# COALAS II. Extended molecular gas reservoirs are common in a distant,
forming galaxy cluster

Z. Chen1,2,3,4, H. Dannerbauer2,3,, M. D. Lehnert5, B. H. C. Emonts6, Q. Gu,
1,4, J. R. Allison7, J. B. Champagne8, N. Hatch 9, B. Indermüehle 10, R. P.
Norris10,11, J. M. Pérez-Martínez2,3,12, H. J. A. Röttgering13, P. Serra14, N.
Seymour15, R. Shimakawa16, A. Thomson17, C. M. Casey8, C. De Breuck 18, G.
Drouart15, T. Kodama 12, Y. Koyama 19, C. Lagos Urbina20,21, P. Macgregor 10,
G. Miley13, J. M. Rodríguez-Espinosa 22, M. Sánchez-Portal23, B. Ziegler24
1 School of Astronomy and Space Science, Nanjing University, Nanjing 210093,
China
2 Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife,
Spain
3 Universidad de La Laguna, Dpto. Astrofísica, E-38206 La Laguna, Tenerife,
Spain
4 Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University,
Nanjing 210093, China
5 Université Lyon 1, ENS de Lyon, CNRS UMR5574, Centre de Recherche
Astrophysique de Lyon, F-69230 Saint-Genis-Laval, France
6 National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA
22903
7 First Light Fusion Ltd., Unit 9/10 Oxford Pioneer Park, Mead Road, Yarnton,
Kidlington OX5 1QU, UK
8 The University of Texas at Austin, 2515 Speedway Blvd Stop C1400, Austin, TX
78712, USA
9 School of Physics and Astronomy, University of Nottingham, University Park,
Nottingham NG7 2RD, UK
10 Australia Telescope National Facility, CSIRO Space $\&$ Astronomy, P.O. Box
76, Epping, NSW 1710, Australia
11 Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia
12 Astronomical Institute, Tohoku University, 6-3, Aramaki, Aoba, Sendai,
Miyagi, 980-8578, Japan
13 Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the
Netherlands
14 INAF- Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047
Selargius (CA), Italy
15 International Centre for Radio Astronomy Research, Curtin University, 1
Turner Avenue, Bentley, WA, 6102, Australia
16 Waseda Institute for Advanced Study (WIAS), Waseda University, 1-21-1 Nishi
Waseda, Shinjuku, Tokyo 169-0051, Japan
17 Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford
Road, Manchester M13 9PL, UK
18 European Southern Observatory, Karl–Schwarzschild–Straße 2, D-85748
Garching bei München, Germany
19 Subaru Telescope, National Astronomical Observatory of Japan, National
Institutes of Natural Sciences, 650 North A’ohoku Place, Hilo, HI 96720, USA
20 International Centre for Radio Astronomy Research (ICRAR), M468, University
of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
21 ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO
3D)
22 Instituto de Astrofísica de Andalucía, CSIC, Glorieta de la Astronomía,
E-18080, Granada, Spain
23 Instituto de Radioastronomía Milimétrica (IRAM), Av. Divina Pastora 7,
Núcleo Central, E-18012 Granada, Spain
24 University of Vienna, Department of Astronomy, Türkenschanzstrasse 17,
A-1180 Vienna
E-mail<EMAIL_ADDRESS>(NJU)

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

This paper presents the results of 475 hours of interferometric observations
with the Australia Telescope Compact Array towards the Spiderweb protocluster
at $z=2.16$. We search for large, extended molecular gas reservoirs among 46
previously detected CO(1-0) emitters, employing a customised method we
developed. Based on the CO emission images and position-velocity diagrams, as
well as the ranking of sources using a binary weighting of six different
criteria, we have identified 14 robust and 7 tentative candidates that exhibit
large extended molecular gas reservoirs. These extended reservoirs are defined
as having sizes greater than 40 kpc or super-galactic scale. This result
suggests a high frequency of extended gas reservoirs, comprising at least
$30\%$ of our CO-selected sample. An environmental study of the candidates is
carried out based on N-th nearest neighbour and we find that the large
molecular gas reservoirs tend to exist in denser regions. The spatial
distribution of our candidates is mainly centred on the core region of the
Spiderweb protocluster. The performance and adaptability of our method are
discussed. We found 13 (potentially) extended gas reservoirs located in nine
galaxy (proto)clusters from the literature. We noticed that large extended
molecular gas reservoirs surrounding (normal) star-forming galaxies in
protoclusters are rare. This may be attributable to the lack of observations
low-J CO transitions and the lack of quantitative analyses of molecular gas
morphologies. The large gas reservoirs in the Spiderweb protocluster are a
potential source of the intracluster medium seen in low redshift Virgo- or
Coma-like galaxy clusters.

###### keywords:

Galaxy: evolution – galaxies: formation – galaxies: clusters: individual:
Spiderweb – galaxies: high-redshift – galaxies: ISM – ISM: molecules

††pubyear: 2023††pagerange: COALAS II. Extended molecular gas reservoirs are
common in a distant, forming galaxy cluster–E

##  1 Introduction

Within the paradigm of hierarchical structure formation models, mass is
assembled inhomogeneously, along walls, filaments, and nodes all of which
constitute the large-scale structure of the Universe or “cosmic web”. Galaxy
protoclusters are the progenitors of the local galaxy clusters, the most
massive virialised systems in the Universe with stellar mass $M\gtrsim
10^{14}M_{\odot}$ (see Overzier 2016 for review). Galaxy protoclusters
residing in the dense regions of the Universe, in which half of the present-
day mass is assembled, contribute significantly to the star formation rate
density (SFRD) at high redshift (Chiang et al., 2017). Molecular gas is the
direct fuel for star formation in galaxies, thus mapping the molecular gas is
essential for studying any potential environmental impact on galaxy evolution
in both the field and protoclusters.

Among tens of galaxy protoclusters discovered (Chiang et al., 2013; Overzier,
2016), the Spiderweb protocluster is an excellent laboratory to conduct
studies of the molecular content of its member galaxies. Multi-wavelength
photometry and spectroscopy data have been accumulated over the last two
decades, making the Spiderweb protocluster one of the best studied among all
the known protoclusters. Based on the discovery of the clumpy morphology and
the surrounding hot, dense magnetised medium from X-ray, optical and radio
observations (Carilli et al., 1997, 1998; Pentericci et al., 1998, 2000),
indications were found that the radio galaxy PKS 1138-262 at z=2.16 is a
proto-brightest cluster galaxy (proto-BCG). Kurk et al. (2000) carried out
narrow-band imaging of the Ly$\alpha$ line with the Very Large Telescope (VLT)
in order to search for a possible overdensity centred around PKS 1138-262 and
found 50 Ly$\alpha$ emitters (LAEs) at the same redshift, of which 15 were
spectroscopically confirmed in Pentericci et al. (2000) through VLT follow-up
observations. A giant Ly$\alpha$ halo ($\sim$ 200 kpc) was discovered, and a
few H$\alpha$ emitters (HAEs) are within the halo (Kurk et al., 2000, 2004a,
2004b). Based on deep HST imaging (Miley et al., 2006), this radio galaxy is
dubbed the “Spiderweb Galaxy” and the protocluster associated was later called
the “Spiderweb protocluster”. A panoramic search for HAEs was carried out with
MOIRCS/Subaru and revealed a similar overdensity as LAEs, spanning the scale
of $\sim$10 Mpc (Koyama et al., 2013; Shimakawa et al., 2014, 2018). Near-
infrared (NIR) spectroscopy with the VLT/KMOS was carried out for several
dozens HAEs in order to study the environmental effect on the ISM through gas-
phase metallicity (Pérez-Martínez et al., 2022). Rigby et al. (2014) found a
Herschel-SPIRE overdensity around the Spiderweb Galaxy based on simultaneously
conducted 250, 350 and 500 $\mu$m observations. Dannerbauer et al. (2014)
complemented this study by revealing an overdensity of intensely star-forming
submillimeter galaxies (SMGs) through APEX-LABOCA 870 $\mu$m observations.
Through observations with the Australian Telescope Compact Array (ATCA) of the
ground transition of carbon monoxide (CO(1-0)) as tracer, large cold molecular
reservoirs have been revealed being physically related to the starbursting
(proto-)BCG (Spiderweb Galaxy) and the star-forming galaxy HAE229 (Emonts et
al., 2016; Dannerbauer et al., 2017). Jin et al. (2021) presented a 21 sq.
arcmin panoramic CO(1-0) survey on the Spiderweb protocluster field with the
ATCA and reported 46 robust cold molecular gas detections spanning
$z=2.09-2.22$, the largest sample of such measurements in a (proto)cluster in
the distant universe. The CO emitters are overdense at $z=2.12-2.21$,
suggesting a galaxy super-protocluster or a protocluster connected to large-
scale filaments with $\sim$120 cMpc size.

There is a growing consensus that the formation of massive galaxies must be a
two-phase process, with an early phase driven by gas-accretion, and a late
phase dominated by galaxy mergers (Oser et al., 2010). The cold molecular gas
content and distribution of galaxies, is influenced by various processes,
e.g., jet-induced positive feedback, gas accretion and galaxy mergers. All
these mechanisms may in principle lead to widespread molecular gas reservoirs.
The ATCA has ultra-compact array configurations, which makes it very well
suited for detecting low-surface brightness ground-transition CO emission, and
thus has played a crucial, leading role in the discovery of extended
reservoirs of gas. With the ATCA, a large reservoir of molecular gas ($\sim$
70 kpc) was found surrounding the Spiderweb radio galaxy, suggesting that the
galaxy is growing from the recycled gas in the circum-galactic medium (CGM)
rather than through direct accretion from the cosmic web (Emonts et al., 2016,
2018). Within the same protocluster, the ATCA detection of an extended
($\sim$40 kpc) rotating molecular gas disk from a normal star-forming galaxy,
HAE229, was reported (Dannerbauer et al., 2017). Besides these two cases
within the Spiderweb protocluster, several other large gas reservoir cases
have been revealed through various CO transitions and atomic carbon (e.g.,
Ginolfi et al. 2017; D’Amato et al. 2020; Umehata et al. 2021; Cicone et al.
2021; Li et al. 2021b). Very recently, examining the ALMA CO(3-2) observations
of seven AGNs (Active Galactic Nuclei) at z$\sim$2-2.5, Jones et al. (2023)
found evidence for wide-spread ($\sim$ 13 kpc) gas emission.

Extended reservoirs of ionised or molecular gas are considered as one of the
characteristics of central galaxies (progenitors of BCGs) in protoclusters
(Overzier, 2016). However, the large reservoirs of molecular gas found in the
normal star-forming galaxy HAE229 (Dannerbauer et al., 2017) indicate that it
might not be restricted only to the central galaxy.

There are multiple processes that likely play a significant role in mass and
energy exchange between the interstellar medium (ISM), the circumgalactic
medium (CGM), and intergalactic medium (IGM; Tumlinson et al., 2017). For
example, a galaxy could lose material from the ISM and CGM through AGN or
stellar driven outflows, and material may be acquired by a galaxy through gas
accretion or recycling the ejected gas within the CGM. The detailed mechanisms
involved in regulating galaxy evolution through IGM/CGM/ISM are debated, and
the dominant role of each may change depending on the physical scale, mass of
the halo, and epoch during which the galaxy is observed. In this paper, the
“extended/large molecular gas reservoirs” refers to the gas reservoirs with
super-galactic scale of tens of kpc ($\gtrsim$ 40 kpc; 40 kpc corresponds to
the typical beam-size of the ATCA mosaic data we used in this paper) just like
those in the Spiderweb galaxy and HAE229. We note that these gas reservoirs
may not necessarily exhibit a smooth distribution, and they can exhibit clumpy
structures within this super-galactic scale. Besides the AGNs, which has a
violent gas exchange with the surrounding environments (e.g., the Spiderweb
galaxy seems to evolve from the recycling of metal-enriched outflow gas;
Nesvadba et al. 2006). There are several ways an extended gas reservoirs could
originate: (1) retaining of the high angular momentum of the accreting gas;
(2) puffing up of the gas in the galaxy by mixing, momentum injection from
stars and AGN, and dynamical heating; and (3) galaxy mergers. Filamentary gas
accretion/inflow into galaxies is expected in a dense environment like
protoclusters, and could be reflected by a gas-phase metallicity gradient.
Theoretically, a galaxy accretes gas with a relative small amount of angular
momentum, and the gas would inflow into the galaxy centre during the
dissipation of angular momentum for a specific timescale (which would further
regulate the star-formation Lehnert et al. 2015); and the pristine gas
accreted along large scale filaments would dilute the central metallicity. Li
et al. (2022) studied gas-phase metallicity gradients of star-forming galaxies
in the massive protocluster, BOSS 1244, at redshift z$\sim$2 based on
spectroscopic data of the Hubble Space Telescope (HST), and found that the
majority of galaxies among their sample have either a negative or flat
gradients. They conclude that the cause could be the cold mode accretion
(Kereš et al., 2005; Dekel et al., 2009), which would flatten or reverse the
gradients (the gas-phase metallicity gradient is normally negative, i.e., the
metallicity decreases from the inside to the outskirt). Galaxy interactions or
mergers may have a similar influence on the gas scales and metallicity
gradient of galaxies (Montuori et al., 2010; Rupke et al., 2010).

As discussed above, the large molecular gas reservoirs of super-galactic scale
are not confined to their “host” galaxies but are undergoing complicated
processes between the galaxies and their surrounding environment. Revealing
the underlying physical mechanism of large gas reservoirs and studying the
exchange of such baryonic materials between protocluster galaxies and their
environment is essential for understanding galaxy evolution and the origin of
gas found in the intracluster medium (ICM) of local clusters and groups. The
panoramic COALAS (CO ATCA Legacy Archive of Star-forming galaxies) survey
offers a significant opportunity for the first systematic search for large gas
reservoirs in a relatively large sample of protocluster galaxies with
molecular gas line detections (Jin et al., 2021).

It is worth emphasising that the ground transition of carbon monoxide,
CO(1-0), is a good tracer of the total molecular gas in star-forming galaxies,
including any low-excitation molecular gas that is spread over large scales of
tens of kpc (e.g., Papadopoulos et al. 2000, 2001; Champagne et al. 2021).
This is because CO(1-0) has a low excitation temperature ($\sim$5 K) and a low
critical density ($\rm n_{crit}$) for collisional excitation ($\rm{10}^{3}$
$\rm{cm}^{-3}$) (Table 1 in Carilli & Walter 2013). Atomic carbon, such as the
transitions [CI] ${}^{3}\mathrm{P}_{1}-^{3}$$\mathrm{P}_{0}$and [CI]
${}^{3}\mathrm{P}_{2}-^{3}$$\mathrm{P}_{1}$, are used as substitute tracer for
CO-dark molecular gas. However, it is less abundant than carbon monoxide (CO),
and has higher excitation temperature than CO (Papadopoulos et al., 2002;
Röllig et al., 2006; Wolfire et al., 2010; Glover & Clark, 2012).

In this work, we developed a customised method to search for large, extended
gas reservoirs of galaxies within the ATCA COALAS CO(1-0) dataset. Our study
is based on the mosaic image presented in Jin et al. (2021), which will be
referred to as ”mosaic” subsequently. Section 2 describes the observations.
Section 3 presents an analysis of the characteristics of a third confirmed
large gas reservoir in the Spiderweb protocluster, COALAS-SW.03, utilising
higher resolution ATCA observations with an angular resolution of
approximately 2-3 arcseconds, equivalent to a physical scale of approximately
17-25 kpc. We compare the morphology and kinematics of COALAS-SW.03 in both
the high-resolution and mosaic datasets, where the latter has an angular
resolution of approximately 4-5 arcseconds at the location of COALAS-SW.03,
equivalent to a physical scale of 34-42 kpc. Our objective is to present a
novel methodology for detecting extended molecular gas reservoirs in
protoclusters using solely low-resolution data. Section 4 presents the
customised method developed to search for extended CO reservoirs (Section 4.1)
and the results of our search (Section 4.2). A catalogue of 14 robust and
seven tentative candidates is provided, and an environmental study is
presented. In Section 5, we then discuss the performance of our method,
present a collection of the (possible) large molecular gas reservoirs from the
literature, and discuss the underlying environmental physical processes that
may create or impact the existence of large molecular gas reservoirs. We
assume a flat $\Lambda$ CDM cosmology with
$\Omega_{\mathrm{m}}=0.3,\Omega_{\Lambda}=0.7$ and
$\mathrm{H}_{0}=70\mathrm{~{}km}^{-1}\mathrm{~{}s}^{-1}\mathrm{Mpc}^{-1}$ in
this paper (Hinshaw et al., 2013). At redshift z=2.16, one arcsec corresponds
to 8.4 kpc.

##  2 Observations

###  2.1 COALAS CO(1-0) survey

Several CO observational projects have been conducted with the ATCA on
galaxies within the Spiderweb protocluster. Observations include several
pointings centred on LABOCA selected sources from Dannerbauer et al. (2014)
(ID: 2014OCTS/C3003 and 2016APRS/C3003: PI: H. Dannerbauer), and follow-up
high resolution observations centred on the SMG DKB01-03 (ID: 2017APRS/C3003,
PI: B. Emonts), the Spiderweb Galaxy, and HAE229 (Emonts et al., 2016;
Dannerbauer et al., 2017).

The COALAS (CO ATCA Legacy Archive of Star-forming galaxies)
project111http://research.iac.es/proyecto/COALAS/pages/en/home.php is an ATCA
large program (C3181; PI: H. Dannerbauer) aiming at studying the environmental
impact on the molecular gas based on the CO(1-0) transition. The observations
were performed from April 2017 to March 2020, for a total 820 h of observing
time. The survey covers both “cluster” and “field” environments in order to
study the environmental effects of galaxy evolution. The two fields are the
Spiderweb protocluster ($z=2.16$) and submillimeter galaxies selected from the
Extended Chandra Deep Field-South (ECDFS), respectively. This work focuses on
the Spiderweb protocluster and the analysis is based on work presented in Jin
et al. (2021). Combining all these observations, we have 13 pointings (with
475 h of observing time) on the Spiderweb protocluster field. Data reduction
was carried out using the software package MIRIAD (Sault et al., 1995). More
details of the observations and data reduction can be found in Jin et al.
(2021).

The 13 pointings were placed in order to maximise the number of known sources
with spectroscopic redshifts per pointing. Various configurations were used
(H75, H168, H214, 750A/C/D, 1.5A; see Table 1 of Jin et al. 2021 for
configurations of each pointing, and the ATCA website 222ATCA configurations
for detailed information). A mosaic datacube was generated by combining
13-pointing observations into a single image (Figure 1 of Jin et al. 2021).
The mosaic datacube spans an area of 21 square arcminutes and covers a
velocity range of $\pm$6500 km/s. The resulting image has varying levels of
noise, ranging from 0.13 to 0.29 mJy root mean square (RMS) in different
regions of the image.

This paper introduces a methodology to effectively identify extended gas
reservoirs from the 46 CO detections reported in Jin et al. (2021), utilising
the 13-pointing mosaic datacube (subsequently referred to as the mosaic/coarse
datacube/data). We refer to this datacube as the “mosaic/coarse
datacube/data”, with the term “coarse” being interchangeable with “mosaic”.
This distinction is made in comparison to the higher resolution data utilised
in the COALAS-SW.03 study. We note that the continuum was separated from the
line by fitting a straight line to the line-free channels in the uv domain
(Jin et al., 2021).

###  2.2 COALAS-SW.03 observations

COALAS-SW.03 (dubbed DKB03 in Dannerbauer et al. 2014) is one of the CO
detections found in Jin et al. (2021). Following two extended molecular gas
reservoirs reported in the literature, the Spiderweb galaxy (COALAS-SW.02 in
Jin et al. 2021) in Emonts et al. (2013, 2016, 2018) and HAE229 (COALAS-SW.01
in Jin et al. 2021) in Dannerbauer et al. (2017), COALAS-SW.03/DKB03 is the
third large molecular gas reservoir confirmed with high-resolution
observations within the Spiderweb protocluster (see Section 3).

Our high-resolution CO(1-0) observations of COALAS-SW.03 (ID: 2017APRS/C3003,
PI: B. Emonts) were performed with the ATCA during June 2nd to 6th 2017 in the
750m configuration (57.5 h in total). The pointing centre of the observations
is on DKB03 (RA: 11:40:57.8; DEC: -26:30:48). Observations were centred around
36.4 GHz, using a channel width of 1 MHz and an effective bandwidth of 2 GHz.
Compared to the ATCA 2014OCTS/C3003 and 2016APRS/C3003 observations in H214
configuration, this 2017APRS/C3003 high-resolution observations employed the
more extended interferometric array configuration 750m, which provides an
angular resolution of $\sim$2-3 arcsec (i.e., $\sim$16.8-25.2 kpc) still
guaranteeing sufficient sensitivity in order to detect extended molecular gas
emission (i.e., low-surface-brightness emission).

Phase and bandpass calibration were performed by observing the strong
calibrator PKS 1124-186, and flux calibration on PKS 1934-638. These data were
reduced in MIRIAD (Sault et al., 1995). Continuum was separated from line-free
channels, continuum-subtracted line data generated, binned into 34 km $\rm
s^{-1}$ channels and subsequently Hanning-smoothed to an effective velocity
resolution of 68 km $\rm s^{-1}$. At the half-power point, the synthesised
beam is 4$\aas@@fstack{\prime\prime}$20$\times$1$\aas@@fstack{\prime\prime}$85
(PA = 5.53∘).

##  3 COALAS-SW.03: an extended gas reservoir confirmed with high-resolution
observations

In this section, we will characterise COALAS-SW.03 based on the high-
resolution ATCA observations in configuration 750m. Then, we compare the
morphological and kinematic features of COALAS-SW.03 in both the high-
resolution and mosaic/coarse data in order to show the feasibility of
searching for large gas reservoirs solely using mosaic data. COALAS-SW.03 was
observed at high-resolution using the ATCA 750m configuration, yielding a
synthesised beam of
4$\aas@@fstack{\prime\prime}$20$\times$1$\aas@@fstack{\prime\prime}$85\. On
the other hand, the mosaic data for COALAS-SW.03 is a combination of
observations from the H214 and 750m configurations, resulting in a synthesised
beam of 4$\aas@@fstack{\prime\prime}$7$\times$4$\aas@@fstack{\prime\prime}$3.

###  3.1 Characteristics of COALAS-SW.03

The molecular gas reservoir of COALAS-SW.03 (dubbed DKB03 in Dannerbauer et
al. 2014) was first discovered during a sample study of submillimeter galaxies
(SMGs) in the Spiderweb protocluster field. Based on the ATCA observations in
the H214 configuration (ID: 2014OCTS/C3003 and 2016APRS/C3003: PI: H.
Dannerbauer), tentative evidence of the spatial widespread cold molecular gas
reservoir ($\sim$ 70 kpc) was found in COALAS-SW.03, and the subsequent high-
resolution ATCA imaging in 750m (ID: 2017APR/C3003, PI: B. Emonts) confirmed
it.

The characteristics of the high-resolution observations in the ATCA 750m
configurations of COALAS-SW.03 are presented in the first row of Figure 1.
Panel (A) shows the spectrum which shows a tentative “double-horned” feature.
Single-Gaussian fitting results in flux $\rm I_{CO}$ = 0.16$\pm$0.02 Jy km
$\rm s^{-1}$, and FWHM=395$\pm$54 km $\rm s^{-1}$. The collapsed image (moment
0) in Panel (B) is generated with the blue shaded spectral range in Panel (A),
composed of multiple components. Along the red and cyan pseudo-slits, we
extract the position-velocity diagrams (PVDs) of COALAS-SW.03 and display them
in Panels (C) and (D). Specifically, we used a slit width corresponding to
approximately 5 arcseconds, equivalent to a physical scale of approximately 40
kpc. Notably, careful examination confirmed that slight variations in the slit
width had minimal impact on the features presented in Figure 1. Both PVDs show
multiple velocity components, and a slight velocity gradient is seen along the
red pseudo-slit (Panel C).

Channel maps derived from high-resolution observations in Figure 2 offer a
complementary slice-by-slice view besides the aforementioned moment 0 and
PVDs. In Figure 2, we show channel maps for a total velocity range of 374 km
$\rm s^{-1}$, with a step in velocity between each map of 34 km $\rm s^{-1}$
(i.e., the velocity range is roughly equal to the FWHM, and the velocity step
follows the binning of channels we applied during the data reduction).
Multiple components are clearly observed in channel maps, e.g., the panel for
a velocity of 85 km $\rm s^{-1}$ shows three separate components.

Either from the projected dimension (collapsed images) or along the line-of-
sight (spectrum, PVDs and channel maps), COALAS-SW.03 is an extended clumpy CO
emitter composed of multiple components, and the projected size is $\sim$70
kpc.

Figure 1: Spectra, collapsed images and PVDs of COALAS-SW.03 (DKB03). The
first row shows the characteristics of the high-resolution data, while the
second row shows the results from the mosaic datacube previously published in
Jin et al. 2021. Panel (A) and Panel (E) are spectra extracted from the
emission peak with aperture sizes of 1$\aas@@fstack{\prime\prime}$5, and the
spectral ranges are [-2500, 2500] km/s. A double-Gaussian fitting was
initially applied to the spectra to highlight the tentative double-horn
features. Panel (B) and Panel (F) are collapsed images (with cut-out sizes of
25$\aas@@fstack{\prime\prime}$0$\times$25$\aas@@fstack{\prime\prime}$0
generated from CO emission line spectral regions shaded in blue in Panel (A)
and Panel (E), white contours are [2, 3, 4] $\times\sigma$ ($\sigma$=0.032 Jy
$\rm{beam}^{-1}$ km $\rm s^{-1}$), and the synthesised beams are shown at the
bottom left of each panel. The white bar at the bottom right of Panel (B)
indicates a physical scale of 40 kpc. The RA axis in this and the following
figures increases from left to right, which is a departure from the common
practice of showing East to the left. However, this orientation choice is not
intended to imply that East is to the left. The PVDs shown in panels (C), (D),
(G), and (H) are extracted from the red and cyan pseudo-slits shown in panels
(B) and (F) for both the mosaic and high-resolution data. With which pseudo-
slit the data have been extracted is indicated in the bottom left corner of
each PVD. Contours on PVDs are [1.0, 2.0, 2.5, 3.0] times of standard
deviation values of each panel. Figure 2: Distribution and kinematics of the
CO-emitting gas. High-resolution CO(1-0) maps obtained with the ATCA at
different velocities, overlaid on a negative grey-scale HST/ACS F814W image.
The velocity centre of each map is indicated in the upper right corner of each
panel, and the velocity steps are 34 km $\rm s^{-1}$ between each map. The
contours are [2.8, 3.5, 4.2, 4.8, 5.5]$\sigma$. The bottom left ellipse in the
first panel shows the synthesised beam (size 4$\aas@@fstack{\prime\prime}$20
$\times$ 1$\aas@@fstack{\prime\prime}$85; position angle: 5.5 deg). The
physical scale of 20 kpc (valid for all shown channel maps) is indicated in
the upper left corner of the first panel.

###  3.2 Similarities and differences of COALAS-SW.03 in the high-resolution
and Mosaic data

Comparison between high-resolution data and the mosaic data of COALAS-SW.03
results in some similarities and differences in spectra, collapsed images, and
PVDs. Although some detailed features are not resolved in the mosaic data,
extended morphologies and multiple components are seen, which is one of the
technical foundations of our work on searching for extended large molecular
gas reservoirs in the Spiderweb protocluster based on the mosaic datacube
(Section 4). To be more specific, the high-resolution observations of COALAS-
SW.03 confirm the extended emission, that was already tentatively seen in the
former, coarser data, which means coarse data can be used to find extended
sources. Furthermore, the high-resolution data revealed more morphological and
kinematics (PVDs) features. However, despite the low resolution, there are
multiple-components in PVDs from coarse data and those can be indicators of
extended gas reservoirs as well.

Spectra, collapsed images and PVDs derived from the mosaic data are presented
in the same format as the high-resolution data in Figure 1 for comparison. The
detailed comparisons are as follows.

First, the spectrum presented in Panel (E) of Figure 1 has a similar flux and
FWHM as the spectrum extracted from the high-resolution data (with the same
aperture). The single-Gaussian fitting results in $\rm I_{CO}$ = 0.16$\pm$0.02
Jy km $\rm s^{-1}$, and FWHM=354$\pm$44 km $\rm s^{-1}$. As we aim to search
for large gas reservoirs, we emphasise that the FWHM of CO emission lines also
reflect the size of gas detections along the line-of-sight, and the underlying
assumption is that a large gas reservoir is supposed to be extended in view of
both the projection and along the line-of-sight.

Second, the collapsed image in Panel (F) is marginally resolved due to the
large beam size, which results in different morphology compared to Panel (B).
Contours in Panel (B) and (F) are plotted based on standard deviation
($\sigma$) values of each 25${}^{\prime\prime}\times 25^{\prime\prime}$ cut-
out collapsed image shown in Panel (B) and (F) without masking the sources,
and the contour levels are [2, 3, 4]$\times\sigma$. The areas encompassed by
the outermost contours are similar between the different
configurations/resolutions (synthesised beams displayed on the bottom left of
Panels B and F).

Finally, the PVDs in Panels (G) and (H) were extracted along the same pseudo-
slits as for the high-resolution data. Black contours are based on the
standard deviations with levels of [1.0, 2.0, 2.5, 3.0]$\times\sigma$. PVDs of
mosaic data show fewer peaks (spatial local maximum) and sub-components than
high-resolution data. For PVDs extracted along red pseudo-slits, there are
four clear components centred around velocity [-200, -50, 50, 200] km $\rm
s^{-1}$ in Panel (C), while only two components are centred around velocity
[200, -50] km $\rm s^{-1}$ in Panel (G). The component at velocity 200 km $\rm
s^{-1}$ is recovered by mosaic data, the two components of velocity [-50, 50]
km $\rm s^{-1}$ are merged into one, and the component at -200 km $\rm s^{-1}$
is not particularly evident at mosaic while being rather an extension of the
[-50, 50] km $\rm s^{-1}$ bin. The PVDs extracted along cyan pseudo-slits, due
to the much smaller beam size along the west-east direction, Panel (D) reveals
more sub-components than Panel (H).

To summarise the similarities and differences of coarse and high-resolution
data of COALAS-SW.03 as follows: (1) the high-resolution data recovers well
the CO flux and FWHM observed in the mosaic data; (2) the collapsed images,
though unresolved in the mosaic data, are of similar isophotal size (comparing
the contour encompassed area based on standard value to the synthesised beam
area) in both data sets; (3) the PVD components have all a roughly similar
morphology, velocity components, and velocity gradient in either data set. In
Section 4, we present the search for large gas reservoirs mainly based on the
spectral FWHM, sizes of collapsed images and features of PVDs.

###  3.3 Feasibility of the mosaic Data

Our comparison between high-resolution and mosaic data demonstrates that the
mosaic/coarse data has the potential to uncover large gas reservoirs in terms
of both kinematics and morphology. To ensure a robust method of gas reservoir
search, we also consider observational conditions for each CO emitter.

The CO mosaic imaging of the Spiderweb protocluster field has inhomogeneities
in observational depth and resolution. To accurately assess whether a
detection represents a large gas reservoir, we must consider not only its
spectral FWHM, collapsed image size, and PVD features (referred to as “source
characteristics”), but also the “observational conditions” specific to each
detection. This includes the number of pointings covering the source, the
configuration and resolution of those pointings, and the positions of the
source within each pointing. For a comprehensive explanation of this
methodology, see Section 4.1 and refer to Figure 10 for a clear illustration
of the criteria related to “source characteristics” and “observational
conditions”.

##  4 Searching for large molecular gas reservoirs

###  4.1 Method

Based on the generated mosaic image (Figure 1 in Jin et al. 2021), we checked
for all these 46 detections their collapsed images with specified locations
and velocity channel ranges. Our aim is to develop a generally applicable
method for identifying large gas reservoir candidates. The presented method,
customised for the COALAS CO(1-0) survey conducted on the Spiderweb
protocluster, exhibits universal applicability to other interferometric-based
investigations targeting extended gas reservoirs.

The search process has five stages: (I) primary check; (II) examination of the
collapsed images and PVDs obtained from the mosaic imaging data; (III) check
for consistencies between the single-pointing and mosaic datasets for all
candidates found in the mosaic data set; (IV) priority ranking based on
assigning binary numbers to each characteristic; and (V) manual classification
of the selected candidates into two classes, i.e., robust and tentative. A
flowchart is shown in Figure 3. We will describe the procedure of the
flowchart in detail in Sec. 4.1.1. In stage IV “Binary Criteria” ranking, we
designed a set of quantified parameters, reflecting the characteristics of the
source and representing the observational conditions. The details of the
parameter set-up of stage IV are described in Sec. 4.1.2. The parameter set-up
is calibrated and explained in Sec. 4.1.3.

Figure 3: Flowchart of the large molecular gas reservoir search procedure. The
procedure is composed by five stages, based mainly on the mosaic data and
complemented with the verification of single pointing data cubes for possible
candidates selected through the first two stages.

####  4.1.1 Search procedure

The procedure of searching for large molecular reservoirs is shown in the
flowchart in Figure 3. The detailed explanation is as follows.

Stage I. Primary Check: visual check of collapsed images and velocity colour
coded maps. We generated cut-outs (sub-datacube) of 46 sources with various
sets of projected spatial (such as 25$\aas@@fstack{\prime\prime}$,
35$\aas@@fstack{\prime\prime}$, 45$\aas@@fstack{\prime\prime}$) and channel
sizes based on CO(1-0) FWHM given in Jin et al. (2021).

Stage II. Fine-tuned: the “fine-tuned” generation and inspection of collapsed
images and PVDs. Based on the first stage, we generated the collapsed images
and PVDs for sources more precisely. The spatial and channel sizes were tuned
iteratively for each source, ensuring the cut-outs fit the full 3-dimension
sizes of sources and minimise the visual influence from the background noise.
We constructed a list of potential candidates by comparing the size of
collapsed images with observational synthesised beam sizes and visual checking
of gradients and multiple components on PVDs.

Stage III. Single-pointing Check: check the single-pointing data of the
candidates we have obtained. Besides the collapsed images and PVDs, we also
extracted the spectra from various apertures (single central pixel,
3$\aas@@fstack{\prime\prime}$0 circular aperture, and full spatial cut-out
size).

Stage IV. Binary Criteria ranking: we employ a binary ranking system which
assigns a score to each candidate based on multiple criteria. These criteria
include: (1) size of collapsed image; (2) PVD features; (3) signal-to-noise
ratio of the CO emission detection; (4) number of pointings with small beam
sizes ($<$7$\aas@@fstack{\prime\prime}$0); (5) fraction of pointings with
small beam sizes; and (6) fraction of pointings in which the source is located
near the edge of the primary beam. The first two criteria reflect the
characteristics of the source, and the last four account for the observational
conditions and the inhomogeneous nature of the data set (i.e.,
configurations/resolutions and background noise levels). Details can be found
in Section 4.1.2 and Appendix A.1. With this scheme, we are able to rank the
46 CO detections, and separate sources which show evidence for large gas
reservoirs from those without (clear) evidence (Section 4.2.1).

Stage V. Final visual inspection: We perform a final manual classification of
large gas reservoir candidates by visually inspecting the kinematic and
morphological features of their collapsed images and PVDs in order to
differentiate between robust and tentative candidates.

####  4.1.2 Ranking Criteria

We propose a “Binary Criteria Ranking” to weight the possibility that a source
has an extended/large molecular reservoir. In such a ranking, we selected a
set of criteria characterising each source, and place these criteria in order
of relevance, prioritising source sizes. The determination of whether a source
is extended or not is based on multiple factors, including but not limited to
the quality and resolution of the observational data. Consequently, our
analysis takes these factors into account, and the established criteria
encompasses two distinct aspects: (1) intrinsic features of the source such as
the source size and morphology of collapsed images, kinematics as gauged from
the PVDs, the spectral SNR of the detection; (2) observational conditions
reflecting the data quality such as the number of pointings covering the
source, the array configurations of the pointings and the position of the
source relative to the beam centre in each pointing.

Each evaluation criterion is assigned a binary number consisting of one to two
bits. To be more precise, if we use a single bit for a criterion, a source can
be divided into two categories, represented by boolean numbers “1” and “0”. On
the other hand, if we use two bits for a criterion, a source can be divided
into four categories, represented by binary numbers “11”, “10”, “01”, and
“00”. These binary numbers are used to represent data in a digital system,
where each bit represents a binary digit (0 or 1) that is used to store and
process information. After this classification process, we concatenate the
binary representation of all criteria to form a new binary number. This newly
formed binary number is then converted as a whole into its corresponding
decimal equivalent, which will be explained in further detail with a specific
criteria set and demonstrated through equation 2. Those binary numbers from
the criteria placed as a priority (located among the first criteria
considered) would contribute more than those of lower priority (which are
among the last of the criteria to be considered). Ideally, a well-designed set
of criteria (both in the sense of the number of possible classifications, 2 or
4, and in the order in which they are considered) would allow us to rank the
sources properly from the most robust candidates to those with no evidence for
extended molecular gas.

We designed the ranking system and adjusted the definition and order with
seven “calibrators” of extended molecular gas reservoir candidates. Those
seven calibrators are either confirmed to be extended with high-resolution
observations or with evidence for having extended gas reservoirs in our visual
inspection process. Five other criteria sets designed previously are explained
in Appendix A.1. The criteria order and the corresponding decimal contribution
of the final criteria set is shown in Figure 4 (and a complementary Figure 10
illustrates the detailed criteria used in assigning decimal values and in
classifying galaxies as being a large gas reservoirs candidate). The binary to
decimal conversion equation is,

$Score=\sum_{i=0}^{N-1}x_{i}\cdot 2^{i}\quad\left(x_{i}=0\text{ or }1\right)$
(1)

$x_{i}$ are the binary values at i-th places, and N is the total binary bits
places for all the criteria. We will refer to the decimal values of the binary
ranking as the ”score”, representing the possibility of being categorised as
an extended molecular gas reservoir.

The six criteria, in order of priority, include the (1) collapsed image size
(Collapsed Size); (2) features observed in the position-velocity diagram
(PVD); (3) Signal-to-noise ratio(SNR); (4) The number of ATCA observational
pointing covering the source with a small-beam-size
($<$7$\aas@@fstack{\prime\prime}$0) (Number of Small-Beam-Size Pointings -
Number SBSP); (5) The fraction of small-beam-pointing pointings
($<$7$\aas@@fstack{\prime\prime}$0) relative to the total number of pointings
that cover the source (Fraction of Small-Beam-Size Pointings - Fraction SBSP);
(6) The fraction of pointings within which the source is located at the edge
(Fraction E). The first three reflect the characteristics of each source, and
the latter three the observational conditions. The detailed explanations of
each criterion are given in Appendix A.1. Combine the binary numbers of each
criteria and convert to decimal value,

$\begin{split}&\text{[Collapsed size] ($x_{8}$)}\oplus\text{[PVD]
($x_{7}$)}\oplus\text{[SNR] ($x_{6}$)}\\\ &\qquad\oplus\text{[Number SBSP]
($x_{5}$ $x_{4}$)}\oplus\text{[Fraction SBSP] ($x_{3}$ $x_{2}$)}\\\
&\qquad\oplus\text{[Fraction E] ($x_{1}$ $x_{0}$)}\\\ &=\text{$x_{8}$ $x_{7}$
$x_{6}$ $x_{5}$ $x_{4}$ $x_{3}$ $x_{2}$ $x_{1}$
$x_{0}$}\quad\text{(combine)}\\\
&\text{$\Rightarrow$}\sum_{i=0}^{N-1}x_{i}\cdot 2^{i}(N=9)\quad\text{(convert
to decimal)}\end{split}$ (2)

operator $\oplus$ means concatenate (combine) the binary numbers.

As shown in Figure 5, we separate the candidates from the rest via setting the
cut-line (lower limit) on the corresponding decimal values 400. A detailed
description about this chosen threshold is presented in Appendix A.2.

Figure 4: Display of the criteria order, and corresponding decimal values. The
first row lists the criteria in order of their weighting, highest to lowest
from left to right. The second row shows the corresponding decimal values each
criteria could contribute. The third row is the overall corresponding decimal
range of all possible combinations. A detailed presentation of quantifying
these criteria into decimal values and classification of candidates is shown
in Figure 10.

####  4.1.3 Calibration

We use calibrators to improve the accuracy of our criteria by adjusting the
number of bits and their order. Specifically, the adjustments we made are: (1)
the order of the criteria representing the weights of each; (2) by adjusting
the number of bits of one criterion, we can have different numbers of
classification classes according to the specific criteria. One bit for two
classes, two bits for four classes, three bits for up to eight classes, and so
forth; and (3) adjusting the boundaries between sources with and without
extended reservoirs.

The seven calibrators used to calibrate our classification method are as
follows: Four of them are large gas reservoirs confirmed through the high-
resolution data, the COALAS-SW.01 (HAE229: Dannerbauer et al. 2017), the
COALAS-SW.02 (Spiderweb Galaxy: Emonts et al. 2013, 2018), the COALAS-SW.03
(DKB03: reported in this paper) and COALAS-SW.06 in Figure 11. The remaining
three have only the mosaic observations but they show clear indications of
extended gas reservoirs: the COALAS-SW.29 which has an obvious
merger/rotating-like kinematic, and the COALAS-SW.23 and COALAS-SW.46 are a
close pair sharing a giant molecular reservoir. We give detailed information
on COALAS-SW.06, COALAS-SW.29, COALAS-SW.23 and COALAS-SW.46 in Appendix B.

In total, we experimented with six different ranking sets with similar
criteria that considered both source characteristics and observational
conditions aspects. Given the importance of the collapsed size in searching
for extended gas reservoirs, we assigned the highest priority to this
criterion in five out of the six sets. During the implementation and
adjustment of the criteria ranking sets, we realised the need to lower the
weights of collapsed size criterion, to potentially allow other criteria to
provide greater contribution to the final ranking. Specifically, according to
the behaviours of the calibrators, the candidates could have sizes comparable
to the beam size, and clear indications from the PVD analysis for an extended
reservoir of gas. To lower the weight of collapsed size criterion, we reduced
the bits numbers of collapsed size criterion from two to one. Furthermore, we
lowered the standard to let in those not obviously observed as extended option
V. In option VII, the PVD criterion was simplified to one bit, which gives
more weight to the criteria besides collapsed size and PVD ones, and thus
calibrators COALAS-SW.06 and COALAS-SW.46 become higher ranked.

Option VII in Table 2 is the final criteria set for ranking the sources
(Figure 4) which works well in separating the promising candidates from the
rest. The obvious break of decimal values around 400 seems to be the adequate
criteria set (Figure 5). Improvements lead to a break in the ranking from the
robust to the tentative one. A clear break implies that this final option is
likely the best for producing a set of robust candidates of sources with
extended gas reservoirs. Additionally, we include a final manual
classification for separating the robust candidates and those which are rather
tentative.

###  4.2 Results

####  4.2.1 Candidate List

As demonstrated above, the final set of criteria consists of six items,
employing nine binary bits, and thus resulting in the corresponding decimal
values ranging from 0 to 511.

$\text{ Score }=\sum_{i=0}^{N-1}x_{i}\cdot 2^{i}\stackrel{{\scriptstyle
N=9}}{{===}}\left\\{\begin{array}[]{l}0\;\;\;\;\;\left(\text{minimum, all
}x_{i}=0\right)\\\ 511\;\left(\text{ maximum, all
}x_{i}=1\right)\end{array}\right.$ (3)

The binary ranking “score” distribution of COALAS CO emitter sample is shown
in Figure 5. The “score” value 400 is where the source number drops, and was
used as a separation line (the red line in Figure 5) between candidates and
non-candidates. The 21 sources whose scores are above 400 are our final
candidates.

Figure 5: Binary ranking “score” distribution of COALAS sample. The red dashed
line is the separation line for the large molecular gas reservoir candidates
(robust and tentative) and the remaining ones.

In accordance with our classification system outlined in Stage V of Section
4.1.1, all identified extended molecular gas reservoir candidates were further
categorised into two distinct groups: robust and tentative candidates.
Collapsed images and PVDs for the 14 robust and seven tentative candidates are
presented in Appendix C and D, respectively. The frequency of extended gas
reservoirs in the Spiderweb Protocluster is $\sim$30 $\%$ (14 out of 46
galaxies), counting the robust candidates only.

####  4.2.2 Environmental study

Due to the handful of discoveries and studies on extended molecular gas
reservoirs, their nature is still unclear. For massive BCGs, the large gas
reservoirs were suggested to be either molecular gas in accretion streams or
recycled gas from the star formation within the galaxy (Emonts et al., 2016,
2018; Ginolfi et al., 2017). However, our extended gas reservoir candidates
were discovered to be spatially distributed over the Spiderweb protocluster
field, not limited to the central galaxies like BCGs. Thus, we cannot directly
apply the aforementioned scenarios to these candidates and require new
explanations for their nature. Nevertheless, if these scenarios are
generalised, the denser local potential well in the nodes of the cosmic web
may have a similar impact on gas accretion and interactions between close-by
galaxies as the (proto)cluster centre.

The measurement of the galaxy environment is carried out in three ways: N-th
nearest neighbour, fixed aperture and annulus (refer to Table 1 in Muldrew et
al. 2012 for a review). We use the N-th nearest neighbour method to determine
galaxy density by counting the number and proximity of neighbouring galaxies.
Based on such a simple concept, one can either define a projected surface
density or a spherical enclosed density. The projected surface density,
${\sigma}_{n}$, is defined as

$\sigma_{n}=\frac{n+1}{\pi r_{n}^{2}}$ (4)

where n is the N-th closest galaxy for each reference galaxy, and $r_{n}$ is
the projected distance between the reference galaxy and the N-th closest
galaxy. This is commonly used for datasets lacking the third space dimension,
i.e., precise redshift (e.g., Dressler 1980, Baldry et al. 2006, Koyama et al.
2013). A severe shortcoming of the 2D surface density is that two galaxies
appearing close to each other could be due to pure alignment along the line-
of-sight and being separated at large distances in the third dimension. Among
the 46 CO emitters in the COALAS survey, several projected close-by sources
have large distances between each other in the three-dimensional aspect.
Therefore, we adopt the 3D-type N-th nearest neighbour method.

Utilising the precise 3-dimensional location information available for all 46
sources, we conducted a calculation of the 3D spherical N-th nearest neighbour
for each individual source. The corresponding volume density of galaxies is
defined in the following way:

$\rho_{n}=\frac{n+1}{(4/3)\pi r_{n}^{3}}$ (5)

where n is the N-th closest galaxy of each reference galaxy and $r_{n}$ is the
distance between the reference galaxy and the N-th nearest galaxy in the
three-dimensional space. Our environmental analysis focuses on the 46 CO
detections ($\geq$ 3.8) reported in Jin et al. (2021), utilising the
corresponding coordinates and CO spectroscopic redshift data (precise to four
decimal places) from the same study. In our sample, each galaxy has 45
neighbours. Regarding each of them as the centre reference galaxy, we
calculated the volume density from 1st to 45th nearest neighbour. We plot the
volume density to N-th nearest neighbour in Figure 6. We separated the robust
candidates, tentative candidates and the rest with blue, cyan, and red
colours, fitted with binomial lines. We found that our candidates tend to be
located in denser regions. We note that the contrast on density between
candidates and non-candidates remains even when fitting the non-candidates
without the four sources located at the sparsest environment.

Figure 6: Volume density to N-th nearest neighbour of CO emitters. Robust
candidates, tentative candidates and the non-candidates were marked with blue,
cyan and red colours, with solid lines indicating best fit polynomials. Error
bars for the fitting are shown at intervals of every 5th nearest neighbour,
with specific horizontal adjustments applied to the error bars of the robust,
tentative, and non-candidates classes to enhance the visual presentation.

The interactive Figure 7 displays the 3D distribution of CO emitters. The
robust, tentative and non-candidates are marked with blue squares, cyan dots
and red crosses, respectively. The Spiderweb galaxy is marked with a blue
star. Alternatively, Figure 8 offers a two-panel view of the spatial and
redshift distributions of 46 CO emitters. The upper panel displays their
spatial distribution, categorised into non-candidates (red crosses), robust
candidates (blue circles), and tentative candidates (cyan circles), with grey
crosses indicating the distribution of all CO emitters. The lower panel
illustrates their redshift distribution, with Gaussian functions used to fit
the distributions for each category, with the fitting lines denoted in the
same colours as their respective categories.

We find that the large gas reservoir candidates are concentrated in the core
of the Spiderweb protocluster, which is consistent with the results of the
N-th nearest neighbour analysis. Spatially, as shown in Figure 7 or the upper
panel of Figure 8, the central region is dominated by candidates, while the
outskirts are conversely occupied more by non-candidates. In terms of
redshift, in contrast to the almost uniform distribution of non-candidates,
the candidates are highly concentrated at a redshift of approximately z=2.16,
which is the centre of the Spiderweb Protocluster.

The inhomogeneous mosaic data have different local RMS levels varying by up to
a factor 2 (0.13 - 0.29 mJy) among the 13 pointings, e.g., pointing “MRC1138”
and “HAE229” are the two deepest fields with rms of value 0.13 mJy, and
“SWpoint7” has the largest rms of value 0.29 mJy (refer to the Table 1 in Jin
et al. 2021). This raises the question if the aforementioned result, extended
gas reservoirs tend to be located at the denser region, is caused by an
observational bias. We thus checked if there is a correlation between the
location of large gas reservoir candidates and local RMS, and found no
evidence of such a correlation.

[controls,loop,width=1.0]2./Animation_3D/SD_136

Figure 7: Spatial distribution (3D) of all 46 CO emitters. Blue star:
Spiderweb galaxy; blue square: robust candidates; cyan: tentative candidates;
red: the others. Figure 8: The upper panel displays the spatial distribution
of 46 CO emitters, including non-candidates (red crosses), robust candidates
(blue circles), and tentative candidates (cyan circles), with grey crosses
indicating the distribution of all CO emitters. The Spiderweb Galaxy is
denoted by a blue star. The lower panel illustrates the distribution of
redshifts among the CO emitters, divided into non-candidates (in red) and
candidates (in dark blue), with the overall CO emitter distribution depicted
in grey. The distribution for candidates is further broken down into two
categories: tentative candidates (represented by the cyan shaded region) and
robust candidates (represented by the blue shaded region). Gaussian functions
have been employed to fit the distributions, with corresponding fitting lines
in the same colours as the respective categories.

##  5 Discussion

###  5.1 Performance of our method

We obtained 14 robust candidates of large molecular gas reservoirs (i.e.,
$\sim$30$\%$ of the total number of candidates). The following aspects support
the credibility of our method and final robust candidate list: (1) The binary
criteria ranking system was calibrated with seven CO detections (four of the
seven calibrators are cases confirmed through high-resolution observations). A
clear border between the candidates and non-candidates resulted in the number
distribution of decimal ranking values (Figure 5). We note that follow-up
high-resolution observations of our candidates are needed for a verification.
(2) Our environmental study of the candidates is in line with the physical
expectations that the gas is accumulating and collapsing in the denser regions
(especially in the cores of protoclusters) where the potential well is deeper.

###  5.2 Large molecular gas reservoirs from the Literature

We conducted a comprehensive search of molecular gas observations of
(proto)clusters and overdensities aiming to identify potential extended gas
reservoirs with a scale of $\gtrsim$40 kpc (corresponding to the scale of
large gas reservoirs we aimed to identify in the Spiderweb protocluster in the
current study). The compilation is listed in Table 1 and focuses on (multiple)
transition(s) of CO. One source, LAB1 in the SSA22 protocluster field, was
revealed through [CII] observations. In total we have identified 13 large
molecular gas reservoirs. Four sources have been already reported before as
such objects: the Spiderweb galaxy (Emonts et al., 2013, 2014, 2016, 2018),
HAE229 (Dannerbauer et al., 2017) in the Spiderweb protocluster, the QSO
Q12287+3128 in the ELANe protocluster survey Li et al. (2021b, 2023) and
MAMMOTH-I in the BOSS1441 protocluster (Emonts et al., 2018). The size scales
of the remaining sources were determined through visual measurements on moment
0 maps based on their contours at approximately 3$\sigma$. However, our
exercise could be only done in cases where these maps have been provided. Thus
our literature search might be not complete.

Protocluster | redshift | Source ID | Emission Lines | Size | Size Given | Reference
---|---|---|---|---|---|---
Jackpot nebular | 2.04 | galaxy1 | CO(3-2) |  $\sim$40 kpc | - | Decarli et al. 2021
PKS1138-262 Protocluster | 2.16 | Spiderweb Galaxy | CO(1-0) |  $\sim$70 kpc | Yes | Emonts et al. (2013, 2014, 2016, 2018)
(Spiderweb) |  |  | CO(4-3) |  $\sim$50 kpc | Yes | Emonts et al. (2018)
|  |  | [CI] |  $\sim$50 kpc | Yes | Emonts et al. (2018)
|  | HAE229 | CO(1-0) |  $\sim$40 kpc | Yes | Dannerbauer et al. (2017)
Protocluster ELANe | 2.22 | QSO Q12287+3128 | CO(4-3) |  $\sim$100 kpc | Yes | Li et al. (2021b, 2023)
Slug nebular | 2.28 | QSO | CO(3-2) |  $\sim$50 kpc | - | Decarli et al. (2021)
BOSS1441 Protocluster | 2.3 | Region A (Q0052) | CO(1-0) |  $\sim$40 kpc | - | Emonts et al. (2019)
(MAMMOTH-I) |  |  | CO(3-2) |  $\lesssim$15 kpc | - | Li et al. (2021a)
|  |  | CO(4-3) |  $\lesssim$15 kpc | - | Li et al. (2023)
CLJ1001 Protocluster | 2.5 | 131077 | CO(1-0) |  $\lesssim$40 kpc | Yes | Champagne et al. (2021)
|  |  | CO(3-2) |  $\lesssim$10 kpc | - | Champagne et al. (2021)
|  |  | CO(1-0) |  $\sim$30 kpc | - | Wang et al. (2016)
|  |  | CO(5-4) |  $\sim$30 kpc | - | Wang et al. (2016)
|  | 130933 | CO(1-0) |  $\sim$60 kpc | - | Wang et al. (2018)
|  | 130842 | CO(1-0) |  $\sim$60 kpc | - | Wang et al. (2018)
HXMM20 Protocluster | 2.6 | S0 | CO(1-0) |  $\sim$45 kpc | - | Gómez-Guijarro et al. (2019)
|  |  | CO(3-2) |  $\sim$30 kpc | - | Gómez-Guijarro et al. (2019)
|  | S2 | CO(1-0) |  $\sim$40 kpc | - | Gómez-Guijarro et al. (2019)
|  |  | CO(3-2) |  $\sim$30 kpc | - | Gómez-Guijarro et al. (2019)
|  | S3 | CO(1-0) |  $\sim$40 kpc | - | Gómez-Guijarro et al. (2019)
|  |  | CO(3-2) |  $\sim$30 kpc | - | Gómez-Guijarro et al. (2019)
SSA22 Protocluster | 3.1 | LAB1 | [CII] |  $\sim$50 kpc | - | Umehata et al. (2017, 2021)
|  |  | CO(4-3) |  $\sim$30 kpc | - | Umehata et al. (2021)
Table 1: Collection from the literature of potential extended molecular gas
reservoirs with scale $\gtrsim$ 40 kpc. In addition to emission lines
indicative of a scale above 40 kpc, other relevant emission lines of the same
sources are also listed exhibiting compact or less extended behavior. Figure
9: The upper panel displays the distribution of emission line numbers for
(potential) extended gas reservoirs, while the bottom panel illustrates the
situation of each individual (proto)cluster/object.

We note that some protoclusters lack molecular gas observations while others
only had relevant observations for the central regions or focused solely on
the central BCGs. The absence of COALAS-like wide field systematic gas surveys
in these protoclusters may have contributed to the rarity of extended gas
reservoir discoveries reported up to now in the literature. For six cases, we
have several CO transitions. Only in the case of the Spiderweb Galaxy all
reported transitions show extended emissions. In the remaining cases the
phenomena is only seen in the lowest CO transition CO(1-0). Statistically,
about half of our (potential) large gas reservoirs are selected based on
CO(1-0) observations, as shown in the upper panel of Figure 9. Increasing the
number CO(1-0) observations of (proto)cluster members would certainly lead to
more detections of extended gas reservoirs. Recent studies show that the
extended molecular gas reservoirs are not only limited to AGNs located in
protoclusters, e.g., star-forming galaxy HAE229 in Spiderweb protocluster
(Dannerbauer et al., 2017), and the COALAS-SW.03 reported in this paper
(starburst galaxy dubbed DKB03 in Dannerbauer et al. 2014).

Existing observations in the literature may have downplayed potential large
gas reservoirs, and some sources of large gas reservoirs may have been missed
due to inadequate observations. Specifically, the low-surface-brightness
ground-transition of CO has not been properly observed, and the lack of
systematic observations has resulted in some sources being completely
overlooked as based on our visual inspection we reported 13 new extended
molecular gas reservoirs. With our work at least we doubled the number of
known extended molecular gas reservoirs.

###  5.3 Environmental-driven physical process: thirty percent of galaxy
members are evolving in extended gas

With our method, we find 14 robust candidates of extended molecular reservoirs
selected from 46 CO emitters physically related to the Spiderweb protocluster.
Thirty percent is a previously unknown large fraction, which means extended
gas might be prevalent in protoclusters and, due to the difficulty in
detecting extended low surface brightness gas, was generally not properly
characterized in the past. More observations and theoretical studies are
needed to understand this result.

Converting the CO line luminosity to the molecular gas mass, we can compare
the ICM in the Spiderweb protocluster with local galaxy clusters (e.g., Coma
and Virgo clusters) and conjecture the future of the Spiderweb protocluster. A
bimodal CO-$H_{2}$ conversion factor is widely adopted in the extragalactic
literature. For star-forming galaxies, commonly the conversion factor
$\alpha=4.6\mathrm{M}_{\odot}\left(\mathrm{Kkms}^{-1}\mathrm{pc}^{2}\right)^{-1}$
is thought to be most appropriate. However, for galaxies with intense star
formation or mergers, which bear resemblance to local ultra-luminous infrared
galaxies,
$\alpha=0.8\mathrm{M}_{\odot}\left(\mathrm{Kkms}^{-1}\mathrm{pc}^{2}\right)^{-1}$
is adopted by many researchers who investigate high-redshift CO emitters
(Solomon & Vanden Bout, 2005; Casey et al., 2014). Assuming a single galaxy
population, we obtained the molecular gas mass for each of the 46 CO emitters,
and the total molecular mass is 1.5 $\times$ ${10}^{13}$ (starburst galaxies)
- 8.7 $\times$ ${10}^{13}$ $M_{\odot}$ (star-forming galaxies). For the
molecular gas in extended morphologies (14 out of 46 robust candidates; thirty
percent of the full sample), the total molecular gas mass is 3.5 $\times$
${10}^{12}$ (starburst galaxies) - 2.0 $\times$ ${10}^{12}$ $M_{\odot}$ (star-
forming galaxies), and this accounts for 23$\%$ of the total molecular gas
mass. Taking all the extended molecular gas and assuming the low molecular-to-
atomic ratio appropriate for local galaxies ($\sim$0.1; Saintonge et al. 2017;
Catinella et al. 2018), we got a total $\sim$ ${10}^{13}$ \- ${10}^{14}$
$M_{\odot}$ of gas for just the galaxies with extended reservoirs of gas. The
mass of Virgo cluster derived from hot gas is $\sim$ 3 $\times$ ${10}^{14}$
within the central 1.7 Mpc (Sparke & Gallagher, 2007). The Spiderweb
protocluster has sufficient amount of gas to evolve into a Virgo-like cluster,
and through the “truncation” process 333galaxy-galaxy encounter or
gravitational interactions between galaxies and the (proto)cluster environment
can result in the distortion, stripping, and truncation of galaxy halos Moore
et al. 1996, 1998; Fujita 1998.. With these assumptions, it is plausible that
if stripped of their gas, these large gas reservoirs may contribute the cold
neutral and molecular phases of a proto-intracluster medium. We note the
diverse dependencies of CO-$H_{2}$ conversion factors, including metallicity,
gas density, temperature, and radiation field (Pavesi et al., 2018; Madden et
al., 2020). Estimations using bimodal conversion factors are simplified.
Therefore, follow-up observations and detailed studies are crucial for better
constraining the gas content, considering these various factors.

Based on the environmental study carried out in Section 4.2.2, it is found
that the large molecular gas reservoirs candidates are located in a locally
denser environment, predominantly concentrated in the central region of the
Spiderweb protocluster. According to Jin et al. (2021), the Spiderweb
protocluster is likely a super-protocluster that is embedded within a larger-
scale filamentary structure, and perhaps half of the CO emitters are still not
bounded to the core region. Hence, it is possible that the Spiderweb
protocluster comprises numerous substructures, and that the constituent
galaxies evolved collectively within separate relatively massive sub-halos.
Our findings suggest that the concentration of galaxies with extended
reservoirs of molecular gas in denser regions of protoclusters may be
indicative of efficient accretion of cold gas flowing along filaments, which
could potentially fuel the growth of the stellar population within these
galaxies. This could explain the observed concentration of massive early type
galaxies in local clusters.

However, the origin of these extended reservoirs is unclear from available
data. If the concentration of galaxies indeed reflects the overall and/or
local gravitational potential, then it follows that these galaxies are
positioned near the (local) centre(s) of the potential well. Consequently, one
can expect the accretion rate of gas to be focused in these regions. Of
course, whether or not gas accretion continues in massive halos and redshifts
like those of the Spiderweb protocluster is not clear (Dekel & Birnboim, 2006;
Cornuault et al., 2018). Moreover, cold streams could potentially penetrate
the early, massive, and hot halos and serve as the primary mode of galaxy
formation (Dekel et al., 2009). Nevertheless, theoretically it is clear that
gas accretion should create large extended reservoirs of gas (e.g., Danovich
et al. 2015). We can demonstrate what we mean by this through a few simple
timescale estimates. For example, let us assume that these extended reservoirs
of gas have order motions. We can calculate a dynamical time, based on the
assumption that the angular momentum resembles that of a rotating-like system,
yields an approximate value of t${}_{orbital}\sim$1.2 Gyr (r/40 kpc)/(vorb/200
km s-1). The gas cannot inspiral into the galaxy potential, say through tidal
effects due to bars or spiral arms or other disk substructure in less than a
dynamical time. Such a long timescale, although crudely estimated, suggest
that these extended reservoirs of molecular gas could be long lived if not
disrupted by external forces (e.g., ram pressure stripping, tidal stipping by
passing/merging gas, etc). Furthermore, if the extended gas is stable, it can
fuel the future growth of these proto-cluster galaxies for a long time, at
least 1 Gyr. So even if gas accretion has ceased, as galaxies fall into the
proto-cluster potential, there is still enough remaining extended gas to
support their growth and star formation rates for approximately the same time
scale.

Even more curiously, we can again estimate a crude crossing timescale if
indeed the Spiderweb proto-cluster is forming and the galaxies are falling
into the potential. Again, just making simple assumptions to provide a sense
of the timescales we are discussing, we can estimate the crossing time or
infall time, albeit crudely, as t${}_{crossing}\sim$1 Gyr
(r/Mpc)/(vinfall/1000 km s-1) (Kuiper et al., 2011). This is the timescale
over which processes like tidal and ram pressure stripping may play a role in
truncating the gas distribution in these galaxies. Comparing the two crude
estimates of the dynamical time of the extended reservoirs of gas and the
crossing or infall time of a galaxy, they are approximately equal (order-of-
magnitude only). Even with this crude comparison, it begs the question, why do
we observe these at all (Dannerbauer et al., 2017)? Observing such reservoirs
is even more puzzling given the recent detection of the S-Z effect in the
SpiderWeb protocluster (Di Mascolo et al., 2023).

Unfortunately, our results raise more questions than they answer. What we have
shown is that extended gas reservoirs may be common and their mere existence
pose many interesting problems and questions. Perhaps these reservoirs are one
of the smoking guns of gas accretion. Smoking gun may be particular
appropriate as a metaphor as these extended reservoirs may be the residual
after accretion has ceased. We simply do not know. If the extended molecular
gas is long-lived, then why was the gas removed by tidal stripping and ram
pressure stripping despite this being a proto-cluster and there is evidence
for a (proto-)intracluster medium. Perhaps the galaxies without extended
reservoirs are the galaxies that were stripped of their material, they may
have contributed to the gas in the ICM. However, it may be that the extended
gas is relatively metal poor, but the ICM of local clusters is metal-rich,
generally containing more metals than the galaxies in the clusters. Therefore,
there must be an ongoing exchange of material between the galaxies and their
surrounding large molecular gas reservoirs, which is due to outflow generated
by young massive stars, type Ia SNe and AGN through their radiation pressure
and radio jets (Tumlinson et al., 2017). This is evidenced by the elevated
levels of gas metallicity observed in the Spiderweb Galaxy and its halo gas
and HAE229 (Emonts et al., 2016; Dannerbauer et al., 2017). In other words,
what ever processes are dominating the nature of the gas in the centre of the
protocluster, it is more complex than the simple picture of gas accretion of
relatively pristine gas and outflows of metal-rich gas via starburst- and AGN-
drive outflows. If the most simple picture (caricature) of inflows and outflow
were correct, the extended gas reservoirs would become diluted due to the
continuous accretion of relatively pristine gas via filaments. This scenario
would lead to a result that is opposite to that observed in the Spiderweb
Galaxy and HAE229. Other processes such a mixing and gas instabilities must
allow inflows and outflows to enrich or dilute each other. If not, these
extended reservoirs become virtually impossible to explain with any reasonable
mass.

Furthermore, it was first discovered in Hatch et al. (2008) that the Spiderweb
Galaxy had an extended stellar halo, which was postulated to originate from
intense star formation fueled by a large (in size) gas reservoir. It was
later, in 2016, that Emonts et al. (2016) discovered this gas reservoir, which
nicely closed the loop on this picture. The gas reservoir appears to be
forming stars at a rate consistent with the Kennicutt-Schmidt law. These stars
are likely to be an early source of intracluster light, further adding to the
complexity of the processes at play.

##  6 Summary

We present a method for searching for large molecular gas reservoirs in 46 CO
emitters from Jin et al. (2021) physically related to the $z=2.16$ Spiderweb
protocluster. To show the feasibility of our method on extended source
searching based on mosaic data, we took COALAS-SW.03 as an example, and
compared the kinematic and morphological features obtained from the high-
resolution and mosaic data. We classify CO emitters through visual inspections
of collapsed images, PVDs, channel maps and integrated spectra. We propose a
binary criteria ranking approach to quantify whether a source is extended or
not. The criteria for ranking reflects both the source characteristics and the
observational conditions of each source. The method is calibrated by seven
sources, including four large gas reservoirs confirmed with high-resolution
observations, and three having strong evidences of extended gas reservoirs
solely based on mosaic observations. The major results we obtained in this
work are:

  * •

We find 14 robust and seven tentative extended gas reservoir candidates and
present their collapsed images and PVDs in Appendix C and D. The rate of
cluster members containing large gas reservoirs is $\sim$30$\%$, and up to
$\sim$50$\%$ if including the tentative detections.

  * •

We collected 13 potential extended gas reservoirs in dense environments from
literature, and highlighted the inadequacy of ground-transition CO
observations, which has resulted in limited discoveries of large gas
reservoirs.

  * •

Through the analysis of the three-dimensional distribution we show that the
candidates are concentrated on the core of the Spiderweb protocluster. Through
our environmental study employing the N-th nearest neighbour method, we find
that the candidates tend to be located in the local denser environments. This
is in line with the scenario that gas was accreted efficiently by gravity in
the denser region where the potential well is deeper.

  * •

We discuss the underlying environmental-driven physical processes of the large
molecular gas phenomenon. The large gas reservoirs might involve mechanisms
like gas truncation, galaxy merger or interaction in a dense protocluster, and
may feed the ICM in future local galaxy clusters like Virgo or Coma.

## Acknowledgements

We thank the anonymous referee for her or his comments that helped us to
improve our arguements and presentation in this paper. ZC acknowledges the
support by China Scholarship Council (CSC). The National Radio Astronomy
Observatory is a facility of the National Science Foundation operated under
cooperative agreement by Associated Universities, Inc. The Australia Telescope
is funded by the Commonwealth of Australia for operation as a National
Facility managed by CSIRO. HD and JMRE acknowledge financial support from the
Agencia Estatal de Investigación del Ministerio de Ciencia e Innovación (AEI-
MCINN) under grant (La evolución de los cíumulos de galaxias desde el amanecer
hasta el mediodía cósmico) with reference
(PID2019-105776GB-I00/DOI:10.13039/501100011033). HD acknowledges support from
the ACIISI, Consejería de Economía, Conocimiento y Empleo del Gobierno de
Canarias and the European Regional Development Fund (ERDF) under grant with
reference PROID2020010107. QSGU acknowledges support from the National Natural
Science Foundation of China (No. 12192222, 12192220 and 12121003). TK
acknowledges financial support by JSPS Kakenhi ($\\#$18H03717) and
International Leading Research ($\\#$22K21349).

## Data Availability

This work is primarily based on the ATCA large program COALAS survey (ID:
C3181, PI: H. Dannerbauer). The other relevant ATCA observations used in this
work includes 2014OCTS/C3003 (PI: H. Dannerbauer), 2016APRS/C3003 (PI: H.
Dannerbauer) and 2017APRS/C3003 (PI: B. Emonts).

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##  Appendix A Criteria Ranking Design and Decimal Separation Line

###  A.1 Criteria Ranking Design

To establish a robust set of criteria for accurately assessing the likelihood
of source extension, we thoroughly identified relevant factors and defined
their parameters. These parameters were then encoded into binary values
consisting of one or two bits. By concatenating these binary values and
converting them into decimal representation, we ranked the sources
accordingly. Throughout the process, we experimented with various sets of
criteria and ultimately selected option VII as the final decision. In the
subsequent paragraphs, we present the details of option VII and elucidate the
adjustments made to arrive at the final version.

In accordance with the details provided in Section 4.1, a set of seven
calibrators, known either for their confirmed extension or for exhibiting
evidence of extended gas reservoirs during our visual inspection process, was
employed to assess and refine the accuracy of our method, specifically the
criteria sets.

In the initial set of criteria, denoted as Option I, we included five key
factors for assessment: (1) collapsed image size (Collapsed Size I), (2)
features observed in the position-velocity diagram (PVD I), (3) the number of
ATCA observational pointings covering the source with a small beam size (¡7”)
(Number of Small Beam Size Pointings - SBSP), (4) the fraction of small-beam-
size pointings (¡7”) relative to the total number of pointings that cover the
source (Fraction of Small Beam Size Pointings - Fraction SBSP), and (5) the
fraction of pointings within which the source located at the edge (Fraction
E). We allocated two bits to each criterion, enabling the classification of a
source into one of four distinct classes for each criterion.

Building upon the initial set of criteria, our aim was to enhance its
effectiveness and accuracy by evaluating the ranking and inclusion of our
seven calibrators in the final candidate list of extended molecular gas
reservoirs. In Option II, our objective was to integrate the signal-to-noise
ratio (SNR) of CO detections from Jin et al. (2021) into the existing criteria
framework (Option I). In accordance with the SNR = 5 threshold specified in
Table 3 of Jin et al. (2021), we assigned a single bit number to this
criterion. Sources with an SNR greater than 5 were assigned a value of 1,
while the remaining sources received a value of 0. Subsequently, in Option
III, we explored a rearrangement of the first and second criteria compared to
the initial set (Option I). Option IV involved combining Option I and Option
II, maintaining the original order of the first two criteria, with emphasis on
the ”Size” criterion as our primary concern in selecting large molecular gas
reservoirs. Additionally, we introduced the SNR criterion after Collapsed Size
and PVD I criteria to further refine our selection process. Upon examining the
outcome of Option IV, which considered the ranking and inclusion of our seven
calibrators, and a thorough analysis of source properties, we identified that
the Collapse Size criterion was over-weighted. To address this, adjustments
were made in Option V, involving a reduction in the bit number from two to one
and a redefinition of the collapsed size, leading to a refined classification
of each source’s Collapse Size properties into two distinct classes.
(Collapsed Size II) 444In the Collapsed Size I classification, we assign ”11”
to sources with collapsing contours that are notably large compared to the
pointing beam size and exhibit interesting shapes (e.g., boomerang shape as
observed in source COALAS-SW.09), ”10” for sources whose collapsing contour
sizes are obviously large, ”01” for collapsing contours comparable to the beam
size (i.e., marginally resolved), and ”00” to those sources that remain
unresolved. In the Collapsed Size II classification, we assign “1” to sources
whose outermost contour of the collapsed image is larger than the synthesized
beam size, and ”0” to the rest of the unresolved sources.. Subsequently, in
Option V, we simplified the PVD criterion by reducing the bit numbers from two
bits (PVD I) to one bit (PVD I) 555In the PVD I classification, we assign “11”
to sources whose PVD exhibits a clear “S” shape, indicating a regular velocity
gradient, “10” to sources with a slight velocity gradient, ”01” to sources
showing multiple components occupying a wide channel/velocity range (evident
from the spectrum aspect with multiple-peak broad spectrum), and ”00” for
sources with compact components (i.e., no gradient, narrow velocity/channel
range) or exhibiting messy PVD behaviours. In the PVD II, we combine the first
three cases, previously classified as “11”, “10”, and “01” into a single “1”,
while the rest remain as ”0.. This adjustment aimed to reduce the relative
importance of PVD and allocate more weight to the remaining criteria, thus
enhancing the overall effectiveness and accuracy of the selection process. In
the final Option VII, we introduce an additional constraint to the PVD II
classification. Specifically, sources classified as “1” in Option VI, but with
spectral FWHM below 300 km/s, are re-classified into “0” (PVD III) in the
Option VII scheme. This constraint is grounded in the rationale that projected
extended sources should also exhibit extension along the line-of-sight
dimension.

After evaluating various sets of criteria options (Table 2), we find that
Option VII closely aligns with our requirements, meeting our selection
criteria most effectively. As a result, we present Option VII as our final
choice for the classification scheme. The detailed description of each
criterion is as following:

Option |  |  | Criteria |  |  |
---|---|---|---|---|---|---
| 1st | 2nd | 3rd | 4th | 5th | 6th
Option I | Collapsed Size I | PVD I | Number SBSP | Fraction SBSP | Fraction E | -
(10 bits) | (2 bits) | (2 bits) | (2 bits) | (2 bits) | (2 bits) |
Option II | Collapsed Size I | PVD I | SNR | Fraction SBSP | Fraction E | -
(9 bits) | (2 bits) | (2 bit) | (1 bits) | (2 bits) | (2 bits) |
Option III | PVD I | Collapsed Size I | Number SBSP | Fraction SBSP | Fraction E | -
(10 bits) | (2 bits) | (2 bits) | (2 bits) | (2 bits) | (2 bits) |
Option IV | Collapsed Size I | PVD I | SNR | Number SBSP | Fraction SBSP | Fraction E
(11 bits) | (2 bits) | (2 bits) | (1 bit) | (2 bits) | (2 bits) | (2 bits)
Option V | Collapsed Size II | PVD I | SNR | Number SBSP | Fraction SBSP | Fraction E
(10 bits) | (1 bit) | (2 bits) | (1 bit) | (2 bits) | (2 bits) | (2 bits)
Option VI | Collapsed Size III | PVD II | SNR | Number SBSP | Fraction SBSP | Fraction E
(9 bits) | (1 bit) | (1 bits) | (1 bit) | (2 bits) | (2 bits) | (2 bits)
Option VII | Collapsed Size III | PVD III | SNR | Number SBSP | Fraction SBSP | Fraction E
(9 bits) | (1 bit) | (1 bits) | (1 bit) | (2 bits) | (2 bits) | (2 bits)
Table 2: The evolution of criteria options and the final classification scheme
for ranking and selecting extended molecular gas reservoirs.

Collapsed image size (Collapsed Size I): assess whether sources are resolved
or not via comparing the size of collapsed images with the size of the
synthesised beam of the corresponding pointing. The area encompassed by the
standard deviation value contour is calculated. Finally, ratios of the
collapsed component area and synthesised beam area are calculated. Sources
whose ratio is greater than one (i.e., the source size is larger than the
synthesised beam) would be classified as resolved. We visually re-checked the
collapsed images afterwards, and excluded sources which have multiple contour-
encompassed regions separately distributed.

Features observed in the position-velocity diagram (PVD I): evaluate whether
sources have multiple components or are velocity gradient on PVDs. An extended
source is more likely to be three-dimensional extended rather than only in the
projected view. Thus, we applied an extra FWHM-cut at 280 km/s. The binary
values of PVDs are determined based on these two factors in a logical
conjunction way.

Signal-to-noise ratio (SNR): SNR values are from Jin et al. (2021). We assign
the bit value to sources whose SNR values are greater than 5.0 and assign
zeros to the others.

The following three criteria are about the observational conditions, and they
are relevant to observational pointings of each source. The ATCA survey of the
Spiderweb protocluster in total has 13 pointings, and each of the 46 CO
emitters are covered by one up to five ATCA observational pointings.

The number of ATCA observational pointings covering the source with a small
beam size ($<$7$\aas@@fstack{\prime\prime}$0) (Number of Small-Beam-Size
Pointings - SBSP): the sources are more likely to be resolved with
observational pointings of smaller beam size. Two bits are employed and
classify the cases into four classes: “11” for sources covered by three or
four small beam size pointings, “10” for two, “01” for one, and “00” for none.

The fraction of small-beam-size pointings ($<$7$\aas@@fstack{\prime\prime}$0)
relative to the total number of pointings that cover the source (Fraction of
Small Beam Size Pointings - Fraction SBSP): two bits are employed and the
cases are divided into four classes:

  1. 1.

“11”: fraction value equal to 1.0 (1/1, 2/2, 3/3, 4/4, 5/5; all the pointings
covering this source have small beams);

  2. 2.

“10”: fraction values equal to 0.6 (3/5), 0.67 (2/3), 0.75 (3/4), and 0.8
(4/5) (more than half pointings have small beams);

  3. 3.

“01”: fraction values equal to 0.2 (1/5), 0.25 (1/4), 0.33 (1/3), 0.4 (2/5),
and 0.5 (1/2, 2/4) (fewer than half pointings have small beams);

  4. 4.

“00”: fraction values equal to 0.0 (0/1, 0/2, 0/3, 0/4, 0/5; none of the
pointings cover this source have a small beam)

The fraction of pointings within which the source is located at the edge
(Fraction E): sources located at the edge of a single-pointing may be subject
to significantly higher noise levels, which can markedly impact the accuracy
of the ranking results. We calculate the distances between sources and the
pointing centre and classify the source as located at the edge of
observational pointings if the distance is greater than 94$\%$ of the primary
beam size radius. We use two bits for this criterion:

  1. 1.

“11”: fraction values equal to 0.0 (0/1, 0/2, 0/3, 0/4, 0/5; within none of
the pointings covering this source, it is located at the edge of the pointing)

  2. 2.

“10”: fraction values equal to 0.2 (1/5), 0.25 (1/4), 0.33 (1/3), 0.4 (2/5),
and 0.5 (1/2, 2/4) (within fewer than half of the pointings covering this
source, it is located at the edge of the pointing);

  3. 3.

“01”: fraction values equal to 0.6 (3/5), 0.67 (2/3), 0.75 (3/4), and 0.8
(4/5) within more than half of the pointings covering this source, it is
located at the edge of the pointing;

  4. 4.

“00”: fraction values equal to 1.0 (1/1, 2/2, 3/3, 4/4, 5/5; within all of the
pointings covering this source, it is located at the edge of the pointing);

###  A.2 Design of the binary criteria ranking: the boundary “score” between
candidates and the others

For better understanding, please refer to Figure A2 while reading the
following explanations of the decimal separation line of ”400”:

  1. 1.

If a source is assigned with highest marks for each criterion (the maximum
case in equation 3: all the $x_{i}$=1, and the corresponding decimal value
maximised to 511), this source would certainly be classified as an extended
gas candidate;

  2. 2.

The case which fails either the “Size of collapsed images” (the first
criteria; fail: bit value “0”) or “Position Velocity Diagram” (the second
criteria; fail: bit value “0”) would not reach the boundary score “400” as the
following equation shows:

$\text{ Score }=\sum_{i=0}^{N-1}x_{i}\cdot 2^{i}\stackrel{{\scriptstyle
N=9}}{{===}}\left\\{\begin{array}[]{l}\leq\;255\;(if\;x_{8}=0;Collapsed\;Size)\\\
\leq\;383\;(if\;x_{7}=0;PVD)\end{array}\right.$ (6)

  3. 3.

Assuming that a source meets the condition of fulfilling the first two
criteria (i.e., both criteria “Size of collapsed images” and “Position
Velocity Diagram” are assigned bit number “1”), the third criteria, SNR, could
be either “1” or “0” to be above the boundary score:

    1. (a)

SNR = “1”, together with two “1” from the first two criteria, will result in a
“score” greater or equal to 448:

$\text{ Score }=\sum_{i=0}^{N-1}x_{i}\cdot 2^{i}\stackrel{{\scriptstyle
N=9}}{{\geq}}448\;(if\;x_{8},x_{7},x_{6}=1)$ (7)

    2. (b)

SNR = “0” requires the binary numbers of the fourth criteria, Number SBSP, to
be greater than “00”, i.e., the source is at least covered by one pointing
with a small beam (i.e., relatively high resolution).

      1. i.

Number SBSP = “11” would result in a decimal value greater or equal to 432;

      2. ii.

Number SBSP = “10” would result in a decimal value greater or equal to 416;

      3. iii.

Number SBSP = “01” would result in a decimal value greater or equal to 400.

In the cases explained above, the first four criteria would be enough to
determine whether a source could be a large gas reservoir candidate or not.
The lower limit for the selection of candidates is the combination [Collapsed
size “1”] + [PVD “1”] + [SNR “0”] + [Number SBSP ‘01”] + [Fraction SBSP “–”] +
[Fraction E “–”] (Figure 10).

Figure 10: Visualisation of the Criteria Ranking Bit Assignments, Calculation
of the Ranking ”Score”, and Selection of Large Gas Reservoir Candidates. The
dark blue boxes represent abbreviations of the six criteria, with higher
priority shown on the left and lower priority on the right. The first three
criteria (Collapsed sizes, PVDs, and SNRs), enclosed within the large blue
box, depict the source characteristics, while the later three criteria (Number
SBSP, Fraction SBSP, and Fraction E), enclosed within the purple box, are
related to the observational conditions. The red box highlights the results of
candidate selection, with selected candidates in orange and non-selected
candidates in blue.

##  Appendix B Criteria Calibrators

The information of seven calibrators are summarised in Table 3, including the
source ID, alias, reference paper, data available, and corresponding figures
of collapsed images and channel maps.

Calibrators | Alias | Reference(extended) / Notes | Data | Figure
---|---|---|---|---
COALAS-SW.01 | HAE229 | Dannerbauer et al. (2017) | High-resolution; mosaic | -
COALAS-SW.02 | Spiderweb galaxy | Emonts et al. (2016, 2018) | High-resolution; mosaic | -
COALAS-SW.03 | DKB03 | This work: extended | High-resolution; mosaic | Figure 1,2
COALAS-SW.06 | - | This work: extended | High-resolution; mosaic | Figure 11
COALAS-SW.29 | - | This work: merger/rotating-like | mosaic | Figure 12
COALAS-SW.23 | - | This work: sharing giant molecular gas with COALAS-SW.46 | mosaic | Figure 13
COALAS-SW.46 | - | This work: sharing giant molecular gas with COALAS-SW.23 | mosaic | Figure 13
Table 3: Seven calibrators of the presented method. The first four are
confirmed large gas reservoirs confirmed through high-resolution observations,
and the final three have strong indicators to be large gas reservoirs with
solely mosaic data. Figure 11: High-resolution plots of COALAS-SW.06. Panel A
is the spectrum extracted from the emission peak with aperture size of
1$\aas@@fstack{\prime\prime}$5\. Panel B is the moment 0 map of COALAS-SW.06,
Panel C and Panel D are PVDs extracted along red and cyan lines shown in Panel
B, and Panel E presented channel maps. The contour levels in the collapsed
images are presented at [1, 2, 3] times the standard deviation values, with
the source delineated by black solid lines, and noise indicated by white
dashed lines. Figure 12: Characterise COALAS-SW.29 based on mosaic data. The
upper left panel is the spectrum of COALAS-SW.29. The following four panels
are collapsed image with black contours representing significance levels of
[2.0, 2.5, 3.0, 3.5] times the standard deviation ($\sigma$ = 0.033 Jy
$\rm{beam}^{-1}$ km $\rm s^{-1}$), PVDs extracted along the cyan and red
lines, and contours of collapsed images from bluer and redder channels
(corresponding to the negative and positive velocity components on PVDs). The
second row shows channel maps of extended CO(1-0). Figure 13: Characterise
COALAS-SW.23 and COALAS-SW.46 based on mosaic data. The upper left panel is
the spectrum of COALAS-SW.23. The following four panels are collapsed image
with black contours representing significance levels of [1.5, 2.5, 3.5, 4.5]
times the standard deviation ($\sigma$ = 0.028 Jy $\rm{beam}^{-1}$ km $\rm
s^{-1}$), PVDs extracted along the cyan and red lines, and contours of
collapsed images from bluer and redder channels (corresponding to the negative
and positive velocity components on PVDs). The second row shows channel maps
of extended CO(1-0).

##  Appendix C Robust Candidates

The collapsed images and PVDs of the 14 robust candidates are presented in
Figure 14.

Figure 14: The figure displays robust candidates in individual rows. The
leftmost panels show the collapsed images, while the middle and right panels
present PVDs extracted from two perpendicular pseudo-slits. The source ID for
each robust candidate is indicated in the upper right corner of the
corresponding collapsed image. The contour levels in the collapsed images are
presented at [1, 2, 3, 4] times the standard deviation values. The emission
contours are depicted in black solid lines, while the noise are represented by
white dashed lines. Figure 1: (Continued.) Figure 1: (Continued.)

##  Appendix D Tentative Candidates

The collapsed images and PVDs of the seven tentative candidates are presented
in Figure 2.

Figure 2: Tentative candidates. Same scheme as Figure 14 Figure 1:
(Continued.)

##  Appendix E Statistical explanation

For the contours of collapsed images in Figure 14 $\&$ Figure 2, we employed
the STandard Deviation (STD) values rather than the commonly used Root Mean
Square (RMS) values.

The equations of RMS is

$RMS=\sqrt{\frac{1}{n}\sum_{i}x_{i}^{2}}$ (8)

where n is number of values, and $x_{i}$ is each values.

The equation of standard deviation is

$STD=\sqrt{\frac{1}{n}\sum\left(x_{i}-\mu\right)^{2}}$ (9)

where n is the number of values, $x_{i}$ is each values, and $\mu$ is the mean
value. In physics, the term root mean square is used as a synonym for standard
deviation when it can be assumed that the input number population has a zero
mean, i.e., referring to the square root of the mean deviation of a signal
from a given baseline or fit.

The reason and feasibility are explained here, taking COALAS-SW.03 as an
example. First, we manually selected four regions with the radius of
3$\aas@@fstack{\prime\prime}$0, obtained the RMS values, and overlaid the [2,
3, 4] $\times$ RMS contours on the collapsed images as shown in the left
column panels in Figure 2. If we apply this method to all the other sources,
we need to be careful when we manually select the regions for such background
RMS calculations. If the regions are too large, they might be contaminated by
the source emission and result in a larger RMS value; if the regions are too
small, this might not be representative; if the positions of regions are
inappropriate, the results might be biassed by some regions of extreme values.
The spatial scales of emission vary among our sample, and thus requires plenty
of manual work on RMS calculation as explained above. Second, to simplify the
work, we tried the contour levels based on standard deviation values. We
calculated the standard deviation values based on these
25$\aas@@fstack{\prime\prime}$0 $\times$ 25$\aas@@fstack{\prime\prime}$0
cutout without masking the emission from the central source. Keeping the level
times the numbers of [2, 3, 4], we obtained the contour plots in the middle
column in Figure 2, whose outermost contour is more conservative/smaller
compared to the panels of the left column. It is reasonable as we included the
source emission when calculating the STD values and these derived STD values
are greater than the RMS values obtained from the background regions. To get
similar contours, we tried the smaller level times [1.5, 2.0, 2.5], and
displayed them in the right panels of Figure 2. To conclude, with a lower
multiple times, we can use the standard deviation values derived without
masking the source to replace the calculations of RMS values requiring lots of
manual work. To conclude, for simplifying the work on presenting the large gas
reservoirs, we employed the [1, 2, 3, 4] $\times$ STD values for collapsed
images in Figure 14 and Figure 2.

Figure 2: Comparison between the usage of Root Mean Square (RMS) values by
STandard Deviation (STD) values. Upper panels are collapsed images based on
the high-resolution data of COALAS-SW.03, and bottom panels are based on the
mosaic/coarse data. In the left columns the overlaid contours are [2, 3, 4]
$\times$ RMS (RMS values are calculated based on four regions with radius of
3$\aas@@fstack{\prime\prime}$0 marked with dashed white circles). In the
middle columns, the contours are [2, 3, 4] $\times$ STD, in the right columns
[1.5, 2.0, 2.5] $\times$ STD.