11institutetext: Dipartimento di Fisica e Astronomia “Augusto Righi”,
Università degli Studi di Bologna, via P. Gobetti 93/2, 40129 Bologna, Italy
22institutetext: INAF-OAS, Osservatorio di Astrofisica e Scienza dello Spazio
di Bologna, via Gobetti 93/3, 40129 Bologna, Italy 33institutetext: SISSA, Via
Bonomea 265, 34136 Trieste, Italy 44institutetext: Department of Physics and
Astronomy, Clemson University, Kinard Lab of Physics, Clemson, SC 29634, USA
55institutetext: Dipartimento di Matematica e Fisica, Università Roma Tre, via
della Vasca Navale 84, I-00146, Roma, Italy 66institutetext: Department of
Physics and Yale Center for Astronomy & Astrophysics, Yale University, New
Haven, CT 06520, USA

# COSMOS2020: Investigating the AGN-obscured accretion phase at $z\sim 1$ via
[Ne v] selection

Luigi Barchiesi<EMAIL_ADDRESS>1122 C. Vignali 1122 F. Pozzi 1122
R. Gilli 22 M. Mignoli 22 C. Gruppioni 22 A. Lapi 33 S. Marchesi 112244 F.
Ricci 5522 C. M. Urry 66

(Accepted 14 February 2024)

The black hole-and-galaxy (BH-galaxy) co-evolution paradigm predicts a phase
where most of the star formation (SF) and BH accretion takes place in gas-rich
environments, namely, in what are likely to be very obscured conditions. In
the first phase of this growth, some of the galactic gas is funnelled toward
the centre of the galaxy and is accreted into the supermassive BH, triggering
active galactic nucleus (AGN) activity. The large quantity of gas and dust
hides the emission and the AGN appears as an obscured (type 2) AGN. The degree
of obscuration in type 2 AGNs may even reach values as high as $N_{H}>10^{24}$
cm-2 (i.e., Compton-thick, CT). Population synthesis models of the X-ray
background (XRB) suggest that a large population of CT-AGN is, in fact, needed
to explain the still unresolved XRB emission at energy above 20 keV.

In this work, we investigated the properties of 94 [Ne v]$3426\AA$-selected
type 2 AGN in COSMOS at $z=0.6-1.2$, performing optical-to-far-infrared (FIR)
spectral energy distribution (SED) fitting of COSMOS2020 photometric data to
estimate the AGN bolometric luminosity and stellar mass, star formation rate,
age of the oldest stars, and molecular gas mass for their host-galaxy. In
addition, we performed an X-ray spectral analysis of the 36 X-ray-detected
sources to obtain reliable values of the AGN obscuration and intrinsic
luminosity, as well as to constrain the AGN properties of the X-ray-undetected
sources.

We found that more than two-thirds of our sample is composed of very obscured
sources ($\rm{N}_{\rm{H}}>10^{23}$ cm-2), with about 20% of the sources being
candidate CT-AGN and half being AGNs in a strong phase of accretion
($\lambda_{\text{Edd}}>0.1$). We built a mass- and redshift-matched control
sample and its comparison with the [Ne v] sample indicates that the latter has
a higher fraction of sources within the main sequence of star-forming galaxies
and shows little evidence for AGNs quenching the SF. As the two samples have
similar amounts of cold gas available to fuel the SF, this difference points
towards a higher efficiency in forming stars in the [Ne v]-selected sample.
The comparison with the prediction from the in situ co-evolution model
suggests that [Ne v] is an effective tool for selecting galaxies in the
obscured growth phase of the BH-galaxy co-evolution paradigm. We find that the
”quenching phase” is still to come for most of the sample and only few
galaxies show evidence of quenched SF activity.

###### Key Words.:

Galaxies: active – galaxies: evolution – (Galaxies) quasars: emission lines –
X-rays: galaxies

##  1 Introduction

The study of obscured (type 2) active galactic nuclei (AGNs) is fundamental to
understanding the evolution phases of AGNs and their influence on galaxy
growth. The presence of scaling relations between the mass of the supermassive
black hole (SMBH) and several physical properties of the host galaxy, such as
galaxy bulge mass, luminosity, and velocity dispersion (e.g., Kormendy &
Richstone 1995; Magorrian et al. 1998; Ferrarese & Merritt 2000; Gebhardt et
al. 2000; Kormendy & Ho 2013), suggest that the growth of the SMBH and of the
galaxy are coupled, leading to the formulation of the AGN-galaxy co-evolution
paradigm (e.g., Hopkins et al. 2007a; Lapi et al. 2014, 2018). In this
scenario, an intense phase of star formation (SF) is triggered by a wet
merger, at least for the most luminous and massive systems (Silk & Rees 1998;
Di Matteo et al. 2005; Treister et al. 2012; Lamastra et al. 2013), or by in
situ processes including fast inflow and cooling of gas clumps (e.g., Lapi et
al. 2018). A fraction of the gas reservoir of the galaxy is funnelled towards
the SMBH and initiates AGN activity. Thus, this phase is characterized by the
growth of both the SMBH and the stellar mass of the galaxy. Due to the large
quantity of gas, the majority of the AGN-emitted radiation is absorbed and the
source appears as an obscured AGN. We can find indications of this phase in
the larger fraction of obscured AGNs found in mergers and post-mergers
galaxies (e.g., Satyapal et al. 2014; Ellison et al. 2019; Secrest et al.
2020), as well as in the detection of AGN activity in strongly star-forming
submillimeter galaxies at high-$z$ (e.g., Archibald et al. 2002; Almaini 2003;
Alexander et al. 2005). As the SF and the AGN consume, heat up, and expel the
gas, the AGN begins to appear less obscured and is identified with a type 1
AGN. Moreover, the decrease in the amount of available gas leads to a decrease
of the SF and, eventually, to the end of the AGN activity, leaving behind a
“red-and-dead” elliptical galaxy (e.g., Hopkins et al. 2007a; Cattaneo et al.
2009). This scenario is supported by the observations of molecular outflows,
extending on kpc scales from the nucleus, in some AGN hosts and ultra-luminous
infrared galaxies (ULIRGs) (e.g., Feruglio et al. 2010; Glikman et al. 2012;
Cicone et al. 2014). In these systems, the mass loss ranges from one to
several times the star formation rate (SFR).

Similarly, using various emission line diagnostics, neutral (H i 21 cm, C ii]
$158\mu$m) and ionized ([O iii] $5007\AA$, H$\alpha$ $6564\AA$) outflows were
also detected (e.g., Nesvadba et al. 2008; Alexander et al. 2010; Harrison et
al. 2012, see Harrison et al. 2018 for a review). Ionized AGN outflows tend to
be more common ($\sim 75\%$, e.g., Brusa et al. 2015, 2016; Perna et al.
2015a, b; Kakkad et al. 2016; Zakamska et al. 2016; LaMassa et al. 2017; Toba
et al. 2017 in high luminosity and high Eddington ratios and in red and
obscured dusty sources, as expected from the evolutionary model by Hopkins et
al. (2007b). Studying the obscured phase and how the AGN gets rid of the
surrounding material is crucial to testing and improving our understanding of
the AGN-galaxy co-evolution scenario.

Furthermore, AGNs are the main contributors to the X-ray background (XRB). The
integrated emission of the AGNs, obtained from the X-ray deepest surveys, can
account for most of the XRB surface brightness below 10 keV (Xue et al. 2011;
Moretti et al. 2012). However, where the XRB spectra peaks ($20-40$ keV) most
of the XRB is still unresolved. Extrapolating at these energies the spectrum
from the deep surveys showed that an additional large population of heavily
obscured, Compton-thick (CT) AGNs with N${}_{\text{H}}>10^{24}$ cm-2 is
required to fully reproduce the XRB spectra. Furthermore, XRB population
synthesis models predict that the maximum contribution to the XRB of the
“missing” CT objects in the $L_{x}^{intr}\approx 10^{42}-10^{44}$ erg/s
luminosity range should peak at $z\approx 1$ (Gilli et al. 2007; Ueda et al.
2014; Ananna et al. 2019). As it is difficult to constrain the abundance and
the properties of these CT AGNs using only XRB synthesis models, studies of
individually detected sources are needed (Gilli 2013).

Although several methods for selecting type 2 AGNs are available (see Vignali
2014 for a review), a complete census of these objects cannot be achieved
using only a single observing band. The X-ray radiation, originated by the hot
corona in the innermost region of the AGN, is a good tracer of the AGN
intrinsic emission, however, when the nucleus is obscured by column densities
as large as $\sim 10^{24-25}\text{cm}^{-2}$, even hard X-rays are severely
depressed. Mid-infrared wavelengths can be effectively used as an X-ray
complementary selection method, as the optical-to-X-ray absorbed radiation is
re-emitted at these wavelengths after being thermally reprocessed by the
obscuring torus. However, distinguishing between the AGN and the SF
contributions to the total infrared (IR) emission is not trivial, especially
for galaxies with high SFR and strong PAH features. Future planned mid-IR
cryogenic observatories (e.g., the PRobe far-Infrared Mission for
Astrophysics, PRIMA, Bradford et al. 2022), with higher sensitivity and better
spectral resolution than what is currently available, will have the
capabilities to both detect these sources up to very high-redshift and to
distinguish the AGN and SF contribution (Spinoglio et al. 2021; Barchiesi et
al. 2021; Bisigello et al. 2021). Finally, obscured sources can also be
identified using mm-observations, as they can be sensible up to $N_{H}\sim
10^{26}\,\rm{cm}^{-2}$ (e.g., Behar et al. 2015; Kawamuro et al. 2022).

Type 2 AGNs can be also selected using narrow, high-ionization emission lines,
such as the [O iii]$5007\AA$, the [Ne v]$3426\AA$ and the C iv$1549\AA$ narrow
emission lines. These lines, produced in the narrow line region (NLR), do not
suffer from the nuclear extinction and their flux is a better proxy of the AGN
intrinsic emission. In particular, the [Ne v] line, despite being $\sim 9$
times fainter than the [O iii] line, allows for AGN selection up to $z\approx
1.5$, whereas the [O iii] is redshifted out of the optical range at $z\approx
0.8$. Moreover, due to its high-ionization potential of 97 eV (vs. 54 eV of [O
iii]), it is an unambiguous marker of AGN activity (e.g., Gilli et al. 2010;
Mignoli et al. 2013; Cleri et al. 2022). Several works have shown that pairing
AGN optical lines selection with X-ray data is an effective method to find
obscured and CT AGNs (e.g., Maiolino et al. 1998; Cappi et al. 2006; Vignali
et al. 2006, 2010; Gilli et al. 2010; Mignoli et al. 2013, 2019). Among those,
Gilli et al. (2010) analyzed a sample of 74 local objects with [Ne v] and
X-ray detection. They showed that the [Ne v] line is a good tracer of AGNs and
that the selection of type 2 AGNs via this line provides a similar fraction of
obscured AGN as the [O iii] selection. They also show that the use of the [Ne
v] line should not be biased toward high-luminosity AGNs, but it could be
toward low NLR extinction, as even a modest value $\rm(E(B-V)=0.5$ would dump
the flux by a factor of 10. Gruppioni et al. (2016) analyzed a sample of 76
Seyfert galaxies and found that the [Ne v]$14.3,24.3\mu\rm{m}$ emission lines
are good tracers of the AGN intrinsic power and calibrated two relations
between the luminosity of these lines and the AGN bolometric luminosity.

The use of different emission lines to select AGNs at various redshifts (i.e.,
$z\lesssim 0.8$ for [O iii], $0.6\lesssim z\lesssim 1.5$ for [Ne v] and
$1.5\lesssim z\lesssim 3$ for C iv) allows for the study of the redshift
evolution of both the AGN and the host properties (Vignali et al. 2010; Gilli
et al. 2010; Mignoli et al. 2013; Vignali et al. 2014; Mignoli et al. 2019).

The X/[Ne v] flux ratio was used by Vignali et al. (2014), hereafter V14, to
trace the obscuration of a sample of [Ne v]-selected type 2 AGN in the
C-COSMOS field. In fact, both the observed X-ray and the [Ne v] fluxes are
linked to the intrinsic AGN emission, but the X-ray flux also suffers from the
source obscuration. Gilli et al. (2010) calibrated a relation between X/[Ne v]
and the N${}_{\text{H}}$ using a sample of 74 bright, nearby Seyferts with
both X-ray and [Ne v] data and for which the column density was determined
unambiguously. They found that the mean X/[Ne v] ratio for unobscured Seyferts
is about 400, about 80% of local Seyferts with X/[Ne v]$<100$ are obscured by
column densities above $10^{23}$ cm-2 and essentially all objects with
observed X/[Ne v]$<15$ are CT (see also Cleri et al. 2022).

In this paper, we present the properties of a sample of 94 [Ne v]-selected
type 2 AGNs, obtained via X-ray spectral analysis and from optical-to-FIR
spectral energy distribution (SED) fitting. The use of the [Ne v] selection
method restricted the sample to AGNs in the $0.65<z<1.2$ redshift range, where
most of the XRB “missing” sources are expected to lie (Gilli 2013). This work
is an extension of previous works (Mignoli et al. 2013, V14) for the AGNs in
the C-COSMOS field. We made use of newer X-ray data from the Chandra COSMOS
Legacy catalog (Civano et al. 2016; Marchesi et al. 2016), which extend the
X-ray coverage of the COSMOS field from 0.9 to 2.2 deg2 and provide a more
uniform coverage. We also studied the hosts of type 2 AGNs to characterize
their parameters, stellar mass, and star formation rate. We investigated
whether these galaxies are different from “normal” galaxies due to the AGN
influence. The optical selection of the sample is presented in § 2, with the
X-ray data in § 2.1 and the photometric data in § 2.2. The X-ray analysis
results are reported in § 3, along with the fraction of CT objects. The SED-
fitting algorithm and its results are presented in § 4. In § 5 we present the
comparison with a stellar mass- and redshift-matched control sample of non-
active galaxies and the interpretation of our results in the light of the in
situ co-evolution scenario is in § 6. Our conclusions are then reported in §
7. Throughout this paper, we adopt the following cosmological parameters:
H${}_{0}=70\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$,
$\Omega_{\text{M}}=0.3,$ and $\Omega_{\Lambda}=0.7$ (Spergel et al. 2003).

##  2 Sample

We studied the [Ne v] type 2 AGN sample described in Mignoli et al. (2013,
hereafter M13). It was derived from the zCOSMOS-Bright spectroscopic survey
(Lilly et al. 2007, 2009), which provided the 5500 – 9700 $\AA$ spectra of
$\sim 20000$ objects in the COSMOS (Scoville et al. 2007) field. From the
zCOSMOS-Bright catalog, we selected 94 type 2 AGNs in the redshift range of
$\sim 0.65-1.20$ on the basis of [Ne v] detections and their spectral
properties. The redshift range assured that both the [Ne v]3346Å and the [Ne
v]3426Å emission line fall within the spectral coverage. Sources previously
identified as type 1 AGNs due to broad (¿1000 km s-1) emission lines in their
spectra were excluded. The sample was composed of sources from redshift
$z=0.6606$ to $z=1.1767$, with mean $z=0.85\pm 0.13$ and a median $z=0.86$.
The mean (aperture corrected) [Ne v] flux was $F_{\text{[Ne\,{v}]}}=(1.81\pm
1.23)\times 10^{-17}$ erg cm-2 s-1, with median
$F_{\text{[Ne\,{v}]}}=1.44\times 10^{-17}$ erg cm-2 s-1; the mean [Ne v]
equivalent width is EW${}_{\text{[Ne\,{v}]}}=18.17\pm 15.81$ Å with median
EW${}_{\text{[Ne\,{v}]}}=13.9$ Å (see M13 for further details).

Due to the complex selection of the [Ne v] sample, judging its completeness is
not trivial, although M13 tried to draw some conclusions based on the
comparison with other selection techniques. They found that the selection via
[Ne v] emission line is complementary to the one based on the lack of broad
emission lines in the optical spectra coupled with a
$L_{\rm{2-10keV}}>10^{42}\,\rm{erg\,s^{-1}}$. On the one hand, a significant
fraction ($\sim 60\,\%$) of both X-ray- and [Ne v]-selected AGNs would not be
classified as AGN via the so-called “blue diagnostic diagram” (i.e.,
exploiting the [O iii] $\lambda 5007$, H$\beta$, and [O ii] $\lambda\lambda
3726,3729$ line ratios), probably due to the fact that in these objects AGN
and SF coexist. On the other hand, only $\sim 10\,\%$ ($\sim 9\,\%$) of the
“blue diagnostic diagram”-selected AGN have [Ne v] (X-ray) detection,
suggesting the complementarity of these selection techniques. The majority
($\sim 80\,\%$) of the [Ne v]-selected AGNs are also AGNs according to the
mass-excitation (MEx) diagram of Juneau et al. (2011). The fact that the other
selection techniques find a sizable number of AGNs without [Ne v] detection
could be linked to obscuration in the host galaxy. In fact, as shown by Gilli
(2013), even a modest $\rm{E}(\rm{B}-\rm{V})$ is able to extinct the [Ne v]
emission. Finally, the M13 analysis of the VIMOS spectra of the [Ne v] sources
showed low $\rm{E}(\rm{B}-\rm{V})$, suggesting again that this selection may
lose some of the [Ne v] emitter AGNs due to extinction in their host-galaxy.

The redshift distribution of the [Ne v] AGNs clearly follows the one of its
parent sample (the zCOSMOS galaxies; see Fig.1 of Mignoli et al. 2013) due to
the magnitude-limited survey selecting equally well host-galaxy dominated type
2 AGNs and normal galaxies. The comparison with other AGN samples from the
literature can be found at the end of § 3.1.

###  2.1 X-ray Data

All 94 [Ne v]-selected sources fall in the Chandra-COSMOS Legacy mosaic, which
is composed of data from the C-COSMOS survey (the central $\sim 0.9\,$deg2;
Elvis et al. 2009) and from the COSMOS Legacy survey (covering the external
$\sim 1.7$ deg2 with a similar depth of the C-COSMOS survey; Civano et al.
2016). The whole mosaic covered $\sim 2.2$ deg2 with a total exposure time of
$\sim 4.6$ Ms. Thanks to the broader coverage of the COSMOS Legacy survey, we
had 23 more sources with X-ray coverage with respect to V14; moreover, we
included two sources which were previously excluded because they fell in bad
positions of the C-COSMOS mosaic.
Following Vignali et al. (2014), we found 36 [Ne v]-selected type 2 AGNs
detected by Chandra within 1.3” from the optical position, with a median
displacement of 0.41”. We visually inspected the 7 sources with counterparts
farther than 0.75” and found that they are good matches. The X-ray spectra
were extracted as described in Marchesi et al. (2016), using the CIAO
(Fruscione et al. 2006) tool specextract from circular regions of radius
$r_{90}$ (i.e., the radius that contains 90% of the PSF in the 0.5 - 7 keV
observed-frame band). The background spectra were extracted from annuli
centered on the source position with inner radius $r_{90}+2.5$” and outer
radius of $r_{90}+20$”, paying attention to avoid the inclusion of X-ray
sources. For each source, the spectra of its observations were combined in a
single spectrum via the CIAO tool combine_spectra.

###  2.2 Photometric data

The optical and IR data used to identify the [Ne v] sources were taken from
the COSMOS 2020 catalog (Weaver et al. 2022) (improved version of the previous
COSMOS 2015 catalog Laigle et al. 2016), which contains photometry in 44 bands
(from 1526Å to 8$\mu$m) for $\sim 1.7$ million objects in the 2 deg2 COSMOS
field, along with matches with X-ray, near-ultraviolet (near-UV), and far-IR
data. We used 3” aperture (corresponding to a physical size of
$23.4\,\rm{kpc}$ at the median redshift of our sample) fluxes from 20
photometric bands and the COSMOS2020 matches with the $24\mu$m band from the
MIPS (Multi-Band Imaging Photometer) detector onboard Spitzer, with the
$100\,\mu$m and $160\mu$m bands and the $250\,\mu$m, $350\,\mu$m, and
$500\,\mu$m bands from the PACS and SPIRE detectors of Herschel, and with the
$850\,\mu$m from the SCUBA instrument at JCMT (we refer to Weaver et al. 2022
for a complete description of the COSMOS2020 catalog and source associations).
In total, we exploited data from 31 filters (see Table 1).

Two sources of the NeV sample were not in the latest COSMOS 2020 catalog (at
the time of writing); for these sources, we used the photometric information
from the COSMOS 2015 catalog. As we analyzed the whole sample also with the
COSMOS 2015 catalog and we found no systematic difference between the values
obtained using one or the other catalog, we are confident in reporting the
results of these two sources along with those obtained with the newest COSMOS
2020 catalog.

Table 1: Summary of COSMOS2020 photometric bands used in this work. The effective wavelength is the median wavelength weighted by transmission and the widths are defined as the difference between the maximum and the minimum wavelengths (calculated as the first and the last wavelengths with a transmission of at least 1%). Instrument | Filter | Effective | Width
---|---|---|---
/Survey |  |  $\lambda$ [Å] | [Å]
MegaCam/CFHT | u* | 3823.3 | 670
Suprime-Cam | IB427 | 4256.05 | 305.6
/Subaru | B | 4400.33 | 1399.1
| IB464 | 4633.48 | 330.5
| IB505 | 5060.57 | 378.1
| IB527 | 5261.1 | 242
| V | 5477.8 | 955
| IB574 | 5764.8 | 271.5
| $r$ | 6136.24 | 1918
| IB679 | 6778.75 | 555.3
| IB709 | 7070.67 | 511.5
| IB738 | 7358.64 | 490.2
| $i^{+}$ | 7630.05 | 1872.5
| IB827 | 8241.69 | 514.3
| $z^{++}$ | 9020.18 | 1960.4
| Y | 9759.16 | 1752.8
VIRCAM | YUD | 10214.2 | 970
/VISTA | JUD | 12534.6 | 1720
(UltraVISTA-DR2) | HUD | 16453.4 | 2900
| K${}^{UD}_{S}$ | 21539.9 | 3090
IRAC/Spitzer | ch1 | 35634.3 | 7460
(SPLASH) | ch2 | 45110.1 | 10110
| ch3 | 57593.4 | 14140
| ch4 | 79594.9 | 28760
MIPS/Spitzer |  $24\mu$m | 232096 | 110494
PACS/Herschel | green | 979036 | 558974
| red | $1.54\times 10^{6}$ | $1.26\times 10^{6}$
SPIRE/Herschel | PSW | $2.43\times 10^{6}$ | $1.26\times 10^{6}$
| PMW | $3.41\times 10^{6}$ | $1.46\times 10^{6}$
| PLW | $4.82\times 10^{6}$ | $2.92\times 10^{6}$
SCUBA/JCMT |  $2.450\,$GHz | $4.48\times 10^{6}$ | $1.04\times 10^{6}$

##  3 X-ray spectral analysis

###  3.1 X-ray-detected sources

Using the XSPEC software (Arnaud 1996) we performed the X-ray spectral
analysis of 36 type 2 AGNs with X-ray detection. The median number of net
(i.e., background-subtracted) counts is 85, four sources have 15 counts or
less. We divided the 36 sources into two sub-samples, on the basis of their
net counts. The high-counts sample is composed of 17 sources with at least 90
net counts, and the low-counts sample of 19 sources with less than 90 net
counts. For the low-counts sample, we used unbinned data and C-statistic (Cash
1979); for the high-counts sample we rebinned the data at 25, 15, and 10
counts per bin (respectively, for sources with net-counts $>500$, $>200,$ and
$>100$) and used Gaussian statistics.

We refer to Appendix A for the description of the X-ray models used in the
spectral fitting, as well as for the complete spectral properties of all the
sources. We first fit the sources with a power-law model, modified by the
Galactic absorption obtaining a mean photon index value of $\Gamma=0.82$ with
a standard deviation of $0.90$. We find that 6 sources have $\Gamma\geq 1.6$,
typical of unobscured AGNs, while 16 objects have $\Gamma\leq 1.0$; of these 7
have negative spectral index, usually found in very obscured sources.

To characterize the sources in terms of obscuration, we fixed the photon index
to a value of $\Gamma=1.8$, typical of unobscured sources, and added an
absorption component to model the source obscuration. The mean
N${}_{\text{H}}$ of the high-count sample is $\approx 7.5\times 10^{22}$ cm-2,
while for the low-count sample we obtained $\approx 32.2\times 10^{22}$ cm-2.
On the basis of their obscuration, we classified nine sources as highly
obscured (N${}_{\text{H}}>10^{23}$ cm-2) and two as CT objects. Twelve sources
have low values of obscuration ($N_{\text{H}}<10^{22}$ cm-2). We computed the
intrinsic (i.e., absorption-corrected) $2-10$ keV rest-frame luminosity of the
sample, obtaining a mean value of $8.3\times 10^{43}$ erg/s for the high-
counts sample and $2.7\times 10^{43}$ erg/s for the low counts sample. The
median (and $16^{\rm{th}}-84^{\rm{th}}$ percentiles) intrinsic $2-10$ keV
rest-frame luminosity of the whole sample is
$\log{(L_{\rm{2-10keV}}/\rm{erg\,s^{-1}})}=43.6_{-0.4}^{+0.6}$.

As the sources have low numbers of counts we preferred using simple
phenomenological models. However, few sources display more complex spectra
that call for deeper investigations. Source lid1840 (COSMOS Legacy ID) with
238 net-counts and N${}_{\text{H}}<0.5\times 10^{22}\,\text{cm}^{-2}$ shows
the possible presence of a 6.9 keV line with a significance of $\approx
2.6\,\sigma$ and an equivalent width of EW${}_{6.9}=0.51\pm 0.38$ keV. Source
cid1508 (C-COSMOS ID) has a spectrum that shows the presence of a possible
soft excess with respect to the absorbed power law model. We substituted the
absorption component with a partial covering fraction absorption (zpcfabs) and
found a lower limit on the covering fraction $f>0.77$, while the value of
N${}_{\text{H}}$ being compatible with the one obtained using the simple
absorption component. For source cid138 (99 net-counts) we found a variation
of the net-count rate of more than a factor of 6 (with a significance of
$6.7\sigma$) between the 2007 and 2014 observations. We did not find any
significant variation in the hardness ratio, spectral index or
N${}_{\text{H}}$. As the flux variation is not accompanied by a variation of
the spectral properties, we hypothesized it may be linked to differences in
the AGN accretion rate.

We computed the 2-10 keV rest-frame flux (not corrected for obscuration) of
the sample, obtaining a median flux of F${}_{2-10}=0.61\times 10^{-14}$
erg/s/cm2. We compared the fluxes with those from V14, which were obtained via
an Xspec spectral fitting with a power-law model with $\Gamma=1.4$. Except for
cid138 the values are in agreement within their errors. We used the 2-10 keV
rest-frame flux and the [Ne v] flux from M13 to compute the X/[Ne v] ratio.
The mean X/[Ne v] is 313 with a standard deviation of 321. Ten sources had
X/[Ne v] $<100$. No source has X/[Ne v] lower than 15. In Fig. 1, we compared
our data with the X/[Ne v] vs N${}_{\text{H}}$ diagram obtained by Gilli et
al. (2010). The plot was produced using the spectral templates of Gilli et al.
(2007). These are AGN X-ray spectral models with a primary power-law with
$\Gamma=1.9$, cut-off energy E${}_{C}=200$ keV, a variety of absorptions (log
N${}_{\text{H}})=21.5,22.5,23.5,24.5,>25$, a 6.4 keV emission line and, in
case of obscured spectra, a 3% soft scattered component. The blue solid line
was obtained using the mean X/[Ne v] ratio of a sample of 74 unobscured
Seyfert galaxies in the local Universe and, starting from it, computing the
expected X/[Ne v] ratio at increasing levels of absorption, using the spectral
templates. The same computation was carried out starting from the mean X/[Ne
v] ratio $\pm 1\sigma$ and $\pm 90\%$, to produce the $1\sigma$ and $90\%$
limits. The procedure is extensively described in Gilli et al. (2010). As we
can see from Fig. 1, the X-ray-detected sources of the [Ne v] sample populate
the obscured quasar region of the diagram, i.e.,
$10^{22}<\text{N}_{\text{H}}<10^{24}$ cm-2, with a few sources in the
unobscured region ($\text{N}_{\text{H}}<10^{22}$ cm-2); the majority of the
sources lie within the 1 $\sigma$ limit.

Figure 1: X/[Ne v] vs N${}_{\text{H}}$ diagram. Red dots are the X-ray-
detected sources of the [Ne v] sample, with N${}_{\text{H}}$ obtained from the
X-ray spectral analysis. The solid line shows the expected X/[Ne v] values as
a function of absorption, as computed by Gilli et al. (2010) (but see also
Cleri et al. 2022) using spectral templates with different N${}_{\text{H}}$,
starting from the mean X/[Ne v] obtained from a sample of unobscured Seyfert
galaxies. The cyan shaded region was computed in the same way, but starting
from the mean X/[Ne v] $\pm 1\sigma$ and the grey shaded region starting from
the mean X/[Ne v] $\pm 90\%$. The [Ne v] sample populates the obscured AGN
region of the diagram, i.e., $N_{H}\gtrsim 10^{22}$ cm-2.

We compared the results of our spectral analysis with those presented by
Marchesi et al. (2016), hereafter M16, and Lanzuisi et al. (2018, who studied
CT-candidate from M16). M16 performed an X-ray spectral analysis of the $\sim
1850$ extragalactic sources in the Chandra COSMOS-Legacy survey with more than
30 net-counts in the $0.5-7\,$keV band. Spectra were fitted with a fixed
photon-index $\Gamma=1.9$ power-law, an absorption component, an optional un-
absorbed second power-law to model the scattered emission, and a $6.4\,$keV
(rest frame) Gaussian to reproduce the iron K$\alpha$ emission line. Out of
our 36 X-ray-detected sources in our sample, 6 of them are not in the M16
work, as they are below the 20 net-counts threshold. For the remaining 30
sources, we found an excellent agreement in
$\text{L}^{\text{intr}}_{2-10\text{keV}}$ and $\text{N}_{\text{H}}$: the
median ($16^{\rm{th}}$ and $84^{\rm{th}}$ percentile) ratio between M16 and
ours $\text{L}^{\text{intr}}_{2-10\text{keV}}$ and $\text{N}_{\text{H}}$ are
$1.000_{-0.003}^{+0.004}$ and $1.02_{-0.02}^{+0.10}$, respectively. Regarding
the two CT X-ray-detected sources, cid1019 is classified as CT in Lanzuisi et
al. (2018) as well, while cid1706 has 15 net counts and was not included in
M16; the other 5 sources that are not in M16 are all obscured AGNs, 2 of them
with $\text{N}_{\text{H}}>10^{23}\,\text{cm}^{-2}$.

Compared to the sub-sample of type 2 AGNs of M16, which is composed of 1111
sources at $0.066<z<4.45$, the current sample covers a narrower redshift range
and is characterized by a lower average redshift ($z=0.85$ vs $z=1.05$ of
M16). As we did not exclude the sources with less than 30 net counts, we found
a lower average number of net counts (85 vs 102) and, on average, slightly
less luminous AGNs with mean ($\pm\sigma$)
$\log{(L^{[Ne\,\textsc{v}]}_{\rm{2-10keV}}/\rm{erg\,s^{-1}})}=43.5\pm 0.5$ vs
$\log{(L^{\rm{M16}}_{\rm{2-10keV}}/\rm{erg\,s^{-1}})}=43.7\pm 0.6$. Finally,
we note that our sample is on average as obscured as the one from M16
($\log{(N_{\rm{H}}^{[Ne\,\textsc{v}]}/\rm{cm^{-2}})}=22.8_{-0.3}^{+0.6}$ vs
$\log{(N_{\rm{H}}^{\rm{M16}}/\rm{cm^{-2})}=22.8\pm 0.3}$), but the inclusion
of AGNs with less than 30 net counts highlights a tail of very obscured
sources.

We also compared our X-ray-detected sample with the results of Iwasawa et al.
(2020, hereafter I20), who studied a sample of 185 bright sources detected in
the XMM-Newton deep survey ($3\,$Ms) of the Chandra Deep Field South. In
particular, we focused on the I20 lowz subsample, which encompassed 56 AGNs in
the $0.4<z<1.0$ redshift range, with a median $z=0.7$ (thus slightly lower
than our [Ne v] sample). Their sample has on average less luminous and less
obscured AGNs ($\log{(L^{\rm{I20}}_{\rm{2-10keV}}/\rm{erg\,s^{-1}})}=43.1\pm
0.07$, $\log{(N^{\rm{I20}}_{\rm{H}}/\rm{cm^{-2}})}=22.0_{-0.1}^{+0.2}$) than
ours.

We selected a subsample of 8 [Ne v] AGNs with the highest number of counts,
sampling different amounts of obscuration. We fitted these sources with more
realistic AGN models. We followed Zhao et al. (2021) and modeled the X-ray
spectra with an absorbed intrinsic continuum, a reprocessed component
(characterized by the borus02 model), and a scattered component. We did not
find any significant difference in intrinsic AGN luminosity and obscuration
with respect to the values obtained with the simpler phenomenological model.
We note, however, that the low-photon statistics forced us to fix the majority
of the parameters (we chose to use the average values found by Zhao et al.
2021 for a sample of very obscured AGNs with optimal X-ray spectral coverage):
the photon index has been fixed at $\Gamma=1.8$, the cut-off energy at
$E_{\rm{cut}}=500\,\rm{keV}$, the torus opening angle to
$\theta_{\rm{Tor}}=48\deg$ (corresponding to a covering factor of
$c_{\rm{f}}=0.67)$, the average column density to $N_{\rm{H,tor}}=1.24\times
10^{24}\,\rm{cm^{-2}}$, and the fraction of scattered emission to
$f_{\rm{scat}}=0.05$. Finally, we chose an inclination of
$\theta_{\rm{obs}}=87\deg$, corresponding to an edge-on view of the sources.

###  3.2 X-ray-undetected sources

Out of the 94 sources of the [Ne v] sample, 58 have no X-ray detection. We ran
a two-sample Kolmogorov–Smirnov (KS) test in order to investigate if X-ray-
undetected sources are such because they fall in regions with shorter
exposure-map derived time than those of the X-ray-detected sources. We built
two empirical distribution functions of the exposure time for the X-ray-
detected sources and for the X-ray-undetected, using the exposure maps derived
from the entire COSMOS Legacy mosaic. We found, with a confidence of 89% (KS
statistic of $D=0.1197$), that the undetected sources are not associated to
lower exposure times.

We used the CIAO tool scrflux to calculate the net count-rate limit for each
undetected source, and the tool modelflux to calculate the flux upper limit.
Count rates were computed using all the observations for which the source
falls in the field of view. Using scrflux we calculated the $0.5-7$ keV
(observed-frame) net count-rate in a circular region centered on the source
position, that contained 90% of the PSF at 1 keV. Background counts were
extracted in an annular region centered on the source position, using inner
and outer radii of one and five times the radius of the source region. The
uncertainties were computed at the 1$\sigma$ confidence level, exploiting the
Gehrels (1986) approximation to confidence limits for Poisson distributions
due to the low number of counts. Because the sources were not detected in the
X-ray band, we can consider their net counts + $1\sigma$ uncertainties as the
upper limits on the source net counts. scrflux computed the (upper limit) net
count-rate by dividing the (upper limit) net counts by the effective (i.e.,
vignetted-corrected) exposure time at the source position. We used modelflux
to calculate, from the upper limit net count-rates, the upper limit for the
flux in the $2-10\,$keV rest-frame energy range. We used a power-law model
with spectral index $\Gamma=0.4$ (the average spectral index of the low count
sample), modified by Galactic absorption. This model takes into account the
source obscuration via a flatter photon index than the intrinsic one
$\Gamma=1.8-1.9$.

We used the rest-frame $2-10\,$keV flux upper limits, and the [Ne v] fluxes to
compute the X/[Ne v] ratio upper limits. 54 sources have an upper limit
$<100$, and 16 sources have X/[Ne v] ratios $<15$. This means that 93% of the
X-ray-undetected sources are candidate to be AGNs with
N${}_{\text{H}}>10^{23}$ cm-2, and 28% to be CT AGNs. We used the X/[Ne v]
upper limits to compute lower limits on the N${}_{\text{H}}$. Using the net-
count rates, the N${}_{\text{H}}$ lower limits, and a fixed $\Gamma=1.8$
spectral index, we estimate the intrinsic (i.e., absorption corrected) X-ray
flux (and luminosity) upper limit via modelflux.

Testing this procedure on the X-ray-detected sources, we found a strong
correlation between the intrinsic luminosities obtained in this way and those
from the X-ray spectral analysis for the high-counts sample. The correlation
is loose for the low-count sample, but for the majority of these sources, the
two luminosities do not differ more than 2 $\sigma$. We did not find any
particular trend between the accuracy of our method and the amount of
obscuration, thus we concluded that it is a reliable way to estimate an upper
limit on the X-ray intrinsic luminosity and that the major source of error is
linked to the uncertainties of estimating the net-counts upper limit in case
of low counts.

Considering the whole (both X-ray-detected and undetected sources) [Ne v]
sample, at least 67% of the sources have X/[Ne v] ratios compatible with
absorption N${}_{\text{H}}>10^{23}$ cm-2, and at least 19% of the sources are
likely CT AGNs. The X/[Ne v] flux ratios are plotted in Fig. 2, the vertical
dashed lines show the threshold, defined by Gilli et al. (2010), between
Compton-thick (leftward direction) and Compton-thin (right-ward direction)
sources. Although our sample is far from complete (see § 2), it is interesting
to note that the fraction of CT-AGN is similar to the $f_{\rm{CT}}=0.24$ found
by Lanzuisi et al. (2018) from a sample of 67 candidate CT-AGNs extracted from
the M16 sample, although lower than the $f_{\rm{CT}}\approx 0.5$ expected from
the distribution of the AGN population of Buchner et al. (2015).

Figure 2: X/[Ne v] ratio distribution. Filled and empty histograms refer to
X-ray detections and upper limits, respectively. The leftward area
($\text{X/[Ne\,{v}]}\leq 15$) is the region defined by Gilli et al. (2010) for
Compton-thick AGNs, while the central area ($15<\text{X/[Ne\,{v}]}\leq 100$)
is where very obscured (N${}_{\text{H}}>10^{23}$ cm-2) and possible CT-AGNs
should be located.

##  4 SED analysis

We used the SED fitting technique to derive AGN and galaxy properties from
photometric data. In Sect. 4.1 we briefly present the SED-fitting algorithm as
well as the AGN torus models we used. The results of the SED-fitting, along
with the comparison with those obtained from the X-ray analysis, are presented
in Sect. 4.2.

###  4.1 SED-fitting algorithm

We made use of the SED-fitting algorithm SED3FIT (Berta et al. 2013), based on
the MAGPHYS (da Cunha et al. 2008) code, that performs SED-fitting with a
combination of three components: stellar emission, dust emission from star
formation and a possible dusty torus and AGN component. The stellar and dust
emission are linked by energy balance arguments. Torus emission is
independently included.

MAGPHYS is a model package to interpret observed SEDs of galaxies (at rest
wavelengths in the range $912\AA\ <\lambda<1$mm) in terms of galaxy-wide
physical parameters pertaining to the stars and the interstellar medium. The
code uses two libraries of models: one that takes into account the stellar
emission and the effects of dust attenuation, generated using the Bruzual
(2007) stellar population synthesis code with the attenuation computed using
the angle-averaged model of Charlot & Fall (2000), the other that includes the
IR emission of the dust, computed using the model of da Cunha et al. (2008).
The optical and infrared libraries are linked together to provide the full SED
of model galaxies from the far ultraviolet to the far-infrared wavelengths.

One of the main assumptions of the MAGPHYS code is that the only significant
source of dust heating is the starlight, thus ignoring any possible
contribution of the AGN to the SED. The SED3FIT code solves this limitation by
adding a warm dust component to the modeled SED emission. It represents dust
surrounding the active nucleus, assumed to be distributed in a toroidal
region. The code uses $\chi^{2}$ minimization to find the best-fit model, by
effectively fitting simultaneously the three components (stellar, dust, and
AGN) to the data (see Berta et al. 2013, for further details).

The torus library we used to model the AGN contribution to the SED assumes
that the AGN dust and gas are distributed in a toroidal shape, i.e., “smooth-
torus” model. It was developed by Fritz et al. (2006) and updated by Feltre et
al. (2012). The geometry of the torus is a flared disc. To reduce the
calculation time, we selected only a sub-sample of 180 models between the
$24\,000$ elements torus library. A detailed explanation of the torus models
and parameters is reported in Appendix B. We instructed the SED-fitting code
to run 100 different normalizations of the chosen torus models, for a total of
$18\,000$ AGN spectra used in the SED-fitting procedure.

As a sanity check, we also performed additional runs of SED-fitting using the
X-CIGALE SED-fitting code (Yang et al. 2020, 2022), the latest version of the
code investigating galaxy emission (CIGALE; Burgarella et al. 2005; Noll et
al. 2009; Boquien et al. 2019), which allowed us to use the newer SKIRTOR
torus models (Stalevski et al. 2012, 2016) and to model it as a “clumpy”
medium. We did not find any significant difference in the AGN and host-galaxy
properties.

###  4.2 SED-fitting results

Figure 3 shows the SED-fitting results for one of the [Ne v] AGNs, source
zCOSMOS 380027, undetected in the X-ray, at $z=0.9307$.

Figure 3: Example SED fit for a [Ne v]-selected AGN of the current sample. The
black points with purple error bars are the photometric data, the dark gray
line is the best-fit SED, composed of the galactic emission (blue line) and
the AGN component (red line). The light grey line is the host galaxy dust
emission, the continuous (dashed) green line refers to the dust-obscured
(intrinsic) stellar emission. The fitting provides a stellar mass of
$\log(M_{*}/\text{M}_{\odot})=10.64\pm 0.05$, a SFR of $51\pm
10\,\rm{M_{\odot}\,yr^{-1}}$, and an AGN bolometric luminosity of
$\log(L_{\text{bol}}^{\text{sed}}/\text{erg\,s}^{-1})=45.6_{-0.1}^{+0.3}$. The
bottom panel shows the residuals, where $\chi=\,$( observation$\,-\,$model
)/error.

#### AGN bolometric luminosity

Unlike type 1 objects, for obscured AGNs it is not possible to obtain the AGN
bolometric luminosity from the optical emission. However, as the SED-fitting
algorithm allows us to disentangle the AGN and the host contributions, one of
the direct outputs of SED3FIT is the AGN bolometric luminosity, derived via
the integration of the spectrum of the central source that illuminates the
torus.

We found that for 18 sources the SED fitting shows a low contribution of the
AGN to the total emission, hence for these sources we have only upper limits
on their AGN bolometric luminosity. The remaining 76 sources have a median
$\log(L_{\text{bol}}^{\text{sed}}/\text{erg$\,$s${}^{-1}$})=44.4\pm 0.7$.

To further confirm the validity of these luminosity estimates, we compared
them with the bolometric luminosities obtained from the X-ray spectral
analysis. We will refer to the bolometric luminosities computed from the SED-
fitting as $L_{\text{bol}}^{\text{sed}}$ and to those obtained from X-ray
analysis as $L_{\text{bol}}^{\text{x}}$. For the sources with X-ray
detections, we were able to compute the intrinsic $2-10$ keV rest-frame
luminosity, as reported in § 3.1. Using the bolometric correction
$K_{\text{bol}}$ from Lusso et al. (2012) (see also Duras et al. 2020), we
obtained the AGN bolometric luminosities L${}_{\text{bol}}^{\text{x}}$ of
these sources, with a median value of
$\log(L_{\text{bol}}^{\text{x}}/\text{erg s}^{-1})=44.7\pm 0.5$. Considering
the X-ray-detected sources, the median (and 16-84${}^{\text{th}}$ percentiles)
L${}_{\text{bol}}^{\text{sed}}/$L${}_{\text{bol}}^{\text{x}}$ ratio is
$1.00_{-0.01}^{+0.02}$. In Fig. 4 we show the comparison of the bolometric
luminosities: except for two sources, the two bolometric luminosities are
compatible within twice their uncertainties, with a Pearson correlation value
$\rm{r}=0.46$ and a p-value of $0.006$ (corresponding to a confidence
$>2.7\,\sigma$). We performed an orthogonal distance regression and found a
best-fit line (red line) with slope $m=1.16\pm 0.17$ and a dispersion of 0.6
dex. We note that Stemo et al. (2020) found a similar scatter of 0.6 dex
between $L_{\text{bol}}^{\text{sed}}$ and $L_{\text{bol}}^{\text{x}}$ for its
sample of $\sim 2100$ AGNs across a wider range of luminosities. We note that
the three detected sources on the bottom right of the plots are among the most
obscured AGNs (lowest X/[Ne v] ratios). For these sources, the lower X-ray-
derived bolometric luminosities are likely linked to an underestimation of the
X-ray luminosity due to the high obscuration. Further causes of the dispersion
between the two bolometric luminosities could be linked to the assumed
bolometric correction and to the fact that the X-ray emission can be affected
by the AGN short-time variability (the X-rays tracing the innermost part of
the AGN emission), absent in the SED-fitting derived bolometric luminosity (as
the SED-fitting relies on the torus emission). In Fig. 4, we included the
upper limit on the bolometric luminosities for the X-ray-undetected sources
(diamonds). In §3.2, we discussed how we computed the upper limit on the
$L_{\rm{bolo}}^{\rm{X-ray}}$ of these sources. We note that, similarly to the
X-ray-detected sample, the X-ray-undetected AGNs with the highest X/[Ne v]
ratios (i.e. the less obscured ones) are the nearest to the 1:1 correlation,
indicating that the obscuration should be the most prominent source of
uncertainties in the $L_{\rm{bolo}}^{\rm{X-ray}}$. Considering only the X-ray-
detected sample, we found that the bolometric luminosities derived from X-rays
and SED-fitting are surprisingly similar, in particular, if we consider the
low number of X-ray net counts and the degeneracies between the AGN and SF
components in the SED-fitting. This correlation between the bolometric
luminosities derived from the X-ray spectral analysis and the SED-fitting is
extremely important as it confirms the reliability of both the SED-fitting
procedure and the X-ray analysis allows us to use the estimate of the AGN
bolometric luminosities derived from optical-to-FIR photometric data for the
X-ray-undetected sources.

Figure 4: Comparison of the AGN bolometric luminosities obtained from the SED-
fitting (L${}_{\text{bol}}^{\text{sed}}$) and from X-ray spectral analysis
(L${}_{\text{bol}}^{\text{x}}$). The L${}_{\text{bol}}^{\text{x}}$ were
computed from the $2-10$ keV rest-frame intrinsic luminosities using the Lusso
et al. (2012) bolometric correction. Circles indicate X-ray-detected sources,
while diamonds are the X-ray-undetected. For these sources, we have only an
upper limit on their L${}_{\text{bol}}^{\text{x}}$. The color code indicates
the X/[Ne v] ratio for the X-ray-detected sources and upper limits for the
X-ray-undetected sources. The orange line is the 1:1 correlation. The red line
is the best-fit relation for the X-ray-detected sources obtained via
orthogonal distance regression.

As we can see from Fig. 5, we also found a correlation (Pearson $\rm{r}\sim
0.6$ with a $p\rm{-value}=7\times 10^{-6}$, i.e., significance at $\sim
4.5\,\sigma$) between the [Ne v] line luminosity and the AGN bolometric
luminosity. The [Ne v] luminosity is aperture-corrected, but it is not
corrected for the extinction in the host-galaxy, as it has been shown by M13
the mean optical extinction, derived from the observed H$\beta$/H$\gamma$ flux
ratio, is low $(\langle E(B-V)\rangle=0.18)$. This relation was expected due
to the fact that the [Ne v] in the NLR (where this line originates from)
should be excited by the emission of the AGN central engine and thus, it
should be a proxy of the AGN intrinsic power (see also Gilli et al. 2010;
Mignoli et al. 2013; Gruppioni et al. 2016). We performed an orthogonal
distance regression (in the $\log-\log$ space) and found a best-fit linear
relation
$\log{(L_{\rm{[Ne\,\textsc{v}]}}/\rm{erg\,s^{-1}})}=0.69\times\log{(L_{\rm{bol}}^{sed3fit}/\rm{erg\,s^{-1}})}+10$.
We excluded from this fit the 18 sources for which we had only an upper limit
on their bolometric luminosity, caused by sed3fit choosing a best-fit model
with a low AGN contribution to the total SED. The
$\L_{\rm{[Ne\,\textsc{v}]}}-L_{\rm{bol}}$ relation, alongside the two similar
relations found for a local sample by Gruppioni et al. (2016) using the IR [Ne
v]$14.3,24.3\mu\rm{m}$ lines, confirm that the [Ne v] emission is a good
tracer of the AGN intrinsic emission and that it can be used to constrain the
AGN bolometric luminosity both in the local universe and at $z\sim 1$.

Figure 5:  Luminosity of the [Ne v] line as a function of the AGN bolometric
luminosity obtained from the SED-fit. We excluded the 18 sources with only
upper limits on their $L_{\rm{bol}}^{\rm{sed3fit}}$. The blue line is the
best-fit relation obtained via an orthogonal distance regression. The [Ne v]
sources are colour coded on the basis of their AGN fraction measured in the
$8-1000\,\mu\rm{m}$ wavelength range.

#### AGN significance

The SED-fitting procedure allowed us to separate the contribution of the AGN
from that of the galaxy. However, this process is subject to a certain
intrinsic degeneracy: an overestimation of the AGN fraction will result in an
underestimation of the IR emission from the galaxy and thus of the SFR and
vice versa. To further assess the reliability of the chosen torus models, as
well as to estimate the importance of the AGN component on the total emission
on a ”per source” basis, we estimated the AGN significance using a Fisher test
(F-test) between the best-fit $\chi^{2}$ with and without AGN component
similarly to what was done in Delvecchio et al. (2014), but see also Bevington
& Robinson (2003). We carried out a second run of sed3fit, using the same
optical and IR models, without any torus model. We compared the obtained
$\chi^{2}_{\text{NO-AGN}}$ with the $\chi^{2}_{\text{AGN}}$ obtained using the
torus models. The F-value was computed as

$F_{\text{test}}=\frac{\chi^{2}_{\text{NO-
AGN}}-\chi^{2}_{\text{AGN}}}{\bar{\chi}^{2}_{\text{AGN}}},$ (1)

where $\bar{\chi}^{2}=\chi^{2}/dof$ and $dof$ is the number of degrees of
freedom. As $dof$ we used the number of photometric points, in the case of the
model without AGN, and the number of photometric points minus one, to take
into account the additional parameter (the torus), for the model with AGN.
Formally, the computed value of the F-statistic corresponds to the F-value of
the “ANOVA F-test in regression analysis of nested non-linear models” and the
AGN significance is simply the p-value probability converted to Gaussian
standard deviation.

We obtained seventy-four sources (79%) with an AGN significance $\geq
1\,\sigma$, forty-eight sources (51%) with $\geq 2\,\sigma$, thirty-three
(35%) with $\geq 3\,\sigma$ and twenty-four (26%) with $\geq 4\,\sigma$.
Considering only the best value of the chi-squared, thirteen sources (14%)
were better fitted with a model without an AGN component; seven of them were
sources for which we had only upper limits on their AGN IR luminosity, due to
the low contribution of the AGN to the total SED. The fact that nearly half of
the sample has an AGN significance $<2\,\sigma$ can be attributed to intrinsic
low torus luminosities, with the torus emission largely diluted in the host-
galaxy emission. In this regard, all thirteen sources that were better fitted
without the AGN component were not detected in the X-ray. Moreover, all the
objects with AGN significance $\leq 1\,\sigma$ are not X-ray-detected, except
for three sources. Two of these, however, have luminosity in the lower end of
our distribution (L${}_{2-10\text{keV,intr}}<10^{43}$ erg/s).

We studied the distributions of the [Ne v] luminosities for the sources with
AGN significance $<2\,\sigma$ and those with AGN significance $\geq
2\,\sigma$. We found a segregation of the sources with low AGN significance at
low [Ne v] luminosities. In fact, while $44\%$ of the sources with $\geq
2\,\sigma$ AGN significance has low [Ne v] luminosity
($L_{\text{[Ne\,{v}]}}<10^{41}$ erg/s), this percentage goes up to $85\%$ for
the sources with AGN significance $<2\,\sigma$. This segregation is in support
of the fact that low AGN luminosities (the [Ne v] emission is a proxy of the
nuclear intrinsic emission) may be challenging in separating the AGN component
from the galaxy emission.

#### Stellar mass

The median (and 16-84${}^{\text{th}}$ percentiles) stellar mass is
$\log{(\text{M}_{*}\,/\,M_{\odot})}=10.91_{-0.46}^{+0.28}$. We noted that the
stellar masses are extremely well constrained by the SED-fitting procedure
with a mean $\Delta\log\text{M}_{*}\approx 0.06$. We did not find any
significant trend of the stellar mass with the X-ray detection.

#### Star formation rate

The SFR of our sample was obtained in two different ways: using the best-fit
model (SFR${}^{\text{sed}}$) and using the $8-1000\,\mu$m SF luminosity
(SFR${}^{8-1000\mu\text{m}}$). The SFR${}^{\text{sed}}$ is the mean SFR of the
last 0.01 - 0.1 Gyr as obtained from the modeling of the stellar component in
the UV-to-NIR regime with sed3fit. The code uses the UV-optical-NIR library of
Bruzual (2007), which produced the optical-to-NIR spectra, by considering the
spectral evolution of stellar populations for different metallicities and star
formation histories and assuming a Chabrier IMF (Chabrier 2003). We obtained a
median SFR${}^{\text{sed}}=12.9_{-9.1}^{+30.4}\,M_{\odot}\,yr^{-1}$
($\Delta\text{SFR}/\text{SFR}\approx 0.6\%$). The SFR${}^{8-1000\mu\text{m}}$
is the SFR averaged over the last 100 Myr computed by the emission of dust
heated by young stars as well as of evolved stellar populations. It is derived
from the IR luminosity, once the AGN contribution is removed, exploiting the
Kennicutt (1998) relation (which assumes a Salpeter IMF)
$\textnormal{SFR}^{8-1000\mu\textnormal{m}}\,(\textnormal{M}_{\odot}/\textnormal{yr})\,=\,4.5\,\times
10^{-44}\,\textnormal{L}_{8-1000\mu\textnormal{m}}\,(\textnormal{erg/s})$ and
using
$\textnormal{SFR}_{\textnormal{Chabrier}}\,=\,0.67\,\times\textnormal{SFR}_{\textnormal{Salpeter}}$
to convert it to a Chabrier IMF. The median SFR is
SFR${}^{8-1000\mu\text{m}}=20.4_{-9.2}^{+43.4}\,M_{\odot}\,yr^{-1}$. Because
the SFR${}^{8-1000\mu\text{m}}$ is heavily dependent on the fitting of the FIR
band, the reliability of this value is linked to the accuracy at which the
far-IR is measured. As we can see from Fig. 6, in which we compared the two
SFR values for each source, we have a systematic offset of $\sim 0.15\,$dex,
but we did not find a clear correlation between this offset and the number of
IR photometric detections nor with the SFR uncertainties.

Figure 6: Comparison between the SFR obtained from the optical-NIR bands with
those from FIR. SFR${}^{\text{sed}}$ are derived through the modeling of the
stellar emission in the UV-to-NIR. The color code indicates the number of
photometric detections for each source in the FIR band. A low number of FIR
detections may influence the goodness of the FIR SED-fitting, hence the
SFR${}^{8-1000\mu\text{m}}$, but we did not find any trend between the
SFR${}^{8-1000\mu\text{m}}-$SFR${}^{\text{sed}}$ offset and the number of IR
photometric detections. The blue line is a 1:1 line; the red line is the best-
fit line with a slope of $m=0.92$ and $c=0.24$, in the
$\log(\textnormal{SFR}^{8-1000\mu\text{m}}/M_{\odot}\,yr^{-1})=c+m\,\log(\text{SFR}^{\text{sed}}/M_{\odot}\,yr^{-1})$
notation.

#### SFR-M∗ relation

We investigated whether the hosts of the [Ne v]-selected AGNs lie within the
SFR-M∗ main sequence (Noeske et al. 2007), as shown in Fig 7 (red dots). We
used the Schreiber et al. (2015) main sequence (MS), in which the SFR is a
function of both the stellar mass and the redshift:

$\log{(\text{SFR}_{\text{MS}}/\text{M}_{\odot}\,\text{yr}^{-1}])}=\,m-m_{0}+a_{0}r-a_{1}[\max(0,m-m_{1}-a_{2}r)]^{2},$
(2)

where $r\equiv\log(1+z)$, $m\equiv\log(\text{M}_{*}/10^{9}\text{M}_{\odot})$,
$m_{0}=0.5\pm 0.07$, $a_{0}=1.5\pm 0.15$, $a_{1}=0.3\pm 0.08$, $m_{1}=0.36\pm
0.3,$ and $a_{2}=2.5\pm 0.6$. Using the masses obtained from the SED-fitting
and the Schreiber et al. (2015) SFR-M∗ relation (eq 2), we obtained a median
SFR${}_{\text{MS}}=(\,33.2_{-14.8}^{+21.0}\,)\,\textnormal{M}_{\odot}/\textnormal{yr}$.
We used the SFR${}_{\text{norm}}=$SFR${}^{\text{sed}}/$SFR${}_{\text{MS}}$ to
trace how much a source deviates from the MS. We found a median
SFR${}_{\text{norm}}=0.48_{-0.37}^{+0.76}$, which indicates that a significant
fraction our sample has a SFR lower than what is expected for SF galaxies.

We investigated if the SFR and the position in the SFR-M∗ plane depend on the
number of IR photometric detections (which are fundamental in constraining the
overall SED in sed3fit). For the sources with at least one IR detection, we
performed another run of SED-fitting without the IR photometric points. The
comparison of the SED-derived properties with those obtained using all the
photometric points shows larger uncertainties in the parameters for the fits
without the IR, but no systematic effect is present.

M13 performed a morphological classification of the [Ne v] sample and a
comparison with the morphologies of a control sample. The galaxies were
classified following Nair & Abraham (2010) using the F814W-band images. The
position of the [Ne v] in our SFR-M∗ plane, with the majority of the galaxies
within the MS, is in agreement with the M13 morphological classification, in
which early-spirals are the most commonly found type for the [Ne v] sample
(rather than irregular or late-spirals). Moreover, M13 found a lower fraction
of elliptical galaxies with respect to their control sample; this is in
agreement with the paucity of low-sSFR galaxies we found in the [Ne v] sample
(see § 5).

Figure 7: Comparison of the positions of the [Ne v] (red) and stellar mass-
and redshift-matched control (blue) samples in the SFR$-$M∗ plane. Upper
panel: Grey solid line is the Schreiber et al. (2015) MS, the grey dashed
lines its $1\,\sigma$ dispersion. The black error bars in the bottom right are
the mean uncertainties for the [Ne v] sample sources. Bottom panel: Fraction
of sources within the $1\,\sigma$ dispersion of the MS. In orange: the adopted
stellar mass binning.

#### SFR$-$Lbolo relation

We investigated the relation between host galaxies and AGNs by comparing the
bolometric luminosity of the AGN with the SFR and the SF-related IR
luminosity. We found a statistically significant but mild correlation between
the SFR and the $L_{\rm{bolo}}$ (Pearson $\rm{R}=0.28$ and $P$-value $=0.02$,
corresponding to $2.3\,\sigma$), and a stronger correlation between
$L_{\rm{IR,SF}}$ and $L_{\rm{bolo}}$ ($\rm{R}=0.44$ and a $P$-value
$=1.6\times 10^{-4}$).

In Fig. 8, we show the position of the [Ne v] AGNs (red dots) in the
$L_{\rm{bolo}}-$SFR plane and the comparison with the AGN sample of Stemo et
al. (2020) and with the model prediction of Bernhard et al. (2018). The orange
points correspond to the median (and $16^{th}$, $84^{th}$ percentiles) SFR of
the [Ne v] sample binned in AGN bolometric luminosity. The green points are
the average SFR binned in $L_{\rm{bolo}}$ for a sample of 2585 X-ray and IR
selected AGNs in the $0.2<z<2.5$ regime from Stemo et al. (2020). In the
$0.8-1.5$ redshift range, we found a similar flat evolution of the SFR with
the AGN bolometric luminosity, however with $\sim 0.4$ dex higher SFR. We
speculate that this could be due to the different selection techniques, as
Stemo et al. (2020) found that most of their sample is composed of quiescent
galaxies, while in ours they are $<10\,\%$. These differences could be related
to the band used for the selection (i.e., X-ray or IR), as the authors note
that it impacts their SFR.

We also plot the published relationships between X-ray luminosity and SFR of
Rosario et al. (2012, 2013, cyan symbols); Stanley et al. (2015, cyan
symbols); Bernhard et al. (2016, cyan symbols) collected by Bernhard et al.
(2018), alongside the prediction of their mass-dependent model (black lines).
We used the Lusso et al. (2012) bolometric correction to compute the
$L_{\rm{bolo}}$ from the AGN X-ray luminosity, and ’converted’ the SFR to a
Chabrier (2003) IMF. As we can see from Fig. 8, our results are extremely
similar to the observed relationships and model predictions.

Figure 8: SFR as function of the AGN bolometric luminosity for the [Ne
v]-selected AGNs (red circles). The average SFR in three bins of SFR is
reported in orange, with the error bar representing the $16^{\rm{th}}$ and
$84^{\rm{th}}$ percentiles. The green points are the average SFR for the
sample of X-ray and IR -selected AGNs of Stemo et al. (2020), while the cyan
symbols represent those from Rosario et al. (2012, 2013); Stanley et al.
(2015); Bernhard et al. (2016) collected by Bernhard et al. (2018). The black
line is the prediction from their mass-dependent model.

#### Eddington ratio

An illustrative way of estimating the SMBH growth is via the Eddington ratio
${\lambda_{\text{Edd}}}=\text{L}_{\text{bol}}/\text{L}_{\text{Edd}}$: the
ratio between the AGN luminosity and the theoretical maximum luminosity that
can be emitted by the AGN (determined by the balance between radiation
pressure and the BH gravitational attraction) and is therefore an indicator of
the small scale accretion process. According to the in situ co-evolution model
(see § 6) the Eddington ratio is strictly connected to the phase of the AGN:
the highly-accreting obscured AGNs should have ${\lambda_{\text{Edd}}}\gtrsim
1$, while once the AGN feedback kicks in and starts removing the gas from the
host-galaxy, a transition to sub-Eddington regimes
(${\lambda_{\text{Edd}}}\lesssim 0.1$) should occur. AGNs may accrete in
multiple short burst phases (e.g., Schawinski et al. 2015), in this case, the
AGN would “quickly” ($\tau\sim 10^{5}\,\rm{yr}$) pass through high- and low-
Eddington ratios multiple times.

We used the Suh et al. (2020) $M_{\text{BH}}-\text{M}_{*}$ relation to
estimate the SMBH masses using the stellar masses obtained from the SED-
fitting. This relation was obtained from a sample of 100 X-ray selected AGNs
in the COSMOS field with host galaxy masses from SED-fitting decomposition and
BH masses computed considering single epoch H$\alpha$, H$\beta$, and Mg ii
broad line widths and line/continuum luminosity as a proxy for the size and
velocity of the broad-line region (BLR). We obtained a median
$\log{(\text{M}_{BH}/M_{\odot})}=7.5_{-0.7}^{+0.4}$. We compared the
$M_{\text{BH}}$ with those obtained using the Reines & Volonteri (2015) and
the Shankar et al. (2016) relations, finding values not significantly
different (KS probabilities of 0.02 and 0.08, respectively). A more detailed
comparison can be found in Appendix C. From the $M_{\text{BH}}$ , we computed
the Eddington luminosity and used it with the AGN bolometric luminosity to
estimate the Eddington ratio (Fig. 9). We found a median
$\lambda_{Edd}=0.12_{-0.10}^{+0.31}$. For 25 sources ($\sim 25\%$) we obtained
an upper limit of their $\lambda_{\text{Edd}}$ only. Forty percent of the
sources have ${\lambda_{\text{Edd}}}\geq 0.1$, and $5\%$ are accreting near or
above the Eddington limit. We must caution that the $\lambda_{\text{Edd}}$ is
heavily dependent on the $M_{\text{BH}}$ , and those were computed assuming
the Suh et al. (2020) relation. Unfortunately, our current knowledge of
${M_{\text{BH}}}-\text{M}_{*}$ relation is mostly local and usually derived
from unobscured AGNs (due to the fact that the $M_{\text{BH}}$ estimates are
obtained from the profile of broad emission lines). Moreover, the advent of
JWST has recently highlighted the presence of several high-$z$ galaxies with
overmassive BH with respect to local relations (e.g., Übler et al. 2023;
Harikane et al. 2023; Pacucci & Loeb 2024) and opened the possibility of a
redshift evolution of the M${}_{\text{BH}}-\text{M}_{*}$ relations. In any
case, using any of the three local investigated functions suggests that a
significant fraction of the [Ne v] sample are AGNs in a high accretion phase.

Figure 9: Eddington ratio distribution of the [Ne v]-selected sample of type 2
AGNs. The ${\lambda_{\text{Edd}}}$ was computed with the MBH obtained from the
stellar mass (using the Suh et al. 2020 M${}_{\text{BH}}-\text{M}_{*}$
relation) and with the AGN bolometric luminosity from the SED fitting. The
sources for which we had only an upper limit on their bolometric luminosity
are reported as a white histogram. $40\%$ of the sources have
${\lambda_{\text{Edd}}}\geq 0.1$, suggesting that a significant fraction of
the [Ne v] sample are in a highly accreting phase.

#### Molecular gas fraction

We used the Kaasinen et al. (2019) relation (eq 3) to estimate the molecular
gas mass of the sample. They obtained this relation linking the L850μm to the
CO luminosity, which, in turn, is a proxy of the molecular gas mass:

$\text{M}_{molgas}^{850\mu m}\,\,(M_{\odot})=\left(\frac{\text{L}_{850\mu
m}}{erg\,s^{-1}\,Hz^{-1}}\right)\left(\frac{1}{6.2\times
10^{-19}\left(\text{L}_{850\mu m}/10^{31}\right)^{0.07}}\right).$ (3)

We computed L850μm from the host-galaxy component, derived via the SED-
fitting. The median molecular gas mass of the sample was
$\log(M_{molgas}^{850\mu m}/M_{\odot})=10.4_{-0.5}^{+0.4}$. We advise taking
these results with a bit of caution as they depend on the L850μm measured from
the best-fit SED, for which the nearest filters at our disposal were the
SCUBA/JCMT at $\lambda_{\rm{rest}}\sim 225\,\mu\rm{m}$ and the SPIRE/Herschel
$\lambda_{\rm{rest}}\sim 250\,\mu\rm{m}$. However, we also found a very good
agreement (with the exception of one source) between the dust mass measured
from the L850μm (using a gas-to-dust mass ratio in the $100-200$ range, e.g.,
Tacconi et al. 2020) and those obtained as a direct output from the sed3fit
fitting, which relies on the fitting of the entire IR SED.

We used the $\text{M}_{molgas}^{850\mu m}$ to obtain the molecular gas
fraction of the galaxies, defined as $f_{\text{mol}}=\text{M}_{molgas}^{850\mu
m}/(\text{M}_{molgas}+\text{M}_{*})$. The sample had a median
$f_{\text{mol}}=0.24_{-0.14}^{+0.30}$. We found that our sample has
f${}_{\text{mol}}$ in agreement with those in Dessauges-Zavadsky et al.
(2020), who collected from the literature the f${}_{\text{mol}}$ for CO
detected main sequence galaxies at $0\leq z\leq 6$. The $f_{\text{mol}}$
distribution indicates that the majority of the [Ne v] sources have cold gas
available to fuel the SF and, in contrast to the “read and dead” elliptical
galaxies, they will likely continue to forming stars, not having depleted
their reservoir yet.

##  5 Comparison with the control sample

To be able to make a comparison between our sources and non-active galaxies in
the COSMOS field, we built a control sample. For each source in the [Ne v]
sample, we selected eight sources in the zCOSMOS20k catalog, matched in
redshift (with a $0.01-0.05$ accuracy) and stellar mass ($0.1\,$dex accuracy).
From this sample, we excluded the 51 sources with the X-ray source flag in the
COSMOS2020 catalog. We performed the SED-fitting in the same way as we did for
the [Ne v] sample (see Section 4) and excluded 30 sources for which the SED-
fitting failed to properly reproduce the emission. We did not replace these
sources as they were uniformly distributed both in stellar mass and redshift,
and we still had a statistically adequate number of sources. The final control
sample was composed of 618 sources, Fig. 10 shows the comparison of the $z$
and $M_{*}$ distributions between the [Ne v] and the control samples. In Table
2, we report the comparison between the main properties of the [Ne v] sample
and of the control sample.

Figure 10: Comparison of redshift (left) and stellar mass (right) distributions of the [Ne v] (red) and control (blue) samples. Table 2: Comparison of the main properties of the [Ne v] sample and of the control sample. We report the median values (with the $16^{th}$ and $84^{th}$ percentiles) for the redshift $z$, stellar mass, SFR, specific SFR (sSFR=SFR/M∗), SFR${}_{\text{norm}}$=SFR$/$SFR${}_{\text{MS}}$, fraction of sources within the Schreiber et al. (2015) MS (f${}_{\text{MS}}$), molecular gas mass (Mmolgas), the molecular gas fraction ( f${}_{\text{mol}}$=M${}_{molgas}/($M${}_{molgas}+$M${}_{*})$), age of the galaxy (t${}_{\text{age}}$, from the SED-fitting), BH mass (M${}_{\text{BH}}$), and Eddington ratio ($\lambda_{Edd}$). | [Ne v] | Control
---|---|---
$z$ | $0.86_{-0.15}^{+0.11}$ | $0.85\pm 0.11$
$\log{(\text{M}_{*}\,/\,M_{\odot})}$ | $10.91_{-0.46}^{+0.28}$ | $10.91_{-0.42}^{+0.30}$
SFR${}^{\text{sed}}$ ($M_{\odot}\,yr^{-1}$) | $12.9_{-9.1}^{+30.4}$ | $4.3_{-3.7}^{+14.4}$
$\log{(\text{sSFR}/yr^{-1})}$ | $-9.7_{-0.7}^{+0.5}$ | $-10.2_{-1.1}^{+0.8}$
SFR${}_{\text{norm}}$ | $0.48_{-0.37}^{+0.76}$ | $0.16_{-0.14}^{+0.56}$
f${}_{\text{MS}}$ | $0.52_{-0.02}^{+0.08}$ | $0.30\pm 0.01$
$\log{(\text{M}_{molgas}\,/\,M_{\odot})}$ | $10.4_{-0.5}^{+0.4}$ | $10.3_{-0.7}^{+0.5}$
f${}_{\text{mol}}$ | $0.24_{-0.14}^{+0.30}$ | $0.20_{-0.15}^{+0.26}$
$\log{(\text{t}_{\text{age}}/yr^{-1})}$ | $9.48_{-0.25}^{+0.20}$ | $9.63_{-0.30}^{+0.15}$
$\log{(\text{M}_{\text{BH}}/M_{\odot})}$ | $7.5_{-0.7}^{+0.4}$ |
$\lambda_{Edd}$ | $0.12_{-0.10}^{+0.31}$ |

The [Ne v] sample has, on average, a higher SFR with respect to the control
sample, although both reach values as high as $\sim\,300M_{\odot}/yr$.
Considering the position in the SFR-M∗ plane, we found that the [Ne v] sample
has a higher fraction of sources in the MS (i.e., a lower fraction of sources
below). As we can see from Fig. 7, for $\log{(\text{M}_{*}\,/\,M_{\odot})}\geq
10.25$, there is a clear difference in the fraction of sources within the MS,
with the control sample having a constant fraction f${}_{\textnormal{MS}}\sim
40\%$, while the [Ne v] f${}_{\textnormal{MS}}\sim 60\%$. This difference
between the two samples appears more evident in Fig. 11: the control sample
specific SFR (sSFR=SFR/M∗) has a bimodal distribution, while the [Ne v] has a
higher fraction of sources at high sSFR and seems to lack a population of
“quiescent” galaxies ($\log(\textnormal{sSFR}/yr^{-1})\leq-11$). The two sSFR
distributions are significantly different (KS-test P$=1.3\times 10^{-7}$). The
comparison of the t${}_{\text{age}}$ (the age of the oldest stars in the
galaxy, as provided by sed3fit) distributions shows a significant difference
(KS-test P$\sim 6\times 10^{-7}$) between the two samples, with the [Ne v]
sources being, on average, younger. This is in agreement with the results from
M13, who compared the morphologies of our sample with those of a mass-matched
control sample of non-active galaxies and found that the [Ne v] selection
prefers early-type galaxies, with a lower fraction of late spiral and
elliptical morphologies.

We investigated the cold gas content of the galaxies to test whether the
difference in sSFR (and the lack of “quiescent” galaxies) originated from a
different amount of gas available to fuel the SF. As in § 4.2, we computed
M${}_{\text{molgas}}$ and f${}_{\text{mol}}$ for both samples. We did not find
any significant difference in the M${}_{\text{molgas}}$ (Fig. 12) and
f${}_{\text{mol}}$ distributions. Moreover, binning in M∗ and SFR, we found
that the median f${}_{\text{mol}}$ in each bin is practically the same for
both samples (with the exception of the lowest M∗ and highest SFR bin, which
have only one [Ne v] source within). We also compared the mean host-galaxy IR
SEDs and found that the two samples have similar SEDs at
$\lambda_{\rm{rest}}>300\,\mu\rm{m}$ (thus explaining the similar amount of
cold gas content), while the [Ne v] sample has, on average, higher mid-IR
emission (i.e., higher SFR). This is linked to the lower fraction of
“quiescent” galaxies in the [Ne v] sample, which have lower mid-IR emission
with respect to main-sequence SF-galaxies. The different shapes of the SED in
the mid-IR regime are linked to the fact that the [Ne v] sample has, according
to the SED-fitting results, a higher fraction of its dust luminosity coming
from the hot ($130-250\,\rm{K}$) and warm ($30-60\,\rm{K}$) dust phases,
namely, a higher emission in the $\lambda_{\rm{rest}}<100\mu\rm{m}$.

We conclude that the highest fraction of sources within the MS for the [Ne v]
sample and the lack of a population of “quiescent” galaxies is not related to
a different amount of cold gas reservoir in the host galaxy, rather it is
linked to a different efficiency in forming stars. We propose three
explanations for this higher SF efficiency: the AGN may have the effect of
enhancing the SF; the AGN is more likely to be triggered in galaxies with
higher SFR; or the [Ne v] selection efficiently allows us to pick up AGNs in
an obscured growth phase, where we expect high SFR and obscured AGN activity.
This last hypothesis is consistent with the [Ne v] sample being slightly
younger on average: the IR host galaxies are still growing and will reach
higher masses than the control sample. While the physical explanation of the
[Ne v]-obscured AGN selection efficiency still needs to be fully understood,
we speculate that the explanation of why the [Ne v] selection may be well
suited to select AGNs in the obscured accretion phase resides in the fact that
its emission is effectively extinguished by even a modest quantity of dust in
their host-galaxy. Thus, sources in the starburst phase (prior to the obscured
accretion phase) are missed due to the (perceived) lack of [Ne v] emission,
while galaxies after the obscured accretion phase (thus transitioning to a
type 1 AGN) are excluded due to our selection of objects with only narrow
lines in their spectra.

Figure 11: Comparison of the specific SFR (sSFR=SFR/M∗) distributions of the
[Ne v] (red) and control (blue) samples. The two sSFR distributions are
significantly different (KS-test P$=1.3\times 10^{-7}$), with the [Ne v]
sample lacking a population of “quiescent” galaxies
($\log(\textnormal{sSFR}/yr^{-1})\leq-11$).

Figure 12: Comparison of the molecular gas mass distributions of the [Ne v]
(red) and control (blue) samples. We obtained the M${}_{\text{mol}}$ from the
L850μm, using the Kaasinen et al. (2019) relation. The two M${}_{\text{mol}}$
distributions are not significantly different.

##  6 Interpretation within the in situ co-evolution model

We place our sources in the context of the AGN-galaxy co-evolution paradigm by
comparing them with the theoretical prediction of the in situ BH-galaxy
evolution model (Mancuso et al. 2016a, b, 2017; Lapi et al. 2018). This model
allows us to easily follow the galaxy evolution, thus interpreting the
properties of the [Ne v] sources in the context of the AGN-galaxy co-
evolution.

In the in situ co-evolution model, the SF is a local process regulated by
energy feedback from supernova explosions (SNe) and from the central SMBH. In
the first phase of the galaxy evolution, the dominant feedback is due to SNe,
with SFR $\propto t^{1/2}$ and $M_{*}\propto t^{2/3}$. The MS emerges as the
locus in the SFR$-M*$ plane where galaxies spend most of their time, thus
where it is most probable to find them. In these early stages, the BH mass
grows exponentially in gas-rich obscured environment, the AGN emits at mildly
super Eddington ratio and its luminosity rises exponentially. After less than
one Gyr (for massive galaxies), the AGN luminosity reaches values similar to
those of the SF and becomes dominant. Via powerful winds and outflows, the AGN
power heats up and removes the gas from the host galaxy, quenching the SF. The
galaxy moves below the MS and the stellar populations evolve passively, while
the residual gas in the central region accretes into the SMBH at lower sub-
Eddington ratios and the AGN luminosity exponentially declines. At the end of
this phase, what is left is a ”red and dead” elliptical galaxy.

In Figure 13 we illustrate the position of the [Ne v] sources in the
SFR$-L_{bol}$ diagram, along with the prediction of the in situ model (Mancuso
et al. 2016a). The [Ne v] AGNs are color-coded on the basis of their tage
(which have a mean uncertainties of $\sim 0.1$ dex). The colored contours show
the number density of sources predicted by the model. The dashed lines
represent two evolutionary tracks from the in situ model for AGNs with
different peak luminosity (the maximum bolometric luminosity an AGN can reach
before the feedback kicks in and lowers the AGN output), with the forward time
direction indicated by the arrows. The evolution of the sources begins from
the left, with the SFR roughly constant while the AGN luminosity grows
exponentially. When the source crosses the blue $L_{bol}=L_{SF}$ line, the AGN
luminosity becomes dominant. In these two phases, the AGN accretes at
Eddington and super Eddington ratios in obscured condition. Then, when the
feedback starts to ”kick in,” the SF is abruptly quenched and the SFR drops
quickly, while the AGN accretes the remaining material at lower sub-Eddington
ratios and its emission fades with a slower trend.

According to the in situ prediction, our sources on the left of the blue line
would be obscured and accreting AGNs, in which the SF is still dominated by
stellar feedback. The sources on the right would be those for which the AGN is
the main actor in the feedback processes. Finally, we note that there is a
segregation of older sources in the lower right locus of the plot. These
sources could be those for which the AGN has started to quench the SF and that
are rapidly moving downward in the plot.

Therefore, according to the in situ model prediction, the [Ne v] sources are
located in the SFR$-L_{bol}$ plane where we expect AGNs in the obscured
accretion phase, with the oldest sources being compatible to be at the
beginning of the ”quenching phase.”

Figure 13: Distribution of the [Ne v] sources on the SFR$-$Lbol plane. The
color code indicates the age of the oldest stars in the host galaxy, as
provided by sed3fit. Colored contours illustrate the number density of
galaxies plus AGN at $z\sim 1$ as predicted by the in situ co-evolution model
(Mancuso et al. 2016a); orange, yellow, green, cyan, light blue, blue, and
dark blue contours refer to number density of $10^{-4}$, $10^{-5}$, $10^{-6}$,
$10^{-7}$, $10^{-8}$, $10^{-9}$ Mpc-1, respectively. The black dashed lines
show two evolutionary tracks (forward time direction indicated by the arrows)
for AGNs with peak bolometric luminosity of $10^{45.5}$ and $10^{46.5}$
erg$/$s. The blue continuous line indicates where the SF luminosity is equal
to the AGN luminosity. The average uncertainty on the $t_{\rm{age}}$ is $\sim
0.1\,$dex.

##  7 Conclusion

In this work, we investigated the AGN and host galaxy properties of a sample
of 94 [Ne v]-selected type 2 AGNs. We performed an X-ray spectral analysis of
the 36 X-ray-detected sources to characterize their AGN intrinsic luminosity
and obscuration. For the X-ray-undetected sources, we used the X/[Ne v] ratio
to estimate their amount of obscuration and the fraction of CT-AGN. We
performed optical-to-FIR SED-fitting, using the sed3fit algorithm, to
characterize both the AGN and the host galaxy properties. We used the stellar
mass to obtain the BH mass and, subsequently, the Eddington ratio of the [Ne
v] sample. Finally, we compared the host galaxy properties (stellar mass, SFR,
sSFR, cold gas content) of the [Ne v] sample with those of a non-active
control sample and interpreted our results in the light of the in situ BH-
galaxy evolution scenario. Our main results are the following:

  1. 1.

The [Ne v] selection is an optimal tool to select very obscured ($N_{H}\geq
10^{23}$ cm-2) and CT-AGNs at $z\sim 1$. More than two-thirds of our sample is
composed of very obscured sources and $\sim 20\%$ of the sources are candidate
CT-AGNs.

  2. 2.

Almost half of the sample is composed of AGNs in a strong episode of SMBH
growth ($\lambda_{\text{Edd}}\geq 0.1$).

  3. 3.

The [Ne v] sample has a significantly higher fraction of sources within the MS
than normal galaxies and seems to lack a population of ”quiescent” (low sSFR)
galaxies.

  4. 4.

This difference is not due to the amount of cold gas reservoir, as both
samples show similar M${}_{\text{mol}}$, but to the higher efficiency in
forming stars of the [Ne v] sample. This higher efficiency could be related to
the AGN enhancing the SF, to the high SF triggering the AGN activity, or it
could be due to a selection effect: with the [Ne v]-selection picking-up AGNs
in their obscured growing phase.

  5. 5.

We interpret our results in the context of the in situ co-evolution scenario
and find that the [Ne v] sample is compatible to be composed by sources in the
”pre-quenching” phase, with only the few oldest sources showing the effect of
the AGN quenching the SF. Therefore we favor the latter hypothesis: [Ne v]
sources are preferentially hosted in obscured AGNs that are efficiently
accreting and forming stars.

Multiwavelength analyses similar to this one, carried out using different
high-ionization lines as selection method (i.e., [O iii] for lower $z$, C iv
for higher $z$), should allow us to study the redshift evolution of the AGN
and host galaxy properties, as well as to unveil the mystery of the BH-galaxy
co-evolution mechanism.

###### Acknowledgements.

The authors would like to thank the anonymous referee for her/his comments and
useful suggestions. R.G. acknowledges financial contribution from the
agreement ASI-INAF n. 2017-14-H.O. A.L. is partly supported by the PRIN MIUR
2017 prot. 20173ML3WW 002 “Opening the ALMA window on the cosmic evolution of
gas, stars, and massive black holes”. C.V. and F.R. acknowledge support from
PRIN MIUR 2017 PH3WAT (“Black hole winds and the baryon life cycle of
galaxies”).

## References

  * Alexander et al. (2005) Alexander, D. M., Bauer, F. E., Chapman, S. C., et al. 2005, ApJ, 632, 736
  * Alexander et al. (2010) Alexander, D. M., Swinbank, A. M., Smail, I., McDermid, R., & Nesvadba, N. P. H. 2010, MNRAS, 402, 2211
  * Almaini (2003) Almaini, O. 2003, Astronomische Nachrichten, 324, 109
  * Ananna et al. (2019) Ananna, T. T., Treister, E., Urry, C. M., et al. 2019, ApJ, 871, 240
  * Archibald et al. (2002) Archibald, E. N., Dunlop, J. S., Jimenez, R., et al. 2002, MNRAS, 336, 353
  * Arnaud (1996) Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17
  * Barchiesi et al. (2021) Barchiesi, L., Pozzi, F., Vignali, C., et al. 2021, PASA, 38, e033
  * Behar et al. (2015) Behar, E., Baldi, R. D., Laor, A., et al. 2015, MNRAS, 451, 517
  * Bernhard et al. (2018) Bernhard, E., Mullaney, J. R., Aird, J., et al. 2018, MNRAS, 476, 436
  * Bernhard et al. (2016) Bernhard, E., Mullaney, J. R., Daddi, E., Ciesla, L., & Schreiber, C. 2016, MNRAS, 460, 902
  * Berta et al. (2013) Berta, S., Lutz, D., Santini, P., et al. 2013, A&A, 551, A100
  * Bevington & Robinson (2003) Bevington, P. R. & Robinson, D. K. 2003, Data reduction and error analysis for the physical sciences
  * Bisigello et al. (2021) Bisigello, L., Gruppioni, C., Feltre, A., et al. 2021, A&A, 651, A52
  * Boquien et al. (2019) Boquien, M., Burgarella, D., Roehlly, Y., et al. 2019, A&A, 622, A103
  * Bradford et al. (2022) Bradford, C., Glenn, J., Armus, L., et al. 2022, Bulletin of the AAS, 54, https://baas.aas.org/pub/2022n6i304p07
  * Brusa et al. (2015) Brusa, M., Bongiorno, A., Cresci, G., et al. 2015, MNRAS, 446, 2394
  * Brusa et al. (2016) Brusa, M., Perna, M., Cresci, G., et al. 2016, A&A, 588, A58
  * Bruzual (2007) Bruzual, G. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 374, From Stars to Galaxies: Building the Pieces to Build Up the Universe, ed. A. Vallenari, R. Tantalo, L. Portinari, & A. Moretti, 303
  * Buchner et al. (2015) Buchner, J., Georgakakis, A., Nandra, K., et al. 2015, ApJ, 802, 89
  * Burgarella et al. (2005) Burgarella, D., Buat, V., & Iglesias-Páramo, J. 2005, MNRAS, 360, 1413
  * Cappi et al. (2006) Cappi, M., Panessa, F., Bassani, L., et al. 2006, A&A, 446, 459
  * Cash (1979) Cash, W. 1979, ApJ, 228, 939
  * Cattaneo et al. (2009) Cattaneo, A., Faber, S. M., Binney, J., et al. 2009, Nature, 460, 213
  * Chabrier (2003) Chabrier, G. 2003, Publications of the Astronomical Society of the Pacific, 115, 763
  * Charlot & Fall (2000) Charlot, S. & Fall, S. M. 2000, ApJ, 539, 718
  * Cicone et al. (2014) Cicone, C., Maiolino, R., Sturm, E., et al. 2014, A&A, 562, A21
  * Civano et al. (2016) Civano, F., Marchesi, S., Comastri, A., et al. 2016, ApJ, 819, 62
  * Cleri et al. (2022) Cleri, N. J., Yang, G., Papovich, C., et al. 2022, arXiv e-prints, arXiv:2209.06247
  * Combes et al. (2019) Combes, F., García-Burillo, S., Audibert, A., et al. 2019, Astronomy and Astrophysics, 623, A79
  * da Cunha et al. (2008) da Cunha, E., Charlot, S., & Elbaz, D. 2008, MNRAS, 388, 1595
  * Delvecchio et al. (2014) Delvecchio, I., Gruppioni, C., Pozzi, F., et al. 2014, MNRAS, 439, 2736
  * Dessauges-Zavadsky et al. (2020) Dessauges-Zavadsky, M., Ginolfi, M., Pozzi, F., et al. 2020, A&A, 643, A5
  * Di Matteo et al. (2005) Di Matteo, T., Springel, V., & Hernquist, L. 2005, Nature, 433, 604
  * Duras et al. (2020) Duras, F., Bongiorno, A., Ricci, F., et al. 2020, A&A, 636, A73
  * Elitzur (2008) Elitzur, M. 2008, New Astronomy Reviews, 52, 274
  * Ellison et al. (2019) Ellison, S. L., Viswanathan, A., Patton, D. R., et al. 2019, MNRAS, 487, 2491
  * Elvis et al. (2009) Elvis, M., Civano, F., Vignali, C., et al. 2009, ApJS, 184, 158
  * Feltre et al. (2012) Feltre, A., Hatziminaoglou, E., Fritz, J., & Franceschini, A. 2012, MNRAS, 426, 120
  * Ferrarese & Merritt (2000) Ferrarese, L. & Merritt, D. 2000, ApJ, 539, L9
  * Feruglio et al. (2010) Feruglio, C., Maiolino, R., Piconcelli, E., et al. 2010, A&A, 518, L155
  * Fritz et al. (2006) Fritz, J., Franceschini, A., & Hatziminaoglou, E. 2006, MNRAS, 366, 767
  * Fruscione et al. (2006) Fruscione, A., McDowell, J. C., Allen, G. E., et al. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6270, Proc. SPIE, 62701V
  * Gebhardt et al. (2000) Gebhardt, K., Bender, R., Bower, G., et al. 2000, ApJ, 539, L13
  * Gehrels (1986) Gehrels, N. 1986, ApJ, 303, 336
  * Gilli (2013) Gilli, R. 2013, Mem. Soc. Astron. Italiana, 84, 647
  * Gilli et al. (2007) Gilli, R., Comastri, A., & Hasinger, G. 2007, A&A, 463, 79
  * Gilli et al. (2010) Gilli, R., Vignali, C., Mignoli, M., et al. 2010, A&A, 519, A92
  * Glikman et al. (2012) Glikman, E., Urrutia, T., Lacy, M., et al. 2012, ApJ, 757, 51
  * Gruppioni et al. (2016) Gruppioni, C., Berta, S., Spinoglio, L., et al. 2016, MNRAS, 458, 4297
  * Harikane et al. (2023) Harikane, Y., Zhang, Y., Nakajima, K., et al. 2023, ApJ, 959, 39
  * Harrison et al. (2012) Harrison, C. M., Alexander, D. M., Swinbank, A. M., et al. 2012, MNRAS, 426, 1073
  * Harrison et al. (2018) Harrison, C. M., Costa, T., Tadhunter, C. N., et al. 2018, Nature Astronomy, 2, 198
  * Hopkins et al. (2007a) Hopkins, P. F., Lidz, A., Hernquist, L., et al. 2007a, ApJ, 662, 110
  * Hopkins et al. (2007b) Hopkins, P. F., Richards, G. T., & Hernquist, L. 2007b, ApJ, 654, 731
  * Iwasawa et al. (2020) Iwasawa, K., Comastri, A., Vignali, C., et al. 2020, A&A, 639, A51
  * Jaffe et al. (2004) Jaffe, W., Meisenheimer, K., Röttgering, H. J. A., et al. 2004, Nature, 429, 47
  * Juneau et al. (2011) Juneau, S., Dickinson, M., Alexander, D. M., & Salim, S. 2011, ApJ, 736, 104
  * Kaasinen et al. (2019) Kaasinen, M., Scoville, N., Walter, F., et al. 2019, ApJ, 880, 15
  * Kakkad et al. (2016) Kakkad, D., Mainieri, V., Padovani, P., et al. 2016, A&A, 592, A148
  * Kalberla et al. (2005) Kalberla, P. M. W., Burton, W. B., Hartmann, D., et al. 2005, A&A, 440, 775
  * Kawamuro et al. (2022) Kawamuro, T., Ricci, C., Imanishi, M., et al. 2022, arXiv e-prints, arXiv:2208.03880
  * Kennicutt (1998) Kennicutt, Robert C., J. 1998, ARA&A, 36, 189
  * Kormendy & Ho (2013) Kormendy, J. & Ho, L. C. 2013, ARA&A, 51, 511
  * Kormendy & Richstone (1995) Kormendy, J. & Richstone, D. 1995, ARA&A, 33, 581
  * Laigle et al. (2016) Laigle, C., McCracken, H. J., Ilbert, O., et al. 2016, ApJS, 224, 24
  * LaMassa et al. (2017) LaMassa, S. M., Yaqoob, T., & Kilgard, R. 2017, ApJ, 840, 11
  * Lamastra et al. (2013) Lamastra, A., Menci, N., Fiore, F., et al. 2013, A&A, 559, A56
  * Lanzuisi et al. (2018) Lanzuisi, G., Civano, F., Marchesi, S., et al. 2018, MNRAS, 480, 2578
  * Lapi et al. (2018) Lapi, A., Pantoni, L., Zanisi, L., et al. 2018, ApJ, 857, 22
  * Lapi et al. (2014) Lapi, A., Raimundo, S., Aversa, R., et al. 2014, ApJ, 782, 69
  * Lilly et al. (2009) Lilly, S. J., Le Brun, V., Maier, C., et al. 2009, ApJS, 184, 218
  * Lilly et al. (2007) Lilly, S. J., Le Fèvre, O., Renzini, A., et al. 2007, ApJS, 172, 70
  * Lusso et al. (2012) Lusso, E., Comastri, A., Simmons, B. D., et al. 2012, Monthly Notices of the Royal Astronomical Society, 425, 623
  * Magorrian et al. (1998) Magorrian, J., Tremaine, S., Richstone, D., et al. 1998, AJ, 115, 2285
  * Maiolino et al. (1998) Maiolino, R., Salvati, M., Bassani, L., et al. 1998, A&A, 338, 781
  * Mancuso et al. (2017) Mancuso, C., Lapi, A., Prandoni, I., et al. 2017, ApJ, 842, 95
  * Mancuso et al. (2016a) Mancuso, C., Lapi, A., Shi, J., et al. 2016a, ApJ, 833, 152
  * Mancuso et al. (2016b) Mancuso, C., Lapi, A., Shi, J., et al. 2016b, ApJ, 823, 128
  * Marchesi et al. (2016) Marchesi, S., Lanzuisi, G., Civano, F., et al. 2016, ApJ, 830, 100
  * Mignoli et al. (2019) Mignoli, M., Feltre, A., Bongiorno, A., et al. 2019, Astronomy and Astrophysics, 626, A9
  * Mignoli et al. (2013) Mignoli, M., Vignali, C., Gilli, R., et al. 2013, A&A, 556, A29
  * Moretti et al. (2012) Moretti, A., Vattakunnel, S., Tozzi, P., et al. 2012, A&A, 548, A87
  * Nair & Abraham (2010) Nair, P. B. & Abraham, R. G. 2010, ApJS, 186, 427
  * Nesvadba et al. (2008) Nesvadba, N. P. H., Lehnert, M. D., De Breuck, C., et al. 2008, in Gas and Stars in Galaxies - A Multi-Wavelength 3D Perspective, 37
  * Noeske et al. (2007) Noeske, K. G., Weiner, B. J., Faber, S. M., et al. 2007, The Astrophysical Journal, 660, L43
  * Noll et al. (2009) Noll, S., Burgarella, D., Giovannoli, E., et al. 2009, A&A, 507, 1793
  * Pacucci & Loeb (2024) Pacucci, F. & Loeb, A. 2024, arXiv e-prints, arXiv:2401.04159
  * Perna et al. (2015a) Perna, M., Brusa, M., Cresci, G., et al. 2015a, A&A, 574, A82
  * Perna et al. (2015b) Perna, M., Brusa, M., Salvato, M., et al. 2015b, A&A, 583, A72
  * Pozzi et al. (2010) Pozzi, F., Vignali, C., Comastri, A., et al. 2010, A&A, 517, A11
  * Reines & Volonteri (2015) Reines, A. E. & Volonteri, M. 2015, ApJ, 813, 82
  * Rosario et al. (2012) Rosario, D. J., Santini, P., Lutz, D., et al. 2012, A&A, 545, A45
  * Rosario et al. (2013) Rosario, D. J., Trakhtenbrot, B., Lutz, D., et al. 2013, A&A, 560, A72
  * Satyapal et al. (2014) Satyapal, S., Ellison, S. L., McAlpine, W., et al. 2014, MNRAS, 441, 1297
  * Schawinski et al. (2015) Schawinski, K., Koss, M., Berney, S., & Sartori, L. F. 2015, MNRAS, 451, 2517
  * Schreiber et al. (2015) Schreiber, C., Pannella, M., Elbaz, D., et al. 2015, Astronomy and Astrophysics, 575, A74
  * Scoville et al. (2007) Scoville, N., Aussel, H., Brusa, M., et al. 2007, ApJS, 172, 1
  * Secrest et al. (2020) Secrest, N. J., Ellison, S. L., Satyapal, S., & Blecha, L. 2020, MNRAS, 499, 2380
  * Shankar et al. (2016) Shankar, F., Bernardi, M., Sheth, R. K., et al. 2016, MNRAS, 460, 3119
  * Silk & Rees (1998) Silk, J. & Rees, M. J. 1998, A&A, 331, L1
  * Spergel et al. (2003) Spergel, D. N., Verde, L., Peiris, H. V., et al. 2003, ApJS, 148, 175
  * Spinoglio et al. (2021) Spinoglio, L., Mordini, S., Fernández-Ontiveros, J. A., et al. 2021, PASA, 38, e021
  * Stalevski et al. (2012) Stalevski, M., Fritz, J., Baes, M., Nakos, T., & Popovic, L. C. 2012, Publications de l’Observatoire Astronomique de Beograd, 91, 235
  * Stalevski et al. (2016) Stalevski, M., Ricci, C., Ueda, Y., et al. 2016, MNRAS, 458, 2288
  * Stanley et al. (2015) Stanley, F., Harrison, C. M., Alexander, D. M., et al. 2015, MNRAS, 453, 591
  * Stemo et al. (2020) Stemo, A., Comerford, J. M., Barrows, R. S., et al. 2020, ApJ, 888, 78
  * Suh et al. (2020) Suh, H., Civano, F., Trakhtenbrot, B., et al. 2020, ApJ, 889, 32
  * Tacconi et al. (2020) Tacconi, L. J., Genzel, R., & Sternberg, A. 2020, ARA&A, 58, 157
  * Toba et al. (2017) Toba, Y., Bae, H.-J., Nagao, T., et al. 2017, ApJ, 850, 140
  * Treister et al. (2012) Treister, E., Schawinski, K., Urry, C. M., & Simmons, B. D. 2012, ApJ, 758, L39
  * Übler et al. (2023) Übler, H., Maiolino, R., Curtis-Lake, E., et al. 2023, A&A, 677, A145
  * Ueda et al. (2014) Ueda, Y., Akiyama, M., Hasinger, G., Miyaji, T., & Watson, M. G. 2014, ApJ, 786, 104
  * Vignali (2014) Vignali, C. 2014, in IAU Symposium, Vol. 304, Multiwavelength AGN Surveys and Studies, ed. A. M. Mickaelian & D. B. Sanders, 132–138
  * Vignali et al. (2006) Vignali, C., Alexander, D. M., & Comastri, A. 2006, MNRAS, 373, 321
  * Vignali et al. (2010) Vignali, C., Alexander, D. M., Gilli, R., & Pozzi, F. 2010, MNRAS, 404, 48
  * Vignali et al. (2014) Vignali, C., Mignoli, M., Gilli, R., et al. 2014, A&A, 571, A34
  * Weaver et al. (2022) Weaver, J. R., Kauffmann, O. B., Ilbert, O., et al. 2022, ApJS, 258, 11
  * Xue et al. (2011) Xue, Y. Q., Luo, B., Brandt, W. N., et al. 2011, ApJS, 195, 10
  * Yang et al. (2022) Yang, G., Boquien, M., Brandt, W. N., et al. 2022, ApJ, 927, 192
  * Yang et al. (2020) Yang, G., Boquien, M., Buat, V., et al. 2020, MNRAS, 491, 740
  * Zakamska et al. (2016) Zakamska, N. L., Hamann, F., Pâris, I., et al. 2016, MNRAS, 459, 3144
  * Zhao et al. (2021) Zhao, X., Marchesi, S., Ajello, M., et al. 2021, A&A, 650, A57

##  Appendix A X-ray analysis

We performed the spectral fitting via the XSPEC package (Arnaud 1996) with two
different models. The first consists of a power-law component (powerlaw)
modified by the Galactic absorption (phabs) at the source position, computed
via the nh tool, which derives it from the HI map by Kalberla et al. (2005).
The second model includes a power-law component with fixed photon index
(representing the intrinsic un-absorbed emission of the AGN), modified by the
AGN torus obscuration via a photoelectric absorption component ($N_{H}$) at
the source redshift (zphabs), and by the Galactic absorption. The photon index
had to be fixed to $\Gamma=1.8$, a typical value for the intrinsic AGN
emission, due to the degeneracy between $\Gamma$ and $N_{H}$ that cannot be
resolved in most of our spectra due to the low number of net-counts: the flat
X-ray spectra of an obscured AGN can be fitted equally well with a steep
power-law and significant absorption as with a flat power-law and very low
absorption. In Table 3, we report the spectral properties of all the X-ray-
detected sources.

Table 3: Properties of the X-ray-detected sample obtained from an X-ray
spectral analysis.

ID | $z$ | Ncts | $\Gamma$ | $\log{(N_{H}/\rm{cm^{-2}})}$ | $\log{(L_{2-10keV}/\rm{L_{\odot}})}$ | X/[Ne v]
---|---|---|---|---|---|---
lid1856 | 0.73 | 1827 | $1.6_{-0.1}^{+0.1}$ | $21.6_{-0.2}^{+0.1}$ | $44.41_{-0.03}^{+0.02}$ | $1456_{-86}^{+147}$
cid339 | 0.69 | 373 | $1.5_{-0.2}^{+0.2}$ | $21.7_{-0.4}^{+0.2}$ | $43.61_{-0.06}^{+0.06}$ | $604_{-84}^{+81}$
cid522 | 0.94 | 336 | $1.1_{-0.2}^{+0.2}$ | $22.5_{-0.1}^{+0.1}$ | $44.10_{-0.05}^{+0.06}$ | $531_{-64}^{+62}$
cid110 | 0.73 | 313 | $1.6_{-0.2}^{+0.2}$ | $<21.7$ | $43.56_{-0.06}^{+0.06}$ | $667_{-167}^{+163}$
cid173 | 1.00 | 242 | $1.5_{-0.2}^{+0.3}$ | $22.0_{-1.3}^{+0.3}$ | $43.99_{-0.08}^{+0.07}$ | $1182_{-150}^{+150}$
lid1840 | 1.01 | 216 | $2.0_{-0.3}^{+0.3}$ | $<21.7$ | $43.71_{-0.06}^{+0.05}$ | $360_{-66}^{+46}$
cid381 | 0.86 | 208 | $0.9_{-0.3}^{+0.2}$ | $22.8_{-0.2}^{+0.2}$ | $43.8_{-0.1}^{+0.1}$ | $284_{-41}^{+38}$
lid279 | 0.88 | 173 | $1.9_{-0.3}^{+0.4}$ | $<21.7$ | $43.46_{-0.07}^{+0.06}$ | $810_{-157}^{+147}$
lid1478 | 0.83 | 168 | $1.0_{-0.3}^{+0.3}$ | $22.6_{-0.3}^{+0.2}$ | $43.7_{-0.1}^{+0.1}$ | $332_{-57}^{+54}$
cid496 | 0.90 | 165 | $1.5_{-0.3}^{+0.3}$ | $22.1_{-1.1}^{+0.3}$ | $43.6_{-0.1}^{+0.1}$ | $98_{-17}^{+15}$
cid456 | 1.02 | 162 | $0.2_{-0.4}^{+0.3}$ | $23.3_{-0.2}^{+0.2}$ | $44.2_{-0.1}^{+0.2}$ | $113_{-18}^{+18}$
cid221 | 0.75 | 142 | $1.8_{-0.3}^{+0.3}$ | $<22$ | $43.3_{-0.1}^{+0.1}$ | $461_{-102}^{+96}$
cid620 | 1.18 | 126 | $0.7_{-0.4}^{+0.4}$ | $23.4_{-0.2}^{+0.2}$ | $44.3_{-0.1}^{+0.1}$ | $146_{-25}^{+27}$
lid1826 | 1.17 | 109 | $1.2_{-0.3}^{+0.3}$ | $22.9_{-0.3}^{+0.2}$ | $44.0_{-0.1}^{+0.1}$ | $122_{-24}^{+26}$
cid138 | 0.70 | 99 | $1.4_{-0.4}^{+0.4}$ | $22.3_{-1.0}^{+0.3}$ | $43.2_{-0.2}^{+0.1}$ | $439_{-108}^{+94}$
cid1126 | 0.96 | 93 | $0.2_{-0.6}^{+0.5}$ | $23.2_{-0.2}^{+0.2}$ | $43.9_{-0.2}^{+0.2}$ | $186_{-58}^{+58}$
lid489 | 0.85 | 93 | $1.7_{-0.5}^{+0.5}$ | $<22.1$ | $43.8_{-0.1}^{+0.1}$ | $643_{-263}^{+224}$
cid717 | 0.89 | 85 | $1.5_{-0.3}^{+0.3}$ | $>21.0$ | $43.2_{-0.1}^{+0.1}$ | $122_{-26}^{+26}$
cid503 | 0.91 | 80 | $0.3_{-0.4}^{+0.4}$ | $22.8_{-0.2}^{+0.2}$ | $43.6_{-0.1}^{+0.1}$ | $566_{-122}^{+122}$
cid426 | 0.86 | 75 | $0.5_{-0.4}^{+0.4}$ | $22.7_{-0.1}^{+0.2}$ | $43.5_{-0.1}^{+0.1}$ | $290_{-66}^{+61}$
cid254 | 0.71 | 60 | $1.2_{-0.4}^{+0.4}$ | $22.1_{-0.5}^{+0.3}$ | $43.0_{-0.1}^{+0.1}$ | $143_{-55}^{+52}$
lid689 | 0.68 | 59 | $2.1_{-0.4}^{+0.4}$ | $<21.6$ | $43.09_{-0.10}^{+0.09}$ | $253_{-71}^{+59}$
lid3483 | 0.66 | 51 | $-0.4_{-0.6}^{+0.5}$ | $23.3_{-0.2}^{+0.2}$ | $43.5_{-0.1}^{+0.1}$ | $310_{-89}^{+80}$
cid1130 | 0.79 | 48 | $1.4_{-0.5}^{+0.5}$ | $>21.9$ | $42.9_{-0.1}^{+0.1}$ | $152_{-52}^{+47}$
cid1019 | 0.73 | 41 | $-1.0_{-1.7}^{+1.9}$ | $24.2_{-0.6}^{+0.3}$ | $44.1_{-1.0}^{+1.1}$ | ¡105
lid1603 | 0.97 | 39 | $1.1_{-0.5}^{+0.6}$ | $>22.7$ | $43.1_{-0.2}^{+0.2}$ | $110_{-39}^{+35}$
cid401 | 0.97 | 39 | $-0.4_{-0.6}^{+0.6}$ | $23.3_{-0.2}^{+0.3}$ | $43.6_{-0.2}^{+0.2}$ | $129_{-49}^{+41}$
lid1869 | 1.17 | 36 | $0.3_{-0.6}^{+0.6}$ | $23.0_{-0.3}^{+0.3}$ | $43.6_{-0.2}^{+0.2}$ | $93_{-26}^{+24}$
cid1230 | 0.75 | 35 | $1.4_{-0.6}^{+0.6}$ | $>22.0$ | $42.6_{-0.1}^{+0.2}$ | $40_{-15}^{+13}$
cid1169 | 0.96 | 21 | $0.9_{-0.8}^{+0.9}$ | $22.6_{-1.0}^{+0.4}$ | $42.9_{-0.3}^{+0.3}$ | $167_{-90}^{+77}$
lid2210 | 0.74 | 18 | $0.8_{-0.9}^{+0.8}$ | $22.6_{-0.4}^{+0.3}$ | $42.7_{-0.3}^{+0.3}$ | $43_{-28}^{+22}$
lid1459 | 1.00 | 17 | $1.0_{-1.0}^{+1.0}$ | $22.8_{-0.3}^{+0.5}$ | $43.3_{-0.3}^{+0.3}$ | $46_{-24}^{+17}$
cid1706 | 0.76 | 15 | $-1.6_{-1.0}^{+1.3}$ | $24.0_{-0.4}^{+0.3}$ | $43.9_{-0.6}^{+0.6}$ | ¡107
cid2454 | 0.76 | 15 | $-0.1_{-2.1}^{+2.2}$ | $23.3_{-1.0}^{+0.7}$ | $43.2_{-0.4}^{+0.3}$ | $84_{-81}^{+57}$
lid3017 | 0.68 | 15 | $-0.1_{-1.2}^{+0.9}$ | $22.9_{-0.5}^{+1.1}$ | $42.7_{-0.4}^{+1.0}$ | $60_{-35}^{+30}$
cid1508 | 0.67 | 11 | $-0.9_{-0.9}^{+1.5}$ | $24.0_{-1.1}^{+0.6}$ | $41.9_{-0.7}^{+0.5}$ | ¡89

111 Ncts refers to the number of net-counts (i.e., background subtracted),
$\Gamma$ to the photon index obtained using a power-law model with Galactic
absorption. The amount of obscuration ($N_{H}$) and intrinsic (i.e. absorption
corrected) $2-10$ keV luminosity are obtained from a model with Galactic
absorption, power-law emission with fixed photon index ($\Gamma=1.8$), and
absorption component at the source redshift to model the source obscuration.

##  Appendix B Torus models

The torus library we used to model the AGN contribution to the SED assumes
that the AGN dust and gas are distributed in a toroidal shape, namely, the
“smooth-torus” model. It was developed by Fritz et al. (2006) and updated by
Feltre et al. (2012). The geometry of the torus is that of a ”flared” disc.
Its size is defined by the outer radius $R_{\text{max}}$ – the inner radius
being defined by the sublimation temperature of dust grains under the
influence of the strong nuclear radiation field - and by the angular opening
angle $\Theta$ of the torus itself. The main dust components are silicate and
graphite grains, in almost equal percentages. The torus density law adopted
is:

$\rho(r,\theta)=\alpha\times r^{\beta}\times e^{-\gamma\,|\cos{\theta}|},$ (4)

where $\alpha$ is a normalization constant and the parameters $\beta$ and
$\gamma$ allow us to create density gradients both in radial ($r$) and in
polar ($\theta$) directions. The models assume that the torus is illuminated
by a central point-like energy source with isotropic emission. Its spectrum is
described as a composition of power-laws with variable indices (see Feltre et
al. 2012). The radiation emitted is given by the sum of the primary source
located in the torus center and a secondary contribution given by thermal and
scattering dust emission.

To reduce the calculation time, we selected only a sub-sample of the $24\,000$
elements torus library. We chose:

  * •

$\mathbf{\Phi=1^{\circ},21^{\circ},41^{\circ},61^{\circ},89^{\circ}}$: to be
able to model different inclination angles between the line of sight and the
torus equatorial plane (i.e., to model both type 1 and type 2 objects).

  * •

$\mathbf{R=30\,:}$ this value limits the models to compact tori of a few
parsec (given that $R_{\text{min}}$ is directly connected to the sublimation
temperature and to the accretion luminosity of the central BH), as done in
Pozzi et al. (2010). In fact, high-resolution IR and recent ALMA observations
support a compact dust distribution in nearby luminous AGNs (i.e., (Jaffe et
al. 2004; Elitzur 2008; Combes et al. 2019)).

  * •

$\mathbf{ct=20^{\circ},40^{\circ},60^{\circ}}$: all the possible values of the
half-width of the torus apertures.

  * •

$\mathbf{\beta=0,-1}$: the first is linked to an homogeneous density
distribution, the second to a density decreasing exponentially with the
distance from the nucleus.

  * •

$\mathbf{\gamma=0}$: we considered only torus with an homogeneous distribution
of density in polar direction.

  * •

$\mathbf{\tau_{\text{eq}}=0.1,0.3,0.6,1,3,6}$: as suggested by Feltre et al.
(2012), we avoided extreme optical depths.

Reducing the torus parameter space allowed us to reduce the calculation time
to an acceptable level while maintaining 180 different torus models. We
instructed the SED fitting algorithm to run 100 normalizations for each torus
model, for a total of $18\,000$ torus SEDs available.

##  Appendix C $M_{\text{BH}}-M_{*}$ relations

Due to the high number of different $M_{\text{BH}}-M_{*}$ relations in
literature, their large uncertainties and the different ways used to estimate
the $M_{\text{BH}}$ we tested three different M${}_{\text{BH}}-\text{M}_{*}$
relations and compared them in Fig.14.

The Suh et al. (2020) $M_{\text{BH}}-\text{M}_{*}$ relation (red line) was
obtained from a sample of 100 X-ray selected AGNs with the BH masses computed
considering single epoch H$\alpha$, H$\beta$, and Mg ii broad line widths and
line/continuum luminosity as proxy for the size and velocity of the BBLR.
Thus, their sample was composed of active galaxies but only of type 1 AGNs.
The Reines & Volonteri (2015) relation (black line) comes from a sample of 262
broad-line AGNs and 79 galaxies. For the AGNs, their $M_{\text{BH}}$
estimations are derived from single epoch spectra of sources with broad
H$\alpha$, using the line FWHM as well as its luminosity, under the virial
assumption. For 15 AGNs, they used reverberation-mapped $M_{\text{BH}}$ from
literature. Finally, the $M_{\text{BH}}$ for the 79 galaxies were obtained
from measurements based on stellar dynamics, gas dynamics, and maser disk
dynamics. The blue line is the Shankar et al. (2016) relation, obtained with
sources from five different literature samples of galaxies with BH dynamical
mass measurements.

For our work, we chose the Suh et al. (2020),$M_{\text{BH}}-\text{M}_{*}$
relation to estimating the $M_{\text{BH}}$ mass for the following
considerations: as our sample is composed of AGNs, we preferred to avoid
relations derived only with non-active galaxies; in addition, the Suh et al.
(2020) relation is a “middle ground” compromise between the three relations
and, considering the uncertainties, is compatible with the other relations.
Finally, we note that in the $10\geq\log{(\rm{M_{*}}/M_{\odot})}\geq 11.2$
mass range where most of our sources are, the scatters in the relationship
overlap significantly.

Figure 14: Comparison of different $M_{\text{BH}}-M_{*}$ relations and
relative uncertainties. The red line refers to the Suh et al. (2020) relation
used in this work, while the black, and blue to the Reines & Volonteri (2015),
and Shankar et al. (2016) respectively. Using the Reines & Volonteri (2015),
or Shankar et al. (2016), does not significantly impact our results.