11institutetext: INAF - Osservatorio di Astrofisica e Scienza dello Spazio di
Bologna, Via Piero Gobetti, 93/3, 40129, Bologna, Italy 22institutetext:
Department of Physics and Astronomy, Clemson University, Kinard Lab of
Physics, Clemson, SC 29634, USA 33institutetext: Dipartimento di Fisica e
Astronomia, Università degli Studi di Bologna, via Gobetti 93/2, 40129
Bologna, Italy 44institutetext: Dipartimento di Fisica e Astronomia,
Università degli Studi di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino,
Firenze, Italy 55institutetext: Istituto Nazionale di Astrofisica (INAF) –
Osservatorio Astrofisico di Arcetri, Largo E. Fermi, I-50125 Firenze, Italy
66institutetext: INAF – Istituto di Astrofisica Spaziale e Fisica Cosmica
Milano, Via A. Corti 12, I-20133 Milano, Italy 77institutetext: Scuola
Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136,
Trieste, Italy 88institutetext: Department of Physics, University of Miami,
Coral Gables, FL 33124, USA 99institutetext: INAF – Istituto di
Radioastronomia, via P. Gobetti 101, 40129 Bologna, Italy

# LBT-MODS spectroscopy of high-redshift candidates in the Chandra J1030
field. A newly discovered $z\sim$2.8 large scale structure

Stefano Marchesi 112233 Marco Mignoli 11 Roberto Gilli 11 Giovanni Mazzolari
3311 Matilde Signorini 4455 Marisa Brienza 1133 Susanna Bisogni 66 Micol
Bolzonella 11 Olga Cucciati 11 Quirino D’Amato 77 Alessandro Peca 88 Isabella
Prandoni 99 Paolo Tozzi 55 Cristian Vignali 3311 Fabio Vito 11 Andrea Comastri
11

We present the results of a spectroscopic campaign with the Multi-Object
Double Spectrograph (MODS) instrument mounted on the Large Binocular Telescope
(LBT), aimed at obtaining a spectroscopic redshift for seven Chandra J1030
sources with a photometric redshift $\geq$2.7 and optical magnitude
$r_{AB}$=[24.5–26.5]. We obtained a spectroscopic redshift for five out of
seven targets: all of them have $z_{\rm spec}\geq$2.5, thus probing the
reliability of the Chandra J1030 photometric redshifts. The spectroscopic
campaign led to the serendipitous discovery of a $z\sim$2.78 large scale
structure (LSS) in the J1030 field: the structure contains four X-ray sources
(three of which were targeted in the LBT-MODS campaign) and two non-X-ray
detected galaxies for which a VLT-MUSE spectrum was already available. We also
find 26 galaxies with a photometric redshift in the range $z_{\rm
phot}$=[2.68–2.88], which we consider candidate LSS members. The X-ray members
of the LSS are hosted in galaxies that are significantly more massive
(log(M∗/M⊙)=[10.0–11.1]) than both those hosting the two MUSE-detected sources
(log(M∗/M⊙)$<$10) and those belonging to the photometric sample (median
stellar mass log(M∗/M⊙)=10.0). Both observations and simulations show that
massive galaxies, and particularly objects having log(M∗/M⊙)$>$10, are among
the best tracers of large scale structures and filaments in the cosmic web.
Consequently, our result can explain why X-ray-detected AGN have also been
shown to be efficient tracers of large scale structures.

###### Key Words.:

X-rays: galaxies – Surveys – Galaxies: active

##  1 Introduction

The formation and evolution of galaxy clusters is a widely debated topic,
involving multiple complex processes. These include, for example, merging and
interaction of gas-rich galaxies, growth of supermassive black holes at galaxy
centers, and the consequent AGN feedback (either positive or negative) on the
intra-cluster medium and on the star formation (SF) processes (e.g, Overzier,
2016). In gas-rich, overdense regions, evolutionary processes likely take
place faster and/or more efficiently than in field galaxies, as shown through
measurements of the mass-metallicity relation at $z\sim$0 (e.g., Peng &
Maiolino, 2014). Furthermore, several works have shown that at $z>$2 the X-ray
AGN activity is enhanced in sources in protoclusters with respect to those in
the field (e.g., Pentericci et al., 2002; Digby-North et al., 2010; Lehmer et
al., 2013; Martini et al., 2013; Vito et al., 2020; Tozzi et al., 2022), and a
similar trend is also observed in terms of star-formation activity (e.g.,
Capak et al., 2011; Umehata et al., 2015, 2019; Gilli et al., 2019; Kubo et
al., 2019; Chapman et al., 2023). The study of large scale structures at $z>$2
hence represents an ideal way to investigate all of these processes, and
understand the evolving path that leads to $z\sim$0 galaxy clusters.

Cosmological simulations show that only a minor part of the whole structure
mass lies within the inner part of a protocluster, in the so-called main halo,
which is the most massive among the many progenitor halos that will eventually
merge in the $z\sim$0 cluster (see, e.g., Muldrew et al., 2015). Indeed, at
$z\sim$2 about 80 % of the protocluster mass and member galaxies are expected
$-$ on average $-$ to reside outside the main halo, over a scale of several
Mpc. Muldrew et al. (2015) also showed that this behavior is mass–dependent,
meaning that the progenitors of more massive clusters extend over larger
scales. For this reason, a full understanding of the physics and evolution of
a large-scale structure requires tracking sources over an area of several Mpc2
(i.e., at $z\sim$2–3, over field of views of at least
$\sim$15${}^{\prime}\times$15′; see also Chiang et al., 2013). To this end,
faint X-ray selected AGN have been shown to be excellent tracers of large
scale structures (LSSs; see, e.g., Gilli et al., 2003; Silverman et al., 2010;
Marchesi et al., 2021). For example, Gilli et al. (2003) identified several
spikes in the redshift distribution of X-ray sources in the Chandra Deep
Field-South, some of which containing 3-4 X-ray sources only. All of these
LSSs were eventually confirmed with extended photometric and spectroscopic
campaigns (Castellano et al., 2007; Salimbeni et al., 2009; Balestra et al.,
2010).

Recently, Chandra targeted with a deep, $\sim$0.5 Ms observation a 335 arcmin2
region centered on the $z$=6.31 quasar SDSS J1030+0525. SDSS J1030+0525 is one
of the first quasars detected at z$\,>\,$6 by the Sloan Digital Sky Survey
(SDSS; Fan et al., 2001). This field is known to be highly biased, since it
hosts both a galaxy overdensity at $z$=6.3, around the SDSS J1030+0525
(Morselli et al., 2014; Balmaverde et al., 2017; Mignoli et al., 2020), and
another overdensity at $z$=1.7, around a Fanaroff-Riley type II (FRII) radio
galaxy (Nanni et al., 2018; Gilli et al., 2019; D’Amato et al., 2020). The
flux limit achieved by the Chandra J1030 survey (Nanni et al., 2020) makes
this the fifth deepest X-ray field to date: the survey contains 256 sources
detected down to a 0.5–2 keV flux limit f${}_{\rm 0.5-2\,keV}$=6$\times$10-17
erg s-1 cm-2. Such a deep flux limit makes J1030 an ideal region to search for
intrinsically faint and/or heavily obscured AGN. Optical/near-infrared (nIR)
counterparts selected in the $r$, $z$, J and 4.5 $\mu$m were associated with
the X-ray sources using standard likelihood-ratio matching techniques.
Spectroscopic and photometric redshifts have been computed in Marchesi et al.
(2021, hereafter M21) for 243 extragalactic sources out of the 256 Chandra
J1030 ones111Out of the remaining 13 objects, seven are stars and six lack an
optical/nIR counterpart and cannot therefore be classified.. As reported in
M21, X-ray sources appear to efficiently trace large scale structures in the
Chandra J1030 field too. In fact, multiple significant X-ray structures are
detected in the field in the redshift range $z$=[0.15–1.5], all of which were
confirmed (mostly with increased significance) when extending the analysis to
non-X-ray sources.

The spectroscopic completeness of deep X-ray surveys, while fairly high when
considering samples in their entirety (up to $\sim$50–70 %; see, e.g., Luo et
al. 2017 on the Chandra Deep Field-South 7 Ms survey; Marchesi et al. 2016a on
the Chandra COSMOS-Legacy survey; M21 on the Chandra J1030 survey), is
significantly biased against high-redshift sources. In particular, at redshift
$z>$3 (i.e., at epochs before the peak in AGN and star formation activity,
see, e.g., Madau & Dickinson 2014; Ueda et al. 2014; Buchner et al. 2015;
Ananna et al. 2019; Peca et al. 2023) only a few hundred X-ray selected AGN
from X-ray surveys have been spectroscopically confirmed222This number does
not include those objects, mostly unobscured Type 1 quasars, that were
detected at other wavelengths and then followed up with X-ray facilities (see,
e.g., Nanni et al., 2017; Vito et al., 2019). Such a result is not surprising,
given that more distant sources are expected to be fainter and therefore more
difficult to be identified spectroscopically. In the Chandra J1030 survey,
while a spectroscopic redshift was measured for 123 out of 256 sources, only
three of them have $z_{\rm spec}>$3, one of which being the $z$=6.3 QSO at the
center of the J1030 field.

Within this framework, we present here the results of a spectroscopic campaign
with the Multi-Object Double Spectrograph (MODS) mounted on the Large
Binocular Telescope (LBT) which targeted Chandra J1030 sources with a
photometric redshift $z_{\rm phot}\geq$2.7. The paper is organized as follows:
in Section 2 we report on new spectroscopic and photometric observations of
the J1030 field we recently performed. In Section 3 we then present the
results of the LBT-MODS spectroscopic campaign, while in Section 4 we use the
new spectroscopic redshifts to report on the discovery of a $z\sim$2.8 large
scale structure in the J1030 field. We finally summarize the results of the
paper in Section 5. In Appendix A we also present the updated photometric
redshifts for the $z>$2 Chandra J1030 sources which we computed using new LBT
Large Binocular Cameras (LBC) $g$ band and Wide-field InfraRed Camera
(WIRCAM)-CFHT Ks band photometry, and use the new redshifts to update the
Chandra J1030 $z>$3 number counts

Through the rest of the work, we assume a flat $\Lambda$CDM cosmology with H0
= 69.6 km s-1 Mpc-1, $\Omega_{m}$=0.29 and $\Omega_{\Lambda}$=0.71 (Bennett et
al., 2014). Errors are quoted at the 90 % confidence level, unless otherwise
stated.

##  2 New spectroscopic and photometric coverage of the J1030 field

Among the 26 Chandra J1030 sources with photometric redshift $z_{\rm
phot}\geq$2.7 and no spectroscopic redshift available in the M21 catalog, we
selected seven targets that were bright enough ($r_{AB}\lesssim$26.5) to
obtain an optical spectrum with LBT-MODS. Since we used a multi-object
spectrograph like MODS, we also included 12 more Chandra J1030 sources that
were randomly located inside the footprint of the two masks and lacked a
spectroscopic redshift. These additional targets had photometric redshift in
the range $z_{\rm phot}$=[0.9–2.2].

Our LBT-MODS observations were performed on January 31 and February 5, 2022:
each of the two masks was observed for a total of four hours. Since LBT is
made of two telescope units of 8.4m diameter each that are equipped with
similar instrumentation (and in particular with the identical MODS1 and MODS2
spectrographs), the total time on target is actually halved. Our MODS spectra
have been obtained in dichroic mode using both the blue G400L (3500$-$5900 Å)
and the red G670L (5400$-$10000 Å) gratings on the blue and red channels. As
shown in the following paragraphs, the wide wavelength range we obtained by
using this specific combined configuration (the same adopted in M21) made it
possible to detect emission and absorption features over a wide range of
wavelengths and to reliably measure a significant number of spectroscopic
redshifts. We reduced the data using the spectroscopic pipeline to reduce
optical/near-infrared data from slit-based spectrographs SIPGI (Bisogni et
al., 2022; Gargiulo et al., 2022).

The data reduction pipeline is organized as follows. We create calibration
frames for both MODS1 and MODS2 for each of the two sets of observations
(i.e., for each of the two masks). Specifically, a bad pixel map is produced
with imaging flats and applied to every observed frame, along with a
correction for cosmic rays. Each frame is independently bias subtracted and
flat-field corrected through a master flat obtained from a set of
spectroscopic flats. The inverse solution of the dispersion, obtained from a
set of arc lamps frames and stored in the master lamp, is applied to
individual frames for the wavelength calibration and the removal of any
curvature due to optical distortion. The mean accuracy we achieved on the
wavelength calibration is 0.09Å for the red and 0.07Å for the blue channel. 2D
wavelength-calibrated spectra are then extracted and sky subtracted. The
sensitivity function, obtained thanks to the observations of the spectro-
photometric standard stars GD153 and GD71, is applied to obtain flux-
calibrated spectra. Finally, wavelength- and flux-calibrated, sky-subtracted
spectra are stacked together and the 1D spectrum of each source is extracted.

The targets redshifts have been measured on the 1D spectra: for the MODS
observations, the wavelength coverage allows a Ly$\alpha$ detection down to
$z=1.9$, where the Ly$\alpha$ emission line is often the only detectable
feature for our faint objects. All the emission line centers were determined
using a Gaussian fit to the line profile: the only exception was the
Ly$\alpha$ feature of XID 011 where, due to the structured shape, we adopted
the line peak to determine the redshift. For all the solutions for which the
single emission line was identified as Ly$\alpha$, we can confidently rule out
other possible redshift solutions. Lower redshift solutions would imply the
detection of other nearby lines, as is the case for the X-ray sources with
$z<$1.5 presented in Appendix B. Also, in all the objects belonging to the
$z\sim$2.78 structure the emission line is asymmetric with a red wing and,
when the spectra signal-to-noise allows it, the underlying continuum shows a
clear break at the wavelength of the Ly$\alpha$ line. Both spectral
characteristics are typical of the high-redshift Ly$\alpha$ line.

Our group was also recently granted time to observe the J1030 field with LBT-
LBC in the $g$ band (observations performed in May, 2021; total exposure 1800
s; PI M. Mignoli) and with WIRCAM-CFHT in the Ks band (observations performed
in February, 2022; total exposure 6400 s; PI M. Mignoli). We will present a
detailed description of the data analysis process, as well as an updated
photometric catalog, in M. Mignoli et al. (in prep.). Here we briefly
summarize the improvement provided by these observations with respect to the
photometric catalog we used in M21.

The $g$ band imaging (3 $\sigma$ magnitude limit $g_{\rm AB}$=27.5) covers a
band that was previously missing in our photometric coverage of the field, and
its depth almost matches the depth we achieved in the adjacent $r$ band
(magnitude limit $r_{\rm AB}$=27.5). The J1030 field was instead already
observed in the Ks band as part of the MUSYC survey. However, our new Ks data
is $\sim$3 magnitudes deeper (3 $\sigma$ magnitude limit KsAB=24) than the
MUSYC K-Wide (Blanc et al., 2008) image we used in M21, and $\sim$1 magnitude
deeper than the MUSYC K-Deep coverage of the central 10${}^{\prime}\times$10′
of the J1030 field (Quadri et al., 2007). In Section 4, we take advantage of
this new photometric information to compute the stellar masses and star
formation rates of the galaxies belonging to a newly detected $z\sim$2.78
large scale structure in the J1030 field, as well as the photometric redshifts
of non X-ray sources in the J1030 field, searching for more candidate members
of the same structure. In Appendix A, we instead show how we used the data
from this imaging campaign to refine the Chandra J1030 photometric redshifts
and to derive the $z>$3 X-ray number counts in the J1030 field.

##  3 Results of the LBT-MODS spectroscopic campaign

We report in Table 1 the redshift values we obtained, together with a
breakdown of the different features detected in the spectra. We measured a
spectroscopic redshift for five out of seven sources in our main sample of
high-redshift candidates: all of them have 2.5$<z_{\rm spec}<$3.1. No clear
feature was instead detected in the spectra of XID 378 and XID 381. As
reported in Table 1, the photometric redshifts computed in M21333All high-$z$
candidates but XID 381 have been observed in at least 11 photometric bands.
XID 381 has been observed in 9 bands. efficiently selected high–redshift
candidates: all five $z\geq$2.7 candidates for which we obtained a
spectroscopic redshift have $z_{\rm spec}\geq$2.5. This increases the Chandra
J1030 spectroscopic completeness at $z>$2.5 (from 8 to 13 out of 40 Chandra
J1030 sources with $z>$2.5, i.e., from 20 % to 33 %) and shows that the
Chandra J1030 photometric redshifts can reliably select high-redshift
candidates. We also measured a spectroscopic redshift for 7 out of the 12
Chandra J1030 filler sources at 0.9$<z<$2.2 lacking a spectroscopic redshift.

ObjID | RA | DEC | $r_{\rm AB}$ | $z_{\rm spec}$ | $Q_{\rm z}$ | Class | $z_{\rm phot,M21}$ | $z_{\rm phot,new}$ | Spectral features (obs $\lambda$)
---|---|---|---|---|---|---|---|---|---
| hh:mm:ss | dd:mm:ss |  |  |  |  |  |  |
XID 007 | 10:30:29.77 | +05:22:32.26 | 25.21 | 2.7799 | 2 | ELG | 3.24${}_{-1.30}^{+1.30}$ | 3.22${}_{-1.28}^{+1.28}$ | Ly$\alpha$ (4595 Å)
XID 008 | 10:30:28.10 | +05:22:58.75 | 24.41 | 2.7797 | 2 | ELG | 3.34${}_{-0.90}^{+0.90}$ | 2.68${}_{-1.02}^{+1.02}$ | Ly$\alpha$ (4597 Å), NV
XID 011 | 10:30:27.89 | +05:23:13.42 | 26.67 | 2.7674 | 2 | ELG | 4.34${}_{-2.10}^{+2.10}$ | 4.16${}_{-1.48}^{+1.48}$ | Ly$\alpha$ (4581 Å)
XID 151 | 10:30:41.54 | +05:26:25.13 | 25.25 | 3.041 | 2 | ELG | 2.74${}_{-0.88}^{+0.88}$ | 2.96${}_{-0.52}^{+0.52}$ | Ly$\alpha$ (4912 Å)
XID 158 | 10:30:28.01 | +05:28:08.35 | 24.83 | 2.505 | 1 | ELG | 3.37${}_{-1.17}^{+1.19}$ | 2.12${}_{-0.88}^{+0.88}$ | Ly$\alpha$ (4262 Å), NV
XID 378 | 10:30:38.13 | +05:24:03.31 | 26.5 | – | 0 | None | 5.45${}_{-1.05}^{+1.03}$ | 1.92${}_{-0.04}^{+2.82}$ | None
XID 381 | 10:30:43.12 | +05:25:26.99 | 25.06 | – | 0 | None | 3.44${}_{-1.56}^{+1.56}$ | 3.86${}_{-1.00}^{+1.00}$ | None
XID 029 | 10:30:38.00 | +05:26:13.09 | 26.66 | – | 0 | None | 2.22${}_{-0.80}^{+0.80}$ | 2.15${}_{-0.77}^{+2.11}$ | None
XID 066 | 10:30:32.31 | +05:28:07.35 | 23.99 | 2.1113 | 2 | ELG | 2.15${}_{-0.39}^{+0.40}$ | 1.84${}_{-0.34}^{+0.34}$ | Ly$\alpha$ (3783 Å), NV
XID 098 | 10:30:31.05 | +05:27:47.32 | 27.3 | – | 0 | None | 1.49${}_{-0.57}^{+0.59}$ | 5.21${}_{-0.89}^{+0.91}$ | None
XID 102 | 10:30:31.61 | +05:29:04.44 | 25.6 | 1.1084 | 2 | ELG | 5.44${}_{-0.46}^{+0.46}$ | 1.72${}_{-1.40}^{+1.78}$ | MgII, [OII], [NeV]
XID 103 | 10:30:29.79 | +05:29:09.09 | 24.65 | 1.4990 | 1 | ELG | 1.44${}_{-0.20}^{+0.20}$ | 1.50${}_{-0.22}^{+0.22}$ | [OII]
XID 153 | 10:30:28.29 | +05:27:40.72 | 27.02 | – | 0 | None | 2.16${}_{-0.26}^{+3.26}$ | 4.44${}_{-1.74}^{+1.74}$ | None
XID 198 | 10:30:39.95 | +05:26:55.23 | 24.1 | – | 0 | None | 1.35${}_{-0.17}^{+0.15}$ | 1.02${}_{-0.22}^{+0.26}$ | None
XID 206 | 10:30:14.76 | +05:29:19.80 |  $>$27.5 | 1.124 | 1 | ELG | 1.48${}_{-1.00}^{+3.44}$ | 1.48${}_{-1.00}^{+3.44}$ | [OII], [NeV]
XID 214 | 10:30:44.59 | +05:25:44.77 | 25.97 | – | 0 | None | 1.38${}_{-0.01}^{+0.54}$ | 1.44${}_{-0.01}^{+0.92}$ | None
XID 365 | 10:30:27.88 | +05:23:48.31 | 25.72 | 1.4159 | 1 | ELG | 1.83${}_{-0.37}^{+0.39}$ | 1.73${}_{-0.31}^{+0.29}$ | [OII], [OIII]
XID 366 | 10:30:28.58 | +05:32:24.61 | 24.52 | 1.0474 | 2 | ELG | 0.92${}_{-0.22}^{+0.22}$ | 0.84${}_{-0.20}^{+0.20}$ | [OII], [NeIII]
XID 369 | 10:30:31.28 | +05:28:02.30 | 24.7 | 0.8248 | 2 | ELG | 1.17${}_{-0.07}^{+0.05}$ | 1.17${}_{-0.03}^{+0.05}$ | [OII], [OIII], H$\gamma$, H$\beta$

Table 1: Summary of the redshift measurements obtained in the LBT-MODS
campaign presented in this work. The identification number is taken from the
Chandra J1030 catalog (Nanni et al., 2020). $r_{\rm AB}$ is the AUTO magnitude
in the $r$ band, as reported in Nanni et al. (2020). $z_{\rm spec}$ is the
source spectroscopic redshift, $Q_{\rm z}$ is the quality flag for $z_{\rm
spec}$ (2: secure; 1: uncertain; 0: no measurement), “Class” is the spectral
classification (ELG: emission line galaxy; None; no classification). $z_{\rm
phot,M21}$ is the photometric redshift computed in Marchesi et al. (2021) and
used to select the high-redshift candidates, while $z_{\rm phot,new}$ is the
updated photometric redshift computed using the new $g-$ and Ks–band
photometric information presented in Section 2, as described in Appendix A.

As reported in Table 1, all the targets for which we computed a spectroscopic
redshift in this work (both the primary targets and the fillers) are
classified as emission line galaxies (ELGs). In M21, we defined ELGs as
sources whose spectra do not show any detectable AGN features, but a flat or
bluish continuum and low–ionization emission lines that are compatible with a
typical star formation activity. These sources optical emission is therefore
dominated by non-AGN processes, and we can assess their AGN nature only thanks
to the X-ray detection, since their X-ray luminosity L2-10keV is way above the
1042 erg s-1 threshold which is commonly adopted to select AGN in the X-rays.
Notably, in M21 the ELG population we sampled had much lower average redshift
($\langle z_{\rm ELG,M21}\rangle$=1.08, with standard deviation $\sigma_{\rm
z,ELG,M21}$=0.58) and was therefore significantly brighter ($\langle r_{\rm
AB,ELG,M21}\rangle$=23.0, with standard deviation $\sigma_{\rm
r,ELG,M21}$=1.8; as a reference, the targets analyzed in this work have
$\langle r_{\rm AB,ELG}\rangle$=25.3, with standard deviation $\sigma_{\rm
r,ELG}$=1.0). In two targets (XID 102, $z$=1.1084; XID 206, $z$=1.124; see
Figures 8 and 9 in the Appendix) we find tentative evidence of the [NeV]
narrow emission line, which is a known tracer of obscured AGN (see, e.g.,
Maiolino et al., 1998; Vignali et al., 2006, 2010; Mignoli et al., 2013; Cleri
et al., 2022; Barchiesi & collaborators, 2023).

From Table 1, as well as from Figure 1, where we report the Chandra J1030
sources total AB magnitudes (from Nanni et al., 2020) as a function of
spectroscopic redshift, it can also be understood how this spectroscopic
campaign significantly increased the spectroscopic completeness of the faint
($r_{\rm AB}\geq$24) Chandra J1030 population, from 28 to 40 sources. It is
worth noting that this new campaign, targeting fainter sources than in M21,
led to the detection of no new broad line AGN (BL-AGN). In the M21 sample, 43
out of 123 sources with a spectroscopic redshift (35 %) were BL-AGN; as it can
be seen in Figure 1, BL-AGN are more easily detected at brighter magnitudes,
so that 21 out of 50 sources with $r_{\rm AB}\leq$23 are BL-AGN (42 %), while
out of 31 sources in M21 with $z_{\rm spec}$ and $r_{\rm AB}\geq$24 only 8 (26
%) were BL-AGN. Following the spectroscopic campaign reported in this work,
the BL-AGN fraction at magnitudes $r_{\rm AB}\geq$24 decreased to 19 %.

In M21, we also extensively discussed how the lack of narrow-band photometry
in the J1030 field makes BL-AGN the class of targets for which the photometric
redshifts are significantly less accurate: more in detail, only 28 out of 43
BL-AGN (i.e., 65 %) had a photometric redshift in agreement with the
spectroscopic one (where the agreement is achieved when ——$z_{\rm
phot}$-$z_{\rm spec}$——/(1+$z_{\rm spec}$)$<$0.15). As a reference, 25 out of
28 ELGs (i.e., 89 %) had photometric redshifts in agreement with the
spectroscopic ones. Consequently, the fact that we did not find any new BL-AGN
in the Chandra J1030 optically faint subsample has also the indirect result of
strengthening the reliability of the photometric redshifts for the 108 targets
lacking a $z_{\rm spec}$. In fact, the vast majority of them (87 out of 108,
81 %) have $r_{\rm AB}\geq$24.

Figure 1: Total AB magnitude in the $r$ band from Nanni et al. (2020) as a
function of spectroscopic redshift for the 122 Chandra J1030 sources with
$z_{\rm spec}$ from M21 (open markers): we do not include in this plot the
$z$=6.3 QSO SDSSJ1030+0525, which is not detected in the $r$-band. BL-AGN are
plotted as blue circles, narrow-line AGN as red squares, emission line
galaxies as cyan diamonds, and early type galaxies as orange stars. The
emission line galaxies reported in this work are plotted as full cyan
diamonds.

Finally,two of the targets in the sample (XID 008, $z_{\rm spec}$ = 2.78; XID
011, $z_{\rm spec}$ = 2.767) were also part of the sample studied in Peca et
al. (2021). That work analyzed a subsample of 54 Chandra J1030 sources having
hardness ratio (i.e., the ratio between the difference between 2–7 keV and
0.5–2 keV source counts, and 0.5–7 keV source counts) HR$>-$0.1 and at least
50 net counts in the 0.5–7 keV band. Since low-energy, soft photons are more
easily absorbed by the obscuring material surrounding accreting supermassive
black holes, sources with larger HR values are more likely to be obscured. In
such targets, features like the fluorescent Iron K$\alpha$ line at 6.4 keV and
the 7.1 keV Iron edge are particularly prominent and can be used to determine
the source redshift through X-ray spectral fitting (see, e.g., Maccacaro et
al., 2004; Civano et al., 2005; Vignali et al., 2015; Simmonds et al., 2018;
Marchesi et al., 2019; Iwasawa et al., 2020). The X-ray spectrum of each of
the 54 targets was then fit leaving the redshift free to vary, and thus using
the X-ray features mentioned above to determine the targets redshifts.

Peca et al. (2021) measured a X-ray redshift $z_{\rm X}$ =
2.80${}_{-0.05}^{+0.05}$ for XID 008, where the Iron K$\alpha$ line was
detected. Such a measurement is in excellent agreement with the spectroscopic
redshift, particularly considering the uncertainties on the measurement, that
are much smaller than the photometric redshift ones. The method was instead
less effective in XID 011, where the X-ray redshift measurement ($z_{\rm X}$ =
1.94${}_{-0.38}^{+1.05}$) was based on the tentative detection of the Iron
edge. Even in this second target, however, the X-ray redshift is consistent
with the spectroscopic one within the errors.

Figure 2: Redshift cumulative distribution function around $z$=2.78 for the
Chandra J1030 sources with a spectroscopic redshift (full markers), and for
all the J1030 sources with a spectroscopic redshift, including the non-X-ray
detected ones (empty markers). The overall cumulative distribution function is
shifted by 0.1 for visualization purposes. The $z\sim$2.78 structure is marked
with an arrow. Other two potential structures can be observed at $z\sim$2.37
and $z\sim$2.51 (see the text for more details).

##  4 A new structure at $z\sim$2.8

As mentioned in the introduction, faint X-ray selected AGN have been shown to
be excellent tracers of large scale structures (LSSs), and in M21 we reported
several J1030 structures detected in the Chandra J1030 up to redshift
$z\sim$1.5. Thanks to the LBT-MODS spectroscopic campaign presented in this
work, we are now able to identify a new large scale structure in the J1030
field, this one located at a significantly larger redshift, $z\sim$2.78. We
report in Table 2 the overdensity members and their properties, while in
Figure 2 we plot the redshift cumulative distribution function around
$z\sim$2.78 of both the Chandra J1030 sources and of all the sources in J1030
having a spectroscopic redshift. As we already discussed in M21, such a
representation provides a good visualization of candidate redshift structures
in the field, which readily appear as sharp cumulative distribution function
rises, and is free of binning issues. Four sources in the overdensity are
X-ray detected, namely XID 007, XID 008, XID 011 and XID 109. In this work, we
measured a spectroscopic redshift for XID 007, XID 008 and XID 011, while the
redshift of XID 109 ($z$=2.771) was already reported in M21 and was also
obtained using the MODS spectrograph. From this same plot, it can be noticed
that two other potential overdensities are observed at $z\sim$2.37 and
$z\sim$2.51. While the signal-to-noise ratios of these two group of sources
are lower than the one we adopt to select an overdensity, S/N=3.8, we plan to
further investigate these candidate structures in a follow-up work.

Besides the four X-ray $z\sim$2.78 sources, there are two more J1030 objects
that are not X-ray detected and have $z_{\rm spec}\sim$2.78: for both targets,
we measured the redshift using the Multi Unit Spectroscopic Explorer (MUSE)
instrument mounted on the European Southern Observatory (ESO) Very Large
Telescope (VLT). A $\sim$1′$\times$1′ region of the J1030 field centered on
the $z$=6.3 quasar was observed by MUSE (Bacon et al., 2010, 2015) between
June and July 2016 under the program ID 095.A-0714 for a total of $\sim$ 6.4
hours of exposure time. The data reduction of the MUSE observations was
presented in Gilli et al. (2019). The final data cube has a wavelength range
of 4750$-$9350 Å, a spectral sampling of 1.25 Å and a spatial sampling of
0.2′′, covering an area of 1 sq-arcmin centered at the sky position of the QSO
SDSSJ1030+0524. The 1D spectra were extracted by combining the spaxels inside
a 3-pixel aperture that matches the seeing full width at half maximum of
0.6′′. The MUSE wavelength coverage did not allow to access the Ly$\alpha$
region at $z\sim$2.78, but the high S/N spectra of the two galaxy members
present a rich plethora of spectral features, both in emission (HeII 1640 Å
and CIII] 1909 Å lines) and in absorption (ISM lines), that provided accurate
redshift measurements via cross-correlation with a high-z star-forming
template (Talia et al., 2012).

We report the flux–calibrated, one-dimensional spectra of the six members of
the LSS in Figure 3. The spectra of the remaining targets for which we
measured a redshift are reported in Appendix B.

Figure 3: Flux-calibrated spectra of the six members of the $z\sim$2.78 large
scale structure: in the top and central panels we report the LBT-MODS spectra
of the four Chandra sources, while in the bottom panels we show the VLT-MUSE
spectra of the two sources that are not detected in the X-rays. The spectrum
of XID 109 was obtained in the previous Chandra J1030 spectroscopic campaign,
which we presented in Marchesi et al. (2021). We highlighted the expected
positions of the main emission lines that fall in the observed spectral range.
On top of each one-dimensional spectrum, we report the two-dimensional one.

Figure 4: LBT-LBC r-band images of the J1030 field. Left: whole field image,
with the Chandra coverage shown in green. The spectroscopically confirmed,
X-ray detected members of the $z\sim$2.78 large scale structure are plotted
with a red circle, while the two non-X-ray detected sources with a MUSE
spectroscopic redshift are plotted in red. Non-X-ray sources with a
photometric redshift in the range $z_{\rm phot}$=[2.68–2.88] are plotted as
yellow circles. Right: inset of the $\sim$4${}^{\prime}\times$4′ region (shown
as a white box in the left panel) where we detect five out of six members of
the LSS. The MUSE coverage of the J1030 field is also shown here for
reference.

For consistency with the approach we used in M21, we use the method presented
in Gilli et al. (2003), and earlier in Cohen et al. (1999), to compute the
significance of the structure. Sources are first distributed in velocity space
$V=c\,\rm{ln}(1+z)$ rather than in redshift space, since $dV$ corresponds to
local velocity variations relative to the Hubble expansion. The velocity
distribution is then smoothed twice: once with a broad Gaussian, having
$\sigma_{B}$ = 1.5$\times$ 104 km s-1, to create the expected background
distribution of the sample; the second one with a narrower Gaussian, having
$\sigma_{S}$ = 300 km s-1, which is the typical velocity dispersion observed
in galaxy structures (e.g., Cohen et al., 1999; Gilli et al., 2003). We then
compute the signal-to-noise ratio S/N = $(S-B)/\sqrt{B}$, where $S$ is the
number of sources within $\Delta V=\pm 800$ km s-1 around the peak $z$=2.775
($S$=4 in the X-ray-detected sample, $S$=6 in the whole one), and $B$ is the
number of background sources in the same interval; $\Delta V$ was chosen to
optimize the S/N value. We obtain a signal-to-noise ratio S/N=6.3 for the
X-ray overdensity and S/N=5.5 when the non X-ray detected J1030 sources are
included in the computation. The Poisson probability of observing $S$ sources
given the estimated background value $B$ is P${}_{\rm Poiss(N\geq N_{\rm
obj,X})}$ = 3 $\times$ 10-4 for the X-ray LSS, while we obtain P${}_{\rm
Poiss(N\geq N_{\rm obj,All})}$ = 5 $\times$ 10-5 for the whole LSS. We note
that this is among the highest redshift X-ray LSSs ever detected: for example,
in the CDF-S 7 Ms (Luo et al., 2017) the two farthest X-ray detected LSSs are
at $z\sim$2.57 and $z\sim$3.47. The SSA22 Chandra survey (Lehmer et al., 2009;
Radzom et al., 2022) found instead 13 X-ray members of the SSA22 protocluster
at $z$=3.09, which was however first detected through a optical spectroscopy
follow-up of candidate $z\sim$3 Lyman break galaxies (Steidel et al., 1998).
We note that the main difference between high-z LSSs detected in the optical
with respect to those detected in the X-rays is the type of sources used to
trace the LSS: in optical surveys the most common tracer are Lyman Break
Galaxies (see, e.g., Toshikawa et al., 2016) and Ly$\alpha$ and H$\alpha$
emitters (e.g., Higuchi et al., 2019; Koyama et al., 2021), while in the
X-rays the tracers are AGN. Thus, by detecting and studying X-ray LSSs one can
simultaneously study the properties of the host and those of the accreting
SMBH, and compare the properties of the AGN with those of AGN at similar
redshifts that are not located in overdensities.

We also compute the distance between the different structure members, assuming
a flat $\Lambda$CDM cosmology (see Introduction). At the average redshift of
the targets in the structure, $z$=2.775, the angular-to-physical conversion
factor is 8.026 kpc/′′. Five out of six targets (namely, XID007, XID008,
XID011 and the two MUSE detected galaxies) are separated by distances in the
range $d_{\rm A}$=100–1360 kpc (see Figure 4, right panel). The closest pairs
of objects are the two MUSE–detected targets ($d_{\rm A}$=101 kpc) and XID008
and XID011 ($d_{\rm A}$=120 kpc). As shown in Figure 4, left panel, XID109 is
located farther away from the rest of the objects, at $\sim$3.3–4.6 Mpc. The
difference in redshift between the targets can also be converted in angular
diameter distances: for the sources in the LSS, it varies in the range 30 kpc
(XID 007 and XID 008; $\Delta z$=2$\times$10-4) to 2 Mpc (XID008 and XID011,
$\Delta z$=1.25$\times$10-2). We note that a separation of several Mpc between
AGN belonging to the same structure was also previously reported in Shen et
al. (2021), where three AGN were found to be part of a protocluster at
$z\sim$3.3. Two of these AGN lied within $\sim$1 Mpc, while the third one was
found at $\sim$5 Mpc from the remaining two.

ObjID | RA | DEC | $z$ | $N_{\rm H}$ | log(L2-10keV) | log(M∗/M⊙) | SFRSED | SFR1.4GHz | log(L1.4GHz)
---|---|---|---|---|---|---|---|---|---
| hh:mm:ss | dd:mm:ss |  | 1022 cm-2 | erg s-1 |  | M⊙ yr-1 | M⊙ yr-1 | W Hz-1
XID 007 | 10:30:29.8 | +05:22:32.3 | 2.7799 |  $<$3.9 | 44.08${}_{-0.08}^{+0.08}$ | 10.49$\pm$0.24 | 165$\pm$107 | 103$\pm$35 | 23.52${}_{-0.18}^{+0.13}$
XID 008 | 10:30:28.1 | +05:22:58.8 | 2.7797 | 47.0${}_{-21.7}^{+23.1}$ | 44.46${}_{-0.12}^{+0.11}$ | 10.36$\pm$0.29 |  $<$188 |  $<$96 |  $<$23.47
XID 011 | 10:30:27.9 | +05:23:13.4 | 2.7674 | 39.4${}_{-18.6}^{+20.0}$ | 44.90${}_{-0.12}^{+0.11}$ | 10.24$\pm$0.71 | 82$\pm$74 |  $<$91 |  $<$23.58
XID 109 | 10:30:41.7 | +05:16:12.5 | 2.771 | 2.0${}_{-2.0}^{+8.3}$ | 44.48${}_{-0.10}^{+0.11}$ | 11.10$\pm$0.13 | 234$\pm$188 | 197$\pm$61 | 23.89${}_{-0.16}^{+0.12}$
MUSE 1 | 10:30:26.4 | +05:25:14.5 | 2.7722 | N/A |  $<$43.15 | 9.49$\pm$0.48 | 85$\pm$81 |  $<$165 |  $<$23.58
MUSE 2 | 10:30:26.8 | +05:25:03.7 | 2.7791 | N/A |  $<$43.15 | 9.11$\pm$0.69 |  $<$87 |  $<$226 |  $<$23.66
Photometric candidates | – | – | 2.78$\pm$0.10 | N/A | N/A | 9.97 (0.43) | 38.3 (60.9) | – | –

Table 2: Properties of the members of the $z\sim$2.78 large scale structure
detected in this work. $z$ is the source redshift. $N_{\rm H}$ and L2-10keV
are the source column density and intrinsic, 2–10 keV luminosity as computed
from the X-ray spectrum (Signorini et al., 2023) Since the two MUSE targets
are not detected in the X-rays, their $N_{\rm H}$ cannot be computed: the
L2-10keV upper limit is computed from the Chandra J1030 survey flux limit in
the 2–10 keV band ($f_{\rm 2-10keV,lim}$=2.7$\times$10-16 erg s-1 cm-2). M∗ is
the stellar mass content of the host galaxy (in units of solar masses) and
SFRSED is the host star formation rate: both these quantities have been
computed through spectral energy distribution fitting. We also report, for
comparison, the median and standard deviation of the stellar mass and star
formation rates of the 26 galaxies in the J1030 field whose photometric
redshift is consistent with $z$=2.78 (see the text for more details). Finally,
SFR1.4GHz is the SFR independently derived from the 1.4 GHz luminosity L1.4GHz
measured from the JVLA J1030 survey (D’Amato et al., 2022). The SFR1.4GHz
values reported here are obtained assuming a Chabrier initial mass function.
Upper limits are reported at the 3 $\sigma$ confidence level.

###  4.1 Candidate overdensity members based on their photometric redshift

By combining the new $g-$ and $K_{s}-$band imaging data presented in Section 2
with the existing multi-band photometry, we computed photometric redshifts for
all the $K_{s}-$selected sources in the J1030 field (M. Mignoli et al. in
prep.). We report in Table 3 the optical/near-infrared photometric bands we
use to compute these photometric redshifts. Following the same approach we
used in M21, the spectral energy distributions (SEDs) of the sources are
fitted using two different codes: Hyperz (Bolzonella et al., 2000) and EAzY
(Brammer et al., 2008). We adopt the Calzetti et al. (2000) extinction law to
take reddening into account, and we use 75 templates dominated by stellar
emission, following the work by Ilbert et al. (2013). More in detail, 19 out
of 75 are empirical templates from the SWIRE template library (Polletta et
al., 2007): 7 for elliptical galaxies, 12 for different classes of spiral
galaxies (S0, Sa, Sb, Sc, Sd and Sdm). Other 12 templates describe the SED of
starburst galaxies, although no emission lines are included in the template.
Finally, the remaining 44 templates are based on the Bruzual & Charlot (2003)
stellar population synthesis models, and have been first introduced in Ilbert
et al. (2009, 2013).

We use photometric redshifts to identify potential members of the $z$=2.78
overdensity. To do so, we conservatively select only those sources which have
photometric redshift in the range $z_{\rm phot}$=[2.68–2.88] according to both
Hyperz and EAzY. We choose such a range because the RMS of the difference
between spectroscopic and photometric redshifts in the J1030 sample at $z>$2
is $\Delta z\sim$ 0.1. Overall, our sample of $z\sim$2.78 photometric
candidates contains 26 galaxies. We report in Figure 4 the distribution of the
sources over the J1030 field.

###  4.2 Host properties of the overdensity members

To better understand the properties of the members of the $z\sim$2.78
overdensity, we take advantage of the excellent multi-wavelength coverage of
the J1030 field to perform a self-consistent SED fitting from the X-rays to
the near infrared. To do so, we use the CIGALE v2022.1 tool (Yang et al.,
2020, 2022). CIGALE v2022.1 fits a source SED and computes the host galaxy
physical properties. With respect to the CIGALE tool (Burgarella et al., 2005;
Boquien et al., 2019), CIGALE v2022.1 allows one to also fit the X-ray
information, if available. This update to the original tool is particularly
helpful to put stronger constraints on the AGN contribution to the SED and,
consequently, to obtain more accurate measurements of the host properties.

For the X-ray detected sources and photometric redshift candidates, we use the
optical/near-infrared photometric information reported in Table 3. For the
four X-ray-detected AGN we also use the 0.5–2 keV and 2–7 keV fluxes reported
in Nanni et al. (2020). Finally, both MUSE targets are detected in our new
K-band image of the J1030 field. We therefore performed aperture photometry at
the KS position of the sources in the $griz$ LBT/LBC bands, as well as in the
WIRCAM/CFHT Y and J ones. The two MUSE targets were also detected in the MUSYC
BVR catalog, and the MUSE 1 source was also detected in the K-Deep catalog. We
therefore included in our SEDs the MUSYC U and V magnitudes from the BVR
catalog and the MUSYC H magnitude from the K Deep one. We note that there is
an excellent agreement ($\Delta{\rm mag}\leq$0.05) between our B and K
magnitudes and the MUSYC BBVR and KKd, a result that support our choice of
using the additional MUSYC data points like we did for the X-ray sources. We
also searched the NASA/IPAC Infrared Science
Archive444https://irsa.ipac.caltech.edu/ for a WISE counterpart of the two
MUSE targets, but we did not find any.

Catalog | Filters | Area | 5 $\sigma$ Depth | Reference
---|---|---|---|---
|  |  | mAB |
MUSYC BVR | UBV | 30${}^{\prime}\times$30′ | 26.0, 26.2, 26.0 | Gawiser et al. (2006)
LBT-LBC | $g$ | 23${}^{\prime}\times$25′ | 26.4 | This work.
LBT-LBC | $riz$ | 23${}^{\prime}\times$25′ | 26.8, 26.1, 25.6 | Morselli et al. (2014)
HST-ACS | F775W | 3.3${}^{\prime}\times$3.3′ | 27.5 | Stiavelli et al. (2005)
HST-ACS | F850LP | 3.3${}^{\prime}\times$3.3′ | 27.5 | Kim et al. (2009)
WIRCAM-CFHT | YJ | 24${}^{\prime}\times$24′ | 24.7, 24.4 | Balmaverde et al. (2017)
HST-WFC3 | F160W | 2${}^{\prime}\times$2′ | 27.5 | D’Amato et al. (2020)
MUSYC K Deep | H | 10${}^{\prime}\times$10′ | 23.6 | Quadri et al. (2007)
WIRCAM-CFHT | $K_{s}$ | 24${}^{\prime}\times$24′ | 23.4 | This work.
Spitzer-IRAC | CH1-2 | 35${}^{\prime}\times$35′ | 22.7, 22.4 | Annunziatella et al. (2018)
Spitzer-IRAC | CH3-4 | 22${}^{\prime}\times$15′ | 22.1, 21.8 | IRSA Archive

Table 3: Properties of the photometric catalogs used in this work.

In Table 2 we report the stellar mass M∗ and star formation rate (SFR) of the
six $z\sim$2.78 LSS members, as well as the median and standard deviation of
both parameters for the sample of 26 galaxies with a photometric redshift
consistent with $z$=2.78. As it can be seen, the four X-ray detected targets
are significantly more massive than the two MUSE-detected ones: the stellar
mass of the X-ray targets varies in the range log(M∗/M⊙)=[10.2–11.1], while
the two non-X-ray detected objects both have log(M∗/M⊙)$<$10\. The sample of
candidate overdensity members having photometric redshift $z_{\rm
phot}$=[2.68–2.88] is also, on average, less massive than the X-ray detected
sources. More specifically, the photometric sample has median stellar mass
log(M∗/M⊙)=9.97 (with standard deviation $\sigma$=0.43); thus, all X-ray
sources have stellar masses above the median mass of the photometric
population. We also note that our photometric galaxies sample is $K-$selected,
and $K-$selected samples are biased in favor of more massive hosts (see, e.g.,
Dunne et al., 2009). This further strengthens the significance of detecting
X-ray sources in more massive hosts.

As it can be seen in Figure 3, the two MUSE targets are brighter (in the B
band which broadly matches the wavelength range shown in the spectra) than the
X-ray targets. More specifically, the two MUSE targets have
$B{\rm{}_{A}B}\sim$25, while the X-ray targets all have $B{\rm{}_{A}B}>$26,
and actually all but one even have $B{\rm{}_{A}B}>$27\. Things change,
however, when moving to redder wavelengths. In particular, the X-ray targets
are significantly brighter in the K-band ($K_{\rm AB}$=[22.2–-22.7]) than the
MUSE ones ($K_{\rm AB}$=[23.4–24.8]). Such a different behavior at different
wavelengths is directly linked to the different host masses observed in the
two subsamples: the MUSE targets are likely young, compact sources with
intense star formation processes ongoing, while the X-ray AGN are hosted in
older (thus redder), more massive galaxies.

Massive galaxies, and in particular those sources with log(M∗/M⊙)$>$10, have
been shown to be among the best tracers of large scale structures and more
specifically of filaments in the cosmic web (see, e.g., Malavasi et al., 2017;
Sarron et al., 2019; Kuchner et al., 2020). In our case, such a tentative
evidence clearly needs to be validated with a larger, statistically more
reliable sample. Nonetheless, the significant mass difference between the
X-ray and the non-X-ray detected host galaxies supports a scenario where the
X-ray AGN (i.e., those sources with X-ray luminosity L${}_{\rm 2-10keV}>$1042
erg s-1) are hosted by the most massive galaxies in a structure and are
therefore more likely to be powered by more massive and more efficient
accreting supermassive black holes. If such a result will be confirmed in
larger samples, it would (at least partially) explain why X-ray detected
targets are such efficient tracers of LSSs.

Quantitatively, using the Suh et al. (2020) MBH–M∗ relation, we find that the
X-ray detected targets have black hole masses in the range MBH = [6$\times$106
M⊙–7$\times$107 M⊙]. Since the Suh et al. (2020) relation was calibrated using
X-ray emitting sources and galaxies with log(M∗/M⊙)$>$10, it cannot be
reliably used to estimate the black hole mass of the two MUSE-detected
sources. Interestingly, the most massive object among the members of the
structure is XID 109, the only one which is not in spatial proximity with the
others. Since more massive galaxies are expected to be located at the center
of the large scale structure (this is, for example, the case for the
protocluster detected at redshift $z\sim$1.7 in the J1030 field; see Gilli et
al., 2019; D’Amato et al., 2020), such a result could hint at the fact that
the center of the structure does not coincide with the region where we
detected five out of six LSS members. Indeed, as shown in Figure 4, left
panel, no clear evidence of clustering is observed when including in the
overdensity the photometric redshift candidates. However, any further
consideration can be validated only by a spectroscopic follow-up campaign of
these candidates.

We plot in Figure 5 the star formation rate as a function of the stellar mass
for the six spectroscopically confirmed targets in the LSS, as well as for the
26 photometric candidates. As a reference, we also plot the Schreiber et al.
(2015) M∗-SFR main sequence at $z\sim$2.95. As it can be seen, the X-ray
detected sources tend to lie on the MS. One of the two MUSE targets has
instead a nominal SFR value well above the MS one for a galaxy with stellar
mass log(M∗/M⊙)$\sim$9.5; however, the uncertainties on SFR for this target
are large, and our measurement is consistent with the MS one within the 90 %
confidence uncertainty. Finally, the majority of photometric candidates also
tend to lie on the MS. A few high-mass sources, however, have SFR much lower
than the expected one, thus suggesting that they could already be in a
passive, non star-forming phase. This tentative trend, if spectroscopically
confirmed, could then suggest that the X-ray sources in the LSS are hosted not
only by the most massive galaxies, but also by objects that are still gas-rich
and star-forming.

Figure 5: Star formation rate as a function of stellar mass for the four X-ray
detected (cyan circles) and the two MUSE detected (red squares) members of the
$z\sim$2.78 overdensity, as well as for the 26 candidate members of the
overdensity having a photometric redshift $z_{\rm phot}$=[2.68–2.88] (yellow
diamonds). Upper limits are plotted as downwards triangles. As a reference, we
also plot the $z$=2.95 main sequence from Schreiber et al. (2015). Both M∗ and
SFR are computed through SED fitting.

In Table 2 we also report, for the four Chandra–detected targets, the source
column density as computed via X-ray spectral fitting (Signorini et al.,
2023). Several observational works have shown evidence for an increasing
fraction of obscured AGN (i.e., sources having column density $N_{\rm H}>$1022
cm-2 moving from the Local Universe to redshift $z\sim$2–3 (e.g., La Franca et
al., 2005; Tozzi et al., 2006; Liu et al., 2017; Lanzuisi et al., 2018; Vito
et al., 2018; Iwasawa et al., 2020; Peca et al., 2023), where sources with
$N_{\rm H}>$1023 cm-2 can reach 70–80 % of the overall AGN population. In such
a scenario, nuclear obscuration from the so-called obscuring torus, that
accounts for almost the totality of obscuration at $z\sim$0, must be
complemented at higher redshifts by non-nuclear absorption taking place within
the host galaxy. In particular, a recent work by Gilli et al. (2022) shows
that the increasing density with redshift of the interstellar medium (ISM) can
by itself explain the obscured fractions observed at $z\sim$2–3.

To test this scenario, we work under the assumption that galaxies where the
ISM is denser are also those where the SFR is larger. We report in Table 2 the
SFR measurements obtained through SED fitting for the six members of the
overdensity. Two out of four X-ray detected targets (XID 008 and XID 011) have
$N_{\rm H}>$1023 cm-2: in XID 011 we measure significant star formation
activity (SFR${}_{\rm SED}\sim$80 M⊙ yr-1), while in XID 008 we can only
compute a fairly loose upper limit (SFR${}_{\rm SED}<$188 M⊙ yr-1). The two
remaining X-ray detected members of the overdensity (XID 007 and XID 109) both
have a column density N${}_{\rm H}<$1023 cm-2: however, for both targets we
measure a fairly large star formation rate, SFR${}_{\rm SED}>$100 M⊙. However,
the fact that we measure no significant obscuration in the X-ray spectrum of
XID 007 and XID 109 could hint at the fact that the source SED is at least
partially contaminated by the AGN emission, which would imply that the SFR
derived from the SED might be over-estimated.

As a consistency check, we therefore independently computed the star formation
rate of the four Chandra J1030 sources in the structure by using the radio
flux density obtained from a deep JVLA L-band observation of the J1030 field
(D’Amato et al., 2022). XID 007 and 109 are both detected in the JVLA image,
while for the remaining two targets we computed a 3 $\sigma$ upper limit (see
Table 2). Since D’Amato et al. (2022) reported that their fluxes $S_{\rm
1.34\,GHz}$ are measured at 1.34 GHz, we applied a correction factor to
compute the 1.4 GHz luminosities reported in Table 2, as follows

$L_{\rm 1.4GHz}=\frac{4\pi D^{2}_{\rm
L}(z)}{(1+z)^{(1+\alpha)}}\left(\frac{1.4\,{\rm GHz}}{1.34\,{\rm
GHz}}\right)^{\alpha}S_{\rm 1.34\,GHz},$ (1)

where $\alpha$ is the radio photon index and is assumed to be $\alpha$=-0.7
for all targets.

We then used the equation reported in Delvecchio et al. (2021) to derive the
SFR,

$\frac{SFR}{M_{\odot}\,yr^{-1}}=f_{\rm IMF}\,\times\,10^{-24}\,10^{q_{\rm
TIR}(z)}\,\frac{L_{\rm 1.4GHz}}{\rm W\,Hz^{-1}},$ (2)

where L1.4GHz it the 1.4 GHz luminosity, while $f_{\rm IMF}$ is a correction
factor related to the initial mass function (IMF) used in the computation:
$f_{\rm IMF}$=1 for a Chabrier IMF; $f_{\rm IMF}$=1.7 for a Salpeter IMF.
Finally $q_{\rm TIR}$($z$) is a factor that parameterizes the evolution with
both redshift and the host stellar mass of the IR-radio correlation,

$q_{\rm TIR}(z,M_{*})\,=\,(2.646\pm 0.024)\,\times\,(1+z)^{-0.023\pm 0.008}\\\
-({\rm log}M_{*}/M_{\odot}-10)\,\times\,(0.148\pm 0.013).$ (3)

Since the stellar masses and star formation rates computed with CIGALE v2022.1
adopted a Chabrier IMF, in Table 2 we report the radio SFR values obtained
assuming $f_{\rm IMF}$=1. As it can be seen, there is a general good agreement
between the SED fitting measurements and the 1.4 GHz ones. In particular, for
XID 007 and XID 109 we measure again SFR${}_{\rm 1.4GHz}>$100 M⊙ yr-1. We
remind, as a caveat, that the Delvecchio et al. (2021) relation has been
computed using star-forming galaxies, rather than AGN, so the values obtained
here are likely upper limits, as part of the radio emission in our targets may
be of nuclear origin.

In summary, we do not observe a clear trend between the l.o.s. column density
computed through X-ray spectral fitting and the host star formation rate
computed either through SED fitting or through the 1.4 GHz luminosity. Such a
result is not in contradiction with the trends discussed in Gilli et al.
(2022), since those should be applied statistically on a large sample of
sources, and not on single targets. For example, all the known $z\sim$6
quasars are by definition unobscured AGN (see, e.g., Nanni et al., 2017; Vito
et al., 2019) despite being hosted by young, gas-rich galaxies experiencing
significant star formation activity.

##  5 Summary and conclusions

In this work, we presented the results of a recent LBT-MODS spectroscopic
follow-up campaign of a sample of Chandra–detected sources in the J1030 field.
We also used the LBT-LBC $g$ band and the CFHT-WIRCAM $K_{\rm s}$ band
photometry we recently obtained on the J1030 field to update the photometric
redshifts of the $z>$2 candidates in the Chandra J1030 sample. The following
are the main results of our analysis.

  1. 1.

Out of seven high-$z$ ($z_{\rm phot}>$2.7) candidates, we measured a
spectroscopic redshift for five sources: all of them have $z_{\rm spec}>$2.5,
thus proving the effectiveness of our photometric redshifts in selecting
high-$z$ candidates.

  2. 2.

All the 12 sources for which we measured a new spectroscopic redshift are
classified as emission line galaxies, which means that their optical emission
is dominated by non-AGN processes. This result suggests that as we increase
the sample spectroscopic completeness at faint magnitudes (all 12 targets have
$r_{\rm AB}>$24) the contribution of the BL-AGN to the overall population
significantly decreases.

  3. 3.

The LBT-MODS spectroscopic campaign led to the serendipitous discovery of a
large-scale structure at $z\sim$2.78 in the J1030 field. The structure
contains six spectroscopically confirmed targets, four of which are X-ray
detected. Five out of six targets are located within a $\sim$1′ radius (i.e.,
within an angular distance $d_{\rm A}<$1.5 Mpc). Other 26 galaxies have a
photometric redshift in the range $z_{\rm phot}$=[2.68–2.88] and are therefore
candidate members of the overdensity.

  4. 4.

We measure a large mass difference between the X-ray detected AGN and the non-
X-ray detected galaxies in the overdensity: the stellar mass of the X-ray
targets varies in the range log(M∗/M⊙)=[10.2–11.1], while the two
spectroscopically confirmed, non-X-ray detected objects both have
log(M∗/M⊙)$<$10, and the photometric candidates have median stellar mass
log(M∗/M⊙)=10.0. Massive galaxies are known to be among the best tracers of
large scale structures: this result, while limited by the small size of the
sample, therefore provides a potential explanation of why X-ray detected AGN
also are efficient LSSs tracers.

  5. 5.

We measure in two independent ways – through SED fitting and from the 1.4 GHz
luminosity – the star formation rate of the galaxies hosting the $z\sim$2.78
overdensity. The two methods give consistent results, and the sources
(particularly the X-ray detected ones) are found to lie on the Schreiber et
al. (2015) SFR-M∗ main sequence.

  6. 6.

With this campaign, we measured a spectroscopic redshift for 12 Chandra J1030
sources, thus increasing the sample spectroscopic completeness to 53 % (135
out of 256 sources).

Future works will focus on obtaining photometric redshifts for the whole non-
X-ray population (M. Mignoli et al. in prep.) in the J1030 field, and
searching for both new members of the LSS and more in general for promising
high-z candidates. With a larger number of sources with good photometric
redshifts at $z\geq$2 it will be possible to search for high-redshift
overdensities using statistical methods such as the Voronoi tessellation Monte
Carlo algorithm (see, e.g., Cucciati et al., 2018; Lemaux et al., 2018; Shen
et al., 2021; Lemaux et al., 2022). These photometric redshifts will also be
used to select candidates for new spectroscopic follow-up campaigns with LBT-
MODS and other facilities.

## Acknowledgments

We thank the referee for the detailed report and the useful suggestion. We
acknowledge the support from the LBT-Italian Coordination Facility for the
execution of observations, data distribution and reduction. The LBT is an
international collaboration among institutions in the United States, Italy and
Germany. LBT Corporation partners are the University of Arizona on behalf of
the Arizona university system; Istituto Nazionale di Astrofisica, Italy; LBT
Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, the
Astrophysical Institute Potsdam, and Heidelberg University; The Ohio State
University, and The Research Corporation, on behalf of The University of Notre
Dame, University of Minnesota and University of Virginia. We acknowledge
financial contribution from the agreement ASI-INAF n. 2017-14-H.O. MB
acknowledges financial support from the Italian L’Oreal UNESCO ”For Women in
Science” program and the PRIN MIUR 2017PH3WAT “Blackout”.

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##  Appendix A Updated Chandra J1030 photometric redshifts and refined high-
redshift number counts

As mentioned in Section 2, we recently observed the J1030 field in the $g$ and
Ks band. We thus decided to re-run the Hyperz tool (Bolzonella et al. 2000) to
obtain more reliable photometric redshifts, particularly at z$\geq$2, where a
deeper Ks coverage can significantly improve the overall quality of the
spectral energy distribution (SED) fitting. The new photometric redshifts were
computed by using the photometric bands reported in Table 3. We followed the
same SED fitting approach we used in M21, to which we refer for a complete
description of the different steps. We also generated the redshift probability
distribution function (PDZ) of each target.

There are 29 Chandra J1030 sources with $z_{\rm spec}\geq$2\. We report in
Figure 6 the distribution of the old and new photometric redshifts as a
function of the spectroscopic ones. Following the standard approach to
estimate a photometric redshift reliability we already used in M21, we assume
that $z_{\rm spec}$ and $z_{\rm phot}$ are in agreement when ——$z_{\rm
phot}$-$z_{\rm spec}$——/(1+$z_{\rm spec}$)$<$0.15. The new photometric
redshifts are significantly more accurate than the old ones: 21 out of 29
objects (72 %) have $\Delta z$/(1+$z_{\rm spec}$)$<$0.15, with normalized
median absolute deviation (Hoaglin et al. 1983) $\sigma_{\rm NMAD,new}$ = 1.48
$\times$ median[——$z_{\rm phot,new}$-$z_{\rm spec}$——/(1+$z_{\rm spec}$)] =
0.143. In M21, instead, only 16 out of 29 targets (55 %) showed an agreement
between the photometric redshift and the spectroscopic one, with $\sigma_{\rm
NMAD,M21}$=0.179. All the 8 outliers in the new photometric redshift sample
are also outliers in the “old” photometric sample; furthermore, two of these
outliers (XID011 and XID022) have $z_{\rm phot,new}>$3\. Therefore, while in
these two targets the photometric redshifts did not accurately pinpoint the
actual source redshift, they were still effective in hinting at a high-
redshift solution.

Figure 6: Photometric redshift as a function of the spectroscopic one for the
29 J1030 sources with spectroscopic redshift $z_{\rm spec}\geq$2\. The black
solid line marks the $z_{\rm spec}$ = $z_{\rm phot}$ relation, while the
dashed lines contain the $z_{\rm phot}$ = $z_{\rm spec}\pm$0.15(1+$z_{\rm
spec}$) region. Sources within this region are deemed to have a reliable
photometric redshift. We note that all the outliers with $z_{\rm phot}<$1.2
are BL-AGN, a class of sources for which photometric redshifts are generally
less reliable (see M21 for more details).

In M21 we computed the $z>$3 number counts in the Chandra J1030 field. We
found evidence of a potential overdensity at $z>$4 with respect to both other
X-ray surveys and the predictions of different AGN population synthesis
models. However, when we published these results only three out of 25 $z>$3
sources had a spectroscopic redshift, one of them (the only one at $z_{\rm
spec}>$4) being the $z$=6.3 J1030 quasar itself. The $z>$4 overdensity we
measured was therefore based on the photometric redshifts, and in particular
on the sources redshift probability distribution functions (PDZs).

The spectroscopic campaign we presented in this work was therefore aimed,
among other things, at increasing the Chandra J1030 spectroscopic completeness
at $z>$3, to put stronger constraints on the overdensity detection. As
reported in Table 1, all the high-$z$ sources which we were able to
spectroscopically confirm are in the range $z_{\rm spec}$=[2.5–3.1]. This,
combined with the new photometric redshifts, could in principle affect the
Chandra J1030 number counts measurements, and in particular reduce the
high$-z$ excess presented in M21. For this reason, we recomputed the Chandra
J1030 $z>$3 number counts following the same approach presented in M21: most
importantly, for sources lacking a spectroscopic redshift and having just a
photometric redshift, we did not use the sources nominal best-fit redshift
value, but rather their probability distribution functions. As discussed in
M21, this is now a common approach when computing the high-$z$ number counts
of X-ray surveys, since their spectroscopic completeness strongly decreases at
$z>$2.5–3 (see, e.g., Marchesi et al. 2016b; Vito et al. 2018).

We report in Figure 7 the Chandra J1030 number counts in the redshift bins
$z$=[3–4], $z$=[4–5] and $z$=[5–6]: we plot the original number counts
reported in M21 as well as the number counts computed using both the new
spectroscopic redshifts and the new photometric redshifts. For comparison, we
also report the predictions of the Gilli et al. (2007) AGN population
synthesis model and the number counts derived from the Vito et al. (2014)
$z>$3 AGN X-ray luminosity function. As it can be seen, the difference between
the number counts computed in M21 and those re-computed in this work using the
new spectroscopic and photometric redshifts is marginal, and all number counts
are consistent within the uncertainties. In particular, the excess observed at
redshift $z>$4 in M21 is still present, and suggests that one or more
additional overdensities can be present in the J1030 field between the
$z$=2.78 and the $z$=6.3 one. We are now working on the computation of
photometric redshifts for all the sources in the J1030 field (M. Mignoli et
al. in prep.) and use them to search for more high-redshift candidates to then
follow-up with spectroscopic campaigns like the one presented in this paper.

Figure 7: Chandra J1030 0.5–2 keV number counts in the redshift bins $z$=[3–4]
(left), $z$=[4–5] (center), and $z$=[5–6] (right). We plot as red circles the
LogN-LogS obtained using both the new spectroscopic redshifts and the new
photometric redshifts presented in this work; we instead plot as blue diamonds
the M21 number counts. The number counts in the same redshift ranges derived
using the Gilli et al. (2007) AGN population synthesis model (black dashed
line) and the Vito et al. (2014) X-ray luminosity function (cyan solid line)
are also shown for comparison. The overdensity measured in M21 at $z>$4 is
still present in the newly refined number counts.

##  Appendix B Spectra

We report in this Appendix, in Figures 8 and 9, the flux-calibrated spectra
for the nine sources targeted by our LBT-MODS campaign for which we computed a
spectroscopic redshift and that are not part of the $z\sim$2.78 LSS; the
spectra of the LSS are reported in Figure 3. The FITS file of these spectra,
as well as of those of the six Chandra J1030 for which we could not measure a
spectroscopic redshift, are available
online555http://j1030-field.oas.inaf.it/~LBTz6/1030/xray_redshift_J1030.html.

Figure 8: LBT-MODS flux-calibrated spectra of six Chandra J1030 sources
targeted by the campaign presented in this work and not belonging to the
$z\sim$2.78 structure. We highlighted the expected positions of the main
emission lines that fall in the observed spectral range. On top of each one-
dimensional spectrum, we report the two-dimensional one.  Figure 9: LBT-MODS
flux-calibrated spectra of three Chandra J1030 sources targeted by the
campaign presented in this work and not belonging to the $z\sim$2.78
structure. We highlighted the expected positions of the main emission lines
that fall in the observed spectral range. On top of each one-dimensional
spectrum, we report the two-dimensional one.