# Observational hints on the torus obscuring gas behaviour through X-rays with
NuSTAR data

N. Osorio-Clavijo,1 O. González-Martín,1 S.F. Sánchez,2 D. Esparza-Arredondo,1
J. Masegosa,3 C. Victoria-Ceballos,1 L. Hernández-García4,5 Y. Díaz,5
1Instituto de Radioastronomía and Astrofisica (IRyA-UNAM), 3-72 (Xangari),
8701, Morelia, Mexico
2Instituto de Astronomía, Universidad Nacional Autónoma de México, A. P.
70-264, C.P. 04510, México, D.F., Mexico
3IAA – Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astonomía,
18008 Granada, Spain
4Millennium Institute of Astrophysics (MAS), Nuncio Monseñor Sótero Sanz 100,
Providencia, Santiago, Chile
5Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de
Valparaíso, Gran Bretaña 1111, Playa Ancha, Valparaíso, Chile e-mail:
<EMAIL_ADDRESS>
(Accepted 2021 December 19. Received 2021 December 16; in original form 2021
March 25.)

###### Abstract

According to theory, the torus of active galactic nuclei (AGN) is sustained
from a wind coming off the accretion disk, and for low efficient AGN, it has
been proposed that such structure disappears. However, the exact conditions
for its disappearance remain unclear. This can be studied throughout the
reflection component at X-rays, which is associated with distant and neutral
material at the inner walls of the torus in obscured AGN. We select a sample
of 81 AGNs observed with NuSTAR with a distance limit of D< 200 Mpc and
Eddington rate $\rm{\lambda_{Edd}\equiv L_{bol}/L_{Edd}<10^{-3}}$. We fit the
3-70 keV spectra using a model accounting for a partial-covering absorber plus
a reflection component from neutral material. We find that the existence of
the reflection component spans in a wide range of black-hole mass and
bolometric luminosities, with only $\sim$13% of our sample (11 sources)
lacking of any reflection signatures. These sources fall in the region in
which the torus may be lacking in the L-MBH diagram. For the sources with a
detected reflection component, we find that the vast majority of them are
highly obscured ($\rm{\log\ N_{H}>23}$), with $\rm{\sim 20\%}$ being Compton-
thick. We also find an increase on the number of unobscured sources and a
tentative increase on the ratio between $\rm{FeK\alpha}$ emission line and
Compton-hump luminosities toward $\rm{\lambda_{Edd}=10^{-5}}$, suggesting that
the contribution of the $\rm{FeK\alpha}$ line changes with Eddington ratio.

###### keywords:

galaxies: active - X-rays: galaxies - galaxies: Seyfert.

††pubyear: 2022††pagerange: Observational hints on the torus obscuring gas
behaviour through X-rays with NuSTAR data–12

##  1 Introduction

Figure 1: Histograms of the distribution of $\rm{M_{BH}}$ (left),
$\rm{L_{bol}}$ (center) and $\rm{\lambda_{Edd}}$ (right), for the final sample
(dashed, 81 sources) versus the full sample with $\rm{M_{BH}}$ measurements
(dotted, 231 sources). The dashed and dotted vertical lines in each panel
represent the mean value of the parameter in the X axis for both the final and
full samples, respectively. Note that in the left panel, six sources fulfill
the accretion criterion but are still excluded from the analysis because they
are classified as starburst or because they are at the center of clusters (see
text).

It has been widely accepted that most galaxies with bulges host a super
massive black-hole (SMBH), sometimes fed by an accretion disk, causing the
release of energy in orders of magnitude that can go up to $\rm{L_{bol}\sim
10^{47}\ erg\ s^{-1}}$ (see Netzer, 2015, for a review). Such objects are
known as Active Galactic Nuclei (AGN). The Unified Model (UM) of AGN
(Antonucci, 1993; Urry & Padovani, 1995) assumes that all AGN have the same
components (accretion disk, broad and narrow line regions, a dusty structure-
the torus and, in some cases a jet) and that the difference in the spectrum
relies on the angle of sight to the observer. This effect may prevent the
observer to see the inner parts of AGN and therefore the existence/absence of
broad lines in the optical spectrum, leading to a purely observational
classification (see Netzer, 2015; Ramos Almeida and Ricci, 2017, for recent
reviews on the topic).

The cornerstone of the UM are both the obscuring structure and the inclination
angle, as well as the existence of the jet. However, some observations suggest
that there are objects lacking the obscuring structure (the so-called true
type 2 AGN, Laor, 2003). This might be explained under the theoretical
prediction that the torus should disappear below a certain luminosity,
assuming that both the torus and broad line region (BLR) are formed from a
wind coming off the accretion disk (Elvis, 2000). In fact, Elitzur and
Shlosman (2006) state that both the torus and the BLR should disappear for
bolometric luminosities below ($\rm{L_{bol}\sim 10^{42}\ erg\ s^{-1}}$), since
the radiation pressure cannot longer counteract the gravity for both
structures. Indeed, González-Martín _et al._ (2017) using mid-infrared (mid-
IR) spectra, have found hints on the torus disappearance in inefficient AGN
(see also González-Martín _et al._ , 2015). Moreover, Elitzur and Ho (2009)
find that the torus might still be absent for luminous AGN, depending on the
efficiency of the accretion disk at feeding the SMBH. Therefore, not only the
luminosity of the AGN gives us hints on the existence of the torus, but also
the efficiency and density of the wind. Both mid-IR and X-ray studies suggest
that the torus is intrinsically different in type-2 AGN than in type-1 AGN
(e.g., Ramos Almeida _et al._ , 2009; Ricci _et al._ , 2011), and that the
fraction of type-2 sources increases for AGN with Eddington rates
$\rm{\lambda_{Edd}\equiv L_{bol}/L_{Edd}\simeq 0.001}$ (Ricci _et al._ ,
2017). Indeed, Khim and Yi (2017) found a complex behaviour where the number
of clouds and covering factor change for high accretion sources (i.e.,
$\rm{0.01<\lambda_{Edd}<1}$), forming a ridge-shaped distribution in the
luminosity versus black-hole mass ($\rm{M_{BH}}$) diagram. However, the
behaviour of the torus for low accretion AGN with $\rm{\lambda_{Edd}<0.001}$,
where the torus should evolve to its disappearance, remains an open question.

Historically, the obscuring matter has been studied through the column density
along the line of sight (LOS) that affects the primary X-ray continuum (e.g.
Matt, Guainazzi, and Maiolino, 2003). Additionally, the torus can also be
studied at X-rays because the inner parts of it can reflect the X-ray emission
from the corona above the disk, placing a reflection component in the X-ray
spectrum. This reflection component has two main signatures: the Compton hump
and the FeK$\alpha$ line. Theoretical works have shown that the resulting
reflection spectrum depends on the shape and distribution of the reflector,
but also on the line-of-sight to the observer, and all of this might have an
impact on the luminosity of this component (e.g. see Furui _et al._ , 2016).
However, it has not been until recent years that studies aiming to detect and
characterize the torus through the reflection component at X-rays have been
developed (e.g. Ricci _et al._ , 2011; Liu and Li, 2014; Ricci _et al._ ,
2014; Furui _et al._ , 2016; Kawamuro _et al._ , 2016), but also thanks to the
unprecedented sensitivity achieved above 10 keV provided by NuSTAR (e.g.,
Panagiotou and Walter, 2019, 2020; Esparza-Arredondo _et al._ , 2019, 2021,
among others).

The aim of this study is to trace the behaviour of the obscuring material and
plausible disappearance of the torus through X-rays for low accretion AGN,
compared to what has already been found for more efficient AGN, by using
_NuSTAR_ data. This work is divided as follows: in Section 2 we present the
sample and the data reduction. In Section 3 we present the model and the
spectral analysis, while in Section 4 we present the results obtained, in
Section 5 we discuss them and finally we present the summary and conclusions
of our work in Section 6. Throughout the analysis, we assume a cosmology of
$\rm{H_{0}=70\ km\ s^{-1}\ Mpc^{-1}}$, $\rm{q_{0}=0}$ and
$\rm{\Omega_{\lambda_{0}}=0.73}$, and all distances are redshift-independent
taken from the NASA Extragalactic Database
(NED111https://ned.ipac.caltech.edu/).

##  2 Sample and data reduction

###  2.1 Sample selection

We search for all available galaxies within a 10 arcmin radius (using SIMBAD
database222http://simbad.u-strasbg.fr/simbad/) for all archived pointings
within the NuSTAR database (until July 2020). We find a total of 1313 galaxies
within a distance of 200 Mpc ($z<0.05$) to sample the nearby Universe. We then
retrieve the activity type, keeping only those galaxies classified as AGN in
either NED or SIMBAD databases. We obtain a total of 463 AGN. We download all
the data from the HEASARC archive333https://heasarc.gsfc.nasa.gov/ and reduce
the observations for these 463 AGN (see section 2.2 reduction procedure),
keeping only the observations with more than 30 bins after producing grouped
spectra, and at least 10 bins above 10 keV. We also remove from the sample
those AGN where the NuSTAR resolution cannot fully isolate the nuclear spectra
for dual AGN. We obtain a total of 301 sources fulfilling these criteria.

We finally search for $\rm{M_{BH}}$. These measurements are needed to obtain
an estimate of the Eddington rate. We firstly look for $\rm{M_{BH}}$
calculated via reverberation mapping (e.g. Laor, 2001, 2003; Woo and Urry,
2002; Vasudevan and Fabian, 2009) and velocity dispersion otherwise (e.g.
McKernan, Ford, and Reynolds, 2010; van den Bosch _et al._ , 2015; van den
Bosch, 2016), by using the M-$\sigma$ relation, $\rm{M_{BH}}$
($\rm{\log(M_{BH}/M_{\odot})=8.27+5.1\log(\sigma/200\ km\ s^{-1})}$ Ferrarese
and Merritt, 2000; Gebhardt _et al._ , 2000). As for the sources for which the
$\rm{M_{BH}}$ is not calculated through the methods reported above, we also
search for the $\rm{M_{BH}}$ in different AGN catalogues where the mass are
compiled from literature (e.g. Khorunzhev _et al._ , 2012; Koss _et al._ ,
2017; Bär _et al._ , 2019). We obtain measurements for 231 out of the 301 AGN.
This sample is now referred to as full sample.

We then fit the spectra of the 231 AGN with an unabsorbed power-law to roughly
calculate the bolometric luminosity, $\rm{L_{bol}}$, from X-rays following the
$\rm{L_{bol}/L_{(2-10\ keV)}}$ conversion from Marconi _et al._ (2004), where
$\rm{L_{bol}}$ is in units of $\rm{L_{\odot}}$:

$\rm{\log[L_{bol}/L_{(2-10\ keV)}]=1.54\ +0.24(L_{bol}-12)}\ +\\\
\rm{0.012(L_{bol}-12)^{2}\ -\ 0.0015(L_{bol}-12)^{3}}.$ (1)

Name | Other name | ra | dec | Redshift | Dist. | $\rm{\log\ M_{BH}}$ | AGN | Galaxy | Obs. date | Obs ID | Exp. time | Ext. radius | N. counts | Bins
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | deg | deg |  | Mpc |  | type | type |  |  | ks | arcmin |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15)
NGC1052 | PKS0238-084 | 40.26999 | -8.25576 | 0.0048 | 20.6 | 8.4 | L2 | E4 | 2017-01-17 | 60201056002 | 59.75 | 0.5 | 91.27 | 738
NGC2655 | ARP225 | 133.90721 | 78.22308 | 0.0057 | 24.4 | 8.0 | L2 | Sa-0 | 2016-11-10 | 60160341004 | 15.95 | 2 | 35.30 | 98
UGC5101 | CGCG289-011 | 143.96539 | 61.35292 | 0.0394 | 168.6 | 8.3 | L1 | S? | 2014-03-21 | 60001068002 | 18.29 | 1 | 24.33 | 51
M81 | NGC3031 | 148.88822 | 69.06530 | 0.0009 | 3.7 | 7.8 | L1.8 | SAab | 2015-05-18 | 60101049002 | 209.09 | 0.5 | 255.69 | 1252
NGC3079 | UGC05387 | 150.49085 | 55.67979 | 0.0038 | 16.4 | 7.2 | L2 | SBc | 2013-11-12 | 60061097002 | 21.54 | 0.5 | 29.85 | 128
UGC5881 | CGCG125-008 | 161.67715 | 25.93155 | 0.0206 | 88.2 | 8.2 | L2 | Sa | 2015-05-17 | 60160409002 | 21.41 | 1 | 37.39 | 169
NGC3628 | UGC06350 | 170.07091 | 13.58949 | 0.0023 | 9.8 | 7.2 | L2 | SAb | 2017-12-23 | 60371004002 | 50.35 | 1 | 32.46 | 86
NGC3718 | ARP214 | 173.14522 | 53.06791 | 0.0034 | 14.7 | 8.3 | L1 | SB | 2017-10-27 | 60301031004 | 90.37 | 0.5 | 44.38 | 208
NGC3998 | UGC06946 | 179.48389 | 55.45359 | 0.0047 | 20.1 | 9.0 | L1.9 | Sa-0 | 2016-10-25 | 60201050002 | 103.94 | 0.5 | 111.02 | 714
NGC4102 | UGC07096 | 181.59631 | 52.71095 | 0.0046 | 19.5 | 8.2 | L2 | SAB | 2015-11-19 | 60160472002 | 20.57 | 0.5 | 39.14 | 198
M106 | NGC4258 | 184.74008 | 47.30372 | 0.0017 | 7.3 | 7.5 | L1.9 | SBbc | 2016-01-10 | 60101046004 | 103.62 | 0.5 | 71.20 | 466
M58 | NGC4579 | 189.43165 | 11.81809 | 0.0043 | 18.4 | 7.9 | L1.9 | Sb | 2016-12-06 | 60201051002 | 117.84 | 0.5 | 116.60 | 738
NGC5005 | UGC08256 | 197.73463 | 37.05894 | 0.0047 | 20.1 | 8.1 | L1.9 | SABb | 2014-12-16 | 60001162002 | 49.70 | 1 | 27.82 | 40
NGC6240 | IC4625 | 253.24525 | 2.40099 | 0.0245 | 104.8 | 9.1 | L2 | S0-a | 2014-03-30 | 60002040002 | 30.86 | 0.5 | 55.62 | 444
MCG+08-31-041 | ARP102B | 259.81038 | 48.98040 | 0.0242 | 103.5 | 8.9 | L1 | E0 | 2015-11-24 | 60160662002 | 22.40 | 1 | 45.28 | 248
NGC7130 | IC5135 | 327.08121 | -34.95131 | 0.0162 | 69.2 | 7.5 | L2 | Sa | 2016-12-15 | 60261006002 | 42.12 | 0.5 | 23.86 | 63
NGC7331 | UGC12113 | 339.26709 | 34.41592 | 0.0031 | 13.4 | 7.8 | L2 | Sbc | 2016-05-03 | 40202013002 | 42.97 | 1 | 38.16 | 153
NGC7479 | UGC12343 | 346.23612 | 12.32288 | 0.0066 | 28.3 | 7.3 | L1.9 | SBbc | 2016-05-12 | 60201037002 | 18.45 | 1 | 27.73 | 82
Table 1: Observational parameters for the LINER sample. (1) Name of the
source; (2) other name (3) right ascension; (4) declination; (5) Redshift; (6)
Redshift-independent distance in Mpc; (7)
$\rm{\log\left(M_{BH}/M_{\odot}\right)}$; (8) AGN classification; (9) Galaxy
type. All galaxy types were retrieved from NED; (10) date of the observation;
(11) Observation ID in NuSTAR; (12) Exposure time of the observation in ksec;
(13) is the extraction radius used in the data reduction; (14) is the number
of counts in the 3-60 keV NuSTAR band when accounting for the background
substraction; and (15) is the number of bins. In columns (1) and (2), 2MXJ
(2MXIJ) is abbreviation for 2MASXJ (2MASXIJ), 2M is the abbreviation for 2MASS
and W is the abbreviation for WISE.

We define low accretion sources as those with $\rm{\lambda_{Edd}<10^{-3}}$,
where $\rm{L_{Edd}}$ is the Eddington luminosity, defined as the maximum
luminosity an object can release without losing the thermal equilibrium. Such
defintion is based on the assumption that the transition from the standard
disk (Shakura and Sunyaev, 1973) to an Advection Dominated Accretion disk
(ADAF, Narayan and Yi, 1995) occurs around this value (see also, Constantin et
al., 2009; Gu & Cao, 2009; Younes et al., 2011; Gültekin et al., 2012; Jang et
al., 2014; Connolly et al., 2016; Hernández-García _et al._ , 2016). This
sample contains a total of 87 sources. This corresponds to $\rm{\sim 20\%}$ of
the total nearby available AGN observed with NuSTAR. Four of these sources
(NGC 3310, Mrk 18, Arp 299C, and M 83) are excluded from the sample because
although they are classified as AGN in SIMBAD/NED, they are also classified as
starbursts. Finally, we exclude NGC 4486 due to the strong thermal and jet
contribution (de Jong _et al._ , 2015), while we exclude Centaurus A due to
strong jet contribution (Hardcastle _et al._ , 2003). Note that we also check
for important thermal/jet contribution for the rest of the sample. Although in
some cases there are reported thermal contribution at X-rays (see González-
Martín _et al._ , 2009), it does not contribute above 3 keV for the rest of
the sources. One consequence , although not the only one, would be a very
steep photon index ((i.e., $\rm{\Gamma}>2$ Nemmen, Storchi-Bergmann, and
Eracleous, 2014) as the one in M 87 ($\Gamma=2.8\pm 0.4$ de Jong _et al._ ,
2015), which is not the case in our sample, see section 4). Our final sample
comprises a total of 81 sources.

Fig. 1 shows the distribution (in logarithmic scale) of $\rm{M_{BH}}$ (left),
$\rm{L_{bol}}$ (center) and $\rm{\lambda_{Edd}}$ (right) for our final sample
of 81 sources, compared to the full sample of 231 sources with $\rm{M_{BH}}$
estimates. The mean of the distributions of the final sample for
$\rm{M_{BH}}$, $\rm{L_{bol}}$ and $\rm{\lambda_{Edd}}$ are
$\rm{<log(M_{BH})>=}$7.9, $\rm{<log(L_{bol})>=}$42.1 and
$\rm{log(\lambda_{Edd})=}$-3.8, compared to $\rm{<log(M_{BH})>=}$7.6,
$\rm{<log(L_{bol})>=}$43.0 and $<\rm{log(\lambda_{Edd})>=}$-2.6, for the full
sample. Thus, our final sample contains lower luminosity AGN with roughly the
same range of $\rm{M_{BH}}$ values compared to the full sample. Note that this
imposes a bias on our sample for Eddington rates above
$\rm{log(\lambda_{Edd})>}$-3. Moreover, once we correct by absorption in the
line-of-sight, Eddington rates will be higher (see section 4.1). Thus, we
might lack objects with low obscuration and intrinsically high Eddington rate
above $\rm{log(\lambda_{Edd})>}$-2.5. Another source of bias is the fact that
our sample relies purely on archival data. For instance, we do not find
available NuSTAR data for the candidates of torus disappearance in González-
Martín _et al._ (2017). Thus, we might also be missing the least luminous
sources as they might not haven been observed yet. We warn the reader on the
fact that our sample is by no means complete, although it does cover a wide
range in $\rm{M_{BH}}$ and Eddington rate.

Several works have studied samples of inefficient AGN in different wavelengths
aiming to understand the nature and behaviour of the reflection component and
will be used to compare with our new results along the text. Here we report a
brief summary on the matching of our sample with theirs. The largest sample
using X-rays is reported by González-Martín _et al._ (2009) where they study a
sample of 82 inefficient AGN using Chandra and XMM-Newton data. We have 12
sources in common with available NuSTAR observations. Kawamuro _et al._ (2016)
also studied a sample of 10 inefficient AGN using Suzaku and we have five
sources in common with them. On the other hand, González-Martín _et al._
(2017) analyzed a sub-sample of those presented by González-Martín _et al._
(2009) together with a complementary Seyfert sample (22 sources). We have a
total of 39 sources in common with the works mentioned above, which is around
50% of our final sample.

Tables 1 and 2 report the observational parameters for the optically
classified as low ionization nuclear emission-line regions (LINER, 18 sources)
and Seyfert (64 sources) samples, respectively.

Name | Other name | ra | dec | Redshift | Dist. | $\rm{\log\ M_{BH}}$ | AGN | Galaxy | Obs. date | Obs ID | Exp. time | Ext. radius | N. counts | Bins
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | deg | deg |  | Mpc |  | type | type |  |  | ks | arcmin |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15)
NGC253 | ESO474-G029 | 11.88806 | -25.28880 | 0.0008 | 3.2 | 6.9 | S2 | SAB | 2012-09-15 | 50002031004 | 157.65 | 0.5 | 83.01 | 431
NGC424 | ESO296-G004 | 17.86516 | -38.08345 | 0.0118 | 50.7 | 7.5 | S1 | SB0-a | 2013-01-26 | 60061007002 | 15.48 | 1 | 32.14 | 145
IC1657 | ESO352-G024 | 18.52924 | -32.65090 | 0.0107 | 45.9 | 7.3 | S2 | SBbc | 2017-01-15 | 60261007002 | 45.16 | 0.5 | 40.39 | 217
2MXJ01142491-5523497 | NGC0454NED0 | 18.60388 | -55.39705 | 0.0121 | 51.9 | 8.5 | S2 | II | 2016-02-14 | 60061009002 | 24.23 | 1 | 34.16 | 144
MCG+08-03-018 | 2MXJ01223442+5003180 | 20.64341 | 50.05496 | 0.0204 | 87.4 | 8.4 | S2 | S? | 2014-01-27 | 60061010002 | 31.66 | 1 | 43.88 | 230
NGC612 | ESO353-G015 | 23.49063 | -36.49328 | 0.0298 | 127.5 | 8.5 | S2 | SA0 | 2012-09-14 | 60061014002 | 16.69 | 0.5 | 31.62 | 158
Mrk573 | UGC01214 | 25.99074 | 2.34987 | 0.0172 | 73.6 | 7.4 | S2 | S0 | 2018-01-06 | 60360004002 | 32.00 | 1 | 29.73 | 66
NGC788 | MCG-01-06-025 | 30.27693 | -6.81587 | 0.0136 | 58.3 | 7.7 | S2 | S0-a | 2013-01-28 | 60061018002 | 15.41 | 0.5 | 35.64 | 198
M77 | NGC1068 | 40.66988 | -0.01329 | 0.0025 | 10.6 | 7.2 | S2 | SAb | 2012-12-18 | 60002030002 | 57.85 | 0.5 | 82.88 | 657
NGC1106 | UGC02322 | 42.66873 | 41.67158 | 0.0145 | 62.0 | 7.5 | S2 | SA0 | 2019-02-22 | 60469002002 | 18.74 | 1 | 26.56 | 67
NGC1125 | MCG-03-08-035 | 42.91792 | -16.65111 | 0.0109 | 46.8 | 7.2 | S2 | SAB0 | 2019-06-10 | 60510001002 | 31.74 | 1 | 36.46 | 123
NGC1142 | UGC02389 | 43.80095 | -0.18355 | 0.0288 | 123.5 | 8.9 | S2 | Spec | 2017-10-14 | 60368001002 | 20.71 | 0.5 | 28.40 | 119
Mrk1066 | UGC02456 | 44.99415 | 36.82050 | 0.0121 | 51.7 | 7.0 | S2 | SB0 | 2014-12-06 | 60001154002 | 30.08 | 1 | 30.03 | 64
NGC1194 | UGC02514 | 45.95463 | -1.10375 | 0.0136 | 58.2 | 7.8 | S1.9 | SA0 | 2015-02-28 | 60061035002 | 31.54 | 0.5 | 39.68 | 224
NGC1229 | ESO480-G033 | 47.04513 | -22.96025 | 0.0363 | 155.4 | 8.3 | S2 | SBb | 2013-07-05 | 60061325002 | 24.92 | 1 | 35.29 | 155
NGC1320 | MRK0607 | 51.20288 | -3.04226 | 0.0088 | 37.7 | 6.9 | S2 | Sa | 2013-02-10 | 60061036004 | 28.00 | 1 | 34.45 | 120
NGC1358 | MCG-01-10-003 | 53.41535 | -5.08951 | 0.0134 | 57.5 | 8.1 | S2 | SAB0 | 2017-08-01 | 60301026002 | 50.00 | 0.5 | 39.72 | 206
NGC1386 | ESO358-G035 | 54.19266 | -35.99927 | 0.0038 | 16.1 | 7.0 | S1 | S0-a | 2016-05-11 | 60201024002 | 26.43 | 1 | 22.29 | 45
UGC3157 | CGCG468-001 | 71.62399 | 18.46091 | 0.0154 | 66.0 | 8.0 | S2 | SBbc | 2014-03-18 | 60061051002 | 20.09 | 1 | 35.16 | 163
2MJ05081968+1721481 | CGCG468-002NED01 | 77.08211 | 17.36336 | 0.0175 | 75.0 | 8.6 | S2 | - | 2012-07-23 | 60006011002 | 15.52 | 0.5 | 51.25 | 368
ESO5-4 | IRAS06220-8636 | 91.42384 | -86.63195 | 0.0060 | 25.9 | 7.6 | S2 | Sb | 2015-11-10 | 60061063002 | 24.70 | 1 | 33.74 | 109
NGC2273 | UGC03546 | 102.53614 | 60.84580 | 0.0068 | 29.0 | 7.0 | S2 | SBa | 2014-03-23 | 60001064002 | 23.23 | 1 | 36.69 | 150
UGC3601 | CGCG204-032 | 103.95638 | 40.00031 | 0.0171 | 73.3 | 8.6 | S1.5 | S? | 2019-01-06 | 60160278002 | 19.67 | 1 | 45.70 | 257
ESO428-14 | MCG-05-18-002 | 109.13003 | -29.32469 | 0.0054 | 23.2 | 7.0 | S2 | SA0 | 2015-01-11 | 60001152002 | 40.25 | 0.5 | 29.46 | 111
2MXJ07561963-4137420 | WAJ075619.61-413742.1 | 119.08182 | -41.62835 | 0.0210 | 90.1 | 8.0 | S2 | - | 2014-07-29 | 60061076002 | 22.75 | 2 | 38.87 | 62
NGC2788A | ESO060-G024 | 135.66418 | -68.22683 | 0.0144 | 61.6 | 8.7 | S2 | Sb | 2019-06-14 | 60469001002 | 27.58 | 0.5 | 27.18 | 99
IC2560 | ESO375-G004 | 154.07795 | -33.56381 | 0.0078 | 33.4 | 7.2 | S2 | SBbc | 2014-07-16 | 50001039004 | 49.56 | 1 | 35.56 | 99
NGC3147 | UGC05532 | 154.22347 | 73.40065 | 0.0092 | 39.6 | 8.7 | S2 | SAbc | 2015-12-27 | 60101032002 | 49.26 | 0.5 | 48.47 | 293
NGC3393 | ESO501-G100 | 162.09778 | -25.16203 | 0.0125 | 53.6 | 7.5 | S2 | SBab | 2013-01-28 | 60061205002 | 15.66 | 0.5 | 25.00 | 87
2MXJ11055897+5856456 | CGCG291-028 | 166.49593 | 58.94603 | 0.0271 | 116.0 | 8.4 | S2 | - | 2019-03-26 | 60160420002 | 15.77 | 2 | 38.17 | 134
NGC3621 | ESO377-G037 | 169.56792 | -32.81260 | 0.0016 | 6.7 | 6.8 | S2 | SA | 2017-12-15 | 60371002002 | 30.78 | 2 | 41.09 | 100
NGC3786 | UGC06621 | 174.92714 | 31.90943 | 0.0118 | 50.6 | 7.5 | S1.8 | SAB | 2014-06-09 | 60061349002 | 21.99 | 2 | 36.08 | 103
IC751 | UGC06972 | 179.71915 | 42.57034 | 0.0312 | 133.6 | 8.6 | S2 | Sb | 2013-02-04 | 60061217004 | 52.02 | 0.5 | 25.72 | 63
M88 | NGC4501 | 187.99673 | 14.42041 | 0.0042 | 18.0 | 7.5 | S2 | SAb | 2018-01-26 | 60375002002 | 62.77 | 1 | 27.45 | 55
IC3639 | ESO381-G008 | 190.22015 | -36.75585 | 0.0109 | 46.8 | 6.9 | S2 | SBbc | 2015-01-09 | 60001164002 | 58.73 | 0.5 | 25.34 | 51
NGC4785 | ESO219-G004 | 193.36382 | -48.74915 | 0.0116 | 49.6 | 8.1 | S2 | SAB | 2014-08-20 | 60001143002 | 48.83 | 0.5 | 40.05 | 208
Mrk231 | UGC08058 | 194.05931 | 56.87368 | 0.0422 | 180.6 | 8.4 | S2 | Sc | 2017-10-19 | 80302608002 | 82.06 | 0.5 | 46.30 | 242
NGC4941 | PGC045165 | 196.05461 | -5.55160 | 0.0033 | 14.2 | 6.9 | S2 | SABa | 2016-01-19 | 60061236002 | 20.66 | 1 | 32.48 | 119
NGC4939 | MCG-02-33-104 | 196.05970 | -10.33953 | 0.0085 | 36.4 | 7.9 | S2 | Sbc | 2017-02-17 | 60002036002 | 22.04 | 0.5 | 36.10 | 181
NGC4945 | ESO219-G024 | 196.36366 | -49.46790 | 0.0010 | 4.2 | 6.3 | S2 | SBc | 2013-06-15 | 60002051004 | 54.62 | 0.5 | 129.04 | 1565
MCG-03-34-064 | PGC046710 | 200.60202 | -16.72836 | 0.0200 | 85.6 | 8.1 | S1.8 | SB? | 2016-01-17 | 60101020002 | 78.50 | 0.5 | 80.69 | 727
NGC5135 | ESO444-G032 | 201.43358 | -29.83368 | 0.0015 | 6.3 | 7.6 | S2 | Sab | 2015-01-14 | 60001153002 | 33.36 | 1 | 34.28 | 88
M51 | ARP085 | 202.46957 | 47.19526 | 0.0017 | 7.3 | 6.6 | S2 | - | 2017-03-17 | 60201062003 | 163.06 | 0.5 | 41.19 | 99
NGC5252 | UGC08622 | 204.56613 | 4.54265 | 0.0195 | 83.6 | 8.9 | S1.9 | S0 | 2013-05-11 | 60061245002 | 19.01 | 0.5 | 65.88 | 523
NGC5283 | UGC08672 | 205.27395 | 67.67222 | 0.0106 | 45.3 | 7.7 | S2 | S0 | 2018-11-17 | 60465006002 | 33.02 | 0.5 | 42.87 | 234
NGC5347 | UGC08805 | 208.32416 | 33.49083 | 0.0050 | 21.6 | 6.8 | S2 | Sab | 2015-01-16 | 60001163002 | 47.30 | 1 | 32.04 | 54
NGC5643 | ESO272-G016 | 218.16991 | -44.17461 | 0.0027 | 11.4 | 7.0 | S2 | Sc | 2014-05-24 | 60061362002 | 22.46 | 1 | 36.54 | 146
NGC5695 | UGC09421 | 219.34223 | 36.56783 | 0.0125 | 53.5 | 7.7 | S2 | SBb | 2018-01-16 | 60368004002 | 41.61 | 1 | 27.60 | 43
NGC5728 | MCG-03-37-005 | 220.59970 | -17.25317 | 0.0071 | 30.3 | 7.8 | S2 | SABa | 2013-01-02 | 60061256002 | 24.36 | 0.5 | 52.02 | 402
NGC5899 | UGC09789 | 228.76355 | 42.04985 | 0.0090 | 38.6 | 8.7 | S2 | SABc | 2014-04-08 | 60061348002 | 23.88 | 0.5 | 54.44 | 383
MCG+14-08-004 | CGCG367-009 | 244.83058 | 81.04650 | 0.0239 | 102.4 | 9.8 | S2 | - | 2014-12-21 | 60061270002 | 29.76 | 1 | 38.54 | 165
ESO137-34 | 2MXJ16351411-5804481 | 248.80881 | -58.08003 | 0.0077 | 33.0 | 8.0 | S2 | SAB0 | 2016-06-07 | 60061272002 | 18.55 | 0.5 | 28.69 | 111
2MXJ16504275+0436180 | NGC6230NED01 | 252.67813 | 4.60508 | 0.0321 | 137.3 | 9.8 | S2 | - | 2017-02-06 | 60061273002 | 21.03 | 0.5 | 56.94 | 409
2MXIJ1802473-145454 | WAJ180247.38-145454.8 | 270.69708 | -14.91528 | 0.0034 | 14.6 | 7.8 | S1 | - | 2016-05-01 | 60160680002 | 19.96 | 0.5 | 80.72 | 595
2MXJ18305065+0928414 | LEDA1365707 | 277.71098 | 9.47830 | 0.0194 | 83.2 | 8.4 | S2 | - | 2015-11-15 | 60061285002 | 22.72 | 1 | 39.73 | 183
IC4995 | ESO186-G034 | 304.99574 | -52.62192 | 0.0161 | 68.9 | 7.2 | S2 | SA0 | 2019-06-03 | 60360003002 | 34.00 | 1 | 32.33 | 70
NGC6921 | UGC11570 | 307.12018 | 25.72339 | 0.0145 | 62.0 | 8.4 | S2 | SA0 | 2013-05-18 | 60061300002 | 19.52 | 1 | 33.67 | 117
NGC7213 | ESO288-G043 | 332.31754 | -47.16669 | 0.0051 | 22.0 | 7.7 | S1.5 | Sa | 2014-10-05 | 60001031002 | 101.62 | 0.5 | 160.49 | 965
NGC7319 | UGC12102 | 339.01501 | 33.97588 | 0.0109 | 46.7 | 7.3 | S2 | SBbc | 2017-09-27 | 60261005002 | 41.88 | 0.5 | 30.20 | 88
UGC12282 | CGCG532-004 | 344.73035 | 40.93221 | 0.0169 | 72.4 | 9.8 | S1.9 | Sa | 2019-11-18 | 60160812002 | 28.56 | 1 | 27.50 | 43
NGC7582 | ESO291-G016 | 349.59842 | -42.37057 | 0.0049 | 21.2 | 7.6 | S1.5 | SBab | 2016-04-28 | 60201003002 | 48.49 | 0.5 | 123.14 | 1100
2MXJ23252420-3826492 | IRAS23226-3843 | 351.35078 | -38.44700 | 0.0359 | 153.8 | 8.2 | S1 | - | 2017-06-11 | 80101001002 | 96.61 | 0.5 | 30.57 | 80
NGC7674 | UGC12608 | 351.98624 | 8.77895 | 0.0174 | 74.5 | 7.6 | S2 | SAbc | 2014-09-30 | 60001151002 | 52.00 | 0.5 | 36.08 | 161
Table 2: Observational parameter for the Seyfert sample. Columns are as in
Tab. 1.

###  2.2 Data reduction

All _NuSTAR_ (Harrison _et al._ , 2013) data were reduced using the data
analysis software _NuSTARDAS_ v.1.4.4 distributed by the High Energy
Astrophysics Archive Research Center (HEASARC). The calibrated, cleaned and
screened event files for both FPMA and FMPB focal plane modules were generated
using the nupipeline task (CALDB 20160502). We automatically extracted three
circular apertures with radius of 0.5, 1, and 2 arcsec centred at the NED
position of the source. For each of them we produced eight backgrounds around
the target. These backgrounds are located at a distance of three times the
aperture radius of the target (i.e. 1.5, 3, or 6 arcsec) with position angles
of 0, 45, 90, 135, 180, 225, 270, and 315 degrees. We produced in this way 24
spectra for each target. The Redistribution Matrix and Auxiliary Response
files (RMF and ARF) were produced with the nuproducts package available in
_NuSTARDAS_. We chose the spectrum that maximises the S/N in the 3-70 keV
band, avoiding off-nuclear contributors. Tables 1 and 2 provide the best
extraction radius for each target. Note the optimal extraction radius is
$\sim$1 arcmin ($D\simeq[1-52]$ kpc) for the vast majority of the objects, due
to the relative faintness of our sources.

We then performed a binning method with a minimum S/N ratio of 3, using the
ftgrouppha task within FTOOLS. The grouping using a minimum S/N ratio is
particularly relevant for faint sources which are probably background
dominated above $\rm{\sim}$25 keV. Note that we also performed the standard
grouping method accounting for a minimum of 30 counts per bin (the grppha
task) finding similar results in the spectral parameters of the sources.
However, the grouping performed with a minimum S/N ratio clearly improves the
error bars at high energies for faint sources as expected.

##  3 Spectral Analysis

###  3.1 Baseline models

In this section we present four models used in the analysis to fit the
spectra, which are fitted using xspec (Arnaud, 1996, version 12.10.0)444
http://cxc.heasarc.gsfc.nasa.gov/docs/xanadu/xspec/. Throughout the analysis,
we use the $\chi^{2}$ statistics. We begin the analysis by modelling the
intrinsic continuum with a power-law affected by a patchy absorber, in what is
known as the partial covering scenario. We add two Gaussian profiles centred
at 6.7 and 6.97 keV, to account for the Fe xxv and Fe xxvi ionized emission
lines as they are the most common ionized lines present at hard X-rays for
AGN. In the software terminology, this model has the following form:

$M_{1}={\tt phabs_{\rm{Gal}}}(({\tt zphabs_{\rm{intr}}}*{\tt zpowerlw})+{\tt
ct}*{\tt zpowerlw}\\\ +{\tt zgauss_{6.7\ keV}}+{\tt zgauss_{6.97\ keV}})$ (2)

where $({\tt zphabs_{\rm{intr}}}*{\tt zpowerlw})+{\tt ct}*{\tt zpowerlw}$
represents the partial-covering scenario, in which the first power-law
component is associated with the intrinsic continuum absorbed by the material
along the LOS to the observer and the second power-law component is the
scattered emission that reaches the observer. The parameters for both power-
laws are linked, including the normalization, to simulate the partial-covering
scenario. The free parameters for this model are the column density
($\rm{N_{H}}$), the constant associated with the covering factor (as
$\rm{ct=1-f_{cov}}$), the photon index ($\rm{\Gamma_{pl}}$), and the
normalization of the power-law. The free parameters of the Gaussian
components, emulating the emission lines are the center, width and
normalization. The widths of the Gaussian components are fixed to be narrow
(0.1 keV555The NuSTAR spectral resolution is 400 eV at 6 keV, see
https://heasarc.gsfc.nasa.gov/docs/nustar/nustar_tech_desc.html) and the
centers are fixed to 6.7 and 6.97 keV, respectively.

For the second and third models we include an extra reflection component as
follows:

$M_{2}=M_{1}+{\tt phabs_{\rm{Gal}}}({\tt pexrav}+{\tt zgauss_{6.4\ keV}})$ (3)
$M_{3}=M_{1}+{\tt phabs_{\rm{Gal}}}({\tt pexmon})$ (4)

For $\rm{M_{2}}$, we choose as reflection component the pexrav model
(Magdziarz and Zdziarski, 1995). This model assumes Compton reflection from
neutral X-ray photons in an optically thick material with plane-parallel
geometry. This model has as free parameters the photon index, high energy
cutoff, relative reflection (R), metal and iron abundances, inclination angle,
and normalization. We have set the photon index of pexrav
($\rm{\Gamma_{pex}}$) to be the same as that of the power-law, assuming that
the reflection occurs in the AGN such that both emissions are correlated. The
energy cutoff is fixed to 300 keV assuming this cutoff to happen above the
NuSTAR energy range. Note that although several works (e.g. Molina _et al._ ,
2019; Younes _et al._ , 2019; Ezhikode _et al._ , 2020) have aimed to find
this cutoff in AGN spectra, it has only been possible for very few objects,
and in most cases, it happens well above the NuSTAR range (e.g Baloković _et
al._ , 2020). Therefore, we do not expect for this parameter to be constrained
nor to affect the overall analysis. We have set R to $-1$ for pexrav to
account for the reflection component only, without contribution from the
intrinsic power-law continuum. Thus, this reflection model with the relative
reflection set to $-1$ plus the power-law component is equivalent to the
pexrav allowing the relative reflection to vary. However, we used with the
relative reflection to $-1$ in order to separate both the intrinsic continuum
and the reflection components.

The rest of the parameters are set to their default values except for the
normalization. Note that in this model version, the addition of an extra
Gaussian profile is necessary to emulate the FeK$\rm{\alpha}$ line, since
pexrav assumes reflection from a neutral material, and does not account for
this line. In this model, the width of the line at 6.4 keV is also fixed to
0.1 keV.

For $\rm{M_{3}}$, we include the reflection component using pexmon (Nandra _et
al._ , 2007). This model is an updated version of pexrav that includes
fluorescence lines such as FeK$\rm{\alpha}$, FeK$\rm{\beta}$ and
NiK$\rm{\alpha}$. This model also accounts for the Compton shoulder, by
assuming a Gaussian line at 6.315 keV with a width of 0.35 keV. Additionally,
it assumes a connection between the equivalent width (EW) of the
FeK$\rm{\alpha}$ line and that of the Compton shoulder. This reflection model
has as free parameters the photon index ($\rm{\Gamma_{pex}}$), relative
reflection, cutoff energy, metal and iron abundances, inclination angle, and
normalization. Similar to $\rm{M_{2}}$, the parameter R is set to $-1$, the
energy cutoff is set to 300 keV and the other parameters, except the
normalization, are set to their default values.

The difference between $\rm{M_{2}}$ and $\rm{M_{3}}$ relies on the fact that
pexmon accounts for the abundance of iron in the medium through the inclusion
of the FeK$\rm{\alpha}$, FeK$\rm{\beta}$ and NiK$\rm{\alpha}$ lines. Indeed,
these lines are correlated with the Compton-reflection as they are fixed to a
fraction of the Compton-shoulder, and they also depend on the photon index of
the intrinsic continuum. pexmon also accounts for the Compton-shoulder, while
pexrav is a simpler model not accounting for such features. Thus, pexmon
already incorporates the $\rm{FeK\alpha}$ line at 6.4 keV while we add this
line using a Gaussian profile in $\rm{M_{2}}$. We use $\rm{M_{2}}$ to
calculate the EW and luminosity of the 6.4 keV line, with the normalization
and error of the line component and the tools equivalent and luminosity within
xspec. $\rm{M_{2}}$ also allows us to isolate the effect of the line from that
of the Compton shoulder. Note that both models are equivalent in the analysis.
However, since pexmon self-consistently accounts for both the continuum and
line emission due to the reprocessing in neutral, distant material, the rest
of the analysis is based on this model. We include $\rm{M_{1}}$ to study the
detection of the reflection component in our sample through the f-statistic
test when comparing models (see below). Note also that regardless of the
model, we account for Galactic absorption and redshift by using the nh tool
within ftools (retrieved from NED666https://ned.ipac.caltech.edu and fixed to
the HI maps of Kalberla _et al._ , 2005).

We also use a fourth model that accounts for reflection dominated sources,
i.e., sources for which the intrinsic continuum is completely covered by the
reflection component in the available X-ray data. This model has the following
form:

$M_{4}={\tt phabs_{\rm{Gal}}}*{\tt pexmon}$ (5)

Figure 2: Spectral fits for $\rm{M_{1}}$ (upper left), $\rm{M_{2}}$ (upper
right), $\rm{M_{3}}$ (lower left) and $\rm{M_{4}}$ (lower right) for NGC7582.
Each color represents each of the components as follows: teal is the total
spectrum, red is the partial-covering component, blue are pexmon (left) and
pexrav (right) components, while green, cyan and purple are the extra lines in
each model version. (see section 3.2)

This analysis does not use sophisticated models as borus (Baloković _et al._ ,
2018) or mytorus (Murphy and Yaqoob, 2009) for neutral torus reflection
because the faintness of the sources in our sample may not allow us to
restrict geometrical parameters for the majority of them. Indeed, we also
tested the mytorus model, but the S/N of the data were too low for parameters
to be restriced in most cases. Instead, we prefer a homogeneous analysis of
the strength and general characteristics of the reflection component in our
sample. This is sufficient to study the dependence of the existence of the
reflection component with the AGN power, which is one of the main purposes of
this analysis. Furthermore, it also avoids the use of ionized disk reflection
components, such as relxill (Dauser _et al._ , 2014) because disk reflection
has been found only for a small fraction of AGN, all of them in the high
accretion regime (Esparza-Arredondo _et al._ , 2021). Finally, this spectral
analysis lacks the inclusion of the Compton scattering, which contributes
specially for Compton-
thick777https://ned.ipac.caltech.edu/level5/March04/Comastri/Comastri_contents.html
(CT) sources. However, the available models within xspec (e.g., cabs) do not
properly account for it as they assume an inadequate cross-section in the
modelling (cf., Murphy and Yaqoob, 2009, and mytorus
manual888http://mytorus.com.). Indeed, we also try the scenario in which cabs
is included but we find the intrinsic luminosity to be unrealistically high in
some cases (see Appendix A). Note that the exclusion of such a component leads
to a systematic uncertainty, which is translated into an underestimation of
the intrinsic luminosities of CT sources. However, our baseline model has been
widely used in several works aimed to find general properties of AGN and
characterize the reflection component, even in CT objects (e.g., Kawamuro _et
al._ , 2016; Panagiotou and Walter, 2019, 2020; Kang, Wang, and Kang, 2020).
Thus, the baseline model used in this work will lead to robust results that
can be easily compared with previous works (e.g., Kawamuro _et al._ , 2016;
Annuar _et al._ , 2015, 2017, 2020).

###  3.2 Spectral fitting

We start the analysis by fitting the spectra to $\rm{M_{1}}$. We then fit the
spectra to $\rm{M_{2}}$, and obtain the EW and the luminosity of the
FeK$\rm{\alpha}$ line as explained above. We then fit the spectra to
$\rm{M_{3}}$ and test if reflection is required by the data using the f-test
tool within xspec. If the f-test throws a probability value below $10^{-3}$,
then the reflection component is required by the data. For those objects for
which the reflection component is required, we also test the statistical need
for a power-law (i.e., we fit the spectra to $\rm{M_{4}}$). Objects for which
such component is not statistically needed will be referred as reflection
dominated.

We also estimate the reflection fraction, defined in this work as
$\rm{C_{ref}=L_{ref}/L_{cont}}$, where $\rm{L_{ref}}$ is the luminosity of the
reflection component and $\rm{L_{cont}}$ is the luminosity of the intrinsic
continuum, modelled with a power-law, with both luminosities calculated in the
3-70 keV energy range. They are computed using the cluminosity command within
xspec. We estimate the 1-$\sigma$ errors for the best-fit parameters. Errors
in the luminosities of the different components, as well as in the EW of the
FeK$\rm{\alpha}$ line are presented as follows: if the 3-$\sigma$ errors are
well constrained, we present the 1-$\sigma$ error; upper/lower limits
correspond to the 3-$\sigma$ estimates otherwise. This makes the analysis more
conservative on the luminosity limit of the reflection component and the
FeK$\rm{\alpha}$ line for those sources where the reflection component or the
FeK$\rm{\alpha}$ line are not recovered by the data since it gives 99.6% the
upper limit of the distribution. As for the reflection fraction, we perform
MCMC simulations to recover its value and error as follows: we choose a random
number within a normal distribution centered at the actual value whenever the
luminosity is well constrained. However, when there is an upper/lower limit of
the luminosity, we choose a random number drawn from an uniform distribution
with limits zero and the upper/lower limit. We then calculate the ratio and
repeat the same procedure 1000 times. Finally, we obtain the median for the
central value and the $25^{\rm{th}}$ and $75^{\rm{th}}$ quartiles as the error
range. Whenever the upper limit is above 1 or the lower limit is below 0, we
report the value as a lower or upper limit, respectively.

Fig. 2 shows the best fit for $\rm{M_{1}}$ (upper left), $\rm{M_{2}}$ (upper
right), $\rm{M_{3}}$ (lower left) and $\rm{M_{4}}$ (lower right) for NGC 7582
as an example of the resulting spectral fits. For this particular object, we
obtain for $\rm{M_{1}}$ a $\rm{\chi^{2}/dof=699/675}$, $\rm{M_{2}}$ a
$\rm{\chi^{2}/dof=655/674}$ for while for $\rm{M_{3}}$ we obtain
$\rm{\chi^{2}/dof=650/674}$, for which the f-test gives a value of
$\rm{10^{-12}}$. Indeed, in the upper left panel of the figure, it is possible
to see the poor fit and large residuals in particular around the
$\rm{FeK\alpha}$ line, indicating the need of an extra component to fit the
spectrum. Also note that although upper right and lower left panels show
different models, they both fit the data well, by accounting for the
reflection component, mostly noticeable through the FeK$\rm{\alpha}$ line. On
the other hand, $\rm{M_{4}}$ fits the data poorly with a
$\rm{\chi^{2}/dof=3115.7/677}$ (see lower right panel). Indeed, although
required, the line accounts only for $\sim 0.9\%$ of the reflection component,
while the latter only accounts for $\sim 20\%$ of the 3-70 keV primary
continuum luminosity. This is an example where the existence of the
$\rm{FeK\alpha}$ emission line, the f-test when comparing with the partial-
covering intrinsic continuum model, and the luminosity detection limit, point
out to the existence of a reflection component for this source.

##  4 Results

Name | $\rm{\chi^{2}/dof}$ | $\rm{\log\ NH}$ | $\rm{f_{cov}}$ | $\rm{\Gamma}$ | $\rm{EW}$ | $\rm{C_{ref}}$ | $\rm{\log\ L_{(2-10)\ keV}}$ | $\rm{\log\ L_{(3-70)\ keV}}$ | ftest
---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | $\rm{continuum}$ | $\rm{reflected}$ | $\rm{continuum}$ | $\rm{reflected}$ |
|  | $\rm{cm^{-2}}$ |  |  | $\rm{eV}$ |  | $\rm{erg\ s^{-1}}$ | $\rm{erg\ s^{-1}}$ | $\rm{erg\ s^{-1}}$ | $\rm{erg\ s^{-1}}$ |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
NGC1052 | $744.71/734$ | ${23.15}_{-0.03}^{+0.03}$ | $1*$ | ${1.78}_{-0.04}^{+0.04}$ | $139.30\pm 27.4$ | ${0.15}_{-0.06}^{+0.06}$ | $41.73\pm 0.01$ | $40.21\pm 0.15$ | $42.14\pm 0.01$ | $41.32\pm 0.15$ | ✓
NGC2655 | $84.87/94$ | ${23.41}_{-0.14}^{+0.12}$ | $1*$ | ${2.05}_{-0.15}^{+0.17}$ | $368.43\pm 105.$ | ${0.56}_{-0.26}^{+0.35}$ | $41.32\pm 0.10$ | $40.30\pm 0.17$ | $41.59\pm 0.07$ | $41.23\pm 0.17$ | x
UGC5101 | $54.98/47$ | ${23.84}_{-0.06}^{+0.06}$ | $1*$ | $<1.26$ | $<451.$ | $<1$ | $42.61\pm 0.09$ | $<41.7$ | $43.45\pm 0.08$ | $<43.4$ | x
M81 | $1372.00/1246$ | ${22.16}_{-0.09}^{+0.13}$ | - | ${1.94}_{-0.01}^{+0.01}$ | $33.78\pm 9.45$ | $<0.024$ | $40.54\pm 0.01$ | $<38.2$ | $40.88\pm 0.15$ | $<39.2$ | x
NGC3079CT | $114.37/123$ | ${24.41}_{-0.05}^{+0.03}$ | ${0.98}_{-0.01}^{+0.01}$ | ${1.68}_{-0.15}^{+0.16}$ | $479.64\pm 210.$ | ${0.10}_{-0.05}^{+0.06}$ | $41.59\pm 0.13$ | $39.83\pm 0.20$ | $42.06\pm 0.05$ | $41.01\pm 0.20$ | ✓
UGC5881 | $136.07/163$ | ${23.43}_{-0.36}^{+0.21}$ | ${0.52}_{-0.25}^{+0.19}$ | ${1.75}_{-0.16}^{+0.16}$ | $215.40\pm 75.1$ | ${0.37}_{-0.26}^{+0.37}$ | $42.37\pm 0.11$ | $41.18\pm 0.33$ | $42.80\pm 0.07$ | $42.31\pm 0.33$ | x
NGC3628 | $64.43/81$ | $<22.07$ | - | ${2.05}_{-0.09}^{+0.09}$ | $<100.$ | $<0.230$ | $40.18\pm 0.20$ | $<38.4$ | $40.32\pm 0.27$ | $<39.3$ | x
NGC3718 | $192.45/202$ | ${23.79}_{-0.13}^{+0.13}$ | $<0.06$ | ${2.21}_{-0.04}^{+0.06}$ | $<91.1$ | $<0.111$ | $41.07\pm 0.25$ | $<39.1$ | $41.43\pm 0.27$ | $<40.1$ | x
NGC3998 | $613.34/709$ | ${22.36}_{-0.49}^{+0.74}$ | - | ${1.98}_{-0.04}^{+0.04}$ | $<18.4$ | ${0.05}_{-0.03}^{+0.07}$ | $41.59\pm 0.17$ | $39.76\pm 0.27$ | $41.89\pm 0.16$ | $40.73\pm 0.27$ | x
NGC4102 | $181.53/194$ | ${23.68}_{-0.07}^{+0.06}$ | $1*$ | ${1.26}_{-0.11}^{+0.11}$ | $<312.$ | ${0.29}_{-0.18}^{+0.22}$ | $41.34\pm 0.06$ | $40.00\pm 0.27$ | $42.08\pm 0.04$ | $41.50\pm 0.27$ | x
M106 | $431.61/460$ | ${23.02}_{-0.03}^{+0.15}$ | $>0.87$ | ${1.86}_{-0.04}^{+0.07}$ | $<112.$ | $<0.151$ | $40.36\pm 0.03$ | $<38.8$ | $40.73\pm 0.03$ | $<39.8$ | x
M58 | $802.22/732$ | ${22.34}_{-0.11}^{+0.09}$ | $1*$ | ${2.01}_{-0.04}^{+0.04}$ | $120.73\pm 21.4$ | ${0.08}_{-0.05}^{+0.05}$ | $41.52\pm 0.01$ | $39.75\pm 0.27$ | $41.81\pm 0.01$ | $40.70\pm 0.27$ | x
NGC5005 | $26.45/34$ | ${22.96}_{-0.48}^{+0.39}$ | ${0.68}_{-0.32}^{+0.32}$ | $>2.37$ | $348.49\pm 145.$ | $>0.05$ | $40.39\pm 0.71$ | $39.58\pm 0.20$ | $40.50\pm 0.61$ | $40.25\pm 0.20$ | x
NGC6240 | $374.82/439$ | ${24.12}_{-0.03}^{+0.03}$ | ${0.95}_{-0.01}^{+0.01}$ | ${1.63}_{-0.07}^{+0.07}$ | $398.33\pm 74.3$ | ${0.17}_{-0.05}^{+0.06}$ | $43.37\pm 0.06$ | $41.87\pm 0.12$ | $43.87\pm 0.02$ | $43.08\pm 0.12$ | ✓
MCG+08-31-041 | $200.10/241$ | $<22.47$ | ${>0.21}$ | ${1.96}_{-0.08}^{+0.09}$ | $150.75\pm 63.9$ | ${0.42}_{-0.20}^{+0.25}$ | $42.64\pm 0.07$ | $41.52\pm 0.20$ | $42.90\pm 0.04$ | $42.51\pm 0.20$ | ✓
NGC7130CT | $43.65/58$ | ${24.27}_{-0.25}^{+0.16}$ | $1*$ | $<1.50$ | $715.41\pm 213.$ | $>0.42$ | $41.54\pm 0.38$ | $40.92\pm 0.26$ | $42.29\pm 0.19$ | $42.44\pm 0.26$ | ✓
NGC7331 | $133.31/147$ | ${22.39}_{-0.43}^{+0.27}$ | $1*$ | ${2.13}_{-0.05}^{+0.16}$ | $<182.$ | $<0.437$ | $40.46\pm 0.04$ | $<39.4$ | $40.69\pm 0.03$ | $<40.2$ | x
NGC7479CT | $71.56/78$ | ${24.78}_{-0.06}^{+0.05}$ | $1*$ | ${1.86}_{-0.34}^{+0.61}$ | $693.07\pm 246.$ | ${0.20}_{-0.17}^{+0.45}$ | $42.73\pm 0.48$ | $40.45\pm 0.48$ | $42.80\pm 0.24$ | $41.51\pm 0.48$ | ✓
Table 3: Spectral fit results for the LINER sample. Column(1) is the name of the source, (2) is the $\rm{\chi^{2}/dof}$, where $\rm{dof}$ are the degrees of freedom. Columns (3)-(7) are the column density, $\rm{\log\ NH}$ in units of $\rm{cm^{-2}}$, the covering factor, the photon index, $\Gamma$, the equivalent width (EW) in units of eV and the reflection fraction respectively, while columns (8)-(11) are the continuum and reflected luminosities in units of $\rm{erg\ s^{-1}}$, in the (2-10 keV) and (3-70 keV) bands, respectively. Colum (12) is the f-test performed between models 1 and 3 in all cases. The checkmark (✓) symbol represents a f-test <1E-4, while the x symbol represents otherwise. In Col. (1), the superscript RD is for reflection-dominated sources, while those marked with CT are the Compton-thick sources in our sample, whereas in Col. (4) the dash means that the covering factor is zero, therefore no emission is scattered, and the $*$ symbol means that the parameter is frozen.  Name | $\rm{\chi^{2}/dof}$ | $\rm{\log\ NH}$ | $\rm{f_{cov}}$ | $\rm{\Gamma}$ | $\rm{Eq.\ Width}$ | $\rm{C_{ref}}$ | $\rm{\log\ L_{(2-10)\ keV}}$ | $\rm{\log\ L_{(3-70)\ keV}}$ | ftest
---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | $\rm{continuum}$ | $\rm{reflected}$ | $\rm{continuum}$ | $\rm{reflected}$ |
|  | $\rm{cm^{-2}}$ |  |  | $\rm{eV}$ |  | $\rm{erg\ s^{-1}}$ | $\rm{erg\ s^{-1}}$ | $\rm{erg\ s^{-1}}$ | $\rm{erg\ s^{-1}}$ |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
NGC253 | $566.66/426$ | ${22.81}_{-0.07}^{+0.04}$ | $>0.84$ | $>2.50$ | $248.08\pm 32.8$ | $<0.008$ | $39.69\pm 0.03$ | $<36.9$ | $39.76\pm 0.02$ | $<37.6$ | x
NGC424R | $146.96/139$ | - | - | ${1.54}_{-0.08}^{+0.08}$ | $992.62\pm 155.$ | $>3.52$ | - | $41.31\pm 0.08$ | - | $42.60\pm 0.08$ | ✓
IC1657 | $224.23/213$ | ${23.44}_{-0.07}^{+0.06}$ | $1*$ | ${1.52}_{-0.09}^{+0.09}$ | $234.92\pm 82.4$ | ${0.36}_{-0.20}^{+0.24}$ | $41.78\pm 0.04$ | $40.58\pm 0.23$ | $42.35\pm 0.05$ | $41.88\pm 0.23$ | x
2MXJ0114-5523 | $133.09/140$ | ${23.55}_{-0.10}^{+0.09}$ | $1*$ | ${1.26}_{-0.13}^{+0.13}$ | $<342.$ | ${0.34}_{-0.23}^{+0.29}$ | $41.73\pm 0.07$ | $40.45\pm 0.30$ | $42.47\pm 0.05$ | $41.95\pm 0.30$ | x
MCG+08-03-018 | $181.87/225$ | ${23.92}_{-0.08}^{+0.07}$ | ${0.90}_{-0.04}^{+0.03}$ | ${2.17}_{-0.13}^{+0.15}$ | $412.61\pm 84.1$ | ${0.37}_{-0.18}^{+0.25}$ | $42.74\pm 0.12$ | $41.62\pm 0.18$ | $42.95\pm 0.07$ | $42.46\pm 0.18$ | ✓
NGC612 | $138.33/153$ | ${23.98}_{-0.06}^{+0.05}$ | ${0.99}_{-0.02}^{+0.01}$ | ${1.66}_{-0.13}^{+0.14}$ | $<280.$ | $<0.090$ | $43.36\pm 0.09$ | $<41.5$ | $43.84\pm 0.03$ | $<42.7$ | x
Mrk573CT | $71.03/60$ | ${25.04}_{-0.24}^{+0.12}$ | $>0.97$ | ${2.30}_{-0.39}^{+0.14}$ | $1096.99\pm 213.$ | ${0.18}_{-0.11}^{+0.26}$ | $42.79\pm 0.26$ | $41.39\pm 0.16$ | $42.95\pm 0.24$ | $42.18\pm 0.16$ | ✓
NGC788 | $179.07/194$ | ${23.79}_{-0.08}^{+0.08}$ | $1*$ | ${1.65}_{-0.10}^{+0.11}$ | $286.80\pm 97.2$ | ${0.53}_{-0.23}^{+0.28}$ | $42.51\pm 0.08$ | $41.49\pm 0.16$ | $43.00\pm 0.04$ | $42.70\pm 0.16$ | ✓
M77CT | $747.04/651$ | ${25.08}_{-0.03}^{+0.03}$ | ${0.97}_{-0.01}^{+0.01}$ | ${2.37}_{-0.04}^{+0.04}$ | $1224.43\pm 64.2$ | ${0.18}_{-0.03}^{+0.04}$ | $41.93\pm 0.05$ | $40.57\pm 0.04$ | $42.05\pm 0.03$ | $41.31\pm 0.04$ | ✓
NGC1106CT | $88.06/62$ | ${24.72}_{-0.11}^{+0.08}$ | $>0.98$ | ${1.64}_{-0.47}^{+0.29}$ | $1916.85\pm 423.$ | $>0.11$ | $42.31\pm 0.68$ | $41.16\pm 0.35$ | $42.81\pm 0.42$ | $42.45\pm 0.35$ | ✓
NGC1125CT | $108.35/119$ | ${24.42}_{-0.05}^{+0.06}$ | $1*$ | ${2.36}_{-0.39}^{+0.14}$ | $523.39\pm 148.$ | ${0.13}_{-0.09}^{+0.16}$ | $42.53\pm 0.26$ | $40.99\pm 0.27$ | $42.63\pm 0.14$ | $41.73\pm 0.27$ | ✓
NGC1142 | $104.67/115$ | ${24.07}_{-0.11}^{+0.11}$ | $1*$ | ${1.79}_{-0.16}^{+0.19}$ | $696.39\pm 174.$ | ${0.54}_{-0.29}^{+0.42}$ | $42.98\pm 0.17$ | $41.98\pm 0.20$ | $43.38\pm 0.08$ | $43.07\pm 0.20$ | ✓
Mrk1066 | $45.16/59$ | ${23.79}_{-0.21}^{+0.19}$ | $1*$ | $<1.42$ | $<333.$ | $>0.51$ | $41.27\pm 0.17$ | $40.60\pm 0.26$ | $42.02\pm 0.13$ | $42.11\pm 0.26$ | ✓
NGC1194 | $148.66/219$ | ${23.84}_{-0.09}^{+0.09}$ | $1*$ | ${1.53}_{-0.08}^{+0.08}$ | $631.45\pm 127.$ | $>0.81$ | $42.06\pm 0.09$ | $41.43\pm 0.12$ | $42.62\pm 0.07$ | $42.72\pm 0.12$ | ✓
NGC1229 | $129.13/151$ | ${23.37}_{-0.14}^{+0.12}$ | $1*$ | ${1.42}_{-0.11}^{+0.10}$ | $448.97\pm 108.$ | $>0.54$ | $42.58\pm 0.07$ | $41.85\pm 0.18$ | $43.22\pm 0.07$ | $43.22\pm 0.18$ | ✓
NGC1320CT | $136.01/114$ | ${24.76}_{-0.17}^{+0.08}$ | $>0.91$ | $>0.35$ | $3827.63\pm 345.$ | $>0.35$ | $41.46\pm 0.53$ | $40.88\pm 0.25$ | $42.09\pm 0.67$ | $42.05\pm 0.25$ | ✓
NGC1358 | $176.34/202$ | ${24.16}_{-0.06}^{+0.06}$ | $1*$ | ${1.48}_{-0.10}^{+0.11}$ | $886.71\pm 165.$ | ${0.47}_{-0.17}^{+0.20}$ | $42.14\pm 0.10$ | $41.06\pm 0.12$ | $42.73\pm 0.04$ | $42.39\pm 0.12$ | ✓
NGC1386CT | $65.02/39$ | ${25.15}_{-0.19}^{+0.20}$ | $>0.92$ | ${2.33}_{-0.16}^{+0.14}$ | $1826.11\pm 326.$ | ${0.18}_{-0.13}^{+0.58}$ | $41.37\pm 0.36$ | $40.01\pm 0.15$ | $41.41\pm 0.42$ | $40.76\pm 0.15$ | ✓
UGC3157 | $121.35/158$ | ${23.57}_{-0.08}^{+0.08}$ | $1*$ | ${1.56}_{-0.12}^{+0.12}$ | $181.35\pm 84.4$ | ${0.31}_{-0.18}^{+0.22}$ | $42.23\pm 0.07$ | $40.95\pm 0.25$ | $42.77\pm 0.04$ | $42.21\pm 0.25$ | x
2MSJ0508+1721 | $354.36/363$ | ${22.49}_{-0.18}^{+0.13}$ | $1*$ | ${1.91}_{-0.07}^{+0.07}$ | $202.44\pm 54.3$ | ${0.40}_{-0.17}^{+0.20}$ | $42.86\pm 0.02$ | $41.77\pm 0.17$ | $43.20\pm 0.03$ | $42.78\pm 0.17$ | ✓
ESO5-4CT | $128.33/104$ | $>25.38$ | $>0.98$ | ${1.92}_{-0.09}^{+0.05}$ | $1622.20\pm 222.$ | $>0.38$ | $41.53\pm 0.28$ | $40.71\pm 0.07$ | $41.92\pm 0.27$ | $41.74\pm 0.07$ | ✓
NGC2273CT | $135.57/144$ | ${25.29}_{-0.14}^{+0.11}$ | $1*$ | ${2.11}_{-0.07}^{+0.05}$ | $1950.97\pm 179.$ | ${0.44}_{-0.19}^{+0.37}$ | $42.06\pm 0.17$ | $41.01\pm 0.07$ | $42.26\pm 0.18$ | $41.90\pm 0.07$ | ✓
UGC3601 | $248.47/252$ | ${22.61}_{-0.58}^{+0.76}$ | - | ${1.89}_{-0.09}^{+0.08}$ | $<211.$ | ${0.16}_{-0.11}^{+0.22}$ | $42.47\pm 0.86$ | $41.07\pm 0.29$ | $42.75\pm 0.17$ | $42.10\pm 0.29$ | x
ESO428-14CT | $105.45/107$ | ${24.48}_{-0.18}^{+0.13}$ | $1*$ | ${2.15}_{-0.24}^{+0.19}$ | $1100.08\pm 178.$ | $>0.24$ | $41.41\pm 0.41$ | $40.56\pm 0.19$ | $41.63\pm 0.31$ | $41.43\pm 0.19$ | ✓
2MXJ0756-4137 | $44.55/58$ | $<22.55$ | $1*$ | ${1.83}_{-0.10}^{+0.16}$ | $<343.$ | $>0.32$ | $41.91\pm 0.05$ | $41.07\pm 0.27$ | $42.30\pm 0.08$ | $42.16\pm 0.27$ | x
NGC2788ACT | $72.35/95$ | ${24.27}_{-0.19}^{+0.14}$ | $1*$ | ${1.41}_{-0.14}^{+0.19}$ | $1714.57\pm 303.$ | $>0.55$ | $41.90\pm 0.28$ | $41.25\pm 0.18$ | $42.53\pm 0.18$ | $42.63\pm 0.18$ | ✓
IC2560CT | $118.75/93$ | $>25.29$ | $1*$ | ${2.31}_{-0.11}^{+0.04}$ | $2639.16\pm 225.$ | ${0.19}_{-0.10}^{+0.29}$ | $42.14\pm 0.27$ | $40.72\pm 0.07$ | $42.39\pm 0.30$ | $41.51\pm 0.07$ | ✓
NGC3147 | $242.65/288$ | $<22.65$ | ${0.10}\bullet$ | ${1.84}_{-0.08}^{+0.08}$ | $126.95\pm 55.3$ | $>0.07$ | $41.68\pm 0.54$ | $40.31\pm 0.29$ | $42.15\pm 0.53$ | $41.38\pm 0.29$ | x
NGC3393CT | $53.01/83$ | ${24.37}_{-0.07}^{+0.06}$ | $1*$ | ${1.73}_{-0.19}^{+0.21}$ | $935.61\pm 336.$ | ${0.17}_{-0.09}^{+0.12}$ | $42.60\pm 0.18$ | $41.07\pm 0.20$ | $43.04\pm 0.07$ | $42.21\pm 0.20$ | ✓
2MXJ1105+5856 | $115.59/129$ | ${23.17}_{-0.52}^{+0.39}$ | ${0.30}\bullet$ | ${1.48}_{-0.15}^{+0.17}$ | $<118.$ | $<1$ | $42.57\pm 0.30$ | $<41.7$ | $43.16\pm 0.25$ | $<43.0$ | x
NGC3621 | $94.55/94$ | ${22.73}_{-0.49}^{+0.18}$ | ${0.14}\bullet$ | $>2.46$ | $<210.$ | $<0.219$ | $39.90\pm 0.32$ | $<38.5$ | $40.00\pm 0.38$ | $<39.2$ | x
NGC3786 | $86.13/98$ | $<22.45$ | $<0.17$ | ${1.71}_{-0.11}^{+0.11}$ | $<161.$ | $<0.302$ | $42.84\pm 0.70$ | $<40.7$ | $43.42\pm 0.57$ | $<41.9$ | x
IC751 | $53.50/59$ | ${23.73}_{-0.10}^{+0.14}$ | $1*$ | $<1.29$ | $<733.$ | $>0.25$ | $42.06\pm 0.12$ | $41.07\pm 0.24$ | $42.91\pm 0.08$ | $42.69\pm 0.24$ | x
M88CT | $94.56/50$ | ${24.37}_{-0.20}^{+0.42}$ | ${0.66}_{-0.34}^{+0.25}$ | $>2.44$ | $<325.$ | $<0.344$ | $40.87\pm 0.55$ | $<39.2$ | $40.94\pm 0.55$ | $<39.9$ | x
IC3639CT | $43.71/46$ | ${24.80}_{-0.13}^{+0.14}$ | $1*$ | ${2.19}_{-0.23}^{+0.18}$ | $1896.55\pm 326.$ | ${0.25}_{-0.15}^{+0.32}$ | $42.03\pm 0.27$ | $40.75\pm 0.19$ | $42.23\pm 0.19$ | $41.58\pm 0.19$ | ✓
NGC4785 | $171.80/204$ | ${23.69}_{-0.05}^{+0.05}$ | $1*$ | ${1.79}_{-0.10}^{+0.11}$ | $187.29\pm 72.9$ | ${0.19}_{-0.10}^{+0.12}$ | $42.06\pm 0.06$ | $40.61\pm 0.23$ | $42.46\pm 0.03$ | $41.71\pm 0.23$ | x
Mrk231 | $232.65/238$ | ${22.93}_{-0.11}^{+0.09}$ | $1*$ | ${1.68}_{-0.09}^{+0.09}$ | $<228.$ | ${0.28}_{-0.17}^{+0.20}$ | $42.76\pm 0.03$ | $41.46\pm 0.27$ | $43.22\pm 0.04$ | $42.63\pm 0.27$ | x
NGC4941 | $111.35/115$ | ${24.03}_{-0.15}^{+0.14}$ | $1*$ | ${1.65}_{-0.17}^{+0.20}$ | $688.08\pm 167.$ | $>0.11$ | $40.81\pm 0.19$ | $39.96\pm 0.23$ | $41.29\pm 0.10$ | $41.15\pm 0.23$ | ✓
NGC4939 | $158.68/177$ | ${23.63}_{-0.07}^{+0.06}$ | $1*$ | ${1.51}_{-0.10}^{+0.10}$ | $204.33\pm 86.2$ | ${0.33}_{-0.18}^{+0.22}$ | $41.88\pm 0.06$ | $40.63\pm 0.23$ | $42.45\pm 0.04$ | $41.94\pm 0.23$ | x
NGC4945CT | $1477.10/1559$ | ${24.53}_{-0.01}^{+0.01}$ | ${0.99}\bullet$ | ${1.65}_{-0.03}^{+0.03}$ | $707.58\pm 71.7$ | ${0.05}_{-0.01}^{+0.01}$ | $41.41\pm 0.02$ | $39.40\pm 0.05$ | $41.90\pm 0.00$ | $40.60\pm 0.05$ | ✓
MCG-03-34-064 | $765.22/722$ | ${23.88}_{-0.05}^{+0.05}$ | ${0.94}_{-0.01}^{+0.01}$ | ${1.73}_{-0.04}^{+0.05}$ | $543.42\pm 44.6$ | $>0.69$ | $42.74\pm 0.05$ | $41.98\pm 0.05$ | $43.18\pm 0.03$ | $43.12\pm 0.05$ | ✓
NGC5135CT | $101.51/83$ | $>25.29$ | $1*$ | ${1.65}_{-0.08}^{+0.09}$ | $1192.03\pm 206.$ | $>0.27$ | $40.20\pm 0.16$ | $39.21\pm 0.10$ | $40.77\pm 0.18$ | $40.41\pm 0.10$ | ✓
M51CT | $85.90/94$ | ${24.72}_{-0.06}^{+0.13}$ | ${0.81}_{-0.03}^{+0.07}$ | ${1.54}_{-0.06}^{+0.24}$ | $1636.52\pm 197.$ | $<0.047$ | $40.93\pm 0.10$ | $37.49\pm 0.40$ | $41.04\pm 0.08$ | $37.49\pm 1.07$ | ✓
NGC5252 | $551.16/518$ | ${23.01}_{-0.43}^{+0.28}$ | ${0.38}\bullet$ | ${1.77}_{-0.05}^{+0.07}$ | $<114.$ | $<0.187$ | $43.17\pm 0.15$ | $<41.6$ | $43.58\pm 0.16$ | $<42.7$ | x
NGC5283 | $216.31/230$ | ${23.10}_{-0.07}^{+0.07}$ | $1*$ | ${1.92}_{-0.08}^{+0.08}$ | $113.85\pm 67.7$ | ${0.42}_{-0.20}^{+0.24}$ | $41.98\pm 0.03$ | $40.90\pm 0.19$ | $42.31\pm 0.04$ | $41.91\pm 0.19$ | ✓
NGC5347CT | $43.70/45$ | ${24.79}_{-0.13}^{+0.15}$ | $>0.94$ | ${1.74}_{-0.13}^{+0.13}$ | $2299.24\pm 326.$ | ${0.09}_{-0.06}^{+0.12}$ | $42.03\pm 0.27$ | $40.06\pm 0.26$ | $42.23\pm 0.19$ | $41.11\pm 0.26$ | ✓
NGC5643CT | $156.54/142$ | ${24.94}_{-0.23}^{+0.25}$ | $1*$ | ${2.47}_{-0.09}^{+0.06}$ | $1137.79\pm 151.$ | ${0.28}_{-0.12}^{+0.24}$ | $41.35\pm 0.21$ | $40.24\pm 0.07$ | $41.42\pm 0.19$ | $40.93\pm 0.07$ | ✓
NGC5695 | $38.99/38$ | ${23.94}_{-0.11}^{+0.39}$ | $>0.77$ | $<1.40$ | $797.16\pm 644.$ | $>0.75$ | $41.05\pm 0.31$ | $40.45\pm 0.26$ | $41.87\pm 0.21$ | $42.07\pm 0.26$ | x
NGC5728 | $336.17/398$ | ${24.05}_{-0.03}^{+0.03}$ | $1*$ | ${1.45}_{-0.06}^{+0.06}$ | $428.24\pm 83.7$ | ${0.26}_{-0.07}^{+0.07}$ | $42.21\pm 0.05$ | $40.87\pm 0.09$ | $42.83\pm 0.02$ | $42.23\pm 0.09$ | ✓
NGC5899 | $308.81/378$ | ${22.98}_{-0.16}^{+0.25}$ | ${0.87}_{-0.32}^{+0.13}$ | ${1.80}_{-0.07}^{+0.07}$ | $95.88\pm 46.9$ | ${0.28}_{-0.14}^{+0.22}$ | $42.16\pm 0.08$ | $40.90\pm 0.17$ | $42.56\pm 0.10$ | $41.99\pm 0.17$ | ✓
MCG+14-08-004 | $130.22/161$ | ${23.24}_{-0.11}^{+0.10}$ | $1*$ | ${1.87}_{-0.12}^{+0.12}$ | $265.59\pm 81.6$ | ${0.31}_{-0.19}^{+0.24}$ | $42.48\pm 0.06$ | $41.25\pm 0.27$ | $42.84\pm 0.05$ | $42.28\pm 0.27$ | x
ESO137-34CT | $96.36/106$ | ${24.49}_{-0.09}^{+0.12}$ | $>0.98$ | ${1.78}_{-0.22}^{+0.20}$ | $1066.66\pm 216.$ | ${0.31}_{-0.18}^{+0.32}$ | $42.14\pm 0.26$ | $40.92\pm 0.19$ | $42.54\pm 0.15$ | $42.02\pm 0.19$ | ✓
2MXJ1650+0436 | $331.00/392$ | $<22.45$ | ${0.52}\bullet$ | ${1.72}_{-0.06}^{+0.06}$ | $93.32\pm 46.1$ | ${0.24}_{-0.12}^{+0.14}$ | $43.29\pm 0.04$ | $41.95\pm 0.21$ | $43.73\pm 0.02$ | $43.09\pm 0.21$ | x
2MXIJ1802-1454 | $605.51/591$ | ${22.45}_{-0.11}^{+0.09}$ | $1*$ | ${2.02}_{-0.05}^{+0.05}$ | $97.45\pm 32.1$ | ${0.18}_{-0.07}^{+0.08}$ | $41.76\pm 0.01$ | $40.35\pm 0.16$ | $42.04\pm 0.02$ | $41.29\pm 0.16$ | ✓
2MXJ1830+0928 | $158.71/179$ | ${23.18}_{-0.07}^{+0.07}$ | $1*$ | ${1.89}_{-0.10}^{+0.10}$ | $224.05\pm 73.6$ | ${0.35}_{-0.19}^{+0.24}$ | $42.37\pm 0.04$ | $41.21\pm 0.23$ | $42.72\pm 0.04$ | $42.23\pm 0.23$ | x
IC4995CT | $66.10/65$ | $>25.30$ | ${0.97}_{-0.02}^{+0.01}$ | ${1.81}_{-0.07}^{+0.14}$ | $1266.81\pm 251.$ | $>0.14$ | $42.43\pm 0.29$ | $41.26\pm 0.20$ | $42.83\pm 0.26$ | $42.34\pm 0.20$ | ✓
NGC6921 | $113.83/113$ | ${24.16}_{-0.09}^{+0.08}$ | $1*$ | ${1.66}_{-0.16}^{+0.19}$ | $692.22\pm 187.$ | ${0.34}_{-0.17}^{+0.21}$ | $42.34\pm 0.15$ | $41.13\pm 0.20$ | $42.82\pm 0.04$ | $42.32\pm 0.20$ | ✓
NGC7213 | $879.92/959$ | ${22.57}_{-0.45}^{+0.10}$ | - | ${1.97}_{-0.03}^{+0.03}$ | $80.68\pm 15.7$ | ${0.04}_{-0.02}^{+0.04}$ | $42.00\pm 0.19$ | $40.14\pm 0.17$ | $42.31\pm 0.19$ | $41.11\pm 0.17$ | x
NGC7319 | $74.48/83$ | ${23.62}_{-0.06}^{+0.22}$ | $>0.83$ | ${1.38}_{-0.12}^{+0.16}$ | $710.94\pm 159.$ | $>0.48$ | $41.40\pm 0.11$ | $40.61\pm 0.20$ | $42.02\pm 0.09$ | $42.00\pm 0.20$ | ✓
UGC12282 | $38.97/39$ | ${24.15}_{-0.25}^{+0.16}$ | $1*$ | ${1.62}_{-0.22}^{+0.30}$ | $1602.02\pm 441.$ | $>0.35$ | $41.70\pm 0.38$ | $41.03\pm 0.29$ | $42.20\pm 0.25$ | $42.25\pm 0.29$ | ✓
NGC7582 | $993.71/1095$ | ${23.48}_{-0.03}^{+0.03}$ | ${0.96}_{-0.01}^{+0.01}$ | ${1.60}_{-0.03}^{+0.03}$ | $83.17\pm 21.9$ | ${0.19}_{-0.04}^{+0.04}$ | $42.16\pm 0.01$ | $40.70\pm 0.08$ | $42.68\pm 0.01$ | $41.94\pm 0.08$ | ✓
2MXJ2325-3826 | $62.91/76$ | $<22.24$ | $1*$ | ${1.93}_{-0.11}^{+0.13}$ | $<219.$ | $<1$ | $42.13\pm 0.03$ | $<41.4$ | $42.46\pm 0.07$ | $<42.4$ | x
NGC7674 | $154.67/156$ | ${23.05}_{-0.14}^{+0.12}$ | $1*$ | ${1.57}_{-0.09}^{+0.09}$ | $258.83\pm 90.5$ | $>0.75$ | $41.80\pm 0.05$ | $41.19\pm 0.15$ | $42.33\pm 0.07$ | $42.45\pm 0.15$ | ✓
Table 4: Spectral fit results for the Seyfert sample. Columns are as in Tab.
3.

Tables 3 and 4 present the best-fit parameters for both the LINER and Seyfert
samples when fitted to the $\rm{M_{3}}$ model. Note that we present the best-
fit values for this model only as the analysis is based on this model version
(see above). Note that for the covering factor, $\rm{f_{cov}}$, we also test
whether is zero or free to vary. In the cases in which it is zero, the source
is not covered, corresponding to unobscured/low-obscured sources or, on the
contrary, it is reflection dominated, thus the partially-covered continuum is
not restricted. We mark the column with a dash line in these cases (six
sources). However, although left free to vary, in many cases it is pegged to
one (42 sources), indicating full covering of the source. As for the f-test,
we conclude that when it is below $\rm{10^{-3}}$, the reflection component is
statistically significant and is marked with the check mark symbol in this
Col.(12). Among the 81 objects, we find that only NGC 424 is reflection
dominated, i.e., the data do not require the addition of a power-law and the
luminosity of this component is not restricted. This object is marked with an
R in the Col. (1) of Table 4. The $\rm{N_{H}}$ cannot be calculated for this
source. Moreover, we also find 18 other sources for which the f-test comparing
models $\rm{M_{3}}$ and $\rm{M_{4}}$ does not favour the addition of a power-
law component, although their $\rm{N_{H}}$ are well constrained. These objects
have a large contribution of the reflection component in the CT regime,
although the power-law continuum is still reachable thanks to the wide
spectral range of NuSTAR data. As for intrinsic luminosities, as it was
previously mentioned in section 3.2, these may be larger for CT objects as we
are inducing a systematic uncertainty by excluding the Compton-scattering
effect. Thus, we warn the reader that intrinsic luminosities reported here for
CT objects should be treated a lower limits, even if they are well constrained
by the spectral fits.

###  4.1 Luminosity Correction

As mentioned in Section 2 we select sources with Eddington rate
$\rm{L_{bol,obs}/L_{Edd}<10^{-3}}$ to study inefficient AGN with the public
data available. However, we use as a proxy of the bolometric luminosity, the
observed 2-10 keV X-ray luminosity (i.e. uncorrected from $\rm{N_{H}}$).
Indeed, the intrinsic luminosity and therefore the Eddington rate are expected
to increase once we take into account the $\rm{N_{H}}$. Fig. 3 shows the
observed versus intrinsic 2-10 keV luminosity, the latter corrected from line-
of-sight (LOS) obscuration according to the best fit reported in Tables 3 and
4.

Figure 3: Observed 2-10 keV luminosity versus the intrinsic 2-10 keV
luminosity. Note that the upper limits refer to the reflection dominated
objects (see text). The dash-dotted, dotted, and dashed lines represent the
1:1, 1:10, 1:100 relations, respectively, indicating the correction factor
that should be applied in order to obtain the intrinsic continuum luminosity
from the observed luminosity. Orange stars, red diamonds, magenta hexagons and
green squares are the $\rm{N_{H}}$ ranges shown in the figure label, while the
cyan triangles are NGC 424 uncorrected (solid) and corrected (semi-
translucent, see text).

The largest shift from the 1:1 relation is found for CT objects (green squares
in Fig. 3), for which the luminosity can change more than a factor of ten.
Note that NGC 424, classified as reflection dominated has long been studied at
X-rays (e.g., Baloković _et al._ , 2014; Hernández-García _et al._ , 2015;
Ricci _et al._ , 2017; Marchesi _et al._ , 2018), finding that this object has
a large contribution of the reflection component, with weak signatures of the
intrinsic continuum.

However, since we are unable to account for such a component, we calculate the
bolometric luminosity through the luminosity of the reflection component as
follows: we assume that the correction in the intrinsic luminosity for a
certain object is given in the following form:
$\rm{\log(L_{cont})=A+\log(L_{refl})}$, where $\rm{A}$ can be calculated
through those CT objects for which the power-law is still detected in the
spectra.

Moreover, by calculating the constant $\rm{A}$ for these objects, we can
estimate how much the intrinsic luminosity changes for a certain amount of
reflection. In practice, we estimate this factor using the green objects in
Fig. 3 (i.e. 25 CT AGN). We find for our sample that $\rm{A=1.5\pm 0.8}$. We
then use this value to estimate the intrinsic luminosity for NGC 424. This
extrapolation can be seen as the semi-transluscent cyan triangle in Fig. 3.

Fig. 4 shows the final distribution for the Eddington rate in our sample when
the obscuration is properly taken into account, compared to the initial
Eddington rate, estimated through the observed X-ray luminosity. Indeed, a
shift towards greater Eddington rates is seen in objects with larger
$\rm{N_{H}}$ (mostly CT objects) and a decrease in objects with lower
Eddington rates. The mean Eddington rate of the sample is
$\rm{<log\,(\lambda_{Edd})>=-3.3}$ (dash-dotted vertical line in Fig. 4) with
a 1$\sigma$ range of $[-5.2,-1.49]$ (see dotted lines in the figure), roughly
expanding four orders of magnitude in Eddington rate. Additionally, the lack
of Compton-scattering may shift CT objects to even higher Eddington rates (as
intrinsic luminosities may be even larger). As it was previously mentioned in
section 2.2, we are aware that our selection criteria bias our sample towards
a large LOS obscuration for Eddington rate between
$\rm{-2.5<\log\lambda_{Edd}<-1.49}$ (14 CT AGN). Thus, we will exclude these
sources from the discussion as we are missing an important portion of objects
residing in this range of Eddington rates (mostly highly obscured objects with
intrinsically higher Eddington rates). Moreover, the discussion will be based
on the remaining 67 sources.

Figure 4: Comparison between the Eddington rate obtained with a rough fit to a
simple power-law (dashed histogram) versus the Eddington rate obtained once a
proper obscuration is accounted for (dotted histogram).  Figure 5: Spectral
fits for our eleven candidates for the disappearance of the torus. Colors and
axis labels are as in Fig. 2. Note that we have ionized lines are present in
all the objects (except for NGC 612) and that we have tested the scenario in
which the FeK$\alpha$ line could be the responsible for the line feature,
finding that such line is not present in any of the spectra. Also note that
for M 88 both FPMA and FPMB modules seem to be misaligned with a normalization
factor of 1.99, well above the overall sample.

###  4.2 Existence of the reflection component

We base our analysis on the existence of the reflection component in three
criteria: (1) the detection of the FeK$\rm{\alpha}$ line; (2) a statistical
significance of the reflection component compared to the model without
reflection (i.e. f-test $<0.001$ when comparing models $\rm{M_{1}}$ and
$\rm{M_{3}}$ ), and (3) the restriction of the reflection luminosity at
3–$\rm{\sigma}$ .

We detect the FeK$\rm{\alpha}$ emission line in 61 out of the 81 sources
($\rm{\sim 75\%}$ of the sample). On the other hand, the inclusion of a
reflection component improves the spectral fit for 46 out of the 81 sources
($\sim 57\%$ of the sample). Additionally, we restrict the luminosity of the
reflection component for 67 out of the 81 sources (i.e. $\rm{\sim 83\%}$). A
total of 45 out of 81 ($\rm{\sim 55\%}$) sources fulfill the three criteria to
establish the existence of the reflection component, while 15 ($\rm{\sim
19\%}$) meet two out of the three criteria, and 9 ($\rm{\sim 10\%}$) meet only
one of the criteria (namely M 81, NGC 3998, NGC 4102, NGC 253, 2MXJ 0114-5523,
UGC 3601, 2MXJ 0756-4137, IC 751, and Mrk 231).

As for the 15 sources fulfilling two criteria, one (Mrk 1066) statistically
needs the reflection component and it is well constrained. However, the
$\rm{FeK\alpha}$ emission line is not well detected at a $3-\sigma$ limit.
Note that the spectrum is a low-quality spectrum (dof$\rm{<}$50) which may
cause a poor restriction of the three lines at 6.4, 6.7 and 6.97 keV. In order
to test this possibility, we use the non-grouped spectrum of the source and
check which line is present. Indeed, the line present in this object is the
$\rm{FeK\alpha}$ emission line. Once we remove both ionized lines from the
fit, and calculate the EW and flux for the $\rm{FeK\alpha}$ emission line for
this source, we obtain a constrained parameter. Thus, we can safely say that
this source fulfills the three criteria.

The remaining 14 objects, with two out of the three criteria, fulfill the
detection of the $\rm{FeK\alpha}$ emission line and a constrained luminosity
for the reflection component. However, statistically speaking, the reflection
component is not needed. Among them, all but NGC 5695 show a relatively low
reflection fraction ($\rm{C_{ref}}$) and/or $\rm{N_{H}}$. Thus, the reflection
component is present mainly through the $\rm{FeK\alpha}$ emission line while
the Compton hump is suppressed under the intrinsic continuum. Under this
scenario, the f-statistic is not suitable to test the presence of the
reflection component because it only affects a narrow range of the spectrum
where the $\rm{FeK\alpha}$ emission line is located. In the case of NGC 5695,
it shows a relatively high $\rm{N_{H}}$. In this case, the quality of the
spectrum for this source might be responsible for the statistical significance
of the reflection component.

As for the objects fulfilling only one criterion, seven objects (NGC 3998, NGC
4102, 2MXJ 0114-5523, UGC 3601, 2MXJ 0756-4137, IC 751 and Mrk 231) meet the
restriction of the luminosity of the reflection component, and the remaining
two objects (M 81 and NGC 253) meet the detection of the $\rm{FeK\alpha}$
emission line. The detection of the reflection component without the
$\rm{FeK\alpha}$ line can be due to a combination of high absorption which can
lead to the detection of a Compton hump and a low S/N spectrum which can lead
to the poor restriction of the line. The detection of the $\rm{FeK\alpha}$
line without statistical significance for the reflection component can again
be explained due to low $\rm{N_{H}}$ and/or low reflection fraction as
indicated above. Moreover, the non-detection of the Compton hump may also
depend on the shape of the spectrum; for highly obscured sources it may only
require data up to 10 keV, while for low obscured sources, the Compton hump
requires high S/N up to 30 keV.

We find that 12 objects do not present any signs of reflection (namely UGC
5101, NGC 3628, NGC 3718, M 106, NGC 7331, NGC 612, 2MXJ 1105+5856, NGC 3621,
NGC 3786, M 88, NGC 5252 and 2MXJ 2325-3826). Note that five out these 12
objects are LINERs while the remaining seven are Seyferts. However, several
works have found traces for the reflection component in UGC 5101 (e.g.,
González-Martín _et al._ , 2009; Oda _et al._ , 2017; La Caria _et al._ ,
2019). In addition, the fact that the spectrum has a low S/N leads us to
exclude it from our final sample of candidates for the disappearance of the
torus. Fig. 5 shows the spectral fits for our final sample of 11 candidates to
the torus disappearance ($\rm{\sim 12\%}$). All but NGC 612 can be modelled
with a single power-law999Note that all of them present ionized emission
lines. with little obscuration, supporting the idea that the reflection
component is not present in these objects.

Altogether, we present 11 candidates which lack the reflection component,
related to the plausible disappearance of the torus using X-rays observations.
Among them, we find that eight sources have studies aiming to find the
reflection component or the torus (through X-rays/mid-IR). For all of them we
find complete agreement with the idea of the absence of the reflection
component associated with the torus in previous works (see Sec. 5).

Figure 6: 3-70 keV band luminosity of the reflection component versus that of
the intrinsic continuum (left) and the $\rm{FeK\alpha}$ emission line
luminosity versus the 3-70 keV reflection luminosity (right). In both cases,
lines represent the percentage of the quantity in the Y axis with respect to
the X axis. From top to bottom 100, 50, 10, 3, 1, and 0.5% of the intrinsic
(large left panel) and reflection (large right panel) luminosities. The red
diamond and green square are objects well fitted with the power-law components
(i.e. no reflection candidates) and with the combination of reflection plus
power-law components, respectively. The thick dotted brown line in both panels
represent the linear correlation found for the quantities in each panel when
the X axis is the independent quantity, while the black dashed line in the
histograms represents the mean of each quantity. The histograms in the top and
right panels are the distribution of the different luminosities (see text).

###  4.3 Reflection strength

We explore here the degree of the reflection component strength for the
objects in our sample. Fig. 6 shows the luminosity distribution for the
intrinsic continuum (left histogram), $\rm{FeK\alpha}$ emission line (upper
right histogram) and reflection (right histogram). Note that for both the
reflection and FeK$\alpha$ line distributions, we only show those sources for
which the parameter is well constrained.

The $\rm{FeK\alpha}$ line luminosity ranges from $\rm{log(L_{6.4\
keV})\sim[38.-41.3]}$, with a mean value of $\rm{<log(L_{6.4\ keV})>=40.1}$,
the reflection luminosity ranges from $\rm{log(L_{ref(3-70\
keV)})\sim[37.5,43.2]}$, with a mean value of $\rm{<log(L_{ref(3-70\
keV)})>=41.9}$, and the intrinsic 3-70 keV luminosity ranges from
$\rm{log(L_{cont(3-70\ keV)})\sim[39.8,43.9]}$, with a mean value of
$\rm{<log(L_{cont(3-70\ keV)})>=42.3}$ (see dashed lines in the histograms).
Thus, all these three luminosities span around four orders of magnitude.

The reflection component represents, on average, 40% of the intrinsic
continuum luminosity of the source, (i.e. $\rm{<C_{ref}>=0.41}$101010Note that
this value is calculated for objects with both luminosities well constrained
(i.e., neglecting upper/lower limits.)). In 20 out of the 81 sources the
reflection is below 20% of the intrinsic continuum (i.e. $\rm{C_{ref}<0.2}$),
28 sources fall in the range $\rm{0.2<C_{ref}<0.6}$, and 5 fall in the range
$\rm{C_{ref}>0.6}$, while the remaining 28 sources have lower limits for
$\rm{C_{ref}}$. On the other hand, around 50% of the sample (41 sources) is
located in the area where FeK$\rm{\alpha}$ luminosity accounts for 1-3% of the
reflection component luminosity, 15% (12 sources) is consistent with 3-10%,
and 6% (five sources) sources present a weak line luminosity, accounting for
less than 1% of the reflection component. As for the remaining 28% (23
sources), either the EW of the FeK$\rm{\alpha}$ line and/or the luminosity of
the reflection component are upper limits, therefore the fraction is an upper
limit as well. Naturally, the 11 candidates lacking of reflection signatures
are included in this group.

In order to study the connection between these luminosities, the large panels
in Fig. 6 show the correlation between the reflection luminosity versus the
intrinsic continuum (left panel) and the FeK$\rm{\alpha}$ emission line (right
panel) luminosities. As expected, the three quantities are well correlated.
Moreover, the reflection component and the FeK$\rm{\alpha}$ emission line are
slightly better correlated (with a Pearson’s coefficient of 0.93) than the
intrinsic continuum and the reflection component (with a Pearson’s coefficient
of 0.89).

In order to obtain the best characterization of the relation between those
parameters, we use a bootstrap method to account for possible outliers in the
correlations, by choosing a random subsample with 80% of the total sample and
repeating this process a total of 100 times. For each random subsample, we
also perform a MCMC simulation similar to that mentioned in section 3.2: for
each luminosity pair, we choose a random number drawn from a normal
distribution whenever the value is well constrained, and from an uniform
distribution whenever there are upper/lower limits involved. We then perform a
binning method in the x axis by dividing it into bins of $dx=0.5$ dex, and
obtain the median and standard deviation along both axes. We calculate the
correlation through a linear regression method and obtain the slope,
intercept, and the r- and p-values. We repeat this process 100 times and then
estimate the mean values of all quantities. As for the correlation between
$\rm{L_{ref}}$ and $\rm{L_{6.4\ keV}}$ we also perform the linear regression
analysis assuming that the luminosity of the reflection component is the
independent component and the luminosity of the line is the dependent one. We
present the best correlation found after performing a bisection method from
both correlations. In this case the fraction of the luminosity of the
FeK$\rm{\alpha}$ line over the Compton hump increases from 1% at
$\rm{log(L_{ref})=43}$ to $\rm{\sim}$5% at $\rm{log(L_{ref})=40}$ and to
$\rm{\sim}$10% at $\rm{log(L_{ref})=38}$. Both correlations can be represented
in the following form (represented as the thick dotted brown lines in Fig. 6):

$\rm{\log(L_{ref})=(1.13\pm 0.22)\log(L_{cont})-(6.43\pm 9.35)}$ (6)
$\rm{\log(L_{ref})=(1.24\pm 0.15)\log(L_{6.4\ keV})-(8.17\pm 6.16)}$ (7)

Note that we also explore if this trend is seen over the intrinsic continuum
or the Eddington rate but no correlation is found.

###  4.4 Obscuration

The LOS obscuration and the reflection might occur in the same structure
(i.e., the torus), thus both the reflection and the obscuration may be
related. Therefore, a proper estimate on the $\rm{N_{H}}$ is necessary in
order to place solid conclusions on the reflection component. For this
purpose, Fig. 7 shows the comparison between the $\rm{N_{H}}$ found in this
analysis compared to those presented in Ricci _et al._ (2017). They analyze
the X-ray properties of the Swift/BAT sample for which we find 53 sources in
common. We find that for most sources, the LOS obscuration found in both works
are well in agreement when their column density is $\rm{N_{H}>3\times
10^{22}cm^{-2}}$. We find discrepancies for seven objects below
$\rm{N_{H}<3\times 10^{22}cm^{-2}}$, which may be expected since _NuSTAR_ does
not cover energies below 3 keV, necessary to constrain low values of
obscuration. Moreover, Fig. 8 (right histogram) shows the $\rm{N_{H}}$
distribution for our sample. We find a mean column density of
$\rm{<log(N_{H})>=23.74}$ (see dashed line in the figure). We also find that
24 sources are CT AGN (i.e., $\rm{\log N_{H}>24.17\ cm^{-2}}$) while 45 out of
the 81 are Compton-thin and 12 are unobscured sources. In addition, the
majority of sources with no clear indication of reflection appear to be below
the CT regime. On the other hand, the EW of the $\rm{FeK\alpha}$ line shows a
mean value of $\rm{<log(EW(FeK\alpha))>=2.89}$ (Fig. 8, top histogram), with
20 sources presenting upper limits. Using Suzaku and Swift/BAT data, Kawamuro
_et al._ (2016) also study a sample of 10 inefficient AGN. Among the seven
objects in common with our sample, three (NGC 3718, NGC 4941 and NGC 5643)
show different values for $\rm{N_{H}}$ (discrepancies around 10-20%). We find
higher $\rm{N_{H}}$ for the three sources, even when accounting for error
bars. However, note that although the model is quite similar, they allow the
reflection fraction in pexrav and the constant (which they relate to the
scattering fraction) free to vary in all cases. The main difference is that we
test whether letting the covering fraction free to vary significantly improves
the fit. This might explain the $\rm{N_{H}}$ differences found in both
analyses.

Figure 7: Comparison between our $\rm{N_{H}}$ estimates and the values
reported in Ricci _et al._ (2017) for the common sample. Sources with a black
dot inside the red star are the candidates for the torus disappearance in our
sample. Note that upper limits in our analysis might be due to the fact that
the sources are low-obscured or unobscured (see text).

Marchesi _et al._ (2018) analyze a sample of 26 sources classified as CT,
using NuSTAR along with other X-ray facilities. Among those objects, we find
14 sources in common with our work, from which 10 have similar value of
$\rm{N_{H}}$ compared to ours, while three have small discrepancies on the
$\rm{N_{H}}$ (i.e. lower than 10%), and one case (NGC 424) for which we have
strong differences: they report a reflection dominated source, with
$\rm{N_{H}}=24.4$, while from our analysis it should be considered as highly
obscured ($\rm{log(N_{H})=23.1}$). Indeed, this source is also reflection
dominated according to our f-test analysis. Thus, statistically speaking, the
obscured power-law associated with the intrinsic continuum is not required by
the data. Moreover, their reflection model is different to ours, which might
be responsible for the small changes in the spectral parameters.

Panagiotou and Walter (2019) also studied six sources in common with this work
(M 106, NGC 1194, NGC 4941, NGC 5643, NGC 5728, and NGC 7582). All but two
(NGC 4941 (24.09$\pm$0.15) and NGC 1194 (23.7$\pm$0.1) present consistent
$\rm{N_{H}}$ values. NGC 4941 and NGC 1194 present higher $\rm{N_{H}}$
compared to ours, even when accounting for error bars. Again, they classify
these two sources as reflection dominated so this might be affecting the
constraint of the LOS absorption due to a weak detection of the instrinsic
continuum. In a second paper of the series, Panagiotou and Walter (2020)
include _NuSTAR_ data for other six sources in common with our analysis (NGC
1052, NGC 2655, M 106, NGC 5252, NGC 5283 and NGC 7213), also showing
consistent $\rm{N_{H}}$. Note that Panagiotou and Walter (2020) exclude in
their sample selection 21 sources in common with our sample; four (M 81, NGC
3998, NGC 7130, and NGC 7479) are excluded due to their LINER nature, two (IC
751 and NGC 7582) due to variability, and the remaining 15 are excluded for
being reflection dominated (although included in Panagiotou and Walter, 2019).

We plot the expected correlation between the $\rm{N_{H}}$ and the
$\rm{EW(FeK\alpha)}$ emission line in the large panel of Fig. 8. The
equivalent width increases when the $\rm{N_{H}}$ does so, with a Pearson’s
linear relation coefficient of 0.85 (linear fit shown as dotted brown line in
the figure). This is well explained by the predicted EW from a uniform shell
of material encompassing the continuum source (blue long-dashed line in large
panel of Fig. 8, see also Fig. 2 in Leahy and Creighton, 1993) . Moreover,
Guainazzi, Matt, and Perola (2005) propose a slight change in this correlation
when the reflection occurs in the inner walls of an optically-thick matter, as
seen through the unobscured LOS, while the continuum is obscured by material
along the LOS (see pink dashed line in Fig. 8 and Fig. 9 in Guainazzi, Matt,
and Perola, 2005). Note that the dispersion on this relation is naturally
explained through the differences in geometry and composition of the
reflector. Therefore, this reinforces the good estimate on the $\rm{N_{H}}$ in
our analysis. This is also reproduced in more recent models with spherical and
torus-like geometries (e.g Ikeda, Awaki, and Terashima, 2009; Tanimoto _et
al._ , 2019) Moreover, we explore how the EW is affected by the amount of
obscuration and the strength of the line (see shaded area in Fig. 8). We
choose NGC 1052 as a test object and vary the normalization of the FeK$\alpha$
line (from $\rm{norm_{6.4keV}}=0.5$ to $\rm{norm_{6.4keV}}=5$), from left to
right, respectively, while changing the $\rm{N_{H}}$ in order to see how the
relation should change. We find that there is a value of $\rm{EW}$ above which
this correlation saturates and thus we would only measure reflection (i.e., in
the cases of reflection dominated sources). The main reason for the
differences between this work and Guainazzi, Matt, and Perola (2005) is the
fact that they do not have very obscured sources in their sample and thus
their best fit does not cover such range. Thus, we confirm that 69 out of the
81 objects ($\rm{\sim 85\%}$) are obscured at X-rays (i.e. $\rm{N_{H}>3\times
10^{22}cm^{-2}}$). This is further discussed in Section 5.

Figure 8: Equivalent width of the $\rm{FeK\alpha}$ line versus the column
density along the LOS. Colors and symbols are as in Fig. 6. The correlation
line is drawn as the brown dotted line while the blue long-dashed line and
pink dashed lines show the expected relation according to Leahy and Creighton
(1993) and Guainazzi, Matt, and Perola (2005), respectively. Moreover, the
gray shaded area corresponds to the case in which the EW changes according to
different levels of obscuration and reflection (see text).

Furthermore, more than half of the sources (42) appear to be completely
covered, 27 present a covering factor $\rm{f_{cov}>0.5}$, while seven show
$\rm{f_{cov}<0.5}$. The remaining five AGN present either upper limits or non-
constrained estimates for the covering factor. Among these objects, all of
them present either low $\rm{N_{H}}$ or upper limits whereas the sources
presenting full covering, also present high obscuration (with only 6 sources
being mildly obscured).

##  5 Discussion

The aim of this work is to study the behaviour of the reflection component and
obscuration at X-rays (classically associated with the torus) at low accretion
rates. In order to trace such a component, we selected a sample of 81 sources
with NuSTAR observations among all the nearby AGN observed so far with
available $\rm{M_{BH}}$ measurements. We performed a spectral analysis with a
model that accounts for the reflection component from neutral material plus a
partially absorbed intrinsic continuum.

Early X-ray observations of local AGN have served as observational proofs of
the AGN unified theories, showing that most type-1 AGN are unobscured while
type-2 AGN tend to show obscuration exceeding $\rm{N_{H}>10^{22}cm^{-2}}$
(Awaki _et al._ , 1991; Bassani _et al._ , 1999). However, since then, several
authors have shown that the fraction of obscured sources might depend on the
evolutionary stage of the sources (see Ramos Almeida and Ricci, 2017, for a
review).

The covering factor of the gas can be estimated studying the absorption
properties of large samples of AGN. In Fig. 9 we compare the results found by
Ricci _et al._ (2017) using the BASS sample and those found in this study
(numbers are reported in Table 5). Using this technique, recent hard X-ray
studies have shown that the fraction of CT sources below
$\rm{\lambda_{Edd}\sim 0.032}$ is $\rm{23\pm 6\%}$ (blue shaded area in Fig.
9). Marchesi _et al._ (2018) find that the fraction of CT sources decreases
when using _NuSTAR_ data thanks to a better covering and sensitivity above 10
keV which allows a better restriction in the LOS obscuration affecting the
intrinsic continuum.

Our results indicate that the fraction of CT sources at
$\rm{\lambda_{Edd}\simeq 10^{-5}}$ is $\rm{15\%}$ (dotted line), while Ricci
_et al._ (2017) find it to be $\rm{\sim 20\pm 4\%}$. Thus, our results are
statistically in agreement with them. Meanwhile, Ricci _et al._ (2017) find
that the peak of obscured sources happens around $\rm{\lambda_{Edd}\sim
10^{-3}}$, rising from 20% to 80% at Eddington rates $\rm{\lambda_{Edd}\simeq
10^{-1}}$ and $\rm{\lambda_{Edd}\simeq 10^{-3}}$, respectively (see red shaded
area in Fig. 9, see also Ricci _et al._ , 2017). Interestingly, our sample
agrees well with these numbers at $\rm{\lambda_{Edd}\simeq 10^{-3}}$ for the
percentage of obscured AGN (dashed line in Fig. 9). Note that our results
indicate a low population of unobscured sources at $\rm{\lambda_{Edd}\simeq
10^{-3}}$. Moreover, a slight decrease on the fraction of Compton-thin
obscured sources is found below $\rm{\lambda_{Edd}\simeq 10^{-3}}$, reaching
$\sim$60% at $\rm{\lambda_{Edd}\simeq 10^{-5}}$. Correspondingly, the fraction
of unobscured sources rises from $\rm{\sim 6}$ at $\rm{\lambda_{Edd}\simeq
10^{-3}}$ to $\rm{\sim 30}$% at $\rm{\lambda_{Edd}\simeq 10^{-5}}$.
Nonetheless, we are aware that this may be due to a bias in the selection
criteria. Indeed, if there were more unobscured sources at these Eddington
rates, they should have been included in our sample. However, we select only
those sources with archival data and a minimum S/N in the spectrum. This has
two main consequences: i) there may be several objects which have not yet been
observed, among which there might be unobscured sources. ii) there might be
more obscured sources for which the flux is so low that they do not fulfill
our S/N criteria. Thus, although our results are in agreement with the
complete sample by Ricci _et al._ (2017), we warn the reader that our sample
is incomplete.

Figure 9: Fraction of Compton-thin and Compton-thick sources for the _Swift_
/BAT sample reported by Ricci _et al._ (2017) (red and blue shaded areas,
respectively) compared to the unobscured, obscured and CT (solid, dashed and
dotted lines, respectively). Note that our sample is limited above
$\rm{\lambda_{Edd}>-2.5}$ due to the selection criteria we use in this work.

The trend found in this analysis might suggest no obscuration for a large
fraction of sources at even lower accretion rates. The scenario in which both
the BLR and the torus can be seen as different regions from a wind coming off
the disk has long been proposed (Elvis, 2000) and it naturally includes the
absence of such regions in some objects (e.g., True-type 2 AGN intrinsically
miss the BLR Tran, 2001; Laor, 2003; Panessa _et al._ , 2006). If the
accretion disk cannot expel material in an efficient way, then the
gravitational force from the SMBH will overcome the radiation pressure from
the wind, causing the wind, and therefore the BLR and the torus, to collapse
(Elitzur and Shlosman, 2006). Therefore, as a first approach, the condition
for the torus disappearance can be related to the bolometric luminosity of the
source and the accretion rate. According to Elitzur and Shlosman (2006), the
BLR should disappear for low-luminosity AGN (i.e., $\rm{L_{bol}<10^{42}\ erg\
s^{-1}}$). Six out of the 11 objects lacking reflection signatures in our
sample are below this threshold. However, in a more recent study it has been
shown that this structure can disappear even for bright sources (e.g. Elitzur
and Netzer, 2016), depending on the properties of the wind, such as the wind
efficiency or the number/density of clouds. In fact, it requires a minimal
column density, implying a minimal outflow rate and thus a minimal accretion
rate. Interestingly, three of our candidates present upper limits on the
$\rm{N_{H}}$ and other five show $\rm{N_{H}\leq 10^{23}cm^{-2}}$. Finally,
three are rather obscured (namely M 106, NGC 612 and M 88). In particular, for
M 106, Kawamuro _et al._ (2016) find that the $\rm{FeK\alpha}$ line is
variable, proposing it might be originated in the accretion disk, while in the
case of NGC 612, Ursini _et al._ (2018) do not find strong features of a
Compton-reflection component, although like us, they find that this source
presents high absorption, proposing that it might originate in an extended
structure rather than the pc-scale torus. Thus, these works are still in
agreement with the lack of reflection originated in the torus. Another
particularly interesting object is M 88, being proposed as a True-Type 2 AGN
(i.e., intrinsically missing the BLR, Brightman and Nandra, 2008). We would
expect for this object to be low-obscured. Although we modelled this source
with an obscured component, the quality of the observations111111The spectra
of M 88 show calibration issues clearly visible in Fig. 5 and resulting in a
calibration factor much larger than for the rest of the sample, with a value
of $\rm{C_{cross}=1.99\pm 0.19}$. may prevent us from finding a reliable value
in the $\rm{N_{H}}$ for this particular source. Thus, almost all our
candidates to the torus disappearance are on the lower end of LOS obscuration
(Fig. 8).

According to Elitzur and Netzer (2016), the BLR/torus may or may not exist in
a delimited zone in the luminosity-$\rm{M_{BH}}$ diagram and both components
should disappear under a certain threshold delimited by the wind parameters.
Fig. 10 shows the bolometric luminosity versus $\rm{M_{BH}}$ diagram for our
sample (large symbols), excluding the sources for which
$\rm{\lambda_{Edd}>-2.5}$ Note that although these sources are mostly CT at
this Eddington rate, it is difficult to asses how many sources we may be
missing due to the selection biases we have imposed and to the available data.

As a comparison sample, we also plot data from the Swift/BAT sample (Koss _et
al._ , 2017, plotted as the small star symbols). We selected sources from that
sample such that they had some estimate on the ${\rm{M_{BH}}}$, with reported
values for the intrinsic 2-10 keV luminosity, to obtain the bolometric
luminosity and LOS obscuration. We discarded sources without constrained
$\rm{\log(N_{H})}$ values and we also neglect the sources in common. We
obtained a total of 195 sources for the comparison sample. Note that all our
sources fall within the region in which the BLR/torus may or may not exist
(red lines), according to Elitzur and Netzer (2016). We also plot with red
triangles our 11 candidates for the torus disappearance. The location of our
candidates is in complete agreement with the idea that the torus disappearance
does not rely solely on the bolometric luminosity of the source, yet, it does
disappear for inefficient sources. Moreover, González-Martín _et al._ (2017)
study a sample of AGN using mid-IR spectra trying to understand the behaviour
of the torus in what is called the gradual resizing. We plot in Fig. 10 (gray
circles) their candidates for the disappearance of the torus from a mid-IR
point of view. Unlike us, they do have objects lacking the torus below the
limit proposed by Elitzur and Netzer (2016), at
$\rm{\lambda_{Edd}=10^{-6}-10^{-5}}$ depending on the $\rm{M_{BH}}$. However,
they also found several candidates in the range between
$\rm{\lambda_{Edd}=10^{-5}-10^{-3}}$. Our study complements theirs by the
inclusion of these 11 new candidates to the torus disappearance; all together
a sample of 25 AGN. Indeed, we may also be missing objects with
$\rm{\lambda_{Edd}<10^{-5.5}}$, either because observations for such low-
luminosity objects have not yet been performed, or because the S/N of the
observations are so low that they do not fulfill our selection criteria.
Moreover, highly obscured objects might be missing because they are more
difficult to detect than unobscured objects.

$\rm{log(\lambda_{Edd})}$ (total) | Unobs. | Obs | CT | No ref.
---|---|---|---|---
| # (%) | # (%) | # (%) | # (%)
(1) | (2) | (3) (4) | (5) |
-5 (7) | 2 (28) | 4 (57) | 1 (14) | 2 (28)
-4 (19) | 6 (31) | 11 (58) | 2 (10) | 4 (21)
-3 (41) | 3 (7) | 28 (68) | 10 (24) | 3 (7)
Table 5:  Number of unobscured, obscured, CT and no reflection sources per
Eddington rate range. In parenthesis it is represented the contribution
percentage for each of the classifications. Note that sources with no
reflection do not sum up to the total contribution in each range, since both
the $\rm{N_{H}}$ classification is independent.

Another interesting result on the obscurer behaviour is the increase on the
narrow FeK$\rm{\alpha}$ line luminosity compared to the reflection luminosity
when the reflection luminosity decreases (Fig. 6, large right panel). This is
present when we compare the reflection luminosity with the intrinsic
luminosity, showing a mean contribution of 40% of reflection for the full
range of the intrinsic luminosity (Fig. 6, large left panel). However, the
FeK${\rm{\alpha}}$ line and reflection component changes are not associated
with the accretion rate, because no correlation is found between the accretion
rate and the luminosity of the reflection component or the FeK$\rm{\alpha}$
line. Although the flux of the narrow FeK$\rm{\alpha}$ line (compared to the
intrinsic X-ray flux) is generally weaker in type-2 AGN than in type-1 AGN for
the same 10-50 keV continuum luminosity (Ricci _et al._ , 2014), this is not
reproduced by the low accretion AGN in our sample. Ricci _et al._ (2014)
suggest that this difference can be explained by means of different average
inclination angles with respect to the torus, as predicted by the unified
model. However, our sample is mostly constituted by type-2 AGN which might
explain why we do not find such behaviour. While the FeK$\rm{\alpha}$ line can
be produced by material with column densities as low as $\rm{N_{H}\simeq
10^{21-23}\,cm^{-2}}$, the Compton hump can only be created by the
reprocessing of X-ray photons in CT material. Thus, the increase on the
fraction of FeK$\rm{\alpha}$ line luminosity compared to the Compton hump
luminosity toward low reflection luminosities might be an indication of a
higher fraction of the emission produced in Compton-thin material associated
with the accretion disk. If the accretion disk contribution is responsible for
this behaviour, we might expect differences on the photon index distributions
that might contribute to the Compton hump and or the FeK$\rm{\alpha}$ line
differently as long as the reflection luminosity decreases. For instance, it
is expected for the photon index of standard disks to be larger for higher
intrinsic luminosities (softer-when-brighter), while it is expected to
decrease with increasing luminosity in radiatively inefficient accretion disks
(harder-when-brighter, Narayan and Yi, 1995; Connolly et al., 2016, and
references therein).

However, the mean of the distribution of the photon index
($\rm{<\Gamma>=1.81}$) is similar to the average photon index found in diverse
AGN samples (e.g. _Swift_ /BAT, Koss _et al._ , 2017), and we do not find any
particular trend on the accretion disk that might explain this behaviour found
in the strength of the line. Another alternative is a smooth transition on the
average iron abundances of the X-ray reflector (i.e. torus, Ricci _et al._ ,
2014). This might imply a smooth transition on the chemistry of the torus as
seen at X-rays as long as the torus luminosity decreases traced by the Compton
hump. In favor, González-Martín _et al._ (2017) also find that a group of
objects with a low contribution from the torus, are not well described with
the clumpy torus model at mid-IR. They suggest that this might imply that the
torus chemistry may be different at low luminosities, consistent with these
findings.

Figure 10: Bolometric luminosity versus $\rm{M_{BH}}$ for our sample (colors
and symbols as in Fig. 6) and the BASS sample (small empty stars). Our 11
candidates are plotted in the larger red triangles. The semi-translucent
circles represent the candidates for torus disappearance found by González-
Martín _et al._ (2017) using mid-IR data. The black dashed lines represent
$\rm{\log(L_{Edd})=[0,-1,-2,-3,-4,-5,-6]}$ from top to bottom, respectively.
The two red lines enclose the region in which the torus may or may not exist
depending on the wind parameters, as proposed by Elitzur and Ho (2009). The
gray-shaded area corresponds to the Eddington rates from the sample not biased
by the selection criteria. Note that those sources with Eddington rates above
$\rm{\log\ \lambda_{Edd}\sim-2.5}$ are not shown in this plot since at those
Eddington rates our sample is not complete.

##  6 Summary and conclusions

We have performed an analysis aimed to find the conditions for the change and
plausible disappearance of the obscuring gas for low-accretion AGN. For that
purpose, we used a sample of 81 sources observed with NuSTAR selected by
having Eddington rates $\rm{\lambda_{Edd}\lesssim 10^{-3}}$. We fitted the
data with a model accounting for a patchy absorber and a reflection component
from neutral material. We found that $\sim 80\%$ of our sample is obscured,
with $20\%$ of CT sources, in agreement with several works (e.g. Ricci _et
al._ , 2017; Marchesi _et al._ , 2018).

In order to directly compare the lack of reflection component with those
sources lacking of the torus at mid-IR wavelengths, fainter X-ray sources,
with luminosities $\rm{L_{X}\sim 10^{38}\ erg\ s^{-1}}$ are required. However,
we found that a small number of sources in our sample ($\sim$15%) seem to lack
the reflection component associated with the torus, while the rest of the
sources are found to have reflection features such as the existence of the
$\rm{FeK\alpha}$ line and/or the reflection hump. The sources lacking of
reflection component features are located in the region where the torus may or
may not disappear according to their $\rm{M_{BH}}$ and bolometric
luminosities. When the reflection component was detected, it accounts for
$40\%$ of the luminosity of the intrinsic continuum. We also found tentative
evidence in favour of an increase of unobscured sources and a change of the
reflector chemistry toward $\rm{\lambda_{Edd}\sim 10^{-5}}$. Our findings are
in agreement with the scenario in which as the AGN becomes less efficient, the
torus is not supported by the radiation field from the wind coming off the
accretion disk and fades. As a final remark, we highlight the importance of
better S/N data and a broader energy coverage in order to apply more complex
models for the reflection component, which includes testing if it may also be
produced in the accretion disk (i.e., ionized reflection), but also testing
different geometries and matter distributions (i.e, homogeneous, clumpy, etc).

## Acknowledgements

We thank the anonymous referee for her/his useful comments which greatly
improved this paper. This research has made use of the NASA/IPAC Extragalactic
Database (NED), which is operated by the Jet Propulsion Laboratory, California
Institute of Technology, under contract with the National Aeronautics and
Space Administration. This research has made use of data and/or software
provided by the High Energy Astrophysics Science Archive Research Center
(HEASARC), which is a service of the Astrophysics Science Division at
NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian
Astrophysical Observatory. NOC would like to thank CONACyT scholarship No.
897887. CVC acknowledges support from CONACyT. We thank the UNAM PAPIIT
project IN105720 (PI OGM). LHG acknowledges funds by ANID – Millennium Science
Initiative Program – ICN12$\\_$009 awarded to the Millennium Institute of
Astrophysics (MAS).

## Data Availability

The data underlying this article are available in at
https://heasarc.gsfc.nasa.gov/. The datasets were derived from sources in the
public domain.

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##  Appendix A Modeling with CABS

We use a model which does not account for the Compton scattering, particularly
important for Compton-thick objects (Annuar _et al._ , 2017; Ricci _et al._ ,
2017; Zhao _et al._ , 2019; Marchesi _et al._ , 2019). xspec has a model to
account for Compton scattering called cabs121212see xspec manual
https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XspecManual.html . This
model component has been reported to present some issues (see e.g. mytorus
manual and Tanimoto _et al._ , 2018), and does not emulate properly the X-ray
spectra of AGN. However, cabs has been used in several recent works to account
for Compton scattering in AGN when using _NuSTAR_ data (see Ricci _et al._ ,
2017; Oda _et al._ , 2017; Tanimoto _et al._ , 2020). In practice, we added
the cabs component to the model in Eq. (4) as follows:

$M_{5}={\tt phabs_{\rm{Gal}}}(({\tt zphabs_{\rm{intr}}}*{\tt cabs}*{\tt
zpowerlw})+{\tt ct}*{\tt zpowerlw}\\\ +{\tt pexmon}+{\tt zgauss_{6.7\
keV}}+{\tt zgauss_{6.97\ keV}})$ (8)

letting the $\rm{N_{H}}$ in the cabs component to be the same as that of the
LOS obscuration. The resulting $\rm{N_{H}}$ values are mostly consistent with
those reported in this work (see below). However, the intrinsic luminosity of
the sources obtained for some objects changes by a factor of $10^{4}$ (see
Fig. 11 shows). Indeed, note that a non-negligible amount of sources fall well
outside the 1:1 relation even when accounting for error bars (black solid
line). Moreover, the error bars are much larger when using cabs than when
excluding it. These luminosities result in Eddington rates close to the
Eddington limit, which are unrealistic values for LLAGN.

These results imply that there is a systematic uncertainty when adding the
Compton-scattering through the cabs component. However, this does not imply
that such a component does not physically exist in the X-ray spectra of AGN.
In fact, the neglection of this component does add a systematic uncertainty to
the general analysis. Indeed, this effect primarily affects the X-ray spectra
of CT objects. Thus, although the addition of cabs does not lead to physically
realistic results, the exclusion of the Compton-scattering effects in our
analysis, imply that all intrinsic luminosities for CT sources reported here
should be treated as lower limits.

Figure 11: Intrinsic luminosity of the power-law component when including cabs
in the spectral modeling (vertical axis) compared to the case in which it is
not used (horizontal axis). The brown dotted and black solid lines are the
best fit to the data and the 1:1 relation, respectively.

We have also checked how the exclusion of this component affects the
$\rm{N_{H}}$ measurement. Fig. 12 shows the change in this parameter. The
black dashed line shows the 1:1 relation. In this case, most of the sources
fall in this line, with only 8 sources falling outside the relation. Note that
this is a result similar to the one by Tanimoto _et al._ (2018, see their Fig.
5a) , where they found larger values for the intrinsic luminosity when using
this model. However, the spectral parameters were not very much affected.

Figure 12: Column density of the sources when cabs is added (vertical axis)
compared to the case in which it is not used (horizontal axis). The black
dashed line is the 1:1 relation.