# BASS XXIX: The near-infrared view of the BLR: the effects of obscuration in
BLR characterisation111This paper includes data gathered with the 6.5 meter
Magellan Telescopes located at Las Campanas Observatory, Chile.

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, Università di
Bologna, via Gobetti 93/2, I-40129 Bologna, Italy  INAF - Osservatorio di
Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129
Bologna, Italy  Ezequiel Treister Instituto de Astrofísica and Centro de
Astroingeniería, Facultad de Física, Pontificia Universidad Católica de Chile,
Casilla 306, Santiago 22, Chile  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,
Colorado 80301  Julian E. Mejía-Restrepo European Southern Observatory, Alonso
de Cordova 3107, Vitacura,Casilla 19001, Santiago de Chile, Chile  Michael J.
Koss Eureka Scientific, 2452 Delmer Street Suite 100, Oakland, CA 94602-3017,
USA  Jakob S. den Brok Institute for Particle Physics and Astrophysics, ETH
Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland  Argelander
Institute for Astronomy, Auf dem Hügel 71, 53231, Bonn, Germany  Mislav
Baloković Center for Astrophysics — Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA  Black Hole Initiative at Harvard University, 20
Garden Street, Cambridge, MA 02138, USA  Yale Center for Astronomy &
Astrophysics, Physics Department, New Haven, CT 06520, USA  Rudolf Bär
Institute for Particle Physics and Astrophysics, ETH Zürich, Wolfgang-Pauli-
Strasse 27, CH-8093 Zürich, Switzerland  Patricia Bessiere Instituto de
Astrofísica de Canarias, 38205, C/ Vía Láctea, s/n, La Laguna, Tenerife, Spain
Turgay Caglar Leiden Observatory, PO Box 9513, 2300 RA Leiden, The Netherlands
Fiona Harrison  Cahill Center for Astronomy and Astrophysics, California
Institute of Technology, Pasadena, CA 91125, USA  Kohei Ichikawa Frontier
Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai
980-8578, Japan  Darshan Kakkad European Southern Observatory, Alonso de
Cordova 3107, Vitacura,Casilla 19001, Santiago de Chile, Chile  Isabella
Lamperti Department of Physics and Astronomy, University College London, Gower
Street, London WC1E 6BT, UK  European Southern Observatory, Karl-
Schwarzschild-Str. 2, 85748 Garching bei München, Germany  Richard Mushotzky
Department of Astronomy and Joint Space-Science Institute, University of
Maryland, College Park, MD 20742, 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  Meredith C. Powell Institute of
Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall,
Stanford, CA 94305, USA  George C. Privon Department of Astronomy, University
of Florida, 211 Bryant Space Science Center, Gainesville, FL 32611, USA
Claudio Ricci Núcleo de Astronomía de la Facultad de Ingeniería, Universidad
Diego Portales, Av. Ejército Libertador 441, Santiago, Chile  Kavli Institute
for Astronomy and Astrophysics, Peking University, Beijing 100871, People’s
Republic of China  George Mason University, Department of Physics & Astronomy,
MS 3F3, 4400 University Drive, Fairfax, VA 22030, USA  Rogerio Riffel
Departamento de Astronomia, Universidade Federal do Rio Grande do Sul Porto
Alegre, Brazil  Alejandra F. Rojas Centro de Astronomía (CITEVA), Universidad
de Antofagasta, Avenida Angamos 601, Antofagasta, Chile  Eleonora Sani
European Southern Observatory, Alonso de Cordova 3107, Vitacura,Casilla 19001,
Santiago de Chile, Chile  Krista L. Smith KIPAC at SLAC, Stanford University
Daniel Stern Jet Propulsion Laboratory, California Institute of Technology,
4800 Oak Grove Drive, MS 169-224, Pasadena, CA 91109, USA  Benny Trakhtenbrot
School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
C. Megan Urry Yale Center for Astronomy & Astrophysics, Physics Department,
New Haven, CT 06520, USA  Sylvain Veilleux Department of Astronomy and Joint
Space-Science Institute, University of Maryland, College Park, MD 20742, USA

(Received 13 December 2020; Revised 28 August 2021; Accepted 31 August 2021)

###### Abstract

Virial black hole mass ($M_{BH}$) determination directly involves knowing the
broad line region (BLR) clouds velocity distribution, their distance from the
central supermassive black hole ($R_{BLR}$) and the virial factor ($f$).
Understanding whether biases arise in $M_{BH}$ estimation with increasing
obscuration is possible only by studying a large (N$>$100) statistical sample
of obscuration unbiased (hard) X-ray selected active galactic nuclei (AGN) in
the rest-frame near-infrared (0.8–2.5 $\mu$m) since it penetrates deeper into
the BLR than the optical. We present a detailed analysis of 65 local BAT-
selected Seyfert galaxies observed with Magellan/FIRE. Adding these to the
near-infrared BAT AGN spectroscopic survey (BASS) database, we study a total
of 314 unique near-infrared spectra. While the FWHMs of H$\alpha$ and near-
infrared broad lines (He i, Pa$\beta$, Pa$\alpha$) remain unbiased to either
BLR extinction or X-ray obscuration, the H$\alpha$ broad line luminosity is
suppressed when $N_{H}\gtrsim 10^{21}$ cm-2, systematically underestimating
$M_{BH}$ by $0.23-0.46$ dex. Near-infrared line luminosities should be
preferred to H$\alpha$ until $N_{H}<10^{22}$ cm-2, while at higher obscuration
a less biased $R_{BLR}$ proxy should be adopted. We estimate $f$ for Seyfert 1
and 2 using two obscuration-unbiased $M_{BH}$ measurements, i.e. the stellar
velocity dispersion and a BH mass prescription based on near-infrared and
X-ray, and find that the virial factors do not depend on redshift or
obscuration, but for some broad lines show a mild anti-correlation with
$M_{BH}$. Our results show the critical impact obscuration can have on BLR
characterization and the importance of the near-infrared and X-rays for a less
biased view of the BLR.

Active galactic nuclei (16), X-ray active galactic nuclei (2035), High energy
astrophysics (739), Active galaxies(17)

††journal: ApJ††facilities: Magellan-LCO, Swift (BAT) ††software: FireHose
(v2; Gagne et al. 2015), molecfit (Smette et al. 2015), pymccorrelation
package (Privon et al. 2020), PySpecKit (v0.1.21; Ginsburg & Mirocha 2011)

##  1 Introduction

Supermassive black holes (SMBHs, with black hole masses $M_{BH}\sim
10^{5}-10^{9}$ M⊙) are ubiquitous in the local Universe, lurking in the
spheroid of almost all local galaxies (Kormendy & Richstone, 1995). During
active accretion phases, the SMBH is no longer dormant but shines as an active
galactic nucleus (AGN), due to a surrounding accretion disk of matter, which
releases gravitational energy as it infalls toward the central dark attractor.
The ultraviolet emission from the inner accretion disk photoionizes nearby
clouds located in the broad line region (BLR). Under the hypothesis of a
virialized BLR, whose dynamics are dominated by the central SMBH, the $M_{BH}$
can be simply determined from the velocity $\Delta V_{BLR}$ of the emitting
gas clouds located at distance $R_{BLR}$ in the BLR as $M_{BH}=G^{-1}\Delta
V_{BLR}^{2}R_{BLR}$, with $G$ being the gravitational constant. To model the
unknown emission-weighted222Note that the geometry and dynamics of the BLR in
so-called single-epoch mass estimates is emission-weighted, but in full
reverberation mapping studies it is more properly responsivity-weighted.
geometry and dynamics of the BLR, the observed width $\Delta W_{obs}$ (either
the full-width-at-half maximum FWHM or the second moment of the line profile,
i.e., the line dispersion $\sigma_{line}$) of a doppler-broadened photoionized
element at distance $R_{BLR}$ from the SMBH is used as a tracer of the true
velocity in the BLR and a correction factor $f$ known as the virial factor is
introduced (Onken et al., 2004):

$M_{BH}=f\,G^{-1}\Delta W_{obs}^{2}R_{BLR}=fM_{vir}\,,$ (1)

where $M_{vir}$ is the so-called virial product or virial mass. Since it is in
practice impossible to spatially resolve the BLR for statistically sized
samples, time-resolved observations substitute for spatially-resolved
information to estimate the BLR radius, adopting the so-called reverberation-
mapping technique (RM; Blandford & McKee, 1982). This is gradually changing
due to campaigns with the VLTI/GRAVITY instrument, which has opened the path
to spatially-resolved observations of the BLR around nearby AGN, allowing high
angular resolution ($<0.1$ milliarcsec) spectral-spatial interferometric
observations of the Pa$\alpha$ (in 3C 273, see, Gravity Collaboration et al.,
2018) and Br$\gamma$ (in IRAS 09149-6206, see, Gravity Collaboration et al.,
2020) line. However, this powerful technique remains limited to a small sample
of AGN.

Extensive RM campaigns have found that the radius of the BLR is linked to the
AGN luminosity, $R_{BLR}\propto L_{AGN}^{\alpha}$ (Bentz et al., 2006, 2009,
2013), where the slope $\alpha$ is consistent with expectations from
photoionization ($\alpha\simeq 0.5$). The AGN continuum and the broad-line
luminosity (see, e.g., Shen, 2013) have been both used as a proxy for the BLR
radius, which has allowed an efficient calibration for single-epoch (SE) BH
mass estimation.

The virial factor $f$ has been directly inferred only for a limited subsample
($<$20) of RM AGN with sufficient high quality data available (Pancoast et
al., 2014, 2018; Grier et al., 2017; Williams et al., 2018; Li et al., 2018).
Hence, previous studies have often adopted an ensemble virial factor $\langle
f\rangle$ that is determined using the $M_{BH}-\sigma_{\star}$ relation
observed in local samples of quiescent galaxies with dynamically-based BH
massses (Grier et al., 2013; Ho & Kim, 2014; Batiste et al., 2017; Yu et al.,
2019)

$M_{BH,\sigma_{\star}}=\langle f\rangle M_{vir}\,.$ (2)

However it is still unclear whether the $M_{BH}-\sigma_{\star}$ relation is
universally followed by all types of galaxies: e.g., barred/unbarred hosts
(Graham, 2008), early/late type hosts (McConnell & Ma, 2013; Sahu et al.,
2019), elliptical and classical-/pseudo- bulges (Kormendy & Ho, 2013; Saglia
et al., 2016; de Nicola et al., 2019). It is also unsettled whether AGN should
follow the scaling relations determined by quiescent galaxies (Woo et al.,
2013; Ricci et al., 2017c; Shankar et al., 2019), since the methods used to
measure the BH masses in active galaxies are not expected to suffer from the
resolution-dependent bias that instead affect dynamical-based BH mass
estimates (Bernardi et al., 2007; Shankar et al., 2016). Moreover, the
$f$-factor could change on an object-by-object basis if it depends on some AGN
properties, such as the bolometric luminosity, Eddington ratio
($\lambda_{Edd}$), $M_{BH}$, obscuration or line-of-sight inclination angle
$\theta$. The only statistically sound correlation found so far is between $f$
and $\theta$, although this is based on a limited number of RM objects with
directly inferred $f$. This correlation is consistent with expectations of the
BLR being a thick disk with clouds moving in a combination of elliptical and
inflowing motions (Williams et al., 2018). This $f-\theta$ relation is
corroborated by statistical studies that used a variety of $f$-independent BH
mass measurements to infer the virial factor, such as the bulge luminosity
based BH mass (Decarli et al., 2008), the stellar velocity dispersion
$\sigma_{\star}$ based BH mass (Shen & Ho, 2014) and the accretion disk based
BH mass (Mejía-Restrepo et al., 2018). These studies only focused on optical
broad-line AGN, for which optical virial-based $M_{BH}$ estimates were
available.

While the use of the H$\alpha$ emission is common practice to derive $M_{BH}$
in statistical samples to study the demography and evolution of the AGN
population, it is unclear whether the H$\alpha$ is completely reliable,
particularly in so-called Sy 1.9 (Osterbrock, 1981), where the level of
extinction due to dust is more relevant than what is usually experienced in
optical broad line Seyferts. Indeed Reines & Volonteri (2015), using a sample
of 262 broad-line AGN in the nearby Universe ($z<$ 0.055) with H$\alpha$
broad-lines measured from the Sloan Digital Sky Survey (SDSS) DR8, find that
AGN-hosts with SE H$\alpha$-based BH masses define a separate
$M_{BH}-M_{\star}$ relation, with a slope similar to that of early-type
galaxies with dynamically detected BHs but with a normalization $\sim 1.2$ dex
lower. Similarly, Koss et al. (2017) show that the SE H$\alpha$-based BH
masses in Sy 1.9 are undermassive than what is expected from the
$M_{BH}-\sigma_{\star}$ relation of elliptical/classical-bulges, with the BH
mass deviation being more extreme in sources with broad H$\alpha$ equivalent
width $EW<50$ Å. Additionally, Caglar et al. (2020) find an offset of $\sim
0.6$ dex between the SE H$\alpha$-based BH masses and those based on the
stellar velocity dispersion in a sample of 19 partially obscured local hard
X-ray selected Seyferts from the LLAMA sample. This discrepancy is reduced in
the LLAMA sample only after accounting for optical extinction, in the
H$\alpha$ measurement, and galaxy rotation, in the $\sigma_{\star}$ estimate
(Caglar et al., 2020). These results can be either explained with the fact
that BH-host scaling relations should be different in active vs inactive
galaxies, or that in some cases the H$\alpha$-based BH masses could be biased
low in presence of extinction (or with a combination of these two effects).

To this end, the rest-frame near-infrared (NIR, 0.8–2.5$\mu$m) band allows to
deeper probe the physical condition of the BLR gas, being at least a factor of
10 less affected by dust extinction than the rest-frame optical emission
(Goodrich et al., 1994; Veilleux et al., 1997; Veilleux, 2002). However, NIR
ground-based spectroscopic observations are more complex and time-consuming
than optical spectroscopy, due to the lower atmospheric transmission that
reduces the observable windows, bright sky background and strong OH sky line
emissions. For these reasons, local AGN samples studied so far have remained
limited to few objects, usually $\lesssim 50$ (Riffel et al., 2006; Glikman et
al., 2006; Landt et al., 2008; Mason et al., 2015; Riffel et al., 2015; Onori
et al., 2017a).

Determining the BLR properties and $f$-factors for a less biased AGN sample is
of paramount importance to assess the uncertainties and systematics in
$M_{BH}$ measurement in active galaxies as a function of obscuration. This is
particularly important for Sy 1.9s, where the only optical broad line
available is the H$\alpha$, and Sy 2s, where sometimes so-called hidden BLR
are found in the NIR ($\sim$30% of cases, see, e.g., Veilleux et al., 1997;
Riffel et al., 2006; Cai et al., 2010; Smith et al., 2014; Lamperti et al.,
2017; Onori et al., 2017a). Such an investigation is only possible by
constructing an obscuration unbiased AGN sample, by means of hard X-ray ($>10$
keV) AGN selection that is almost unaffected by interviening obscuring
material, at least up to $N_{H}\sim 10^{23.5}-10^{24}$ cm-2 (Ricci et al.,
2015; Koss et al., 2016), due to the decline of the photoelectric cross-
section with increasing photon energy. A sensitive all-sky survey in the
ultra-hard X-ray band (14–195 keV), such as the one carried out by the the
Burst Alert Telescope (BAT, Barthelmy, 2000) on the Neil Gehrels Swift
Observatory (Swift/BAT), coupled with NIR spectroscopy and ancillary optical
spectroscopic information, is the ideal database to quantify the effects of
obscuration on BLR characterisation and thus BH mass estimation. The BAT AGN
Spectroscopic Survey (BASS)333https://www.bass-survey.com/ has for the first
time increased the sample size of AGN surveyed with NIR spectroscopy to more
than 100 beginning with the DR1 (Lamperti et al., 2017).

Figure 1: Left: The $L_{14-195\,\rm{keV}}-z$ distribution of the FIRE sample,
BASS NIR DR1 (Lamperti et al., 2017), BASS NIR DR2 (den Brok et al.,,
submitted) and BAT 105-month sample (Oh et al., 2018). Colors and symbols
according to the legend. Right: histogram of the hard X-ray luminosities.

In this work, we present NIR Magellan spectra of 65 local Seyferts, selected
from the 70-month Swift/BAT catalog (Baumgartner et al., 2013), as part of the
BASS survey. We complement our near-infared Magellan sample with the NIR BASS
database, NIR DR1 (Lamperti et al., 2017), DR2 (den Brok et al.,,
submitted)444We note that the NIR BASS DR2 (den Brok et al.,, submitted) does
not contain the spectral measurements already published in the NIR BASS DR1
(Lamperti et al., 2017) since the data analysis is very consistent between the
two different BASS data releases., to construct the largest sample of local
Seyferts with NIR and X-ray spectral information available to date, for a
total of 314 unique NIR spectra. We further complement the NIR analysis with
optical spectral information on the broad component of the H$\alpha$ from the
optical BASS DR2 (Mejía-Restrepo et al.,, submitted), to quantify and compare
the BLR characterisation in both optical and NIR. We finally make use of the
optical stellar velocity dispersion measurements available in BASS DR2 (Koss
et al.,, in prep.; Caglar et al.,, in prep.), to infer the individual $f$
factors of our sample.

The work is organized as follows: Sect. 2 presents the Magellan data selection
and reduction; Sect. 3 describes the Magellan spectral fitting of the most
important NIR emission lines; Sect. 4 is devoted to the descriptions of two
independent BH mass measurement methods adopted to derive the virial factors
$f$. Results are described in Sect. 5, where we investigate the fraction of
hidden BLRs detected in Sy 1.8-1.9-2 (Sect. 5.1), the effects of X-ray
obscuration and BLR extinction on the BLR velocity and radius tracers derived
from optical (i.e., H$\alpha$) and NIR emission lines (He i$\lambda$10830 Å,
Pa$\beta$ $\lambda$12821 Å, Pa$\alpha$ $\lambda$18756 Å) in Sy 1-1.9 (Sect.
5.2) and in Sy 1-2 (Sect. 5.4). In Sect. 5.3 we explore the connection between
the material repsonsible for BLR extinction and the one absorbing the X-rays.
The virial factors of our sample are derived in Sect. 5.5, where we test
whether $f$ depends on some parameters, e.g., $z$, $N_{H}$ and BH mass.
Section 6 is devoted to discussions and conclusions, while Sect. 7 briefly
summarises our main results. We adopt the concordance cosmological model,
$\Omega_{M}=0.3$, $\Omega_{\Lambda}=0.7$ and $h=0.7$.

##  2 Data

Here we present the NIR spectroscopic data (PI: E. Treister, F. Ricci, M.
Baloković)555Proposals number: CN2018A-70, CN2018B-85, CN2019A-10 obtained at
Magellan using the Folded-port InfraRed Echellette (FIRE; Simcoe et al.,
2008). The Magellan/FIRE sample was selected from the hard X-ray (14-195 keV)
70-month catalog (Baumgartner et al., 2013) without near-infared coverage in
the BASS DR1 (Lamperti et al., 2017), as part of an effort within the BASS
collaboration to obtain NIR coverage for an obscuration unbiased census of
local accreting SMBHs. The 70-month catalog (Baumgartner et al., 2013) listed
838 AGN, 102/838 were targeted in the BASS DR1 (Lamperti et al., 2017) and
118/838 were observed as part of the DR2 (den Brok et al.,, submitted) which
selected as well additional 50/1016 AGN from the latest 105-month source
catalog (Oh et al., 2018). The combined sample totals 314 hard X-ray selected
AGN with unique NIR spectra. The FIRE sample was chosen to target the more
obscured sources, to estimate the $M_{BH}$ also in obscured Seyfert class AGN
(i.e., Sy 1.8-1.9-2). The FIRE sample is composed of 65 targets selected at
$z\lesssim 0.2$, divided into 52 obscured AGN (i.e., Sy 1.8-1.9-2) and 13
optical broad-line AGN (i.e., Sy 1-1.2-1.5), whose Seyfert classification is
defined according to the Osterbrock (1981) standard criteria, using optical
spectra collected by BASS (e.g., BASS optical DR2, Mejía-Restrepo et al.,,
submitted). Figure 1 shows the $L_{14-195\,\rm{keV}}-z$ distribution of the
FIRE targets (red stars), BASS NIR DR1 (green triangles, Lamperti et al.,
2017), BASS NIR DR2 (orange filled circles, den Brok et al.,, submitted) and
the latest 105-month Swift/BAT catalog (dark gray open squares, Oh et al.,
2018).

Table 1:  Magellan/FIRE observation log

BAT ID | Counterpart Name | Class | Obs. date | Exposure | Airmass | J | $z$ | slit/aperture | $\log L_{2-10\,\rm{intr}}$
---|---|---|---|---|---|---|---|---|---
|  |  | dd.mm.yy | [s] |  | [mag] |  | [′′] | [kpc] | [erg s-1]
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
7 | SDSSJ000911.57-003654.7 | Sy2 | 30.09.18 | $4\times 306$ | 1.14 | 14.74 | 0.073 | 0.6/0.74 | 0.93/1.15 | 43.60
10 | LEDA1348 | Sy1.9 | 30.09.18 | $4\times 370$ | 1.02 | 14.67 | 0.095 | 0.6/0.68 | 1.28/1.44 | 44.40
80 | 2MASXJ01290761-6038423 | Sy2 | 30.09.18 | $4\times 370$ | 1.17 | 15.17 | 0.203 | 0.6/0.82 | 4.23/5.80 | 45.23
118 | 3C62 | Sy2 | 30.09.18 | $4\times 370$ | 1.04 | 15.43 | 0.147 | 0.6/0.69 | 2.39/2.74 | 44.50
238 | LEDA745026 | Sy2 | 05.04.18 | $8\times 190$ | 1.33 | 15.44 | 0.147 | 0.6/0.34 | 2.41/1.36 | 44.42
262 | ESO553-22 | Sy2 | 30.09.18 | $4\times 190$ | 1.13 | 13.89 | 0.042 | 0.6/0.76 | 0.52/0.66 | 43.38
272 | IRAS05189-2524 | Sy2 | 30.09.18 | $4\times 190$ | 1.07 | 13.11 | 0.042 | 0.6/0.54 | 0.52/0.46 | 43.40
305 | LEDA17883 | Sy2 | 30.09.18 | $4\times 190$ | 1.28 | 14.63 | 0.050 | 0.6/0.86 | 0.62/0.89 | 43.51
329 | ESO121-28 | Sy1.9 | 05.04.18 | $8\times 190$ | 1.29 | 13.89 | 0.040 | 0.6/1.00 | 0.50/0.83 | 43.63
372 | 1RXSJ072720.8-240629 | Sy1.9 | 30.09.18 | $4\times 370$ | 1.33 | 15.06 | 0.123 | 0.6/0.52 | 1.83/1.59 | 44.34

††footnotetext: Columns are: (1) 70-month Swift/BAT ID
(https://swift.gsfc.nasa.gov/results/bs70mon/); (2) associated counterpart
name; (3) optical Seyfert classification, as defined by Osterbrock (1981); (4)
observation date; (5) exposure time; (6) airmass at the midpoint of the
observation; (7) J-band Vega mag (from 2MASS extended, e.g., Jarrett et al.,
2000); (8) redshift from the [O iii] BASS DR2; (9-10) slit width and aperture
of the spectral extraction, in arcsec and kpc; (11) intrinsic 2-10 keV
luminosity from Ricci et al. (2017a). (This table is available in its entirety
in a machine-readable form in the online journal. A part is shown as guidance
for the reader regarding its content.)

**footnotetext: Readout mode used was Fowler 4 rather than SUTR.

The FIRE data is complementary to the BASS NIR DR1 and DR2, spanning $\sim$3
dex of overlap in X-ray luminosity (see, right panel in Fig. 1), and aside
from some lower $L_{X}$ and lower-$z$ object of the DR1 and some higher
$L_{X}$ and higher redshift source in the DR2, all the three BASS samples
should be studying AGN with similar properties. The combined NIR dataset is
representative of the parent BAT AGN sample.

Figure 2: Examples of FIRE/Magellan NIR spectra in units of $\times 10^{-17}$
erg/s/cm2/Å, redshift-corrected and flux calibrated. The wavelength position
of some of the most relevant emission lines are indicated with dashed vertical
lines and labeled at the top. Regions of low telluric transmission are shown
in gray. The complete figure set for the 65 AGN is available in 7 images in
the online journal, ordered by BAT ID.

The 65 NIR 0.8–2.5 $\mu$m spectra were observed using the FIRE instrument in
the high-resolution echelle mode in four visiting runs carried out between
April 2018 and April 2019. FIRE is a dual-mode IR spectrometer mounted at the
Magellan Baade telescope at Las Campanas Observatory (LCO), Chile. Its primary
mode employs a combination of a diffraction grating and four prisms to deliver
cross-dispersed spectra covering the whole NIR bandpass in a single exposure,
with nominal wavelength resolution of $R=\lambda/\Delta\lambda\approx 6000$
for a 0$\farcs$6-slit width, i.e., $\Delta v\simeq 50$ ${\rm km\,s}^{-1}$.
This slit width was adopted for our program, with the exception of two
targets, namely BAT 677 and 1085, which were observed with a 0$\farcs$45-slit
width (i.e., $R\approx 8000$, $\Delta v\simeq 37$ ${\rm km\,s}^{-1}$), since
those were expected to have low $M_{BH}$. Our observations took place the
nights UT 2018 April 5, UT 2018 September 30, UT 2019 March 9 and on UT 2019
April 14-15 during gray time. The observations were executed under clear skies
with different airmass conditions (see Tab. 1) and visual seeing variying
between 1$\farcs$5 to 0$\farcs$4, with an average of 0$\farcs$75.

For each target, the individual spectra were obtained using the nodding
technique in a sequence of ABBA acquisitions, with exposure times ranging
between 190 to 623 s (multiples of 10.6 s, since sample-up-the-ramp SUTR
readout mode was used for all targets but the ones marked with an asterisk in
Tab. 1, which were observed using Fowler 4 readout), depending on target
magnitude and observing conditions. The acquisition sequence involved a short
arc frame (ThAr) just after the target observation in order to correct for
telescope flexure and obtain the wavelength solution. For long ($>$300 s)
exposures, OH airglow was used to improve the wavelength calibration. By
default, the wavelengths are calibrated in vacuum. Sky and dome (Qz) flats
were acquired to correct for detector illumination and pixel gain variations
across the slit, respectively. Data was reduced with the Interactive Data
Language (IDL) pipeline FireHose v2 package (Gagné et al., 2015), which
performs 2D sky subtraction and extracts an optimally weighted 1D spectrum.
Nearby A0V stars were observed during the night in order to derive relative
flux calibrations. We corrected the atmospheric absorption features (H2O, CO2,
CH4 and O2) using the software tool molecfit (Smette et al., 2015). Molecfit
uses a radiative transfer code to simulate the atmospheric transmission taking
into account local weather parameters (temperature, pressure, humidity, etc.),
recorded at the LCO/Magellan site.

Flux-calibrated and redshift-corrected NIR spectra of the 65 AGN are shown in
Fig. 2 (as a figure set) smoothed using a Savitzky-Golay filter, which
preserves the average resolving power. The spectra are ordered by their BAT ID
in Fig. 2. Regions of low telluric transmission are plotted in gray. The
locations of some of the most intense NIR emission lines are labeled and
indicated with dashed purple lines in Fig. 2. The reduced spectra will be
available on the BASS survey website666https://www.bass-survey.com/.

Figure 3: Examples of spectral emission-line fits of the Pa$\gamma$ (left),
Pa$\beta$ (center) and Pa$\alpha$ (right) regions for a Sy 1 (BAT 744, top)
and a Sy 1.9 (BAT 557, bottom). The best-fit Gaussians are plotted in blue. As
explained in Sect. 3.1, a broad Gaussian component is discarded if its
intensity is below $3\sigma$ (dashed purple line) with respect to the fitting
continuum. The continuum has been evaluated in the regions highlighted in
green and subtracted off. In red the resulting total model is shown. Residuals
are plotted offsetted in dark gray. The fit quality flags are: 2, 2 and 1 in
the Pa$\gamma$, Pa$\beta$ and Pa$\alpha$ regions of BAT 744, respectively; and
2, 1 and 4 in the Pa$\gamma$, Pa$\beta$ and Pa$\alpha$ regions of BAT 557,
respectively. The complete figure set with all the 65 FIRE/Magellan spectral
emission line fits in the Pa$\gamma$, Pa$\beta$ and Pa$\alpha$ regions is
available in the online journal.

##  3 Spectral Measurements

Below we describe the NIR emission line fitting analysis of the FIRE spectra.

###  3.1 Near-infrared Spectral fitting procedure

Our emission-line fitting approach is similar to the one adopted for the BASS
NIR DR1 (e.g., Lamperti et al., 2017) and DR2 (den Brok et al.,, submitted).
We use PySpecKit (v0.1.21), an extensive spectroscopic analysis toolkit for
astronomy, which uses a Levenberg-Marquardt algorithm (Ginsburg & Mirocha,
2011). We fit the Pa$\zeta$ (0.9$-$0.96 $\mu$m), Pa$\gamma$ (1.04$-$1.15
$\mu$m), Pa$\beta$ (1.15$-$1.30 $\mu$m), and Pa$\alpha$ (1.80$-$2.00 $\mu$m)
spectral regions separately, to ease the fitting convergence. Each so-defined
independent spectral region contains at maximum three lines coming from
permitted species in the BLR. There are only few differences with the emission
lines considered in Lamperti et al. (2017, see their Tab. A1), which are the
following: we fit also the [N i]$\lambda$10404 Å in the Pa$\gamma$ region and
the Br$\epsilon$$\lambda$18179.1 Å, H 2$\lambda$18345 Å, He i$\lambda$18635 Å,
and [S xi]$\lambda$19196 Å in the Pa$\alpha$ region, while we did not include
in the fit [Fe ii]$\lambda$9227 Å in the Pa$\zeta$ spectral region, since it
is a faint iron emission and was not detected in our FIRE observations.

We first deredden the spectra using the Galactic extinction value $E(B-V)$
(Schlafly & Finkbeiner, 2011) as listed in the IRSA Dust Extinction
Service777https://irsa.ipac.caltech.edu/applications/DUST/, and redshift
correct the spectra. We employ a single first-order power-law fit to model and
remove the continuum. For each spectral region, we estimate the continuum
level using sections of the wavelength range free of emission lines, i.e.,
excluding 20 Å around the narrow lines and 150 Å where a broad component was
expected, e.g., in permitted species.

As the focus of our investigation is to study the BLR properties, the main
goal is to derive the FWHM and flux of broad line species. Emission lines are
modeled using a combination of Gaussian profiles, namely one component for all
line species associated with the NLR and an additional Gaussian to account for
the BLR component in all permitted transitions of each spectral region. The
relative central wavelength of the narrow lines are tied together, but are
allowed to shift together by a maximum of 500 ${\rm km\,s}^{-1}$ with respect
to the systemic redshift listed in Tab. 1. As an initial input value for the
width of the narrow lines, we used the best-fit width of the [S
iii]$\lambda$9531 Å line, which is the strongest (and the narrowest, see,
e.g., Fig. 3 in Riffel et al., 2013) narrow emission line in the rest-frame
NIR wavelength range, with only a minor blending with the Pa$\epsilon$ on its
red side. The width of the narrow components in each spectral region are then
tied together.

The threshold between narrow and broad components is set at FWHM $=1200$ ${\rm
km\,s}^{-1}$, as consistent with the division defined in BASS NIR DR1
(Lamperti et al., 2017). The central wavelengths of the broad components are
allowed to shift up to $\approx$1000 ${\rm km\,s}^{-1}$ (Shen et al., 2016).
Since the widths of the broad components in each spectral region are likely to
be similar, we tie them together to avoid unnecessary complexity and
degeneracy888We checked that the best-fit NIR broad lines in separate regions,
that have been fitted independently, thus without imposing any common
constraint on their widths, are consistent within the uncertainties, as also
previously reported in the literature (see Landt et al., 2008; Ricci et al.,
2017b; Lamperti et al., 2017; Onori et al., 2017a).. As each spectral region
is fitted separately, the resulting best-fitting BLR component can be
different in each region. The same applies to the NLR estimate, which might
vary in different spectral regions. The fit is thus run a first time. Lines
are detected if their amplitude is $>3\sigma$, where $\sigma$ is the root-
mean-square of a line-free zone in each spectral region. After the first
minimization, $1)$ if the strongest narrow transition of each region is not
detected, we fixed the width of the narrow component to the [S
iii]$\lambda$9531 Å, and $2)$ if the broad component of a line is below the
detection threshold, we discard the component as an unreliable detection, and
we run again the fit, using only a single narrow Gaussian component. In a few
cases, after visual inspection, additional Gaussian components were added to
the model in order to improve the fit. These additional velocity components do
not contribute to the broad component used to compute the BH mass (Sect. 4) as
they are not considered as BLR tracers999We note that even considering the
additional component as coming from the BLR, our results do not change since
those (few) cases do not fulfill one or more of the criteria we adopt in the
subsequent analysis.. In particular, in the Pa$\gamma$ region 7/65 spectra
required one additional intermediate velocity component in the He
i$\lambda$10830 Å, (i.e., BAT IDs 372, 488, 577, 698, 744, 1064, and 1079), in
the Pa$\alpha$ region 1/65 required an additional intermediate velocity
component in the Pa$\alpha$ (BAT 1079) and 1/65 required one additional
intermediate velocity component in the Pa$\alpha$ and two additional lines H
2$\lambda$18345 Å and H 2$\lambda$189205 Å (BAT 372). The model with
additional Gaussians was run twice as in the normal case, in order to discard
the components in case those were below the detection threshold. We then
correct the measured FWHMs to account for instrumental resolution, even though
it is not a substantial correction for broad lines.

To estimate the uncertainties related to emission line measurements in each
spectral region, we repeated the fit ten times, adding each time an amount of
noise $\sigma$ randomly drawn from a normal distribution with the deviation
equal to the noise level. We computed the median absolute deviation of the ten
measurements and we used this value as an estimate of the uncertainty at the
one-sigma confidence level (c.l.). We estimate the flux upper limits (at
$3\sigma$) on the (undetected) broad line components by assuming a FWHM=4200
${\rm km\,s}^{-1}$, which is the average FWHM of the broad line detections in
our FIRE dataset. We then visually inspected all the fits and assigned quality
flags, following the classification nomenclature of the first BASS paper (Koss
et al., 2017). Quality flag 1 refers to spectra that have small residuals and
very good fits. Flag 2 means that the fits are not perfect, but still
acceptable. Flag 3 is assigned to not completely satisfactory fits for high
S/N sources due to the presence of either absorption lines, additional
components in the fit or structure in the residuals, making the fit
decomposition more uncertain. Flag 4 refers to spectra with low S/N and/or
strongly affected by telluric residuals, the best-fit NLR and BLR estimates
are highly uncertain. Flag 9 refers to spectra where no emission line is
detected. The results of the broad emission line fits are presented in Tables
4-6 for the Pa$\gamma$, Pa$\beta$ and Pa$\alpha$ broad lines. Tables 7-8
report the few cases that needed additional components in their spectral fit.
Figure 3 shows examples of emission-line fits for a Sy 1, BAT 744 (top
panels), with fit quality flags 2 (2,1) in the Pa$\gamma$ (Pa$\beta$,
Pa$\alpha$) regions, and for a Sy 1.9, BAT 557 (bottom panels), with fit
quality flags 2 (1,4) in the Pa$\gamma$ (Pa$\beta$, Pa$\alpha$) regions. The
remainder of the best-fit models derived for the full FIRE dataset in the
spectral regions Pa$\gamma$, Pa$\beta$ and Pa$\alpha$ are shown as figure set
in Fig. 3 (available on the online journal) ordered by increasing BAT number.

##  4 $M_{BH}$ measurements

Below we briefly describe the two independent $M_{BH}$ estimates adopted in
order to understand if the NIR view of the BLR gives consistent BH mass
estimates compared to the more often adopted H$\alpha$-based BH mass estimate,
in case of Sy 1 up to Sy 1.9 AGN, and the $\sigma_{\star}$-based BH mass
estimates, which include Sy 2 AGN lacking broad H$\alpha$ line and strong AGN
continua but with NIR broad lines. Combining Eqs. 1-2, we evaluate the
individual virial factors $f$ of our sample as:

$f=\frac{M_{BH,\sigma_{\star}}}{M_{vir,line}}\,,$ (3)

where $M_{BH,\sigma_{\star}}$ is the BH mass estimated from the optical
stellar velocity dispersion (Sect. 4.1), and $M_{vir,line}$ is the virial-
based BH mass estimated for each near-infared broad line considered in our
study (see Sect. 4.2).

###  4.1 BH mass estimate from the $M_{BH}-\sigma_{\star}$ scaling relation

The relation between $M_{BH}$ and the bulge stellar velocity dispersion is
probably the most fundamental and most used BH-host scaling relation due to
its instrinsic small scatter ($\sim 0.3$ dex Kormendy & Ho, 2013; van den
Bosch, 2016; Saglia et al., 2016; Shankar et al., 2016; de Nicola et al.,
2019; Marsden et al., 2020), and lack of strong redshift evolution, at least
until $z\sim 1$ (e.g., Shen et al., 2015; Sexton et al., 2019). There are
several $M_{BH}-\sigma_{\star}$ calibrations available in the literature, some
of which take into account the host morphology (late/early type McConnell & Ma
2013; Sahu et al. 2019; barred/unbarred Graham 2008; elliptical and
classical-/pseudo-bulges Kormendy & Ho 2013; Saglia et al. 2016; de Nicola et
al. 2019). We adopt the $M_{BH}-\sigma_{\star}$ relation proposed by Kormendy
& Ho (2013), that is calibrated on dynamical-based $M_{BH}$ measurements of
local ellipticals and classical-bulges, and for which an average virial factor
$\langle f\rangle$ has already been estimated (Ho & Kim, 2014; Yu et al.,
2019). More recent estimates of the average virial factor determined by
Batiste et al. (2017) and Yu et al. (2019) are consistent, within their
(large) uncertainties, with the values found by Grier et al. (2013) and Ho &
Kim (2014).

The $M_{BH}-\sigma_{\star}$ relation of elliptical and classical bulges from
Kormendy & Ho (2013) is amongst the highest relations in normalization in the
$M_{BH}$ vs $\sigma_{\star}$ plane up to date (see, e.g., Fig. 2 in Ricci et
al., 2017c). This means that at given velocity dispersion it predicts the
largest SMBH masses, at least until predicted $M_{BH}\approx 10^{9}$ M⊙. In
other words, the $f$-factors derived using Eq. 3 are the largest that can be
possibly predicted with the currently calibrated $M_{BH}-\sigma_{\star}$
relations, even considering the most recent updates (Saglia et al., 2016; de
Nicola et al., 2019). We will discuss later how this assumption affects the
virial factors $f$ and our analysis.

###  4.2 BH mass estimate from the virial method

The virial $M_{BH}$ estimate implicitly assumes that the motion of clouds in
the BLR is virialized. Thanks to the $R-L$ relation established by RM
campaigns (see, e.g., Bentz et al., 2013), Eq. 1 can be rewritten using
easily-accessible quantities, like broad emission line or continuum
luminosity. We adopted the mixed virial BH mass estimator put forward by Ricci
et al. (2017b), for a similar mixed $M_{BH}$ virial estimator see also
Bongiorno et al. (2014); La Franca et al. (2015). The virial BH mass estimator
proposed by Ricci et al. (2017b) is based on either optical (e.g., H$\beta$ or
H$\alpha$) or NIR (Pa$\alpha$, Pa$\beta$ or He i$\lambda$10830 Å101010From now
onward, He i$\lambda$10830 Å is called just He i.) FWHM and on hard X-ray
luminosities, either 2-10 or 14-195 keV. Thus, we can compute the virial BH
mass $M_{vir,line}$ using the 14-195 keV luminosity $L_{X}$ and any single
broad line reliably detected, i.e., He i, Pa$\beta$ and Pa$\alpha$. The use of
the observed BAT luminosity does not affect our analysis since the majority of
our sample has $N_{H}<10^{23.5}$ cm-2, and the observed 14-195 keV luminosity
is almost unaffected by X-ray absorbing columns up to at least $N_{H}\sim
10^{23.5}-10^{24}$ cm-2 (Ricci et al., 2015; Koss et al., 2016).

We can also compute the mass with the FWHM of all the reliable detections and
with the weighted111111The weights are the square of the inverse of the
measured broad-line FWHM uncertainties, $1/\sigma_{i}^{2}$ average, in
presence of more than one reliable detection. We call this case $NIR$121212The
term $NIR$ in italic should not be confused with the general term NIR that
indicate the 0.8–2.4 $\mu$m wavelength range. in all subsequent analysis. The
mixed virial mass is thus $M_{vir,line}\propto FWHM(line)^{2}\times
L_{X}^{0.5}$, with $line$ being He i, Pa$\beta$, Pa$\alpha$, and $NIR$
samples. The statistical uncertainties on the virial BH mass estimate are then
the combination of the errors on the broad FWHM and on the X-ray luminosity
$L_{14-195\,\rm{keV}}$. For simplicity, we assumed a 5% uncertainty on the
hard X-ray luminosity, while for the FWHM we used the uncertainties determined
from the spectral fit. The aforementioned statistical uncertainty does not
take into account the intrinsic spread of virial BH mass estimates, which is
of the order of $\sim 0.5$ dex (McLure & Jarvis, 2002; Vestergaard & Peterson,
2006; Ricci et al., 2017b).

As for the majority of the virial BH mass estimators, the relations in Ricci
et al. (2017b) were calibrated against a sample of local RM AGN with H$\beta$
measurements, and therefore an average virial factor $\langle f\rangle$ was
adopted. This $\langle f\rangle$ changes depending on whether the RM
calibrating virial masses are based on the FWHM or the second moment of the
line profile $\sigma_{line}$ (see, e.g., Onken et al., 2004; Collin et al.,
2006) such that

$f_{\sigma}=f_{FWHM}\times\left(\frac{FWHM}{\sigma_{line}}\right)^{2}\,.$ (4)

The relations calibrated by Ricci et al. (2017b) adopt as a calibration sample
the RM virial masses based on the H$\beta$ line dispersion measured from the
rms spectra, $\sigma_{H\beta,rms}$ (Ho & Kim, 2014), and in particular the
value $\langle f_{\sigma}\rangle=4.31\pm 1.05$, derived in Grier et al. (2013)
by requiring that RM AGN reproduce the $M_{BH}-\sigma_{\star}$ relation found
in quiescent galaxies by Woo et al. (2013). Alternatively, Ricci et al.
(2017b) also calibrated BH mass estimators considering the bulge morphology,
proposing BH mass estimators also for classical-bulges, $\langle
f_{\sigma}\rangle=6.3\pm 1.5$, and pseudo-bulges, $\langle
f_{\sigma}\rangle=3.2\pm 0.7$. These $\langle f_{\sigma}\rangle$ values were
determined in Ho & Kim (2014) to put RM AGN virial BH masses on the
$M_{BH}-\sigma_{\star}$ relation of classical-bulges, given by Kormendy & Ho
(2013), and the one followed by pseudo-bulges, determined by Ho & Kim (2014).
For more details on the BH mass estimators, see Table 4 in Ricci et al. 2017b.

Since the chosen reference BH-$\sigma_{\star}$ relation is the one from
Kormendy & Ho (2013) (see Sect. 4.1), we adopt the BH mass relation based on
the $\langle f_{\sigma}\rangle=6.3$, that is relation b3 in Tab. 4 of Ricci et
al. (2017b), in the classical bulge case

$\left(\frac{M_{BH}}{M_{\odot}}\right)=10^{a}\cdot\left[\left(\frac{FWHM}{10^{4}~{}\rm
km~{}s^{-1}}\right)^{2}+\left(\frac{L_{X}}{10^{42}~{}\rm
erg~{}s^{-1}}\right)^{0.5}\right]\,,$ (5)

with $a=(7.96\pm 0.02)$.

In order to more easily compare with literature works about the $f$-factor
(see, e.g., Collin et al., 2006; Decarli et al., 2008; Shen & Ho, 2014; Mejía-
Restrepo et al., 2018), we convert the individual $f$-factors from
$f_{\sigma}$ to $f_{FWHM}$ using Eq. 4 and assuming the FWHM/$\sigma_{line}$
ratio for a single Gaussian case, i.e., $\sqrt{8\ln 2}\approx 2.355$. This is
equivalent to rescale the $\langle f_{\sigma}\rangle$ adopted as
$6.3/(2.355)^{2}$. We denote this rescaled average virial factor as $f_{0}$.
The symbol $f_{0}$ is hence the equivalent to writing $\langle
f_{FWHM}\rangle$, and it is the average value adopted to convert the virial BH
mass $M_{vir,line}$ to the BH mass $M(line)$, i.e., $M(line)=f_{0}\times
M_{vir,line}$. With this notation, the $f$ derived in Sect. 5.5 using Eq. 3
will be, strictly speaking, a $f_{FWHM}$. From now on, we will drop the suffix
FWHM and simply write $f$ when referring to $f_{FWHM}$.

When optical broad H$\alpha$ mass estimates are available from the BASS DR2
(Mejía-Restrepo et al.,, submitted), we compare them to the NIR-based virial
BH mass estimated here (see, Sect. 5.2). These optical BH masses are computed
with the prescription proposed by Greene & Ho (2005, see, e.g., their Eq. 6),
based on the FWHM and luminosity of the broad H$\alpha$, with virial factor of
unity (Mejía-Restrepo et al.,, submitted).

##  5 Results

Figure 4: H$\alpha$ vs NIR BLR velocities for BASS targets, from left to
right: He i, Pa$\beta$, Pa$\alpha$ and $NIR$ broad lines samples,
respectively. The $NIR$ sample is the collection of reliably detected NIR
broad-line FWHM, being the weighted average FWHM in case there is more than
one reliable broad-line detection. The colored circles mark the Sy 1-1.5
(blue), Sy 1.8 (cyan), and Sy 1.9 (orange) types. Only targets with reliable
H$\alpha$ and NIR detection in each line, as defined in Sect. 5.1 and 5.2.1
are shown. The black filled squares are the more robust optical measurements,
having $<10\%$ uncertainties in the broad FWHM (H$\alpha$). Pearson
correlations coefficients $r$ computed for the more robust subsample (black
squares), without separating between Sy subclasses, are reported in each
panel.

To help the reader, we here present a brief summary of the topics in the
results section. In Sect. 5.1 we introduce the sample of Sy 1.8-1.9-2 types
for which we reliably detect NIR broad lines. We compare in Sect. 5.2 the NIR
and optical, i.e., H$\alpha$, broad line widths to understand if the ability
of measuring the BLR velocity and radius changes with increasing
obscuration/extinction. We then examine how the medium responsible for
obscuring the BLR is related to the material absorbing the X-rays in Sect.
5.3. By investigating the effect of X-ray obscuration on H$\alpha$ and NIR
broad line luminosities we demonstrate that the use of H$\alpha$ (Sect. 5.2.2)
and NIR (Sect. 5.4) broad line luminosities in SE BH mass determinations
induce a bias in the BH mass measurements when the column density is above a
certain threshold. Finally in Sect. 5.5 we compare two independent
obscuration-unbiased BH mass measurements, derive the virial factors and
examine whether they depend on some additional parameters.

###  5.1 Broad line detection in reddened Seyferts

presented in this work is composed of 33 Sy 2, 18 Sy 1.9 and 1 Sy 1.8, or a
total of 52 reddened Sy types. As stated in the introduction, in $\sim$30% of
cases Sy 1.8 to 2 with narrow emission lines in the rest-frame optical spectra
have been found to exhibit broad hydrogen and helium recombination lines,
i.e., Pa$\alpha$, Pa$\beta$ and He i. We focus mainly on these three emission
lines since all higher order Paschen transitions are strongly blended with
emission lines from other elements, and He i, even though blended with
Pa$\gamma$, is among the most intense rest-frame NIR lines (see, e.g., Fig. 9
in Riffel et al., 2006), and therefore it is possible to detect and deblend
faint broad components relatively easily. The rest-frameNIR also contains the
hydrogen Brackett series, the strongest emission being the Br$\gamma$
$\lambda$21661Å. The Br$\gamma$ is isolated, located in a region less affected
by low atmospheric transmission, and redder than Pa$\alpha$, thus effects of
dust extinction are expected to be even lower. However, its intensity is
rather low compared to the Paschen and helium lines
(Br$\gamma$/Pa$\beta\approx 0.16$ in case B with T=104 K and density
$n=10^{6}$ cm-3, see e.g., Osterbrock & Ferland, 2006), thus we do not
investigate its properties in this work. Based on the fact that the He i,
Pa$\beta$ and Pa$\alpha$ lines have been found to have similar FWHMs in Sy 1
and in intermediate types (Landt et al., 2008; Ricci et al., 2017b; Lamperti
et al., 2017; Onori et al., 2017a, see also Sect. 5.2 and in particular Fig.
4), we can also examine the collection of near-infrared broad-line
measurements, that we call $NIR$. When more than one observation was present,
we chose the one with the highest S/N evaluated on the continuum, in each
spectral region. Combining the DR1, DR2 and FIRE observations the total parent
sample is thus composed of 235 obscured BASS AGN, divided into 168 Sy2, 60 Sy
1.9 and 7 Sy 1.8.

Considering only the most reliable measurements, i.e., only the cases where
the spectral fit quality is good (quality flag equal to 1 or 2) and the
relative uncertainty on the measured broad FWHM is $<10\%$, the final reliably
detected broad lines are 63/235 ($27^{+4}_{-3}\%$) combining the number of
detections of at least one of the above transitions. The broad-line detection
rate is expected to be consistent in the three BASS samples since the targeted
AGN should be similar in their properties (see, Fig. 1)131313The FIRE/BASS
sample shows a higher detection rate of hidden BLRs compared to the other two
BASS works, even though consistent within $\lesssim$2$\sigma$ given the
poissonian uncertainties. This might be caused by the higher resolving power
of this work (R$\sim$6000) with respect to the BASS DR1 (most observations
have R=800, $\Delta v=375$ ${\rm km\,s}^{-1}$, see, Tab. 4 in Lamperti et al.
2017) and with the better observing conditions, resulting in slightly higher
S/N, of this FIRE dataset in comparison to the DR2 (average seeing 0$\farcs$7
in the BASS/FIRE sample vs 1′′ in the DR2, den Brok et al., submitted)..

Table 2: Statistical information of the optical and near-infrared BLR velocity
measurements.

N | sample |  $\langle$ FWHM(H$\alpha)~{}\rangle$ |  $\langle$ FWHM(He i) $\rangle$ | r | P(r)
---|---|---|---|---|---
|  | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] |  |
(1) | (2) | (3) | (4) | (5) | (6)
60 | all | 3872$\pm$249 | 3669$\pm$212 | 0.67 | 3.4E-09
41 | Sy 1-1.5 | 3665$\pm$260 | 3644$\pm$266 | 0.77 | 5.1E-09
19 | Sy 1.8-1.9 | 4319$\pm$549 | 3724$\pm$356 | 0.58 | 9.5E-03
42 | all more robust | 3942$\pm$298 | 3869$\pm$265 | 0.65 | 2.9E-06
28 | Sy 1-1.5 more robust | 3674$\pm$275 | 3853$\pm$340 | 0.75 | 4.1E-06
14 | Sy 1.8-1.9 more robust | 4477$\pm$701 | 3900$\pm$430 | 0.64 | 1.3E-02
N | sample |  $\langle$ FWHM(H$\alpha)~{}\rangle$ |  $\langle$ FWHM(Pa$\beta)~{}\rangle$ | r | P(r)
|  | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] |  |
(1) | (2) | (3) | (4) | (5) | (6)
47 | all | 3176$\pm$214 | 3478$\pm$215 | 0.81 | 6.4E-12
35 | Sy 1-1.5 | 3117$\pm$220 | 3304$\pm$210 | 0.87 | 1.0E-11
12 | Sy 1.8-1.9 | 3346$\pm$559 | 3987$\pm$571 | 0.74 | 6.0E-03
31 | all more robust | 3157$\pm$260 | 3342$\pm$261 | 0.85 | 1.2E-09
22 | Sy 1-1.5 more robust | 3169$\pm$254 | 3285$\pm$267 | 0.87 | 1.3E-07
9 | Sy 1.8-1.9 more robust | 3125$\pm$673 | 3480$\pm$648 | 0.84 | 4.7E-03
N | sample |  $\langle$ FWHM(H$\alpha)~{}\rangle$ |  $\langle$ FWHM(Pa$\alpha)~{}\rangle$ | r | P(r)
|  | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] |  |
(1) | (2) | (3) | (4) | (5) | (6)
50 | all | 3159$\pm$218 | 3299$\pm$235 | 0.66 | 1.4E-07
38 | Sy 1-1.5 | 3269$\pm$233 | 3188$\pm$272 | 0.69 | 1.4E-06
12 | Sy 1.8-1.9 | 2808$\pm$539 | 3650$\pm$468 | 0.71 | 9.6E-03
33 | all more robust | 3192$\pm$244 | 3403$\pm$313 | 0.62 | 1.2E-04
25 | Sy 1-1.5 more robust | 3320$\pm$225 | 3318$\pm$357 | 0.61 | 1.1E-03
8 | Sy 1.8-1.9 more robust | 2792$\pm$744 | 3669$\pm$688 | 0.75 | 3.1E-02
N | sample |  $\langle$ FWHM(H$\alpha)~{}\rangle$ |  $\langle$ FWHM($NIR$) $\rangle$ | r | P(r)
|  | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] |  |
(1) | (2) | (3) | (4) | (5) | (6)
86 | all | 3593$\pm$192 | 3467$\pm$158 | 0.73 | 1.6E-15
58 | Sy 1-1.5 | 3557$\pm$199 | 3358$\pm$187 | 0.83 | 8.4E-16
28 | Sy 1.8-1.9 | 3669$\pm$427 | 3694$\pm$295 | 0.62 | 4.0E-04
60 | all more robust | 3620$\pm$232 | 3486$\pm$194 | 0.75 | 5.5E-12
40 | Sy 1-1.5 more robust | 3573$\pm$216 | 3362$\pm$227 | 0.82 | 6.0E-11
20 | Sy 1.8-1.9 more robust | 3715$\pm$555 | 3734$\pm$365 | 0.72 | 3.5E-04

††footnotetext: Columns: (1)-(2) sample size and type, (3) average FWHM of the
broad H$\alpha$, (4) average broad near-infrared line, (5)-(6) Pearson
correlation coefficient and probability.

###  5.2 Optical and near-infrared view of the BLR in Sy 1-1.9

Figure 5: Ratio of the FWHM velocities measured in the NIR to the ones
measured from the broad H$\alpha$ as a function of the line-of-sight X-ray
column $N_{H}$. The panels from left to right compare He i, Pa$\beta$,
Pa$\alpha$ and $NIR$, respectively. Symbols are plotted with the same color
scheme as in Fig. 4. For each panel, the gray solid line shows where the
velocities are equal, and the dashed lines mark the $\pm$1$\sigma$ intrinsic
scatter. The solid black lines are the best-fit Bayesian relations derived
using linmix_err together with the 68% c.l. region plotted in green. The best-
fit slope $\beta$ and intercept $\alpha$ with their uncertainties are reported
as well. The normalizations $y_{0}$ and $x_{0}$ in Eq. 6 are set to 1 and
$10^{22}$ cm-2, respectively.

It is important to understand whether the measured H$\alpha$ broad line width
and luminosity are accurately tracing the underlying BLR motion and radius,
particularly for intermediate Sy 1.8 and 1.9 where the extinction is higher
than in normal optical broad-line AGN. The NIR offers a view of the BLR
complementary to the optical, as it can help penetrate into the innermost and
fastest moving BLR clouds. Together with X-ray ancillary data provided by BASS
(Ricci et al., 2017a), NIR spectroscopy can help to understand biases or
systematics in BLR measurements, e.g., the BLR velocity and radius, obtained
from the H$\alpha$ (BASS DR2 Mejía-Restrepo et al.,, submitted).

Indeed, a large community effort is being spent to find intermediate mass
black holes (IMBHs, $M_{BH}<10^{5}$ M⊙, Greene & Ho, 2004, 2007; Reines et
al., 2013; Moran et al., 2014; Baldassare et al., 2017; Mezcua, 2017; Mezcua
et al., 2018; Chilingarian et al., 2018; Martínez-Palomera et al., 2020), as
this population has a huge impact on several aspects concerning BH seed
formation and BH growth at high redshift (see, e.g., Volonteri et al., 2008;
Treister et al., 2013; Pacucci et al., 2018; Inayoshi et al., 2020). One of
the most commonly used lines in the local Universe to this end is H$\alpha$
(Reines & Volonteri, 2015; Baldassare et al., 2016), since it is about three
times more intense than H$\beta$, and it is in practice the only line
available in the rest-frame optical in case of Sy 1.9.

Figure 6: Ratio of the FWHM velocities measured in the near-infrared to the
ones measured from the broad H$\alpha$ as a function of the broad line flux
ratios H$\alpha$ to near-infrared. The $x$-axis has been plotted showing the
direction of increasing extinction (towards the right). The panels from left
to right compare He i, Pa$\beta$, Pa$\alpha$, respectively. Symbols are
plotted with the same color scheme as in Fig. 4. For each panel, the gray
solid line shows the locus where the velocities are equal, and the dashed
lines mark the $\pm$1$\sigma$ intrinsic scatter. The solid black lines are the
best-fit Bayesian relations derived using linmix_err together with the 68%
c.l. region shown in green. The best-fit slope $\beta$ and intercept $\alpha$
with their uncertainties are reported as well. The normalizations $y_{0}$ and
$x_{0}$ in Eq. 6 are both set to 1. The red line in the center and right
panels is the value of the flux ratios expected assuming case B recombination
(see text for more details).

####  5.2.1 BLR velocity estimates from H$\alpha$ and near-infrared lines

Figure 4 reports the measured broad H$\alpha$ from BASS DR2 (Mejía-Restrepo et
al.,, submitted) compared to the measured broad near-infrared lines from BASS
NIR DR1, DR2 and FIRE targets, separated into Sy 1-1.5 (blue circles), Sy 1.8
(cyan circles), and Sy 1.9 (yellow circles) where both optical and NIR BLR
components are detected. We recall that we consider the collection of reliably
detected broad-line measurements as the $NIR$ line sample (in italic, see
footnote in Sect. 4.2), being the weighted average FWHM in case there is more
than one near-infrared broad-line detection. The sample of reliable near-
infrared, as defined in Sect. 5.1, and H$\alpha$ broad lines141414From the
BASS H$\alpha$ DR2 database we excluded BAT 557 whose observation does not
have nightly flux calibrations, thus resulting in higher uncertainties on the
flux measurement (e.g., Koss et al., 2017). contains 60, 47, 50 and 86 AGN
with He i, Pa$\beta$, Pa$\alpha$ and $NIR$ broad lines, respectively. The
sample with robust optical measurements, i.e., with $<10\%$ uncertainty in the
measured FWHM H$\alpha$, contains 42, 31, 33 and 60 AGN with He i, Pa$\beta$,
Pa$\alpha$ and $NIR$ broad lines, respectively (see black filled squares in
Fig. 4). The measurements show some dispersion around the one-to-one locus,
with the Paschen-line FWHM being on average higher than the H$\alpha$ one,
which might be driven by the less extincted view in the NIR with respect to
the optical band, though the averages velocities measured from H$\alpha$ and
all the NIR lines considered are consistent ($<1\sigma$) within the
uncertainties of the mean (see Tab. 2).

Figure 7: Ratio of the broad line fluxes measured from H$\alpha$ and NIR lines
He i (left), Pa$\beta$ (center) and Pa$\alpha$ (right) as a function of the
line-of-sight X-ray column density (Ricci et al., 2017a). The $y$-axis has
been plotted showing the direction of increasing extinction (towards the top).
Symbols are plotted with the same color scheme as in Fig. 4. The solid black
lines are the best-fit Bayesian relations derived using linmix_err together
with the 68% c.l. region shown in green. The best-fit slope $\beta$ and
intercept $\alpha$ with their uncertainties are reported as well. The
normalizations $y_{0}$ and $x_{0}$ in Eq. 6 are set to 1 and $10^{22}$ cm-2,
respectively. The red line in the center and right panels is the value of the
flux ratios expected assuming case B recombination (see text for more
details).

We found that for the whole sample (see ‘all’ in Tab. 2), the Pearson
coefficients are high ($>$0.66) and statistically significant, as also
confirmed by a Student’s T-test. This means that the H$\alpha$ and NIR
measurements of the BLR velocities are statistically describing the same
velocity field. The intrinsic spreads with respect to the H$\alpha$ are 0.14,
0.10, 0.15 and 0.13 dex for He i, Pa$\beta$, Pa$\alpha$ and $NIR$,
respectively. Note that these correlations between optical and NIR broad lines
do not depend on our fitting approach, since we are comparing broad lines that
come from different spectral regions that are fit independently.

In order to verify whether some particular classes of Sy are strongly
influencing the result, we split the sample into Sy 1-1.5 and Sy 1.8-1.9 and
compare the more secure optical and NIR detections (i.e., the black symbols in
Fig. 4 and the ‘more robust’ cases in Tab. 2). The results are confirmed: the
optical and NIR BLR measurements give consistent estimate of the BLR velocity
fields. Additionally, the FWHM measured in Sy 1-1.5 vs Sy 1.8-1.9 come
statistically from the same parent population in both NIR and optical. Similar
statistical conclusions are derived even adopting the Kolmogorov-Smirnov test
and a non-parametric test like the Kendall $\tau$ and bootstrapping to
consider measured errors on the FWHM (e.g., pymccorrelation python package,
Privon et al., 2020). Therefore, we can conclude that once a broad H$\alpha$
line is securely detected, the H$\alpha$ width is in agreement within the
intrinsic scatter, with the broad-line width as measured in the NIR. This
scatter might be partially explained by AGN variability since the
spectroscopic measurements of the optical and NIR are often obtained from non-
simultaneous observations.

We examine in Fig. 5 the difference in the measured BLR velocities as a
function of the line-of-sight column density $N_{H}$ measured in the X-rays
(Ricci et al., 2017a). In order to verify the dependencies between the $y$ and
$x$ variables, we adopt a standard forward regression using the linmix_err
routine of Kelly (2007), that employs a fully Bayesian approach, and we fit
linear log-log relations

$\log(y/y_{0})=\alpha+\beta\,\log(x/x_{0})\,.$ (6)

The linmix_err routine can include censored data (i.e., upper limits) on the
$y$-variable. In our analysis, all the times upper limits are on the
$x$-variable, being the $N_{H}$. The $N_{H}$ upper limits are objects with
$N_{H}<10^{20}$ cm-2, so lacking evidence of absorbing columns in the broad-
band X-ray spectral analysis (see BASS X-ray DR1 Ricci et al., 2017a). These
objects should, in principle, have at least some obscuration along our line of
sight coming from their host galaxy, but it is impossible to detect because of
the intervening obscuration in the Milky Way. We adopt as minimum
$N_{H}=10^{19}$ cm-2 (Ryan-Weber et al., 2003; Güver & Özel, 2009; Treister et
al., 2009), so treating the $N_{H}$ upper limits as measurements at
$N_{H}=10^{20}$ cm-2 with an uncertainty of $\log N_{H}$=1 dex.

In all the subsamples inspected, the Bayesian best-fit linear regressions
(solid black lines in Fig. 5 with the 1$\sigma$ c.l. regions in green) are
rather flat, indicating no significant effect of $N_{H}$ on the difference in
the line widths due to $N_{H}$. We note that the best-fit slope $\beta$ found
for He i has an opposite sign than what is found for the Pa$\beta$ and
Pa$\alpha$ samples, though all slopes are statistically consistent with zero
(p-value $>$0.1). The reason for this might be the ionization structure in the
BLR, since the ionization potential of He i is much higher ($\approx$6 times)
than the one of Pa$\alpha$, Pa$\beta$ and H$\alpha$. We can conclude that
there is a lack of correlation between the NIR-to-optical BLR velocity
measurement ratio and the column density $N_{H}$, at least until $N_{H}\simeq
10^{23}$ cm-2. At higher $N_{H}$, the sample is too small to derive meaningful
conclusions. This result nicely complement what can be seen using the larger
statistical sample of optical BASS DR2 (Mejía-Restrepo et al.,, submitted)
having both H$\alpha$ broad line and $N_{H}$ measurements (Ricci et al.,
2017a). In particular, the FWHM(H$\alpha$) - $N_{H}$ plane shows a decrease in
the optical H$\alpha$ width in Sy 1.9 at $N_{H}>10^{23}$ cm-2, while below
this column density the FWHM - $N_{H}$ distribution is rather flat (see, e.g.,
their Fig. 9).

Observationally, the line-of-sight X-ray column density $N_{H}$ has shown a
correlation with occultation events in the X-rays, due to gas clumps located
in a dust-free region or at the inner edge of the dusty torus (see, e.g.,
Risaliti et al., 2007, 2011; Maiolino et al., 2010; Markowitz et al., 2014;
Ricci et al., 2016; Zaino et al., 2020). More prevalent eclipsing events are
linked to higher covering factors, placing at least some of the X-ray
obscuring material in the dust-free BLR (see also Schnorr-Müller et al.,
2016). In fact, Gandhi et al. (2015) have argued that narrow iron K$\alpha$
line-emitting material could reside in between the BLR and the putative dusty
torus. In addition, some works have suggested that the accretion disk could
partially contribute to the observed column density in Compton-thick AGN, as
they have large inclination angles (e.g., Masini et al., 2016; Ramos Almeida &
Ricci, 2017). Those observations imply the presence of gas inside the
sublimation radius. However, the X-ray column density $N_{H}$ is a line-of-
sight local measurement, that is very unlikely to strongly obscure the full
BLR. Therefore, we calculated the optical-to-NIR broad line flux ratios as a
way to measure the extinction experienced by the broad H$\alpha$ with respect
to the broad NIR emission lines. Figure 6 shows only a mild trend,
statistically consistent with being flat given the dispersion (p-value
$>$0.05), when comparing the BLR velocity ratio with the broad H$\alpha$ to
near-infrared broad line fluxes.

From Figs. 5 and 6 we can then conclude that neither the X-ray obscuration nor
the BLR extinction significantly affect the measurement of the width of the
broad H$\alpha$ line and of the NIR broad lines, at least among the total
local hard X-ray selected AGN sample up to columns $N_{H}\simeq 10^{23}$ cm-2,
once the broad H$\alpha$ line detection is secure.

Figure 8: Difference between the virial BH mass estimates from the optical and
NIR as a function of obscuration (left) or broad line fluxes (right), proxy
for the BLR extinction. As previously done in Fig. 6 and 7, the $x$-axes in
the right panels show the direction of increasing BLR extinction (towards the
right). Each row reports a NIR line, from top to bottom: He i, Pa$\beta$ and
Pa$\alpha$. Symbols are plotted with the same color scheme as in Fig. 4. The
gray solid lines mark the identity relation. The shaded rectangles in the left
panels show the average BH mass difference (together with the error on the
mean) computed in two bins of $N_{H}$, low $N_{H}$ in green and high $N_{H}$
in magenta. Red stars show the difference between the BH mass measurements for
Sy 1.9 when the $M_{vir,H\alpha}$ is estimated using the same prescription as
in the NIR, that is to use the hard X-ray luminosity instead of the H$\alpha$
broad line luminosity. The vertical panels show the histograms of the BH mass
difference in the case of completely H$\alpha$-based (black dashed histogram)
or when the hard X-ray luminosity is adopted instead of the broad H$\alpha$
line luminosity (solid red histogram). In the latter case, the distribution of
the mass difference is more consistent with scatter around zero.

Figure 9: Comparison between $A_{V}$ expected from gas absorption and $A_{V}$
towards the BLR due to dust extinction, computed from the broad-line flux
ratio of Pa$\beta$ (left) and Pa$\alpha$ (right) to H$\alpha$. Symbols are
plotted with the same color scheme as in Fig. 4. The 1:1 is shown in solid
gray.

####  5.2.2 H$\alpha$ line intensity suppression with $N_{H}$ in Sy 1.9

Rather than affecting the width of the H$\alpha$ broad line, increasing
obscuration might simply diminish the entire line intensity, and therefore the
flux, of the broad H$\alpha$. Such line suppression would preferentially
affect the rest-frame optical lines more than the NIR broad lines. Figure 7
investigates whether there is an increasing trend between the optical/NIR BLR
extinction and X-ray column obscuration. This correlation is only marginally
significant for the Pa$\alpha$ sample (p-value $\lesssim 0.05$), while it is
not significant for the He i and Pa$\beta$ (p-value $>$0.10 for both). We find
similar results employing the bootstrapping and point perturbation method with
the pymccorrelation package. This observed trend, though only weakly seen for
the Pa$\alpha$, is consistent with results from the BASS optical DR2 (Mejía-
Restrepo et al.,, submitted, see their Fig. 8), where the broad H$\alpha$ to
14-150 keV X-ray luminosity ratio shows a sharp decrease of $\lesssim$1 dex at
$N_{H}\gtrsim 10^{22}$ cm-2 for Sy 1.9 AGN, while this ratio remains rather
constant up to $N_{H}\approx 10^{23}$ cm-2 for Sy 1-1.5 types.

Figure 10: Ratio of the broad-line luminosities to the BAT 14-195 keV hard
X-ray luminosities, from left to right: H$\alpha$, He i, Pa$\beta$ and
Pa$\alpha$. The H$\alpha$ measurements are BASS targets with robustly detected
NIR and H$\alpha$ broad lines (the H$\alpha$+NIR is thus only a subsample of
the BASS DR2, see e.g., Mejía-Restrepo et al., submitted). Symbols are plotted
with the same color scheme as in Fig. 4, with the addition of Sy 2 as red
circles. The dashed areas show the average luminosity ratio (together with the
error on the mean) computed in two bins of $N_{H}$, low $N_{H}$ in green and
high $N_{H}$ in magenta (see text for more details). The filled squares are
the averages in quantiles of $\log N_{H}$ for Sy 1-1.5 (black) and Sy
1.8-1.9-2 (dark red), with bars reporting the error on the mean of the
luminosity ratio and the bin size in $\log N_{H}$.

Figure 11: The FWHM-$N_{H}$ plane for BASS AGN having reliable broad detected
NIR lines as reported in the labels. Symbols plotted as in Fig. 10.

A trend of increasing H$\alpha$ line suppression as a function of $N_{H}$
implies that $M_{BH}$ measurements based on the H$\alpha$ broad line
luminosity is biased in presence of obscuration. Figure 8 shows the ratio
between the virial (i.e., $f_{0}=1$) H$\alpha$-based BH mass,
[$M_{vir,H\alpha}=M_{vir}(FWHM(H\alpha),L_{H\alpha})$], and the virial
NIR+$L_{X}$-based BH mass for each NIR line,
[$M_{vir,line}=M_{vir}(FWHM(line),L_{X})$], as a function of the X-ray
obscuration (left) and broad lines flux ratios, used as proxy for the BLR
extinction (right). The difference between the BH mass estimates increases
with increasing obscuration and extinction, more prominently for Sy 1.9 AGN,
indicating that the H$\alpha$-based BH mass is biased low in presence of
obscuration. The trend expected if the NIR-based BH mass was underestimating
the true virial $M_{BH}$ at a given H$\alpha$-based BH mass would be positive
with increasing $N_{H}$ and increasing BLR extinction, while the opposite
trend is observed.

By dividing the sample in two bins of obscuring column and running a Student’s
T-statistic test on the values in the two bins, we find a statistically
significant decrement of $\Delta=0.23\pm 0.14$ ($0.44\pm 0.17$, $0.46\pm
0.13$) dex with p-value of $4\times 10^{-2}$ ($1.7\times 10^{-4}$, $1.3\times
10^{-3}$) in the BH mass difference between H$\alpha$ and He i (Pa$\beta$,
Pa$\alpha$) in the two groups at low and high $N_{H}$. There is a significant
bias when the H$\alpha$ broad line luminosity is used in SE BH mass estimates
in presence of obscuration $N_{H}>10^{21}$ cm-2, as can bee seen in the two
shaded bins in the left panels of Fig. 8 that report the average BH mass
difference in the $N_{H}$ bin together with the uncertainty on the mean.
Indeed the presence of a bias for the H$\alpha$-based BH masses can be seen in
the dashed black histogram of the BH mass differences, that are skewed to high
(negative) values.

When the same prescription is adopted to measure the optical BH masses, i.e.,
using the hard X-ray luminosity instead of the broad H$\alpha$ luminosity as a
proxy of the BLR radius (see the red stars for Sy 1.9), the difference between
the BH masses derived in the optical and NIR is consistent with scatter around
zero offset (see red solid histograms in Fig. 8), with no obvious trend versus
obscuration or BLR extinction. Therefore, we can conclude that a mixed BH mass
estimate based on the hard X-ray luminosity, as put forward by Ricci et al.
(2017b, see also ), can overcome the biases due to extinction and obscuration
of the optical H$\alpha$ broad line in Sy 1.9 and in galaxy-dominated AGN,
where the UV/optical continuum emission can be diluted by the host starlight.
Whereas, as long as a broad line is reliably detected and the hard X-ray
luminosity is higher than what is expected from the emission coming from X-ray
binaries and hot extended gas in the host galaxy, the mixed BH mass estimator
can be used to get an unbiased BH mass measurement. We note that adopting
$L_{X}$ instead of the UV/optical luminosity may introduce a weak dependence
on $M_{BH}$ and/or $L_{Edd}$ (see Liu et al., 2021; Lusso et al., 2010, albeit
there is significant scatter in the correlations). However, the extremely
tight ($\sim$0.2 dex) non-linear $L_{X}$-$L_{UV}$ relation has been
extensively used to compute Hubble diagrams for quasars, after accounting for
flux-limit related biases and testing for additional systematics (Lusso et
al., 2020, and references therein). Further investigation on possible
$L_{Edd}$ dependencies will be addressed in a forthcoming paper (F. Ricci et
al. in prep).

###  5.3 Dust extinction toward the BLR and gas absorption in the X-rays

The central and right panels of Figs. 6 and 7 report the expected value of the
H$\alpha$/Pa$\beta$ and H$\alpha$/Pa$\alpha$ flux ratio for case B
recombination at $T=10^{4}$ K and $n=10^{6}$ cm-3 (Osterbrock & Ferland,
2006). We see a wide range of these ratios, with the Paschen lines ruling out
case B recombination in most of the X-ray obscured objects, (see also Soifer
et al., 2004; Glikman et al., 2006; Riffel et al., 2006; La Franca et al.,
2015).

If anyhow we assume that the Paschen lines respect the case B recombination,
we can use those broad-line flux ratios to quantify the amount of extinction
toward the BLR $A_{V}(BLR)$. Then we could check whether the decline by dust
extinction observed in Fig. 7 is consistent with the gas absorption, by
assuming the Galactic dust-to-gas ratio.

We compute the dust extinction toward the BLR $A_{V}(BLR)$ following Domínguez
et al. (2013, see their Eq. 3): we assumed the reddening curve $k(\lambda)$
from Calzetti et al. (2000), and that the relationship between the nebular
emission line color excess and the Paschen-to-H$\alpha$ decrement is given by

$\begin{split}E(B-V)&=\frac{E(H\alpha-
Pa)}{k(\lambda_{H\alpha})-k(\lambda_{Pa})}=\\\
&=\frac{2.5}{k(\lambda_{H\alpha})-k(\lambda_{Pa})}\log\left[\frac{(Pa/H\alpha)_{obs}}{(Pa/H\alpha)_{case\,B}}\right]\end{split}$
(7)

where $E(H\alpha-Pa)$ is the $E(H\alpha-Pa\beta)$ and $E(H\alpha-Pa\alpha)$
excess, the $k(\lambda_{H\alpha})$ and $k(\lambda_{Pa})$ are the Calzetti et
al. (2000) reddening curve evaluated at the H$\alpha$, Pa$\beta$ and
Pa$\alpha$ wavelengths and (Pa/H$\alpha$) are the broad-line flux ratio
Pa$\beta$/H$\alpha$ and Pa$\alpha$/H$\alpha$. We also assume that
$A_{V}(BLR)=3.1\times E(B-V)$. We then calculate the $A_{V}(N_{H})$ from the
Galactic dust-to-gas ratio, $N_{H}/A_{V}=2.69\times 10^{21}$ cm-2 (Nowak et
al., 2012). The comparison between the two independent $A_{V}$ estimates is
presented in Fig. 9. Figure 9 shows a separation with Seyfert subclasses: most
of the Sy 1s lie above the 1:1, thus the $A_{V}(N_{H})$ is somewhat
underestimating the BLR extinction, whereas Sy 1.9s have $A_{V}(BLR)\sim 1-5$
and their $A_{V}(BLR)$ are mostly below the 1:1, thus the $A_{V}$ derived from
dust extinction is less than what is expected from gas absorption. This result
is in agreement with what has been found in Shimizu et al. (2018, see, their
Fig. 3), where the $A_{V}(BLR)$, estimated from the broad H$\alpha$-to-hard X
luminosity ratio, in Sy 1.9 is lower than what is expected from the Galactic
dust-to-gas ratio, particularly for $A_{V}(BLR)>3$. We note that we adopt a
single Galactic dust-to-gas ratio of $2.69\times 10^{21}$ cm-2, while in the
literature it spans a range from $1.79\times 10^{21}$ cm-2 (Predehl & Schmitt,
1995) to the value we assume. Furthermore, there is evidence that in AGN the
dust-to-gas ratio is not Galactic (Maiolino et al., 2001). If we adopt the
average dust-to-gas ratio from Maiolino et al. (2001), e.g., $1.1\times
10^{22}$ cm-2, then the derived $A_{V}(N_{H})$ would be a factor
$1.1/0.269\simeq 4.1$ smaller than what is shown in Fig. 9.

Figure 9 suggests that the extinction towards the BLR and line-of-sight X-ray
$N_{H}$ are distinct, i.e. they are due to separate obscuration medium. This
difference might arise because the BLR extinction is a “global” diffuse
measurement while the $N_{H}$ is a more “local” line-of-sight measurement, or
if there is gas within the BLR. Alternatively, it might suggest that the dust-
to-gas ratio is somehow different from the Galactic value for BASS AGN. Given
the large spread in Galactic dust-to-gas ratio and the uncertainty in what is
the $A_{V}/N_{H}$ in AGN environments, we cannot distinguish between these two
possibilities.

###  5.4 Near-infrared line suppression with obscuration in Sy 1.8-1.9-2
types?

We might then ask whether the same effect of line luminosity suppression is
similarly experienced by Paschen and helium lines in the NIR as observed for
the broad H$\alpha$ line. Figure 10 shows the ratio of the broad H$\alpha$
(left) and NIR emission lines to the BAT 14-195 keV hard X-ray luminosity as a
function of the X-ray column density for all BASS targets with reliable NIR
broad-line detections and with available $N_{H}$. There is a decreasing trend
of the NIR to X-ray luminosity ratio with increasing X-ray obscuration, as
similarly observed for the H$\alpha$. Binning the data in quantiles of $\log
N_{H}$ and splitting the sample into Sy 1-1.5 (black squares) and Sy 1.8-1.9-2
(dark red squares), Sy 1-1.5 AGN exhibit a roughly constant average
$L(line)/L_{X}$ across the $N_{H}$ range probed by our sample, while the
$L(line)/L_{X}$ of Sy 1.8-.9-2 types seems to decrease as $N_{H}$ grows. This
effect seems particularly more prominent at shorter wavelengths. Running a
Student’s T-statistic test we find a statistically significant decrement of
$\Delta=0.54\pm 0.15$ ($0.54\pm 0.12$, $0.46\pm 0.14$, $0.27\pm 0.12$) dex
with p-value of $6.8\times 10^{-6}$ ($4.9\times 10^{-5}$, $2.1\times 10^{-3}$,
$3.3\times 10^{-2}$) in the H$\alpha$ (He i, Pa$\beta$, Pa$\alpha$) to hard
X-ray luminosity ratio between the two groups divided at $\log(N_{H}/\rm
cm^{-2})=21.25$ (21.75, 21.45, 21.85), as can be seen in the two shaded
rectangles in Fig. 10 that report the average luminosity ratio in the two
$N_{H}$ bins together with the uncertainty on the mean. The decrement observed
in the H$\alpha$ to X-ray luminosity can explain the bias observed in Fig. 8.
We note that the decrement in the H$\alpha$ to X-ray luminosity happens at a
column density level that is slightly lower than what observed in the other
NIR lines, which might be explained considering that dust attenuation
diminishes when moving to longer wavelengths. Near-infrared line luminosity,
when available, should be preferred to the H$\alpha$ broad line luminosity as
a proxy for the BLR radius when estimating $M_{BH}$ using single-epoch
techniques.

Figure 12: Histograms of the normalized virial factor $f/f_{0}$, i.e. BH mass
deviation $M_{BH,\sigma_{\star}}/M(line)$, for each line subsample, as labeled
in each panel. Total sample in black, Sy 1-1.5 in blue, Sy 1.8 in cyan, Sy 1.9
in orange and Sy 2 in red. The shaded area defines the $IQR$, that is the
region enclosing the 25th to the 75th percentile of the total distribution.
The 50th percentile is overplotted with a solid green vertical line.

Finally, the last question we ask is the following: is NIR really penetrating
into the BLR or is the NIR BLR velocity estimate as good as the H$\alpha$
(e.g., see Figs. 4, 5 and 6) just because both are biased in the same way with
increasing column density? Figure 11 can help address this, showing the
FWHM-$N_{H}$ plane for all the BASS Sy AGN having reliable NIR broad line
detection and available $N_{H}$. The H$\alpha$ BLR velocity estimate is also
reported for the subsample of the optical BASS DR2 with $N_{H}$ and both NIR
and H$\alpha$ reliable broad-line detections. When binning in quantiles in
$\log N_{H}$, the average FWHM measured in the NIR in Sy 1.8-1.9-2 remains
quite constant across the $N_{H}$ range, with only a slight decrease in the
highest $N_{H}$ bin ($\log(N_{H}/\rm{cm}^{-2})\gtrsim 23.5$); the error bars
are fully consistent with a constant trend versus obscuration. This behaviour
is in agreement with the results presented in Onori et al. (2017b), who used a
much smaller sample of local hard X-ray BAT selected obscured AGN (N=17). Also
among Sy 1-1.5 types the average FWHM is rather constant, given the
uncertainties, until $\log(N_{H}/\rm{cm}^{-2})\simeq 22$, while in the last
$N_{H}$ bin there is an upturn. We note that a similar behaviour is observed
as well in the optical BASS DR2 in the FWHM(H$\beta$) - $N_{H}$ plane (see,
Fig. 9 of Mejía-Restrepo et al., submitted). This upturn behaviour in Sy 1-1.5
might be related just to small sample statistics, since type 1 AGN with high
$N_{H}$ are quite rare. However taken at face value, we can speculate that it
might be related to a transition in Sy type when the FWHM is smaller than 4000
${\rm km\,s}^{-1}$and $N_{H}\gtrsim 10^{22}$ cm-2. At high X-ray columns and
high inclinations, the optical photons might in some cases still find their
way through the obscuring medium by experiencing multiple scatterings. If this
hypothesis were plausible, the fraction of optical polarized light in this
particular sample of Sy 1 with high $N_{H}$ should be higher than what is
usually found in normal Sy.

From Figs. 10-11 we conclude that 1) the H$\alpha$ and near-infrared FWHMs are
not affected by obscuration, at least up to $\log(N_{H}/\rm{cm}^{-2})\approx
23.5$, and 2) the near-infrared line luminosities are not as strongly
extincted as the H$\alpha$ and can be used in SE BH mass measurements until
$\log(N_{H}/\rm{cm}^{-2})\approx 21.5-22$, depending on the specific line
chosen.

###  5.5 The virial factor $f$

We finally verify if the BH mass estimates obtained from two independent
methods, i.e., the NIR+$L_{X}$ based BH mass $M(line)$ and the
$\sigma_{\star}$-based BH mass $M_{BH,\sigma_{\star}}$, are consistent and, if
not, what are the quantities possibly driving the difference.

Figure 13: Comparison of $M_{BH,\sigma_{\star}}$ vs $M(line)$ in BASS Sy AGN
color-coded according to the FWHM(line). The 1:1 relation is shown in solid
gray, with dashed gray lines indicating the intrinsic spread. The measurements
are evenly distributed around the one-to-one relation, with a clear gradient
in FWHM(line): objects with faster BLR velocities are preferentially below the
unity locus, while smaller FWHMs are mostly located above the 1:1 relation, in
all the lines examined.

The resulting sample is composed of 60, 37, 39 and 88 local BASS Sy having
optical $\sigma_{\star}$ (Koss et al.,, in prep.; Caglar et al.,, in prep.)
and He i, Pa$\beta$, Pa$\alpha$ and $NIR$ robustly detected broad lines
available, respectively. We were able to gather optical $\sigma_{\star}$
measurements inside BASS DR2 for $\sim$62-68% of the sample with near-infrared
broad line detections, as there are only 30, 23, 24 and 41 sources without
available optical $\sigma_{\star}$ for the He i, Pa$\beta$, Pa$\alpha$ and
$NIR$ sample, respectively. We show in Fig. 12 the histograms of the
normalized virial factor $f/f_{0}$ which is basically the ratio
$M_{BH,\sigma_{\star}}/M(line)$. Each panel reports the distribution of
$f/f_{0}$ separately for each line subsample, color coded according to the Sy
classification as shown in the legend. The vertical green line marks the 50th
percentile, and the shaded area encloses the 25th to 75th percentiles of the
whole sample (black histogram), also known as interquartile range $IQR$. The
histograms are all roughly centered around 0, meaning that the normalized
virial factor is of the order of unity, with a distribution ranging from -1 to
1. Some sources show high $f/f_{0}$ values, e.g., $1<\log f/f_{0}<2$ and
$-2<\log f/f_{0}<-1$ , being considered as outliers. These sources have the
ratio of BH masses deviating from each other more than one order of magnitude.
We discuss the possible reasons why these sources are outliers in Appendix B.
In all the subsequent analysis and plots, these most deviating objects are
reported as black crosses, and are omitted when performing linear regression
fits. Table 9 lists the broad line measurements of the samples and ancillary
quantities.

Figure 14: Comparison between the offset $M_{BH,\sigma_{\star}}/M(line)$,
i.e., the normalized virial factor $f/f_{0}$, as a function of: (left)
redshift, color-coded with $M_{BH,\sigma_{\star}}$; (center) $N_{H}$, color-
coded according to $M(line)$; (right) $M(line)$, color-coded according to the
$N_{H}$ (when available, if not available the symbols are gray asterisks). The
row shows the sample of each line, from the top: He i; Pa$\beta$; Pa$\alpha$;
average $NIR$. The color of the outer circle labels different Sy classes, as
reported in the legend. Black crosses mark outliers. Black solid lines refer
to log-log linear best-fit regressions, with relative 68% c.l. in green.
Pearson correlation coefficients $r$ are reported in the lower left of each
panel, see also Tab. 3.

In Fig. 13 we compare $M_{BH,\sigma_{\star}}$ and $M(line)$. The panels show
separately the BH mass comparison for each reliably detected line, e.g., He i
(top-left panel), Pa$\beta$ (top-right panel), Pa$\alpha$ (bottom-left panel),
and for the average $NIR$ FWHM (bottom-right panel). The sample is divided
according to Sy classification. Each panel also shows the sample color-coded
according to the measured broad FWHM of each considered line. The measurements
are evenly distributed around the 1:1 relation (solid gray line in Fig. 13)
with some intrinsic scatter of $\sim 0.4-0.57$ dex (marked with dashed lines
in the figure).

As can be seen from the color gradient in Fig. 13, some of the scatter between
$M_{BH,\sigma_{\star}}$ and $M(line)$ estimates might be driven by the
observed FWHM; smaller FWHMs (lighter pink) are located above the 1:1 locus
while broader lines (darker red) are below it. This difference in the BH mass
estimates, i.e., the virial factor $f$, is expected in case the FWHM gets
broadened with inclination (see, e.g., Collin et al., 2006; Decarli et al.,
2008; Shen & Ho, 2014; Mejía-Restrepo et al., 2018).

We now investigate whether the scatter between the two different mass
estimates depends on additional variables by examining the ratio between the
two mass estimates, $M_{BH,\sigma_{\star}}/M(line)$, as a function of either
redshift (left panels in Fig. 14), X-ray column $N_{H}$ (center panels in Fig.
14) or BH mass estimate based on the virial assumption $M(line)$ (right panels
in Fig. 14). In all panels, the solid gray line shows the 1:1 zeropoint and
the dashed gray lines are indicating the $\pm 1\sigma$ scatter computed
earlier. Color bars in each panel shows the values of $M_{BH,\sigma_{\star}}$
(left), $M(line)$ (center) and column density $N_{H}$ (right) when available.
The rows in Fig. 14 show $f/f_{0}$ for each line sample, respectively, from
top to bottom: He i, Pa$\beta$, Pa$\alpha$ and average $NIR$. In order to
quantify the presence of possible correlations between $f/f_{0}$ and other
physical quantities, we perform a forward regression Bayesian fit as outlined
in Eq. 6, where $x$ is either redshift, column density or the NIR+$L_{X}$
virial-based BH mass estimate $M(line)$ and $y/y_{0}$ is $f/f_{0}$. Table 3
reports the best-fit parameters obtained using the IDL routine linmix_err, and
solid black lines in Fig. 14 show the log-log linear best fit regression with
1$\sigma$ c.l. In each panel the Pearson correlation coefficient is also
reported.

Table 3: Best fit log-log linear regression as outlined in Eq. 6.

Sample | $\log z$ |
---|---|---
| $\alpha$ | $\beta$ | r | P(r) | p-value ($\beta\neq$ 0) |
(1) | (2) | (3) | (4) | (5) | (6) |
He i | -0.02$\pm$0.29 | -0.09$\pm$0.19 | -0.14 | 3.1E-01 | 6.3E-01 |
Pa$\beta$ | -0.38$\pm$0.34 | -0.22$\pm$0.20 | -0.16 | 3.5E-01 | 2.6E-01 |
Pa$\alpha$ | 0.08$\pm$0.32 | 0.06$\pm$0.21 | 0.065 | 6.9E-01 | 7.6E-01 |
$NIR$ | -0.13$\pm$0.23 | -0.16$\pm$0.15 | -0.12 | 2.6E-01 | 2.9E-01 |
Sample | $\log\dfrac{N_{H}}{10^{22}~{}{\rm cm^{-2}}}$ |
| $\alpha$ | $\beta$ | r | P(r) | p-value ($\beta\neq$ 0) |
(1) | (2) | (3) | (4) | (5) | (6) |
He i | 0.171$\pm$0.071 | 0.127$\pm$0.065 | 0.29 | 5.6E-02 | 5.5E-02 |
Pa$\beta$ | -0.003$\pm$0.081 | -0.060$\pm$0.081 | -0.16 | 3.6E-01 | 4.7E-01 |
Pa$\alpha$ | -0.084$\pm$0.084 | -0.014$\pm$0.079 | -0.062 | 7.3E-01 | 8.6E-01 |
$NIR$ | 0.104$\pm$0.058 | 0.031$\pm$0.054 | 0.066 | 5.9E-01 | 5.7E-01 |
Sample | $\log\dfrac{M(line)}{10^{7.5}~{}M_{\odot}}$ |
| $\alpha$ | $\beta$ | r | P(r) | p-value ($\beta\neq$ 0) | p-value ($\beta\neq$ -1)
(1) | (2) | (3) | (4) | (5) | (6) | (7)
He i | 0.202$\pm$0.066 | -0.31$\pm$0.11 | -0.35 | 7.3E-03 | 6.3E-03 | 6.8E-08
Pa$\beta$ | 0.031$\pm$0.078 | -0.16$\pm$0.12 | -0.25 | 1.4E-01 | 1.8E-01 | 5.6E-08
Pa$\alpha$ | 0.053$\pm$0.083 | -0.20$\pm$0.12 | -0.28 | 8.9E-02 | 9.7E-02 | 4.0E-08
$NIR$ | 0.187$\pm$0.053 | -0.297$\pm$0.088 | -0.34 | 1.5E-03 | 1.2E-03 | 9.7E-12

††footnotetext: Columns are: (1) sample of each line; (2-3) the zero point and
slopes of the best-fit relations; (4-5) the Pearson correlation coefficients
with the related probability; (6) the probability of the slople being
different from zero; (7) same test with the null hypothesis of $\beta=-1$,
carried out only for the $f/f_{0}$ vs $M(line)$ correlation.

At fixed aperture, with increasing redshift a bigger part of the host (bulge)
is sampled in 1D spectra, possibly producing an increase on the measured
stellar velocity dispersion and therefore an enhancement of
$M_{BH,\sigma_{\star}}$, particularly relevant in late-type systems (Falcón-
Barroso et al., 2017). The BAT AGN are typically found in massive spirals with
strong bulges (with high concentration index) in between spirals and
ellipticals (Koss et al., 2011). As such, the aperture corrections go in
different directions and it is not straightforward to determine what is the
appropriate aperture correction to apply (this issue is further explored by
Caglar et al.,, in prep.). Moreover, line-of-sight velocity dispersion could
be broadened due to the disc rotation (Bennert et al., 2011; Har et al., 2012;
Kang et al., 2013; Caglar et al., 2020), and this effect should be higher
outside the spheroid. In the left panels of Fig. 14 we can see that there is
no strong gradient of $M_{BH,\sigma_{\star}}$ along the $x$-axis, while there
is some gradient along the $y$-axis, meaning that at each redshift there is a
range of measured $M_{BH,\sigma_{\star}}$. This implies that
$M_{BH,\sigma_{\star}}$ has a negligible dependence on redshift. As a matter
of fact, the log-log relation (solid black line) has always a flat slope in
all cases consistent with zero (see Tab. 3) and there is no clear correlation
between $f/f_{0}$ and redshift. Therefore we can conclude that aperture
effects are most probably not important for this sample. As a matter of fact,
the optical slit width is typically $\approx 1\farcs 5$ in BASS DR2, and at
$z=0.1$ the sampled region would be of $1.85$ kpc/arcsec $\times 1\farcs
5\simeq 2.8$ kpc. The average effective radius in SDSS late-type galaxies (Sa,
Sb, Sc) is $\sim$2.7 kpc (Oohama et al., 2009), therefore the spectral
extraction would still be roughly within the bulge or spheroid, even at the
highest redshift probed in this work.

If obscuration was biasing the NIR+$L_{X}$ virial-based BH masses, the sample
should exhibit a gradient with $M(line)$ as a function of the X-ray column,
and also we should see a positive correlation between the $f/f_{0}$ and the
column density. Our sample shows at most the opposite behaviour, a mild anti-
correlation between $f/f_{0}$ and $N_{H}$, and no clear gradient in $M(line)$
at increasing $N_{H}$ (center panels in Fig. 14). The derived best-fit
relations cannot be statistically distinguished from a relation with a zero
slope, thus again there is no statistical evidence for a dependence with X-ray
obscuration. This is indeed not surprising since we show in Sect. 5.4 that the
FWHM measured from NIR lines is not affected by obscuration until high X-ray
column densities $\log(N_{H}/\rm{cm}^{-2})\gtrsim 23.5$.

Finally, we explore whether there is an anti-correlation between $f/f_{0}$ and
$M(line)$, which could be inherited by the adopted definition of $f$, such
that $f\propto M(line)^{-1}$ (we recall that $M(line)=f_{0}\times
M_{vir,line}$, see Sect. 4.2). The right panels in Fig. 14 show that indeed
there is an anti-correlation, but the best-fit slopes are always flatter than
$-1$. The correlations between $f$ and $M(line)$ are statistically different
from the $-1$ slope expected simply by definition (see Tab. 3, p-value
$<7\times 10^{-8}$), while the statistical dependence is significantly
different from a zero slope only in the He i and $NIR$ cases. Similar
conclusions are reached when boostrapping and point perturbation analysis are
adopted. We note that this $f-M(line)$ mild anticorrelation might as well be
driven by a more fundamental relation with the FWHM, since $M(line)\propto
FWHM(line)^{2}$, and already from Fig. 13 it is evident that there is a
dependency of the scatter between the two $M_{BH}$ estimates and FWHM. A
thorough investigation of the $f-FWHM$ dependence will be carried out in a
separate publication (F. Ricci et al. in prep.).

##  6 Discussion and Conclusions

In this work we present 0.8–2.5 $\mu$m NIR spectroscopic observations of 65
local BASS selected AGN obtained at Magellan/FIRE, splitted into 13 Sy 1-1.5
and 52 Sy 1.8-1.9-2 types. We fit four NIR spectral regions (0.9-0.96 $\mu$m,
1.04-1.15 $\mu$m, 1.15-1.30 $\mu$m, and 1.80-2.00 $\mu$m) to study the most
characteristic NIR BLR properties, i.e., the BLR velocities and radii,
estimated from the most prominent NIR hydrogen (Pa$\alpha$ and Pa$\beta$) and
helium (He i10830Å) transitions. We combine our NIR FIRE sample with the whole
BASS NIR database (DR1; Lamperti et al., 2017, and DR2; den Brok et al.,
submitted), finding NIR broad emission lines in 64/235 Seyferts 1.8-1.9-2. The
results of this analysis confirm the possibility of using the NIR band to
deeper probe the BLR conditions also in optical narrow-line AGN. The line
showing the highest success rate of broad-line detection in reddened Seyferts
is He i (43/235), followed by Pa$\alpha$ (24/235) and Pa$\beta$ (20/235),
suggesting a possible correlation between the NIR line intensity and the
higher ability of isolating faint BLR components reliably in Sy 1.8-1.9-2
types.

We then complement the NIR BLR view with the one obtained from the optical,
namely the H$\alpha$, from BASS DR2 (Mejía-Restrepo et al.,, submitted). In
this way we constructed the largest NIR sample of hard X-ray selected local Sy
having robust ancillary data available from BASS. In terms of $\mathbf{L_{X}}$
and $z$, our sample is representative of the BASS AGN sample, even though the
fraction of Seyfert types is not (in the BASS DR1 there is an equal portion of
Sy 1 and Sy 2; see, e.g., Koss et al., 2017), since our program was aimed at
detecting the BLR in the most elusive Seyferts 1.8-1.9-2 (235/314 objects,
$\approx$75%).

With this obscuration unbiased sample in hand, we investigate the presence of
possible systematics in the BLR characterisation taking advantage of the
X-ray, H$\alpha$ and NIR spectral information in Sy 1 up to Sy 1.9 (and Sy 2,
without the H$\alpha$ but with NIR broad line detection). We verify that the
FWHM measured from H$\alpha$ and NIR lines are consistent in Sy 1 up to Sy
1.9. The same results are found even when splitting the sample according to
the Sy subclassification. The H$\alpha$ and NIR FWHM broad line measurements
statistically describe the same velocity field in the BLR. Thus, once a broad
H$\alpha$ line is reliably detected, its FWHM is in agreement with the NIR
FWHM within some scatter ($\approx 0.10-0.15$ dex, depending on the specific
line). We then demonstrate that the H$\alpha$ and NIR BLR velocity estimates
are not significantly affected by neither obscuration nor BLR extinction, as
measured by the flux decrement of the broad H$\alpha$ flux to the NIR broad
line flux, at least until $\log(N_{H}/\rm{cm}^{-2})\approx 23$, as also
consistently found in the optical BASS DR2, where the FWHM(H$\alpha$)-$N_{H}$
distribution remains constant up to $\log(N_{H}/\rm{cm}^{-2})\approx 23$
(Mejía-Restrepo et al.,, submitted).

Rather than the H$\alpha$ FWHM, it is the entire H$\alpha$ broad line
intensity that gets suppressed with increasing obscuration, implying that the
optical H$\alpha$ photons are obscured by a uniform screen placed outside the
BLR. The ratio of broad H$\alpha$-to-NIR broad lines flux shows a mild
decreasing trend with $N_{H}$ for the Pa$\alpha$ sample, while the statistical
evidence is weaker for He i and Pa$\beta$. We quantify the amount of dust
extinction towards the BLR and the level of gas absorption measured in the
X-rays, finding a clear separation in Seyferts subclasses. This has been shown
already by several other works (Burtscher et al., 2016; Schnorr-Müller et al.,
2016; Shimizu et al., 2018). The comparison of two different $A_{V}$ estimates
suggests that either the material obscuring the BLR is distinct from the one
producing the absorption in the X-rays, or that the dust-to-gas ratio in local
hard X-ray selected AGN environments is not Galactic (see, e.g., Maiolino et
al., 2001). There are some limitations in the approach adopted to estimate the
$A_{V}(BLR)$, the most notable being the assumption of case B recombination,
which might not hold for Paschen lines (Soifer et al., 2004; Glikman et al.,
2006; Riffel et al., 2006; La Franca et al., 2015). Additionally, we stress
that the broad-line ratios Paschen-to-H$\alpha$, not only depend on dust
extinction but also on collisional effects (i.e., by the ionization parameter
$U$ and particle density $n$) taking place at the high densities of the BLR,
$10^{10-11}$ cm-3 (see, e.g., Schnorr-Müller et al., 2016). Therefore the
observed dispersion in broad line flux measurements is likely due to
collisional effects in addition to extinction.

We then explore if the line intensity suppression with increasing X-ray column
is similarly experienced by NIR line as found in the H$\alpha$. We find a
decrement in the broad lines to hard X-ray luminosity ratio of $0.54\pm 0.15$
dex for H$\alpha$, decreasing at longer wavelengths to $0.27\pm 0.12$ dex in
case of Pa$\alpha$, occurring at a level of obscuring column density
$\log(N_{H}/\rm cm^{-2})=$21.25 for H$\alpha$, moving to higher $N_{H}$ levels
going to longer wavelengths, up to $\log(N_{H}/\rm cm^{-2})=21.85$ for
Pa$\alpha$. The H$\alpha$ broad line intensity suppression with increasing
$N_{H}$ induce a bias in SE H$\alpha$-based BH masses of $\approx$0.2–0.45
dex, depending on the specific line chosen to compare the H$\alpha$ with. The
NIR line luminosity should be preferred to the H$\alpha$ line luminosities,
when available, to estimate $M_{BH}$ using single-epoch relations (Kim et al.,
2010; La Franca et al., 2015). Notwithstanding, in presence of substantial
obscuration $\log(N_{H}/\rm{cm}^{-2})\gtrsim 22$ the NIR line luminosity can
be underestimated, particularly in Sy 1.9-2. Thus to overcome these
shortcomings, it is preferable to use a more unbiased luminosity as proxy to
estimate the BLR radius, and a mixed NIR+$L_{X}$ approach as put forward by
Ricci et al. (2017b, see also, ) is a more unbiased estimate of the virial BH
mass. The NIR FWHMs seem as well to be much less susceptible to obscuration,
at least up to columns $\log(N_{H}/\rm{cm}^{-2})\approx 23.5$.

We finally evaluate the consistency between $\sigma_{\star}$-based (from the
optical BASS DR2, Koss et al.,, in prep.; Caglar et al.,, in prep.) and mixed
NIR+$L_{X}$ virial based BH mass estimates, finding that the two quantities
agrees within $\sim$0.4–0.57 dex scatter. The scatter expected in this case is
at least the combination of two factors: i) there is an inherent scatter in
the $M_{BH}-\sigma_{\star}$ relation of the order of 0.3 dex, and ii) the
intrinsic scatter of virial-based $M_{BH}$ estimates is $\simeq$0.4-0.5 dex.
Thus, combining the two log-normal contributions, the expected scatter is of
the order of 0.5-0.58 dex, which is consistent with what we find. We note
however that there are some works suggesting that the $M_{BH}-\sigma_{\star}$
intrinsic scatter might be higher if the host morphology is not properly taken
into account (e.g., Falcón-Barroso et al., 2017), thus we caution the reader
that the $M_{BH}$ based on $\sigma_{\star}$ for single BASS targets might be
characterised by a systematic uncertainty $>$0.3 dex (e.g., Gültekin et al.,
2009), as there is an inherent difficulty in applying morphology-based
corrections to the BAT AGN sample that is composed primarily by massive
spirals and lenticulars with strong bulges, with a high fraction of disturbed
mergers (Koss et al., 2010, 2011), adding further complexity to aperture
corrections for stellar kinematics.

The ratio of two independent BH mass estimates is here used to derive the
virial factor $f$, for the first time for a less biased sample, since we also
consider the Sy 1.8-1.9-2 showing BLR components in the NIR. The
BH-$\sigma_{\star}$ scaling relation adopted to derive $M_{BH,\sigma_{\star}}$
is the one proposed by Kormendy & Ho (2013) calibrated for elliptical and
classical bulges. Still, by normalizing the virial factor $f$ with the
ensemble virial factor $f_{0}$ we essentially minimize the effects due to the
choice of the BH-$\sigma_{\star}$ scaling relation. As long as the
BH-$\sigma_{\star}$ relation for pseudo-bulges and/or late-type galaxies
differ from the one of elliptical/classical-bulges by only a normalization
term, as it occurs for the $M_{BH}-\sigma_{\star}$ relation of pseudo-bulges
proposed by Ho & Kim (2014), the different normalization is absorbed in
$f_{0}$. If instead the $M_{BH}-\sigma_{\star}$ relation of pseudo-bulges or
late-type galaxies has a different slope than the one observed for classical-
bulges, then this effect is not absorbed in the $f_{0}$ normalization.

Examining the distributions of normalized virial factors $f/f_{0}$ divided
according to the Seyfert subclassification, our data do not show evidence of
different $M_{BH}$ between type 1 and type 2 AGN, as instead claimed by Onori
et al. (2017b) and Ricci et al. (2017c). These works used a small sample of
BAT-selected local Seyferts 1.8-1.9-2 with NIR broad lines and compare their
$M_{BH}$ to the well-known and best studied BAT-selected type 1 AGN with RM-
based BH masses. By matching type 1 and obscured Seyferts in hard X-ray
luminosity and stellar velocity dispersion they find that Sy 1.8-1.9-2 are
undermassive than RM AGN. This BH mass difference is mainly driven by small
sample statistics, since i) their small obscured Seyfert sample do not span
the same FWHM range of type 1, being limited to FWHM$\lesssim 3600$ ${\rm
km\,s}^{-1}$, and ii) the type 1 control sample is biased to higher FWHM,
having FWHM$\gtrsim 1600$ ${\rm km\,s}^{-1}$, while in this work, thanks to
the additional spectra obtained with FIRE and Xshooter, we much better
populate the FWHM-$L_{X}$ plane for both AGN populations.

Dependencies of the normalized virial factor $f/f_{0}$ with redshift,
obscuration and virial-based BH mass estimate have been explored, only finding
a mild dependency with $M(line)$. This mild anti-correlation might be actually
due to a more fundamental relation with the FWHM. Indeed, using a sample of
about 600 local SDSS optical broad line AGN, Shen & Ho (2014) show that the
virial factor, estimated as $M_{BH,\sigma_{\star}}/M(H\beta)$, is
anticorrelated with the FWHM(H$\beta$), and claim that this effect is a by-
product of the line broadening due to inclination of clouds moving in a disk-
like BLR (see, e.g., Collin et al., 2006). Similarly, an earlier attempt by
Decarli et al. (2008) demonstrated that there is an anticorrelation between
the virial factor $f$, computed as the ratio of the BH mass estimated from the
BH-bulge luminosity $M_{BH}-L_{bul}$ relation and the virial H$\beta$-based BH
mass, and the broad H$\beta$ FWHM, and this inclination effect might bias
single-epoch virial-based BH masses. At higher redshift, using accretion-disk
models to get a BH mass estimate independent of the virial assumption, Mejía-
Restrepo et al. (2018) have further demonstrated that this $f$-FWHM
anticorrelation is found not only for the H$\beta$ line but also in H$\alpha$,
Mg ii and C iv, and can be explained with inclination effects on the
measurements of the velocities of clouds moving in a thin disk BLR. We aim to
further investigate this possibility with a more detailed analysis on this
issue in a separate paper, exploring possible BLR parameters space consistent
with our data (F. Ricci et al. in prep.).

Our findings corroborate that the use of a mixed virial-based NIR BH mass
estimator gives a less biased view of the BLR properties, and that the use of
a single ensemble average virial factor $f_{0}$ for the whole AGN population,
might bias our understanding about the AGN demographics and evolution, since
we showed that $f$ is at least related (though weakly) to $M(line)$ in two
broad lines samples (He i and $NIR$ line data sets). Hopefully in the near
future, the astronomical community will take advantage of the James Webb Space
Telescope (JWST), that will essentially allow to explore the rest-frame NIR
properties of AGN and galaxies also at higher redshift. Indeed, the Pa$\beta$
line at $z\sim 2-3$ can be observed in the $1-5~{}\micron$ wavelength range
with NIRSpec on board JWST. Additionally, being a satellite, the limitations
due to ground-based observations will be overcome and more efficient NIR
observation will be carried out, opening the path to the construction of large
statistical samples of AGN with rest-frame NIR coverage at higher redshifts.

##  7 Summary

With the largest and least-biased sample of local hard X-ray selected AGN with
restframe NIR spectroscopy, we characterise three key BLR properties directly
related to virial-based BH mass measurements, i.e., the BLR velocity,
estimated from broad line widths FWHM, the average BLR radius, from broad line
and X-ray luminosities, and BLR geometry/dynamics, enclosed in the virial
factor $f$. Our findings are the following:

  1. 1.

the FWHMs measured from H$\alpha$ and NIR broad lines He i, Pa$\beta$ and
Pa$\alpha$ are consistent in Sy 1 up to Sy 1.9, within an intrinsic scatter of
0.10–0.15 dex, thus the optical and NIR statistically describe the same
velocity field in the BLR. Moreover, the FWHM measurements do not depend on
the level of BLR extinction or X-ray column density, at least up to
$\log(N_{H}/\rm cm^{-2})\approx 23.5$;

  2. 2.

the H$\alpha$ broad line luminosity gets suppressed with increasing
obscuration, with a decrement of 0.54$\pm$0.15 dex in the $L(H\alpha)/L_{X}$
ratio occurring at $\log(N_{H}/\rm cm^{-2})=$ 21.25 cm-2. This effect produce
a bias in SE H$\alpha$-based $M_{BH}$ when $N_{H}\gtrsim 10^{21}$ cm-2;

  3. 3.

the material obscuring the BLR is distinct from the one responsible of the
X-ray absorption, or the dust-to-gas ratio is not Galactic in hard X-ray
selected local Seyfert environments;

  4. 4.

NIR broad lines are suppressed with increasing obscuration, but the decrement
is smaller than the H$\alpha$ one ($0.54\pm 0.12$, $0.46\pm 0.14$ and $0.27\pm
0.12$ for $L({\rm He~{}\textsc{i}})/L_{X}$, $L(Pa\beta)/L_{X}$ and
$L(Pa\alpha)/L_{X}$, respectively) and occurs at slightly higher $N_{H}$
levels, $\log(N_{H}/\rm cm^{-2})=21.75$, 21.45 and 21.85 for He i, Pa$\beta$
and Pa$\alpha$, respectively. Even NIR broad line luminosities should not be
used in SE $M_{BH}$ estimates when $N_{H}\gtrsim 10^{22}$ cm-2, and a less
biased BLR radius proxy should be used, as the hard X-ray luminosity $L_{X}$;

  5. 5.

using two obscuration-unbiased BH mass estimates, one based on the
$\sigma_{\star}$ and the other based on the mixed near-infared+$L_{X}$ virial
mass, we show that the two BH mass measurements agree with each other with an
intrinsic scatter of 0.4–0.57 dex;

  6. 6.

we quantify the virial factors $f$ as the ratio of these two independent BH
mass measurements and verify that Sy 1 and Sy 1.8-1.9-2 types have the same
distribution of virial factors and that our virial factors are not biased with
$z$ or $N_{H}$ but show a mild anti-correlation with $M(line)$. This last
finding might be driven by a more fundamental anti-correlation with the
observed FWHM expected due to inclination effects.

We thank the anonymous referee for the useful comments that improved our
manuscript. FR thanks the LCO Instrument & Operations Support Specialists that
supported our runs at LCO using Magellan/FIRE, and in particular G. Prieto for
sharing the record of local weather data used to run the molecfit correction
on our FIRE observations. We acknowledge support from FONDECYT Postdoctorado
3180506 (FR) and 3210157 (ARL); from PRIN MIUR 2017 project “Black Hole winds
and the Baryon Life Cycle of Galaxies: the stone-guest at the galaxy evolution
supper”, contract #2017PH3WAT (FR); FONDECYT Regular 1190818 (ET,FEB) and
1200495 (FEB,ET); ANID grants CATA-Basal AFB-170002 (FR,ET,FEB); ANID Anillo
ACT172033 (ET); from Millennium Nucleus NCN19_058 TITANs (ET); and Chile’s
Ministry of Economy, Development, and Tourism’s Millennium Science Initiative
through grant IC12_009, awarded to The Millennium Institute of Astrophysics,
MAS (FEB); from NASA through ADAP award NNH16CT03C (MK); the ANID+PAI
Convocatoria Nacional subvencion a instalacion en la academia convocatoria año
2017 PAI77170080 (CR); from the State Research Agency (AEI-MCINN) and from the
Spanish MCIU under grant ”Feeding and feedback in active galaxies” with
reference PID2019-106027GB-C42 (PSB); from the Israel Science Foundation grant
number 1849/19 (BT); the National Research Foundation of Korea
(NRF-2020R1C1C1005462, KO); the Japan Society for the Promotion of Science
(JSPS, ID: 17321, KO); the Jet Propulsion Laboratory, California Institute of
Technology, under a contract with NASA.

##  Appendix A FIRE/Magellan broad line fit measurements

In this Sect. we list the spectral emission line fit measurements of the He i
and Pa$\gamma$ (Tab. 4), Pa$\beta$ (Tab. 5), and Pa$\alpha$ (Tab. 6) broad
lines for the whole FIRE/Magellan sample. The few cases in which additional
components in the Pa$\gamma$ or Pa$\alpha$ region were required are presented
in Tab. 7-8.

Table 4: Broad line measurements of the He i and Pa$\gamma$.

BAT ID | flag | noise | He i flux | Pa$\gamma$ flux | FWHM He i | FWHM Pa$\gamma$ |  $\Delta$v He i |  $\Delta$v Pa$\gamma$
---|---|---|---|---|---|---|---|---
|  |  |  |  | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$]
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
7 | 2 | 4.21E-17 |  $<$6.00 |  $<$2.59 |  |  |  |
10 | 2 | 1.12E-17 | 1.968$\pm$0.064 |  $<$0.65 | 7072$\pm$273 |  | -312$\pm$42 |
80 | 2 | 2.19E-16 |  $<$10.91 |  $<$5.14 |  |  |  |
118 | 2 | 1.42E-17 |  $<$0.69 |  $<$0.75 |  |  |  |
238 | 9 | 2.45E-17 |  $<$0.72 |  $<$0.79 |  |  |  |
262 | 4 | 3.88E-17 |  $<$4.61 |  $<$2.48 |  |  |  |
272 | 4 | 4.65E-17 | 0.92$\pm$0.37 | 1.238$\pm$0.082 | 1302$\pm$521 | 1289$\pm$203 | 1000$\pm$232 | 1000$\pm$232
305 | 2 | 3.75E-17 | 1.342$\pm$0.028 |  $<$2.44 | 1297.76$\pm$0.03 |  | -53.4$\pm$6.3 |
329 | 9 | 4.92E-17 |  $<$4.95 |  $<$15.78 |  |  |  |
372 | 3 | 2.91E-17 |  $<$4.55 | 7.44$\pm$0.78 |  | 11552$\pm$306 |  | 534$\pm$142

††footnotetext: Columns: (1) BAT ID, (2) quality fit flag, (3) noise measured
in the continuum in erg/cm2/s/Å, (4)-(6)-(8) He i flux (in units of 10-14
erg/cm2/s), FWHM and velocity shift, respectively, (5)-(7)-(9) Pa$\gamma$ flux
(in units of 10-14 erg/cm2/s), FWHM and velocity shift, respectively. Values
in columns (4) - (5) preceded by ‘$<$’ indicate upper limits. The upper limits
on the broad line fluxes have been computed using a FWHM=4200 ${\rm
km\,s}^{-1}$. (This table is available in its entirety in a machine-readable
form in the online journal. A part is shown as guidance for the reader
regarding its content.)

Table 5: Broad line measurements of the Pa$\beta$.

BAT ID | flag | noise | Pa$\beta$ flux | FWHM Pa$\beta$ |  $\Delta$v Pa$\beta$
---|---|---|---|---|---
|  |  |  | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$]
(1) | (2) | (3) | (4) | (5) | (6)
7 | 4 | 3.50E-17 |  $<$17.87 |  |
10 | 9 | 9.81E-18 |  $<$13.43 |  |
80 | 4 | 1.20E-16 |  $<$2.79 |  |
118 | 9 | 1.67E-17 |  $<$0.51 |  |
238 | 9 | 1.54E-15 |  $<$3.00 |  |
262 | 9 | 3.56E-17 |  $<$1.78 |  |
272 | 2 | 4.82E-17 | 5.549$\pm$0.019 | 1750$\pm$10 | -28.9$\pm$3.5
305 | 1 | 3.52E-17 |  $<$3.40 |  |
329 | 9 | 6.91E-17 |  $<$2.29 |  |
372 | 3 | 4.26E-17 |  $<$3.33 |  |

††footnotetext: Columns: (1) BAT ID, (2) quality fit flag, (3) noise measured
in the continuum in erg/cm2/s/Å, (4)-(5)-(6) Pa$\beta$ flux (in units of 10-14
erg/cm2/s), FWHM and velocity shift, respectively. Values in columns (4)
preceded by ‘$<$’ indicate upper limits. The upper limits on the broad line
fluxes have been computed using a FWHM=4200 ${\rm km\,s}^{-1}$(5). (This table
is available in its entirety in a machine-readable form in the online journal.
A part is shown as guidance for the reader regarding its content.)

Table 6: Broad line measurements of the Pa$\alpha$.

BAT ID | flag | noise |  Pa$\alpha$ flux |  FWHM Pa$\alpha$ |  $\Delta$v Pa$\alpha$
---|---|---|---|---|---
|  |  |  |  [${\rm km\,s}^{-1}$] |  [${\rm km\,s}^{-1}$]
(1) | (2) | (3) | (4) | (5) | (6)
7 | 2 | 1.52E-17 |  $<$10.65 |  |
10 | 3 | 6.40E-18 | 1.69 |  8590$\pm$61 | -1000
80 | 4 | 1.89E-17 |  $<$3.41 |  |
118 | 2 | 7.97E-18 |  $<$1.00 |  |
238 | 2 | 1.52E-17 |  $<$1.91 |  |
262 | 2 | 1.49E-17 |  $<$3.18 |  |
272 | 4 | 6.93E-17 | 21.81 |  2419$\pm$10 |  7.1$\pm$2.5
305 | 2 | 1.25E-17 |  1.51$\pm$0.013 |  1527$\pm$27 |  31.2$\pm$7.2
329 | 4 | 2.78E-17 |  $<$5.49 |  |
372 | 3 | 9.86E-18 |  7.667$\pm$0.024 |  11907$\pm$32 | -1000

††footnotetext: Columns: (1) BAT ID, (2) quality fit flag, (3) noise measured
in the continuum in erg/cm2/s/Å, (4)-(5)-(6) Pa$\alpha$ flux (in units of
10-14 erg/cm2/s), FWHM and velocity shift, respectively. Values in columns (4)
preceded by ‘$<$’ indicate upper limits. The upper limits on the broad line
fluxes have been computed using a FWHM=4200 ${\rm km\,s}^{-1}$. (This table is
available in its entirety in a machine-readable form in the online journal. A
part is shown as guidance for the reader regarding its content.)

Table 7: Additional Gaussian component of the He i in the Pa$\gamma$ spectral
region.

BAT ID | flag | He i flux | FWHM He i |  $\Delta$v He i
---|---|---|---|---
|  |  | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$]
(1) | (2) | (3) | (4) | (5)
372 | 3 | 2.86 | 1957 | 277
488 | 3 | 2.880$\pm$0.059 | 1627.1$\pm$0.03 | -324.6$\pm$6.2
577 | 3 | 0.31$\pm$0.22 | 735$\pm$186 | -397$\pm$16
698 | 3 | 0.13$\pm$0.0020 | 856$\pm$13 | -993.3$\pm$4.2
744 | 2 | 4.425$\pm$0.062 | 3463$\pm$44 | 238$\pm$10
1064 | 2 | 7.97$\pm$0.64 | 1212$\pm$270 | -364$\pm$22
1079 | 2 | 7.432$\pm$0.027 | 1008.8$\pm$3.1 | -287.3$\pm$1.4

††footnotetext: Columns: (1) BAT ID, (2) quality fit flag (same as in Tab. 4),
(3)-(4)-(5) flux (in units of 10-14 erg/cm2/s), FWHM and velocity shift of the
additional Gaussian component in the He i. These components were not used to
measure the virial black hole masses.

Table 8: Additional Gaussian component of in the Pa$\alpha$ spectral region.

BAT ID | flag | Pa$\alpha$ flux | H2 a flux | H2 b flux | FWHM Pa$\alpha$ | FWHM H2 a | FWHM H2 b |  $\Delta$v Pa$\alpha$ |  $\Delta$v H2 a |  $\Delta$v H2 b
---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$] | [${\rm km\,s}^{-1}$]
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
372 | 3 | 1.609$\pm$0.014 |  |  | 3017.48$\pm$0.05 |  |  | 593.3$\pm$5.4 |  |
1079 | 4 | 0.73$\pm$0.24 | 2.599$\pm$0.013 | 0.642$\pm$0.011 | 299.45$\pm$0.01 | 2974.68 | 29758 | -148.25$\pm$8.9 | -453.62$\pm$6.86 | -999

††footnotetext: Columns: (1) BAT ID, (2) quality fit flag (same as in Tab. 6),
(3)-(6)-(9) flux (in units of 10-14 erg/cm2/s), FWHM and velocity shift of the
additional gaussian component in the Pa$\alpha$, respectively, (4)-(7)-(10)
flux (in units of 10-14 erg/cm2/s), FWHM and velocity shift, of the H2 a, i.e.
H2 $\lambda$18345Å, and (5)-(8)-(11) flux (in units of 10-14 erg/cm2/s), FWHM
and velocity shift of the H2 b, i.e. H2 $\lambda$18920Å. These additional
Pa$\alpha$ components were not used to measure the virial black hole masses.

##  Appendix B $f/f_{0}$ outliers

There are some targets showing an outlier nature in the $f/f_{0}$
distributions that have been omitted in our analysis. These sources are five
in total, namely: IDs 670, 677, 1131, 1465 and 1470. The outliers are mostly
(4/5) located above the 1:1 line in Fig. 13, meaning that either the
$M_{BH,\sigma_{\star}}$ is overestimated, or that the NIR BH mass is
underestimated. The former case would indicate that the measured optical
stellar velocity dispersion is unreliable for those sources, due to AGN
contamination of the stellar absorption features, aperture effects or to host
galaxy rotation contamination, while the latter case would happen if there is
substantial obscuration along the line of sight, such that the highest
velocity clouds of the BLR are not observable, being embedded in some
obscuring medium. These four outliers are IDs 670, 1131, 1465 and 1470.

For BAT IDs 670, 1131, 1465 and 1470 the NIR+$L_{X}$ based BH mass is somehow
underestimated. Those are part of the NIR DR2 (den Brok et al.,, submitted):
those NIR spectra show only broad He i line, as Pa$\alpha$ is located in a
heavily affected telluric region and Pa$\beta$ is only detected, marginally,
as a narrow line. All the other higher-order Paschen lines are missing as
well. For ID 670, the broad He i transition might not be (fully) tracing the
BLR, since a blueshifted outflow in the [O iii] has been detected, with
$v_{max}=1072^{+80}_{-990}$ ${\rm km\,s}^{-1}$ (Rojas et al., 2020).

For IDs 1131, 1465 and 1470 (Sy 1.8, 2 and 2, respectively), such information
is not available since they were not part of the sample studied in Rojas et
al. (2020). However, the optical BASS DR2 spectrum of BAT 1131 appears to have
some ionized outflows in the [O iii], as the residuals from a single Gaussian
fit are rather prominent, blueshifted and asymmetric. Therefore the broad
component detected in the He i might not be describing the BLR. Additionally,
this source, a Sy 1.8, is particularly AGN-dominated in the optical spectrum,
making the stellar velocity dispersion measurement a bit tricky.

Finally, we note that for ID 1470 the Galactic extinction is fairly important,
$E(B-V)=0.48$ (corresponding to an $A_{J}=0.354$ mag according to the IRSA
dust database151515https://irsa.ipac.caltech.edu/applications/DUST/), while
for 1465 is quite relevant, $E(B-V)=3.03$ ($A_{J}=2.150$ mag according to the
IRSA database), probably affecting the NIR spectrum measurement.

One source is instead located below the 1:1 relation, at $\log f/f_{0}<-1$,
namely BAT 677. In this case, the NIR+$L_{X}$ based $M(line)$ (e.g.,
$M(NIR)=10^{7.140\pm 0.023}$ M⊙) is about two orders of magnitude higher than
the $\sigma_{\star}$-based BH mass estimate (e.g.,
$M_{BH,\sigma_{\star}}=10^{5.47\pm 0.29}$ M⊙). BAT 677 is part of the FIRE
sample, and has a good Pa$\beta$ fit (FWHM=2401$\pm$8 ${\rm km\,s}^{-1}$, fit
quality 2). The $M_{BH,\sigma_{\star}}$ is computed from a rather small
velocity dispersion measurement $\sigma_{\star}=41\pm 5$ ${\rm km\,s}^{-1}$
performed on the CaT region. We note that the BH-$\sigma_{\star}$ relation is
not calibrated for $\sigma_{\star}<65$ ${\rm km\,s}^{-1}$, thus extrapolating
to such low velocity dispersion might introduce a higher error budget on the
$M_{BH,\sigma_{\star}}$ estimation. We finally note that if instead of
$\sigma_{\star}=41$ we adopt $\sigma_{\star}=68$ ${\rm km\,s}^{-1}$, as
measured from the Ca ii and Mg i absorptions, the resulting
$M_{BH,\sigma_{\star}}$ is about an order of magnitude higher
($M_{BH,\sigma_{\star}}=10^{6.44\pm 0.20}$ M⊙) and it is more consistent with
the virial NIR+$L_{X}$ based estimate.

Therefore, for the former four sources the NIR+$L_{X}$ based $M(line)$ is not
reliable, either due to the possible presence of outflows in ionized material
disguised as BLR components (670, also possibly 1465 and 1470) or high
Galactic extinction in our line of sight (1465, 1470). For BAT 1131 both the
$\sigma_{\star}$ and the NIR measurements are not trustable, for strong AGN
contamination in the optical spectrum and for possible outflows in ionized
material. Finally for BAT 677 the $M_{BH,\sigma_{\star}}$ is more uncertain
being located in the low-velocity dispersion extrapolation of the
BH-$\sigma_{\star}$ scaling relation.

Table 9: Physical properties of the sample having both NIR reliable broad line
detection and optical stellar velocity dispersion measurements available
inside BASS.

BAT ID | Sy class | FWHM [${\rm km\,s}^{-1}$] | $\log M(NIR)$ | $\log f_{NIR}$ | $\log N_{H}$
---|---|---|---|---|---
|  | He i | Pa$\beta$ | Pa$\alpha$ | $NIR$ | [M⊙] |  | [cm-2]
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
10 | 1.9 | 5906$\pm$336 |  |  | 5906$\pm$336 | 8.827$\pm$0.054 | 0.91$\pm$0.15 | 21.98
53 | 2 | 3260$\pm$188 |  |  | 3260$\pm$188 | 7.910$\pm$0.055 | 0.705$\pm$0.092 | 23.54
63 | 2 |  | 1429$\pm$36 |  | 1429$\pm$36 | 6.664$\pm$0.032 | 1.42$\pm$0.11 | 23.30
72 | 1.9 | 2347$\pm$76 | 6673$\pm$183 |  | 2975$\pm$70 | 7.797$\pm$0.031 | 1.059$\pm$0.068 | 22.01
73 | 1.2 | 2226$\pm$30 | 5960$\pm$80 |  | 2690$\pm$28 | 8.020$\pm$0.025 | 1.43$\pm$0.10 | 20.00
193 | 2 | 3351$\pm$271 |  |  | 3351$\pm$271 | 7.904$\pm$0.074 | 1.77$\pm$0.10 | 24.32
202 | 1.9 | 6122$\pm$203 |  |  | 6122$\pm$203 | 8.728$\pm$0.037 | 0.457$\pm$0.065 | 23.03
217 | 2 | 4634$\pm$128 |  |  | 4634$\pm$128 | 8.283$\pm$0.033 | 1.141$\pm$0.063 | 22.89
218 | 2 |  | 1750$\pm$68 |  | 1750$\pm$68 | 7.477$\pm$0.041 | -0.10$\pm$0.16 | 23.84
246 | 1.9 | 5355$\pm$155 |  |  | 5355$\pm$155 | 8.582$\pm$0.034 | 0.522$\pm$0.064 | 22.18

††footnotetext: Columns are: (1) BAT ID; (2) optical Seyfert classification;
(3-6) near-infrared broad line measurements, from either BASS DR1 (Lamperti et
al., 2017), DR2 (den Brok et al.,, submitted) or from this work, i.e., FIRE
spectra; (7) logarithm of the mixed NIR+$L_{X}$-based BH mass, calculated
using the FWHM($NIR$); (8) logarithm of the virial factor computed as the
ratio of the $\sigma_{\star}$-based BH mass with velocity dispersions from the
BASS DR2 (either from Koss et al.,, in prep., or Caglar et al., in prep.) and
$M(NIR)$; (9) column density derived from X-ray spectral fitting (Ricci et
al., 2017a). Upper limits on the X-ray columns are denoted with $<$. (This
table is available in its entirety in a machine-readable form in the online
journal. A part is shown as guidance for the reader regarding its content.)

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