# Giant radio galaxies in the LoTSS Boötes deep field

M. Simonte,1 H. Andernach,2 M. Brüggen,1 D. J. Schwarz,3 I. Prandoni,4 A. G.
Willis5
1 Hamburger Sternwarte, University of Hamburg, Gojenbergsweg 112, 21029
Hamburg, Germany
2Departmento de Astronomía, DCNE, Universidad de Guanajuato, Callejón de
Jalisco s/n, Guanajuato, C.P. 36023, GTO, Mexico<EMAIL_ADDRESS>
3 Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501
Bielefeld, Germany
4 INAF – Istituto di Radioastronomia, via Gobetti 101, I-40129 Bologna, Italy
5 Independent Researcher, 310 Yorkton Avenue, Penticton, BC V2A 6Z8, Canada
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Giant radio galaxies (GRGs) are radio galaxies that have projected linear
extents of more than 700 kpc or 1 Mpc, depending on definition. We have
carried out a careful visual inspection in search of GRGs of the Boötes LOFAR
Deep Field (BLDF) image at 150 MHz. We identified 74 GRGs with a projected
size larger than 0.7 Mpc of which 38 are larger than 1 Mpc. The resulting GRG
sky density is about 2.8 (1.43) GRGs per square degree for GRGs with linear
size larger than 0.7 (1) Mpc. We studied their radio properties and the
accretion state of the host galaxies using deep optical and infrared survey
data and determined flux densities for these GRGs from available survey images
at both 54 MHz and 1.4 GHz to obtain integrated radio spectral indices. We
show the location of the GRGs in the P-D diagram. The accretion mode onto the
central black holes of the GRG hosts is radiatively inefficient suggesting
that the central engines are not undergoing massive accretion at the time of
the emission. Interestingly, 14 out of 35 GRGs for which optical spectra are
available show a moderate star formation rate (10-100 $\rm
M_{\odot}~{}yr^{-1}$). Based on the number density of optical galaxies taken
from the DESI DR9 photometric redshift catalogue, we found no significant
differences between the environments of GRGs and other radio galaxies, at
least for redshift up to $z=0.7$.

###### keywords:

galaxies: active – galaxies: jets – radio continuum: galaxies

††pubyear: 2022††pagerange: Giant radio galaxies in the LoTSS Boötes deep
field–Appendix A: Notes on individual sources

##  1 Introduction

Giant radio galaxies (GRGs) are radio galaxies that have linear extents of
more than 700 kpc or 1 Mpc, depending on definition (Willis et al., 1974;
Schoenmakers et al., 2000a; Kuźmicz & Jamrozy, 2012; Kuźmicz et al., 2018).
The total number of GRGs known to date is relatively small, even though over
the past 20 years their number has increased substantially (Ishwara-Chandra &
Saikia, 1999; Schoenmakers et al., 2000a; Lara et al., 2000; Machalski et al.,
2001; Saripalli et al., 2005; Machalski et al., 2006; Jamrozy et al., 2008;
Kuźmicz & Jamrozy, 2012; Dabhade et al., 2017; Kuźmicz et al., 2018; Dabhade
et al., 2020a, b; Dabhade et al., 2020c; Kuźmicz & Jamrozy, 2021; Andernach et
al., 2021; Mahato et al., 2022). Their origin and the cause for their huge
sizes are still not understood.

In particular, it is unclear whether their environments or their host
properties are responsible for the large extent of GRGs (e.g, Subrahmanyan et
al., 2008; Safouris et al., 2009; Kuźmicz et al., 2019). The environment of
GRGs might play a key role, affecting the accretion mode onto the central
black hole and suppressing the expansion of the radio lobes in the case the
GRG resides in a dense region. This would in turn lead to larger sources in
more isolated galaxies (Dabhade et al., 2020a; Andernach et al., 2021).
Alternatively, the large size of these galaxies might be the result of a long-
term evolution of normal radio galaxies (Kaiser & Alexander, 1997a, b).

The advent of large-area radio surveys, such as the Faint Images of the Radio
Sky at Twenty-cm (FIRST, Becker et al., 1995), Westerbork Northern Sky Survey
(WENSS, Rengelink et al., 1997), NRAO VLA Sky Survey (NVSS, Condon et al.,
1998) and the Sydney University Molonglo Sky Survey (SUMSS, Mauch et al.,
2003) ushered in a new era during which systematic studies of GRGs were
carried out. Early studies (Subrahmanyan et al., 1996; Saripalli et al., 1996;
Mack et al., 1998) investigated the radio properties of GRGs (such as the
axial ratio) finding similarities with those of smaller radio galaxies,
indicative of self-similarity in the evolution of such sources (Kaiser &
Alexander, 1997a). These authors also found that GRGs preferentially reside in
low-density environments. Furthermore, Schoenmakers et al. (2000a) and Lara et
al. (2000) found their radio spectra to be steep ($0.8<\alpha<1.2$) in the
lobes of GRGs, corresponding to ages of 10 -100 Myr. More recently, Jamrozy et
al. (2008), using data from the Giant Metrewave Radio Telescope (GMRT,
Ananthakrishnan, 1995), estimated spectral ages in the range 5 - 40 Myr,
observing a steeper spectral slope at high luminosities and high redshifts.
They also found steeper spectra for larger GRGs. Safouris et al. (2009) and
Subrahmanyan et al. (2008) found that asymmetries in the radio morphology of
GRGs may be driven by the inhomogeneities of the surrounding medium. In
particular, both studies suggest that the jets of GRGs expand into regions
that are relatively sparsely populated by galaxies. Machalski et al. (2008)
argued that a combination of a low-density environment and jet speeds of about
0.1c - 0.2c has led to the formation of J1420-0545 which is now the second
largest GRG known (Oei et al., 2022) with a linear size of 4.69 Mpc.

Subsequent work tried to model the radio data to infer the age, the spectral
index and the environment of GRGs (e.g. Machalski et al., 2007, 2009)
confirming a spectral age between 10-100 Myr. In particular, Machalski (2011),
using the DYNAGE algorithm (Machalski et al., 2007), found a relation between
the difference in value of the exponent describing the external gas density
profile ($\rho_{\rm IGM}\propto r^{-\beta}$) for the opposite lobes and the
ratio of their volume, suggesting the non-uniformity of the environment of the
GRGs.

More recent work on GRGs boosted the study providing larger samples (Dabhade
et al., 2017; Kuźmicz & Jamrozy, 2021; Dabhade et al., 2020a; Andernach et
al., 2021), but a clear theory of the evolution of such radio sources is still
missing. In those studies a few per cent of GRGs were found to reside in
galaxy clusters, challenging the idea that they are typically associated with
underdense environments. According to these studies, GRGs have radio powers
similar to normal (i.e. smaller) radio galaxies, in agreement with the
evolutionary theory (Kaiser & Alexander, 1997a). Altogether these analyses
revealed a prevalence of FRII (Fanaroff & Riley, 1974) morphology among GRGs,
altough other morphologies have been detected, such as double-double radio
galaxies (DDRGs, Schoenmakers et al., 2000b), Hybrid Morphology Radio Sources
(HyMoRS, Gopal-Krishna & Wiita, 2002), which are radio galaxies with a FRI
type radio lobe on one side of the active nucleus and a FR II type lobe on the
opposite side, and Wide Angle Tailed radio galaxies (WAT, Owen & Rudnick,
1976).

Infrared and optical surveys can be exploited to identify GRG host galaxies
and investigate the galaxy distribution around them (e.g., Lan & Prochaska,
2021). Among these surveys are the Panoramic Survey Telescope and Rapid
Response System (Pan-STARRS; Flewelling et al. 2020), Sloan Digital Sky Survey
(SDSS; York et al. 2000; Stoughton et al. 2002; Alam et al. 2015), Dark Energy
Spectroscopic Instrument survey (DESI; Dey et al., 2019; Zhou et al., 2021)
and the Wide-field Infrared survey Explorer (WISE; Cutri et al. 2013; Marocco
et al. 2021). A large amount of data have been used to infer information on
the optical counterpart and the distribution of galaxies around GRGs (e.g.,
Lan & Prochaska, 2021). For instance, the SAGAN project (see Dabhade et al.,
2020b, for details) aims to create a catalogue of all GRGs published to date
including the properties of the host galaxies.

There is ample theoretical work on the evolution of radio galaxies (e.g. Burns
et al., 1991; Kaiser & Alexander, 1997b; Machalski et al., 2021). Recent and
refined studies investigated the propagation of powerful jets and the impact
with the surrounding environment (interstellar or intergalactic medium) at
distances of tens to hundreds of kiloparsecs (Mignone et al., 2010; English et
al., 2016; Hardcastle, 2018; Perucho et al., 2021; Yates-Jones et al., 2022).
However, the computational limitations make the study of the long-term
simulations with an adequate resolution challenging.

The LOw-Frequency ARray (LOFAR Van Haarlem et al., 2013) with its relatively
high resolution and sensititvity to very low surface brightness sources
heralds a new era in the study of very large and high redshift radio galaxies.
In this paper we searched for GRGs in the Boötes LOFAR Deep Field (BLDF) image
at 150 MHz (Tasse et al., 2021; Kondapally et al., 2021). The resulting sample
contains 74, mostly newly detected, GRGs. By cross-matching with other radio
data, we obtained the radio spectral information and by cross-matching with
optical and infrared data, we inferred the properties of the host galaxies as
well as environments of the GRGs.

The outline of this paper is as follows: we describe the analysis of the radio
data, as well as the infrared data in Sec. 2. In Sec. 3 we present the results
of our analysis and compare them to previous work. Finally, we draw our
conclusions in Sec. 4. Throughout this work we adopt a flat $\rm\Lambda CDM$
cosmology with $H_{0}$ = 70
$\rm~{}km~{}s^{-1}~{}Mpc^{-1},~{}\Omega_{m}=0.3,~{}\Omega_{\Lambda}=0.7$ and a
radio source spectral index $\alpha$ defined as $S_{\nu}\propto\nu^{-\alpha}$.

##  2 Observations and multi-frequency data

The LOFAR Two-metre Sky Survey (LoTSS; Shimwell et al. 2017, 2019, 2022) is
performed using high-band antenna (HBA) observations of the northern sky in
the 120-168 MHz band and images at both 20$\rm"$ and 6$\rm"$ resolution are
available. The sensitivity of the latter image is about 1$\sigma=80\rm~{}\mu
Jy~{}beam^{-1}$. LoTSS provides the astrometric precision that is required for
multi-wavelength cross-matching. As part of this survey, dedicated deeper
observations have been carried out of the Boötes, the Lockman Hole (Tasse et
al., 2021) and the ELAIS-N1 fields (Sabater et al., 2021). The long
integration time ($>$ 80 hours) combined with a sensitivity to a wide range of
angular scales, makes these deep fields ideal for a search for the faintest
and most distant GRGs. We have carried out a systematic search of GRGs in the
Boötes LOFAR Deep Field (centered on 14h32m03.0s +34∘16′33′′ J2000) which
covers an area of 26.5 deg2 and with a noise level of $\sim$30 $\rm\mu
Jy~{}beam^{-1}$ in the inner 3 deg2. A dedicated search for GRGs in the other
deep fields will be part of a future study.

The inspection of LOFAR images was carried out by eye. The largest angular
size (LAS) in arcmin, was measured on the full resolution 6$\rm"$ image.
Kuźmicz & Jamrozy (2021) showed that an estimate based on 3-$\sigma$ contours
would make the source appear larger by at least one beam size for sources of
FR-II type with bright compact hotspots at the outer edges of their lobes.
Therefore, while for FRI we used the 3-$\sigma$ contours to measure the LAS,
for FRII type GRGs we measured the distance between the two opposite hotspots,
identified on VLA Sky Survey images (VLASS, Lacy et al., 2020) if available.
On the other hand, we believe that an angular size measurement based on the
3-$\sigma$ contours underestimates the real size of those sources of FR I
type, or those which have no clear terminal hotspots in their lobes, some of
which clearly extend beyond the 3-$\sigma$ contour. For this reason, for the
faintest GRGs we measure the angular size in a straight line from one end of
the source to the opposite one, carefully avoiding to push our measurement in
regions where the radio emission of the sources is not very clear. The same
method has been used to measure the angular size of bent sources; any measure
different from this would imply assumptions on the 3D structure of the source
which we can only guess. We found 74 GRGs with a linear extent larger than 0.7
Mpc (which we refer to as the "Boötes LOFAR Deep Field" or BLDF-GRG sample).
The only GRG reported in a GRG catalogue is J1427+3625 in Kuźmicz & Jamrozy
(2021), while J1430+3519 was studied in the radio and X-ray band by Masini et
al. (2021). 16 GRGs were listed in other catalogues of radio galaxies but they
were published without their linear size (Williams et al., 2013; van Weeren et
al., 2014; Coppejans et al., 2015; Williams et al., 2016; Mingo et al., 2022).
Among our sample, 38 GRGs have a linear extent larger than 1 Mpc. The
resulting sky density is about 2.8 GRGs deg-2 for GRGs with linear size larger
than 0.7 Mpc and 1.43 deg-2 for those larger than 1 Mpc. This result is in
agreement with recent work by Delhaize et al. (2021), who found two GRGs in
the 1 square degree COSMOS field, and higher than in Brüggen et al. (2021) who
found a sky density of radio galaxies with largest linear size $>0.7$ Mpc of
1.7 deg-2 in ASKAP observation of the Abell 3395-Abell 3391. This field has
similar noise level, but lower angular resolution (10$"$) than the BLDF.

The host galaxies were identified using optical and infrared surveys: SDSS
(York et al., 2000), WISE (Wright et al., 2010) and its multiple catalogues
such as AllWISE (Cutri et al., 2013), unWISE (Schlafly et al., 2019) and
CatWISE (Marocco et al., 2021), DESI (Dey et al., 2019; Zhou et al., 2021) and
Pan-STARRS (Flewelling et al., 2020). Once the host galaxy has been identified
we looked for available redshifts (either spectroscopic or photometric) in
multiple catalogues such as El Bouchefry (2009), Chung et al. (2014), Brescia
et al. (2014), Luo et al. (2015), Bilicki et al. (2016), Zou et al. (2019),
Duncan et al. (2021). If various redshifts were available for a single source
we computed their mean. For spectroscopic redshifts we do not report errors
since they are generally more accurate (typical errors are usually around
0.00015) than the precision we can achieve on the linear sizes and
luminosities given our errors in measuring angular size and total flux. The
identification of the host galaxy in widely separated radio components without
an obvious core emission between them is challenging. We first checked whether
any of the outer components have a convincing host by itself. In such cases,
they were recorded as separate extended radio galaxies. If a convincing
optical galaxy between the external radio components is detected in neither
optical nor infrared surveys, we discarded the source as genuine GRG. On the
other hand, we take the presence of a host galaxy with AGN colour (e.g.,
Mateos et al., 2012; Assef et al., 2013) near the geometrical centre of the
radio galaxy as a strong sign of the genuineness of the GRG, even if that host
does not show a radio core. Furthermore, the presence of a radio bridge or
radio emission elongated along the suspected radio axis sometimes indicates
the structures to be connected. In case of uncertainties about the likely host
we chose the brighter or lower redshift host. In such sources, the largest
linear size (LLS) derived from the LAS and redshift should serve as a lower
limit. Three GRGs, namely J1421+3521, J1423+3340 and J1434+3214C, do not have
a redshift estimate in any of the mentioned catalogues and they are not
detected in DESI DR9. The photometric redshift provided by the DESI DR9
photometric redshift catalogue (accessible via the NOIRlab
portal111https://astroarchive.noirlab.edu/portal/search/) for the faintest
objects is around 1.3. For this reason, we assumed that the GRG hosts are
located at redshift z=1.1-1.5. However, the exact value of the redshift is
quite irrelevant for converting LAS to LLS since the LAS-z curve is
practically flat in the relevant redshift range (see the LAS-z diagram in
sect. 3.2), so it does not affect the LLS significantly.

We used the full resolution 6$\rm"$ images to measure the total radio flux at
150 MHz. We prepared cutouts of 0.5 degrees on a side, centered on the GRG
host and integrated the flux of GRGs taking into account only those pixels
whose intensity is larger than $3\sigma_{\rm rms}$, where $\sigma_{\rm rms}$
is the noise level in the source neighbourhood. This noise level varies with
the distance from the centre of the BLDF image, but it is rather constant
within each cutout. The flux error was calculated as $\sqrt{\sigma_{\rm
rms}^{2}+\sigma_{\rm cal}^{2}}$, where $\sigma_{\rm cal}$ is the uncertainty
on the calibration of the flux scale which is assumed to be 10% of the total
flux (Sabater et al., 2021). We measured the noise of the cutout, $\sigma_{\rm
rms}$, via an iterative method. For each iteration, we calculated the rms, we
removed those pixels with an intensity larger than 5 times the rms and,
consequently, we re-measured the rms. The convergency criterion is dictated by
the difference between two consecutive rms measurement; the treshold was set
equal to 1%. Thus, we multiply the noise measurement by the square root of the
area of flux integration, measured in units of beam areas. We noticed that a
3-$\sigma$ clipping applied to the faintest GRGs clearly underestimates the
total flux of the source as some genuine emission coming from the bridge is
not included. Thus, we integrated the flux of such sources, marked by an
asterisk appended to the flux measure in Table LABEL:tab:list, considering all
the pixels belonging to the region of the radio emission. Radio powers at 150
MHz for GRGs were calculated following Donoso et al. (2009):

$P_{150}=4\pi D_{L}^{2}S_{150}(1+z)^{\alpha-1},$ (1)

where $D_{L}$ is the luminosity distance, $S_{150}$ is the measured radio flux
density at 150 MHz, $(1+z)^{\alpha-1}$ is the standard k-correction used in
radio astronomy and $\alpha$ is the radio spectral index for which we adopted
a typical value of 0.7. The median radio power is $P_{\rm med}=6.61\times
10^{25}\rm~{}W~{}Hz^{-1}$ and the GRGs span a wide range of redshift, up to
$z\sim 2.8$, with a median redshift of $z_{\rm med}=0.80$. Kuźmicz et al.
(2018) list 10 GRGs with $10^{23}<P_{1400}<10^{24}$ at low redshift, while
Dabhade et al. (2017) and Dabhade et al. (2020a) found GRGs down to
Log($P_{150}$) $\sim 24$. The median r-band magnitude of the host galaxies in
our BLDF-GRG sample is 21.68, compared to 20.7 for the 181 GRGs that Andernach
et al. (2021) found by inspecting the 888-MHz Rapid ASKAP Continuum Survey
(RACS, McConnell et al., 2020), showing the Boötes LOFAR deep field to allow
finding fainter and more distant radio galaxies. A quantitative comparison
with some of the most recent and largest samples of GRGs is shown in Table 1.
The columns are: (1) reference and survey used, (2) the observing frequency,
(3) number of GRGs in the sample, (4) minimum and median flux of the sample at
the observing frequency, (5) minimum and median decimal logarithm of the power
of the sample at 150 MHz calculated assuming a spectral index $\alpha$=0.7,
(6) median of the redshift of the host galaxies. It is worthwhile to notice
that the median flux of the BLDF-GRGs is the lowest among the reported
samples, while the median redshift is the second largest, only slightly
surpassed by Kuźmicz & Jamrozy (2021) who carried out a dedicated search for
extended radio galaxies with LLS$>$1 Mpc from spectroscopic QSOs from SDSS
DR14Q.

The list of our sources is provided in Table LABEL:tab:list. A "C" appended to
the GRG name indicates that it is a candidate, meaning that either the host
itself, or its redshift, or its LAS are uncertain. Fig. A1 shows the cutouts
of the BLDF image around the GRGs. The size of these cutouts is proportional
to the LAS of the GRG and it is smaller than the size of the cutouts used for
the flux integration. The cyan circle identifies the position of the galaxy
host. Notes on individual GRGs are reported in the appendix.

(1) |  (2) |  (3) |  (4) |  (5) |  (6)
---|---|---|---|---|---
Survey,Reference |  Freq. |  N of |  $S_{\rm min,med}$ |  $P_{\rm min,med}^{150}$ |  $z_{\rm med}$
|  GHz |  GRGs |  mJy |  W/Hz |
Literature1 |  0.8/1.4 |  349 |  5.20,164 |  23.7,26.2 |  0.24
NVSS2 |  1.4 |  25 |  28.0,95.0 |  24.7, 25.8 |  0.22
LOTSS3 |  0.15 |  239 |  2.00,218 |  24.0,26.1 |  0.53
NVSS4 |  1.4 |  161 |  3.00,209 |  24.4,25.3 |  0.23
NVSS,SDSS5 |  1.4 |  76 |  —-,—- |  26.0,26.7 |  0.82
RACS6 |  0.888 |  181 |  5.00, 40.0 |  24.0,26.4 |  0.66
BLDF, this work |  0.15 |  74 |  3.6, 29.2 |  24.5,25.8 |  0.80
Table 1: Comparison between our BLDF-GRG and previous samples. References:
1-Kuźmicz et al. (2018), 2-Dabhade et al. (2017), 3-Dabhade et al. (2020a),
4-Dabhade et al. (2020b), 5-Kuźmicz & Jamrozy (2021), 6-Andernach et al.
(2021). References 5 and 6 are compilations of GRGs with LLS larger than 1
Mpc, while all the others include GRGs with LLS $>$ 0.7 Mpc.

###  2.1 LoLSS and NVSS data

Data from radio surveys carried out at different frequencies allow an analysis
of the spectra of the radio sources. However, the low surface brightness of
GRGs makes their detection challenging, especially at higher frequencies. The
only deep observation in the Boötes field at higher frequencies is presented
in de Vries et al. (2002) although the image is not available. Moreover, the
APERture Tile In Focus (Apertif) survey (van Cappellen et al., 2022) is not as
complete as NVSS in this region. For this reason, we looked for the BLDF-GRGs
in the NVSS (Condon et al., 1998) which covers the sky north of -40 deg
declination at 1.4 GHz. The NVSS has an angular resolution of 45$\rm"$ and is
very sensitive to sources with low surface brightness. The rms noise level is
0.45 $\rm mJy~{}beam^{-1}$ (Stokes I). Finally, the LOFAR LBA Sky Survey
(LoLLS, de Gasperin et al., 2021) covers the very low-frequency
($<100\rm~{}MHz$) regime. The LoLLS Boötes deep field was observed with the
Low Band Antennas (LBA) at 34-75 MHz for 56 hours (Williams et al., 2021). The
integration time makes this observation the first sub-mJy survey below 100
MHz, with an rms noise of 0.7 $\rm mJy~{}beam^{-1}$. The resulting image has
an angular resolution of 15$\rm"$.

###  2.2 Infrared data

We cross-matched the GRG hosts with infrared data from the WISE survey in
order to determine the accretion mode of the central engine. The Wide-field
Infrared Survey (Wright et al., 2010) is an all-sky survey conducted in four
spectral bands: W1 ($3.4\mu$m), W2 ($4.2\mu$m), W3($12\mu$m), W4 ($22\mu$m)
with angular resolution 6.1, 6.4, 6.5, 12$\rm"$, respectively. AllWISE (Cutri
et al., 2013) is the resulting catalogue of the combination of WISE and
NEOWISE (Mainzer et al., 2011) surveys. The AllWISE source catalogue contains
accurate positions, proper motion measurements, four-band fluxes and flux
variability statistics.The CatWISE2020 (CWISE) catalogue contains objects
selected from WISE and NEOWISE survey data at 3.4 and 4.6 $\mu$m (W1 and W2)
and it is the most extensive dataset of the full mid-infrared sky. We found
that the CatWISE catalogue often (in about 25% of cases) provides multiple
matches for a single position with a distance between the matches less than
the angular resolution of the telescope. Moreover, often the source with the
brighter magnitude appears with lower S/N ratio, opposite to expectation.
Furthermore, the catalogue does not have data at 12 and 22 $\mu$m that are
used in the WISE color-color diagram. Comparing the AllWISE and CatWISE
magnitudes, we found that the W1 and W2 magnitudes in both catalogues are
consistent with each other (see Fig. 1). We decided to use the AllWISE data
for our infrared analysis. The CWISE catalogue contains fainter sources than
AllWISE and eight of the GRG hosts are only detected in CWISE. Hence, we did
not consider these for the infrared analysis. We noticed that two types of
magnitudes are listed, namely "Wipro" and "Wimag", where i=1,2,3,4 refers to
the WISE band. The former is the magnitude measured with profile-fitting
photometry, while the latter is the magnitude measured in an 8.25$\rm"$ radius
circular aperture centered on the source position (see Cutri et al., 2013, for
more details) 222
https://wise2.ipac.caltech.edu/docs/release/allwise/expsup/sec2_1a.html. The
NASA/IPAC Infrared Science Archive 333
https://wise2.ipac.caltech.edu/docs/release/allsky/ provides the WISE
magnitudes "Wipro" and the associated errors in the four bands.

Figure 1: Comparison between the magnitudes in the W1 (black) and W2 (blue)
bands in the AllWISE and CWISE catalogue. The yellow line marks the one-to-one
relation.

##  3 Results

###  3.1 Distribution of the largest linear sizes

The distribution of the LLS of the (giant) radio galaxies can give clues as to
whether GRGs are just extreme cases of the general population of radio
galaxies (RGs), or constitute an independent class of sources.

There are several distributions that describe either the extreme values of
another underlying distribution, such as the distribution of the largest size
for a given sample of RGs, or distributions for random objects above a given
threshold, such as the exponential, or the Pareto distribution (see e.g.
Coles, 2001, for more details). GRGs are part of the latter type of
distributions as they are RGs whose size exceeds 0.7 Mpc. As a consequence, we
restrict our analysis to exponential (as a special case) and generalised
Pareto (Coles, 2001) distributions. The latter is commonly used to estimate
the probability of exceedances over a high threshold (see Zaninetti & Ferraro,
2008; Bouillot et al., 2015; Aschwanden, 2015, for applications). The
generalised version of such a distribution is:

$f_{P}(x)=\frac{1}{\sigma}\left(1+c\frac{x-\mu}{\sigma}\right)^{-1-\frac{1}{c}},$
(2)

where $c$ is the shape parameter. For $c>0$ the support of the distribution is
$x\geq\mu$, while for $c<0$ it is limited to $\mu\leq x\leq\mu-\sigma/c$. The
exponential distribution is a special case of the generalised Pareto
distribution obtained by taking the limit $c\rightarrow 0$:

$f_{E}(x)=\frac{1}{\sigma}e^{-\frac{x-\mu}{\sigma}},\quad x\geq\mu.$ (3)

In Eqs. (2) and (3), $\mu$ and $\sigma>0$ are the location (the threshold
value) and scale parameters, respectively.

Recently, Oei et al. (in prep.) carried out a detailed analysis of the
distribution of the LLS using about 500 GRGs. Assuming a Pareto distribution,
the authors found a slope of $-4$, thus $c=1/3$ (see Eq. 2). These authors
mostly focused on local GRGs ($z<0.2$) with an angular size larger than 5′,
while Andernach et al. (2021) observed a similar slope in the cumulative size
distribution of a compilation of GRGs found by visual inspection of sources in
the RACS survey (McConnell et al., 2020) complete down to an angular size of
$\sim 2\rm^{\prime}$ and independent of redshift, which resulted in 178 new
GRGs larger than 1 Mpc.

In this work, we carried out a simple statistical analysis on the LLS
distribution of our GRGs, using the complete sample of extended RGs provided
by Miraghaei & Best (2017) (MB17 hereafter). This sample provides measurements
of the largest linear sizes for 1329 extended RGs (we revised the measurement
of the LAS at 1.4 GHz of some sources and consequently re-calculated the
linear size by using the listed redshifts) with hosts selected from SDSS. The
flux density threshold of this sample is 40 mJy, which corresponds to roughly
200 mJy at LoTSS frequencies for $\alpha=0.7$. The catalogue shows a lack of
RGs with linear extents smaller than 50 kpc and complete catalogues for the
smallest RGs are missing in literature (Capetti et al., 2017, 2020). For this
reason, we did not include the RGs with LLS $<$ 50 kpc in our analysis.

We used maximum likelihood estimation to fit the two distributions to the LLS
of our GRGs and the RGs listed in MB17. The parameters of the fit are the
location and scale parameters; the shape parameter, $c$, is considered only in
the generalised Pareto distributions. In this analysis, the location parameter
is the minimum size of the RGs of the two samples (50 kpc and 700 kpc for the
MB17 and BLDF sample respectively). Thus, we performed a Kolmogorov-Smirnov
(KS) test between our samples and randomly generated data coming from the
resulting best-fit distributions for 1000 times, averaging the p-values
obtained from each iteration. Such a test is commonly used to decide whether
two samples derive from the same population; the closer the p-value is to 0
the more confident we are in rejecting that the samples were drawn from the
exponential or Pareto distribution. The results are summarised in Table 2 and
we show the fit in Fig. 2. The location and scale parameters are given in
units of Mpc .

For the MB17 sample we found $c=0.02\pm 0.01$ when fitting the generalized
Pareto distribution, which indicates that the distribution of the LLS is very
close to exponential. The p-value resulting from the KS test between the MB17
sample and the exponential distribution is $0.52$, confirming that the
exponential distribution provides an acceptable description of the data.
Similarly, both distributions are reasonable fits to the sample of the LLS of
the GRGs. The rather small value of the shape parameter, $c=0.22\pm 0.12$,
suggests that also the LLS of the GRGs follows a fairly steep Pareto
distribution. It is also consistent with an exponential distribution with the
same scale parameter.

However, the scale parameters of the RG and GRG samples are different. The
scale parameter of the MB17 sample, which is 140 kpc, is well above the cutoff
suggesting that the typical size of the extended RGs is larger than 50 kpc. On
the other hand, the scale for GRGs is 0.52 Mpc which is below the cutoff,
showing that GRGs are indeed larger than the intrinsic scale of the
distribution. These results indicate that, even though we are not probing the
same distribution for both RGs and GRGs, an exponential distribution
reasonably describes the general features of both samples. The analysis also
has some limitations. First of all, the two samples are selected at two
different frequencies; in particular at 1.4 GHz the emission of cores is often
more prominent and lobes are usually more difficult to observe. Moreover, MB17
selected only sources with a flux density larger than 40 mJy at 1.4 GHz
($\sim$ 200 mJy at 150 MHz for $\alpha=0.7$), while there are only 9 GRGs with
a correspondingly larger flux density in the BLDF sample. Furthermore, the
BLDF sample is not complete in the range $0.7$ Mpc $<$ LLS $<1$ Mpc. These
limitations might explain the difference of the inferred typical scales of the
two samples.

|  MB17 sample |  BLDF-GRG sample
---|---|---
Pareto |  $c=0.02\pm 0.01$,scale $=0.14\pm 0.01$ |  $c=0.22\pm 0.12$,scale$=0.52\pm 0.03$
|  $p=0.47$ |  $p=0.94$
Exponential |  scale $=0.14\pm 0.01$ |  scale $=0.52\pm 0.02$
|  $p=0.52$ |  $p=0.70$
Table 2: Results of the fit to the linear size distribution of the RGs
provided from Miraghaei & Best (2017) and the BLDF-GRG sample. According to
the p-value obtained by a KS-test, we cannot reject the hypothesis that
exponential and Pareto distributions fit the LLS distribution of both RGs and
GRGs.

Figure 2: Top panel: Distribution of the largest linear sizes of a sample of
RGs provided by Miraghaei & Best (2017). Lower panel: Distribution of the
largest linear sizes in the BLDF-GRG sample. The solid red and dotted orange
lines are the best fit of the Pareto and exponential distribution
respectively. The $y$-axis represents the probability that a (G)RG has a
certain LLS.

###  3.2 Redshift evolution and P-D diagram

We show the LAS-z diagram for our BLDF-GRG sample in Fig. 3, along with some
reference lines that represent the angular size of the "standard rulers" of
four different sizes as function of redshift. On the upper and right sides of
Fig. 3 we show the distributions of redshifts and LAS, respectively. The red
histogram in the upper panel shows the distribution of the spectroscopic
redshifts. It is worth emphasising that the minimum required angular size of
RGs to be labeled as giant with LLS $>$ 0.7 Mpc is 1.3′ and 2.0′ with LLS $>$
1 Mpc, and these minima occur near redshifts $\sim$1.7

Figure 3: The LAS-z diagram in the BLDF-GRG sample along with some reference
lines of four "standard rulers", whose sizes are listed in the upper-right
legend. Their distributions in redshift (upper panel) and LAS (right panel)
are also shown. The red histogram shows the spectroscopic redshifts.

In Fig. 4 we show the radio powers of BLDF-GRGs as a function of redshift. The
solid red line shows the evolution of the power of a GRG with a surface
brightness equal to 30 $\mu$Jy beam-1 which is the noise level of the BLDF in
the inner 3 $\rm deg^{2}$. We approximated the shape of GRGs by ellipses with
a major and minor axis of 0.7 and 0.2 Mpc, respectively. The dashed blue line
is the power of a point source with a brightness of 30 $\mu$Jy beam-1 as
function of redshift. These two lines correspond to the flux-limit of the
Boötes LOFAR survey and they provide a lower limit for the observed radio
power. This result suggests that the clear trend we observe, with more
powerful RGs at high redshifts, is likely due to a combination of the
Malmquist bias and the surface brightness dimming proportional to $(1+z)^{-4}$
which is certainly important for extended or diffuse sources. Furthermore,
inverse-Compton losses, due to interaction of the relativistic electrons with
CMB photons will be larger than synchrotron radiative losses in the evolution
of the lobes of giant radio sources (Machalski et al., 2001; Konar et al.,
2004). Inverse-Compton losses are proportional to the initial energy of the
CMB photon, leading to larger energy losses at high redshift due to the
increasing CMB energy density which is proportional to $(1+z)^{4}$. Note also
that in Fig. 4 there may be an artificial clustering at z$\approx$1 due to
photometric redshift values in DESI DR9 rarely exceeding $z\approx$1.1.

Figure 4: The relation between the radio power at 150 MHz, $P_{150}$, and the
redshift, $z$, in the BLDF-GRG sample. The solid red line shows the power of a
GRG with a surface brightness equal to the noise level of the BLDF and
integrated over its respective area of emission, at various redshifts. The
dashed blue line traces the redshift evolution of the power of a point source
with a flux density equal to 30 $\mu$Jy beam-1.

The P-D diagram shows the relation between the radio power at a specific
frequency and the linear size (Baldwin, 1982). With such a diagram it is
possible to trace the evolution of RGs (Ishwara-Chandra & Saikia, 1999;
Machalski et al., 2004). The P-D diagram of our BLDF-GRG sample along with
GRGs from recent samples (Dabhade et al., 2017, 2020a, 2020b; Kuźmicz &
Jamrozy, 2021; Andernach et al., 2021) is shown in Fig. 5. We used a standard
spectral index, $\alpha=0.7$, to compute the power at 150 MHz for those
sources with a flux estimated at other frequencies. As found before (e.g.,
Ishwara-Chandra & Saikia, 1999; Kuźmicz & Jamrozy, 2012; Dabhade et al.,
2020a; Kuźmicz & Jamrozy, 2021), the larger RGs are less powerful. A deficit
of GRGs is clearly visible in the upper-right corner, where powerful and large
RGs should reside, suggesting that the luminosity of RGs decreases as they
evolve to giant radio sources which is likely the latest stage of the
evolution according to models (e.g., Kaiser & Alexander, 1997a). The electron
energy losses due to adiabatic expansion and radiation over the lifetime of
the lobes could cause such a deficit. Fig. 5 also shows a lack of GRGs with
large linear sizes and small radio powers. This result might suggest that RGs
have to be powerful enough in order to reach the largest sizes. However, the
most extended RGs have a rather low surface brightness, thus their detection
becomes more difficult with increasing size. As a matter of fact, we have been
starting to observe large ($>$ 1 Mpc) and faint ($\sim 10^{24}\rm
W~{}Hz^{-1}$) GRGs only with the most recent observations with LOFAR and ASKAP
(Andernach et al., 2021).

Figure 5: P-D diagram that shows the specific power at 1500 MHz versus the LLS
of the BLDF-GRGs. Other GRG samples are included for comparison, such as
Dabhade et al. (2017), Dabhade et al. (2020a), Kuźmicz & Jamrozy (2021),
Dabhade et al. (2020b) and Andernach et al. (2021). The high sensitivity of
the observations in this field enables us to detect several new GRGs at lower
power ($\sim 10^{24}\rm W~{}Hz^{-1}$).

###  3.3 Spectral indices

Radiative ageing affects the radio spectra since more energetic electrons
suffer higher energy losses and, consequently, have shorter lifetimes. This
induces a steepening of the spectra at high frequencies ($\gtrsim$ GHz) and
the spectral index can give an estimate of the age of a radio source. In order
to compute the integrated spectral index (i.e., estimated from the total flux
of the source) we performed the following steps: First, we convolved the
higher-resolution images (LoLLS and LBDF) to the (lower) resolution of
45$\rm"$ of NVSS and regridded the images to a size of 0.2∘ centered on the
sky coordinates of the source. This step is necessary because the measured
flux can change with the resolution of the image. We performed sigma-clipping
at a level of $3\sigma_{\rm rms}$, where $\sigma_{\rm rms}$ is the rms noise
of the individual convolved image, and integrated the flux of the sources. If
the source is undetected in the NVSS, we considered an upper limit for the
flux of such source equal to $3\sigma_{\rm rms}$. For sources that are
detected neither in NVSS nor in LoLSS we did not estimate the spectral index.
We also excluded those GRGs that were blended with other sources after
convolution. Once the fluxes at different frequencies are calculated, we
performed a linear regression to calculate the spectral indices. In order to
compute a more robust error, we carried out a simple bootstrapping to
determine the errors in the fit parameters. This routine generates Gaussian-
distributed random fluxes whose mean is equal to the initially estimated flux
and a standard deviation that is determined from the error of this flux. Then,
a fit is performed for each dataset and the final variance of the multiple
fits is used as the error of the spectral index.

In Fig. 6 we show the relation between the spectral index and the linear size
in our BLDF-GRG sample. We find spectral indices around 0.8 and no substantial
spectral steepening with increasing LLS, mainly because the integrated flux is
dominated by the regions with recently injected or re-accelerated particles
(the core and hotspots). Moreover, Fig. 7 does not suggest a relation between
the spectral index and the redshift. On the other hand, Dabhade et al. (2020b)
recently found a weak correlation between the spectral index and linear size
and the redshift in a larger sample of GRGs, in agreement with Blundell et al.
(1999) and Jamrozy et al. (2008). Large and complete samples are needed to
establish whether GRGs exhibit a correlation between these properties, as well
as high-resolution spectral index maps to trace a possible steepening of the
spectra along the lobes. We also discuss the contribution of the core to the
total flux at 150 MHz, that is the core fraction, $f_{c}$, defined as the
ratio between the flux of the core and the total flux. The emission of the
core of the RGs is dominated by the recent ejecta launched by the central
black hole and it usually has a flatter ($\alpha<0.5$) or inverted spectral
index ($\alpha<0$) (Konar et al., 2004, 2008). This would in turn flatten the
integrated spectral index calculated from the total flux of the radio source.
Thus, we calculated the flux of the core of GRGs in the BLDF image. In case of
absence of core emission or indistinguishable core, we did not calculate the
flux. Fig. 8 shows the integrated spectral index against the core fraction.
For better visualisation, all spectral indices are treated as absolute
measurements with a relative error, irrespective of whether they are upper
limits or not. An expected trend of the spectra becoming flatter for larger
values of $f_{c}$ can be seen and for $f_{c}\approx 0.2$ the spectral index is
about $0.5$. This indicates a flattening of the integrated spectral index
induced by the relatively large contribution of the emission of the core of
some GRGs. Such a core fraction suggests that most GRGs are not entirely
passive and might be in a phase of restarted activity.

Figure 6: Spectral index in the range 50-1400 MHz for the BLDF-GRG sample
against the linear size. The typical slope of radio spectra in such RGs is
about -0.8, which is denoted by the red line. GRGs do not show a substantial
steepening at the largest linear extent, mainly because we detect the regions
with recently injected or re-accelerated particles (e.g., hotspots). Figure 7:
Spectral index in the range 50-1400 MHz for the BLDF-GRG sample against the
redshift of the host galaxies. The spectral index does not show a clear trend
with redshift. Figure 8: Spectral index in the range 50-1400 MHz for the BLDF-
GRG sample against the core fraction $f_{c}$. Due to the increasing
contribution of the core to the total emission, the radio spectra flatten in
the range $0<f_{c}<0.2$, while the spectral index is constant for larger
values of the core fraction.

###  3.4 HERG and LERG dichotomy

Based on their optical spectra, AGN can be classified as High-Excitation Radio
Galaxies (HERG) and Low-Excitation Radio Galaxies (LERG). The former have an
accretion rate onto the black hole between one and ten per cent of the
Eddington ratio. They are hosted by bluer, star-forming galaxies and lower-
mass black holes. In contrast, LERGs are likely hosted by high-mass galaxies
with a central black hole that experiences accretion below one percent of the
Eddington limit (Best & Heckman, 2012).

The host galaxies in our BLDF-GRG sample are usually too faint to allow a SED
fitting and provide a classification based on the optical spectra.
Nevertheless, mid-IR data can be used to classify AGN (Assef et al., 2010;
Jarrett et al., 2011; Stern et al., 2012; Mateos et al., 2012; Assef et al.,
2013). Gürkan et al. (2014) have shown that HERGs and LERGs have different
mid-IR luminosities. The former are mostly luminous sources in the infrared
band and an empirical cutoff can be drawn in the $22\mu$m - 151 MHz luminosity
plot (e.g., Fig. 9), with LERGs showing a mid-IR luminosity below $4-5\times
10^{43}\rm~{}erg\,s^{-1}$ ($4-5\times 10^{36}\rm~{}W$). Moreover, while LERGs
lie in the bottom-left region of the WISE colour-colour plot (which is shown
in Fig. 10), HERGs are mostly located on the right side. The $y$-axis is the
difference between the magnitude in the W1 and W2 band, while the $x$-axis
shows the colour obtained from W2 and W3. Fig. 9 shows the relation between
the radio power at 150 MHz and the infrared power at $22\mu$ m for the BLDF
GRGs. It is worth noting that most of our sources have values or upper limits
for the infrared power below the orange horizontal line, indicating that in
our sample the optical host galaxies are predominantly LERGs. This is also
confirmed by the WISE colour-colour plots (Fig. 10; W2-W3 vs W1-W2). In this
figure, we coloured the host galaxies according to the classification into
HERGs (black) and LERGs(blue) suggested from Fig. 9. Even though only a few
sources lie in the region delimited by W1 - W2 $<$ 1 and W2 - W3 $<$ 2.5
(namely the LERGs region), almost all of them are upper limits (arrows), in
agreement with Fig. 9, and may shift into the LERG region with deeper mid-
infrared observations. A source has an upper limit in the infrared power if
the signal-to-noise ratio is lower than 2, either in the W3 or W4 band. The
red points in both plots are either spectroscopically identified quasars or
quasar candidates in our sample and lie in the upper region (W1 -W2 $\gtrsim
1$ and W2 - W3 $\gtrsim 2$). Our sample is drawn from the faintest sources,
which poses a limitation to our analysis since most of the GRG hosts are not
detected in the W4 band.

Figure 9: Infrared ($22\mu$m, W4) - radio (150 MHz) power plot for BLDF-GRG
sample. The arrows are upper limits with a signal-to-noise ratio lower than 2
in the W4 band. The orange line is an empirical boundary between HERGs and
LERGs (Gürkan et al., 2014). The plot indicates a predominance of LERGs in our
sample. The red points are either spectroscopically identified quasars or
candidate quasars.  Figure 10: WISE colour-colour diagram in the BLDF-GRG
sample. Red dots mark either spectroscopically identified quasars or candidate
quasars. Almost every GRG host lies in the HERG region of the plot. However,
half of them are upper limits (arrows), which means that the source has a
signal-to-noise ratio smaller than 2 in the W3 band. The classification as
HERGs or LERGs is based on the infrared power relation criterion (Fig. 9).

Best et al. (subm.) and Mingo et al. (2022) provide an AGN classification into
HERG and LERG performed by SED fitting in the optical band. Therefore, we
validated our results by crossmatching our BLDF-GRG sample with these
catalogues. We found 35 matching GRGs, of which only ten are radiatively
efficient AGN. Recently, Mingo et al. (2022) reported that the majority of
FRII galaxies experience low accretion rates, especially for the low-power
($L_{150}<10^{26}\rm~{}W~{}Hz^{-1}$) AGN population. Here, we confirm this
result for GRGs as most of them seem to be in a radiative inefficent mode,
regardless of the radio power. Based on the excitation state, it does not
appear that GRGs are undergoing massive, radiatively efficient accretion at
the present time. However, it is possible that the central engine has gone
through a series of recurrent AGN events that have allowed the GRGs to grow to
its extreme size.

During the inspection of the BLDF, we found 152 extended RGs which have a
linear size in the range 10-700 kpc. We selected the RGs by angular size,
trying to be reasonably complete for LAS $\gtrsim$ 1.3′. For this reason, only
3 of them have a linear extent smaller than 100 kpc. We compared the stellar
mass and star formation rate (SFR) of GRGs and smaller radio galaxy (RG) hosts
in Fig. 11. The total sample contains 243 sources (GRGs+RGs), 87 (35 GRGs and
52 RGs) of which have either SFRs or stellar mass values from either Best et
al. (subm.) or Mingo et al. (2022). In our sample, GRG hosts have high stellar
masses ($>10^{10.5}M_{\odot}$) and the median decimal logarithm of the stellar
mass for RGs (11.24) and GRGs (11.13) is similar. Nevertheless, the
distribution of GRG hosts shows an excess of stellar stellar masses lower than
$\rm M_{*}=10^{11.5}\rm M_{\odot}$ with respect to RG hosts. The result is in
agreement with previous studies which claimed that GRGs are usually hosted by
luminous elliptical galaxies dominated by the emission of evolved giant stars
(Lara et al., 2001; Machalski et al., 2001; Clarke et al., 2017; Dabhade et
al., 2017; Seymour et al., 2020). These are effectively dead systems in which
most of the star formation and black hole growth have already come to an end,
suggesting that GRGs are the last stage of the evolution of RGs. However, very
rare, massive spiral galaxies that host relativistic jets and lobes that
extend to Mpc scale have been found as well (e.g, Mao et al., 2015, and
reference therein). Moreover, Kuźmicz et al. (2019) performed a detailed
analysis of the star formation history in a sample of GRGs finding an
’intermediate’ stellar population with an age between $9\cdot 10^{8}-7.5\cdot
10^{9}$ yr, besides the common old stellar population residing in the host
galaxies ($t>10^{10}$ yr). Similar results have been found in the GRG ESO
422–G028 by Zovaro et al. (2022). This is indicative of star formation
activity at least in some GRG hosts, as shown in the lower panel of Fig. 11.
In fact, we see an excess of GRGs at SFR values of 10-100 $\rm
M_{\odot}~{}yr^{-1}$ with respect to RGs.

Figure 11: Upper panel: Distribution of the stellar mass in GRG (blue) and RG
(red) hosts. The former are usually very massive galaxies
($>10^{10.5}M_{\odot}$), while the latter that span the entire range from
$10^{10}$ to $10^{12}M_{\odot}$. Lower panel: SFR distribution for GRGs (blue)
and RGs (red). The distribution of GRGs is uniform, indicating star formation
activity in at least 10 out of 23 GRG hosts.

###  3.5 GRG environment

Several studies have addressed the role of the environment in the evolution of
RGs in the past. It is known that only a small percentage of GRGs reside in
galaxy clusters or groups (e.g., Dabhade et al., 2020a; Andernach et al.,
2021) and it is commonly believed that the intracluster medium can frustrate
the expansion of jets and lobes in the local environment (Subrahmanyan et al.,
2008; Safouris et al., 2009).

We tested the conjecture that GRGs are preferentially located in underdense
environments using photometric redshifts from the DESI Legacy Imaging Survey
(Dey et al., 2019), assuming that the galaxies trace the distribution of the
intergalactic medium. The DESI DR9 photometric redshift catalogue includes
observations from the Beijing-Arizona Sky Survey (BASS, Zou et al., 2017),
DECam Legacy Survey (DECaLS) and Mayall z-band Legacy Survey (MzLS) (Dey et
al., 2019). In order to look for differences in the environments of GRGs and
ordinary RGs, we performed this analysis for our BLDF-GRG sample, as well as
for the sample of smaller RGs we found in the BLDF. Due to the depth limit of
the DESI survey, we restricted our analysis to $z<0.7$ yielding 35 GRGs (23 of
which have linear sizes larger than 1 Mpc) and 96 RGs. To examine the source
environments, we first have to create a volume-limited sample, by cutting out
those galaxies with an absolute magnitude (luminosity) in the $r$ band
brighter than the absolute magnitude (luminosity) of a galaxy with an apparent
magnitude equal to the flux limit, in the $r$ band, located at the maximum
redshift considered ($z=0.7$). Such a cut limits our analysis since it is
based on the most luminous galaxies which are the rarest as well. As a
consequence, we might miss galaxies that are members of galaxy clusters and
understimate the overdensities. We then performed a similar analysis dividing
the sample into three redshift bins, $0\leq z<0.3$, $0.3\leq z<0.5$, $0.5\leq
z<0.7$. This method enables us to utilise a larger number of galaxies at low
redshifts and increase the robustness of the measurement of the overdensities.
The results of the two analyses are similar and, due to the poor statistics of
the second method, we decide to report the findings of the first method
described. We counted the number of galaxies within a sphere with a radius
equal to a comoving distance of 10 Mpc centred on the coordinates of the (G)RG
hosts. We approximated the redshift of the source with the redshift value
reported in Tab. LABEL:tab:list, without taking into account the error. We
show the distribution of GRGs (blue) and RGs (grey) with surface number
density of galaxies, $\Sigma_{\rm gal}$, within 10 Mpc in Fig. 12. When
testing for differences in the galactic environments around GRGs and RGs, the
KS test yields a p-value of 0.17. This result shows that there is no evidence
that GRGs reside in environments different from other RGs, in agreement with
Komberg & Pashchenko (2009) and Lan & Prochaska (2021).

Dividing the sphere of radius 10 Mpc into 15 shells with equal volumes, we
compute the radial profile of the surface number density of the galaxies (Fig.
13). GRGs have a tendency to reside in sparser environment with respect to
ordinary RGs as the latter have a larger number density of galaxies at almost
every radius. However, the p-value of 0.83 of a KS test comparing GRGs with
ordinary RGs suggests that this result is not statistically significant.

Figure 12: Distribution of the surface number density of galaxies within 10
Mpc of the GRGs (blue) and RGs (grey). According to the KS test, we cannot
rule out the hypothesis that the samples are drawn from the same distribution
at a level of significance of 90%. Nevertheless, the figure shows that GRGs
have a tendency to reside in underdense environment. Figure 13: Radial
distribution of the surface number density of galaxies within 10 Mpc of the
GRGs (blue) and RGs (grey). The KS test suggests that the two populations
inhabit similar environments.

Our results are in agreement with Oei et al. (2022), who found the largest GRG
known to date (LLS=5 Mpc, $z=0.25$) and it has only 5 galaxies within 10 Mpc,
leading to a surface number density of 0.05 Mpc-2, and does not have a single
galaxy within 5 Mpc. The value of the surface number density and the number of
the galaxies are similar to those reported in Lan & Prochaska (2021), albeit a
direct comparison with their radial profile is impossible as the authors
considered only the neighbouring galaxies within a sphere of radius $R=1$ Mpc
centred on the GRG hosts. Finally, we studied the location of the galaxies
close to the GRGs with respect to the direction of the major axis of the
source or that of the lobe expansion. With such an analysis, we tested the
hypothesis whether jets expand preferentially into the direction of underdense
regions. We calculated the acute angle, $\Delta\theta$, between the vector
connecting the GRG host with each of the neighbouring DESI galaxies and the
orientation of the source major axis, with $\Delta\theta$=0 indicating a
neighbouring galaxy along the major source axis, and $\Delta\theta$=90∘ a
galaxy which is located perpendicular to the source major axis. The
distribution of $\Delta\theta$ appears uniform (Fig. 14). To test this, we
carried out a simple bootstrapping to generate 1000 random uniform
distributions of the same size as the number of GRGs of our sample, and then
performed a KS test comparing our distribution with each of these generated
samples, yielding a median p-value of 0.6.

Figure 14: Distribution of the orientation of galaxies surrounding GRGs with
respect to the direction of the expansion of jets. The distribution is
consistent with being uniform.

Based on a sample of 19 GRGs in the redshift range 0.05-0.15, Malarecki et al.
(2015) found that GRG hosts live in overdense environments and that GRG lobes
are shorter on the side that has a higher concentration of galaxies. Our
analysis of the environment suggests that GRGs have a tendency to reside in
underdense regions, even though a similar results is found for RGs as well. We
found that the environment of GRG hosts on larger scales than 1-2 Mpc is not
related to the orientation of the source major axis. As a consequence, only
the inhomogeneities in the surrounding medium within $\sim$ 1 Mpc might play a
major role in the radio galaxy evolution. Previous studies have shown that
asymmetries in radio morphology (e.g., length of the lobes) can be attributed
to a density gradient of the external medium (Konar et al., 2008; Safouris et
al., 2009; Subrahmanyan et al., 2008; Malarecki et al., 2015; Machalski,
2011).

Some former studies have suggested an evolution of the linear sizes of RGs
with redshift, which might be explained by the redshift evolution of the
intergalactic medium (Kapahi, 1989; Machalski et al., 2007; Onah et al.,
2018). However, Brüggen et al. (2021) found no dependence of the median linear
size or the median radio luminosity on the redshift and hence no evidence for
cosmological evolution of the population of GRGs. In our sample, the linear
sizes of RGs do not show a decrease up to $z=2$, even though the scatter is
large. At higher redshifts the sample is too small to establish a trend (Fig.
15). Due to the sensitivity limitations we are not able to detect extremely
large sources, especially those with low radio powers at higher redshift.
Moreover, $\sim 80\%$ of the BLDF-GRG have a redshift larger than 0.5,
favouring the idea of GRGs being rare, so they are mainly detected at high
redshift. We find that the volume number density of GRGs is $\rm n_{\rm
grg}(\textit{z}_{\rm max}=1.8)$ = 1.00 (100 Mpc)-3 (we excluded the only GRGs
with $z>2$) which is smaller than the estimate predicted by Oei et al, in
prep. who used a sample of 525 GRGs at relative low redshift.

Figure 15: LLS-z scatter plot in our sample which includes both GRGs and RGs.
The two variables do not show any decreasing trend up to $z=2$. The red line
marks the selected threshold of 0.7 Mpc.

##  4 Conclusions

In this paper we carried out a detailed search for GRGs in the Boötes LOFAR
deep field at 150 MHz (Tasse et al., 2021) where we identified 74 GRGs with a
linear size larger than 0.7 Mpc. The highest redshift GRG in our sample is a
spectroscopically confirmed quasar at $z=2.84$.

We studied the properties of the host galaxies using deep optical and infrared
survey data such as SDSS, DESI and WISE. We cross-matched our GRGs in the
LOFAR LBA and NVSS images and investigated their integrated spectral index.
Finally, the DESI DR9 photometric redshifts enabled us to inspect the
environment in which GRGs reside. The main results can be summarised as
follows:

  * •

The GRG surface number density based on our sample is 2.8 GRGs deg-2, which is
higher than the estimates previously reported in the literature (e.g.,
Delhaize et al., 2021; Brüggen et al., 2021).

  * •

The P-D diagram shows a lack of GRGs with large linear sizes ($>$ 2 Mpc) and
large radio powers ($P_{150}>10^{27}$ W Hz-1), suggesting an evolution of the
radio luminosity of such sources. In particular, the adiabatic expansion and
radiative losses play a role. On the other hand, the high sensitivity of the
Boötes LOFAR Deep Field allowed us to detect GRGs at smaller radio powers
($10^{24}\rm W~{}Hz^{-1}$) at 150 MHz (or $3\cdot 10^{23}\rm W~{}Hz^{-1}$ at
1.4 GHz for $\alpha$=0.7).

  * •

The integrated spectral index is independent of the linear size of the GRG. In
our analysis we find spectral indices of $\alpha$ = 0.7-0.8. However, this
result may be biased by the dominance of hotspots that usually have flatter
spectra.

  * •

Most GRG hosts are LERGs, showing that FRII radio galaxies can be produced by
a (currently) low accretion rate in agreement with Mingo et al. (2022). In our
sample, the optical hosts of the GRG and RG populations have a similar stellar
mass distribution. In particular, both RGs and GRGs show high stellar masses
($>10^{10.5}M_{\odot}$). The GRG hosts can be either quiescent galaxies with
SFR $<1\rm M_{\odot}~{}yr^{-1}$ or galaxies with a moderate SFR around 10-100
$\rm M_{\odot}~{}yr^{-1}$.

  * •

Based on the number density of galaxies with DESI DR9 photometric redshifts,
we found no significant differences between the environment density of GRG and
RGs nor did we find the sources major axes to be oriented preferentially
toward lower-density sectors.

  * •

We tested whether the linear size of GRGs (LLS$>$0.7 Mpc) and smaller RGs
(LLS$<$0.7 Mpc) have a similar distribution. We found a good agreement with
the exponential and generalized Pareto distributions in both populations, even
though the different scale parameters suggest that we might not probe the same
distribution. The scale parameter in the BLDF-GRG sample is below the minimum
size required to classify a radio galaxy as giant showing that in this work we
study the extreme population of RGs.

In the future, we will expand our work to the two other LOFAR deep fields
(ELAIS-N1 and Lockman Hole) and eventually LoTSS DR2 (Shimwell et al., 2022).
Moreover, modelling the spectra from high-resolution images might help to
reconstruct the evolution of AGN activity of GRGs as well as constrain the
properties of the environment around these peculiar objects.

## Acknowledgements

We thank the referee for their careful reading of the paper and constructive
comments. We thank L. Rudnick for preparing a low-resolution image of the
LoTSS Bootes Deep Field, which was filtered to enhance large-scale diffuse
structures.

This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) under Germany’s Excellence Strategy – EXC 2121 “Quantum
Universe” – 390833306 as well as grant DFG BR2026/27.

HA has benefited from grant CIIC 138/2022 of Universidad de Guanajuato,
Mexico. IP acknowledges support from INAF under the SKA/CTA PRIN “FORECaST”
and the PRIN MAIN STREAM “SAuROS” projects.

LOFAR (Van Haarlem et al., 2013) is the Low Frequency Array designed and
constructed by ASTRON. It has observing, data processing, and data storage
facilities in several countries, which are owned by various parties (each with
their own funding sources), and that are collectively operated by the ILT
foundation under a joint scientific policy. The ILT resources have benefited
from the following recent major funding sources: CNRS-INSU, Observatoire de
Paris and Université d’Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science
Foundation Ireland (SFI), Department of Business, Enterprise and Innovation
(DBEI), Ireland; NWO, The Netherlands; The Science and Technology Facilities
Council, UK; Ministry of Science and Higher Education, Poland; The Istituto
Nazionale di Astrofisica (INAF), Italy. This research made use of the Dutch
national e-infrastructure with support of the SURF Cooperative (e-infra
180169) and the LOFAR e-infra group. The Jülich LOFAR Long Term Archive and
the German LOFAR network are both coordinated and operated by the Jülich
Supercomputing Centre (JSC), and computing resources on the supercomputer
JUWELS at JSC were provided by the Gauss Centre for Supercomputing e.V. (grant
CHTB00) through the John von Neumann Institute for Computing (NIC). This
research made use of the University of Hertfordshire high-performance
computing facility and the LOFAR-UK computing facility located at the
University of Hertfordshire and supported by STFC [ST/P000096/1], and of the
Italian LOFAR IT computing infrastructure supported and operated by INAF, and
by the Physics Department of Turin university (under an agreement with
Consorzio Interuniversitario per la Fisica Spaziale) at the C3S Supercomputing
Centre, Italy.

## Data Availability

The datasets used for the analysis of this paper are publicly available at
https://lofar-surveys.org/deepfields.html. Table LABEL:tab:list will be made
available at the CDSn and through the VizieR service
(https://vizier.cds.unistra.fr).

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## Appendix A: Notes on individual sources

J1419+3337 has two elongated straight and symmetric relic-type lobes. The
compact source NE of the N end of the N lobe is DESI J214.7968+33.6483,
$r$=14.18, and unrelated to the GRG.

J1421+3431 has a radio core slightly extended towards two faint, diffuse outer
lobes.

J1421+3521 is a rather symmetric classical FR II source along PA $\sim
100^{\circ}$. The E lobe lies at the S end of an unrelated remnant-type radio
galaxy hosted by 2MASX J14220065+3523086 with LAS$\sim 3.3\rm^{\prime}$, with
its N lobe outside of our cutout.

J1422+3320 is a very straight FR II type source with relatively narrow lobes
showing emission decreasing in surface brightness from the hotspots right to
the host galaxy. Also displayed in Williams et al. (2016).

J1422+3255 No radio core is detected, and the source may also be hosted by
DESI J215.6873+32.9360, $r$=24.69, with $z_{ph}=1.020$, although this would
not alter its LLS.

J1423+3600 is a restarted or double-double radio galaxy with an inner double
of $\sim$24′′ size and both inner and outer double having stronger N lobes.

J1423+3403 shows some evidence for being restarted with two faint inner lobes
$\sim$24 ′′ apart and outer lobes being of remnant type. About 32′′ NNE of the
host a compact radio source (SDSS J142337.34+340330.2 at $z_{\rm ph}\sim$0.42)
is superposed on the NNE lobe.

J1423+3302: The BLDF image is slightly affected by sidelobes, but both VLASS
epoch 1 and 2 images confirm this is a restarted source, with an inner double
of $\sim$27 ′′. The ENE outer lobe is resolved out in VLASS while the WSW
outer lobe shows two hotspots, though the W hotspot may be hosted by DESI
J215.8935+33.0419, $r$=23.79, at a similar redshift as the host.

J1423+3529 has the second-largest linear size (3.4 Mpc) in our sample. It is a
restarted source with an inner asymmetric double of LAS$\sim$1.6 ′. The 6′′
BLDF image shows rather disrupted, and generally straight outer lobes, but the
LoTSS-DR2 low-resolution image leaves no doubt that the source is a physical
entity. Only the host is detected as a faint point source in VLASS.

J1423+3340 is a symmetric and straight FR II source with a core slightly
brighter than the lobes in BLDF. The host is only detected in CWISE, thus we
estimate a redshift of at least $\sim$1.5.

J1423+3605 is a WAT-type source with radio tails due SSE and W in a poor
cluster or group. An apparent loop of radio emission in BLDF W of the host is
caused by extended radio emission of a pair of galaxies at the same redshift
and $\sim$11′′ SW of the host.

J1424+3609 is a very large and straight FR II source with clear diffuse
emission trailing back from the outer extremities of the NNE and SSW lobes
towards the host. Only the NNE lobe shows a hotspot in VLASS while the end of
SSW lobe is diffuse and of very low surface brightness in VLASS. A compact
radio source $\sim$20′′ SSW of the host has no optical or IR counterpart and
is likely a knot of the SSW jet. The source was first noticed by us in
Williams et al. (2016).

J1424+3436 is likely a restarted radio galaxy with inner lobes of size
$\sim$50′′ but no clear hotspots in VLASS. Beyond the NE inner lobe a
collimated radio feature connects with the diffuse outer NE lobe, while beyond
the SW inner lobe the radio emission connecting with the SW lobe seems
bifurcated. The outer lobes show distinct radio morphologies with only the SW
one showing two hotspots in VLASS. First seen by us in the 62-MHz cutouts by
van Weeren et al. (2014), albeit with much lower sensitivity than BLDF.

J1425+3633 is a regular, straight, but slighty asymmetric FR II with outer
lobes highly dilute in VLASS and no hotspots.

J1425+3506 is an FR II source with faint, dilute lobes. The host could also be
DESI J216.2998+35.1115, r=25.00, with $z_{\rm ph}$=0.971,1.308,1.56 from Zhou
et al. (2021), Duncan et al. (2021), Chung et al. (2014) in which case its LLS
would be $\sim$1.1 Mpc.

J1425+3557 is a core-dominated source with very dilute remnant-type lobes
extending due E and W. An extended brightening $\sim$30′′ from the host due W
has no optical or IR counterpart and may qualify it as a hybrid-morphology
source (HyMORS).

J1426+3407C is a candidate FR II source since the SSE lobe has SDSS
J142625.73+340657.8 as a possible host, and the NNW lobe features SDSS
J142622.04+340902.0 at its S end.

J1426+3320 is an FR II source where both lobes bend from the E-W direction
towards S, giving it a C shape. It is completely resolved out in VLASS with no
hotspots.

J1426+3236 is a regular, straight and symmetric FR II source completely
resolved out in VLASS, suggesting that the hotspots have already disappeared.
Also listed in Mingo et al. (2022).

J1426+3222 is an FR II source with diffuse lobes towards E and W, already
shown with a lower-sensitivity image by Williams et al. (2016). From the inner
parts of each lobe faint radio plumes stretch out due N.

J1427+3625 is an asymmetric, slightly bent FR II source extending along
PA$\sim$48∘, with the NE lobe featuring a curved ridge of emission stretching
from the hotspot first due SE and then SW towards the host. The SW lobe only
shows a short trail from the end of the lobes towards the host. This is the
only source in our sample that has been reported before as a giant radio
quasar by Kuźmicz & Jamrozy (2021).

J1427+3312: Its host was detected in X-rays (CXOXB J142718.3+331205) by Brand
et al. (2006). The radio emission features a strong, short NW lobe and a much
longer and lower surface brightness SE lobe whose exact length is somewhat
uncertain, making it a hybrid morphology source.

J1427+3328C: the source with the largest angular size in our sample with very
inflated and low surface brightness lobes, with the E lobe slightly flattened
with major axis along PA$\sim$70∘ and the W lobe closer to the host and
extended in the N-S direction, almost perpendicular to the major axis of the
source. Several compact sources are superimposed on the lobes and it is
difficult to state a precise total flux. There is no radio emission detected
at the location of our proposed host 2MASX J14273770+3328081. However, it is
the brightest galaxy in both the optical and MIR (unWISE) in the entire region
of the radio emission. Also, its angular and linear sizes may be larger in
more sensitive future radio images. No radio emission detected at the location
of our proposed host 2MASX J14273770+3328081. However, it is the brightest
galaxy in both the optical and mid-infrared (unWISE) in the entire region of
the radio emission. There is in fact a second-brightest galaxy in this region
46′′ SSW of 2MASX J14273770+3328081, SDSS J142736.24+332726.0, $r$=18.03,
$z_{sp}$=0.231 (Kochanek et al., 2012), which does coincide with a radio
source of 150-MHz flux of 0.37-mJy in the LoTSS Bootes Deep Field. which is
also closer to lying mid-way between the flux-weighted centers of each lobe.
If this were the true host, its $LLS$ would be 2.0 Mpc.

J1427+3255C is a straight, symmetric classical FR II source along
PA$\sim$135∘. The SE lobe shows a diffuse radio tail (or plume) due N from the
termination point, while the NW lobe is fainter and more compact in the BLDF
image. We consider it a candidate GRG, although neither lobe has a suitable
optical or IR counterpart.

J1428+3432 is a remnant-type FR II radio galaxy with a clear core but very
diffuse, non-collinear lobes due NE and S.

J1428+3631 is a classical FR II source already shown by Williams et al. (2016)
with lobe emission almost all the way from the hotspots (clearly seen in
VLASS) and the radio core (faint, but detected in VLASS). There is another,
smaller and unrelated FR II source $\sim$1.6′ SW of the host.

J1428+3446 is a core-dominated FR II type source with rather straight and very
low surface brightness lobes along PA$\sim$150∘. Background sources are
superposed due W of the S lobe, as well as to the SW and NE of the N lobe.

J1428+3525 is a remnant-type radio galaxy with a clear core, a shorter and
stronger W lobe, and a longer and fainter E lobe. Both lobes are of very low
surface brightness and are aligned with the host, suggesting that a few
starlike optical objects in these lobes are superposed accidentally.

J1429+3326: the source features an unusual emission spur or plume emanating
from the SW lobe, close to the host, in the NW direction and perpendicular to
the main source axis, also seen in Fig. A1 of Williams et al. (2016) but too
faint to be seen in the 62-MHz image by van Weeren et al. (2014). The source
is completely resolved out in VLASS. Such features have been seen in both
lobes of X-shaped sources like in PKS 2014$-$55 Cotton et al. (2020) but in
J1429+3326 we see it only in one lobe.

J1429+3355 is a straight and slightly asymmetric FR II radio galaxy with the
shorter NW lobe being strong and featuring a hotspot in VLASS, while the SE
lobe is fainter in BLDF and undetected in VLASS suggesting the absence of a
hotspot. This source was first noticed by us in a 325-MHz VLA image kindly
supplied by R. Coppejans (Coppejans et al., 2015), but is also displayed in
Williams et al. (2016).

J1429+3356 is a core-dominated FR II source with a collimated (jet?) feature
half-way from the core to the NW lobe. This feature is very faint in VLASS
which also detects the end of the NW lobe as a diffuse feature (no hotspot),
while the SE lobe is completely undetected. The BLDF image shows some
background sources $\sim$30′′ SW of the SE lobe and $\sim$30′′ N of the end of
the NW lobe. This source was first noticed by us in a 325-MHz VLA image kindly
supplied by R. Coppejans (Coppejans et al., 2015).

J1429+3717 is a remnant-type radio galaxy which shows a clear core, a short E
lobe and a much larger SW lobe which has an unrelated strong FR II source
superposed. The latter does not permit us to measure a reliable size for the
diffuse source which is completely resolved out in VLASS.

J1429+3230C: this source, supposedly a large FR II with major axis along
PA$\sim$165∘, is somewhat speculative, since the faint S lobe has optical and
IR objects superposed. However, the N lobe is elongated along the source major
axis and does not feature suitable optical or IR counterparts. The suggestion
of a $\sim$2.2′ wide double source straddling the host along PA$\sim$100∘ is
due to two sources aligned with the host but with clear counterparts.

J1430+3519 is a symmetric and straight FR II radio galaxy with strong, but
very diffuse remnant-type lobes. Unusual features are two compact sources, one
at the SW edge of the SE lobe and another close to the middle of the NW lobe,
neither one having an obvious optical or IR counterpart. This source has the
steepest radio spectrum in our sample and was first seen by us in Williams et
al. (2016).

J1430+3322C: this faint source features an inner FR I-type structure of
$\sim$32′′ E-W extent, with the core faintly detected in VLASS, including a
slight E-W extent. The stronger W lobe is closer to the host than the more
detached E lobe located $\sim$1.8′ from the host. The source may well extend
further into a WAT-type source in future, more sensitive images.

J1431+3345 is probably a good example of an FR I source with continuous jets
from the host towards both lobes which seem to end in a strong bend, perhaps
seen in project in the SW lobe. Due to the presence of these outer lobes we
classify it as an FR I/II. While the jets appear rather straight for the first
arcmin from the host, their PA differs by about 7∘. The host is the brightest
cluster galaxy in cluster WHL J143103.5+334542 (Wen et al., 2012). This source
was first noticed by us in a 325-MHz VLA image kindly supplied by R. Coppejans
(Coppejans et al., 2015), but is also seen in Williams et al. (2016).

J1431+3535C is a relatively straight FR II source with lobes of different
morphology. Both lobes have optical/IR objects superposed, but in our opinion
these are less likely to explain the radio structure. There is a circularly
extended source immediately NW of the host, perpendicular to the major source
axis, which has no optical/IR counterpart. The strong extended radio source
$\sim$1′ W of the N end of the source is the bright foreground starburst
galaxy MCG +06-32-056 with a dust lane. The r=18.1 mag low surface brightness
galaxy is superposed on the SW lobe, but its blue color and low zphot suggest
it is a starforming galaxy in the foreground.

J1431+3440 is a straight and symmetric FR II source with diffuse lobes, each
of them showing plumes due W. The source is difficult to recognize due to
various compact sources due W and NW of the host.

J1431+3427 is a straight and symmetric FR II source with a faint radio core.
This source was first noticed by us in a 325-MHz VLA image kindly supplied by
R. Coppejans (Coppejans et al., 2015), but is also displayed in Williams et
al. (2016).

J1432+3411 is a symmetric, though slightly bent FR II source with no detected
hotspots in VLASS. The BLDF image suggests the jets feeding the lobes to have
a difference in PA of $\sim$7∘. This source was first noticed by us in a
325-MHz VLA image kindly supplied by R. Coppejans (Coppejans et al., 2015),
but is also displayed in Williams et al. (2016).

J1432+3328 is a rather asymmetric, though straight, FR II with an armlength
(or lobelength) ratio of 2.8. The source is listed in Mingo et al. (2022).

J1432+3545 is a very extended WAT-type source hosted by the brightest galaxy
of cluster WHL J143233.9+354540 (aka GMBCG J218.14135+35.76114 and MaxBCG
J218.14136+35.76113). The angular size we list may well be exceeded by future
more sensitive observations.

J1432+3220 is a symmetric FR II source with faint hotspots and a faint core
detected in VLASS. This source was first noticed by us in a 325-MHz VLA image
kindly supplied by R. Coppejans (Coppejans et al., 2015) and is also seen in
Williams et al. (2016).

J1432+3154C is a rather faint FR II source with diffuse lobes and a core
symmetrically placed between these lobes. We consider it a candidate because
each lobe has optical/IR objects which may explain the lobes as separate
sources. No part of the source is detected in VLASS.

J1432+3647 is an FR II source with detached, diffuse, low surface brightness
lobes bent at an angle of $\sim$25∘ with respect to the host. The NE lobe
appears bifurcated. Only the radio nucleus is detected in VLASS.

J1433+3220 is a possible restarted FR II source with an inner double of
$\sim$38′′ along PA$\sim$104∘, very close to the PA connecting the diffuse,
low surface brightness outer lobes. Since these lobes are large, some
optical/IR objects are seen superposed, but they are unlikely to explain each
lobe as a separate source. The host itself is undetected in both BLDF and
VLASS, which does not detect any part of the source.

J1433+3328 is a core-dominated straight FR II source oriented E-W and hosted
by a QSO at $z_{\rm sp}$=1.609. While the W lobe has a typical FR II
morphology being brightest at the end in BLDF with a barely detected hotspot
in VLASS, the E lobe is brightest about half way down the lobe, and is
undetected in VLASS. It is thus a possible hybrid-morphology source.

J1433+3450 is a classical, slightly bent FR II source with a faint core
detected in both BLDF and VLASS. While our proposed host coincides with that
radio core, it differs from that proposed by Morabito et al. (2017) which is
off the main radio ridge. The hotspots are strong in VLASS, albeit with much
shorter trails towards the host than those in BLDF. This source was first
noticed by us in van Weeren et al. (2014) and is also seen in Williams et al.
(2016). This is the source with the highest radio luminosity in our sample.

J1433+3145C is a low surface brightness diffuse radio galaxy without a clear
radio core. The LoTSS DR2 low-resolution image suggests a WAT-type source
whose host may also be located further South, e.g. SDSS J143320.32+314544.0
with $z_{\rm ph}\sim$0.4 which would make its LLS about 0.77 Mpc, but still
large enough to be a GRG. The strongest compact 150-MHz source at the S end of
the emission region, ILT J143320.57+314529.1 of $\sim$1 mJy, does not have any
optical/IR counterpart.

J1434+3428 is a complex, slightly bent FR II source with several radio knots
along the E lobe. Both lobes feature hotspots in BLDF which are also faintly
detected in VLASS, but which are located due N of the symmetry axis of the
lobes. The host of this source is still unclear. We have chosen the brighter
one, but $\sim$19′′ E of it there is WISEA J143430.65+342757.0 with more
typical AGN colors, undetected in the optical in DESI DR9, but found to be a
member of cluster ISCS J1434.5+3427 with $z_{\rm sp}$=1.240 from Alberts et
al. (2016), also detected as X-ray source 2CXO J143430.6+342757, and as FIRST
J143430.6+342757 in the radio. Adopting the latter host this source would be
only slightly larger and more radio luminous, as well as a candidate restarted
source. The source was first noticed by us in a 325-MHz VLA image kindly
supplied by R. Coppejans (Coppejans et al., 2015).

J1434+3214C has a clearly detected inner source of $\sim$1.0′ extent that is
accompanied by fainter lobes more or less symmetrically placed on the E and W
side of the latter, making it more of an FR I rather than FR II type source.
The source fades away below noise at LAS$\sim$3.7′ but may continue further in
more sensitive images.

J1434+3648 is an almost straight FR II source with low-surface brightness or
remnant-type lobes along PA$\sim$140∘. Some optical/IR objects in the area of
the lobes seem unlikely to explain them individually, so we consider the
source as genuine.

J1434+3328C is a very large diffuse source of oval shape with major axis near
PA$\sim$160∘ with a low surface brightness extension from the end of the N
lobe towards SW. The N lobe is much brighter and of FR II type, while the S
lobe is fainter and of FR I type, thus it is a candidate hybrid morphology
source. The innermost source shows a compact radio knot $\sim$6′′S of the
host, also seen in VLASS and Coppejans et al. (2015). An additional diffuse
source is seen $\sim$16′′ from the host with no optical/IR counterpart. The
host itself is a broadline QSO at $z_{\rm sp}$=0.19756 (from SDSS) and is
apparently located in a compact triple of galaxies. However, while the 2nd-
brightest member of that triple, SDSS J143444.88+332817.3 $\sim$6′′WSW of the
host has a $z_{\rm ph}$ compatible with the host, the 3rd-brightest member
(SDSS J143445.33+332823.5) $\sim$3′′N of the host is a galaxy at $z_{\rm
sp}$=0.24565, so apparently in the background. The host was also detected in
X-rays as 1RXS J143445.8+332814 and more recently with Chandra (Masini et al.,
2020) and Kostrzewa-Rutkowska et al. (2018) report the host to have featured a
Gaia transient. The host had been proposed as a blazar candidate by D’Abrusco
et al. (2019). It is thus possible that the source is oriented at a large
angle with respect to the plane of the sky and is intrinsically much larger.
The peak of the emission of the N lobe in the full-res. Deep Field coincides
with SDSS J143442.62+333015.8 with zphot indistinguishable from the QSO host’s
zspec, so that galaxy could be the host of a WAT-like source that consititute
most of the NNW lobe including the circular wings running to SSE and SSW,
making the inner source only about 3.4′ (LLS = 0.67 Mpc), and N WAT-type
source would have 3′ or LLS=0.59 Mpc.

J1435+3404 is a rather faint Z-shaped source with a clear radio nucleus and
evidence for precessing jets or lobes starting in the E-W direction and
gradually turning S in the E lobe and N in the W lobe.

J1435+3547: the BLDF image shows this to be a straight and symmetric restarted
FR II radio galaxy with inner lobes of LAS$\sim$32′′. Except for very faint
hotspots it is not detected in VLASS, suggesting both inner and outer lobes
having aged substantially, which is consistent with the fact that it is the
source with the second-steepest radio spectrum in our sample.

J1436+3416 is a straight, restarted FR II with asymmetric inner lobes of
LAS$\sim$1.1′. The inner lobes have well-detected hotspots in VLASS but no
detection of the host. The hotspot of the inner NE lobe is displaced
significantly from the galaxy SDSS J143654.42+341726.9 near the middle of that
lobe and we regard this galaxy as accidentally superposed. The outer lobes are
undetected in VLASS. Our proposed host is undetected in WISEA, and closer to
the center between the inner hotspots there is WISEA J143653.20+341657.1 with
AGN-like WISE colors and undetected in DESI DR9, but listed with $z_{\rm
ph}$=1.54 in Duncan et al. (2021), which would imply an LLS of $\sim$1.88 Mpc.
Some 52′′ NW of the host the very bright foreground galaxy MCG +06-32-076
appears as a strong radio source.

J1437+3650 is a slightly asymmetric remnant-type FR II source with low surface
brightness lobes along PA$\sim$140∘. Part of the farther SE lobe may be caused
by emission from superposed objects.

J1437+3233 is a WAT-type source with indications of the far WSW lobe showing a
bend of $\sim$150∘, perhaps due to projection. The host is too faint to
recognize any cluster around it on optical images, but the unWISE image (Lang,
2014) suggests a concentration of objects around the source.

J1438+3445C is a slightly bent FR II source with very detached lobes. Only the
stronger SE lobe, which has no optical/IR counterpart, shows a faint
indication of a hotspot in VLASS.

J1438+3526 is a straight, core-dominated FR II source with a stronger NE lobe
terminating in what appears as a hotspot, which is undetected in VLASS. The SW
lobe is of very low surface brightness and suggests a bend due SE near its
end.

J1438+3355: this is the third-largest source in angular size but the one of
largest linear size (3.8 Mpc) in our sample. The outer lobes are very detached
from the host, but both show the characteristic (though short) trail of radio
emission from the far end of the lobes towards the host. The lobe length ratio
is only 1.4 (NE/SW lobe) and both lobes are aligned with the host to within
1.5∘. The source has a radio luminosity in the upper quartile and a rather
steep spectrum ($\alpha>1.17$).

J1438+3539 is a rather asymmetric source with the southern more compact lobe
reaching twice as far from the host than the northern, more diffuse lobe. A
faint hotspot is seen in the S lobe in VLASS, separated from two WISE objects
E of it. This, together with the fact that the S lobe has a faint, low surface
brightness spur due NE, suggests that this is in fact the S lobe of a large
source. Also, the lobe orientations with respect to the host are aligned to
within 2∘.

J1439+3251C: this candidate radio galaxy features two symmetric, low surface
brightness lobes along PA$\sim$54∘, and we include in its size a compact
source at the end of the NE lobe which we interpret as a hotspot since it does
not show any optical/IR counterpart.This hotspot is the only part of the
source detected in VLASS. We chose the host as it features an apparent radio
core in BLDF, while a similarly bright galaxy due E (SDSS J143903.20+325135.9)
does not.

J1439+3254 is a straight, symmetric FR II source of high radio luminosity.
VLASS shows diffuse lobes with indications of two hotspots in the stronger N
lobe and a very faint one in the S lobe. This source was first noticed by us
in a 325-MHz VLA image kindly supplied by R. Coppejans (Coppejans et al.,
2015).

J1439+3221C is a core-dominated remnant-type source of intermediate FR type.
The N lobe shows some wiggling before it reaches its maximum brightness at its
end, though a hotspot is not detected in VLASS. The S lobe shows continuous
very low surface brightness emission in the low-resolution LoTSS DR2 image
before it seems to fade away below noise $\sim$2.5′ S of the host, but may in
fact continue for another 1.3′ due S.

J1440+3211 is one of the angularly largest sources in our sample, this is an
FR II source with very detached lobes, both of them showing radio trails from
their end towards the host, which both lobes being oriented parallel to within
less than 1∘. The host is barely detected in BLDF, and undetected in VLASS.
The N lobe shows a prominent hotspot in VLASS while in the S lobe none is
detected.

J1440+3348: this source is similar to the protypical FR I sources with
precessing jets (like 3C 31 or 3C 449), though the jets are below the
detection limit of VLASS.

J1442+3457 is a rather straight FR II type source with a very detached NW lobe
and a more diffuse SE lobe, both of low surface brightness. The more compact
source $\sim$30′′ N of the N lobe has a separate host and is thus unrelated.

J1442+3605: this FR II type source has one of the highest radio luminosities
in our sample and VLASS resolved the lobes into broad, almost circular
emission regions of almost constant surface brightness, albeit with hotspots
embedded in them. These hotspots are not located at the outer edges of the
lobes, such that the distance between them is 1.5′ compared to 1.84′ for the
total projected size of the source.

J1442+3243 is a straight, asymmetric FR II type source with strong lobes in
VLASS showing constant surface brightness over an oval region in which a
hotspot (or at least a "spine") is embedded. The exact size of this source is
difficult to measure on its E side where it overlaps with the NE lobe of
J1442+3242. This source was first noticed by us in a GMRT 150-MHz image by
Williams et al. (2013).

J1442+3242: the host of this FR II source is only $\sim$18′′ SE of the E
hotspot of J1442+3243, thus its diffuse NNE lobe overlaps with the E lobe of
J1442+3243. Only the stronger SSW lobe shows a well-detected hotspot in VLASS
surrounded by a faint envelope of diffuse emission. Future, improved VLASS
images may confirm a possible LAS of up to 2.0′.

J1444+3445C is one of the sources with the lowest radio luminosity in our
sample. It has an FR I type inner region with two very low surface brightness
lobes due W and ESE with a bending angle of $\sim$25∘ between them. Some
optical/IR objects are superposed on the outer lobes which we consider
unlikely to account for the lobes, which are entirely undetected in VLASS.

J1444+3348: this source has an uncertain radio morphology and features a faint
(if any) radio core, a strong but diffuse W lobe close to the host and a
longer, more collimated E lobe which bends due N close to its end.

J1444+3444 is a rather straight FR II source oriented along PA$\sim$157∘ and
is difficult to recognize due to a compact source superposed $\sim$18′′ WNW of
the host. It features a continuous SSE lobe of moderate surface brightness
that curves due W before its end, and a more detached and patchy NNW lobe. No
part of this source (except the superposed one) is detected in VLASS.

Table A1: Col. (1), name of the giant radio galaxy. The superscript refers to the reference of the catalogue that reported the source: 1-Coppejans et al. (2015), 2-Williams et al. (2016), 3-van Weeren et al. (2014), 4-Kuźmicz & Jamrozy (2021), 5-Williams et al. (2013), 6-Mingo et al. (2022), 7-Masini et al. (2021). Col. (2) and Col. (3), right ascension and declination (J2000) of the host galaxy in degrees. Col. (4), largest angular size. Col. (5), classification of GRGs according to the Fanaroff–Riley classification. Col. (6), redshift of the host galaxy. Col. (7), redshift error when available. Errors of the spectroscopic redshifts are not reported since they are generally more accurate than the precision we can achieve on the linear sizes and luminosities. Col. (8), type of the redshift: p for photometric, s for spectroscopic and e if estimated. Col. (9), references for the redshift. These are either spectroscopic measurements, such as 3-SDSS(Beck et al., 2016), 8-LAMOST(Luo et al., 2015), 9-Huchra et al. (2012), 10-Kochanek et al. (2012), or photometric estimates: 1-DESI (Zou et al., 2019; Zhou et al., 2021), 2-Duncan et al. (2021), 4-Pan-STARRS (Beck et al., 2021), 5-Chung et al. (2014), 6-Bilicki et al. (2016), 7-Brescia et al. (2014). Col. (10), name of the host galaxy. Col. (11) type of host galaxy: galaxy (G) or QSO (Q) or candidate quasars (Qc). Col. (12), largest linear size. Col. (13), magnitude of the host galaxy in the r-band if available from the DESI DR9 photometric catalogue; the label W1 and W2 indicates that the magnitude is taken from either WISEA or CWISE catalogue. Col. (14), total flux at 150 MHz from the full resolution 6$"$ image. An asterisk is appended to the flux estimate of the source if the flux integration is computed by considering all the pixels belonging to the region of the radio emission. Col. (15) total flux 1$\sigma$ error from the 6$"$ image. Col. (16), log10 of power at 150 MHz. Col. (17) spectral index $\alpha$ measured by using NVSS (1.4GHz), LOFAR HBA (150MHz) and LOFAR LBA (50MHz) data. Col. (17), spectral index error.  (1) |  (2) |  (3) |  (4) |  (5) |  (6) |  (7) |  (8) |  (9) |  (10) |  (11) |  (12) |  (13) |  (14) |  (15) |  (16) |  (17) |  (18)
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Name |  RAJ |  ${\rm Dec}_{J}$ |  LAS |  FR |  $z$ |  $\Delta z$ |  ztype |  ref |  Hostname |  type |  LLS |  mag |  $S_{150}$ |  $\sigma_{S}$ |  $\log_{10}P_{150}$ |  $\alpha$ |  $\Delta\alpha$
LBDF-GRG |  ∘ |  ∘ |  (′) |  type |  |  |  |  |  |  |  (Mpc) |  (mag) |  (mJy) |  |  (W/Hz) |  |
J1419+3337 |  214.8027 |  33.6328 |  1.8 |  II |  1.09 |  0.16 |  p |  1,4 |  DESI J214.8027+33.6329 |  ? |  0.9 |  23.41 r |  9.6 |  1.4 |  25.7 |  |
J1421+3431 |  215.4634 |  34.5289 |  1.5 |  II |  1.02 |  0.25 |  p |  1 |  DESI J215.4634+34.5289 |  G |  0.7 |  24.59 r |  4.1 |  0.8 |  25.2 |  0.66 |  0.19
J1421+3521 |  215.4909 |  35.3570 |  2.2 |  II |  1.1 |  |  e |  - |  CWISE J142157.80+352125.3 |  ? |  1.1 |  17.31 W2 |  58.6 |  5.9 |  26.5 |  0.93 |  0.05
J1422+3320 |  215.6373 |  33.3354 |  2.8 |  II |  0.94 |  0.11 |  p |  1,4 |  DESI J215.6373+33.3353 |  G |  1.3 |  23.83 r |  145 |  15 |  26.7 |  |
J1422+3255 |  215.6913 |  32.9322 |  1.7 |  II |  1.07 |  0.23 |  p |  1 |  DESI J215.6913+32.9322 |  G |  0.8 |  24.17 r |  53.8 |  5.5 |  26.4 |  |
J1423+3600 |  215.7846 |  36.0052 |  2.0 |  II |  1.09 |  0.21 |  p |  1 |  DESI J215.7846+36.0053 |  G |  1.0 |  24.16 r |  55.6 |  5.7 |  26.5 |  0.94 |  0.05
J1423+3403 |  215.9003 |  34.0506 |  2.7 |  I/II |  0.561 |  |  s |  3 |  SDSS J142336.06+340302.1 |  G |  1.1 |  20.17 r |  9.9 |  1.4 |  25.0 |  0.86 |  0.12
J1423+3302 |  215.9105 |  33.0484 |  1.9 |  II |  1.03 |  0.19 |  p |  1,4 |  DESI J215.9106+33.0483 |  G |  0.9 |  23.82 r |  258 |  26 |  27.1 |  |
J1423+3529 |  215.9201 |  35.4888 |  7.5 |  II |  0.83 |  0.05 |  p |  1,3,4 |  SDSS J142340.83+352919.7 |  G |  3.4 |  21.91 r |  20.4 |  3.0 |  25.7 |  1.10 |  0.12
J1423+3340 |  215.9259 |  33.6693 |  1.5 |  II |  1.5 |  |  e |  - |  CWISE J142342.22+334009.6 |  ? |  0.8 |  18.05 W1 |  3.6 |  0.9 |  25.6 |  0.48 |  0.14
J1423+3605 |  215.9486 |  36.0946 |  2.8 |  I |  0.36 |  0.02 |  p |  1,3,6 |  SDSS J142347.66+360540.5 |  G |  0.8 |  18.73 r |  40.7 |  4.2 |  25.2 |  |
J1424+36092 |  216.0397 |  36.1547 |  7.3 |  II |  0.58 |  0.07 |  p |  1,3,4 |  SDSS J142409.52+360917.0 |  G |  2.9 |  20.89 r |  191 |  19.3 |  26.4 |  0.74 |  0.04
J1424+34362,3 |  216.1358 |  34.6127 |  4.2 |  I/II |  0.586 |  |  s |  3 |  SDSS J142432.58+343645.8 |  G |  1.7 |  20.14 r |  486 |  49 |  26.8 |  0.85 |  0.04
J1425+3633 |  216.2942 |  36.5612 |  2.3 |  II |  0.70 |  0.08 |  p |  1,3,4,7 |  SDSS J142510.60+363340.3 |  G |  1.0 |  21.13 r |  217 |  22 |  26.6 |  0.89 |  0.04
J1425+35066 |  216.2995 |  35.1045 |  2.1 |  II |  0.71 |  0.05 |  p |  1,2,3,4 |  SDSS J142511.88+350616.1 |  G |  0.9 |  22.09 r |  14.3 |  1.7 |  25.4 |  0.94 |  0.12
J1425+3557 |  216.3287 |  35.9574 |  3.7 |  II |  0.419 |  |  s |  3 |  SDSS 142518.87+355726.7 |  G |  1.2 |  18.54 r |  14.6 |  1.7 |  24.9 |  |
J1426+3407C |  216.6021 |  34.1285 |  2.7 |  II |  0.75 |  0.14 |  p |  1,2,3,4 |  SDSS J142624.49+340742.6 |  G |  1.2 |  21.96 r |  42.8 |  4.5 |  26.0 |  1.02 |  0.06
J1426+33206 |  216.6026 |  33.3373 |  2.1 |  II |  0.82 |  0.15 |  p |  1,2 |  DESI J216.6026+33.3373 |  G |  1.0 |  23.66 r |  62.2 |  6.3 |  26.2 |  1.19 |  0.05
J1426+32366 |  216.6109 |  32.6024 |  2.0 |  II |  0.96 |  0.11 |  p |  1,2 |  DESI J216.6109+32.6024 |  G |  0.9 |  24.05 r |  46.8 |  4.8 |  26.2 |  |
J1426+32222 |  216.7126 |  32.3717 |  2.8 |  II |  0.68 |  0.12 |  p |  1,2,3,4,5 |  SDSS J142651.02+322218.0 |  G |  1.2 |  21.36 r |  386 |  39 |  26.8 |  0.92 |  0.04
J1427+36254 |  216.8259 |  36.4170 |  2.4 |  II |  0.851 |  |  s |  3 |  SDSS J142718.21+362501.1 |  Q |  1.1 |  18.02 r |  200 |  20 |  26.8 |  0.72 |  0.04
J1427+3312 |  216.8265 |  33.2016 |  2.1 |  I/II |  0.93 |  0.28 |  p |  1,2,4,11 |  DESI J216.8265+33.2016 |  G |  1.3 |  22.89 r |  18.3 |  1.9 |  25.8 |  1.12 |  0.11
J1427+3328C |  216.9070 |  33.4688 |  9.0 |  II |  0.150 |  |  s |  3,10 |  2MASX J14273770+3328081 |  G |  1.4 |  16.66 r |  64.7* |  7.2 |  24.6 |  $>$0.26 |
J1427+3255C |  216.9363 |  32.9289 |  2.7 |  II |  2.18 |  1.65 |  p |  2 |  SSTSL2 J142744.69+325543.9 |  G |  1.4 |  16.49 W2 |  7.5* |  1.0 |  26.3 |  |
J1428+3432 |  217.0151 |  34.5361 |  1.4 |  II |  1.02 |  0.11 |  p |  1,2,4 |  SDSS J142803.63+343210.0 |  G |  0.7 |  23.24 r |  3.9 |  0.7 |  25.2 |  $>$0.30 |
J1428+36312 |  217.0284 |  36.5249 |  2.4 |  II |  0.59 |  0.19 |  p |  1,3,7 |  SDSS J142806.81+363129.5 |  G |  0.9 |  21.60 r |  602 |  60 |  26.9 |  |
J1428+3446 |  217.0977 |  34.7752 |  1.9 |  II |  0.588 |  |  s |  11 |  SDSS J142823.44+344630.6 |  G |  0.7 |  20.67 r |  7.5 |  1.0 |  25.0 |  |
J1428+3525 |  217.1499 |  35.4271 |  2.8 |  II |  0.88 |  0.23 |  p |  1,2,4,5 |  DESI J217.1498+35.4271 |  G |  1.3 |  23.16 r |  10.9 |  1.4 |  25.5 |  |
J1429+33262,3 |  217.2997 |  33.4437 |  2.6 |  II |  0.320 |  |  s |  8 |  SDSS J142911.92+332637.5 |  G |  0.7 |  18.83 r |  270 |  27 |  25.9 |  |
J1429+33551,2 |  217.3171 |  33.9270 |  2.8 |  II |  1.059 |  |  s |  3 |  SDSS J142916.10+335537.4 |  G |  1.4 |  23.03 r |  137 |  14 |  26.8 |  0.92 |  0.04
J1429+33561,2,4 |  217.4277 |  33.9486 |  2.2 |  II |  1.124 |  |  s |  3 |  SDSS J142942.63+335654.8 |  Q |  1.1 |  18.97 r |  92.9 |  9.3 |  26.7 |  0.88 |  0.04
J1429+3717 |  217.4724 |  37.2914 |  2.8 |  II |  0.65 |  0.06 |  p |  1,3 |  SDSS J142953.37+371728.9 |  G |  1.1 |  21.95 r |  22.6 |  2.4 |  25.5 |  |

J1429+3230C |  217.4756 |  32.5127 |  6.1 |  I/II |  1.17 |  0.26 |  p |  1,2,3,4 |  SDSS J142954.06+323045.8 |  Qc |  3.0 |  22.67 r |  11.6 |  1.6 |  25.8 |  0.81 |  0.12
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
J1430+35192,7 |  217.5410 |  35.3329 |  4.0 |  II |  0.629 |  |  s |  3 |  SDSS J143009.83+351958.2 |  G |  1.7 |  20.76 r |  52.0 |  5.3 |  25.9 |  1.74 |  0.23
J1430+3322C |  217.6154 |  33.3804 |  3.7 |  I |  0.512 |  |  s |  3 |  SDSS J143027.69+332249.4 |  G |  1.4 |  19.52 r |  14.6 |  1.5 |  25.1 |  $>$0.11 |
J1431+33451,2,5 |  217.7644 |  33.7616 |  3.6 |  I/II |  0.238 |  |  s |  3 |  2MASX J14310340+3345414 |  G |  0.8 |  16.77 r |  166 |  17 |  25.4 |  0.67 |  0.04
J1431+3535C |  217.8483 |  35.5976 |  2.6 |  II |  1.04 |  0.18 |  p |  1,2,4 |  DESI J217.8484+35.5975 |  G |  1.3 |  23.01 r |  24.0* |  2.7 |  26.0 |  |
J1431+3440 |  217.8485 |  34.6681 |  2.2 |  II |  0.79 |  0.09 |  p |  1,2,3,4 |  SDSS J143123.56+344005.0 |  G |  1.0 |  21.68 r |  8.2 |  0.9 |  25.3 |  |
J1431+34271,2 |  217.8639 |  34.4506 |  3.0 |  II |  0.44 |  0.15 |  p |  1,3 |  SDSS J143127.33+342702.3 |  G |  1.0 |  20.82 r |  116 |  11 |  25.9 |  0.88 |  0.04
J1432+34111,2 |  218.0479 |  34.1926 |  2.4 |  II |  1.04 |  0.15 |  p |  1,2,3,4,5 |  SDSS J143211.50+341133.2 |  G |  1.2 |  22.68 r |  65.7 |  6.6 |  26.5 |  1.03 |  0.05
J1432+33286 |  218.1046 |  33.4770 |  1.8 |  II |  1.30 |  0.04 |  p |  1,2,4,5 |  DESI J143223.46+332852.5 |  Qc |  0.9 |  21.84 r |  114 |  11 |  26.9 |  1.13 |  0.04
J1432+35452 |  218.1413 |  35.7612 |  5.0 |  I |  0.185 |  |  s |  3 |  2MASX J14323389+3545397 |  G |  0.9 |  16.71 r |  84.0 |  8.5 |  24.9 |  0.77 |  0.04
J1432+32201,2 |  218.1777 |  32.3459 |  1.6 |  II |  0.81 |  0.08 |  p |  1,2,4 |  SDSS J143242.64+322045.4 |  G |  0.7 |  22.30 r |  107 |  11 |  26.4 |  |
J1432+3154C |  218.2283 |  31.9030 |  3.3 |  II |  0.88 |  0.15 |  p |  1 |  DESI J218.2283+31.9030 |  G |  1.6 |  23.15 r |  5.2 |  1.7 |  25.2 |  0.68 |  0.15
J1432+3647 |  218.2430 |  36.7894 |  1.5 |  II |  2.836 |  |  s |  3 |  SDSS J143258.30+364721.7 |  Q |  0.7 |  22.20 r |  13.1 |  1.6 |  26.8 |  0.52 |  0.25
J1433+3220 |  218.2569 |  32.3435 |  5.9 |  II |  0.552 |  |  s |  3 |  SDSS J143301.66+322036.7 |  G |  2.3 |  20.40 r |  12.3 |  2.5 |  25.12 |  |
J1433+3328 |  218.3156 |  33.4830 |  1.4 |  I/II |  1.609 |  |  s |  8 |  SDSS J143315.74+332858.6 |  Q |  0.7 |  22.76 r |  28.4 |  2.9 |  26.6 |  0.68 |  0.05
J1433+34502,3 |  218.3258 |  34.8485 |  1.7 |  II |  1.00 |  0.14 |  p |  1,2,4,5 |  DESI J218.3257+34.8485 |  G |  0.8 |  22.79 r |  1628 |  163 |  27.8 |  1.00 |  0.04
J1433+3145C |  218.3367 |  31.7665 |  2.4 |  II |  0.69 |  0.06 |  p |  1,3,4 |  SDSS J143320.81+314559.2 |  G |  1.0 |  22.13 r |  5.1 |  1.4 |  24.9 |  0.84 |  0.15
J1434+34281,2 |  218.6212 |  34.4668 |  2.6 |  II |  0.96 |  0.04 |  p |  1,2,3,4 |  SDSS J143429.09+342800.4 |  G |  1.2 |  22.71 r |  145 |  14 |  26.7 |  0.96 |  0.04
J1434+3214C |  218.6639 |  32.2407 |  2.7 |  I |  1.5 |  |  e |  - |  CWISE J143439.34+321426.6 |  ? |  1.4 |  17.83 W2 |  3.7 |  1.2 |  25.6 |  0.40 |  0.18
J1434+3648 |  218.6889 |  36.8099 |  2.3 |  I |  0.429 |  |  s |  3 |  SDSS J143445.33+364835.5 |  G |  0.8 |  19.27 r |  10.6 |  1.4 |  24.8 |  |
J1434+3328C |  218.6890 |  33.4724 |  4.7 |  II |  0.198 |  |  s |  3 |  2MASX J14344537+3328211 |  Q |  0.9 |  16.72 r |  54.8 |  5.7 |  24.8 |  |
J1435+3404 |  218.8812 |  34.0780 |  2.1 |  II |  0.546 |  |  s |  3 |  SDSS J143531.49+340440.9 |  G |  0.8 |  21.82 r |  5.6* |  0.8 |  24.8 |  |
J1435+3547 |  218.9370 |  35.7978 |  1.7 |  II |  1.63 |  0.27 |  p |  1,2,3,4 |  SDSS J143544.87+354752.2 |  G |  0.9 |  22.72 r |  30.1 |  3.1 |  26.6 |  1.43 |  0.19
J1436+3416 |  219.2216 |  34.2807 |  3.7 |  II |  0.25 |  0.15 |  p |  1,2,3,4 |  SDSS J143653.19+341650.5 |  G |  0.9 |  21.67 r |  69.8 |  7.1 |  25.1 |  0.95 |  0.05
J1437+3650 |  219.3635 |  36.8387 |  3.3 |  II |  0.94 |  0.09 |  p |  1,3,4 |  SDSS J143727.24+365019.3 |  G |  1.6 |  23.31 r |  8.0 |  1.6 |  25.5 |  0.67 |  0.15
J1437+3233 |  219.4135 |  32.5566 |  1.5 |  I |  1.02 |  0.21 |  p |  1,3,4 |  SDSS J143739.23+323323.8 |  G |  0.7 |  23.46 r |  6.3 |  0.8 |  25.4 |  0.75 |  0.13
J1438+3445C |  219.5403 |  34.7591 |  3.2 |  II |  0.58 |  0.05 |  p |  1,2,3,4,7 |  SDSS J143809.66+344532.8 |  G |  1.3 |  21.11 r |  9.5 |  1.5 |  25.1 |  |
J1438+3526 |  219.5529 |  35.4368 |  1.6 |  II |  0.86 |  0.08 |  p |  1,3 |  SDSS J143812.69+352612.6 |  G |  0.8 |  22.32 r |  11.0 |  1.2 |  25.5 |  0.90 |  0.11
J1438+3355 |  219.5877 |  33.9290 |  7.5 |  II |  1.80 |  0.17 |  p |  2,5 |  SDSS J143821.02+335544.4 |  Qc |  3.8 |  15.77 W2 |  21.5 |  2.7 |  26.5 |  $>$1.17 |
J1438+3539 |  219.6260 |  35.6545 |  7.1 |  II |  0.262 |  |  s |  3,10 |  SDSS J143830.23+353916.1 |  Q |  1.7 |  18.36 r |  17.9 |  2.3 |  24.5 |  0.65 |  0.05
J1439+3251C |  219.7544 |  32.8586 |  3.0 |  II |  0.57 |  0.11 |  p |  1,3,4,6,9 |  SDSS J143901.04+325131.0 |  G |  1.2 |  21.41 r |  4.0 |  1.2 |  24.7 |  0.40 |  0.41
J1439+32541,2 |  219.8133 |  32.9137 |  1.7 |  II |  0.80 |  0.04 |  p |  1,3,4 |  SDSS J143915.18+325449.4 |  G |  0.8 |  21.35 r |  228 |  23 |  26.8 |  0.88 |  0.04
J1439+3221C |  219.9937 |  32.3575 |  4.9 |  II |  0.50 |  0.02 |  p |  1,3,4 |  SDSS J143958.48+322126.9 |  G |  1.8 |  20.54 r |  23.2* |  3.1 |  25.3 |  $>$0.77 |
J1440+3211 |  220.0520 |  32.1865 |  7.5 |  II |  0.49 |  0.12 |  p |  1,3,4 |  SDSS J144012.47+321111.3 |  G |  2.7 |  20.48 r |  149 |  15 |  26.1 |  0.61 |  0.15
J1440+3348 |  220.1655 |  33.8009 |  2.0 |  I/II |  0.542 |  |  s |  3 |  SDSS J144039.70+334803.2 |  G |  0.8 |  20.43 r |  17.4 |  1.9 |  25.2 |  |
J1442+3457 |  220.5530 |  34.9617 |  3.0 |  II |  0.532 |  |  s |  3 |  SDSS J144212.71+345742.2 |  G |  1.1 |  20.17 r |  9.7* |  1.2 |  25.0 |  0.56 |  0.14
J1442+3605 |  220.6305 |  36.0897 |  1.8 |  II |  1.10 |  0.15 |  p |  1 |  DESI J220.6304+36.0893 |  G |  0.9 |  23.17 r |  457 |  46 |  27.4 |  |
J1442+32435 |  220.6456 |  32.7242 |  2.9 |  II |  0.48 |  0.20 |  p |  1,3,7 |  SDSS J144234.93+324326.9 |  Qc |  1.1 |  19.02 r |  344 |  34 |  26.4 |  |
J1442+3242 |  220.6844 |  32.7163 |  1.9 |  II |  0.80 |  0.05 |  p |  1,3 |  SDSS J144244.26+324258.6 |  G |  0.8 |  22.30 r |  166 |  17 |  26.6 |  |
J1444+3445C |  221.0615 |  34.7596 |  3.3 |  II |  0.259 |  |  s |  3 |  SDSS J144414.75+344534.5 |  G |  0.8 |  17.69 r |  16.5* |  1.9 |  24.5 |  |
J1444+3348 |  221.1075 |  33.8054 |  1.8 |  ? |  0.91 |  0.07 |  p |  1,3,4 |  SDSS J144425.80+334819.3 |  G |  0.9 |  22.69 r |  15.0 |  2.2 |  25.7 |  |
J1444+3444 |  221.1722 |  34.7425 |  1.7 |  II |  0.77 |  0.03 |  p |  1,3,4 |  SDSS J144441.33+344433.0 |  G |  0.8 |  21.71 r |  39.6 |  4.3 |  26.0 |  0.64 |  0.05

Figure A1: Cutouts of the BLDF image around our GRGs at 150 MHz with 3 and
24-$\sigma_{rms}$ red contours superimposed. The resolution of the images is
6$\rm"$. The cyan circle identifies the position of the host galaxy. The bar
in the bottom-right corner represents an angular size of 1′, while the name
and the largest linear size (in Mpc) of the GRGs are reported in the top-left
and top-right corners, respectively.