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# The 700 ks Chandra Spiderweb Field I: Evidence for widespread nuclear
activity in the protocluster

P. Tozzi 11 L. Pentericci 22 R. Gilli 33 M. Pannella 44 F. Fiore 55 G. Miley
66 M. Nonino 55 H.J.A. Röttgering 66 V. Strazzullo 55 C. S. Anderson 77 S.
Borgani 44558899 A. Calabrò 22 C. Carilli 1010 H. Dannerbauer 11111212 L. Di
Mascolo 44 C. Feruglio 55 R. Gobat 1313 S. Jin 1111 A. Liu 1414 T. Mroczkowski
1515 C. Norman 16161717 E. Rasia 5588 P. Rosati 1818 A. Saro 44558899

###### Abstract

Aims. We present an analysis of the 700 ks Chandra ACIS-S observation of the
field around the radio galaxy J1140-2629 (the Spiderweb Galaxy) at $z=2.156$,
focusing on the nuclear activity in the associated large-scale environment.

Methods. We identified unresolved X-ray sources in the field down to flux
limits of $1.3\times 10^{-16}$ and $3.9\times 10^{-16}$ erg/s/cm2 in the soft
(0.5-2.0 keV) and hard (2-10 keV) band, respectively. We searched for
counterparts in the optical, near-infrared (NIR), and submillimeter catalogs
available in the literature to identify X-ray sources belonging to the
protocluster and derived their X-ray properties.

Results. We detect 107 X-ray unresolved sources within 5 arcmin (corresponding
to 2.5 Mpc) of J1140-2629, among which 13 have optical counterparts with
spectroscopic redshift $2.11<z<2.20$, and 1 source has a photometric redshift
consistent with this range. The X-ray-emitting protocluster members are
distributed approximately over a $\sim 3.2\times 1.3$ Mpc2 rectangular region.
An X-ray spectral analysis for all the sources within the protocluster shows
that their intrinsic spectral slope is consistent with an average
$\langle\Gamma\rangle\sim 1.84\pm 0.04$. Excluding the Spiderweb Galaxy, the
best-fit intrinsic absorption for five protocluster X-ray members is
$N_{H}>10^{23}$ cm-2, while another six have upper limits of the order of a
few times 1022 cm-2. Two sources can only be fitted with very flat $\Gamma\leq
1$, and are therefore considered Compton-thick candidates. The 0.5-10 keV
rest-frame luminosities of the 11 Compton-thin protocluster members corrected
for intrinsic absorption are greater than $2\times 10^{43}$ erg/s. These
values are typical for the bright end of a Seyfert-like distribution and
significantly greater than X-ray luminosities expected from star formation
activity. The X-ray luminosity function of the AGN in the volume associated to
the Spiderweb protocluster in the range $10^{43}<L_{X}<10^{44.5}$ erg/s is at
least ten times higher than that in the field at the same redshift and
significantly flatter, implying an increasing excess at the bright end. The
X-ray AGN fraction is measured to be $25.5\pm 4.5$% of the spectroscopically
confirmed members in the stellar mass range $\log(M_{*}/M_{\odot})>10.5$. This
value corresponds to an enhancement factor of $6.0^{+9.0}_{-3.0}$ for the
nuclear activity with $L_{0.5-10keV}>4\times 10^{43}$ erg/s with respect to
the COSMOS field at comparable redshifts and stellar mass range.

Conclusions. We conclude that the galaxy population in the Spiderweb
protocluster is characterized by enhanced X-ray nuclear activity triggered by
environmental effects on megaparsec scales.

###### Key Words.:

galaxies: clusters: general – galaxies: active – X-rays: galaxies: clusters

##  1 Introduction

Protoclusters are defined as overdense regions in the high-$z$ Universe and
are expected to evolve into massive, virialized clusters of galaxies at the
present epoch (see Overzier, 2016, for a review). Finding and characterizing
protoclusters is key to studying the large-scale structure of the Universe and
the transformational processes that affect star formation and nuclear activity
in the member galaxies, such as powerful mergers, gas cooling, and feedback
effects. In practice, although a protocluster is observationally identified as
a high-z structure that is overdense compared to its surroundings, the
dynamical state of the structure, and therefore whether it will evolve into a
low-z cluster, is usually highly uncertain (see, e.g., Muldrew et al., 2015).
At present, there are no standard methods to systematically search for bona
fide protoclusters, and this is why biased-tracer techniques are often used to
identify interesting targets. One of these consists in searching around high-
redshift, powerful radio galaxies, which are often found to be a beacon for
overdense regions (see Miley et al., 2006). Independently of the selection
method, in order to confirm their nature and to trace the activity of several
processes occurring during their rapid evolution, protocluster candidates must
be followed up intensively with multiwavelength campaigns.

In this respect, X-ray observations play a key role, particularly for
studying: (1) unresolved emission from active galactic nuclei (AGN) indicative
of accretion onto nuclear supermassive black holes (SMBHs); (2) the less
intense emission from strongly star forming galaxies; and (3) diffuse emission
from hot gas and/or relativistic plasma. Unfortunately, $z\gtrsim 2$
protoclusters are usually very faint in the X-rays and therefore only deep,
high-resolution observations can provide useful information in this band.
Until now only a few deep ($t_{\rm exp}\geq 200$ ks) observations of
protoclusters have been made with Chandra or XMM-Newton. In a few cases a
faint, extended emission has been interpreted as the signature of a low-mass
virialized halo (Gobat et al., 2011; Valentino et al., 2016; Wang et al.,
2016). In some other studies, the thermal or relativistic nature of the
diffuse emission is still unclear (Gilli et al., 2019; Champagne et al.,
2021). In addition to the fact that X-ray data on protoclusters are so few,
another clear requirement to search for and characterize the diffuse emission
in high-z protoclusters and at the same time the unresolved emission from AGN
members is data of sufficiently high sensitivity and angular resolution ($\sim
1$ arcsec).

Regarding the X-ray nuclear activity, there is increasing evidence that this
is enhanced in overdense, protocluster regions. Lehmer et al. (2009) and
Digby-North et al. (2010) found, respectively, 12 and 4 X-ray sources with
$L_{2-10keV}\geq 3-5\times 10^{43}$ erg s-1 probably associated to the
protoclusters identified in the SSA22 and HS1700+64 fields. These numbers
exceed the X-ray source counts in deep fields at the same redshifts by a
factor of 10-20, although the uncertainties are large (see also Krishnan et
al., 2017). The enhancement of X-ray AGN in high-z protoclusters is
particularly impressive when compared with the overdensity of X-ray sources in
evolved clusters at $z\sim 0.5$, which is only a factor of $\sim 3$ (Martini
et al., 2006; Branchesi et al., 2007; Kocevski et al., 2009; Ehlert et al.,
2015). However, we note that the physical quantity that should be measured is
not the X-ray source density, but the AGN fraction among protocluster members,
and therefore the ratio of this fraction to the same quantity measured in the
field, defined as the enhancement factor $f_{\rm enh}$. To be meaningful, this
quantity should be evaluated in a well-defined stellar mass range, and
possibly differentiated between star-forming and passive galaxies, in order to
compare the full distribution of AGN accretion rates in the protocluster
members to those in field galaxies at comparable redshift. A robust
characterization of $f_{\rm enh}$ in protoclusters that accounts for the
dependence on redshift and on the mass scale is still not available.
Furthermore, the lack of quantitative estimates on the luminosity function of
AGN in protoclusters and on their obscuration implies large uncertainties on
an important, related quantity, namely the energy budget released in the
surrounding medium by the nuclear activity.

Finally, another relevant missing piece of information in protoclusters is the
measurement of the hot component in the surrounding diffuse baryons (the
forming intracluster medium, ICM), which can be used to constrain the
virialization status of the halo. Characterization of the proto-ICM, including
its morphology and its thermodynamical and chemical properties, can provide an
independent and direct measure of the heating efficiency associated to the
feedback and, at the same time, of the gas accretion into the protocluster
potential well. In addition, feedback processes not only affect the ICM, but
can also couple directly with the member galaxies. An interesting example was
recently found in the field of the high-redshift quasar SDSSJ1030 (observed by
Chandra with a 500 ks exposure), where a protocluster at $z\sim 1.7$ centered
on a bright FRII radio galaxy shows star-forming member galaxies apparently
triggered by the AGN radio jet (Gilli et al., 2019). If confirmed, this
phenomenon may shed new light on the strong interplay between the member
galaxies and the surrounding medium in the first stages of formation of large
structures.

As of today, the available data are providing tantalizing evidence for the
complex and intricate phenomena that occur in such high-density, rapidly
evolving regions at cosmic noon. A comprehensive physical picture of the
accretion, aggregation, and phase transformation of baryons in protoclusters
will require large sample statistics (still limited by the number of currently
known protoclusters) and a multiwavelength approach, including high-resolution
X-ray observations. Here we address these issues using deep Chandra ACIS-S
observations ($\sim 700$ ks) of the remarkable Spiderweb Galaxy (J1140-2629)
complex at $z=2.156$ (redshift obtained from low-resolution spectroscopy by
van Ojik, 1995). The central, powerful radio galaxy, which is embedded in a
giant Ly$\alpha$ halo (Pentericci et al., 1997; Miley et al., 2006), is
surrounded by a $\gtrsim 2$ Mpc-sized overdensity (corresponding to a radius
of 4 arcmin) of star forming galaxies (Ly$\alpha$ and H$\alpha$ emitters),
dusty starbursts, and red galaxies likely in the process of shaping a nascent
red sequence (Zirm et al., 2008). The complex around the Spiderweb Galaxy is
considered to be a typical protocluster region and is expected to evolve into
a massive cluster in less than 1.5 Gyr, with the radio galaxy itself showing
characteristics of a cD progenitor (Miley et al., 2006).

In the present paper, we focus on the nuclear activity in the protocluster
members, while the physics associated to the diffuse emission surrounding the
Spiderweb Galaxy is investigated in a companion paper based on X-ray and SZ
data (Tozzi et al. in preparation; DiMascolo et al. in preparation). This
paper is organized as follows. In Section 2 we summarize the properties of the
Spiderweb Galaxy complex on the basis of previous observations. In Section 3
we briefly describe the multiwavelength data set used in this work. In Section
4 we outline the X-ray data acquisition and reduction techniques. Section 5
deals with the identification all the X-ray sources in the field and their
number counts. In Section 6 we list the galaxies associated to the large-scale
structure (protocluster members) and characterize their nuclear activity in
terms of X-ray luminosity and spectral properties. In Sections 7 and 8, we
present the X-ray luminosity function and the AGN fraction of the protocluster
members, respectively. In Section 9, we discuss the enhancement factor implied
by our new measurements and discuss our results in comparison to previous
X-ray studies of protoclusters. Possible extensions of this work in promising
directions are briefly discussed in Section 10. Finally, our conclusions are
summarized in Section 11. For the sake of clarity, we refer to the radio
galaxy and its immediate surroundings as the Spiderweb Galaxy, or J1140-2629,
while ”Spiderweb Complex” indicates the large-scale structure potentially
associated to the radio galaxy in a broad redshift range ($2.0<z<2.3$). The
term ”protocluster” is instead used to include only the galaxies in the
narrower redshift range $2.11<z<2.20$ (see also Jin et al., 2021), assuming
that all the protocluster members will end up in a massive ($\sim$few times
10${}^{14}M_{\odot}$) cluster today. Throughout this paper, we adopt the
seven-year WMAP cosmology with $\Omega_{\Lambda}=0.73$, $\Omega_{m}=0.27$, and
$H_{0}=70.4$ km s-1 Mpc-1 (Komatsu et al., 2011). In this cosmology, at
$z=2.156$, 1 arcsec corresponds to 8.473 kpc, the Universe is 3.13 Gyr old,
and the lookback time is 77% of the age of the Universe. Quoted error bars
correspond to a 1 $\sigma$ confidence level unless noted otherwise.

##  2 The Spiderweb Complex: previous observational campaigns and main results

Since its discovery in 1994, the Spiderweb Galaxy (J1140-2629) and the
Spiderweb Complex have become an intensively studied region. In the last 25
years, 54 papers have been published about this field including observations
in radio, sub-millimeter (submm), infrared (IR), optical, and X-ray
wavelengths. In this section, we summarize the main results that have been
obtained so far, focusing on the protocluster environment.

###  2.1 Discovery and peculiarities

The Spiderweb Galaxy was discovered during the implementation of an ESO Key
Program designed to find high-z radio galaxies (HzRG) by targeting ultra-steep
spectrum radio sources (Roettgering et al., 1994). The object was noticed as
peculiar because of its unusually clumpy and bent radio morphology coupled
with an exceptionally high rotation measure ($\sim 6200$ rad/m), indicating
that the radio synchrotron jet is surrounded and its propagation constrained
by a dense ($10^{-1}-10^{-2}$cm-3) external medium (Carilli et al., 1997;
Pentericci et al., 1997; Athreya et al., 1998). Optical follow-up classified
it as a narrow emission-line galaxy at $z=2.156$ (see Roettgering et al.,
1997), and revealed a clumpy optical continuum morphology and a spectacular
Ly$\alpha$ halo (still one of the largest known in the Universe) with a
luminosity of $42.5\times 10^{44}$ erg/s elongated along the jet. The total
stellar mass inferred from the K-band luminosity is $10^{12}M_{\odot}$
(Pentericci et al., 1997), confirmed by Spitzer data (Seymour et al., 2007),
making the Spiderweb one of the most massive high-z galaxies known. Using the
Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) observations,
the clumpy features, embedded in the 200 kpc Ly$\alpha$ halo, whose
distribution resembles that of flies trapped in a spiderweb, have been shown
to correspond to approximately ten star-forming satellite galaxies moving with
peculiar velocities of several hundred km/s and presumed to be merging with
the central radio galaxy (Miley et al., 2006).

Eventually, Nesvadba et al. (2011) found that the optical and near-infrared
(NIR) spectrum of the nucleus of J1140-2629 shows a broad, spatially
unresolved H$\alpha$ line (blended with [NII]) with a FWHM of $\sim 14900$
km/s. The presence of broad nuclear lines is rare in optical counterparts of
high-redshift radio sources typically classified as TypeII AGN. The black hole
mass is estimated to be $M_{\Large\bullet}\sim 2\times 10^{10}M_{\odot}$,
putting J1140-2629 a factor of $\sim 2$ above the local
$M_{\Large\bullet}-\sigma$ relation, in agreement with its expected evolution.
Taken together, the observed characteristics suggest that the Spiderweb is
indeed a massive radio galaxy forming at the center of a dynamically evolving
protocluster region and is likely to evolve into a brightest cluster galaxy.
The Spiderweb is therefore one of the most revealing laboratories for studying
the evolution of a protocluster in the early Universe, and may represent a
typical phase in the formation of massive galaxy clusters with prominent
central galaxies.

###  2.2 Identification of protocluster members and their properties

The search for protocluster members of the Spiderweb Complex was based on a
series of works with spectroscopic follow-up and narrow band imaging in the
field. A first sample of 50 candidate Ly$\alpha$ emitters in a $6\times 6$
arcmin2 field (Kurk et al., 2000) provided support to the existence of several
star forming galaxies in the protocluster. Of these candidates, 15 were
eventually confirmed to have redshift in the range $2.16\pm 0.02$ with VLT-
FORS spectroscopy by Pentericci et al. (2000). One of these confirmed sources
shows clear signs of AGN activity with very broad Ly$\alpha$ and CIV emission
lines, while all the others simply show narrow Ly$\alpha$ emission. More
extensive VLT imaging in NB0.38, B, R, and I bands with FORS2 and in the
$J_{s}$, H, $K_{\rm S}$, and NB2.07 bands with ISAAC identified 40 H$\alpha$
candidate emitters and 44 extremely red objects (EROs) consistent with $z\sim
2$, whose density increases towards the central galaxy suggesting a physical
association (Kurk et al., 2004b). Estimated star formation rates (SFRs)
without dust correction are in the range 2-50 $M_{\odot}$/yr and 0.4-4.3
$M_{\odot}$/yr for the H$\alpha$\- and Ly$\alpha$-emitter candidates,
respectively. The SFR per unit mass, estimated from K-band magnitudes, are
$2.5$ times higher than in local massive clusters.

In a spectroscopic follow-up in the IR band with ISAAC on the VLT, an
additional nine H$\alpha$ emitter candidates within 0.6 Mpc from J1140-2629
were confirmed as protocluster members (Kurk et al., 2004a). The narrowness of
the emission lines of eight of the nine confirmed sources indicates that they
are powered by star formation dominated by a very young ($<100$ Myr) stellar
population with moderately high metallicity. Only in one of the emitters does
the H$\alpha$ appear extremely broad with a FWHM exceeding 5000 km/s. The
contribution of these nine candidates to the SFR density in the protocluster
shows it to be at least an order of magnitude larger than that found at
$\langle z\rangle=2.23$ in the HDF-N.

Near-infrared spectroscopy of narrow-band-selected H$\alpha$ emitters with
MOIRCS on Subaru presented by Shimakawa et al. (2014, 2018) significantly
increased the number of spectroscopically confirmed protocluster members. An
additional 4 protocluster members were identified among 13 H$\alpha$ emitter
candidates using ALMA CO(3–2) ($\nu_{rest}=345.796$ GHz) observations (Tadaki
et al., 2019), all of them also detected in CO(4–3) by Emonts et al. (2018).
Recently, Jin et al. (2021) obtained 46 CO(1-0) detections in the range
$2.09<z<2.22$, using 13 individual pointings with ATCA.

Photometric studies also helped to characterize the protocluster population.
Infrared Surveys indicated an overdensity of 3-4 $\sigma$ with respect to the
field at $24\mu$m (Mayo et al., 2012), with Spitzer IRAC colors (Galametz et
al., 2012), and with Herschel SPIRE (Valtchanov et al., 2013; Rigby et al.,
2014). The distribution of IR protocluster galaxy candidates confirms the
approximate filamentary shape of the protocluster, previously obtained using
optical narrowband selection. In the submm band, an overdensity of a factor of
four is observed with APEX LABOCA at 870 $\mu$m (Dannerbauer et al., 2014).
The submm flux distribution at the protocluster redshift would imply an SFR
that is higher by about an order of magnitude with respect to the
H$\alpha$-derived values. The sample of narrow-band-selected candidates was
extended to 68 H$\alpha$ emitters with the MAHALO Deep Cluster Survey
(Shimakawa et al., 2018) with the Subaru Telescope, 17 of which are newly
discovered. In addition, $Bz^{\prime}K_{s}$ selection identified 34 distant
red galaxies, half of which have photo-z consistent with being protocluster
members.

Overall, the galaxy population of the Spiderweb Complex appears to be a mix of
active and star forming galaxies, and already massive, passive galaxies that
constitute a nascent red sequence (Kodama et al., 2007; Zirm et al., 2008,
2012), and that approximately follow an elongated structure extending $\sim 5$
Mpc in diameter. Tanaka et al. (2013) found that the weak red sequence is
consistent with a formation redshift in the range $3<z<4$. In addition, Koyama
et al. (2013) found that the properties of the H$\alpha$ emitters are
consistent with them having formed a large part of their stellar mass at
$z>2$, but observed in a still intense star-forming phase. The presence of
both star forming and red galaxies may be related to a typical phase
associated to environmental effects driven by the protocluster collapse that
accelerates their formation and evolution.

Finally, we note that four out of six ($60$%) massive $H_{\alpha}$ emitters
(HAEs) ($M_{*}>10^{11}M_{\odot}$) were previously identified as bright X-ray
sources (see Pentericci et al., 2002; Croft et al., 2005). Also, Croft et al.
(2005) confirmed two X-ray sources as protocluster members using LRIS Keck
spectroscopy, and classified both as AGN due to the presence of NV, CIV, and
[CIII] in the spectrum, bringing the total number of X-ray-emitting members to
five. This finding suggests that protocluster members that host X-ray AGNs may
be in the transition stage from dusty star-forming galaxies to passive
populations.

###  2.3 Role of the new X-ray observations

The nature of the galaxy population of the Spiderweb Protocluster will be
further investigated in this work thanks to the addition of our deep X-ray
data. Our study relies on a collection of 252 unique sources in the field that
have spectroscopic or narrow-band/photometric redshift in the range
$2.0<z<2.3$ (see Section 3). A detailed list of all the spectroscopic members
and color- or narrow-band-selected candidates, and the identification of the
Spiderweb Complex candidates, is shown in Section 3.

Using our deep Chandra observation, we explore the following aspects: (i) the
frequency of X-ray nuclear activity among the protocluster members; (ii) the
enhancement of nuclear activity in the protocluster; (iii) the distribution of
phases in the diffuse baryons in the halo of the Spiderweb Galaxy, and the
relation with its strong nuclear activity; and (iv) the presence of diffuse
thermal emission possibly associated to the virialization of a central halo.
In this paper, we focus on the AGN population. The presence of hot, diffuse
baryons around the Spiderweb Galaxy and their relation to its nuclear activity
is discussed in two papers based on X-rays and the SZ signal (Tozzi et al. in
preparation; Di Mascolo et al. in preparation). The main results and the data
products of the present paper can be found on the project
webpage111http://www.arcetri.inaf.it/spiderweb/.

##  3 Multiwavelength data used in this work

In this work, we exploited part of the large set of multiwavelength data
publicly available for the Spiderweb Complex field. We used the HST images for
the central regions and the Subaru images —which cover the entire Chandra
field of view (FOV)— to identify the optical counterparts of the X-ray
sources. In particular, we used a 23 ks exposure in the F814W band with ACS
(HST Proposal 10327, PI H. Ford), and B, $r^{\prime}$, $z^{\prime}$ exposures
obtained with the Suprime camera at the Subaru telescope and covering a
$\approx$ $30\times 30$ arcmin2 field. We also used VLT-VIMOS imaging data in
the U band, and VLT-HAWKI images in Y, H, and K bands. The Suprime B,
$r^{\prime}$, and $z^{\prime}$ raw data were retrieved from the SMOKA archive
(Baba et al., 2002). The images were reduced with a custom pipeline because of
the four-ports-readout layout of the camera chips. Images have been overscan,
master bias, and master flats corrected. We then used an improved version of
own pipeline as described in (Nonino et al., 2009), which currently uses Scamp
(Bertin, 2006) with GAIA-EDR3 as astrometric reference, and Swarp (Bertin et
al., 2002) for the final coaddition. A similar approach was used for the VLT-
VIMOS and VLT-HAWKI images, with the raw data retrieved from the ESO Archive.
Removal of the instrumental signatures was performed using IRAF222IRAF was
distributed by the National Optical Astronomy Observatory, which was managed
by the Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation.. For the NIR HAWKI
images, the appropriate darks were retrieved from the ESO Archive, stacked and
applied to the raw data. For the optical data, the bias and the flats were
used to create static weights which account for chips defects. For the NIR
data, darks and flats were instead used.

We used optical and NIR photometry to estimate host galaxy masses and rest-
frame luminosities of the X-ray AGNs in our sample. Detailed descriptions of
the photometric measurements, the multi-wavelength catalog, the photometric
redshift, and our stellar mass estimation will be provided elsewhere (Pannella
et al., in preparation). In the following, for the sake of completeness we
briefly summarize the data and procedures relevant here.

Table 1: Optical and NIR data.

Filter | Instrument | FWHM | 5$\sigma$ | Science Archive
---|---|---|---|---
| /Telescope | (arcsec) | (AB) | /Project ID(s)
$U$ | VIMOS/VLT | 0.86 | 26.4 | ESO - 383.A-0891
$B$ | S-Cam/Subaru | 1.12 | 25.8 | SMOKA - o17409
$r^{\prime}$ | S-Cam/Subaru | 0.73 | 25.2 | SMOKA - o17409
$z^{\prime}$ | S-Cam/Subaru | 0.65 | 24.4 | SMOKA - o10144
$Y$ | HAWK-I/VLT | 0.46 | 24.5 | ESO - 088.A-0754, 091.A-0106
$H$ | HAWK-I/VLT | 0.58 | 23.2 | ESO - 088.A-0754, 091.A-0106
$K_{\rm S}$ | HAWK-I/VLT | 0.40 | 22.8 | ESO - 088.A-0754, 091.A-0106
333The first to fourth columns indicate filter name, instrument/telescope,
seeing FWHM, and $5\sigma$ limiting magnitude in a 2 arcsec diameter aperture,
respectively. In the fifth column we list the science archive and proposal ID
of the raw dataset.

We used Very Large Telescope (VLT) and Subaru stacked images to create a
multi-wavelength catalog with seven passbands
(U,B,$r^{\prime}$,$z^{\prime}$,Y,H,Ks) from U to K. In Table 1 we summarize
the main properties of the dataset used. We used SExtractor in dual image mode
to measure photometry. The $K_{\rm S}$-band HAWK-I image was adopted as the
primary detection image, because it represents the best compromise —among all
available bands— between the need for a robust tracer of galaxy stellar mass
and sufficient angular resolution ($\simeq$0.4”), which simplifies catalog
assembly and photometry measurements. The whole catalog contains 2 279 objects
over the $K_{\rm S}$ image field of approximately 84 arcmin2 and down to an AB
magnitude of 22.8 (i.e., the image 5$\sigma$ limiting magnitude). The images
used here have very different resolutions. Rather than convolving all images
to the lower resolution, which would result in a significant loss of
information, we account for this in the estimate of aperture colors by
applying PSF-matching corrections based on the growth curve of point-like
sources. To limit uncertainties in such corrections we use 2” diameter
apertures to sample the galaxy spectral energy distributions (SEDs).

Photometric redshifts are computed using EAZY (Brammer et al. 2008). Global
photometric zero points are adjusted iteratively by minimizing the difference
between the various photo-z values and the available spectroscopic redshifts
(e.g., Gabasch et al., 2004; Ilbert et al., 2010; Pannella et al., 2015). By
comparison with the available spectroscopic sample, the rms of
$(z_{phot}-z_{spec})/(1+z_{spec})$ is $\sim$6%. Stellar masses are derived
using a modified version444https://github.com/cschreib/fastpp of FAST (Kriek
et al., 2009), adopting the Salpeter (1955) IMF, Bruzual & Charlot (2003)
stellar population synthesis models, delayed exponentially declining star
formation histories (SFHs), the Calzetti et al. (2000) dust extinction law
(with AV = 0 to 4), and solar metallicity. In deriving the stellar mass, we
use the photo-z obtained using the FAST code, while we use the spectroscopic
redshifts when available.

To compile a comprehensive list of spectroscopic redshifts, we use a
collection of catalogs of all the spectroscopically confirmed protocluster
members, member candidates selected on the basis of color or narrow-band
photometry, and random sources with redshift in the field. The 17 catalogs,
based on 12 different publications, are listed in Table 2. The catalogs have a
significant overlap, because several of them include and extend previous
results. The total number of unique sources with any redshift information in
the field is 252, out of which 161 have spectroscopic redshifts. We also
compile a complementary list of 91 protocluster member candidates that were
identified thanks to narrow-band or color selection in previous works. Most
(90%) of the sources (both confirmed and candidate members) are included in a
box of $6.3\times 3.7$ arcmin2 (corresponding to $3.13\times 1.84$ Mpc at
$z=2.156$) roughly centered on the Spiderweb Galaxy and elongated along the
E-W direction. Only nine sources with redshift information are outside a
circle of 5 arcmin centered on the Spiderweb Galaxy, and none of them are in
the range $2.0<z<2.3$.

The distribution of the 161 available spectroscopic redshifts is shown in
Figure 1. Clearly the majority of the redshift values are close to the
Spiderweb redshift $z=2.156$, because mostly protocluster member candidates
have been targeted. We consider a redshift interval $\Delta z=0.3$ roughly
symmetric with respect to the Spiderweb redshift, corresponding to a velocity
difference of $\Delta v\sim c\times\Delta z/(1+z)$ associated to the Hubble
flow. This interval spans all the sources possibly associated to the Spiderweb
large-scale structure. If we consider the range $2.0<z<2.3$, corresponding to
a maximum $\Delta v\sim 28500$ km/s, we find 112 sources. We do not expect to
see a normal distribution for the redshift, and therefore we adopt the
biweight estimator for the central value and the standard deviation, as
suggested by Beers et al. (1990) for sample size $n\geq 100$555See equations
5, 6 and 9 in Beers et al. (1990). We find $z_{BI}=2.15754$ and
$\sigma_{BI}=0.0208612$. Therefore, two- and three-sigma intervals centered on
$z_{BI}$ are $2.116<z<2.1996$ and $2.095<z<2.220$, respectively. We decided to
assume the $2\sigma$ intervals (approximated as $2.11<z<2.20$) as the
protocluster redshift range.

In the range $2.11<z<2.20$, corresponding to a maximum $\Delta v\sim 8500$
km/s, we find 96 sources. We compute the formal velocity dispersion
$\sigma_{v}$ in this range and find $\sigma_{v}\sim 1490\pm 150$ km/s. This
value should be compared to that expected for a flat distribution in the same
redshift range as expected for sources following the Hubble flow, which is
$\sim 2700$ km/s. We conclude that the sources are clearly detached from the
Hubble flow, and show a global velocity dispersion that would correspond to a
very-high-mass ($M>10^{15}\,M_{\odot}$), virialized single halo. Given the
mass scale and the distribution of sources in the sky, the virialized, single-
halo hypothesis is clearly unrealistic. In addition, we notice that excluding
the new spectroscopic sources identified by Jin et al. (2021) with the CO(1-0)
line, the velocity dispersion drops to $\sigma_{v}=980\pm 100$ km/s (that
would correspond to a temperature of $\sim 6$ keV for a virialized halo). As
already shown in Jin et al. (2021), this points out that the CO sources show a
different dynamical behavior, and are probably distributed along a large-scale
filament or a galaxy superprotocluster. In addition, half of the CO emitters
have measured velocities larger than the escape velocities of any realistic
virialized halo hosting the Spiderweb Galaxy, suggesting that the outer
regions traced by the CO sources are still far from being accreted onto the
main halo. In this work we do not attempt to further investigate the dynamical
structure of the Spiderweb complex. However, the number of spectroscopically
confirmed members in the Spiderweb Complex is now the highest for a single
structure at $z>2$ and a detailed, spatially resolved dynamical analysis will
be a relevant piece of information to constrain the current status and the
future evolution of the structure.

In summary, in this paper we consider the 96 sources included in the narrow
redshift bin $2.11<z<2.20$ as belonging to the protocluster, while the
additional 16 sources included in the range $2.0<z<2.3$ are considered part of
the large-scale structure associated to the Spiderweb Complex, and are most
likely not dynamically bound. The corresponding redshift intervals are shown
in Figure 1 with vertical dashed lines.

Table 2: Catalogs of spectroscopically confirmed protocluster members and
member candidates used in this work.

Reference | Selection method | Members
---|---|---
Spectroscopic |  |
Pentericci et al. (2000) | Ly$\alpha$ emission | 15
Kurk et al. (2004a) | H$\alpha$ emission | 9
Croft et al. (2005) | Ly$\alpha$ emission | 7 [17]
Doherty et al. (2010) | H$\alpha$ emission | 2 [2]
Kuiper et al. (2011) | OII emission | 15 [1]
Tanaka et al. (2013) | OII/OIII emission | 4 [10]
Dannerbauer et al. (2014) | Specz | 11 [4]
Shimakawa et al. (2014) | H$\alpha$ emission | 23
Tadaki et al. (2019) | CO emission | 4
Jin et al. (2021) | CO emission | 46
Color or narrow-band selected |  |
Pentericci et al. (2002) | photo-z | 3
Kurk et al. (2004b) | Ly$\alpha$ emitter | 40
Kurk et al. (2004b) | H$\alpha$ emitter | 40
Kurk et al. (2004b) | EROs | 44
Dannerbauer et al. (2014) | FIR photo-z | 2 [4]
Shimakawa et al. (2018) | H$\alpha$ emitter | 68
Tadaki et al. (2019) | H$\alpha$ emitter | 9
666In the second column, we list the identification/selection method, while in
the third column we report the number of confirmed or candidate members of the
Spiderweb complex ($2.0<z<2.3$). Occasionally, the number of random sources in
the Spiderweb field outside the range $2.0<z<2.3$ is reported in square
brackets. The catalogs were obtained independently in different works, but
often overlap significantly because they are often derived from the same
datasets. The total number of unique sources is 252. We find 161 sources with
spectroscopic redshifts, of which 112 are in the range $2.0<z<2.3$.

Figure 1: Redshift distribution in the Spiderweb field. Upper panel:
Distribution of all the 161 spectroscopic redshifts measured in the field.
Lower panel: redshift distribution in the range $2.0<z<2.3$. Vertical dashed
lines show the redshift of the Spiderweb Galaxy as measured with low
resolution spectroscopy by van Ojik (1995) (black line), the range adopted to
define the Spiderweb Complex (magenta lines) and the protocluster (green
lines), as discussed in the text.

##  4 X-ray data reduction

Table 3: Chandra observations of the Spiderweb Galaxy Complex.

Obsid | date | Exptime (s)
---|---|---
898 | 2000-06-06 | 27 378
21483 | 2019-11-18 | 49 312
22924 | 2020-02-26 | 33 475
22923 | 2020-02-28 | 34 598
23175 | 2020-03-01 | 29 938
22925 | 2020-03-06 | 39 541
22926 | 2020-03-07 | 43 375
22921 | 2020-03-17 | 24 642
23190 | 2020-03-17 | 24 736
23069 | 2020-03-23 | 19 648
23201 | 2020-03-26 | 27 613
21482 | 2020-04-02 | 34 492
22927 | 2020-04-02 | 32 534
23205 | 2020-04-03 | 23 514
22928 | 2020-04-10 | 29 572
23215 | 2020-04-13 | 19 803
21484 | 2020-04-22 | 46 504
22929 | 2020-04-23 | 51 231
23186 | 2020-06-13 | 14 770
22922 | 2020-07-22 | 18 487
21481 | 2020-08-13 | 40 383
22905 | 2020-08-04 | 49 291
777In the last column we list the exposure time after data reduction.

The Spiderweb Galaxy was observed with a Chandra Large Program observation of
700 ks with ACIS-S granted in Cycle 20 (PI P. Tozzi). The observations were
completed in the period November 2019 –August 2020, split into 21 separate
pointings. To this data set, we add the first X-ray observation with ACIS-S,
dating back to June 2000 for a total of 39.5 ks. All the 22 Obsid used in this
work are listed in Table 3.

Data reduction is performed starting from the level = 1 event files with CIAO
4.13, with the latest release of the Chandra Calibration Database at the time
of writing (CALDB 4.9.4). We run the task destreak to flag and remove spurious
events (with moderate to small pulse heights) along single rows, which is
particularly important for ACIS-S4. We run the tool acis_detect_afterglow to
flag residual charge from cosmic rays in CCD pixels. Finally, as all our new
observations are taken in the VFAINT mode we run the task acis_process_events
with the parameter apply_cti=yes to flag background events that are most
likely associated to cosmic rays and reject them. With this procedure, the
ACIS particle background can be significantly reduced compared to the standard
grade selection. The data are then filtered to include only the standard event
grades 0, 2, 3, 4, and 6. The level 2 event files generated in this way are
visually inspected for flickering pixels or hot columns left after the
standard reduction but we find none after filtering out bad events. We also
carefully inspect the image of the removed photons, particularly to verify
whether we have pile-up
effects888https://cxc.cfa.harvard.edu/ciao/ahelp/acis_pileup.html. We find
that slightly more than 100 net counts in the total band are removed at the
position of the nucleus of J1140-2629 across the 22 exposures. This indicates
that the source, which is by far the brightest in the field, suffers some
amount of pile-up. However, we verify a posteriori that this effect does not
impact the spectral analysis of the nucleus and therefore it is not worth
giving up the VFAINT cleaning to recover less than 1% of the flux in the
nucleus. In particular, the VFAINT cleaning is very important for
characterization of the diffuse emission, which is presented in detail in
further papers from the collaboration focused on the inverse Compton emission
associated to the radio jets (Carilli & Anderson, 2022; Anderson & Carilli,
2022) and on the thermal component (Tozzi et al. in preparation; see also Di
Mascolo et al. in preparation).

Finally, time intervals with high background are filtered by performing a
3$\sigma$ clipping of the background level. The light curves are extracted in
the 2.3–7.3 keV band, and binned with a time interval of 200 s. The time
intervals when the background exceeds the average value by $3\sigma$ are
removed with the tool deflate. The final total exposure time after data
reduction and excluding the dead-time correction amounts to 715 ks
(corresponding to the LIVETIME keyword in the header of Chandra fits files),
including the first observation. The average removed time interval for the new
observations amounts to only $\sim 0.3$% of the observing time, except for
Obsid 898, where $\sim 30$% of the exposure time has been removed due to high-
background time intervals. The monochromatic exposure maps are created at the
energies of 1.5 and 4.5 keV for the soft and hard band respectively by running
the tools mkinstmap and mkexpmap.

The 22 level 2 event files are merged together with the tool reproject_obs,
using the reference coordinates of Obsid 21483. The exposure maps are
reprojected onto the reference frame of Obsid 21483 with the tool
reproject_image, and are then added together weighting each map by the
fractional exposure time of the corresponding Obsid. Images for source
detection are created in the 0.5-2 keV, 2-7 keV and total (0.5-7 keV) bands,
with no binning to preserve the full angular resolution of $\sim 1$ arcsec
(FWHM) at the aimpoint (1 pixel corresponds to 0.492 arcsec). The images
include all the CCDs that were ”on” while observing, namely ACIS-S3 (where the
aimpoint is always located), ACIS-S2, ACIS-S4, and ACIS-I3 (except Obsid=898,
in which also ACIS-S5 and ACIS-I2 were on). As the aimpoint is approximately
the same for the 22 Obsid, and considering the geometry of the CCD positions,
the effective exposure is optimal within a radius of few arcmin from the
J1140-2629 position, while it is significantly lower in a wide annulus covered
by the flanking CCDs. We identify a region with a radius of 5 arcmin centered
on J1140-2629, roughly coincident with all the points with an effective area
larger than 240 cm2. This radius corresponds to $\sim 2.5$ Mpc at $z=2.156$.
Within this region, the sensitivity falls by a factor of about two from the
center to the border. Beyond this radius, the flanking CCDs cover a larger
area up to a radius of $\sim 14$ arcmin, but with a much lower sensitivity and
a significantly degraded angular resolution. The two regions drawn on the
monochromatic 1.5 keV exposure map of the field are shown in Figure 2. The
region at off-axis angle between 5 and 14 arcmin is not studied in this work.

Figure 2: Time-weighted, monochromatic exposure map at 1.5 keV of the
Spiderweb Complex field. The maximum value is 470 cm2. The innermost (red)
circle shows the circular region investigated in this work, with a radius of 5
arcmin ($\sim 2.5$ Mpc at $z=2.156$). All the points inside this circle have
an effective area of larger than 240 cm2. The outer annulus, with radii of 5
and 14 arcmin, has a much lower effective exposure, and a degraded angular
resolution, and is not included in the present analysis.

The upper panels of Figure 3 show an image of the central part of the field (a
box $12\times 9$ arcmin by side) in the soft and hard band. The images have
been smoothed with a $\sim 1$ arcsec kernel to emphasize the unresolved
sources. The color scales are the same in both bands (max 200 counts in log
scale) and therefore the larger background in the 2-7 keV band with respect to
the soft 0.5 -2 keV band is noticeable. In the lower panels, close-up images
of the Spiderweb Galaxy (a box of $3\times 2$ arcmin by side, no smoothing
applied) are shown in the soft and hard band. The radio contours in the 10 GHz
band obtained with JVLA (Carilli & Anderson, 2022) are shown in red. Upon
visual inspection, we see that the unresolved sources surrounding the
Spiderweb Galaxy are distributed approximately along the jet directions, as
already noticed for the spatial distribution of the narrow-band selected
sources. Finally, we note that the extended emission in the soft band appears
not only along the jets but also in the direction perpendicular to the jet
axis.

Figure 3:  Chandra X-ray images of the Spiderweb Galaxy field. Upper panels:
Chandra ACIS-S images in the soft 0.5-2 keV (left) and hard 2-7 keV band
(right). A box of $12\times 9$ arcmin by side centered on J1140-2629 is shown.
The images have been smoothed with a $\sim 1$ arcsec Gaussian kernel to
emphasize the unresolved sources. Sources at the outskirts of the image appear
larger due to the effect of the increase of the PSF. Lower panels: Close-up of
the Spiderweb Galaxy ($3\times 2$ arcmin by side) at full angular resolution,
in the soft (0.5-2 keV, left) and hard (2-7 keV, right) band. Extended
emission is clearly visible in both bands. Red contours show radio emission
observed in the 10 GHz band with the JVLA (see Carilli & Anderson, 2022) at
levels of $0.03$, $0.2$, $2$ and $20$ mJy/beam.

To perform spectral analyses, we extract the spectra and compute the ancillary
response file (ARF) and redistribution matrix file (RMF) at the source
position for each observation separately with the commands mkarf and
mkacisrmf. Our default spectral analysis of unresolved sources uses a local
background that, given the small extent of the sources, is directly extracted
from a source-free region on the same chip. This applies both to the
unresolved sources and the diffuse emission. Below, a more careful treatment
is applied to the analysis of the nucleus of the Spiderweb Galaxy, which is
embedded in the diffuse emission. For most of the sources in the field, the
soft and hard band fluxes are estimated simply by converting the count rate
obtained by aperture photometry to energy flux through the conversion factors.
We prefer aperture photometry to a more model-dependent photometry, relying on
the modelization of the point spread function (PSF), because this last
procedure can introduce systematic biasing effects that may be hard to
control. On the other hand, the Poissonian noise associated to aperture
photometry can be handled with simple statistical methods. The fluxes obtained
in this way account for the full uncertainty due to Poisson noise, allowing us
to obtain a reliable measurement for the entire source population across three
orders of magnitude. The derivation of the conversion factors is detailed in
the following subsections.

##  5 X-ray sources in the Spiderweb Complex

In this paper, we focus on the field of view within a radius of 5 arcmin
(corresponding to $\sim 2.5$ Mpc at $z=2.156$) centered on the nucleus of the
Spiderweb, which results in a total of 78.5 arcmin2. This region includes the
solid angle covered by our observation with a sensitivity that is greater than
about half of the highest sensitivity reached at the aimpoint, and with an
angular resolution that is higher than 3 arcsec (FWHM). This allows us to have
a smooth sky coverage, thereby avoiding large corrections when evaluating the
number counts.

###  5.1 X-ray source detection

X-ray source detection was performed with a hybrid procedure combining visual
inspection and a standard detection algorithm (wavdetect). The goal is to
maximize the completeness of the final source list. In the first step, we
considered the entire FOV included in the $\sim 14$ arcmin radius, and
visually identify 238 sources in at least one of the three images (soft, hard,
and total band), with approximate position and size.

We then ran wavdetect999https://cxc.cfa.harvard.edu/ciao/threads/wavdetect/,
setting the scale parameter to scales = "2 4 8 16 32" and the detection
threshold set to sigthresh = 1e-05. This parameter should be approximately
equal to the number of pixels in the image, a choice that implies about one
background fluctuation detected as a source. As we are searching for sources
within 5 arcmin, we have about $1.17\times 10^{6}$ pixels, setting sigthresh =
1e-05 means approximately 12 strong background fluctuations detected as
sources101010https://cxc.cfa.harvard.edu/ciao/ahelp/wavdetect.html#plist.sigthresh.
Our choice is therefore optimal for selection of unresolved sources down to
low signal and low significance, with an acceptable level of contamination.
Considering that our final selection is based on a threshold in the $S/N$ of
aperture photometry, our final list of sources show a significantly higher S/N
than the lower limit of the wavdetect selection, implying a much lower number
of spurious sources with respect to the initial selection. We expect to have a
completeness of very close to unity, particularly in the inner 5 arcmin, where
the angular resolution is a few arcsecs. However, we note that running
wavdetect with pixel scales below and equal to $32$ is less efficient for
detecting extended sources, or sources at off-axis angle $\sim 7$ arcmin and
larger, where the angular resolution of Chandra rapidly deteriorates. As we
focus on the sky region at off-axis angle $<5$ arcmin, this choice does not
affect our results. In addition, visual inspection confirms that there are no
relevant extended sources in the field within 5 arcmin. The extended emission
surrounding the Spiderweb Galaxy will instead be discussed in a separate
publication.

We find 249, 289, and 381 unresolved source candidates in the soft, hard, and
total-band images, respectively, selected by wavdetect. We match the
wavdetect-detected sources with the visually selected sample assuming a
matching radius of 1 arcsec, and collect the wavdetect positions for all the
matched sources, with the exception of the source candidates identified only
by visual inspection. We then obtain a master catalog with 398 sources. All
but 11 of the visually identified sources are recovered by the wavdetect
algorithm, and these latter are at more than 5 arcmin from the Spiderweb, and
therefore have no impact on this work. We define a circular extraction region
for each source to perform aperture photometry. The extraction radius $r_{\rm
ext}$ is computed with a simple relation depending only on the off-axis angle
$\theta$. We set $r_{\rm
ext}=2.55\times(0.67791-0.0405083*\theta+0.0535066*\theta^{2})$ arcsec (see
Rosati et al., 2002, and references therein). We find that this choice ensures
that at least 95% of the expected flux is included in the circular extraction
region, both in the soft and hard band111111For details see
https://space.mit.edu/cxc/marx/tests/PSF.html. We manually adjusted the
position and size of the extraction regions to avoid overlapping of nearby
source candidates: in three cases we manually reduced $r_{\rm ext}$ by one
pixel ($0.5$ arcsec) and shifted the centroid by 1 arcsec; in three other
cases we simply reduced the $r_{\rm ext}$ by three pixels ($1.5$ arcsec). We
verified a posteriori that, on average, the photometry of the six sources
(flagged in Table 7) changes by less than 10%, with a negligible impact on our
final results. The background was estimated locally in an annulus around each
source (outer radius $r_{\rm ext}+3^{\prime\prime}$, inner radius $r_{\rm
ext}+1^{\prime\prime}$) after removing nearby unresolved sources. This choice,
thanks to the depth of the total exposure, ensures a fair sampling of the
background, and takes into account local variation of the background.

We estimated the Poisson probability of being a background fluctuation $P{i}$
for each candidate source $i$ following the procedure described in Puccetti et
al. (2020). First, we computed a radius $r_{\rm max}$ (with $r_{\rm
max}<r_{\rm ext}$) within which the $S/N$ is maximum. We then computed

$P_{i}=e^{-B_{i}}\Sigma_{j=C_{i},\infty}(B_{i})^{j}/j!,$ (1)

where $B_{i}$ is the estimated background counts within $r_{\rm max}$, and
$C_{i}$ is the total counts within $r_{\rm max}$. Puccetti et al. (2009)
showed that assuming $P_{i}<2.0\times 10^{-5}$ ensures a very high
reliability, and so we can use this threshold to select a sample of sources
with a negligible spurious component. On the other hand, computing the
completeness as a function of $P_{i}$ requires extensive simulations to take
into account the sensitivity and the PSF effects across the field of view.
Therefore, for the completeness we prefer to use a criterion directly relying
on the S/N from aperture photometry. This approach has been shown to be
reliable in deep Chandra surveys such as the Chandra Deep Field South (CDFS),
where we adopted a threshold of $S/N>2.0$ to compute the point-source sky
coverage (see Giacconi et al., 2001; Tozzi et al., 2001). In this work we
combine these two criteria to best exploit the sensitivity of the Chandra data
whilst maintaining the very high purity of the sample.

We split our candidate list according to the distance from the Spiderweb
Galaxy, finding 264 candidates at more than 5 arcmin and 134 detection
candidates within 5 arcmin. For the remainder of the paper, we consider only
the candidate detections in the central FOV. We computed $P_{i}$ in the soft,
hard, and total (0.5-7 keV) bands for each source, and consider any source
that satisfies $P_{i}<2.0\times 10^{-5}$ in any of the three bands to be a
detection. This step selects 107 source candidates. We then applied our
completeness criterion $S/N>2.0$, and find that 9 out of 107 sources do not
reach the S/N threshold in any band. However, we find that 5 of them have
$S/N>1.8$ in the hard band, and after a careful revision by visual inspection,
we decided to keep them in the final source list, while discarding the
remaining 4 sources.

In addition, we search for robust candidates that may have been missed by our
reliability criterion by searching for sources with $P_{i}>2\times 10^{-5}$ in
all three bands, but selecting only sources with $S/N>2$ in the soft or hard
bands. We find only four such sources and all have a $P_{i}$ value very close
to our threshold (of the order of $3-4\times 10^{-5}$). After visual
inspection, we decided to include them in the final sample, which, after this
final step, includes 107 sources.

Incidentally, the same selection procedure identifies a final list of 176
sources in the outer ring, which has a field of view 6.8 times larger than the
central 5 arcmin radius circle. This shows that the detected source density in
the outer ring is on average four times lower. Considering that sources at
more than 5 arcmin from the aimpoint have significantly larger errors on
position and photometry due to the rapid degradation of the PSF, and that the
multiwalength data coverage essentially drops at distances $>5$ arcmin, we
strengthen the conclusion that the data quality in the field beyond 5 arcmin
does not allow us to further extend the study of the Spiderweb Complex with
the current dataset. The analysis of the field at distances larger than 2.5
Mpc from the Spiderweb is potentially interesting, in particular to
investigate the possible extension of the Spiderweb Complex at radii larger
than 2.5 physical Mpc, but requires additional data and must be postponed to a
future work.

###  5.2 Measurement of source fluxes

The exposure-corrected count rates are estimated by rescaling the measured net
count rate by the ratio of the exposure map values at the aimpoint to the
emission-weighted exposure within the extraction region. The average
monochromatic exposure map values at the aimpoint are $470.8$ cm2 and $367.4$
cm2 in the soft and hard band, respectively. Soft- and hard-band fluxes are
computed from the net count rates corrected for vignetting and assuming the
typical conversion factors $C_{\rm soft}$ and $C_{\rm hard}$ in the
corresponding band. The conversion factors clearly depend on the spectral
shape, which itself is well known to depend on average on the source flux (see
Tozzi et al., 2001), and can be approximately described with a power law with
a slope in the range $1.2<\Gamma<1.9$. Slopes in the range $\Gamma=1.7-1.9$
are typical of unabsorbed AGN, as measured in deep surveys such as the CDFS
(see Liu et al., 2017, and references therein). Harder spectra are mostly due
to intrinsic absorption, which depends on the intrinsic column density and
source redshift. Clearly, this information is not available for the full
catalog. We proceed by assuming an average redshift of 1.5 (representative of
AGN in the CDFS; see Figure 23 in Luo et al., 2017), and a typical intrinsic
absorption $N_{H}\sim 10^{22}$ cm-2. We find that the conversion factor
obtained with these assumptions, and allowing for at least a factor of three
variation in the average redshift and absorption, is well inside the range
that we obtain assuming $1.2<\Gamma<1.9$. Therefore, without providing a
detailed description of the spectral shape of our unresolved sources, we adopt
the full range $1.2<\Gamma<1.9$ and consider the corresponding variation in
the conversion factors as a systematic uncertainty. This is a fair choice for
the estimation of the source flux and a reliable measurement of the number
counts. The X-ray sources identified as members of the Spiderweb Complex are
further investigated with a detailed spectral analysis (see Section 6.4).

After correcting for a Galactic absorption column density of $N_{\rm
H}=3.18\times 10^{20}$ cm-2, we obtain $C_{\rm soft}=(8.77\pm 0.65)\times
10^{-12}$ cgs/ counts/s in the soft band. In the hard band, we derive two
conversion factors of $C_{\rm hard}=(1.87\pm 0.11)\times 10^{-11}$
cgs/counts/s and $C_{\rm hard}=(2.66\pm 0.35)\times 10^{-11}$ cgs/count/s to
convert from the 2-7 keV count rate to the 2-7 keV and 2-10 keV fluxes,
respectively. We note that we apply a factor 1.05 to account for the average
flux loss outside the extraction region, and also note that while the net
detected counts in the hard band refer to the 2–7 keV energy range, we compute
the energy fluxes in the 2–10 keV band, for a better comparison with the
literature, despite our unresolved sources showing very little signal above 7
keV. The list of 107 sources with X-ray position, net count rate in both
bands, and soft and hard fluxes is shown in Table 7. A negative count rate may
be measured when a source is detected only in one band, in which case we
report the 2$\sigma$ upper limit for the energy flux.

Table 4: Conversion factors

Count rate | Energy | Conversion factor
---|---|---
band (keV) | band (keV) | cgs/counts/s
0.5 - 2.0 | 0.5 - 2.0 | $(8.77\pm 0.65)\times 10^{-12}$
2.0 - 7.0 | 2.0 - 7.0 | $(1.87\pm 0.11)\times 10^{-11}$
2.0 - 7.0 | 2.0 - 10.0 | $(2.66\pm 0.35)\times 10^{-11}$
121212The conversion factors are computed at the aimpoint and corrected for
Galactic absorption. The central value and the associated error correspond to
a power-law spectrum with a slope in the range $1.2<\Gamma<1.9$, as discussed
in the text.

###  5.3 X-ray number counts

To derive the number counts, we first compute the point-source sky coverage as
a function of the energy flux. To do that, we first create images of the soft
and hard background. These are obtained by removing all the detected sources
and replacing the signal in the extraction region with a Poisson realization
of the emission measured in the background annulus. Using the same conversion
factors, and the monochromatic exposure maps, we then compute the solid angle
in which a source of a given soft or hard flux is detected according to our
completeness criterion $S/N>2.0$. As shown in Figure 4, the sky coverage
rapidly drops to zero at fluxes of $1.3\times 10^{-16}$ erg/s/cm2 and
$3.9\times 10^{-16}$ erg/s/cm2 in the soft and hard band,
respectively131313Formally, the flux limit is defined as the flux at which the
sky coverage drops to 1/10 of the full field of view of 78.5 arcmin2.. The
deepest X-ray field to date (and until a new X-ray mission with arcsec
resolution), is provided by the CDFS (Giacconi et al., 2001; Rosati et al.,
2002; Luo et al., 2017) which has reached the unparalleled depth of 7 Ms.
Comparison with the sky coverage of the CDFS shows that the field of view
analyzed in this work is five times smaller than the maximum solid angle
covered in the CDFS. The flux limit is about 13 and 10 times higher than in
the CDFS in the soft and hard band, respectively. We note that the flux limits
of the two fields roughly scale as the ratio of the total exposure times (a
factor of 10), despite the sensitivity loss due to the contamination build-up
over ACIS. This is because we take advantage of the larger effective area of
the back-illuminated CCD in ACIS-S with respect to the front-illuminated CCDs
in ACIS-I (used for the CDFS), partially compensating the sensitivity loss.

Figure 4: Thick lines show the point-source sky coverage of the innermost
region of 5 arcmin of the Spiderweb field investigated in this work, in the
soft (red) and hard (blue) band. Thin lines show the point-source sky coverage
in the CDFS from Luo et al. (2017).

The cumulative number counts (logNlogS) are computed directly as

$N(>S)=\Sigma_{S_{i}>S}{1\over{\Omega_{i}}},$ (2)

where $S_{i}$ and $\Omega_{i}$ are the flux and the corresponding sky coverage
of the $i^{\rm th}$ source, respectively. To compute the soft and hard number
counts, we consider only the sources with $S/N>2$ in the corresponding band.
We select 72 sources in the soft and 96 sources in the hard band, which,
combined together, add up to a total of 107 unique sources within the 5 arcmin
radius.

The soft band logNlogS is shown in Figure 5. The shaded area shows the formal
$1\sigma$ uncertainty obtained as the sum in quadrature of the statistical
error due to the source statistics and the error on the source fluxes. The
last error is in turn the sum in quadrature of the Poissonian photometric
error and the systematic error associated to the conversion factors. The
uncertainty is dominated by the source statistics at large fluxes, and by the
photometric errors at low fluxes. The same figure shows the soft band logNlogS
measured in the CDFS by Luo et al. (2017), and the predicted logNlogS based on
the X-ray background synthesis model developed by Gilli et al.
(2007)141414http://cxb.oas.inaf.it/, see also Hasinger et al. (2005)., which
includes an exponential decline in the AGN space density at redshifts above
$z=2.7$ to cope with the results from wide-area surveys (e.g., SDSS Richards
et al., 2006; Fan, 2006). As the Gilli et al. (2007) model includes only AGN,
we add the steep galaxy number counts as measured by Luo et al. (2017) in the
CDFS (see also Marchesi et al., 2020). Normal (star forming) galaxies are
relevant only at fluxes well below $10^{-16}$ erg/s/cm2, and therefore have a
negligible impact on our results. In particular, the expected contribution of
normal galaxies is equal to that of AGN at $10^{-17}$ erg s-1 cm-2 both in the
0.5-2 keV and 2-7 keV bands (see Figure 31 in Luo et al., 2017). The hard-band
logNlogS is shown in Figure 6. In both cases, we find very good agreement with
the model expectation, while both model and counts in the Spiderweb Field
appear to be $\sim 20$% higher than the CDFS in the soft band at fluxes $\sim
10^{-15}$ erg/s/cm2. The measured counts in the hard band show a $\sim 30$%
excess in a small range around fluxes $\sim 10^{-14}$ erg/s/cm2 with respect
to the model and CDFS. Overall, the logNlogS in the Spiderweb Field appear to
be broadly in line with expectations, with the small hint of an excess on a
limited flux range. Whether or not this excess is related to the presence of
the Spiderweb Complex is investigated in Section 6.

Figure 5: Cumulative number counts in the soft band in the Spiderweb field
within 5 arcmin from the Spiderweb Galaxy (red shaded area). The shaded area
shows the uncertainty due to the combination of source statistics, photometric
errors, and systematic uncertainty on the conversion factors. The blue dashed
line shows the soft counts in the CDFS from Luo et al. (2017). The black solid
line shows the prediction from the AGN model of Gilli et al. (2007) plus the
contribution from normal galaxies from Luo et al. (2017).  Figure 6:
Cumulative number counts in the hard band in the Spiderweb field within 5
arcmin from the Spiderweb Galaxy (red shaded area). The shaded area shows the
uncertainty due to the combination of source statistics, photometric errors,
and systematic uncertainty on the conversion factors. The blue dashed line
shows the hard counts in the CDFS from Luo et al. (2017). The black solid line
shows the prediction from the AGN model of Gilli et al. (2007) plus the
contribution from normal galaxies from Luo et al. (2017).

##  6 Identification of X-ray-emitting protocluster members

On the basis of the shallow Chandra observation (Obsid 898 Pentericci et al.,
2002), only five X-ray sources have been identified among the
spectroscopically confirmed or narrow-band-selected protocluster members.
These sources are firmly identified in the X-ray band as bright AGN in the
2–10 keV luminosity range 0.8-4$\times 10^{44}$ erg s-1. No emission has been
detected from any of the remaining galaxies in the protocluster down to a
rest-frame 2–10 keV luminosity limit of $4\times 10^{43}$ erg s-1. Four out of
these five sources are aligned along the radio and X-ray diffuse emission
(Croft et al., 2005). However, this is not surprising because confirmed and
candidate protocluster members, irrespective of their selection, appear to be
aligned in the same direction as the radio jets and the X-ray emission. The
relatively high AGN fraction estimated around the Spiderweb Galaxy, despite
the low statistics, suggests that the AGN were probably triggered by the
ongoing formation of the protocluster. Another possible mechanism may be
associated to the radio-mode feedback of the central radio galaxy, in a
scenario similar to the observation of the protocluster in the SDSSJ1030 field
(Gilli et al., 2019). However, the extension of the jets in the case of the
Spiderweb Galaxy is limited to less than 100 kpc from the nucleus, making it a
different case with respect to the SDSSJ1030 protocluster, where the jet
extension is significantly larger (about 700 kpc between the two lobes). In
any case, to demonstrate a trigger effect on the protocluster members, it is
necessary to compute the fraction of X-ray-emitting (at the Seyfert level or
higher) members over the entire protocluster population. In this section, we
proceed to identify all the secure X-ray-emitting protocluster members, with
the final goal to estimate the AGN fraction in the Spiderweb system.

###  6.1 Matching X-ray sources to spectroscopic members

We match the X-ray sources with the optical source list, both with
spectroscopic and photometric redshift, or narrow-band-selected sources. Based
on the accuracy of the X-ray centroid and of the error on the position of the
CO-selected sources, and neglecting the errors on the optical and NIR
positions, we assume an initial matching radius of 1 arcsec for optical and
NIR sources, and 2 arcsec for CO sources. Based on these values, we can
immediately compute the expected number of false matches. Considering the
entire FOV (a circle of 5 arcmin radius), and a cross-section of $\pi$
arcsec2, we have a total fractional cross-section of $2.8\times 10^{-3}$ for
the 252 unique sources (including spectroscopic redshifts and narrow-band-
selected members). If the 107 X-ray sources are randomly distributed in this
field of view, the expected number of random matches to protocluster members
(confirmed or candidate) is 0.30. Therefore we expect significantly less than
one spurious counterpart.

We obtain a list of 14 X-ray-emitting protocluster members (including the
Spiderweb), 13 of which matched with members with spectroscopic redshift
(including the Spiderweb), and 1 (XID 73) with an ERO from Kurk et al.
(2004b). Incidentally, we note than none of the ”flies” are X-ray emitting.
This is not surprising, because given the measured mass range
$10^{8}<M_{*}<10^{10}M_{\odot}$ and SFR range $0.5-26\,M_{\odot}$ yr-1 (Hatch
et al., 2009), the corresponding cumulative X-ray emission from star formation
only is estimated to be more than an order of magnitude lower than our current
flux limit. The selected sources were visually checked on the X-ray, HST, and
Subaru images to identify potentially spurious counterparts. We find that all
the counterparts are unique within 1 arcsec except XID 90, which has a
secondary counterpart that has also been selected as an ERO candidate at
$z\sim 2.16$ Kurk et al. (2004b). Therefore, XID 90 may be considered, at
worst, to be another X-ray member candidate without spectroscopic
confirmation, similarly to XID 73.

The scatter plot of the offsets between all the X-ray counterparts and all the
optical matches from the catalogs we used in this work is shown in Figure 7.
The closest counterparts for each single source are marked with a white dot
inside the red (spectroscopic) or green (photometric) point, showing that all
the counterparts are well within 1 arcsec from the X-ray centroid, with most
of them within 0.5 arcsec. We inspected the two sources (XID 12 and XID 80)
that have an offset of $\sim 1$ arcsec, and find that their X-ray centroid is
not coincident with the X-ray peak, but is slightly displaced because of an
apparent extension of the X-ray emission. The signal is too weak to classify
these X-ray sources as extended 151515The extension may be associated to radio
jets, an occurrence that will be tested when the wide-field, high-resolution
radio images are available., but when considering the X-ray peak instead of
the X-ray centroid, the offsets drop below $0.5$ arcsec. Therefore, we find
that, overall, we can safely assume that the offsets between the X-ray sources
and the spectroscopic counterparts can be considered equal to or less than 0.5
arcsec, which brings the expected number of spurious matches below 0.1. We
carefully inspected all the counterparts in the HST and Subaru images, finding
no alternative optical counterpart candidates except those already mentioned.
In the rest of the paper, we consider a sample of 12 X-ray spectroscopically
confirmed members (excluding the Spiderweb) and an additional X-ray color-
selected member candidate. Considering the 112 and 96 spectroscopically
confirmed sources in the range $2.0<z<2.3$ and $2.11<z<2.20$, this corresponds
to a fraction of $11.0\pm 0.5$% and $13.0\pm 0.5$%, respectively. However,
this fraction does not take into account the dependence on the stellar mass,
which is a key quantity that must be considered when computing the AGN
fraction. This aspect is discussed in Section 8.

In Figure 8 we show the X-ray image of the field in the 0.5-7 keV band with
the X-ray-emitting protocluster members marked with blue circles, and all the
spectroscopically confirmed protocluster members marked with red circles. For
better visualization, here we show only a box of $460\times 240$ arcsec
entirely comprised within 5 arcmin from the Spiderweb Galaxy (the FOV we
consider), which includes all but two (which are nonX-ray-emitting) of the
spectroscopic protocluster members. The filamentary distribution appears to be
more evident in the X-ray sources than in the spectroscopically confirmed
members, but given the low statistics, the difference is not significant.

In Figure 9 we plot the azimuthally averaged fraction of sources of a given
class as a function of the distance from the Spiderweb Galaxy, finding that
the protocluster members are clearly more clustered than the bulk of the X-ray
sources. This is not surprising because the clustered distribution of the
spectroscopic members was already noted in all the works listed in Table 2. On
the other hand, when compared to the spectroscopically confirmed protocluster
members, the X-ray-emitting members show only a slightly higher concentration,
which is not statistically significant. This suggests that, based on current
data, there is no evidence of enhanced X-ray activity closer to the Spiderweb
Galaxy. We checked whether or not the 15 sources considered to be part of the
Spiderweb Complex but not in the protocluster (therefore belonging to the
ranges $2.00<z<2.11$ and $2.20<z<2.30$) show a different behavior, but we find
their distribution similar to that of the protocluster members. We note that
our conclusion on the X-ray activity being independent on the distance from
the protocluster center relies on the assumption of spectroscopic
completeness, an aspect that nevertheless cannot be properly quantified given
the composite nature of our spectroscopic sample.

Finally, in Figure 10 we plot the redshift distribution of the X-ray sources
identified as protocluster members including the ERO (magenta filled
histogram) compared to the redshift distribution of all the sources in the
field with spectroscopic redshift in the range $2.0<z<2.3$. The two
distributions are statistically equivalent, showing again that the X-ray-
emitting members are drawn uniformly in redshift among the spectroscopically
confirmed members.

Figure 7: Scatter plot of the offsets for the 13 X-ray sources identified as
members of the Spiderweb Complex, excluding the Spiderweb Galaxy. Red points
corresponds to spectroscopic counterparts, while green points to color-
selected counterparts. The offsets of the closest counterpart for each source
are shown with a white dot inside the red or green points, while other points
corresponds to other counterparts listed in independent catalog from Table 2.
The large red circles correspond to 0.5 and 1 arcsec offsets. Figure 8: Hard
(0.5-7.0 keV) band image of the center of the field (a box of $460\times 240$
arcsec) with the X-ray-emitting protocluster members marked with blue circles,
and all the other spectroscopically confirmed protocluster members
($2.0<z<2.3$) marked with red circles. The image has been smoothed with a 1
arcsec Gaussian filter for clarity. X-ray members are labeled with the source
ID, the original selection: Ha, Lya, ERO, and CO for $H_{\alpha}$,
$Ly_{\alpha}$, red color, and CO-line selection, respectively, and ”spec” for
spectroscopic selection. Finally, the sources labeled with ”X” were previously
identified as X-ray sources in the literature, as described in Section 2.2.
Figure 9: Fraction of sources within a given radius from the Spiderweb Galaxy.
X-ray cluster members (shown in blue) have the same distribution as all the
spectroscopically confirmed protocluster members in the $2.11<z<2.20$ range
(shown in red). On the other hand, the distribution of all the X-ray sources
(dominated by the field) is clearly less clustered. The thin black line shows
a perfectly uniform source distribution. The shaded area corresponds to an
uncertainty of $1\sigma$.  Figure 10: Redshift distribution of the X-ray
sources identified as protocluster members, including the one without
spectroscopic confirmation (magenta filled histogram) compared to the redshift
distribution of all the sources in the field with spectroscopic redshift in
the range $2.0<z<2.3$. The dashed, vertical lines correspond to the
protocluster redshift range.

###  6.2  A note on the X-ray sources not associated to the protocluster

In addition to the X-ray sources identified as cluster members in the
innermost 5 arcmin (13 spectroscopically confirmed, including the Spiderweb
Galaxy, plus 1 color-selected member), we find counterparts for 9 sources with
redshift $z<2$, which are therefore in the foreground (6 of them are
identified in the spectroscopic survey of X-ray sources in the field by Croft
et al. (2005), and 3 are found in NED by chance). In the innermost 5 arcmin,
we have 84 X-ray sources that have no redshift information. Clearly, the most
important question is whether or not we should expect more X-ray-emitting
protocluster members among this set of sources. To give a first-cut estimate,
we report here some preliminary results on the photo-z measurements of $K_{\rm
S}$ band-detected sources in the field (Pannella et al. in preparation)
obtained with the method described in Section 3. Driven by the comparison of
spectroscopic and photometric redshifts in the field, we conservatively
consider all the sources with $1.7<z_{\rm phot}<2.6$ as potentially associated
to the protocluster. We have 20 additional X-ray-emitting sources in this
sample. If we assume a flat distribution of the true redshift in this range,
we expect approximately two additional X-ray sources belonging to the
protocluster ($2.11<z<2.20$).

Also, there are 58 X-ray sources within the central 5 arcmin that are matched
with $K_{\rm S}$ sources with $z_{\rm phot}<1.7$ or $z_{\rm phot}>2.6$. As it
is very unlikely for these sources to have redshift in the protocluster range,
we consider them as foreground and background sources. These leave out 15
X-ray sources without any redshift information. By visual inspection, most of
these sources do not have a possible counterpart in the HST and Subaru images,
and therefore some of them may be high-z sources. Therefore, a reasonable
assumption is to consider that all the 15 sources without any redshift
information are outside the $2.11<z<2.20$ range. We also note that the
fraction of X-ray sources without optical counterparts ($\sim 10\%$) is larger
than that found in deep multiwavelength surveys like the CDFS (a few %). This
effect is not significant and depends on the depth and solid angle of the
available optical and NIR coverage. This aspect will be further investigated
in forthcoming papers (Pannella et al. in preparation).

As a final step, we selected all the $K_{\rm S}$ band detected sources
complementary to the spectroscopy- and narrow-band-selected candidates we
considered in this work and find 380 sources within 5 arcmin with $1.7<z_{\rm
phot}<2.6$. Following the previous argument, we may expect an additional
approximately 38 protocluster members without X-ray emission. If we focus on
sources with ${\rm log}(M_{*}/{\rm M}_{\odot})>10.5$, we may expect about 75%
of these sources above this threshold (see Section 8), therefore an additional
28 protocluster members. In summary, preliminary results on the SED of
galaxies detected in the Spiderweb field show that further spectroscopic
follow-up campaigns may increase the number of protocluster members by a
$\sim$ 20%–30%. Nevertheless, this simple order-of-magnitude estimate of the
X-ray protocluster members that could have been missed is useful to bracket
the AGN fraction and AGN enhancement factor in the Spiderweb protocluster, as
discussed in Section 8 and Section 9.

###  6.3 Number counts in the $2.11<z<2.20$ redshift range

To quantify the overdensity of X-ray sources with respect to the field, we
computed the X-ray number counts separately in a narrow redshift bin centered
on the Spiderweb Galaxy. We decided to adopt the range $2.11<z<2.20$, and
compute the logNlogS inside and outside this redshift range, both in the data
and in the model of Gilli et al. (2007).

The left panel of Figure 11 shows the logNlogS in the soft band after
excluding the X-ray sources identified in the $2.11<z<2.20$ range compared to
the model expectations. We find substantial agreement, with the counts in the
Spiderweb field being slightly below the model, in line with the CDFS data.
The right panel of Figure 11 shows the soft-band logNlogS only for the
redshift interval $2.11<z<2.20$ compared with the expected number counts from
the model (black solid line). A much higher normalization is observed, and a
different slope, showing that the excess is at relatively bright fluxes.
Clearly, the excess above fluxes $10^{-14}$ at soft erg/s/cm2 is merely due to
the presence of the Spidwerweb Galaxy. However, at fluxes $\sim 10^{-15}$
erg/s/cm2 the excess can be robustly estimated and is found to be more than a
factor of $\sim 5$, and more than an order of magnitude at $\sim 10^{-14}$
erg/s/cm2. We find the same behavior in the hard band, as shown in Figure 12.
Also in this case, the excess is more than a factor of $\sim 5$ at fluxes
$\sim 10^{-15}$ erg/s/cm2, and up to $\sim 10$ at $\sim 10^{-14}$ erg/s/cm2.
Finally, we note that the strikingly different slopes in the range
$2.11<z<2.20$ is due to the presence of relatively bright ($\sim 10^{-15}$ erg
s-1 cm-2) sources, which are therefore not affected by any means by our
completeness correction. Therefore, we are able to confirm an excess in the
number of X-ray sources per square degree at the same level estimated from
spectroscopy-, narrow-band-, or color-selected sources. The different shape of
the number counts with respect to the model may be a sign that the X-ray
population in this redshift range is not uniformly extracted from the field
population, but there may be some environmental effect at play.

Figure 11: Soft-band cumulative number counts in different redshift ranges.
Left panel: Soft-band logNlogS in the Spiderweb field (within a radius of 5
arcmin) after excluding the X-ray sources identified in the $2.11<z<2.20$
range compared to the expectations from the model of Gilli et al. (2007) in
the same redshift range. The shaded area corresponds to an uncertainty of
$1\sigma$. Right panel: Soft-band logNlogS in the Spiderweb field only for the
redshift interval $2.11<z<2.20$ compared to the expectations from the model of
Gilli et al. (2007) in the same redshift range. The shaded area corresponds to
an uncertainty of $1\sigma$. We note the different scales between the two
panels.

Figure 12: Hard-band cumulative number counts in different redshift ranges.
Left panel: Hard-band logNlogS in the Spiderweb field (within a radius of 5
arcmin) after excluding the X-ray sources identified in the $2.11<z<2.20$
range, compared to the expectations from the model of Gilli et al. (2007) in
the same redshift range. The shaded area corresponds to an uncertainty of
$1\sigma$. Right panel: Hard-band logNlogS in the Spiderweb field only for the
redshift interval $2.11<z<2.20$, compared to the expectations from the model
of Gilli et al. (2007) in the same redshift range. The shaded area corresponds
to an uncertainty of $1\sigma$. Note the different scales between the two
panels.

###  6.4 Properties of X-ray-emitting protocluster members

We then investigated how different the population of X-ray protocluster
members is with respect to the bulk of the field X-ray sources in the
Spiderweb Galaxy field. As a first check, we plotted the differential
distribution of soft and hard-band fluxes; see Figure 13. We note that in the
soft and hard bands, the distribution of X-ray fluxes of the protocluster
members is slightly shifted towards higher values with respect to the entire
X-ray sample.

Figure 13: Flux distributions. Top panel: Differential normalized distribution
of the soft fluxes in the Spiderweb Galaxy field. The total sample of X-ray
sources is shown with a thin line, while the subsample of the 14 protocluster
members is shown with a thick line. Bottom panel: Same as in the top panel but
in the hard band.  Table 5: X-ray properties of the 14 protocluster members

ID | $N_{H}$ | $\Gamma$ | EW | $L_{X}(0.5-2keV)$ | $L_{X}(2-10keV)$
---|---|---|---|---|---
|  $10^{22}$ cm-2 |  | keV |  $10^{44}$ erg/s |  $10^{44}$ erg/s
7 | $40.1_{-8.4}^{+9.7}$ | $2.00_{-0.28}^{+0.29}$ | $0$ | $3.47\pm 0.33$ | $4.01\pm 0.27$
36 | $1.13_{-1.05}^{+1.16}$ | $1.86_{-0.14}^{+0.15}$ | $0.22_{-0.17}^{+0.20}$ | $1.27\pm 0.08$ | $1.86\pm 0.15$
57 | $<1$ | $1.89_{-0.28}^{+0.30}$ | $0$ | $0.21\pm 0.04$ | $0.28\pm 0.07$
58 | $4.26_{-0.32}^{+0.33}$ | $1.90_{-0.031}^{+0.032}$ | $0.016_{-0.016}^{+0.024}$ | $31.92\pm 0.44$ | $42.85\pm 0.68$
74 | $<2.7$ | $1.59_{-0.20}^{+0.21}$ | $0.47_{-0.31}^{+0.37}$ | $0.17\pm 0.02$ | $0.39\pm 0.07$
75 | $0.33_{-0.32}^{+0.65}$ | $1.83_{-0.09}^{+0.10}$ | $0.07_{-0.07}^{+0.15}$ | $2.05\pm 0.09$ | $3.11\pm 0.17$
80 | $18.0_{-3.9}^{+4.6}$ | $1.96_{-0.20}^{+0.23}$ | $0.34_{-0.12}^{+0.13}$ | $3.26\pm 0.21$ | $4.15\pm 0.25$
86 |  $<2$ ($>150$)∗ | $1.10\pm 0.20$ | $0.51_{-0.32}^{+0.38}$ |  $0.07\pm 0.01$ † |  $0.34\pm 0.05$ †
9 | $<2.2$ | $1.80$ | $-$ | $0.086\pm 0.020$ | $0.135\pm 0.051$
12 | $19.4_{-19.4}^{+19.8}$ | $1.80$ | $-$ | $0.12\pm 0.04$ | $0.18\pm 0.10$
34 | 0 ($>150$)∗ | $-0.76_{-0.84}^{+0.70}$ | $-$ |  $<0.01$ † |  $0.026\pm 0.009$ †
73 | $13.3_{-6.1}^{+7.6}$ | $1.80$ | $-$ | $0.15\pm 0.05$ | $0.23\pm 0.05$
87 | 0 | $2.2\pm 0.4$ | $-$ | $0.18\pm 0.04$ | $0.15\pm 0.09$
90 | $14.8_{-5.8}^{+7.5}$ | $1.80$ | $-$ | $0.18\pm 0.04$ | $0.28\pm 0.07$
161616X-ray properties from the spectral fit for the 14 protocluster members
identified in the X-ray, including the Spiderweb Galaxy (XID 58). The two
sources flagged with the symbol ∗ are considered Compton-thick candidates, and
therefore have an estimated intrinsic absorption $>1.5\times 10^{24}$ cm-2.
The corresponding luminosity values flagged with the symbol † correspond to
the observed luminosity and not to the intrinsic, unabsorbed values, as for
the other sources.

We then proceeded with a standard X-ray spectral analysis of the sources. We
adopted a simple model consisting in an intrinsically absorbed power law,
using the model components zwabs and powerlaw within Xspec. Galactic
absorption is described with the model tbabs, and its value was fixed to
$3.18\times 10^{20}$ cm-2 (HI4PI Collaboration et al., 2016). We also added a
Gaussian line with intrinsic width below the spectral resolution, at an energy
corresponding to the redshift neutral iron Kα line at 6.4 keV rest-frame,
which was allowed to vary in energy by 5% around this interval (corresponding
to a redshift uncertainty of $\Delta z\sim 0.1$). We formally measured the
equivalent width in the observed band of this Gaussian component without
making an attempt to quantify the confidence level of a line detection given
the low signal regime. We leave the two shape parameters $N_{H}$ and $\Gamma$
both free to vary when a source has more than 40 counts in at least one
observed band (0.5-2 keV or 2-7 keV), while we fix $\Gamma=1.8$ in the other
cases. The best-fit values are shown in Table 5. In addition, we performed a
simplified spectral analysis for the remaining six sources, where the
intrinsic spectral slope is frozen to $\Gamma=1.8$, and the intrinsic
absorption is estimated. In Appendix B, we show the spectra of the 8 sources
suitable for spectral analysis, along with the best-fit model, and the spectra
of the fainter 6 sources, despite the coarse binning. In this section, we
discuss the X-ray properties of the 13 protocluster members, while the
Spiderweb Galaxy, apart from a few basic spectral parameters, will be
discussed in a companion paper (Tozzi et al. in preparation).

First, we note that we are able to measure the intrinsic slope with good
accuracy in eight sources, finding an average $\langle\Gamma\rangle=1.75$.
Source XID 86 has un unusual, hard slope (with an hardness ratio $HR\sim 0$)
and a measured equivalent width for the neutral Fe $K_{\alpha}$ line of $\sim
0.5$ keV, close to the value expected for reflection-dominated, Compton-thick
sources (see, e.g., Norman et al., 2002; Gilli et al., 2011; Iwasawa et al.,
2020). We consider it a Compton-thick candidate with $N_{H}>1.5\times 10^{24}$
cm-2. Therefore, the slope of its spectrum is not representative of the
spectral shape of the intrinsic emission. If we exclude this source, we
measure an average intrinsic slope of $\langle\Gamma\rangle=1.86\pm 0.05$, in
line with expectations (see, e.g., Tozzi et al., 2006; Iwasawa et al., 2020).
Another source with an unusually flat spectrum is XID 34. This source is the
faintest among the protocluster X-ray members (17 net counts in the 0.5-7 keV
band) and cannot be meaningfully fitted with a frozen $\Gamma=1.8$. We
tentatively considered it another Compton-thick candidate.

For all the remaining sources, we are able to directly measure the intrinsic
absorption or an upper limit for it. In Figure 14 we show the distribution of
the intrinsic absorption for the 14 protocluster members (including the
Spiderweb Galaxy). We also include upper limits (shown with the dashed
histogram), while we exclude the two Compton-thick candidates. The five
sources (not including the Spiderweb) for which we robustly measure $N_{H}$
unsurprisingly have $N_{H}>10^{23}$ cm-2, which is simply a consequence of the
high-redshift and the low-signal regime. We also show $1\sigma$ upper limits
for six sources, finding values of $N_{\rm H}$ of less than a few times 1022
cm-2. The limited statistics and the low signal prevent us from making any
general conclusions as to the distribution of $N_{\rm H}$ among the
protocluster members. A visual comparison with the distribution of $N_{\rm H}$
expected in the model by Gilli et al. (2007) in the redshift bin $2.0<z<2.2$
(black line) normalized to the number of sources in our small sample suggests
that the number of strongly absorbed sources (7 sources with $N_{\rm
H}>10^{23}$ cm-2) is broadly consistent with that expected in the field at the
same redshift. However, we note that the Compton-thin source with the highest
intrinsic absorption that we are able to measure (XID 7, $N_{\rm H}=4.0\times
10^{23}$ cm-2) is still more than four times less absorbed than the most
absorbed sources detected in protoclusters (see Gilli et al., 2019; Vito et
al., 2020).

Figure 14: Intrinsic absorption in AGN protocluster members. The red histogram
shows the distribution of the intrinsic absorption of the eight protocluster
members (including the Spiderweb) for which a robust measurement of $N_{H}$
has been possible. The blue dashed histogram shows the upper limits on $N_{H}$
obtained for six sources. The black solid line shows the distribution of
$N_{H}$ expected in the model of Gilli et al. (2007) at the flux limit of our
observations. The two Compton-thick candidates with a reflection-dominated
spectrum are not included.

Having the intrinsic absorption, and an estimate of the intrinsic power law,
we can compute the unabsorbed luminosity in the rest frame 0.5-2 and 2-10 keV
bands. The unabsorbed luminosities of all sources but the two Compton-thick
candidates and the Spiderweb Galaxy are shown in Figure 15. All sources have a
rest-frame, hard-band luminosity of greater than $10^{43}$ erg/s. The
luminosity range puts all these sources in the Seyfert regime, far from normal
star forming galaxies. In principle, we may expect obscured star formation at
a high level, up to 1000 $M_{\odot}$/year. Using the average $L_{2-10keV}-SFR$
relation in the redshift range 2.0-2.5 as measured from deep fields by Lehmer
et al. (2016), we obtain $L_{2-10keV}\sim 10^{42}$ and $\sim 10^{43}$ erg/s
for a SFR of 100 and 1000 $M_{\odot}$/yr, respectively. On the other hand,
sources with high intrinsic absorption are unambiguously dominated by nuclear
emission with absorption due to an optically thick torus, while absorption at
the level of $N_{H}\sim 10^{22}$ cm-2 and below can be associated to the
interstellar medium of the host, if sufficiently dense (but see recent results
in Norman et al. 2021, where column densities of $N_{H}\sim 10^{23}$ cm-2 can
be reached at $z\sim 2$). In Figure 16 we plot the intrinsic $N_{H}$ as a
function of $L_{2-10keV}$ and show with green lines the corner where $N_{H}$
and $L_{2-10keV}$ are consistent with being powered by star formation at the
level of 100 and 1000 $M_{\odot}$/yr. We conclude that all the X-ray sources
detected in the protocluster are consistent with being in the Seyfert and QSO
regime.

We made an attempt to detect variations in the average properties of the X-ray
protocluster members as a function of the distance from the Spiderweb Galaxy.
We find that half of the spectroscopically confirmed protocluster members are
distributed within a radius of 90 arcsec (corresponding to $\sim 760$ kpc).
Therefore, we consider the properties of the X-ray-emitting protocluster
members below and above this radius. As already shown in Figure 9, the
distribution of the X-ray sources is very similar to that of all the
spectroscopically confirmed members. The fraction within and beyond 90 arcsec
is $14\pm 5$% and $13\pm 5$%, respectively. If we consider only protocluster
members with $log(M_{*})>10.5$ (see Section 8), we find $33\pm 13$% and $29\pm
12$% within and beyond 90 arcsec, respectively. The X-ray properties do not
change either. The distribution of intrinsic absorption in the two subsamples
is almost exactly symmetric (with one C-thick candidate per side) apart from
source ID=7, which shows the highest measured $N_{H}$ and is the closest to
the Spiderweb. Also, the average soft (hard) band luminosity is
$0.87\,(1.21)\times 10^{44}$ erg/s and $0.82\,(1.1)\times 10^{44}$ erg/s,
within and beyond 90 arcsec, respectively. Our preliminary investigation shows
(possibly) marginally higher X-ray fraction, intrinsic absorption, and lower
luminosities towards the protocluster center. However, this trend, if present,
can only be reliably measured with a much larger sample, implying population
studies of protoclusters with comparable X-ray depth.

Finally, apart from the X-ray-detected sources, we note that there are no
protocluster members that have been identified as AGN from the optical and NIR
spectrum. A detailed discussion of the single sources can be found in Appendix
C.

Figure 15: Distribution of the X-ray luminosity of the 11 protocluster members
(excluding the Spiderweb and the two Compton-thick candidates) in the soft
(thin red line), hard (thin blue line), and total band (thick magenta line).
For clarity, the histograms for the soft and hard luminosities are shifted by
0.05 and 0.1 dex, respectively.  Figure 16: Scatter plot of $N_{H}$ and
$L_{2-10keV}$ for 11 sources (excluding the Spiderweb and the two Compton-
thick candidates). Red circles correspond to measured $N_{H}$ values, while
green triangles to $1\sigma$ upper limits. The green box shows the parameter
space still consistent with star formation at the level of $1000$ M⊙/yr or
$100$ M⊙/yr (vertical dashed line).

###  6.5 Average X-ray properties of X-ray silent, spectroscopic, and color-
selected protocluster members

We investigated the presence of X-ray emission below our detection threshold
in the other spectroscopically identified protocluster members. We extracted a
list of 82 sources with spectroscopic redshift in the range $2.0<z<2.3$ after
removing the sources already detected in the X-ray band, and all the sources
embedded in the diffuse emission close to the Spiderweb Galaxy within a radius
of 12 arcsec (the so called flies). We then used the background images already
used to compute the sky coverage, where all the 107 identified X-ray sources
have already been removed. These soft and hard-band “background-only” images
were obtained simply by cutting out the X-ray-detected sources and replacing
the signal at their position with random noise consistent with the signal in
the annular region surrounding it. These images therefore contain only the sky
X-ray emission from sources below our detection threshold. We then simply
stack the images at the position of the 82 optical sources previously
selected. The resulting images, shown in Figure 17, provide an estimate of the
cumulative emission from spectroscopically confirmed, nonX-ray-detected
protocluster members in the soft and hard band. If we perform a simple
aperture photometry in a circle of 2 arcsec (corresponding to a reasonable
photometric aperture enclosing 95% of the flux in our field), we do not obtain
significant detection in either band, formally measuring $39\pm 30$ and $49\pm
40$ in the soft and hard band, respectively. However, in the total (0.5 - 7
keV) band we have $89\pm 50$ net counts, which formally has a statistical
significance of $\sim 2\,\sigma$. If we consider this as a marginal detection,
after correction for average vignetting ($\sim 5$%), we obtain a soft-band
flux of $\sim 6.2\times 10^{-18}$ erg/s/cm-2 and a hard-band flux of $\sim
1.6\times 10^{-17}$ erg/s/cm-2 per source. Assuming a typical spectrum with
$\Gamma=1.8$ and $N_{\rm H}\sim 10^{22}$ cm-2, this gives an intrinsic, rest-
frame luminosity range of $2.3-3.0\times 10^{41}$ erg/s and $3.6-4.8\times
10^{41}$ erg/s (after correcting for intrinsic and Galactic absorption) in the
0.5-2.0 and 2-10 keV bands, respectively. The average, total band X-ray
luminosity of these sources is therefore well below $\sim 10^{42}$ erg/s,
which in turn corresponds to a maximum SFR of significantly less than $100$
M⊙/yr per source. This shows us that, with current Chandra capabilities, we
can barely detect the average X-ray signal from spectroscopically confirmed
members at the level of approximately one net count in our deep 715 ks
exposure. At the same time, this would imply a widespread star formation
activity at the level of a few tens of M⊙/yr on average for all the
protocluster members, while optical and NIR spectroscopy do not confirm this.
Therefore, if such a weak X-ray signal were confirmed, it may be ascribed to
the combination of low-level nuclear activity and moderate star formation.
Clearly, to explore the low-X-ray-luminosity regime of the bulk of the
protocluster members, we should increase the current exposure by at least a
factor of five. This would allow us to explore the star formation regime
corresponding to $20-50$ M⊙/yr in each single source, implying that all the
strong-starburst galaxies may be detected. We conclude that X-ray silent
spectroscopic members do not contribute to the AGN luminosity function of the
protocluster, but they may be hosting starburst events or low-level AGN
activity. This is currently beyond the capability of Chandra (considering
regular and large programs) and it definitely constitutes an interesting
luminosity range to be explored by future high-angular-resolution X-ray
missions, such as Lynx (The Lynx Team, 2018) and AXIS (Mushotzky & AXIS Team,
2019; Marchesi et al., 2020).

Figure 17: Stacked X-ray images. Left panel: Stacked image of the 82
spectroscopically confirmed protocluster members in the soft band. The size of
the cutout is $20\times 20$ arcsec, while the red circle shows the 2 arcsec
radius region used to perform aperture photometry on the stacked image. Right
panel: Same as in the left panel but in the hard band.

We then applied the same procedure to the 81 color- or narrow-band-selected
sources that have no X-ray detection, and find similar results, possibly with
a more convincing detection in the soft band, as shown in Figure 18. The usual
aperture photometry within a circle of 2 arcsec provides $60\pm 30$ net counts
in the soft band, and therefore a formal detection at $2\sigma$. The soft band
photometry corresponds to a soft flux of $(9.4\pm 5)\times 10^{-18}$
erg/s/cm-2, and, assuming the usual mildly absorbed power law and $z=2.156$,
to a luminosity of $(3.6\pm 1.8)\times 10^{41}$ and $(5.6\pm 2.8)\times
10^{41}$ erg/s per source in the soft and hard band, respectively. This
luminosity range is typical of starburst galaxies with SFR of the order of
$30-50$ M⊙/yr. In the hard band, we obtain only an upper limit (formally the
photometry gives $13\pm 39$ net counts), which translates to $2\sigma$ upper
limits of $4.0\times 10^{41}$ and $6.0\times 10^{41}$ erg/s per source in the
soft and hard band, respectively. This tells us that the average source is
softer than the adopted, AGN-like model. Despite the small signal obtained in
the soft band, we further split the 81 color- or narrow-band-selected sources
without X-ray detection into four subsamples according to their selection
criteria: $H_{\alpha}$ emitter, $Ly_{\alpha}$ emitter, ERO (Kurk et al.,
2004b), and photo-z (Dannerbauer et al., 2014; Shimakawa et al., 2018; Tadaki
et al., 2019). We find 1 $\sigma$ positive photometry in the soft band for
$Ly_{\alpha}$ (13)- and ERO (29)-selected sources, and 1.5 $\sigma$ positive
photometry for photo-z (30). In the hard band we have both positive and
negative photometry. Therefore, the $2\sigma$ signal in the soft band is
confirmed, and is contributed mostly by the 30 protocluster member candidates
selected by photo-z. However, we have no control on the contamination of this
list of protocluster member candidates. This aspect, coupled to the large
statistical uncertainty associated to stacked emission measurements, hampers
any conclusion on the X-ray emission from color-selected protocluster member
candidates, except that we do not expect them to host significant nuclear
activity.

Our general conclusion is that there is no significant X-ray emission that we
have missed so far among all the confirmed or candidate protocluster members
that have not been X-ray detected. However, the obtained marginal detections
confirm that potentially we are able to detect star formation in the
protocluster galaxies at the level of $\sim 30-50$ M⊙/yr by stacking their
X-ray emission. Additional work must be done before we can draw any strong
conclusion, in particular it is necessary to increase the number of
spectroscopically confirmed members by more than a factor of two. From this
perspective, future observations of this target with JWST and further
spectroscopic follow-up may have strong synergy with the available X-ray data
and reveal further relevant properties of the galaxy population in the
Spiderweb protocluster.

Figure 18: Stacked X-ray images. Left panel: Stacked image of the 81 color- or
narrow-band-selected protocluster member candidates in the soft band. The red
circle shows the 2 arcsec radius region used to perform aperture photometry on
the stacked image. Right panel: Same as in the left panel but in the hard
band.

##  7 X-ray luminosity function of protocluster members

To compute a cumulative luminosity function in the protocluster region, we
need a comoving volume representative of our sample. If we consider the
comoving volume corresponding to a circle of 5 arcmin centered on the
Spiderweb Galaxy, and the difference in the comoving radial distance between
$z=2.11$ and $z=2.2$, we find a value of $2.584\times 10^{4}$ Mpc3. The
comoving mass corresponding to this volume in the assumed cosmology is $M_{\rm
com}=1.05\times 10^{15}M_{\odot}$, which is in the range of predicted virial
mass at $z=0$ for the Spiderweb protocluster. However, this is rather a lower
limit to the mass included within a radius of 5 arcmin, because the central
part of the protocluster is definitely overdense with respect to the ambient
cosmic density.

Second, we need an estimate of the intrinsic luminosity of the Compton-thick
candidates. As mentioned above, the luminosity values listed in Table 5 for
XID 86 and XID 34 simply refer the observed luminosity that, in the case of a
reflection-dominated spectrum, is only a fraction of the intrinsic power. We
conservatively assume that the observed hard (2-10 keV) luminosity is $\sim
10$% of the intrinsic one (corresponding to the upper envelope of the values
observed for local Compton-thick AGN; see Marchesi et al., 2019; Zhao et al.,
2021), and that the soft-band luminosity is 1.6 times the hard-band
luminosity, roughly corresponding to a power-law spectrum with $\Gamma=1.8$.
This very crude approximation allows us to obtain a first-order estimate of
the intrinsic luminosity of the two Compton-thick candidates, and therefore to
have the soft- and hard-band luminosities for all the 13 protocluster members.

Finally, we need to include the sky coverage correction in the luminosity
function. We collected the weight factor corresponding to the soft- and hard-
band fluxes of each source, which is similar to our method used to compute the
number counts. We then considered the smallest weight for each source,
computed according to Equation 2. Given the relatively high luminosities of
the protocluster members, we only have a small ($\sim 1.15$) correction for
the two faintest sources (XID 12 and XID 34). For the sake of clarity, we note
that their S/N in the corresponding detection bands is $\sim 3$, which is far
enough from the detection limit and therefore corresponds to a very mild sky
coverage correction.

In Figure 19 we show the cumulative rest-frame luminosity in the soft and hard
band after excluding the Spiderweb Galaxy. In both cases we show this
luminosity with and without the two Compton-thick candidates, given the large
uncertainties in their estimated luminosities. We also plot the cumulative
luminosity function predicted at $z\sim 2.2$ in the model of Gilli et al.
(2007). As expected, the excess measured in the Spiderweb protocluster volume
is consistent with the excess previously measured in the number counts. The
excess is always about an order of magnitude at the lowest end and increases
with luminosity, reaching a factor of 20 and beyond at $L_{X}\sim 10^{44}$
erg/s in both bands. This is also clear in Figure 20, where we show the ratio
of the X-ray AGN luminosity function in the Spiderweb protocluster to the
field luminosity function in the field from the model by Gilli et al. (2007).
To compute the ratio we include the Compton-thick candidates. Removing them
will result in a lower excess, decreased by a factor of $\sim 1.5$, as shown
in Figure 19. As discussed above, this excess is due to the combination of the
average galaxy overdensity in the protocluster region and the enhancement
factor. In Section 9, we provide an estimate of the enhancement factor alone.

Figure 19:  AGN luminosity functions. Left panel: Cumulative rest-frame, soft-
band luminosity function of the AGN in the Spiderweb protocluster normalized
to the comoving volume defined by $2.11<z<2.20$ shown by the red, solid line
with the red-shadowed area, and a circle of 5 arcmin centered on the Spiderweb
Galaxy. The cyan solid line with the pink-shadowed area is the same without
the luminosity correction for the two C-thick candidates. The black solid line
is the XLF in the field from the model of Gilli et al. (2007). Shaded areas
correspond to $1\,\sigma$ uncertainty. The Spiderweb Galaxy is not included in
the luminosity function. Right panel: Same as left panel but in the rest-
frame, 2-10 keV hard band.  Figure 20: Ratio of the soft and hard band X-ray
AGN luminosity functions in the Spiderweb protocluster to the field luminosity
function from the model by Gilli et al. (2007).

##  8 AGN fraction in the Spiderweb protocluster

The measurement of the AGN fraction as a function of the environment is an
important observable that can provide insight into the SMBH feeding
mechanisms. Several studies in the X-ray band have been performed for
relatively low redshift in massive systems. Typically, the AGN fraction among
cluster members increases with distance from the center, and reaches values
comparable with the field (of the order of $\sim 1$%) when considering the
full X-ray luminosity range ($10^{41}$-$10^{44}$ erg/s), or significantly
lower than the field when focusing on luminosities $>10^{43}$ erg/s (see
Puccetti et al., 2020, and discussion therein). Overall, the X-ray nuclear
emission in cluster galaxies (with the noticeable exception of the central
galaxy) is expected to be triggered by interactions (see Ehlert et al., 2015),
or by ram pressure in the outskirts (Poggianti et al., 2017), while several
other mechanism are contributing in the field. The situation is expected to be
significantly different in protoclusters, where the lower density of galaxies,
the different velocity distribution, and the much larger availability of cold
gas, may contribute to produce an AGN fraction that is significantly larger
than in the field. Here we focus on the AGN fraction, and try to compare the
results we obtained in the Spiderweb Complex with the literature, focusing on
the best-studied protoclusters.

The first aspect to notice is that the presence of activity (star formation
and/or nuclear) in galaxies has some dependence on the environment and on the
cosmic epoch at the same time. The two dependencies cannot be easily
decoupled, because the main characteristics of dense environments change with
epoch as well. Locally, it is well established that star formation and nuclear
activity —at least at the bright end— are suppressed in dense environments
such as massive, virialized halos. At the same time, the AGN fraction seems to
increase in cluster progenitors at redshift $z\geq 2$ (Martini et al., 2013;
Alberts et al., 2016; Kalita et al., 2021), while several studies have found
intense star formation in at least some cluster cores at $z\geq 1.5$ (Tran et
al., 2010; Brodwin et al., 2013; Santos et al., 2014, 2015; Coogan et al.,
2018), suggesting an inversion of the SF-density anticorrelation observed in
local clusters. An important aspect is the large diversity among the cluster
population in the range $1.5<z<2.0$, with some of them hosting passive evolved
galaxies, and some a rapidly evolving active population.

This is consistent with an increase (possibly a co-evolution) of SF and AGN in
massive halos in the range $1.5<z<2.0$ when approaching their formation epoch.
At present, we do not have a comprehensive understanding of how the connection
between AGN activity and large-scale galaxy environment proceeds with
redshift. This connection may be particularly effective when entering the
regime of protoclusters. The deep Chandra observation of the Spiderweb Complex
presented in this work gives us the possibility to measure the X-ray AGN
fraction in a protocluster environment, and the X-ray AGN enhancement factor
with respect to the field at the same redshift. Clearly, the member galaxy
selection is key in this case, because protocluster members are usually picked
up from a selection of Ly$\alpha$ emitters, or from color–color-selected
subsamples, potentially introducing a bias associated to galaxy type. Here, a
convenient parameter is the stellar mass.

We recall that the fraction of X-ray AGN among Ly$\alpha$ emitters is usually
low, both in the field and in protoclusters (see, e.g., Malhotra et al., 2003;
Zheng et al., 2016). However, several works have claimed that there is
enhanced nuclear activity in massive protoclusters. Apart from early claims in
the Spiderweb based on two spectroscopically confirmed X-ray-detected AGN and
three X-ray member candidates (Pentericci et al., 2002), a high AGN fraction
at the level of $15-20$% has been found in 2QZ (Lehmer et al., 2013) at $z\sim
3$, DRC at $z\sim 4$ (Vito et al., 2020), and at lower redshift in
Cl0218.3-0510 at $z=1.62$ (Krishnan et al., 2017). Recently, AGN identified
through optical spectroscopy of X-ray data in the Planck-selected protocluster
at $z\sim 2.16$ have been shown to amount to $(20\pm 10)$% of all the
identified protocluster members (Polletta et al., 2021). In all cases, the
limited statistics make the uncertainty on the AGN fraction significantly
larger than $30\%-50$%. On the other hand, other protoclusters in the range
$2<z<3$ appear to have a significantly lower fraction, implying an enhancement
factor consistent with unity (Lehmer et al., 2009; Digby-North et al., 2010;
Macuga et al., 2019). The fraction of X-ray-emitting AGN in protoclusters
measured so far in the literature is shown in Table 6.

Table 6: X-ray AGN fraction in a sample of protoclusters Protocluster | z | X-ray AGN fraction | Ref
---|---|---|---
Cl0218.3-0510 | 1.62 |  $17^{+6}_{-5}$% | Krishnan et al. (2017)
Spiderweb | 2.156 |  $25.5\pm 4.5$% | This work
PHz G237.01 | 2.16 |  $20\pm 10$% | Polletta et al. (2021)
2QZ | 2.23 |  $17^{+16}_{-9}$% | Lehmer et al. (2013)
HS1700 | 2.3 |  $2.9^{+2.9}_{-1.6}$% | Digby-North et al. (2010)
USS 1558-003 | 2.53 |  $2.0^{+2.6}_{-1.3}$% | Macuga et al. (2019)
SSA22 | 3.09 |  $5.1^{+6.8}_{-3.3}$% | Lehmer et al. (2009)
DRC | 4.002 |  $15^{+20}_{-10}$% | Vito et al. (2020)
Figure 21: Distribution of $M_{*}$ among the protocluster members in the
redshift range $2.11<z<2.20$ (red histogram) and among the X-ray-emitting
members (blue histogram). The first bin ($9.5<{\rm log}(M_{*})<10.0$) is an
upper limit where we include all the sources that do not have a $K_{\rm
S}$-band counterpart in our image.

To measure the AGN fraction in the Spiderweb protocluster, we need to control
the selection in stellar mass. As detailed in Section 3, we estimated stellar
masses $M_{*}$ for about 80% of the sample. Among the 96 protocluster members
($2.11<z<2.20$), we have a robust measurement of $M_{*}$ for 62 of them, while
34 are not detected. We assume a nominal upper limit of ${\rm log}(M_{*}/{\rm
M}_{\odot})=10$ (which is irrelevant in this work). We note that most of the
sources without a $K_{\rm S}$ counterpart are from the COALAS survey. In fact,
from Table 3 of Jin et al. (2021), we notice that half of them are not
detected in the $K_{\rm S}$ band, while 90% of them are detected in the $I$
band, and therefore these sources should correspond to relatively low-mass
galaxies.

The distribution of $M_{*}$ in the protocluster is shown in Figure 21. We note
that we include all the sources that do not have a $K_{\rm S}$ band
counterpart in our image in the first bin $9.5<{\rm log}(M_{*})<10.0$. This is
clearly an oversimplification but has no effect on our results. Ideally, we
may compute an AGN fraction as a function of $M_{*}$, but given the low
statistics, we simply consider all the sources with ${\rm log}(M_{*}/{\rm
M}_{\odot})>10.5$. For completeness, we briefly discuss preliminary results on
the distribution of protocluster sources in the $L_{X}-M_{*}$ plane in Section
D. Finally, we reiterate that, apart from the X-ray-detected sources, there
are no protocluster members that have been identified as AGN from the optical
and NIR spectrum. Therefore, excluding the Spiderweb Galaxy, we have 13 X-ray
AGN (11 excluding the source with a photometric counterpart and the one with a
double counterpart) over a total of 44 sources for an X-ray AGN fraction with
$L_{2-10keV}>10^{43}$ erg/s of $29.5$% ($25$%). To bracket this value, we
consider a maximum of $\sim 28$ additional members, two with X-ray emission,
as discussed in Section 6.2. Their inclusion would bring the AGN fraction to
$21$%. Considering this as a lower limit, we can estimate the AGN fraction in
the Spiderweb protocluster as $25.5\pm 4.5$%, where the error bar also
accounts for the maximum systematic uncertainty. We stress that the
uncertainty we quote here, based on the photometric study of Pannella et al.
(in preparation), also includes the effect of the different area coverage
between X-ray data and spectroscopic or color/emission line selection. A
detailed treatment of the effects of the protocluster member selection within
5 arcmin would imply a significant additional effort and would only mildly
reduce the uncertainty we have estimated.

As shown in Table 6, this value is somewhat higher but consistent with the
measurement from Krishnan et al. (2017) at $z=1.62$ and to the highest values
found at $2<z<4$ by Lehmer et al. (2013, 2QZ), and by Vito et al. (2020,
DRC)171717We note that Vito et al. (2020) considers only X-ray selection among
submm-detected galaxies, revising for example the value found in SSA22 to
$50^{+39}_{-24}$%.. Three different works instead find values in the range of
2%–5%, within an uncertainty of a factor of 2. We plot these values in Figure
22, where the measurement in this work is marked with a blue dot. We present
this plot simply to compare the different values obtained in the literature so
far, with no attempt to explore a possible behavior with redshift. The main
problem with the measurement of the evolution of the AGN fraction in
protoclusters is that these values were obtained from data with different
X-ray depth and different selection for the protocluster membership; the first
aspect is not an issue, because all the medium-deep Chandra data used in these
works reach luminosity levels of $\sim 10^{43}$ erg/s in both bands. On the
other hand, we lack an homogeneous and complete selection of the protocluster
members in the optical. As of today, the only robust constraint on the
evolution of the X-ray AGN fraction is a clear increase from the low local
values at the level of $1$% to $>10$% in a few protoclusters at $z>2$. Similar
but slightly larger uncertainties are found for the enhancement factor, which
is discussed in the following section.

Figure 22: Fraction of X-ray AGN over the total number of identified
protocluster members from Table 6. The Spiderweb Protocluster is marked with a
blue dot. The plot is meant to show measurements of the AGN fraction available
in the literature, and necessarily includes measurements for different
populations and different stellar mass ranges.

##  9 AGN enhancement factor in the Spiderweb protocluster

To compare the AGN fraction in the Spiderweb protocluster with that in the
field, we refer to the few works in the literature that provide an estimate of
this latter, key quantity. Lehmer et al. (2009) estimate an average fraction
of $1.9^{+2.6}_{-1.3}$% and $0.7^{+1.6}_{-0.6}$% from $z\sim 2-3.4$ Lyman
Break Galaxies and $z=3.1$ Ly$\alpha$ emitters in the CDF + SSA22 field,
respectively, for ${\rm log}(M_{*}/M_{\odot})>10.5$. These values were
obtained for $\log(L_{8-32keV})>43.5$, which, for a power law with
$\Gamma=1.8$, corresponds to $\log(L_{0.5-10keV})>43.66$. Only seven sources
satisfy this threshold, or nine if we consider the Compton-thick candidates
and assume that the hard-band intrinsic luminosity is ten times the observed
one. Therefore, the fraction of AGN with $\log(L_{0.5-10keV})>43.66$ in our
spectroscopic sample is $18.0\pm 2.0$%. In this case, we find the enhancement
factor for $\log(L_{0.5-10keV})>43.66$ in the Spiderweb protocluster to be
$f_{\rm enh}=9.5^{+16}_{-4.0}$ or $f_{\rm enh}=26^{+100}_{-16}$, depending on
the assumed field value.

Another estimate of the field X-ray AGN fraction is provided by Lehmer et al.
(2013), who use an independent sample of $z=2.216-2.248$ HAEs from the High
Redshift Emission Line Survey (HiZELS) in the wide-area $\sim 1.6$ deg2 COSMOS
survey field (Sobral et al., 2013). Lehmer et al. (2013) found 10 Chandra
sources matched to the 210 HiZELS HAEs within the C-COSMOS footprint, giving
an AGN fraction in the low-density environment of $3.0^{+4.0}_{-2.0}$%. The
COSMOS flux limit of $1.3\times 10^{-15}$ erg/s/cm2 in the 0.5–10 keV (see
Marchesi et al., 2016) corresponds to $L_{0.5-10keV}\sim 4\times 10^{43}$
erg/s. This limit is equivalent to that previously used for a comparison with
LBG and HAE sources in the CDF + SSA22 field. In this case, the enhancement
factor is found to be $6.0^{+9.0}_{-3.0}$.

Previous estimates of the enhancement factor range from $2.1\pm 0.7$ (Krishnan
et al., 2017) to $3.5^{+3.8}_{-2.2}$ (Lehmer et al., 2013) and
$6^{+10.3}_{-3.6}$ (Lehmer et al., 2009), in broad agreement with our results.
However, as mentioned above, there are works that measure substantially lower
X-ray AGN fractions in protoclusters, concluding that there is no enhancement
with respect to the field (Digby-North et al., 2010; Macuga et al., 2019).
This difference may simply reflect the diversity among protoclusters and their
different dynamical stage, as expected in such a rapidly evolving phase.

In all these cases, the uncertainties on the AGN fraction in the field clearly
dominate the error budget. Nevertheless, we find that we always obtain an
enhancement factor in the range 5-20 for X-ray AGN with $L_{0.5-10keV}>{\rm
few}\times 10^{43}$ erg/s and ${\rm log}(M_{*}/{\rm M}_{\odot})>10.5$. On the
other hand, it is well known that the enhancement factor drops below 1 in all
the virialized halos at relatively low redshift ($z<1$), except in the cluster
outskirts (Koulouridis & Bartalucci, 2019). Therefore, we confirm the
existence of a strong evolution of the X-ray AGN enhancement factor in the
central regions of clusters and protoclusters with redshift. However, we do
expect to also see a strong dependence on the environment, and therefore a
large diversity among the observed protoclusters, as probably suggested by the
different conclusions on the enhancement factor at $z>2$ presented in the
literature. Only by disentangling the complex pattern due to the combination
of environmental effects and cosmic evolution can we hope to reach a
comprehensive picture of the galaxy population evolution in clusters.

##  10 Future perspectives

There are several promising approaches to extending this work in order to gain
further insight into the evolution of nuclear activity in protoclusters and
connect it to the dearth of activity in virialized, mature clusters. In
addition to the difficult characterization of the protocluster candidates
already discussed in Sect. 1, the first obvious key aspect is the selection of
the protocluster members, which largely differ among the few cases presented
in the literature. Ideally, the protocluster membership should have a well-
defined completeness as a function of stellar mass and distance from the
center. Stellar mass should be used to compute AGN fraction above a given mass
limit (typically, $M_{*}>{\rm few}\times 10^{10}M_{\odot}$). The information
on the stellar mass of the active galaxies may also provide clues as to the
physical mechanisms that trigger the activity. Krishnan et al. (2017) explore
the distribution of the stellar mass of the X-ray-emitting AGN in the field
and in protoclusters, and find no differences. These authors suggest that
triggering mechanisms are similar in both environments and that the higher
X-ray AGN fraction in protoclusters is simply due to the same mechanism
occurring more frequently because of the denser environment. However, Monson
et al. (2021) recently speculated that the enhanced AGN fraction in the
protocluster SSA22 at $z=3.1$ is due to the larger masses (a factor of 2) of
the LBG with respect to the field rather than an enhanced merger activity.
This issue is also relevant for the process quenching the rapidly star forming
galaxies that are observed as quiescent galaxies in the protocluster, forming
the mentioned nascent red sequence. Similarly, a census of the nuclear
activity in the radio band is needed to complete the picture offered by the
X-ray data and provide robust constraints on the feedback processes in the
member galaxies.

Focusing on the Spiderweb protocluster, we foresee the following next steps.
First, an extension of the protocluster membership based on NIR images and
eventual spectroscopic follow-up, to achieve a well-defined and complete
stellar-mass function. Then, a detailed investigation of the archival high-
resolution HST data, that, coupled to the submm data, may provide clues as to
the role of interactions and/or the presence of cold gas in triggering nuclear
activity. Finally, we plan to exploit new radio data in the L band with JVLA
and GMRT to characterize the protocluster population in this band.

Such efforts would make the Spiderweb an ideal science case for the study of
protoclusters. In this respect, the role of X-ray data with high-angular
resolution will be key for the extension of this approach to a large sample.
Currently, Chandra is the only facility that can provide data of the required
quality. The future of this science case heavily depends on the future of
high-resolution X-ray astronomy, which is currently embodied in the Lynx (The
Lynx Team, 2018) and AXIS (Mushotzky & AXIS Team, 2019) mission concepts.

##  11 Conclusions

We present the deep (715 ks) X-ray observation of the radio galaxy J1140-2629
(the Spiderweb Galaxy) and the surrounding large-scale structure with Chandra.
The deep X-ray data allow us to map the nuclear activity in a dense
environment down to the low-luminosity end of the Seyfert galaxy population,
and to test whether dense large-scale structure environments enhance X-ray
nuclear activity, a phenomenon that has been investigated only recently at
such a high redshift and only with shallower X-ray data. In addition, the
sensitivity and exquisite angular resolution of Chandra allow us to
characterize the extended emission around the Spiderweb Galaxy and possibly
identify thermal X-ray emission from the ICM, a key piece of information with
which to constrain both the dynamical state of the protocluster and the
feedback mechanism at work in the Spiderweb complex, and ultimately, to
provide an overview of the baryon cycling in such an active environment at
$z\sim 2$. In this first paper, we focus on the nuclear activity of the
galaxies in the Spiderweb protocluster, exploiting the combination of our deep
X-ray data in the field and the large body of multi-wavelength and
spectroscopic data available from the literature. The main results and the
data products used in this work are made available on the project
webpage181818http://www.arcetri.inaf.it/spiderweb/. Our results can be
summarized as follows:

  * •

We identify 107 X-ray sources within a radius of 5 arcmin centered on the
Spiderweb Galaxy, down to flux limits of $1.3\times 10^{-16}$ erg/s/cm2 and
$3.9\times 10^{-16}$ erg/s/cm2 in the soft and hard band, respectively. We
compute the cumulative number counts which are found to be consistent with
results from X-ray deep fields in the literature.

  * •

We identify 13 X-ray sources with spectroscopically confirmed counterparts
belonging to the Spiderweb Complex (including the Spiderweb Galaxy itself) and
1 with a color-selected member candidate. As these sources are found in the
redshift range $2.11<z<2.20$, we classify them as protocluster members (as
opposed to member of the Spiderweb Complex, which includes a larger redshift
window $2.0<z<2.3$). The X-ray-emitting protocluster members are distributed
over an approximately rectangular region with $\sim 3.2$ and $1.3$ Mpc by
side.

  * •

The X-ray spectral analysis finds five strongly absorbed AGN ($N_{H}>10^{23}$
cm-2), two sources with flat spectra, which we classify as Compton-thick
candidates with reflection-dominated spectrum, and seven sources with moderate
or low absorption. After correcting for Galactic and intrinsic absorption, and
with an educated guess for the intrinsic luminosity of the two Compton-thick
candidates, the rest-frame 0.5-10 keV luminosities are found to be above
$10^{43}$ erg/s for all the sources. By combining intrinsic absorption and
intrinsic luminosities, we conclude that all the X-ray-emitting protocluster
members are powered by nuclear activity. We do not find hints of a change of
the X-ray properties of the protocluster members with the distance from the
Spiderweb Galaxy.

  * •

We stack the images of all the X-ray silent, spectroscopically confirmed
members, finding a marginal detection corresponding to average luminosities
below $\sim 10^{41}$ erg/s, showing that there is no significant nuclear
activity at about one order of magnitude below our detection threshold. A
slightly stronger detection is obtained for the stacked emission of the color
or narrow-band selected members, consistent with being powered by star
formation at the level of $30-50$ M⊙/year, but the unknown contamination
fraction prevents us from deriving robust conclusions on their nature.

  * •

The X-ray luminosity function of AGN in the volume associated to the Spiderweb
protocluster is more than an order of magnitude larger than in the field at
the same redshift in the range $10^{43}<L_{X}<10^{44}$ erg/s in both bands,
and significantly flatter, implying an increasing excess at the bright end.

  * •

For $L_{2-10keV}>10^{43}$ erg/s, we measure an X-ray AGN fraction of $25.5\pm
4.5$% among galaxies with ${\rm log}(M_{*}/M_{\odot})>10.5$, which is higher
but still consistent with the values found at least in four protoclusters at
similar redshift.

  * •

The measured AGN fraction in the Spiderweb protocluster at
$L_{0.5-10keV}>4\times 10^{43}$ erg/s corresponds to an enhancement factor