AGNs (Sy1.9s), and use the rich BASS
data-set to better understand these systems.

###  4.1 Preliminaries: linking broad Balmer lines with X-ray measurements

As a first step, we look into the most basic links between the broad Balmer
line measurements, and the key properties deduced from the X-ray analysis of
the BASS AGNs (Ricci et al., 2017a). Namely, we examine the observed links
between (i) the broad H$\alpha$ and ultra-hard X-rays luminosities
($L\left({\rm b}{\text{H}}\alpha\right)$, $L_{14-150\,{\text{keV}}}$), and
(ii) the broad Balmer decrement ($L\left({\rm
b}{\text{H}}\alpha\right)/L\left({\rm b}{\text{H}}\beta\right)$, or simply
${\text{H}}\alpha/{\text{H}}\beta$ in what follows) and the line-of-sight
column densities ($N_{\rm H}$).

Figure 6: Broad H$\alpha$ emission line luminosity ($L\left({\rm
b}{\text{H}}\alpha\right)$) vs. ultra-hard X-ray luminosity
($L_{14-150\,{\text{keV}}}$) for BASS/DR2 AGNs. Symbol colors mark AGNs of
different (emission line) sub-classes, as indicated in the legend. The dashed
line marks a scaling of $\log(L[{\rm
b}{\text{H}}\alpha]/L_{14-150\,{\text{keV}}})=-1.5$, which describes the
general trend seen in most of our bona-fide broad line AGNs. The broad
H$\alpha$ emission in Type 1.9 AGNs, however, appears suppressed relative to
$L_{14-150\,{\text{keV}}}$.

In Figure 6 we show $L\left({\rm b}{\text{H}}\alpha\right)$ vs.
$L_{14-150\,{\text{keV}}}$ for the 434 non-beamed AGNs with reliable broad
H$\alpha$ measurements in BASS/DR2, further highlighting the different AGN
sub-classes. Unsurprisingly, the two independently-measured emission probes
show a roughly-uniform scaling for the vast majority of AGNs. However, for
Sy1.9 sources, $L\left({\rm b}{\text{H}}\alpha\right)$ deviates downwards from
the general scaling, by roughly 0.8 dex. Thus, broad H$\alpha$ emission seems
to be suppressed in Sy1.9 sources relative to all other AGNs with detectable
broad H$\alpha$ emission (Sy1-1.5 sources) at any given
$L_{14-150\,{\text{keV}}}$. We note that this apparent suppression is not
limited to particularly high- or low-luminosity sources (in terms of
$L\left({\rm b}{\text{H}}\alpha\right)$ and/or $L_{14-150\,{\text{keV}}}$). In
the following section we further investigate this suppression and how it may
be linked to other basic AGN observables and properties.

When considering the measured decrements between the broad H$\alpha$ and
H$\beta$ emission lines, we first note that close to 30% of the AGNs in our
sample are Type 1.9 AGNs where the broad H$\beta$ line cannot be detected, and
thus formally have $L\left({\rm b}{\text{H}}\beta\right)=0$ (and infinite
H$\alpha$/H$\beta$). Deducing a robust upper limit on $L\left({\rm
b}{\text{H}}\beta\right)$ (and thus a robust lower limit on
H$\alpha$/H$\beta$) for such sources is challenging, and requires a full
spectral decomposition of the (stellar) host emission. In addition, about 40%
of those sources with detectable broad H$\beta$ show
${\text{H}}\alpha/{\text{H}}\beta>3$, which–if taken at face value–may
indicate significant attenuation over the H$\beta$ wavelength regime, perhaps
by dusty BLR gas (see, e.g., Dong et al., 2008; Baron et al., 2016, and
references therein).

Figure 7:  The Balmer decrement ($L\left({\rm
b}{\text{H}}\alpha\right)/L\left({\rm b}{\text{H}}\beta\right)$) for broad-
line BASS/DR2 AGNs. Left: The distribution of $\log(L\left({\rm
b}{\text{H}}\alpha\right)/L\left({\rm b}{\text{H}}\beta\right))$ among
unbeamed, broad-line BASS/DR2 AGNs, excluding Type 1.9 sources and further
split to sources with $\log(N_{\rm H}/{\rm cm}^{-2})>20$ and $\log(N_{\rm
H}/{\rm cm}^{-2})\leq 20$ (top - probability distribution function; bottom -
cumulative distribution function). Right: $\log(L\left({\rm
b}{\text{H}}\alpha\right)/L\left({\rm b}{\text{H}}\beta\right))$ vs.
$\log(N_{\rm H}/{\rm cm}^{-2})$ for AGNs with $\log(N_{\rm H}/{\rm
cm}^{-2})>20$, again excluding Type 1.9 sources. Note the mild (yet
statistically significant) positive correlation between the sources In all
panels we mark the median values for the $\log(N_{\rm H}/{\rm cm}^{-2})\leq
20$ (completely unobscured) and $\log(N_{\rm H}/{\rm cm}^{-2})>20$ sub-
samples, as well as two reference values from the literature (see legends and
text for details).

In Figure 7 we show the available Balmer decrement measurements for our
sample, and how it varies with $N_{\rm H}$. The left-hand-side panels show the
distribution of ${\text{H}}\alpha/{\text{H}}\beta$ for all the BASS/DR2 AGNs
for which these quantities are robustly measured, i.e. omitting Type 1.9 AGNs.
We further split our sample to AGNs with $\log(N_{\rm H}/{\rm cm}^{-2})>20$
and “completely unobscured” AGNs, which formally have $\log(N_{\rm H}/{\rm
cm}^{-2})=20$ in the Ricci et al. (2017a) catalog. Note that this latter sub-
sample includes sources with upper limits on $N_{\rm H}$, so in practice it
covers $\log(N_{\rm H}/{\rm cm}^{-2})\leq 20$ (see Ricci et al. 2017a for
details). The right panel of Fig. 7 shows ${\text{H}}\alpha/{\text{H}}\beta$
vs. $N_{\rm H}$ for broad-line BASS/DR2 AGNs with $\log(N_{\rm H}/{\rm
cm}^{-2})>20$, again excluding Type 1.9 AGNs. All panels of Fig. 7 also mark
the canonical value of ${\text{H}}\alpha/{\text{H}}\beta=2.87$, derived for
Case B recombination in H ii regions, as well as
${\text{H}}\alpha/{\text{H}}\beta=3.1$ which is more relevant for AGNs. The
latter is commonly adopted for the low-density NLR in AGN, and is also
consistent with what is found for the broad Balmer lines (emitted from the
high-density BLR) in large samples of optically-selected quasars (see Dong et
al., 2008, and references therein).

The median Balmer decrements for our sub-samples of $\log(N_{\rm H}/{\rm
cm}^{-2})\leq 20$ and $\log(N_{\rm H}/{\rm cm}^{-2})>20$ AGNs are
$\log\left({\text{H}}\alpha/{\text{H}}\beta\right)=0.52$ and $0.58$
(respectively), and the scatter measures (standard deviations) in
${\text{H}}\alpha/{\text{H}}\beta$ for these two sub-samples are 0.24 and 0.41
dex, respectively. The median Balmer decrements in our BASS/DR2 AGNs are in
agreement with what is found for optically-selected SDSS quasars (e.g., Dong
et al., 2008, see reference lines in Fig. 7). The scatter we find is higher
than what is found for SDSS quasars (i.e., $\sim$0.05 dex; Dong et al., 2008).
This is expected given that SDSS quasars are pre-selected based on their blue
continuum colors, tracing unobscured accretion disk emission Richards et al.
(2002), while our Swift/BAT-selected broad-line AGNs indeed cover a wider
range of (circumnuclear) obscuration.

Among the $\log(N_{\rm H}/{\rm cm}^{-2})>20$ BASS/DR2 broad-line AGNs, there
is a (mild) trend of increasing Balmer decrement with increasing column
density, with a significant amount of scatter (right panel of Fig. 7). This
trend seems to involve objects of all sub-classes (i.e., Sy1s, 1.2s and 1.5s).
A formal Spearman correlation test confirms that the correlation between
$L\left({\rm b}{\text{H}}\alpha\right)/L\left({\rm b}{\text{H}}\beta\right)$
and $N_{\rm H}$, for all Sy1-1.8 AGNs with $\log(N_{\rm H}/{\rm cm}^{-2})>20$,
is statistically significant but rather weak ($r_{\rm s}=0.28$, $P_{\rm
s}=0.01$). Given the large scatter and the limited strength of the
correlation, we refrain from fitting a formal relation that links $L\left({\rm
b}{\text{H}}\alpha\right)/L\left({\rm b}{\text{H}}\beta\right)$ and $N_{\rm
H}$.

The Balmer decrements we measure are far lower than what is expected from the
corresponding column densities. For reference, for $\log(N_{\rm H}/{\rm
cm}^{-2})=22$ one would expect a Balmer decrement of roughly
${\text{H}}\alpha/{\text{H}}\beta\simeq 17$, assuming a standard Galactic
absorption scaling (i.e., gas-to-dust ratio; Bohlin et al., 1978) and a
Cardelli et al. (1989) extinction law. This is barely consistent with the
highest ${\text{H}}\alpha/{\text{H}}\beta$ we measure for AGNs with comparable
$N_{\rm H}$ (Fig. 7, right). For higher $N_{\rm H}$, the discrepancy grows
substantially and quickly (expected ${\text{H}}\alpha/{\text{H}}\beta>500$ by
$\log(N_{\rm H}/{\rm cm}^{-2})=22.5$). This is consistent with several
previous works, which found that the $E(B-V)/N_{\rm H}$ ratio in AGNs is lower
than Galactic by a factor ranging from $\sim$3 and up to $\sim$100 (e.g.
Maiolino et al., 2001a, b), perhaps indicating that the material obscuring the
central X-ray source is in part dust-free (e.g., Burtscher et al., 2016).
Alternatively,  the X-ray obscuring material may be arranged in a compact
configuration, which does not (generally) affect the BLR radiation. The recent
study by Jaffarian & Gaskell (2020) further discusses these and other
scenarios for the differences between the levels of extinction deduced from
Balmer line ratios and from (X-ray) hydrogen column densities. We’ll come back
to this issue when discussing intermediate Type AGNs, in Section 4.2.

###  4.2 H$\alpha$ Line Attenuation in Partially-obscured AGNs

Figure 8: Broad Balmer line strength relative to ultra-hard X-rays for
$L\left({\rm b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ (left) and
$L\left({\rm b}{\text{H}}\beta\right)/L_{14-150\,{\text{keV}}}$ (right), vs.
line-of-sight column density, $N_{\rm H}$, and the projected distributions of
these quantities. Broad-line BASS/DR2 AGNs of various AGN sub-types are marked
with different colors and symbols (see legend). Large crosses represent the
median values of $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ and $L\left({\rm
b}{\text{H}}\beta\right)/L_{14-150\,{\text{keV}}}$ within equally-spaced bins
of $\log N_{\rm H}$, and the corresponding 90% confidence intervals as
determined from bootstrapping. Black thin crosses represent Type 1, 1.2 and
1.5 AGNs, while red thick crosses represent Type 1.9 sources. Type 1.9 AGNs
typically have $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ that are significantly
lower than those of Type 1-1.5 AGNs, but only in the $\log(N_{\rm H}/{\rm
cm}^{-2})\gtrsim 22$ regime.

In Figure 8 we show $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ (left) and $L\left({\rm
b}{\text{H}}\beta\right)/L_{14-150\,{\text{keV}}}$ (right) vs. $\log(N_{\rm
H}/{\rm cm}^{-2})$ for our BASS/DR2 broad-line AGNs, with the respective
distributions of these quantities (ancillary panels in each plot), and
distinguishing the different AGN sub-classes. The first thing to notice in
Fig. 8 is that Sy1.9 sources tend to have higher $N_{\rm H}$ than Sy1-1.5
sources. This difference is statistically significant, as confirmed by both
Kolmogorov-Smirnov (KS) and Wilcoxon rank sum (WRS) tests. The $P$-values
associated with the null hypotheses, i.e., the probability of having the
$\log(N_{\rm H}/{\rm cm}^{-2})$ distribution in Sy1.9s to be drawn from the
same $\log N_{\rm H}$ distribution as of Sy1-1.5s, are $\ll 10^{-10}$ (for
both tests).

Second, the left panel of Fig. 8 shows that the median $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ ratio in Sy1-1.5 AGNs
stays roughly constant across the full range in $\log N_{\rm H}$ covered by
our sample. The same behavior is observed in the right panel where the median
$L\left({\rm b}{\text{H}}\beta\right)/L_{14-150\,{\text{keV}}}$ is also
roughly constant within the full $\log N_{\rm H}$ range. For Sy1.9 AGNs,
however, the behavior is more complex, and can be split into two different
regimes, with sources having column densities either above or below
$\log(N_{\rm H}/{\rm cm}^{-2})=22$. In the  $\log(N_{\rm H}/{\rm cm}^{-2})<22$
regime, the $L\left({\rm b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$
ratios of Sy1.9 sources are broadly consistent with those of Sy1-1.5 sources,
with the former being only slightly lower than the latter (red vs. black
crosses, respectively, in the left panel of Fig. 8). Specifically, for
$20<\log(N_{\rm H}/{\rm cm}^{-2})<22$ AGNs, the median $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ for Sy1.9s is
$(11^{+6}_{-4})\times 10^{-3}$, compared to $(34^{+4}_{-3})\times 10^{-3}$ for
Sy1-1.5s. In the  $\log(N_{\rm H}/{\rm cm}^{-2})>22$ regime, the $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ ratios of Sy1.9s are
significantly lower than those of Sy1-1.5s. Specifically, the corresponding
median values for sources with  $22<\log(N_{\rm H}/{\rm cm}^{-2})<24$ are
$(4_{-1}^{+2})\times 10^{-3}$ and $(29_{-7}^{+8})\times 10^{-3}$ for Sy1.9s
and Sy1-1.5s, respectively. The $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ ratios of Sy1.9 sources
with  $\log(N_{\rm H}/{\rm cm}^{-2})>22$ are thus lower by a factor of
$\sim$8.5 times than what is found for the Sy1-1.5 AGN population. This
difference is statistically significant, as confirmed by the appropriate KS
and WRS tests ($P<10^{-6}$ for both tests). The more general trend of
decreasing $L\left({\rm b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$
with increasing $N_{\rm H}$ in Sy1.9 AGNs is only marginally significant, with
$P\simeq 0.03$ and $P\simeq 0.13$ for the Spearman and Pearson correlation
tests, respectively.

We conclude that for AGNs with relatively weak broad Balmer line emission,
that is Type 1.9 AGNs, the (relative) strength of the broad H$\alpha$ emission
line at fixed ultra-hard X-ray luminosity is linked to the presence of large
gas columns along the line of sight, independently determined from X-ray
spectral modeling. This may suggest that in Type 1.9 AGNs, but not in Type
1-1.5s, the broad H$\alpha$ emission is partially absorbed by the same gas
that also accounts for the large neutral gas columns.

The association of weak broad H$\alpha$ emission with dust obscuration may be
challenged by the typical column densities of order $\log(N_{\rm H}/{\rm
cm}^{-2})\simeq 23$ in our Sy1.9s: for a standard (Galactic) dust-to-gas ratio
(Bohlin et al., 1978), the corresponding optical extinction
($A[{\text{H}}\alpha]\sim 30$ mag) would be expected to completely suppress
the optical AGN broad line emission. The fact that our Sy1.9s do show broad
H$\alpha$ emission therefore requires either (1) that the Balmer emission is
only partially obscured, or (2) that the  dust-to-gas ratio of the obscurer is
significantly lower than ISM values. Partial obscuration of the broad
H$\alpha$ line could also occur if the line-of-sight to the BLR “grazes” the
obscuring torus, which completely obscures the line-of-sight to the (X-ray
emitting) central engine (see discussion in, e.g., Goodrich, 1995; Trippe et
al., 2010).

A drastically different interpretation is that the narrow H$\alpha$ emission
in our Sy1.9s is intrinsically strong compared to the broad H$\alpha$
emission, as is common in low luminosity AGNs (Stern & Laor, 2012). Strong
narrow line emission may be due to galaxy-scale gas covering a large fraction
of sight-lines to the AGN. A large abundance of gas in the galaxy may also
enhance the typical hydrogen columns along the line of sight to the X-ray
source as seen in our Sy1.9s (see also, e.g., Maiolino & Rieke, 1995; Koss et
al., 2020). This latter scenario, however, stands in contrast to some evidence
for the high-$N_{\rm H}$ material in (BASS) AGNs to be confined to the nuclear
region (e.g., Ricci et al., 2017b), and in contrast to constraints on galaxy-
wide contributions to $N_{\rm H}$ (e.g., $\log(N_{\rm H}/{\rm
cm}^{-2})\lesssim 22.5$ by Buchner & Bauer 2017; see also Ramos Almeida &
Ricci 2017 for a review).

Since the BASS/DR2 data do not have the spatial information required to
thoroughly test this alternative scenario, we next turn our attention to the
kinematic information available for our BASS/DR2 AGNs, and particularly for
the Sy1.9s, to gain further insight regarding the interplay between (X-ray)
obscuration and (suppressed) broad Balmer emission, and the nature of the gas
structures at play.

###  4.3 Attenuation of the Highest-velocity H$\alpha$ Emission Region

After establishing a link between the detailed attenuation of broad Balmer
line emission and X-ray determined line-of-sight column densities, we now use
our BASS/DR2 AGN sample to better understand the nature of the relevant
obscuring material.

Figure 9: H$\alpha$ FWHMs vs. $N_{\rm H}$ and the projected distribution of
these quantities for Sy1 (light-blue), Sy1.2 (orange), Sy1.5 (light-green) and
Sy1.9 (red) AGNs. Horizontal error-bars represent the bin edges and vertical
error-bars represent the errors in the median FWHM from each bin estimated
from bootstrapping.  For completeness, Fig. 16 shows the complementary
FWHM(H$\beta$) vs. $N_{\rm H}$ parameter space.

In Figure 9 we show FWHM(H$\alpha$) vs. $\log N_{\rm H}$, as well as the
respective projected cumulative distributions for these quantities, for our
sample of broad-line BASS/DR2 AGNs.  For the sake of completeness, we also
show a similar figure for FWHM(H$\beta$) in Fig. 16 (in Appendix F). A simple
visual inspection of Fig. 9 suggests that sources with no detected broad
H$\beta$ emission (i.e., Sy1.9 sources) are clustered towards higher column
densities ($\log(N_{\rm H}/{\rm cm}^{-2})\gtrsim 22$) and narrower H$\alpha$
(${\text{FWHM}}({\text{H}}\alpha)\lesssim 3000\,{\rm km\,s}^{-1}$), compared
with the $\log N_{\rm H}$ and FWHM(H$\alpha$) distribution of sources with
detected broad H$\beta$ (i.e., Sy1-1.5s). Indeed, formal KS and WRS
statistical tests indicate that the FWHM(H$\alpha$) distribution in Sy1.9 is
significantly different from that of Sy1-1.5s ($P\lesssim 10^{-5}$ for the
null hypotheses of both tests). The broad H$\alpha$ emission lines in Sy1.9s
are thus generally narrower than in Sy1-1.5s. More specifically, most Sy1.9s
with $22<\log(N_{\rm H}/{\rm cm}^{-2})<24$ have
${\text{FWHM}}({\text{H}}\alpha)\lesssim 2500\,{\rm km\,s}^{-1}$, and the
median value for such sources is $2452^{+494}_{-197}\,{\rm km\,s}^{-1}$,
compared to a median FWHM(H$\alpha$) in Sy1-1.5s of
$4337.0^{+1159}_{-610}\,{\rm km\,s}^{-1}$ (across the entire $\log N_{\rm H}$
range). In contrast, the median FWHM(H$\alpha$) in Sy1.9s with $\log(N_{\rm
H}/{\rm cm}^{-2})<22$ ($3598^{+358}_{-316}\,{\rm km\,s}^{-1}$) is consistent
with that of Sy1-1.5s ($3677^{+142}_{-157}\,{\rm km\,s}^{-1}$).

Figure 10: Median FWHM(H$\alpha$) for objects with $N_{\rm H}$ smaller than
the $N_{\rm H}$ in the $\log N_{\rm H}$ (horizontal) axis. The error-bars are
obtained from bootstrapping and correspond to a confidence level of 90%. Type
1.9 AGNs, which tend to have higher column densities ($\log(N_{\rm H}/{\rm
cm}^{-2})>22$) typically also have narrower H$\alpha$ broad emission lines.

To further illustrate this point, in Figure 10 we show the median
FWHM(H$\alpha$) of Sy1-1.5s and Sy1.9s which have $\log N_{\rm H}$ smaller
than (or equal to) the corresponding value on the $\log N_{\rm H}$
(horizontal) axis. Evidently, for $\log(N_{\rm H}/{\rm cm}^{-2})\lesssim 21.5$
the median values of FWHM(H$\alpha$) in Sy1-1.5s and in Sy1.9s are in good
agreement. However, when $\log(N_{\rm H}/{\rm cm}^{-2})\gtrsim 21.5$, Sy1.9s
start to show narrower profiles than Sy1-1.5s, with a clear break point around
$\log(N_{\rm H}/{\rm cm}^{-2})\gtrsim 23$ where the difference becomes more
prominent and exceeds the 90% confidence level (that is, exceeds the
corresponding error bars).

Figure 11: Left: $L\left({\rm H\alpha}\right)/L\left({\rm 14-150KeV}\right)$
vs FWHM$\left({\rm H}\alpha\right)$. Right: $L\left({\rm
H\alpha}\right)/L\left({\rm 14-150KeV}\right)$ vs $\log N_{\rm H}$ color-coded
by FWHM$\left({\rm H}\alpha\right)$. The vertical error-bars squares represent
the median values of $L\left({\rm H\alpha}\right)/L\left({\rm
14-150KeV}\right)$ after binning in FWHM$\left({\rm H}\alpha\right)$ (left
panel) and $\log N_{\rm H}$ (right panel) in equally spaced quantiles.
Horizontal error-bars represent the bin edges and vertical error bars the
errors in the median $L\left({\rm H\alpha}\right)/L\left({\rm
14-150KeV}\right)$ estimated from bootstrapping.

In order to further characterize the apparent high velocity suppression in the
broad H$\alpha$ profiles, in the left panel of Figure 11 we show $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ vs. FWHM(H$\alpha$) for
Sy1-1.5 and Sy1.9 sources, with large crosses representing the median values
within FWHM(H$\alpha$) bins (and corresponding error-bars; see figure
caption). Figure 11 (left) shows that, in general, Sy1.9s tend to have
systematically lower $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ ratios across the full
range of FWHM(H$\alpha$), compared to Sy1-1.5 sources. Moreover, the Sy1.9s
with the narrowest H$\alpha$ profiles
(${\text{FWHM}}({\text{H}}\alpha)\lesssim 3000\,{\rm km\,s}^{-1}$) show yet
weaker broad H$\alpha$ (in terms of $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$) than their broader-
profile counterparts (i.e., Sy1.9s with
$3000\lesssim{\text{FWHM}}({\text{H}}\alpha)/{\rm km\,s}^{-1}\lesssim 5000$).

The right panel of Figure 11 shows $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ vs. $\log N_{\rm H}$ for
all our broad-line AGNs, irrespective of their sub-class (c.f. Fig. 8, left),
with each AGN color-coded by its FWHM(H$\alpha$). It is again evident that the
FWHM(H$\alpha$) of heavily obscured AGNs, mostly dominated by Type 1.9
sources, show narrow and weak broad H$\alpha$ emission lines. We note here
that the general trend of decreasing $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ with increasing $\log
N_{\rm H}$, among all AGNs in our sample, is highly significant ($P\simeq
10^{-7}$, as indicated).

With the insights gained from Figures 8, 9, and 11, we infer that the heavily
obscured Type 1.9 AGNs ($\log(N_{\rm H}/{\rm cm}^{-2})\gtrsim 22.5$) generally
show narrower and weaker H$\alpha$ broad emission line profiles (i.e., lower
$L\left({\rm b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$), compared
with (lower-$N_{\rm H}$) Type 1-1.5 AGNs.

Combining these findings with those presented in Section 4.2, we conclude that
our BASS/DR2 sample shows evidence that the attenuation of the broad H$\alpha$
line emission in Type 1.9 AGNs predominantly affects the highest-velocity line
emitting gas. Thus, the obscuring material (which is also related to the
higher column densities) must be, at least partially, located on scales
comparable with the innermost parts of the BLR.

In two parallel BASS studies, NIR spectroscopy is used to model (broad)
Paschen emission lines (Brok et al., 2022; Ricci et al., 2022). One of the
results of the Brok et al. (2022) study is that the FWHM ratio between NIR and
H$\alpha$ lines in Sy1.9s increases monotonically (from $\sim$1.2 to 2) with
increasing line-of-sight obscuration (from $\log(N_{\rm H}/{\rm cm}^{-2})=21$
to $\log(N_{\rm H}/{\rm cm}^{-2})=25$). In principle, this may further support
the scenario in which the highest-velocity H$\alpha$ emitting regions tend to
be suppressed by obscuration. However, this finding is based on a limited
number of sources ($\sim$10). Moreover, the Ricci et al. (2022) study
essentially finds no statistically significant trend between the FWHM ratio
and $N_{\rm H}$, at least up to $\log(N_{\rm H}/{\rm cm}^{-2})\simeq 23$.

Figure 12: Left: Broad H$\alpha$ based versus $\sigma_{\star}$ based $M_{\rm
BH}$ estimates. Right: $\log\left({M}_{\rm BH,BLR}/{M}_{\rm
BH,\sigma_{\star}}\right)$ vs $\log N_{\rm H}$. In both panels, light-shaded
symbols mark objects for which the measurement-related (fitting-related)
uncertainties on $M_{\rm BH}$ estimates from $\sigma_{\star}$,
$\Delta\log{M}_{\rm BH,\sigma_{\star}}$, are larger than 0.1 dex.

###  4.4 Comparing Broad-line Based and Stellar-velocity Based $M_{\rm BH}$
Estimates in AGNs

In this Section we provide a preliminary analysis of the differences that we
find between $M_{\rm BH}$ estimates derived from broad H$\alpha$ emission
lines ($M_{\rm BH,BLR}$, from this paper) and those derived from the stellar
velocity dispersion ($\sigma_{\star}$) measured in the AGN hosts ($M_{\rm
BH,\sigma_{\star}}$).

The $\sigma_{\star}$ measurements are described in detail in a dedicated
BASS/DR2 paper (Koss et al. 2022c; see also Caglar in prep.). Here we briefly
note that  these $\sigma_{\star}$ measurements are based on high-quality
spectroscopy and analysis of the spectral regions that include the Ca ii
H+K$\,\lambda\lambda 3935,3968$, Mg i $\lambda 5175$, and/or Calcium triplet
(near 8500 Å) absorption features. The corresponding $M_{\rm
BH,\sigma_{\star}}$ estimates are then derived through the relation of
Kormendy & Ho (2013). In principle, aperture size effects may be an important
factor in $\sigma_{\star}$ estimates, particularly for surveys that cover a
wide redshift range. In practice, however, most of our spectra were taken with
slits of $\sim$1.5″width, corresponding to $\sim$0.5-3.6 kpc scales for BASS
AGNs at $z\simeq 0.015-0.14$, which encompasses 80% of our sources. Moreover,
large galaxy samples show a rather limited diversity of $\sigma_{\star}$
radial profiles ($\lesssim$15% variation Ziegler & Bender, 1997; Cappellari et
al., 2006; Falcón-Barroso et al., 2017). We therefore expect only about 15%
systematic uncertainty in our $\sigma_{\star}$ estimates.

In the left panel of Figure 12 we directly compare the two sets of $M_{\rm
BH}$ estimates – from broad H$\alpha$ emission ($M_{\rm BH,BLR}$) and from
$\sigma_{\star}$ ($M_{\rm BH,\sigma_{\star}}$), for the 75 BASS/DR2 AGNs for
which both types of measurements are available. $M_{\rm BH,\sigma_{\star}}$
estimates are generally larger than $M_{\rm BH,BLR}$, with median deviations
of $\sim$0.69 and $\sim$0.89 dex for Sy1-1.5 and Sy1.9 sources, respectively.
This result is in agreement with the recent studies of Caglar et al. (2020) on
a sample of 19 local X-ray selected AGNs from the LLAMA project (Davies et
al., 2015), where they find median offsets of 0.60 and 1.0 dex for Sy1s and
Sy1.9s, respectively.666The  virial factor $f$ of $M_{\rm BH,BLR}$ in Fig. 12
has been rescaled to 1.14 to better match the virial factor used in Kormendy &
Ho (2013), which is in turn used to estimate $M_{\rm BH,\sigma_{\star}}$ in
BASS/DR2 (Koss et al., 2022c).

In the right panel of Figure 12, we present the differences between the two
types of $M_{\rm BH}$ estimates, in terms of $\Delta\log M_{\rm
BH}\equiv\log(M_{\rm BH,BLR}/M_{\rm BH,\sigma_{\star}})$, vs. line-of-sight
column densities, $\log N_{\rm H}$. When considering all available data
points, there is a large scatter and no clear correlation between the two
quantities. However, given the difficulties to measure $\sigma_{\star}$,
especially in systems where the optical continuum is AGN-dominated, we also
consider a restricted subset of measurements, for which the uncertainties on
$M_{\rm BH,\sigma_{\star}}$ measurements are below 0.1 dex (white filled
circles). For this subset of higher-quality measurements, we can see that
$\Delta\log M_{\rm BH}$ is roughly $-0.74$ dex for unobscured and mildly
obscured AGNs, i.e., $\log(N_{\rm H}/{\rm cm}^{-2})\leq 22.5$. This is in
agreement with the findings of previous studies, such as Woo et al. (2013,
2015) and Shankar et al. (2016), and more recently by Shankar et al. (2019)
and Caglar et al. (2020). These works explored several scenarios to explain
this offset, which we discuss below. For higher column densities, above
$\log(N_{\rm H}/{\rm cm}^{-2})\approx 22$ – that is, the regime dominated by
Sy1.9s and where dust is expected to more strongly affect $L\left({\rm
b}{\text{H}}\alpha\right)$ measurements – $\Delta\log M_{\rm BH}$ further
decreases, strongly and monotonically, from about $-0.74$ dex to $-1.94$ dex
at $\log(N_{\rm H}/{\rm cm}^{-2})\simeq 24$. A formal fit of our robustly-
measured AGNs with $\log(N_{\rm H}/{\rm cm}^{-2})\geq 22.5$, derived using the
emcee MCMC sampler yields the best-fit relation

$\Delta\log M_{\rm BH}=\\\ (-0.64^{+0.26}_{-0.29})\times\log(N_{\rm
H}/10^{22}\,{\rm cm}^{-2})-(0.52^{+0.20}_{-0.23})\,,$ (4)

where the quoted uncertainties represent 95% confidence intervals. A fit using
the BCES(Y$|$X) method provides a highly consistent relation, with slope and
intercept of $-0.59\pm 0.09$ and $0.62\pm 0.11$, respectively. The reason for
this difference can be directly attributed to the fact that Sy1.9 sources show
systematically lower $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ and narrower
FWHM(H$\alpha$) (as shown in detail in the preceding sections), which
contributes to lower $M_{\rm BH,BLR}$ (see Eq. 1 and Table 3).

One possible explanation for the discrepancy between broad-line-based and
host-based determinations of $M_{\rm BH}$ in nearby AGNs, as discussed in
Shankar et al. (2016, 2019), is that the $M_{\rm BH}$-$\sigma_{\star}$
relation determined for inactive galaxies is biased against low mass BHs
because of the difficulties in resolving the sphere of influence and
subsequently determine the black hole mass in these systems. According to
these analyses, this bias artificially flattens the power-law index and
enhances the intercept of the observed $M_{\rm BH}-\sigma_{\star}$ relation of
inactive galaxies. These, in turn, may amount to a discrepancy of about 0.7
dex with respect to the (assumed) intrinsic $M_{\rm BH}-\sigma_{\star}$
relation – in broad agreement with what is seen in our analysis of the
BASS/DR2 sample, as well as other AGN samples.

Two additional possible explanations are related to selection biases against
low and high luminosities in the sample of reverberation-mapped, broad-line
AGNs that is used to calibrate BLR-based mass prescriptions, as discussed in
Woo et al. (2013). On one hand, this RM sample can be slightly biased against
low luminosity AGNs and therefore against low mass SMBHs because of their weak
broad emission lines. On the other hand, a more important bias in such a
sample is against luminous AGNs that are expected to preferentially harbor
high mass SMBHs. This is due to a variability bias caused by the anti-
correlation between the amplitude of variability and AGN luminosity (e.g.,
Caplar et al., 2017, and references therein), that makes it difficult to
measure the reverberation time lags in the most luminous systems. Another
issue with highly luminous systems highlighted by Woo et al. (2013) is the
great difficulty in measuring $\sigma_{\star}$ when the optical spectrum is
dominated by a prominent, accretion disk powered component, which dilutes the
weak stellar absorption features  (see, e.g., Grier et al. 2013). The study by
Woo et al. (2013) explicitly showed that addressing these limitations of the
RM sample can indeed account for the observed discrepancies seen between BLR-
based and host-based determinations of $M_{\rm BH}$.

A final possibility is that discrepancies between broad-line-based and
$\sigma_{\star}$-based $M_{\rm BH}$ estimates are caused by an overall
different phase of evolution of the inactive and active galaxies populations.
In such a scenario, the SMBHs of those galaxies observed to be active are
still growing, and have yet to reach their “final” location in the $M_{\rm
BH}-\sigma_{\star}$ plane. While growing, active systems may indeed be located
“below” the BH-host relations of inactive galaxies, and will eventually reach
them, as expected from some co-evolutionary models (e.g., Silk & Rees, 1998;
King, 2003) and simulations (e.g., Anglés-Alcázar et al., 2017; Bower et al.,
2017; Lapiner et al., 2021). We note that the (late) evolution of active
galaxies in the $M_{\rm BH}-\sigma_{\star}$ plane is far from being well-
understood, and radically different scenarios have been explored in numerous
studies that address the (redshift resolved) AGN and galaxy populations (e.g.,
Caplar et al., 2018, and references therein).

Unfortunately, the BASS/DR2 sample cannot be used to directly address these
previously published scenarios as the vast majority (50 out of 75, or 66%) of
the objects in our sample with both broad-line-based and
$\sigma_{\star}$-based $M_{\rm BH}$ estimates are Sy1.9 sources, which exhibit
much larger mass discrepancies (Fig. 12). Taken at face value, these large
discrepancies in dust-obscured Sy1.9 mass estimates (of up to 2 dex) may hint
at the possibility that dust obscuration and/or circumnuclear (dusty) gas may
play a role in where a given AGN appears in the $M_{\rm BH}-\sigma_{\star}$
plane. However, our analysis has demonstrated that it is much more likely that
the seemingly low broad-line-based $M_{\rm BH}$ estimates of Sy1.9s are due to
the diminished emission of the (high-velocity) H$\alpha$ line.

In order to more directly address the issue of $M_{\rm BH}$ discrepancies, the
BASS team is pursuing two complementary directions. Caglar (in prep.) focuses
on a highly-complete sample of Sy1 sources with both broad-line-based and
$\sigma_{\star}$-based estimates of $M_{\rm BH}$, and little sign of
obscuration ($\log(N_{\rm H}/{\rm cm}^{-2})\lesssim 22$). As mentioned above,
Ricci et al. (2022) uses NIR broad-line based $M_{\rm BH}$ estimates in Sy1.9s
using, e.g., broad Pa$\alpha$ and Pa$\beta$ lines, which are far less affected
by dust (compared to H$\alpha$).

The findings presented here have important implications for determination of
$M_{\rm BH}$ in individual AGNs, and of the distributions of $M_{\rm BH}$
(i.e., the BHMF) in AGN samples that are based solely on the identification of
broad H$\alpha$ emission. In such surveys, some portion of Sy1.9 sources may
not be robustly identified (and excluded), while some portion of the ones that
are identified will have $M_{\rm BH}$ measurements that are underestimated by
as much as 2 dex. Conversely, this would lead to $L/L_{\rm Edd}$ being
overestimated by up to 2 dex. To remedy this when using large samples, one may
consider focusing on those sources which have a robust identification of broad
H$\beta$ emission, or in which broad-band (X-ray) spectral analysis suggests
limited dust obscuration ($\log(N_{\rm H}/{\rm cm}^{-2})\lesssim 22$).

Another practical remedy would be to derive empirical corrections for the key
observables, and the $M_{\rm BH}$ estimates, of Type 1.9 sources. We calibrate
such corrections in the next section.

###  4.5 Correcting Single epoch $M_{\rm BH}\left({\rm
b{\text{H}}\alpha}\right)$ Estimates in Type 1.9 AGNs

Our analysis shows that Type 1.9 AGNs exhibit suppression of the broad
H$\alpha$ line emission, particularly the highest-velocity emission, likely
caused by dust obscuration. These effects become more prominent with
increasing $N_{\rm H}$. Given that the determination of $M_{\rm BH}$ from BLR
properties depends (almost solely) on $L\left({\rm b}{\text{H}}\alpha\right)$
and FWHM(H$\alpha$) measurements, these effects may have a direct impact on
the determination of $M_{\rm BH}$ in AGN samples, introducing a bias of
underestimated $M_{\rm BH}$ in (partially) obscured AGNs.

How can one overcome this tendency to underestimate $M_{\rm BH}$ in Sy1.9
sources? Given that our BASS/DR2 AGNs sample has only 50 Sy1.9 sources with
both types of $M_{\rm BH}$ estimates, we prefer to provide only simple, median
corrections – that is, corrections that will bring the median quantities to
agreement – which can be applied to Sy1.9s in various regimes of key
observables. Below we provide such corrections to $L\left({\rm
b}{\text{H}}\alpha\right)$ and FWHM(H$\alpha$) in Sy1.9 sources, using
$L_{14-150\,{\text{keV}}}$ (whenever it is available). To this end, we divide
the $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}-{\text{FWHM}}({\text{H}}\alpha)$
parameter space into three regimes. We then simply identify the multiplicative
corrections in $L\left({\rm b}{\text{H}}\alpha\right)$ and FWHM(H$\alpha$)
that bring the median values of these quantities in Sy1.9s to agree with the
medians of the Sy1-1.5s. The uncertainties on these corrections were derived
through a bootstrapping procedure, and represent the central 68th percentiles
(i.e., $1\sigma$ equivalent). We also report the corresponding corrections to
$\log M_{\rm BH}$, which are derived by combining the corrections in
$L\left({\rm b}{\text{H}}\alpha\right)$ and FWHM(H$\alpha$), through our
$M_{\rm BH}$ prescription.

The corrections for various ranges in $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}$ and FWHM(H$\alpha$) are:

  1. 1.

${\text{FWHM}}({\text{H}}\alpha)_{\rm obs}{\lesssim}2400\,{\rm km\,s}^{-1}$
and $L\left({\rm
b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}{<}10^{-2}$:

     * •

$L\left({\rm b}{\text{H}}\alpha\right)_{\rm
corr}=\left(21.6^{+20.2}_{-9.8}\right)\times L\left({\rm
b}{\text{H}}\alpha\right)_{\rm obs}$

     * •

${\text{FWHM}}({\text{H}}\alpha)_{\rm
corr}=\left(2.05^{+0.66}_{-0.32}\right)\times{\text{FWHM}}({\text{H}}\alpha)_{\rm
obs}$

     * •

$\Delta\log M_{\rm BH}\simeq 1.28^{+0.41}_{-0.30}$ dex

  2. 2.

${\text{FWHM}}({\text{H}}\alpha)_{\rm obs}{\gtrsim}2400\,{\rm km\,s}^{-1}$ and
$L\left({\rm b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}{<}10^{-2}$:

     * •

$L\left({\rm b}{\text{H}}\alpha\right)_{\rm
corr}=\left(8.4^{+3.9}_{-2.5}\right)\times L\left({\rm
b}{\text{H}}\alpha\right)_{\rm obs}$

     * •

${\text{FWHM}}({\text{H}}\alpha)_{\rm
corr}=\left(0.93^{+0.32}_{-0.22}\right)\times{\text{FWHM}}({\text{H}}\alpha)_{\rm
obs}$
(consistent with no correction).

     * •

$\Delta\log M_{\rm BH}\simeq 0.53^{+0.09}_{-0.09}$ dex

  3. 3.

$L\left({\rm b}{\text{H}}\alpha\right)/L_{14-150\,{\text{keV}}}{>}10^{-2}$:

     * •

$L\left({\rm b}{\text{H}}\alpha\right)_{\rm
corr}=\left(1.4^{+0.3}_{-0.4}\right)\times L\left({\rm
b}{\text{H}}\alpha\right)_{\rm obs}$.
(consistent with no correction).

     * •

${\text{FWHM}}({\text{H}}\alpha)_{\rm
corr}=\left(0.99^{+0.12}_{-0.34}\right)\times{\text{FWHM}}({\text{H}}\alpha)_{\rm
obs}$
(no correction needed).

     * •

No correction needed for $M_{\rm BH}$.

In practice, most AGN surveys lack measurements of $L_{14-150\,{\text{keV}}}$,
which would render the above corrections impractical. First, we note that the
much more common, lower-energy measurements of $L_{2-10\,{\text{keV}}}$ may be
used as a proxy for $L_{14-150\,{\text{keV}}}$. Specifically, for a photon
index of $\Gamma_{\rm X}=1.8$, the luminosities scale as
$L_{2-10\,{\text{keV}}}=0.42\times L_{14-150\,{\text{keV}}}$. Second, we have
also derived an additional set of corrections, where the infrared (IR)
emission serves as a proxy of the (ultra-hard) X-rays, motivated by many
previous studies of the link between these spectral regimes in AGNs (e.g.,
Lutz et al., 2004; Fiore et al., 2009; Gandhi et al., 2009; Asmus et al.,
2015; Stern, 2015; Lansbury et al., 2017; Ichikawa et al., 2017, and
references therein). Specifically for our BASS/DR2 sample, we used the IR
measurements described in Ichikawa et al. (2019), and find that the flux at
(rest-frame) 12$\mu$m shows the tightest correlation with ultra-hard X-ray
emission ($r_{\rm s}=0.55$, $P_{\rm s}\ll 10^{-10}$), again consistent with
previous studies (Asmus et al., 2015; Ichikawa et al., 2017). We also
confirmed that $L\left({\rm b}{\text{H}}\alpha\right)/L_{12\,{\rm\mu m}}$
preserves the correlation with $\log N_{\rm H}$ with a similar significance
(see Fig. 15 in Appendix E). Below we provide median corrections to
$L\left({\rm b}{\text{H}}\alpha\right)$, FWHM(H$\alpha$) and $M_{\rm BH}$ for
Sy1.9 sources whenever $L_{12\,{\rm\mu m}}$ is available. For this, we have
repeated our analysis while dividing the Sy1.9s in our sample into three
regimes in $L\left({\rm b}{\text{H}}\alpha\right)/L_{12\,{\rm\mu m}}$ and
FWHM(H$\alpha$). The corresponding median corrections are:

  1. 1.

${\text{FWHM}}({\text{H}}\alpha)_{\rm obs}{\lesssim}2400\,{\rm km\,s}^{-1}$
and $L\left({\rm b}{\text{H}}\alpha\right)/L_{12\,{\rm\mu
m}}{<}7{\times}10^{-3}$:

     * •

$L\left({\rm b}{\text{H}}\alpha\right)_{\rm
corr}=\left(17.0^{+16.9}_{-7.6}\right)\times L\left({\rm
b}{\text{H}}\alpha\right)_{\rm obs}$

     * •

${\text{FWHM}}({\text{H}}\alpha)_{\rm
corr}=\left(1.92^{+0.41}_{-0.22}\right)\times{\text{FWHM}}({\text{H}}\alpha)_{\rm
obs}$

     * •

$\Delta\log M_{\rm BH}\sim 1.40^{+0.23}_{-0.37}$ dex

  2. 2.

${\text{FWHM}}({\text{H}}\alpha)_{\rm obs}{\gtrsim}2400\,{\rm km\,s}^{-1}$ and
$L\left({\rm b}{\text{H}}\alpha\right)/L_{12\,{\rm\mu m}}{<}10^{-2}$:

     * •

$L\left({\rm b}{\text{H}}\alpha\right)_{\rm
corr}=\left(16.0^{+5.4}_{-5.3}\right)\times L\left({\rm
b}{\text{H}}\alpha\right)_{\rm obs}$

     * •

${\text{FWHM}}({\text{H}}\alpha)_{\rm
corr}=\left(0.88^{+0.42}_{-0.18}\right)\times{\text{FWHM}}({\text{H}}\alpha)_{\rm
obs}$
(consistent with no correction).

     * •

$\Delta\log M_{\rm BH}\sim 0.68^{+0.09}_{-0.10}$ dex

  3. 3.

$L\left({\rm b}{\text{H}}\alpha\right)/L_{12\,{\rm\mu m}}{>}10^{-2}$:

     * •

$L\left({\rm b}{\text{H}}\alpha\right)_{\rm
corr}=\left(2.4^{+1.1}_{-0.8}\right)\times L\left({\rm
b}{\text{H}}\alpha\right)_{\rm obs}$

     * •

${\text{FWHM}}({\text{H}}\alpha)_{\rm
corr}=\left(1.03^{+0.28}_{-0.25}\right)\times{\text{FWHM}}({\text{H}}\alpha)_{\rm
obs}$
(no correction needed).

     * •

$\Delta\log M_{\rm BH}\sim 0.21^{+0.10}_{-0.09}$ dex

We finally note that, as part of our search for ways to improve $M_{\rm BH}$
estimates in (Sy1.9) BASS AGNs, we have also checked the possibility that
FWHM(H$\alpha$) is correlated with $L(\left[{\rm
O}\,\textsc{iii}\right])/L({\rm n}{\text{H}}\beta)$, as found by Baron &
Ménard (2019) in their (spectral stacking) analysis of the SDSS/DR7 quasar
sample. This correlation is proposed as a promising method to provide $M_{\rm
BH}$ estimates for narrow-line AGNs and – in the context of the present study
– may thus be used to improve mass estimates in Sy1.9 sources. We do find that
FWHM(H$\alpha$) and $L(\left[{\rm O}\,\textsc{iii}\right])/L({\rm
n}{\text{H}}\beta)$ are correlated in our BASS/DR2 sample, with the Pearson
and Spearman correlating tests resulted in $P=0.006$ and ${\approx}10^{-4}$,
respectively. However, these correlations are weak ($r_{\rm s}=0.14$ and
$0.19$, respectively) and the scatter is huge, which prevents us from using
the correlation to improve our $M_{\rm BH}$ estimates. We stress that we are
not evaluating the correlation on stacked data, as was done in Baron & Ménard
(2019), but rather on individual spectra in which measuring $L(\left[{\rm
O}\,\textsc{iii}\right])/L({\rm n}{\text{H}}\beta)$ is much more challenging.
Proper stacking analysis is beyond the scope of the present study.

##  5 Summary and conclusions

In this paper we presented broad emission line measurements for the 2nd data
release of the BAT AGN Spectroscopic Survey (BASS/DR2), which consists of 512
AGNs selected in the ultra-hard X-rays and for which high-quality fits of the
H$\alpha$, H$\beta$, Mg ii, and/or C iv emission lines are now made available.
These detailed spectral measurements are used to also determine the masses
($M_{\rm BH}$) and Eddington ratios ($L/L_{\rm Edd}$) of the SMBHs that power
these AGNs. The key features of this new catalog, compared to BASS/DR1, are:

  1. 1.

We provide broad line measurements and derived BH masses for 689 AGNs, of
which 512 are drawn from the 70-month Swift/BAT catalog (i.e., almost 60% of
the 70-month sources, that constitute the main DR2 sample). In addition, we
provide measurements for 177 AGNs detected in deeper BAT data

  2. 2.

At its core, lower-redshift focus, our BASS/DR2 catalog has 445 unbeamed,
$z<0.7$ AGNs drawn from the 70-months Swift/BAT catalog, with reliable
determinations of $M_{\rm BH}$ from the broad H$\alpha$ and/or H$\beta$
emission lines.

  3. 3.

We provide improved spectral measurements and BH determinations for $>$200
BASS AGNs, for which the BASS/DR2 efforts resulted in higher-quality data
and/or analysis.

  4. 4.

The larger fraction of sources with a wide spectral coverage allows for a more
complete identification of sub-classes using optical line ratios.

  5. 5.

BH masses are estimated using a more consistent set of prescriptions,
particularly the virial factor ($f=1$).

The BASS/DR2 broad emission line catalog is released as part of this paper (in
machine-readable form) and is available on the BASS
website.777http://www.bass-survey.com.

In the second part of the paper, we used the unprecedentedly large compilation
of BASS/DR2 multi-wavelength data, to investigate the properties of “partially
obscured” broad-line systems–so-called Type 1.9 AGNs (or Sy1.9s), which show
broad H$\alpha$ emission lines but no bluer broad (Balmer) lines. We compared
these Type 1.9 sources to those AGNs with both broad H$\alpha$ and H$\beta$
emission lines, i.e. Type 1-1.5 sources. Our main findings regarding partially
obscured, Type 1.9 AGNs can be summarized as follows:

  1. 1.

Type 1.9 AGNs tend to exhibit high column densities, typically $\log(N_{\rm
H}/{\rm cm}^{-2})\gtrsim 22$, compared to Type 1-1.5 AGNs which typically have
$\log(N_{\rm H}/{\rm cm}^{-2})\lesssim 22$.

  2. 2.

The strength of the broad H$\alpha$ emission line (relative to the X-ray
continuum) decreases with increasing $N_{\rm H}$, and is particularly
suppressed in Type 1.9 AGNs. This suggests that the broad line emission is
affected by dust.

  3. 3.

The broad H$\alpha$ suppression particularly affects the highest-velocity
parts of the line profile, that is the inner-most parts of the H$\alpha$
emitting region in the BLR.

  4. 4.

These effects result in a significant underestimation of BLR-based $M_{\rm
BH}$ determinations in Type 1.9 AGNs, with a discrepancy of 0.8 dex at
$\log(N_{\rm H}/{\rm cm}^{-2})\simeq 22.5$ and up to 2 dex at $\log(N_{\rm
H}/{\rm cm}^{-2})\simeq 24$.

  5. 5.

To remedy the potential $M_{\rm BH}$ discrepancies, we provide simple,
empirical corrections for $L\left({\rm b}{\text{H}}\alpha\right)$ and
FWHM(H$\alpha$), applicable to Type 1.9 AGNs with either (ultra-hard) X-ray or
near-IR measurements.

As an alternative to our corrections, if near-IR spectroscopy is available,
then one should consider using $M_{\rm BH}$ prescriptions that are based on
broad Paschen emission lines (e.g., Ricci et al., 2017c; Kim et al., 2018), as
this spectral regime is less affected by dust.

Our work provides the community with a large, highly-complete compilation of
reliable determinations of $M_{\rm BH}$ (and $L/L_{\rm Edd}$), while also
highlighting some of the challenges associated with partially-obscured
sources, and with AGN surveys where broad Balmer emission lines are used for
$M_{\rm BH}$ determinations. As such, we hope our catalog and analysis can be
useful for detailed investigations of individual AGN and/or of SMBH
demographics in the local Universe, particularly when combined with the rich
compilation of multi-wavelength measurements available through BASS. Several
complementary works, published as part of the BASS/DR2 effort, indeed pursue
such investigations.

##

We thank the anonymous referee for their constructive comments, which helped
us improve the paper. We also thank Lea Marcotulli for her assistance with
identifying beamed AGN candidates, and Jonathan Stern for his insightful
comments.

B.T. acknowledges support from the Israel Science Foundation (grant number
1849/19) and from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation program (grant agreement number
950533). M.K. acknowledges support from NASA through ADAP award NNH16CT03C.
K.O. acknowledges support from the National Research Foundation of Korea
(NRF-2020R1C1C1005462). C.R. acknowledges support from the Fondecyt Iniciacion
grant 11190831. We also acknowledge support from ANID grants CATA-Basal
AFB-170002 (F.R., F.E.B., E.T.) and FB210003 (C.R., F.E.B., E.T., R.J.A.);
FONDECYT Regular 1190818 (E.T., F.E.B.), 1191124 (R.J.A.), and 1200495
(F.E.B., E.T.); FONDECYT Postdoctorado 3180506 (F.R.) and 3210157 (A.R.);
Anillo ACT172033 (E.T.); and Millennium Science Initiative ICN12_009 (MAS;
F.E.B.) and Millenium Nucleus NCN19_058 (TITANs; E.T.). D.A. acknowledges
funding through the European Union’s Horizon 2020 and Innovation programme
under the Marie Sklodowska-Curie grant agreement no. 793499 (DUSTDEVILS). The
work of K.I. is supported by the Japan Society for the Promotion of Science
(JSPS) KAKENHI (18K13584, 20H01939).

This work relies on data collected with a large variety of facilities and
analyzed using several tools. We acknowledge the work that the Swift BAT team
has done to make this project possible, and the teams of the various
observatories that obtained the data used in this paper. Specifically, this
work is based on observations collected at the European Organisation for
Astronomical Research in the Southern Hemisphere under 29 ESO programmes:
60.A-9024(A), 60.A-9421(A), 062.H-0612(A), 086.B-0135(A), 089.B-0951(A),
089.B-0951(B), 090.A-0830(A), 090.D-0828(A), 091.B-0900(B), 091.C-0934(B),
092.B-0083(A), 093.A-0766(A), 095.B-0059(A), 098.A-0062, 098.A-0635(B),
099.A-0403(A), 099.A-0403(B), 099.A-0442(A), 099.B-0785(A), 0101.A-0765(A),
0101.B-0456(B), 0101.B-0739(A), 0102.A-0433(A), 0103.A-0521(A),
0103.B-0566(A), 0104.A-0353(A), 0104.B-0959(A), 0106.A-0521(A), 385.B-1035(A),
and 2100.B-5018(B).

BASS/DR2 also relies on observations from seven CNTAC programs: CN2016A-80,
CN2018A-104, CN2018B-83, CN2019A-70, CN2019B-77, CN2020A-90, and CN2020B-48
(PI C. Ricci); and from NOIRLab program 2012A-0463 (PI M. Trippe). Funding for
SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/. The authors wish to recognize and acknowledge the very
significant cultural role and reverence that the summit of Mauna Kea has
always had within the indigenous Hawaiian community. We are most fortunate to
have the opportunity to conduct observations from this mountain.

This research made use of the NASA/IPAC Extragalactic Database (NED), which is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration and the
SIMBAD database, operated at CDS, Strasbourg, France (Wenger et al., 2000).

##  Appendix A Fit quality examples

In Figure 13 we show several examples of H$\alpha$ and H$\beta$ fits of
different fit-quality classes ($f_{\rm Q}=1,2$, and $3$), as assigned during
our visual inspection of the spectra and best-fit models. We recall that only
sources with $f_{\rm Q}<3$ provide acceptable spectral measurements, while
those with $f_{\rm Q}=3$ should be discarded from any analysis. For the most
cautious analyses we further recommend to focus on $f_{\rm Q}\leq 2$ (i.e.,
omitting objects with $f_{\rm Q}=2.5$, as we did in the present study).

Figure 13: Spectral fit quality flag ($f_{\rm Q}$) examples, in order of
descending quality for the H$\beta$ (top) and H$\alpha$ (bottom) spectral
complexes: $f_{\rm Q}=1$ (left), $f_{\rm Q}=2$ (center) and $f_{\rm Q}=3$
(right). In each case, the observed spectrum (solid black line) should be
compared with the total spectral model (red). We also show the broad Balmer
emission lines model (green), the blended iron emission (blue), and the narrow
emission lines (dashed black). The black solid line at the bottom of each
panel represents the fit residuals.

##  Appendix B Comparing broad line measurements in BASS DR2 and DR1

Here we compare the line width and $M_{\rm BH}$ measurements from the new
BASS/DR2 catalog presented here to those of our our previous release, DR1. As
mentioned in section 2.2, compared to DR1, DR2 includes not only new optical
spectra but also a more homogeneous spectral modeling procedure to derive
broad line properties and black hole masses.

###  B.1 FWHM Comparison

In the top-left panel of Fig. 14 we compare the FWHM(H$\alpha$) obtained from
BASS/DR2 catalog to those measured in DR1, for sources which were included in
both catalogs. The DR2 measurements are slightly narrower than the DR1 ones,
with a median offset of about 7% (see diagonal lines in Fig. 14). Similarly,
in the top-right panel of Fig. 14 we compare the FWHM(H$\beta$) measurements
in the DR1 and DR2 catalogs. In this case, the two sets of measurements are in
very good agreement up to 8000 km s-1, with a median offset from the 1:1
relation only 2%. The reason for the good agreement between DR1 and DR2
FWHM(H$\beta$) measurements is that in both cases we followed a very similar
fitting procedure. On the other hand, the slightly larger offset in the
FWHM(H$\alpha$) measurements is very likely caused by the differences in the
fitting procedures - in DR1 the H$\alpha$ spectral complex was modeled with
rather simplistic, ad-hoc procedures, while for DR2 we adopt the more
elaborate and AGN-tailored procedures of Mejía-Restrepo et al. (2016).

###  B.2 Black hole Mass Comparison

In the bottom panels of Fig. 14 we compare the H$\alpha$-based (bottom-left)
and H$\beta$-based (bottom-right) BH mass estimates obtained in DR2 to those
obtained in DR1. The H$\beta$-based $M_{\rm BH}$ estimates from both DRs are
in very good agreement, with a negligible offset (median of -0.02 dex).
However, when it comes to H$\alpha$ there is a clear disagreement of 0.23 dex
between DR1 and DR2 $M_{\rm BH}$ measurements, in the sense that DR2
measurements are systematically larger than DR1 ones. One of the main reasons
for this discrepancy is the usage of different virial factors in DR1 and DR2:
while for DR1 we used $f_{{\text{FWHM}}({\text{H}}\alpha)}=0.75$ and
$f_{{\text{FWHM}}\left({\text{H}}\beta\right)}=1$, in DR2 we instead use
$f_{{\text{FWHM}}({\text{H}}\alpha)}=f_{{\text{FWHM}}\left({\text{H}}\beta\right)}=1$.
The reason for this choice is to keep consistency between the masses derived
through the two emission lines, and to more recent calibrations that are based
on the comparison of virial (SE) and $\sigma_{\star}$-based $M_{\rm BH}$
estimates (e.g., Woo et al., 2015). This update of the virial factor accounts
for 0.13 dex on the total offset. The remaining $\sim$0.1 dex is explained by
the usage in DR2 of an alternative $R_{\rm BLR}-L\left({\rm
b}{\text{H}}\alpha\right)$ calibration, which includes more RM measurements
towards the low luminosity end (Greene & Ho, 2005), together with slight
differences between the DR1 and DR2 FWHM(H$\alpha$) measurements.

Figure 14: Comparison DR1 and DR2 measurements: line widths (FWHM; top) and
black hole masses ($M_{\rm BH}$; bottom), for both H$\alpha$ (left) and
H$\beta$ (right). In all panels, black solid lines represent the 1:1 relation
and black dashed lines trace the median offsets between DR1 and DR2
measurements.

##  Appendix C Sources with double-peaked broad emission lines

Table 4 lists the BASS DR2 AGNs which we’ve identified to have double-peaked
H$\alpha$ and/or H$\beta$ broad emission lines.

Table 4: AGNs with double-peaked broad Balmer emission lines.

BAT ID | AGN NameaaThis includes fringing (or otherwise ‘wavy’ spectral features), problems with flux calibration, and other artifacts. |  | Double-peaked…bbIndicating a strong absorption feature superimposed on the (broad) emission line, which limits our ability to properly model the latter.
---|---|---|---
|  |  | H$\alpha$ | H$\beta$
45 | SWIFT J$0101.5-0308$ |  | 0 | 1
48 | SWIFT J$0103.8-6437$ |  | 1 | 0
107 | SWIFT J$0207.0+2931$ |  | 1 | 0
135 | SWIFT J$0235.3-2934$ |  | 1 | 0
136 | SWIFT J$0238.2-5213$ |  | 1 | 0
147 | SWIFT J$0244.8+6227$ |  | 0 | 1
170 | SWIFT J$0312.9+4121$ |  | 1 | 0
172 | SWIFT J$0318.7+6828$ |  | 1 | 0
207 | SWIFT J$0405.3-3707$ |  | 1 | 1
270 | SWIFT J$0519.5-4545$ |  | 1 | 0
371 | SWIFT J$0726.5+3659$ |  | 1 | 0
372 | SWIFT J$0727.4-2408$ |  | 1 | 0
403 | SWIFT J$0803.4+0842$ |  | 1 | 0
413 | SWIFT J$0818.1+0120$ |  | 1 | 0
414 | SWIFT J$0819.2-2259$ |  | 0 | 1
454 | SWIFT J$0923.6-2136$ |  | 1 | 0
525 | SWIFT J$1103.4+3731$ |  | 1 | 1
607 | SWIFT J$1217.3+0714$ |  | 1 | 1
618 | SWIFT J$1227.8-4856$ |  | 0 | 1
686 | SWIFT J$1341.9+3537$ |  | 0 | 1
690 | SWIFT J$1347.1+7325$ |  | 1 | 0
713 | SWIFT J$1416.9-1158$ |  | 1 | 1
715 | SWIFT J$1417.7+6143$ |  | 1 | 0
776 | SWIFT J$1542.0-1410$ |  | 1 | 0
800 | SWIFT J$1617.8+3223$ |  | 1 | 1
876 | SWIFT J$1719.7+4900$ |  | 1 | 1
882 | SWIFT J$1723.2+3418$ |  | 1 | 1
907 | SWIFT J$1742.2+1833$ |  | 1 | 1
923 | SWIFT J$1747.7-2253$ |  | 1 | 1
1079 | SWIFT J$2030.2-7532$ |  | 1 | 1
1151 | SWIFT J$2223.9-0207$ |  | 1 | 1
1179 | SWIFT J$2301.4-5916$ |  | 1 | 1
1196 | SWIFT J$2327.4+1525$ |  | 1 | 0
1200 | SWIFT J$2333.9-2342$ |  | 1 | 0

aafootnotetext: Unique AGN names from the Swift/BAT 70-month catalog.

bbfootnotetext: Binary flags indicating which of the two key broad Balmer
lines has a double-peaked profile.

##  Appendix D Broad Line Measurements Catalog

Tables 5, 6, 7, and 8 describe the contents of our measurement catalogs, for
the spectral regions including the broad H$\alpha$, H$\beta$, Mg ii $\lambda
2798$, and C iv $\lambda 1549$ emission lines (respectively).

Table 5: Column description for the H$\alpha$ measurements table.

Column | Name | Description
---|---|---
1 | BAT_ID | BASS identifier
2 | Subsample | The source of the optical spectrum (facility, instrument, etc.).
3 |  $f_{\rm Q}$(H$\alpha$) | Quality flag for the fit: 1 for a good fit and 2 for an acceptable one
4 | FWHM(bH$\alpha$) [km s-1] | FWHM of the broad H$\alpha$ emission line.
5 |  $\Delta^{-}$ FWHM(bH$\alpha$) [km s-1] | Lower error on FWHM(bH$\alpha$)
6 |  $\Delta^{+}$ FWHM(bH$\alpha$) [km s-1] | Upper error on FWHM(bH$\alpha$)
7 |  $\log L\left({\rm b}{\text{H}}\alpha\right)$ [erg s-1] | Broad H$\alpha$ line luminosity
8 |  $\log L\left({\rm b}{\text{H}}\alpha\right)$ [erg s-1cm-2] | Broad H$\alpha$ line integrated flux
9 |  $\Delta^{-}\log L\left({\rm b}{\text{H}}\alpha\right)$ [erg s-1] | Lower error on $\log L\left({\rm b}{\text{H}}\alpha\right)$
10 |  $\Delta^{+}\log L\left({\rm b}{\text{H}}\alpha\right)$ [erg s-1] | Upper error on $\log L\left({\rm b}{\text{H}}\alpha\right)$
11 |  $\log L_{6200}$ [erg s-1] | Monochromatic luminosity at rest-frame 6200 Å, $\lambda L_{\lambda}$(6200 Å)
12 |  $\log F_{6200}$ [erg s-1cm-2] | Monochromatic flux at rest-frame 6200 Å, $\lambda F_{\lambda}$(6200 Å)
13 |  $\Delta^{-}\log L_{6200}$ [erg s-1] | Lower error on $\log L_{6200}$
14 |  $\Delta^{+}\log L_{6200}$ [erg s-1] | Upper error on $\log L_{6200}$
15 | EW(bH$\alpha$) [Å] | Rest-frame equivalent width of the broad H$\alpha$ line
16 |  $\Delta^{-}$EW(bH$\alpha$) [Å] | Lower error on EW(bH$\alpha$)
17 |  $\Delta^{+}$EW(bH$\alpha$) [Å] | Upper error on EW(bH$\alpha$)
18 |  $\log L_{\rm peak}$(bH$\alpha$) [erg s-1 Å-1] | Monochromatic luminosity of the broad H$\alpha$ line at peak
19 |  $\log F_{\rm peak}$(bH$\alpha$) [erg cm-2 s-1 Å-1] | Monochromatic flux of the broad H$\alpha$ line at peak
20 |  $\Delta^{-}\log L_{\rm peak}$(bH$\alpha$) [erg s-1 Å-1] | Lower error on $\log L_{\rm peak}$(bH$\alpha$)
21 |  $\Delta^{+}\log L_{\rm peak}$(bH$\alpha$) [erg s-1 Å-1] | Upper error on $\log L_{\rm peak}$(bH$\alpha$)
22 |  $\Delta v_{\rm peak}$(bH$\alpha$) [km s-1] | Velocity shift of the broad H$\alpha$ line peak
23 |  $\Delta^{-}\Delta v_{\rm peak}$(bH$\alpha$) [km s-1] | Lower error on $\Delta v_{\rm peak}$(bH$\alpha$)
24 |  $\Delta^{+}\Delta v_{\rm peak}$(bH$\alpha$) [km s-1] | Upper error on $\Delta v_{\rm peak}$(bH$\alpha$)
25 |  $\Delta v_{\rm cent}$(bH$\alpha$) [km s-1] | Velocity shift of the broad H$\alpha$ line centroid
26 |  $\Delta^{-}\Delta v_{\rm cent}$(bH$\alpha$) [km s-1] | Lower error on $\Delta v_{\rm cent}$(bH$\alpha$)
27 |  $\Delta^{+}\Delta v_{\rm cent}$(bH$\alpha$) [km s-1] | Upper error on $\Delta v_{\rm cent}$(bH$\alpha$)
28 |  $\log M_{\rm BH}$(bH$\alpha$) [$M_{\odot}$, GH05] | Broad H$\alpha$-based BH mass estimate, following Greene & Ho (2005)
29 |  $\Delta^{-}\log M_{\rm BH}$(bH$\alpha$) [$M_{\odot}$] | Lower error on $\log M_{\rm BH}$(bH$\alpha$)
30 |  $\Delta^{+}\log M_{\rm BH}$(bH$\alpha$) [$M_{\odot}$] | Lower error on $\log M_{\rm BH}$(bH$\alpha$)
31 |  $\log L$([S ii]) [erg s-1] | Luminosity of the narrow [S ii] $\lambda 6731$ emission line
32 |  $\log F$([S ii]) [erg s-1cm-2] | Integrated flux of the narrow [S ii] $\lambda 6731$ emission line
33 |  $\Delta\log L$([S ii]) [erg s-1] | Error on $\log L$([S ii])
34 |  $\Delta v$([S ii]) [km s-1] | Velocity shift of the [S ii] $\lambda 6731$ line peak/centroid
35 |  $\Delta\Delta v$([S ii]) [km s-1] | Error on $\Delta v$([S ii])
36 | FWHM([S ii]) [km s-1] | FWHM of the narrow [S ii] $\lambda 6731$ emission line
37 |  $\Delta$FWHM([S ii]) [km s-1] | Error on FWHM([S ii])
38 |  $\log L$(nH$\alpha$) [erg s-1] | Luminosity of the narrow H$\alpha$ line
39 |  $\log F$(nH$\alpha$) [erg s-1cm-2] | Integrated flux of the narrow H$\alpha$ line
40 |  $\Delta\log L$(nH$\alpha$) [erg s-1] | Error on $\log L$(nH$\alpha$)
41 |  $\Delta v$(nH$\alpha$) [km s-1] | Velocity shift of the narrow H$\alpha$ line peak/centroid
42 |  $\Delta\Delta v$(nH$\alpha$) [km s-1] | Error on $\Delta v$(nH$\alpha$)
43 | FWHM(nH$\alpha$) [km s-1] | FWHM of the narrow H$\alpha$ emission line
44 |  $\Delta$FWHM(nH$\alpha$) [km s-1] | Error on FWHM(nH$\alpha$)
45 |  $\log L$([N ii]) [erg s-1] | Luminosity of the narrow [N ii] $\lambda 6584$ line
46 |  $\log F$([N ii]) [erg s-1cm-2] | Integrated flux of the narrow [N ii] $\lambda 6584$ line
47 |  $\Delta\log L$([N ii]) [erg s-1] | Error on $\log L$([N ii])
48 |  $\Delta v$(nH$\alpha$) [km s-1] | Velocity shift of the narrow [N ii] $\lambda 6584$ line peak/centroid
49 |  $\Delta\Delta v$([N ii]) [km s-1] | Error on $\Delta v$([N ii])
50 | FWHM([N ii]) [km s-1] | FWHM of the narrow [N ii] $\lambda 6584$ emission line