# Conditions for direct black hole seed collapse near a radio-loud quasar 1
Gyr after the Big Bang

Roderik A. Overzier Observatório Nacional/MCTIC, Rua General José Cristino,
77, São Cristóvão, Rio de Janeiro, RJ 20921-400, Brazil  Institute of
Astronomy, Geophysics and Atmospheric Sciences, University of São Paulo, Rua
do Matão, 1226, São Paulo, SP 05508-090, Brazil

###### Abstract

Observations of luminous quasars and their supermassive black holes at
$z\gtrsim 6$ suggest that they formed at dense matter peaks in the early
universe. However, few studies have found definitive evidence that the quasars
lie at cosmic density peaks, in clear contrast with theory predictions. Here
we present new evidence that the radio-loud quasar SDSS J0836+0054 at $z=5.8$
could be part of a surprisingly rich structure of galaxies. This conclusion is
reached by combining a number of findings previously reported in the
literature. Bosman et al. (2020) obtained the redshifts of three companion
galaxies, confirming an overdensity of $i_{775}$-dropouts found by Zheng et
al. (2006). By comparing this structure with those found near other quasars
and large overdense regions in the field at $z\sim 6-7$, we show that the SDSS
J0836+0054 field is among the densest structures known at these redshifts. One
of the spectroscopic companions is a very massive star-forming galaxy
($\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})=10.3_{-0.2}^{+0.3}$) based
on its unambiguous detection in a Spitzer 3.6 $\mu$m image. This suggests that
the quasar field hosts not one, but at least two rare, massive dark matter
halos ($\mathrm{log}_{10}(\mathcal{M}_{h}/M_{\odot})\gtrsim 12$),
corresponding to a galaxy overdensity of at least 20. We discuss the
properties of the young radio source. We conclude that the environment of SDSS
J0836+0054 resembles, at least qualitatively, the type of conditions that may
have spurred the direct collapse of a massive black hole seed according to
recent theory.

Radio loud quasars (1349), Galaxy environments (2029), Lyman-alpha galaxies
(978), High-redshift galaxies (734), Reionization (1383), Black holes(162)

††facilities: HST(ACS), Spitzer(IRAC)††software: astropy (Astropy
Collaboration et al., 2013, 2018), CosmoCalc (Wright, 2006), BagPipes (Carnall
et al., 2018), Source Extractor (Bertin & Arnouts, 1996), Colossus (Diemer,
2018)

##  1 Introduction

Since their discovery, the study of luminous quasars within the first billion
years of cosmic time has intersected with numerous areas in astrophysics from
black holes to cosmology (Fan et al., 2000). Although they are the most
luminous hydrogen-ionizing photon producing sources at their epoch, their
relatively low number density impies that they probably did not play a major
role in driving the overall reionization of the universe (Bouwens et al.,
2015). Ironically, however, their rest-frame UV spectra offer some of the most
direct ways we currently have of assessing the rapidly evolving neutral
fraction of the intergalactic medium (IGM) (e.g., Mortlock et al., 2011;
Becker et al., 2015; Eilers et al., 2017; Davies et al., 2018; Wang et al.,
2020; Yang et al., 2020; Bosman et al., 2020). Estimates of the masses of
their supermassive black holes (SMBHs) using established techniques indicate
that at least some of these objects were able to accumulate masses similar to
the SMBH at the center of the local giant elliptical M87 within less than 1
Gyr of the Big Bang, defying the most simple maximum accretion scenarios
especially for the highest redshifts (e.g., Bañados et al., 2018b).

One of the main uncertainties at the current moment relates to the population
of “seed” black holes from which they originated (e.g., Bromm & Yoshida, 2011;
Greene, 2012; Mezcua, 2017; Inayoshi et al., 2020). Although in principle a
$\sim 10^{9}$ $M_{\odot}$ SMBH could form from a 100 $M_{\odot}$ seed
accreting at the Eddington rate for under 1 Gyr, it is not clear whether such
high accretion rates could be sustained for such a long time (or shorter
periods of super-Eddington accretion), especially in the presence of supernova
feedback from the forming galaxy. One possible solution includes mergers
between light black hole seeds in clusters of stellar remnants or at the
centers of merging (mini)halos, but long black hole merger time scales and the
effect of merger recoil kicks could pose a problem for such a scenario (see
Piana et al., 2021). An attractive, alternative scenario starts with the
formation of a much more massive seed. In order to accomplish this, models and
simulations typically require some kind of control mechanism that stimulates
the formation of a massive seed, either through an enhanced local Lyman-Werner
photon flux or through the dynamical heating of merging (mini)halos. These
mechanisms, which could operate alone or in tandem, may prevent halos from
forming stars at least until reaching the atomic cooling stage, at which point
a runaway collapse to a massive seed occurs, either directly or by forming
first a shortlived, supermassive star (e.g., Latif et al., 2018; Wise et al.,
2019; Lupi et al., 2021; Piana et al., 2021).

Based on their low co-moving space density, high accretion power and large
black hole masses, it is frequently argued that the first luminous quasars
must have formed in very dense regions of the cosmic web (e.g., Fan et al.,
2000; Springel et al., 2005; Li et al., 2007; Sijacki et al., 2009). It has
thus been expected that these luminous quasars will be situated in or near
large overdensities of dark matter, gas and galaxies that, in principle, we
should be able to detect. Precisely this expectation has been tested for the
last two decades in many different and complementary ways, but it has been
challenging to interpret that work in a straightforward and clear-cut way
(see, e.g., Overzier et al., 2009a; Overzier, 2016; Mazzucchelli et al., 2017;
Decarli et al., 2017; Mignoli et al., 2020, and references therein for a
variety of observational findings related to the environments of quasars).

These results are even more puzzling in the light of several significant
large-scale overdensities that have been detected at similar redshifts with
relative ease in fields not known to host luminous quasars (e.g., Ouchi et
al., 2005; Toshikawa et al., 2012; Ota et al., 2018; Calvi et al., 2019).
Although obscuration, variability or duty cycle can easily explain the real or
apparent absence of luminous quasars in any of these structures, there are no
obvious mechanisms that could temporarily hide any large-scale structure
around the known quasars, if present. This is a rather strong, albeit
indirect, argument against the explanation that the structures associated with
the quasars are simply being missed because we lack observational sensitivity
at these redshifts.

Another common explanation given for the apparent absence of galaxies
clustered near quasars is that strong radiative feedback has raised the
temperature floor of the surrounding IGM, thereby preventing the condensation
of gas into galaxies (e.g., Utsumi et al., 2010; Bañados et al., 2013;
Mazzucchelli et al., 2017). In this case, the quasars would still be
surrounded by large matter overdensities as expected from theory, but those
would be devoid of galaxies within the quasar ionization cone. In this
scenario, however, it seems challenging to suppress any structure on scales
out to many Mpc, uniformly around the quasar, and throughout its active and
inactive phases as the observations appear to require. Besides, galaxies have
been found within the ionization cones of some quasars (e.g., Mignoli et al.,
2020; Bosman et al., 2020).

The apparent lack of clearly identifiable overdense environments around most
quasars at $z\sim 6$ studied to date is even more puzzling given current
theories for massive seed formation. As explained above, these theories
require large matter overdensities that could (1) provide a large Lyman-Werner
photon background, and (2) enhanced merger rates of small dark matter halos
that stimulate the collapse of a massive gas cloud into a so-called direct
collapse black hole (DCBH) seed (e.g., Wise et al., 2019; Lupi et al., 2021).
Once the massive seed of $\simeq 10^{3}-10^{5}$ $M_{\odot}$ has formed, the
high merger and accretion rates in the overdense environment would be
sufficient to achieve the 4-6 orders of magnitude growth necessary to form the
SMBH in just a few hundred million years. Without invoking the DCBH scenario,
it is a real challenge to explain the very large SMBH masses in at least some
of the quasars at $z\gtrsim 6$.

Quasar SDSS J0836+0054 at $z=5.8$ (denoted J0836 throughout this paper) is
among a handful of objects for which a large potential overdensity of galaxies
was found in early observations using the HST (Zheng et al., 2006). However
suggestive this result, direct spectroscopic evidence for an overdensity
associated with J0836 was still lacking. Recently, however, three galaxies
having redshifts near that of the quasar were found as part of the study of
Bosman et al. (2020), confirming close association with the quasar for two
objects from the Zheng et al. (2006) sample, plus one new source. As we show
in this paper, one of the companion galaxies is very bright at 3.6 $\mu$m,
indicative of a very high stellar mass. Based on these new results, we
conclude that the reality of a structure of galaxies associated with J0836 has
now been established. We compare the structure around J0836 with model
expectations and recent literature results, including another recently
confirmed large structure associated with quasar SDSS J1030+0524 at $z=6.3$
(Mignoli et al., 2020) as well as several field overdensities at $z\sim 6-7$.
From these comparisons, we conclude that J0836 lies in a rather exceptional
environment that at least qualitatively resembles the type of overdense
environments required by the DCBH scenario.

We set the cosmological parameters to $H_{0}=69.6$ km s-1 Mpc-1,
$\Omega_{M}=0.286$, $\Omega_{\Lambda}=0.714$, which gives a spatial scale of
5.95 physical kpc arcsec-1 and an age of 0.98 Gyr at $z=5.8$ (Bennett et al.,
2014). We will use the prefix ‘p’ to indicate physical scales (e.g., pkpc) and
the prefix ‘c’ to indicate co-moving scales (e.g., cMpc). We use AB
magnitudes.

Figure 1: HST/ACS false color image of the region around SDSS J0836+0054 at
$z=5.8$ using the $i_{775}$ image for the blue channel,
($i_{775}$+$z_{850}$)/2 as the green channel and $z_{850}$ as the red channel.
The quasar is marked by the white square. Photometric dropouts from Zheng et
al. (2006) and spectroscopic Ly$\alpha$ emitting objects from Bosman et al.
(2020) are indicated by the green and blue circles. The large yellow circle
referred to in this study has a radius of 1$\farcm$26 (radius of 0.45 pMpc).
Scalebars of length 1′ and 1 cMpc are shown in the bottom-left.

##  2 Data and samples

###  2.1 SDSS J083643.85+005453.3 (J0836)

The quasar J0836 was discovered as part of the Sloan Digital Sky Survey (SDSS)
quasar survey (Fan et al., 2001), and is one of the brightest quasars at
$z>5.7$ in the optical (Bañados et al., 2016), radio (Bañados et al., 2021)
and X-rays (Wolf et al., 2021). Various redshift determinations in the range
$z\simeq 5.77-5.83$ exist (Fan et al., 2001; Stern et al., 2003; Freudling et
al., 2003; Kurk et al., 2007; Jiang et al., 2007; Shen et al., 2019), but we
follow Bosman et al. (2020) who determined $z=5.804\pm 0.002$ based on the O
ii 1305 Å and C ii 1335 Å emission lines. J0836 is also one of the most
distant known radio-loud quasars: it has a flux density of 1.1 mJy at 1.4 GHz,
a 5 GHz (rest-frame) luminosity of $1.1\times 10^{25}$ W Hz-1 sr-1, a radio
spectral index of -0.9 between 1.5 and 5 GHz, and is marginally resolved at
VLBI resolutions of $\sim 10$ mas ($\sim$40 pc) (Petric et al., 2003; Frey et
al., 2003, 2005). Wolf et al. (2021) presented new observations at low radio
frequency, showing that the radio spectral index flattens significantly below
1.4 GHz, consistent with a peaked radio spectrum. The compact radio size,
steep spectral index and the evidence for a peaked spectrum may suggest that
this is a young radio source in which the jets are still confined to (sub-)kpc
scales. J0836 has an estimated black hole mass of
$\mathrm{log}_{10}(\mathcal{M}_{\mathrm{BH}}/M_{\odot})=9.48\pm 0.55$ (see
Sect. 3.2 below).

Table 1: Objects in the field of J0836.  ID | $\alpha$ | $\delta$ | $z_{\mathrm{phot}}^{a}$ | $z_{\mathrm{spec}}^{b}$ | $\Delta z^{\dagger\dagger}$ |  EW${}_{\mathrm{Ly}\alpha}^{b}$ | $L_{\mathrm{Ly}\alpha}^{b}$
---|---|---|---|---|---|---|---
| (J2000) | (J2000) |  |  |  |  |
J0836 | 08:36:43.871 | +00:54:53.15 | – | $5.804\pm 0.002$ | 0.0 | – | –
B-B20 | 08:36:46.280 | +00:54:10.55 | – | $5.793\pm 0.003$ | –0.011 | $76^{+55}_{-34}$ | $43.03_{-0.03}^{+0.03}$
A-Z06 / A-B20 | 08:36:45.248 | +00:54:10.99 | $5.8^{+1.4}_{-0.2}$ | $5.856\pm 0.003$ | +0.052 | $>10.1$ | $42.63^{+0.05}_{-0.04}$
B-Z06 / C-B20 | 08:36:47.053 | +00:53:55.90 | $5.9^{+1.0}_{-1.0}$ | $5.726\pm 0.003$ | –0.078 | $55^{+8}_{-5}$ | $42.93^{+0.15}_{-0.11}$
B′-A06 | 08:36:47.127 | +00:53:56.20 | $5.70^{+0.03}_{-0.05}$ | – | – | – | –
C-Z06 | 08:36:50.099 | +00:55:31.16 | $5.9^{+1.1}_{-0.5}$ | – | – | – | –
C2-Z06 | 08:36:50.058 | +00:55:30.54 | $5.9^{+1.4}_{-1.5}$ | – | – | – | –
C3-Z06 | 08:36:50.010 | +00:55:30.27 | $7.0^{+0.0}_{-0.7}$ | – | – | – | –
D-Z06 | 08:36:48.211 | +00:54:41.19 | $5.8^{+1.2}_{-0.7}$ | – | – | – | –
E-Z06 | 08:36:44.029 | +00:54:32.79 | $5.2^{+1.7}_{-0.7}$ | – | – | – | –
F-Z06 | 08:36:42.666 | +00:54:44.00 | $5.7^{+1.2}_{-0.7}$ | – | – | – | –
G-Z06† | 08:36:44.809 | +00:55:04.41 | $5.7^{+1.2}_{-0.8}$ | – | – | – | –
a Objects A-Z06 to G-Z06 from Zheng et al. (2006) and object B′-A06 from Ajiki
et al. (2006).
b From Bosman et al. (2020).
† During this work a mistake was found in the coordinates for object G used in
Table 1 and Figure 1 of Zheng et al. (2006).
Here we give the correct coordinates.
†† Redshift difference of spectroscopic galaxies and J0836, $\Delta
z=z_{\mathrm{obj}}-z_{\mathrm{QSO}}$.

###  2.2 HST/ACS and Spitzer/IRAC images

We use images obtained with the HST/ACS in the filters F775W ($i_{775}$; 4676
s) and F850LP ($z_{850}$; 10,778 s). These data are described in detail in
Zheng et al. (2006). For the analysis in this paper, we retrieved the pipeline
reduced mosaics from the Hubble Legacy Archive111https://hla.stsci.edu/, and
performed new measurements using Source Extractor version 2.25.0 (Bertin &
Arnouts, 1996). We applied a Galactic extinction correction of 0.1 and 0.07
mag to the $i_{775}$ and $z_{850}$ magnitudes, respectively. We also use
Spitzer/IRAC 3.6 $\mu$m observations with a total exposure time of 17 ks taken
from Overzier et al. (2009b).

###  2.3 Galaxy samples and redshifts

The samples discussed in this paper are the following. We use the sample of
photometrically selected $i_{775}$-dropouts detected with HST/ACS from Zheng
et al. (2006). The dropout galaxies have $z_{850}$$<$26.5 mag and colors
1.3$<$$i_{775}$–$z_{850}$$<$2.0, consistent with $z\sim 5.8$. There are seven
objects in this sample (labeled A–G). Below, when referring to the Zheng et
al. (2006) objects we will use these IDs together with the suffix “Z06”. One
of the dropouts (C-Z06) has two close companions in projection (labeled C2 and
C3) that are fainter than the imposed limit in $z_{850}$.

Ajiki et al. (2006) carried out broad and narrowband observations using the
Subaru Suprime-Cam with filters
$B$,$V$,$r^{\prime}$,$i^{\prime}$,$z^{\prime}$, and the narrowband filter
$NB816$ sensitive to Ly$\alpha$ at $z=5.65-5.75$. They found one strong
Ly$\alpha$ emitting candidate at $z\approx 5.7$ about 1″ or 6 kpc from object
B-Z06. We will refer to this object as B′-A06. The remainder of the Zheng et
al. (2006) objects were not detected in $B$,$V$,$r^{\prime}$, which is
consistent with them being genuine $i$-dropouts and not foreground
interlopers.

Finally, and key to the results presented in this paper, we use three
spectroscopically confirmed Ly$\alpha$ emitting objects from Bosman et al.
(2020). Their selection was also based on the Subaru data from Ajiki et al.
(2006). They used color selection criteria optimized to the redshift range
$5.65\leq z\leq 5.90$, and supplemented spectroscopic targets with a
photometric redshift selection. Of 19 candidates found in the region
overlapping with the HST data, 3 corresponded to objects from Zheng et al.
(2006): A-Z06, B-Z06 and F-Z06. 11 of these were targeted with the
Keck/DEIMOS, including A-Z06 and B-Z06. When referring to objects from the
spectroscopic sample, we will use the suffix “B20”. Redshifts were obtained
for three objects: “Aerith A” at $z=5.856\pm 0.003$ (A-B20 which is identical
to A-Z06), “Aerith B” at $z=5.793\pm 0.003$ (B-B20 has no counterpart in Zheng
et al. (2006) because of its relatively small $i_{775}$–$z_{850}$ color) and
“Aerith C” at $z=5.726\pm 0.003$ (C-B20 which is identical to B-Z06).

Object A-Z06/A-B20 is also detected in the NB816 narrowband, which is
interpreted as continuum emission blueward of Ly$\alpha$ (Bosman et al.,
2020). Object B-B20 is not detected in the NB816. The redshift of B-Z06/C-B20
places the wavelength of its Ly$\alpha$ emission in the NB816. A relatively
bright object (B′-A06) has indeed been detected, as first reported by Ajiki et
al. (2006). However, as explained in Bosman et al. (2020), the redshift of
B-Z06/C-B20 was obtained at the location of its $z^{\prime}$-band continuum,
which is offset from the NB816 source B′-A06 by about 6.3 kpc. It is thus
possible that there are two galaxies at this location having approximately the
same redshift. Bosman et al. (2020) report no other objects with redshifts
close to that of J0836, while Meyer et al. (2020) report on a fourth source at
$z=5.284$ that is not relevant to this paper.

Details on the samples are summarized in Table 1.

##  3 Analysis and results

###  3.1 Basic structure

In Fig. 1 we show a false color image of the archival HST/ACS $i_{775}$ and
$z_{850}$ bands of the J0836 field. The quasar itself is marked by white
square. The $i_{775}$-dropouts from Zheng et al. (2006) are marked by green
circles, and the spectroscopically confirmed objects from Bosman et al. (2020)
by cyan circles. The work of Bosman et al. (2020) is significant because it
has confirmed, for the first time, that 2 out of the 7 objects from Zheng et
al. (2006) have redshifts close to that of the quasar (much closer than one
would expect for a randomly distributed sample of $i_{775}$-dropouts, see
below). Moreover, they also found an additional object (B-B20), that lies
closer to the quasar redshift than the other two. The proper distances along
and perpendicular to the line of sight (l.o.s.) to the quasar
($R_{\parallel}$, $R_{\perp}$) are (3.64,0.28) pMpc for A-Z06/A-B20,
(–0.67,0.33) pMpc for B-B20 and (–5.03,0.44) pMpc for B-Z06/C-B20, where a
minus sign indicates objects in the foreground of the quasar. As further
illustrated by Fig. 2, the three objects lie along a narrow cylinder oriented
along the line of sight with a total length of about 8.7 pMpc (corresponding
to the maximum redshift difference of $\Delta z=0.13$) and the quasar about
mid-way.

Figure 2: Locations of the spectroscopically identified galaxies with respect
to the quasar in proper physical coordinates. The $Z$-axis was chosen for the
direction along the line of sight, and the $X$\- and $Y$-axes were chosen to
indicate the directions along Right Ascension and Declination, respectively.
The structure can be approximated by a narrow cylinder elongated along the
line of sight. When this cylinder is seen face-on, as in the case of the HST
observations shown in Fig. 1, the structure appears highly compact.

###  3.2 The quasar

Kurk et al. (2007) estimated a black hole mass of $2.7\pm 0.6\times 10^{9}$
$M_{\odot}$ based on the Mg ii line. We have updated their estimate using
newer measurements and calibrations. We use the black hole mass calibration
from Vestergaard & Osmer (2009) together with the FWHM(Mg ii)$=3600\pm 300$
measurement of Kurk et al. (2007) and the 3000 Å rest-frame luminosity of
$10^{47.01}$ erg s-1 from Shen et al. (2019), finding
$\mathrm{log}_{10}(\mathcal{M}_{\mathrm{BH}}/M_{\odot})=9.48\pm 0.55$,
consistent with the estimate of Kurk et al. (2007), but $\sim$0.4 dex below
the estimate of Shen et al. (2019) based on the problematic C iv line.

A dynamical mass estimate for the quasar host galaxy does not yet exist, but
an order of magnitude estimate can be made by taking the results for a sample
of $z\sim 6$ quasars from Neeleman et al. (2021) (see also Venemans et al.,
2016). They find that, on average, the quasar host galaxy dynamical masses are
a factor of 7 lower than expected for their black hole mass and assuming the
Kormendy & Ho (2013) $\mathcal{M}_{\mathrm{BH}}-\mathcal{M}_{\star}$ relation
for local bulges. With an estimated black hole mass of $\sim 10^{9.5}$
$M_{\odot}$, this would imply a stellar (bulge) mass of $\sim 0.7\times
10^{11}$ $M_{\odot}$. If we assume a typical stellar-to-dark-matter mass ratio
of $\sim 30-50\times 10^{-3}$ appropriate for the high mass end of the halo
mass function at $z\sim 6$ (Stefanon et al., 2021), this would imply a quasar
host halo mass of $(1-2)\times 10^{12}$ $M_{\odot}$. Although the uncertainty
of this estimate is large, it is consistent with recent derivations based on
the density profile in the proximity zones of $z\sim 6$ quasars by Chen et al.
(2021), who found a typical host halo mass of
$\mathrm{log}_{10}(\mathcal{M}_{h}/M_{\odot})=12.5_{-0.7}^{+0.4}$.

Figure 3: HST/ACS image stamps in $i_{775}$ (left) and $z_{850}$ (right) of
the three sources confirmed by Bosman et al. (2020) with A-Z06/A-B20 in the
top, B-B20 (no Z06 counterpart) in the middle, and B-Z06/C-B20 in the bottom
panels. The boxes measure 2″$\times$2″. The image pixel size is 0$\farcs$04
and the data is shown unsmoothed. In the bottom panels, the dashed circle
marks the narrow-band excess object B′-A06 about 1″ East of B-Z06/C-B20
detected in the Subaru NB816 image by Ajiki et al. (2006). See text for
details.  Table 2: Magnitudes and sizes of the confirmed objects.

ID | Filter | $r_{50}^{\dagger}$ | $r_{90}^{\dagger}$ | $m_{AB}$
---|---|---|---|---
|  | (arcsec) | (arcsec) | (mag)
A-Z06/A-B20 | $i_{775}$ | 0.20 | 0.37 | $26.84\pm 0.17$
| $z_{850}$ | 0.16 | 0.38 | $25.44\pm 0.05$
| 3.6 $\mu$m | – | – | $23.78\pm 0.09$
B-B20 | $i_{775}$ | 0.16 | 0.26 | $26.57\pm 0.12$
| $z_{850}$ | 0.12 | 0.29 | $26.07\pm 0.08$
B-Z06/C-B20 | $i_{775}$ | 0.13 | 0.39 | $27.58\pm 0.36$
| $z_{850}$ | 0.18 | 0.38 | $25.89\pm 0.08$
B′-A06 | $i_{775}$ | 0.10 | 0.35 | $27.53\pm 0.20$
| $z_{850}$ | 0.10 | 0.16 | $27.14\pm 0.15$

† The sizes quoted are the radii containing 50 and 90% of the total flux as
returned by Source Extractor. They were not corrected for the HST seeing of
about $0\farcs 07$ (FWHM).

###  3.3 Massive companion galaxy A

Overzier et al. (2009b) presented Spitzer/IRAC observations of the J0836
structure, and showed that object A-Z06/A-B20 is very bright at 3.6 $\mu$m
with $m_{3.6}=23.78\pm 0.09$ mag. Assuming that its redshift was indeed $z\sim
6$, they concluded that it is among the brightest and most massive
$i_{775}$-dropout galaxies. Here we will revisit the analysis of A-Z06/A-B20.
The $z_{850}$ and 3.6 $\mu$m images are shown in Fig. 4.

Using the redshift firmly established by Bosman et al. (2020), we can now make
a much more secure determination of the properties of A-Z06/A-B20 based on the
available photometry. Although the $z_{850}$–[3.6] color is sensitive to age,
dust, SFH and metallicity (and redshift), the 3.6 $\mu$m flux probing rest-
frames of around 5000 Å is an accurate (albeit relative) gauge of stellar mass
at these redshifts (e.g., see Overzier et al., 2009b; Duncan et al., 2014;
Bhatawdekar et al., 2019; Stefanon et al., 2021). We used the BagPipes code
(Carnall et al., 2018) to fit the $z_{850}$ and 3.6 $\mu$m photometry. The
$i_{775}$-band was excluded because it does not add any information about the
intrinsic SED. The redshift was fixed to $z=5.856$. We fit constant and
exponential star formation histories with a Kroupa & Boily (2002) IMF. We set
the maximum age to the age of the universe at $z=5.8$. Because galaxies at
$z\sim 6$ are known to have a relatively strong contribution from emission
lines (mainly [O iii] 4959,5007 Å) to their 3.6 $\mu$m broadband flux, we used
the option to include nebular emission with an ionization parameter $U=0.01$.
Assuming a constant star formation history and attenuation by dust according
to the Calzetti et al. (2000) law, we find a stellar mass
$\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})=10.34_{-0.16}^{+0.30}$ with
a mass-weighted age of $0.27_{-0.14}^{+0.28}$ Gyr ($z_{f}\approx 7.5$), a
metallicity $\mathrm{log}_{10}(Z/Z_{\odot})=0.86_{-0.45}^{+0.86}$, and
$A_{V}=0.7_{-0.1}^{+0.3}$ mag (see Fig. 5). The stellar mass and mass-weighted
age returned for an exponential star formation history model are essentially
the same. Without the nebular emission, the stellar mass is about 0.1 dex
higher. Restricting the metallicity to $\leq 0.4Z_{\odot}$ as in Stefanon et
al. (2021), we find a stellar mass
$\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})=10.2_{-0.2}^{+0.3}$
($\mathrm{log}(\mathcal{M}_{\star}/M_{\odot})=10.40_{-0.14}^{+0.23}$) with
(without) the nebular emission with little change to the other parameters.
Below we will use our first estimate of
$\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})=10.34_{-0.16}^{+0.30}$ for
the stellar mass of A-Z06/A-B20, as the other estimates are consistent within
the errors. This stellar mass is two orders of magnitude higher than the
minimum halo mass that was inferred by Bosman et al. (2020).

We can compare these results with recent results for the stellar mass function
and stellar-to-halo mass ratios of galaxies at $z\sim 5.8$ in the field from
Stefanon et al. (2021). The stellar mass of A-Z06/A-B20 places it in the
highest mass bin considered in that paper
($\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})=10.4\pm 0.2)$, taking into
account a division by a factor of 1.5 to convert from their Salpeter to our
kroupa IMF. If we use their best-fit
$\mathrm{log}(\mathcal{M_{\star}}/M_{\odot})-M_{UV}$ relation with
$M_{UV}=-21.3$ mag measured for A-Z06/A-B20, we would naively expect
$\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})\approx 9.3$, a full 1 dex
below the actual mass measurement and thus indicative of the significant
obscuration in this source.

The stellar mass estimate allows us to make an estimate of the mass of the
typical dark matter halos that host objects like A-Z06/A-B20. Using an
abundance-matching method, Stefanon et al. (2021) provide an estimate of the
typical stellar-to-halo mass ratio for objects of this mass of $\sim
30-50\times 10^{-3}$, implying that A-Z06/A-B20 is hosted by a dark matter
halo of $\mathrm{log}_{10}(\mathcal{M}_{h}/M_{\odot})\sim 12$. The J0836 field
thus hosts at least one other massive dark matter halo, besides the quasar
itself. Halos of this mass correspond to a virial radius of $r_{200}\simeq 50$
kpc, so the halos are really two individual halos given that their separation
is about 3.6 pMpc. Although there are no structural measurements for the
quasar host galaxy, for object A-Z06/A-B20 we measured a seeing-corrected
half-light radius of 0.14″ in the $z_{850}$-band. This corresponds to a
physical half-light radius of 0.83 kpc, giving a stellar mass surface density
of $\Sigma_{\star}\lesssim\mathcal{M}_{\star}/(2\pi r_{50}^{2})=10^{9.8}$
$M_{\odot}$ kpc-2. This should be considered an upper limit because the
optical size is likely larger than that measured in the UV. These measurements
place object A-Z06/A-B20 near the transition region between massive (compact)
quiescent and star-forming galaxies at $z\sim 4$ (Straatman et al., 2015),
indicating that A-Z06/A-B20 may be near the end of its active star-forming
phase.

###  3.4 Other companions

We checked the IRAC image for the other confirmed companions, but object B-B20
was not detected and object B-Z06/C-B20 (and thus also B′-A06) lies too close
to a very bright foreground object to attempt a flux measurement. A direct
stellar mass estimate can thus not be made. However, assuming that, unlike
object A-Z06/A-B20, these objects do follow the
$\mathrm{log}_{10}(\mathcal{M_{\star}}/M_{\odot})-M_{UV}$ relation of Stefanon
et al. (2021) (reddening by dust can be neglected at these magnitudes, Bouwens
et al. (2007)), the stellar masses would be a few times $10^{9}$ $M_{\odot}$
for B-B20 and B-Z06/C-B20 and a few times $10^{8}$ $M_{\odot}$ for B′-A06. The
halo masses would be a few times $10^{11}$ and $10^{10}$ $M_{\odot}$,
respectively, based on the abundance matching results from Stefanon et al.
(2021). The HST images of the objects are shown in Fig. 3 and basic
measurements are given in Table 2.

In Sect. 4 below we will analyze the J0836 structure in terms of the
probabilities of finding objects like the massive companion A-Z06/A-B20 and
the more typical star-forming galaxies B-Z06/C-B20 and B-B20.

##  4 Overdensity analysis

In Zheng et al. (2006) it was estimated that the number of 7 photometric
dropouts to $z_{850}$$\sim$26.5 mag in the central 5 arcmin2 region around
J0836 represents a factor 6 overdensity with respect to a large control field
of similar quality data from the Great Observatories Origins Deep Survey
(GOODS), with no single 5 arcmin2 region (a circle with a radius of
1$\farcm$26) randomly drawn from GOODS containing as many as 7 objects and 4
being the highest (Bouwens et al., 2006). Overzier et al. (2009a) constructed
a 4$\fdg$4$\times$4$\fdg$4 mock survey of galaxies at $z\sim 6$ and showed
that (surface) overdensities like J0836 are indeed a relatively rare
occurrence, but certainly not the rarest due to the existence of extremely
dense regions mostly associated with (forming) galaxy clusters. However, a
definitive conclusion about the J0836 structure was not possible due to the
lack of spectroscopic redshifts.

With the new spectroscopic data from Bosman et al. (2020), we can now quantify
the nature of the overdensity associated with J0836 much more precisely. It is
interesting that while only 2 of the 7 objects from Zheng et al. (2006) were
targeted spectroscopically by Bosman et al. (2020), they represent 2/3 of the
spectroscopically confirmed objects near J0836. These two objects are also the
brightest among the Zheng et al. (2006) sample ($z_{850}$-band magnitudes of
25.5 and 26 mag). The typical surface density and redshift distribution of
$i_{775}$-dropouts selected with HST is well known. According to Bouwens et
al. (2007), the cumulative surface density is $0.328\pm 0.044$ arcmin-2 to
$z_{850}$=26.5 mag, and based on their redshift distribution the (random)
probability of finding a dropout in the redshift range $z=5.73-5.86$ ($\Delta
z=0.13$) is 0.16. In this redshift range and in an area of 5 arcmin2 we would
thus naively expect to find $0.3\pm 0.04$ objects. With two Zheng et al.
(2006) objects spectroscopically confirmed in this region, the three-
dimensional overdensity thus appears sigificant as well
($\delta=n/\bar{n}-1\approx 6$). Here we did not take into account the third
confirmed object from Bosman et al. (2020) because it did not pass the
$i_{775}$-dropout selection criteria used in Zheng et al. (2006).

We assume the redshift distribution of Bouwens et al. (2007) for
$i_{775}$-dropouts and that of Inami et al. (2017) as presented by Mignoli et
al. (2020) for LAEs. According to these distributions the probabilities of
finding a single LBG and LAE in the redshift range $z=5.73-5.86$ are 0.16 and
0.073, respectively. Of the 7 Zheng et al. (2006) dropouts, two spectra were
taken and both objects fell into this range, giving a probability of 0.026
based on the binomial distribution (2 out of 2 with $P=0.16$). Among the
spectroscopic targets of Bosman et al. (2020), four objects with Ly$\alpha$
were found, three of which fell in the redshift range $\Delta z=0.13$ near
J0836. The probability of this occurrence at random is 0.0015 again using
binomial statistics (3 out of 4 with $P=0.073$).

These small (but non-zero) probabilities are suggestive that the presence of
the quasar J0836 has some effect on the clustering observed.

Figure 4: HST/ACS $z_{850}$ and Spitzer/IRAC 3.6 $\mu$m images of the object
A-Z06/A-B20 discussed in Sect. 3.3. The boxes measure 2″$\times$2″ as in Fig.
3. The HST object is clearly detected at 3.6 $\mu$m. The (deblended) object
flux was extracted by simultaneously fitting point sources at the locations of
the four objects seen near the central part of the image (see Overzier et al.,
2009b).

Figure 5: Results of the constant star formation model fits to the $z_{850}$
and 3.6 $\mu$m fluxes of object A-Z06/A-B20 at $z=5.856$ described in Sect.
3.3. The top panel shows the best-fit spectral energy distribution (curve)
together with the photometry (data points). The bottom panels show the
probability distributions of the SFR, mass-weighted age, stellar mass and
specific SFR with the 16, 50 and 84 percentiles indicated by dashed vertical
lines.

###  4.1 Clustering of two massive halos

In Section 3.3 we showed that one of the J0836 companions is an extremely
massive galaxy, and the close clustering between the quasar and this object
can provide additional strong constraints on the overdensity in this region.
Above we showed that the massive companion A-Z06/A-B20 has a stellar mass of
around
$\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})=10.34_{-0.16}^{+0.30}$ and
inferred halo mass $\mathrm{log}_{10}(\mathcal{M}_{h}/M_{\odot})\sim 10^{12}$.
Based on the analysis of several hundreds of square arcminutes with deep HST
and Spitzer/IRAC coverage, Stefanon et al. (2021) show how rare such massive
objects are: the number density of $i_{775}$-dropouts with
$\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})=10.4\pm 0.2$ is
$0.06_{-0.05}^{+0.14}\times 10^{-4}$ dex-1 Mpc-3. The volume of the J0836
structure is approximately 1724 cMpc3, estimated by taking a cylinder with
radius of 3.1 cMpc and a length of 58.5 cMpc (corresponding to $\Delta
z=0.13$). In this volume we thus expect to find $0.002-0.035$ of such massive
$i_{775}$-dropouts at random, while at least 1 was found (object A-Z06/A-B20)
not counting the quasar. The discovery of such a rare massive object as part
of the J0836 structure is thus additional evidence that the environment of the
quasar is exceptional.

We can try to estimate how exceptional the J0836 environment is based on the
clustering statistics of quasars and galaxies. The typical overdensity of
galaxies found in a biased region depends on the amplitude of the quasar-
galaxy cross-correlation function, $\xi^{QG}(r)=(r/r_{0}^{QG})^{-\gamma}$, and
the volume $V_{\mathrm{eff}}$:

$\displaystyle\langle\delta_{g}\rangle$ $\displaystyle=$
$\displaystyle\frac{1}{V_{\mathrm{eff}}}\int_{V}\xi^{QG}(r)dV$ (1)
$\displaystyle=$ $\displaystyle\int_{0}^{R}2\pi
R\mathrm{d}R\int_{0}^{Z}\mathrm{d}Z\left(\frac{\sqrt{R^{2}+Z^{2}}}{r_{0}^{QG}}\right)^{-\gamma},$
(2)

The quasar-galaxy cross-correlation length has not been measured directly for
the redshift and samples of our interest, but assuming that the clustering of
both the quasars and the galaxies is described by power laws with similar
slopes, their cross-correlation length is given by
$r_{0}^{QG}=\sqrt{r_{0}^{GG}r_{0}^{QQ}}$. Using the results from galaxy
clustering measurements together with a halo occupation distribution model,
Harikane et al. (2021) find that dark matter halos with average masses in the
range $\mathrm{log}_{10}(\mathcal{M}_{h}/M_{\odot})\approx 11.8-12.2$ at
$z\approx 5.9$ correspond to bias parameters of 7.7–10.1. A similar result is
obtained using the Colossus222http://bitbucket.org/bdiemer/colossus
cosmological framework (Diemer, 2018), which gives a bias of 8.7 for halos of
$\mathrm{log}_{10}(\mathcal{M}_{h}/M_{\odot})=12$ (peak-height of 5.5). The
auto-correlation length of $z\sim 6$ galaxies with a similar bias parameter or
halo mass was measured by Khostovan et al. (2019). They found
$r_{0}=15.56_{-2.71}^{+2.51}$ $h^{-1}$ Mpc ($r_{0}=16.16_{-3.52}^{+3.80}$
$h^{-1}$ Mpc) for LAEs with halo mass
$\mathrm{log}_{10}(\mathcal{M}_{h}/M_{\odot})\approx 12.3\pm 0.2$
($\mathrm{log}_{10}(\mathcal{M}_{h}/M_{\odot})\approx 12.4\pm 0.3$) at
$z\approx 5.79$ ($z\approx 5.56$). In the analysis below we will therefore
take $r_{0}^{GG}\approx 15$ $h^{-1}$ cMpc as an approximate value. With a
quasar auto-correlation length of $r_{0}^{QQ}\approx 22.3$ h-1 cMpc (see
García-Vergara et al., 2017), the quasar-galaxy cross-correlation length in
Eq. 2 becomes $r_{0}^{QG}\approx 26.1$ cMpc. If we assume a clustering power
law slope $\gamma=1.8$, and a cylindrical volume with radius $R=3.1$ cMpc and
length $Z=58.5$ cMpc, the overdensity of $10^{12}$ $M_{\odot}$ halos expected
in the J0836 field (not counting the quasar) is
$\langle\delta_{g}\rangle=23.8$ (29.6 for $\gamma=2.0$).

From this we can then estimate the absolute number of such galaxies expected:

$N_{g}=(\langle\delta\rangle+1)\bar{n}_{g}V_{\mathrm{eff}}$ (3)

For an average field density of $\bar{n}_{g}=1.1-3.7\times 10^{-5}$ cMpc-3
(appropriate for objects of halo mass of order $10^{12}$ $M_{\odot}$;
Khostovan et al., 2019; Stefanon et al., 2021), we then expect to find 0.5–1.6
of such objects in our cylindrical volume around the quasar, matching the one
object that was found.

We can do a similar exercise for star-forming galaxies in more typical halos.
The average co-moving abundance of dropouts with $M_{UV}<-20.13$ is
$\bar{n}_{g}\approx 4\times 10^{-4}$ cMpc-3. Assuming a typical bias of 5 and
a correlation length of 5.5 $h^{-1}$ cMpc, appropriate for this population of
relatively bright dropout galaxies in halos of around $10^{11}$ $M_{\odot}$ at
$z\sim 6$ (Overzier et al., 2006a; Barone-Nugent et al., 2014; Khostovan et
al., 2019), the quasar-galaxy cross-correlation length in Eq. 2 would be 15.8
cMpc.

In Fig. 6 we show the cumulative number of massive and typical companion
galaxies expected in the J0836 field following these calculations with the
light- and dark-shaded regions, respectively. We plot the number of objects as
a function of the projected co-moving radius of a cylinder with a fixed length
of 58.5 cMpc. The finding of 1 massive companion within 3.1 cMpc is consistent
with the enhancement in clustering over the random expectation due to the
presence of the massive quasar halo (upper light-shaded curve and large
circle). Doing the same calculation for more typical star-forming galaxies in
lower mass halos, the number of 3 objects detected (small dark circle with
arrow) is lower than that expected (upper dark-shaded region) by a factor of
2–3, but it is important to keep in mind that the spectroscopic sample is
highly incomplete (for example, there are at least an additional 5 objects
from Zheng et al. (2006) that have not been targeted).

This analysis shows that the clustering observed in the J0836 field is
consistent with what we would expect from the presence of a massive quasar
halo. In Section 4.2 below we will compare the J0836 structure to several
other dense structures of galaxies discovered in recent years, both near
quasars and in the general field at $z\sim 6$. In this way we will be able to
address the relative rarity of the J0836 structure in yet another way.

Figure 6: Number of companion galaxies expected in a cylinder of length 58.5
cMpc as a function of its projected radius. The dark shaded regions correspond
to typical galaxies in the case of no clustering (bottom) and in the case of
strong cross-clustering between quasars and galaxies (top). The light shaded
regions correspond to massive companion galaxies in the case of no clustering
(bottom) and in the case of strong cross-clustering between quasars and
galaxies (top). Vertical dotted lines mark radii of 3.1 and 4.1 cMpc,
corresponding to the fiducial cylinder used for the J0836 structure in this
paper and the half-width of the HST/ACS field, respectively. The large light
circle represents the massive companion object A-Z06/A-B20. The small dark
circle represents all three spectroscopically confirmed objects from Bosman et
al. (2020). The widths of the shaded regions reflect the uncertainties in the
average number densities, and not the uncertainties in the correlation
amplitudes. See Sect. 3.3 for details. This figure was inspired by a similar
figure in Decarli et al. (2017).

###  4.2 Comparison with other $z\sim 6$ structures

In Sect. 3 above we presented statistical and theoretical evidence that the
J0836 field appears to be much richer than the average cosmic region at $z\sim
6$ based on (1) the photometric overdensity of Zheng et al. (2006), (2) the
spectroscopic overdensity of Bosman et al. (2020), and (3) the presence of a
very massive companion galaxy. However, we cannot escape the fact that these
calculations are a simplification as they do not take into account, for
example, the complicated selection functions of candidates and confirmed
objects and the small number statistics. One way of addressing these issues
has been to use numerical simulations to evaluate the impact of such effects,
as selection effects are easily incorporated and simulations offer large
volumes from which statistics can be derived (e.g., Overzier et al., 2009a).
On the other hand, however, we should be careful with this approach as well,
as many aspects of these simulations remain to be tested by the very
observations we try to interpret, and one cannot escape some degree of
circular reasoning when comparing the two. Therefore, in this section we will
try yet another approach of quantifying the J0836 structure, by comparing with
a variety of structures that have been found near other quasars and in the
field at $z\sim 6-7$.

####  4.2.1 SDSS J1030+0524

Among the luminous quasars at $z\sim 6$, there is currently only one other
object for which the observations show a certain resemblance to J0836. Quasar
SDSS J1030+0524 (J1030) at $z=6.308$ has been among a few, rare quasars with
strong evidence for companion structure. The evidence consists of significant
overdensities of (photometric) dropout galaxies on various scales (Stiavelli
et al., 2005; Morselli et al., 2014; Balmaverde et al., 2017), and more
recently spectroscopic evidence in the form of 4 LBGs and 2 LAEs within a
$\Delta z=0.2$ of the quasar redshift (Decarli et al., 2019; Mignoli et al.,
2020). The confirmed LBGs lie at $\sim$8–9′ away from the quasar, and at
present we have no way of comparing this to the environment of J0836 on these
scales. However, Mignoli et al. (2020) also found two LAEs much closer to
J1030, LAE1 at (-4.98,0.14) pMpc and LAE2 at (2.6,0.13) pMpc using our
cosmology. Although the proper distances along the l.o.s. are comparable, the
projected separations are smaller by a factor of $\sim$2 in the case of the
J1030 LAEs. However, it is important to note that they were selected in a very
different way using a blind spectroscopic survey over a 1′$\times$1′ field
centered on the quasar with VLT/MUSE. The LAEs in the J0836 field were found
by targeting photometric dropout objects with slit spectroscopy. The physical
properties of the two populations of LAEs are quite different: the J1030 LAEs
are fainter in absolute magnitude ($M_{UV}\gtrsim-20.5$ mag) compared to those
in J0836 ($\lesssim$–20.8 mag). The EWs of the two LAEs near J1030
($EW_{0}\simeq$11–27 Å) also appear somewhat lower than the three near J0836
($EW_{0}\simeq$10–76 Å). The relatively high EWs and bright UV magnitudes of
the J0836 LAEs are curious because typical LAEs show the opposite trend (e.g.,
De Barros et al., 2017), and could be related to the large quasar proximity
zone in which they are situated (Bosman et al., 2020). We have checked that
the LAEs in neither field are affected by Ly$\alpha$ fluorescence due to the
quasar’s strong ionizing radiation to a few % at most (see also Bosman et al.,
2020). Again, we note that the selection techniques used in the two studies
were very different. In the case of J0836, current data does not allow us to
search for objects as faint as the two LAEs found near J1030. On the other
hand, the fact that the J1030 integral field observations did not find any
dropout objects with Ly$\alpha$ as bright as the three objects found near
J0836 means that they do not exist near J1030. Summarizing, the comparison
shows that both J0836 and J1030 have a large spectroscopic excess of objects
relatively close to the quasar (in terms of the projected separation, objects
near J1030 are about twice closer than those near J0836), but the physical
properties of these objects appear somewhat different (objects near J0836 are
brighter in the UV and Ly$\alpha$ than those near J1030).

####  4.2.2 VIKING J030516.92–315056.0 at $z=6.61$

Ota et al. (2018) have detected a large-scale overdensity of star-forming
galaxies around the quasar VIKING J030516.92–315056.0 at $z=6.61$. Although
several overdense peaks of (candidate) LBGs are found at $\sim$20–40 cMpc away
from the quasar, just a single LBG candidate lies within the central 12
arcmin2 equivalent to one HST/ACS pointing. There are also no candidate LAEs
in this region with a limiting rest-frame Ly$\alpha$ $EW_{0}$ of 15 Å and
$L_{Ly\alpha}\gtrsim 10^{42.4}$ erg s-1, and the surface density of LAEs on
larger scales appears to be underdense compared to a control field. There is
thus no observational evidence that this particular quasar is surrounded by a
structure of galaxies that is similar to that found near J0836, at least not
on the relatively small scales probed by our study.

####  4.2.3 Other quasars at $z\sim 6$

A very useful literature overview of searches for structures associated with
quasars at $z\simeq 5-7$ is given in Table 2 from Mazzucchelli et al. (2017).
If we limit this list only to quasars for which there exists spectroscopic
evidence for associated galaxies on scales similar to that probed by our J0836
study, only 4 out of the original 14 quasars stand out with reported
overdensities. Among the $z\sim 6$ quasars, this includes only J0836 itself,
and J1030 at $z=6.3$ described in detail in Section 4.2.1 above. The two
remaining objects are quasars at $z\approx 5$ studied by Husband et al.
(2013). In one of these, there are 3 objects within $\Delta z=0.11$ in an area
similar in scale as the J0836 structure. In the other field, there are 6
confirmed LBGs within $\Delta z=0.06$ (plus an additional quasar), but except
for one object these all lie on scales beyond that probed for J0836. Thus, it
appears that J0836 and J1030 both represent quite remarkable environments,
among all the $z\sim 6$ quasars studied to date.

In addition, Decarli et al. (2017) derived unique information on the
environments of quasars at $z\gtrsim 6$ based on the occurrence of companion
objects identified based on the [C ii] 158$\mu$m emission line (see also
Trakhtenbrot et al., 2017, for similar findings at $z\sim 5$). In a survey of
25 quasars, four quasars had close companions (within a projected 600 kpc and
600 km s-1). The companion galaxies are not detected in the rest UV, and
represent a population of dusty star-forming objects with dynamical masses
similar to those of their companion quasars. These massive, close companion
objects are consistent with the expected cross-clustering between quasars and
star-forming galaxies measured at lower redshifts (García-Vergara et al.,
2017). However, the fact that only 4/25 quasars showed [C ii] 158$\mu$m
companions, indicates that this type of environment is far from typical. It is
important to note that the ALMA observations probe a much smaller field of
view than in the other studies described in this paper (survey volume of 400
cMpc3), making any quantitative comparison difficult. Despite it being much
further away from the quasar, the stellar mass of the massive companion of
J0836 is similar to that of the companion objects identified by Decarli et al.
(2017). However, no [C ii] 158$\mu$m observations exist for the former.

Vito et al. (2021) also found evidence for a quasar at $z=6.5$ involved in a
close pair, and Yue et al. (2021) found the first example of a pair of quasars
at $z\approx 5.7$ (projected separation of $<$10 pkpc). The separations are
much smaller than the virial radius of the likely dark matter halos,
suggesting that merger-induced triggering could play a role in at least a
small fraction of the quasars.

####  4.2.4 COSMOS AzTEC-3 structure at $z=5.3$

Capak et al. (2011) found strong clustering near the source COSMOS AzTEC-3 at
$z=5.299$ consisting of a spectroscopically confirmed dropout object at
$z=5.295$ and several photometric dropouts within a 2 cMpc (0.3 pMpc) radius
(see also Riechers et al., 2014). A quasar at $z=5.30$ lies further away (at
13 cMpc). Although a detailed quantitative comparison is difficult because of
the different selections and spectroscopic completeness involved, there appear
to be strong similarities between J0836 and this structure in terms of the
photometric and spectroscopic overdensities.

####  4.2.5 SXDF protocluster at $z=5.7$

The Subaru XMM-Newton Deep Field (SXDF) hosts one of the densest structures
known at $z\sim 5.7$ (Ouchi et al., 2005; Jiang et al., 2018; Shibuya et al.,
2018; Higuchi et al., 2019; Harikane et al., 2019). The structure labeled
z57OD corresponds to an overdensity of LAEs with overdensity $\delta=11.5$ and
significance of 7.2$\sigma$ when defined using a cylindrical region of 10 cMpc
radius and 40 cMpc depth. The core of the structure is characterized by a
narrow range in redshift ($\Delta z\approx 0.02$), but can be seen in maps
with $\Delta z\approx 0.12$. In Fig. 7 we show the z57OD structure using the
spectroscopic data from Harikane et al. (2019). Objects having absolute rest
UV magnitudes brighter than -20.2 mag are indicated with large circles, and
objects having Ly$\alpha$ luminosities larger than 1042.6 erg s-1 are marked
by red squares. The large dotted circle marks a circular 5 arcmin2 region that
maximizes the number of known structure members, containing 4 members. Because
the SXDF and J0836 structures are, respectively, narrow-band and dropout
selected, it is difficult to make a direct quantitative comparison. However,
the 4 objects encircled in Fig. 7 all have Ly$\alpha$ luminosities at least as
high as the 3 confirmed objects near J0836, and 2 of these have UV
luminosities similar to those near J0836. Thus, at least on these scales, the
J0836 and z57OD structures appear quite similar.

Figure 7: Map of the large-scale structure z57OD at $z\approx 5.7$ in the SXDF
from Harikane et al. (2019). The circle with a radius of 1$\farcm$26 (radius
of 0.45 pMpc) that maximizes the number of z57OD galaxies similar to those in
the J0836 field has been indicated. There are two objects that would plausibly
pass the same selection criteria as those in the J0836 field (large black
circles). See Sect. 4.2.5 for details.

####  4.2.6 HUDF structure at $z\approx 5.9$

Malhotra et al. (2005) identified a structure of $i_{775}$-dropout galaxies at
$z=5.9\pm 0.2$ in the HUDF. They followed up 29 ($i_{775}$–$z_{850}$$)\geq$0.9
objects with the ACS grism, finding 23 $z\sim 6$ objects of which 15 are part
of an overdensity of at least a factor of 2 along the line of sight. In Fig. 8
we show the HUDF structure, indicating objects with
($i_{775}$–$z_{850}$$)\geq$1.3 (small circles) and those brighter than
$z=26.5$ mag (large circles). Objects within the $z=5.9\pm 0.2$ redshift spike
are marked red. The large dotted circle marks a circular 5 arcmin2 region that
maximizes the number of structure members. In this region, there are 7
galaxies, with 3 being brighter than $z=26.5$ mag. The grism redshifts have an
accuracy of $\Delta z\approx 0.15$, so we will only be able to compare the two
structures within $\Delta z=0.2$. The 3 objects thus appear to lie in a
redshift interval that is at least as wide as that found for the confirmed
objects around J0836. More importantly, the spectroscopic completeness of the
Malhotra et al. (2005) sample is much higher than for the J0836 sample (about
62% versus 29%). The J0836 structure thus appears significantly more overdense
compared to the HUDF structure, at least at the magnitude limits considered.

Figure 8: Map of the large-scale structure at $z\sim 5.9$ in the HUDF from
Malhotra et al. (2005). The circle with a radius of 1$\farcm$26 (radius of
0.45 pMpc) that maximizes the number of galaxies has been indicated. There are
four objects that would plausibly pass the same selection criteria as those in
the J0836 field (large red and black circles), but they have a wider redshift
distribution. See Sect. 4.2.6 for details.

####  4.2.7 SDF protocluster at $z=6.01$

Among the most impressive large-scale structures known at $z\sim 6$ is the
protocluster discovered by Toshikawa et al. (2012, 2014) in the Subaru Deep
Field (SDF). Among 28 spectroscopically confirmed $i$-dropout objects at
$z\sim 6$ lies a structure of 10 objects at $z=5.984-6.047$ ($\Delta z=0.06$)
and measuring $20\times 20$ cMpc on the sky. The selection of these objects is
similar to the dropout selections of Zheng et al. (2006) and Bosman et al.
(2020), and the spectroscopic followup similar to that performed by Bosman et
al. (2020) in the J0836 field. In Fig. 9 we show the SDF structure, indicating
which objects have spectroscopic redshifts (red squares), which objects are
brighter than $z=26.5$ mag (large circles), and which objects lie within
$\Delta z=0.13$ of the $z=6.01$ redshift spike. The large dotted circle marks
a circular 5 arcmin2 region that maximizes the number of structure members. In
this region, there are 5 member galaxies, with 3 being brighter than $z=26.5$
mag. This indicates that the J0836 field resembles the densest part of the
Toshikawa et al. (2014) structure.

Figure 9: Map of the large-scale structure at $z\approx 6.01$ in the SDF from
Toshikawa et al. (2012, 2014). The circle with a radius of 1$\farcm$26 (radius
of 0.45 pMpc) that maximizes the number of galaxies in the SDF structure
similar to those in the J0836 field has been indicated. There are three
objects that would plausibly pass the same selection criteria as those in the
J0836 field (large red circles). See Sect. 4.2.7 for details.

####  4.2.8 CFHTLS structures at $z\sim 6$

Toshikawa et al. (2016) performed a color selection of $i$-dropouts in the
CFHTLS Deep Fields to a depth of $z\sim 26.3-26.5$ mag (about
$M_{UV}^{\star,z=6}$). They searched for $>4\sigma$ surface overdensities in
regions with a radius of 1 pMpc (2.9′), suitable for the identification of
massive cluster progenitors according to numerical simulations and previous
studies (Toshikawa et al., 2012, 2014, 2016). Five regions were found, and the
two most significant overdensities (D1ID01 of 6.1$\sigma$ and D3ID01 of
7.6$\sigma$) were targeted by spectroscopy to confirm the dropout candidates.
Three redshifts were obtained in D1ID01, with two objects separated by $\Delta
z=0.08$ and 53″ ($\sim$0.32 pMpc) and a third object not physically associated
at much higher redshift. Two redshifts were obtained in D3ID01, with the two
objects separated by $\Delta z=0.007$ and 83″ ($\sim$0.49 pMpc). There are no
quasars known to be associated with either structure. The three confirmed
objects in the J0836 field lie within a projected 0.4 pMpc from the quasar
(and about 0.1 pMpc from each other) and have $\Delta z=0.13$. Based on the
available photometric and spectroscopic evidence, the J0836 structure thus
appears at least as densely populated as the two CFHTLS regions, which
themselves represent significant overdensities compared to the general field
at $z\sim 6$.

####  4.2.9 LAGER-z7OD1 protocluster at $z\approx 7$

Hu et al. (2021) presented a large overdensity of LAEs at $z\approx 7.0$,
LAGER-z7OD1. The LAEs were narrow-band selected and have minimum Ly$\alpha$
luminosities comparable to the LAEs near J0836 (
$\mathrm{log_{10}}L_{Ly\alpha}/(\mathrm{erg~{}s^{-1}})\gtrsim 42.6$). They
find 16 spectroscopic LAEs clustered in a region $66\times 30\times 26$ cMpc3,
where the last dimension corresponds to the redshift depth of $\Delta
z=0.072$. Drawing again random circular regions with a radius of 1$\farcm$26,
the maximum number of LAEs encountered is 3, centered around two peaks in the
sky distribution of LAGER-z7OD1 (see Fig. 10). This shows that on these scales
the structure found around J0836 is not too different from the densest peaks
within this large-scale overdense region at $z\approx 7$.

Figure 10: Map of the large-scale structure at $z\approx 7$ associated with
the LAGER-z7OD1 protocluster from Hu et al. (2021). Two circles with a radius
of 1$\farcm$26 that maximize the number of galaxies similar to those in the
J0836 field have been indicated. There are two locations, each with three
objects, that would plausibly pass the same selection criteria as those in the
J0836 field. See Sect. 4.2.9 for details.

####  4.2.10 SC4K survey of LAEs at $z\approx 5.7$

To assess the random chance of finding a given number of LAEs in the field, we
used data from the $\sim$2 deg2 SC4K survey (Sobral et al., 2018). We select
all narrow-band excess objects detected in the NB816 filter, which is
sensitive to Ly$\alpha$ at $z=5.7\pm 0.05$ (FWHM), and thus comparable to the
redshift width of the objects in the J0836 field ($\Delta z=0.13$). The
contamination by foreground objects in this sample is estimated at about 15%.
It is important to note that the J0836 sample was not narrow-band selected,
and the comparison is thus somewhat skewed. However, the LAEs in the SC4K
survey have redshifts, Ly$\alpha$ luminosities ($\gtrsim 10^{42.6}$ erg s-1)
and rest-frame EWs ($\gtrsim$50 Å) comparable to the dropout objects confirmed
in the J0836 field by Bosman et al. (2020). The SC4K survey can thus be used
as a conservative reference field for estimating the clustering statistics of
these objects (in other words, if we were to perform a survey like SC4K on the
J0836 field, we are likely to find even more objects than currently selected,
and thus the SC4K reference gives the maximum expectation). In Fig. 11 we show
the sky distribution of LAEs from the SC4K survey. We performed a counts-in-
cells analysis using a circular region with radius of 1$\farcm$26 similar to
that used in the J0836 field. The chance of randomly finding 2 LAEs in such a
small area is at most 1%, and the chance of finding 3 LAEs is 0.1% (note that
these numbers are likely skewed high due to the contamination of about 15% and
the fact that the J0836 objects were not narrow-band selected). We can
conclude from this analysis that the J0836 field contains a number of LAEs
that is at least as large as only the densest location in the whole $\sim$2
deg2 SC4K survey.

Figure 11: Map of the large-scale structure of LAEs at $z\approx 5.7$ in the
SC4K survey from Sobral et al. (2018). LAEs with rest-frame EW $>$25 Å ($>$50
Å) are indicated by the small (large) circles. A circular region with a radius
of 1$\farcm$26 (0.45 pMpc) similar to the area studied in the J0836 field has
been indicated for reference (dashed circle). The area within the large box
was used for a counts in cells analysis. The chance of encountering two
(three) LAEs that could plausibly pass the same selection criteria as those in
the J0836 field amounts to 1% (0.1%). See Sect. 4.2.10 for details.

####  4.2.11 Summary of the comparisons

Based on the various comparisons with known $z\sim 6-7$ structures given
above, it appears justified to conclude that the J0836 field is comparably
rich as the peaks in other rare large-scale structures found at these
redshifts. J0836 shows some characteristics of other quasar fields, such as
the overdensity of star-forming galaxies found near SDSS J1030+0524 at $z=6.3$
(Mignoli et al., 2020) and the evidence of massive companion galaxies found
near some quasars (Decarli et al., 2017; Yue et al., 2021; Vito et al., 2021),
although the scales are very different for the latter. Compared to the non-
quasar fields, the J0836 field appears as rich as some of the densest regions
known in the field to date. However, the latter include many spectroscopically
confirmed surface overdensities extending over angular scales that are much
larger than we can probe with the J0836 data, and it is not known whether the
similarities between J0836 and these fields would hold on those scales as
well.

##  5 Summary and discussion

###  5.1 Summary

We have shown that the luminous radio-loud quasar J0836 at $z=5.8$ is likely
part of a relatively rich structure of galaxies in the early universe. The
evidence consists mainly of a photometric overdensity previously found by
Zheng et al. (2006), a spectroscopic overdensity identified by Bosman et al.
(2020), and the presence of at least one very massive companion galaxy
detected at 3.6 $\mu$m with Spitzer/IRAC by Overzier et al. (2009b) allowing a
stellar mass estimate. Based on a cross-correlation analysis of galaxies and
quasars, we showed that the presence of these companion objects can plausibly
be explained by an overdense environment associated with the quasar. We
compared the global properties of the J0836 structure with those found near
other quasars and in the field at similar redshifts, concluding that the
structure resembles the densest peaks in the cosmic density field currently
known at $z\sim 6-7$, at least at similar depths and scales as probed by our
observations.

This study is significant for a number of reasons. First, it provides new
evidence that the first luminous quasars are associated with relatively dense
peaks in the cosmic density field. Second, the J0836 structure appears
relatively unique among the population of $z\sim 6$ quasars studied to date,
with one system showing a similar propensity of clustered companion galaxies
(Mignoli et al., 2020), and several other quasars showing evidence for direct
interactions on much smaller scales (e.g., Decarli et al., 2017; Vito et al.,
2021; Yue et al., 2021). Third, although the J0836 structure appears, in some
aspects, similar to some of the most clustered regions of star-forming
galaxies known at $z\sim 6-7$, these regions are clearly not unique to the
quasars given that overdensities of galaxies have been discovered in the field
as well, sometimes larger and more significant than what has been found near
any quasar to date (e.g., Toshikawa et al., 2014; Harikane et al., 2019; Hu et
al., 2021).

By combining these different clues, we will discuss a number of important open
questions related to the formation of SMBHs, quasar environments and radio
jets.

###  5.2 Insights into seed formation

One of the most important questions in the study of galaxies relates to the
origin of the SMBHs. This question is particularly pertinent to the population
of luminous quasars at $z\gtrsim 6$, given that the masses of their SMBHs
managed to rival that of M87 ($\mathcal{M_{\mathrm{BH}}}=6.5\pm 0.2\pm
0.7\times 10^{9}$ $M_{\odot}$; Event Horizon Telescope Collaboration et al.,
2019) within 1 Gyr of the Big Bang. This notion has led to a substantial
effort in theoretical modeling of possible seed black hole populations and
their accretion histories with stellar mass and intermediate mass BHs emerging
as the main candidates for the seeds (for reviews see, e.g., Bromm & Yoshida,
2011; Inayoshi et al., 2020; Volonteri et al., 2021).

The slightly longer cosmic times available to quasars at $z\lesssim 6$ make it
significantly “easier” to go from a 100 $M_{\odot}$ seed to a SMBH of a few
times $10^{9}$ $M_{\odot}$ compared to the quasars at $z\gtrsim 7$ (e.g.,
Bañados et al., 2018b; Marinello et al., 2020; Pacucci & Loeb, 2021). For
example, assuming constant accretion with Eddington ratios of 0.8–1.3 onto a
seed formed at $z_{f}=20-10$ is able to produce a SMBH like that in J0836 by
$z=5.82$, while the quasar ULAS J1342+0928 at $z=7.54$ requires the existence
of a $>$1000 $M_{\odot}$ seed as early as $z=45$ assuming standard Eddington
rate accretion (Bañados et al., 2018b). There are at least two problems with
the latter scenario: (1) it is not clear if such massive seeds could exist
that early, and (2) it is not clear if such an efficient accretion rate could
be sustained over such a long cosmic time.

In scenarios where the growth of SMBHs is allowed to start with an
intermediate mass BH (IMBH) seed, the constraints on formation redshift,
accretion rates and growth times are significantly relaxed. The biggest
uncertainty with these scenarios, however, is whether there exist a viable
channel for IMBH formation at early times. Models and simulations have
identified a number of ways in which IMBH seeds can form, for example through
the merging of numerous stellar mass seeds or through the collapse of massive
gas clouds into a DCBH seed (see Sect. 1).

The results presented in this paper cannot constrain any of these scenarios,
but the association of J0836 with a relatively dense cosmic structure is very
interesting in light of a number of recent model predictions for DCBH
formation. The various DCBH scenarios proposed all have in common that they
require the quasar to form in an overdense region. The overdense region
ensures that the primordial gas cloud is heated through an enhanced local
Lyman-Werner photon flux and a high rate of merging (mini)halos (e.g., Wise et
al., 2019; Lupi et al., 2021). After the collapse, the overdense environment
can further ensure a steady accretion rate to form a SMBH and power a quasar.

The simulations of Wise et al. (2019) specifically point to a scenario in
which the presence of an overdense region of star-forming galaxies several
tens of kpc away stimulates the formation of a DCBH seed. When combined with
sufficient dynamical heating of atomic cooling halos (ACHs) that are rapidly
growing, the nearby star-forming complex only needs to provide a fraction of
the LW flux assumed by earlier models. They find a density of DCBHs in
overdense regions at $z=15$ of $10^{-7}-10^{-6}$ cMpc-3, with the density
being lower by a factor of at least 10,000 in normal and void regions. It is
important to point out that the overdense region chosen by Wise et al. (2019)
corresponds to a dark matter halo of a few times $10^{10}$ $M_{\odot}$ at
$z=6$, which is still two orders of magnitude below the typical halo mass of
the luminous quasars studied here. If overdense environments indeed enhance
the number density of DCBHs by orders of magnitude, perhaps the proto-J0836
environment would make an ideal site.

The galaxies detected as part of the J0836 structure are unlikely the same as
the ones that provided the required LW background at early times. For
instance, if we take our model fit results for object A-Z06/A-B20 from Sect.
3.3 ($\mathrm{log}_{10}(\mathcal{M}_{\star}/M_{\odot})=10.34_{-0.16}^{+0.30}$
with a mass-weighted age of $0.27_{-0.14}^{+0.28}$ Gyr), we can see that even
this massive galaxy likely was not around at $z_{f}\gtrsim 10.5$. Its distance
from J0836 is also much too great to have provided a significant Lyman-Werner
intensity near the inferred site of seed formation (several Mpc instead of
tens of kpc). However, the J0836 structure suggests that an overdense region
that predates the formation of the quasar was probably present from early
times. It is difficult to be more quantitative at this point. Deep
observations with ALMA and JWST could be used to quantify quasar environments
on smaller scales and down to fainter galaxies of much lower bias, and these
could then be compared to tailored simulations of DCBH collapse as performed
by Wise et al. (2019).

Lupi et al. (2021) revisit the idea of synchronized pairs (SPs) of ACHs
(Visbal et al., 2014), where two halos separated by $<$1 kpc and star
formation commencing in one halo $<$5 Myr prior to that in the other provides
a high LW flux to drive the formation of a DCBH. They compare this scenario to
the dynamical heating (DH) driven collapse similar to that discussed by Wise
et al. (2019), but focusing specifically on the progenitor of a $3\times
10^{12}$ $M_{\odot}$ at $z=6$. Although the dense environment stimulates the
formation of SPs, the pristine halos of the pairs are also easily polluted by
metals due to the enhanced supernova activity in the region. These polluted
halos are assumed to cool and fragment, and no longer considered candidates
for DCBH formation. Comparing this with the DH scenario in the same overdense
region shows that, because of the clustering of LW sources in the overdense
region, several DH seeds may be formed for each SP seed, although the initial
mass of the DH seeds may be lower than the SP seeds. The studies by Wise et
al. (2019) and Lupi et al. (2021) thus point in the same direction that
overdense regions in the early universe may be a necessary ingredient for the
formation of DCBHs.

One could argue that in principle each quasar at $z\gtrsim 6$ must have formed
in such an overdense environment given their high halo masses (Chen et al.,
2021). However, the finding of relatively rich environments around quasars
such as J0836 and J1030 compared to other quasars must then imply that the
conditions required for DCBH formation as suggested by theory may have been
particularly well met for the progenitor regions of these sources.

###  5.3 Relevance of the radio jets

The fast growth rates of the SMBHs powering the $z\sim 6$ quasars implies that
we are seeing them at a time of potentially significant impact on the growth
of the host galaxies through AGN feedback. The (small) subset of quasars that
are radio-loud are the first sources in which we could study, in principle,
the interaction between powerful radio jets and the forming interstellar
medium. Even though the fraction of quasars that is radio-loud is relatively
small ($\sim$10%, independent of redshift, see Bañados et al. (2015)), there
is growing evidence that at least at low redshift faint radio structures
present also in radio-quiet quasars may be disproportionally responsible for
the feedback observed (e.g., Jarvis et al., 2021).

At these redshifts, there are still relatively few radio sources known. J0836
appears as the 8th most distant radio-loud AGN in the overview of Bañados et
al. (2021, their Table 6). While optically the most luminous, it has the
lowest radio-loudness parameter ($R_{2500}=16\pm 1$). We determine a
bolometric luminosity of $L_{\mathrm{bol}}=5.3\pm 0.02\times 10^{47}$ erg s-1
using Richards et al. (2006), and with a black hole mass
$\mathrm{log}_{10}(\mathcal{M}_{\mathrm{BH}}/M_{\odot})=9.48\pm 0.55$, we find
an Eddington ratio of $L_{\mathrm{bol}}/L_{\mathrm{Edd}}=1.4_{-1.0}^{+3.5}$.
This range indicates that J0836 lies along the upper envelope of Eddington
ratios found for high redshift quasars compiled by Bañados et al. (2021).

The compact radio size (Frey et al., 2005), steep spectral index and evidence
for a peaked radio spectrum (Wolf et al., 2021) suggest that J0836 is not
beamed and that it is a young radio source in which the jets are still
confined to the inner kpc scales. With a (projected) size of 40 pc and
assuming a typical hot spot advancement speed of ($0.2\pm 0.1$) $h^{-1}$ $c$
(Giroletti & Polatidis, 2009), the kinematic age in the young source scenario
is in the range $\approx 300-1000$ yr. If the jets have an inclination angle
as small as 1° along the line of sight (still large enough such that it does
not become a blazar), the radio age could be as high as $\approx 3\times
10^{4}$ yr. This is much shorter than the most recent quasar phase of $\sim
2\times 10^{5-7}$ yr estimated by Bosman et al. (2020). Given these relatively
short jet life-times compared to the black hole and quasar accretion time
scales inferred for J0836, it appears unlikely that the (current) radio jets
have had any meaningful impact on the growth of the SMBH. Alternatively, the
radio jets could be recurrent, or the radio source is much older than inferred
from its maximum linear size, as expected in the case of jets that are
confined by a dense ISM (e.g., O’Dea & Saikia, 2021).

What does seem relevant, however, is the fact that J0836 represents yet
another case of a high redshift radio-loud AGN associated with a relatively
dense environment (e.g., Overzier et al., 2006b; Venemans et al., 2007; Hatch
et al., 2014; Overzier, 2016). The ability of SMBHs to form strong radio jets
is generally assumed to scale as a function of black hole mass, accretion rate
and spin (Blandford & Znajek, 1977; Fanidakis et al., 2011), and all three
parameters may be expected to be enhanced in overdense regions due to the
enhanced gas accretion rates and merger activity. On the other hand, radio
jets may be the consequence of energy extracted from the accretion disk, in
which case the SMBH grows much faster due to higher accretion rates (Blandford
& Payne, 1982). A recent discussion of this relevant to the jets in radio-loud
quasars at $z\sim 6$ is given by Connor et al. (2021).

Quasar J0836 is different from the radio-loud quasar PSO J352.4034-15.3373 at
a very similar redshift (Bañados et al., 2018a; Rojas-Ruiz et al., 2021;
Connor et al., 2021), mainly in the sense of its very compact linear size
($\sim$40 pc versus $\sim$1.6 kpc; Frey et al., 2005; Momjian et al., 2018),
radio power (rest-frame $L_{\nu,1.4}\sim 7\times 10^{26}$ W Hz-1 versus $\sim
5\times 10^{27}$ W Hz-1; Wolf et al., 2021; Bañados et al., 2018a), and radio
loudness parameter ($16\pm 1$ versus $1358\pm 141$; Bañados et al., 2021). It
also appears to be quite different from the distant radio galaxy TGSS
J1530+1049 at $z=5.72$ discovered by Saxena et al. (2018) with rest-frame
$L_{\nu,1.4}=1.6\times 10^{28}$ W Hz-1 and a radio morphology consisting of
two radio components with a linear extent of $\sim$2.5 kpc Gabányi et al.
(2018). However, all these sources are consistent with being relatively young
radio sources in which the radio structures are comparable or within the scale
of the host galaxies. These sources thus offer an excellent opportunity for
investigating the interaction between radio jets, galaxy formation and SMBH
growth.

###  5.4 Concluding remarks

The answer to the question of what were the seeds of today’s SMBHs is coming
within our reach. Likely it will require the synthesis of data and clues from
a wide variety of independent upcoming experiments. Gravitational wave
astronomy has already begun to map the BH mass gap, and the proposed ESA/LISA
and Einstein Telescope will significantly widen the mass and distance range of
detectable BH mergers, thereby addressing directly the mass distribution of
the population as a function of redshift. JWST could in principle detect
massive DCBH seeds — if they exist — through their unique spectral signatures
in the infrared, provided they are not too rare. The Nancy Grace Roman Space
Telescope, due to its much wider field of view, could perform an even better
search. A non-detection of DCBH candidates could be interpreted as evidence
that DCBH seeds do not exist, focusing modeling efforts on Population III
stars instead. In any case, JWST will also map for the first time in detail
the amount of black hole activity in typical galaxies during the first billion
years, and the masses of SMBHs in (faint) quasars, thereby constraining the
total black hole demographics. Evidence for Population III stars either at
high redshift or in the Local Group could constrain the range of the masses of
this first generation of stars and thus the mass range that their end-products
could realistically achieve. Searches for IMBHs in globular clusters and dwarf
galaxies will provide yet another unique constraint on the seed population.
The search for distant obscured black holes will greatly benefit from the new
capacity in the X-rays provided by the ESA/Athena or NASA/Lynx missions.
Extremely Large Telescopes will then be needed to confirm and characterize the
sources found. Yet another window on the first stages of black hole formation
will be provided at radio wavelengths. Deep radio surveys with the Square
Kilometer Array will find the most distant objects in the universe capable of
hosting radio jets, the smoking gun of massive, spinning black holes.

In the more immediate future, it will be extremely interesting to see (1) to
what extend the compact radio structures seen in the most distant radio
galaxies and quasars interact with the ISM of their young, forming host
galaxies, (2) if there is any evidence for environmental triggers of this
radio activity, and (3) to establish definitively what are the typical
environments of the radio-loud and radio-quiet AGN at this important epoch.
Several programs have been scheduled on the HST and the James Webb Space
Telescope (JWST) that aim to do just that within the next two years (e.g., HST
programs 16258/16693 and JWST programs 1205/1554/1764/2028/2078).

The author is grateful to Catarina Aydar, Sarah Bosman, Roberto Decarli,
Benedikt Diemer, Marco Mignoli and Mauro Stefanon for comments or answering
questions during the preparation of this manuscript. The author was supported
in this work by a productivity grant (302981/2019-5) from the National Council
for Scientific and Technological Development (CNPq).

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