11institutetext: Cosmic Dawn Center (DAWN), Denmark
11email<EMAIL_ADDRESS>22institutetext: DTU Space, Technical University of
Denmark, Elektrovej 327, DK-2800 Kgs. Lyngby, Denmark
22email<EMAIL_ADDRESS>33institutetext: Niels Bohr Institute, University of
Copenhagen, Jagtvej 128, DK-2200 Copenhagen, Denmark 44institutetext: AIM,
CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris
Cité, F-91191 Gif-sur-Yvette, France 55institutetext: School of Astronomy and
Space Science, Nanjing University, Nanjing 210093, China
55email<EMAIL_ADDRESS>66institutetext: Key Laboratory of Modern
Astronomy and Astrophysics (Nanjing University), Ministry of Education,
Nanjing 210093, China 77institutetext: IRAM,300 rue de la piscine, F-38406
Saint-Martin d’Hères, France 88institutetext: Purple Mountain Observatory,
Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, China
99institutetext: Instituto de Astrofísica de Canarias, C. Vía Láctea, s/n,
38205 La Laguna, Tenerife, Spain 1010institutetext: Universidad de La Laguna,
Dpto. Astrofísica, 38206 La Laguna, Tenerife, Spain 1111institutetext:
Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla
4059, Valparaíso, Chile 1212institutetext: Department of Physics & Astronomy,
University of California Los Angeles, 430 Portola Plaza, Los Angeles, CA
90095, USA 1313institutetext: Max-Planck-Institut für Extraterrestrische
Physik (MPE), Giessenbachstrasse 1, 85748 Garching, Germany 1414institutetext:
INAF-Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34131, Trieste,
Italy 1515institutetext: IFPU-Institute for Fundamental Physics of the
Universe, Via Beirut 2, 34014, Trieste 1616institutetext: European Southern
Observatory, Karl-Schwarzschild-Str. 2, D85748 Garching bei Munchen, Germany
1717institutetext: Department of Astronomy, University of Geneva, Chemin
Pegasi 51, 1290 Versoix, Switzerland 1818institutetext: Department of
Astronomy, Tsinghua University, Beijing 100084, China 1919institutetext:
Chinese Academy of Sciences South America Center for Astronomy (CASSACA),
National Astronomical Observatories of China (NAOC), 20A Datun Road
2020institutetext: INAF- Osservatorio Astronomico di Brera, via Brera 28,
I-20121, Milano, Italy & via Bianchi 46, I-23807, Merate, Italy
2121institutetext: Department of Physics, University of Helsinki, Gustaf
Hällströmin katu 2, FI-00014 Helsinki, Finland 2222institutetext: School of
Physics and Astronomy, Institute for Astronomy, University of Edinburgh, Royal
Observatory, Blackford Hill, EH9 3HJ Edinburgh, UK 2323institutetext: Sub-
Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH,
UK 2424institutetext: Department of Physics and Astronomy, University of the
Western Cape, Robert Sobukwe Road, 7535 Bellville, Cape Town, South Africa
2525institutetext: Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa,
Chiba 277-8583, Japan 2626institutetext: Inter-university Institute for Data
Intensive Astronomy, Department of Physics and Astronomy, University of the
Western Cape, 7535 Bellville, Cape Town, South Africa

# NOEMA formIng Cluster survEy (NICE): Characterizing eight massive galaxy
groups at $1.5<z<4$ in the COSMOS field††thanks: Tables C1 to C8 are only
available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/.

Nikolaj B. Sillassen 1122 Shuowen Jin 1122Marie Curie FellowMarie Curie Fellow
Georgios E. Magdis 112233 Emanuele Daddi 44 Tao Wang 5566 Shiying Lu 445566
Hanwen Sun 5566 Vinod Arumugam 77 Daizhong Liu 88 Malte Brinch 1122 Chiara
D’Eugenio 991010 Raphael Gobat 1111 Carlos Gómez-Guijarro 44 Michael Rich 1212
Eva Schinnerer 1313 Veronica Strazzullo 14141515 Qinghua Tan 88 Francesco
Valentino 111616 Yijun Wang 5566 Mengyuan Xiao 1717 Luwenjia Zhou 5566 David
Blánquez-Sesé 1122 Zheng Cai 1818 Yanmei Chen 5566 Laure Ciesla 44 Yu Dai 1919
Ivan Delvecchio 2020 David Elbaz 44 Alexis Finoguenov 2121 Fangyou Gao 5566
Qiusheng Gu 5566 Catherine Hale 2222 Qiaoyang Hao 5566 Jiasheng Huang 1919
Matt Jarvis 23232424 Boris Kalita 2525 Xu Ke 5566 Aurelien Le Bail 44 Benjamin
Magnelli 44 Yong Shi 5566 Mattia Vaccari 2626 Imogen Whittam 23232424
Tiancheng Yang 5566 Zhiyu Zhang 5566

(Received XX / Accepted XX)

The NOrthern Extended Millimeter Array (NOEMA) formIng Cluster survEy (NICE)
is a NOEMA large programme targeting 69 massive galaxy group candidates at
$z>2$ over six deep fields with a total area of 46 deg2. Here we report the
spectroscopic confirmation of eight massive galaxy groups at redshifts
$1.65\leq z\leq 3.61$ in the Cosmic Evolution Survey (COSMOS) field.
Homogeneously selected as significant overdensities of red IRAC sources that
have red Herschel colours, four groups in this sample are confirmed by CO and
[CI] line detections of multiple sources with NOEMA 3mm observations, three
are confirmed with Atacama Large Millimeter Array (ALMA) observations, and one
is confirmed by H$\alpha$ emission from Subaru/FMOS spectroscopy. Using rich
ancillary data in the far-infrared and sub-millimetre, we constructed the
integrated far-infrared spectral energy distributions for the eight groups,
obtaining a total infrared star formation rate (SFR) of 260-1300 ${\rm
M_{\odot}}$ yr-1. We adopted six methods for estimating the dark matter masses
of the eight groups, including stellar mass to halo mass relations,
overdensity with galaxy bias, and NFW profile fitting to radial stellar mass
densities. We find that the radial stellar mass densities of the eight groups
are consistent with a NFW profile, supporting the idea that they are collapsed
structures hosted by a single dark matter halo. The best halo mass estimates
are $\log(M_{\rm h}/{\rm M_{\odot}})=12.8-13.7$ with a general uncertainty of
0.3 dex. Based on the halo mass estimates, we derived baryonic accretion rates
(BARs) of $(1-8)\times 10^{3}\,{\rm M_{\odot}/yr}$ for this sample. Together
with massive groups in the literature, we find a quasi-linear correlation
between the integrated SFR/BAR ratio and the theoretical halo mass limit for
cold streams, $M_{\rm stream}/M_{\rm h}$, with ${\rm SFR/BAR}=10^{-0.46\pm
0.22}\left({M_{\rm stream}/M_{\rm h}}\right)^{0.71\pm 0.16}$ with a scatter of
$0.40\,{\rm dex}$. Furthermore, we compared the halo masses and the stellar
masses with simulations, and find that the halo masses of all structures are
consistent with those of progenitors of $M_{\rm h}(z=0)>10^{14}\,{\rm
M_{\odot}}$ galaxy clusters, and that the most massive central galaxies have
stellar masses consistent with those of the brightest cluster galaxy
progenitors in the TNG300 simulation. Above all, the results strongly suggest
that these massive structures are in the process of forming massive galaxy
clusters via baryonic and dark matter accretion.

###### Key Words.:

Galaxy: evolution – galaxies: high-redshift – submillimeter: galaxies –
galaxies: clusters: general

##  1 Introduction

Galaxy clusters are the largest virialized structures in the local Universe,
and their progenitors (see Overzier, 2016, for a review) are suspected to be
massive galaxy groups and protoclusters in the early Universe (Muldrew et al.,
2015). At high redshifts, massive groups and protoclusters represent the
earliest massive collapsed structures hosted by massive dark matter halos
(Wang et al., 2016; Willis et al., 2020; Di Mascolo et al., 2023).
Characterizing their dark matter halos provides key constraints on
cosmological parameters that can be used to test structure formation theories
(Overzier, 2016). On the other hand, the evolutionary track between the early
structures and local clusters is a major topic in modern astrophysics but
remains poorly understood (Chiang et al., 2013; Shimakawa et al., 2018). These
early ($z>2$) massive structures host a large number of star-forming galaxies
rich in dust and gas (e.g. Dannerbauer et al. 2014; Oteo et al. 2018; Gobat et
al. 2019). The most massive members of these structures are often found to
have vigorous starbursts (e.g. Oteo et al., 2018; Miller et al., 2018; Zhou et
al., 2024), while some members are already quiescent at $z>2$ (e.g. Kubo et
al., 2021; Kalita et al., 2021; McConachie et al., 2022; Ito et al., 2023; Jin
et al., 2024). The diverse populations of member galaxies and their rapid
evolution make them an ideal laboratory for studying the formation of clusters
and brightest cluster galaxies (BCGs; Shi et al., 2024; Jin et al., 2024).
Therefore, studying a large sample of galaxy groups and (proto-)clusters
before cosmic noon (i.e. the peak of star formation at $z\sim 2$; Madau &
Dickinson, 2014), where groups and (proto-)clusters are expected to contribute
significantly to the cosmic star formation rate (SFR) density, is essential to
unveiling the evolution and formation of massive galaxies and clusters (Chiang
et al., 2017).

In the last decade, massive groups and (proto-)clusters have been discovered
at cosmic noon and out to the epoch of re-ionization ($z\gtrsim 6-8$; e.g. Hu
et al. 2021; Brinch et al. 2023; Jones et al. 2023; Arribas et al. 2023;
Morishita et al. 2023) using various techniques. To date, most structures have
been selected by mapping overdensity of galaxies, including the overdensities
of optical/near-infrared (NIR) sources (e.g. Gobat et al., 2011; Wang et al.,
2016), dusty star-forming galaxies (e.g. Dannerbauer et al., 2014), and star-
forming galaxies detected in the radio (e.g. Daddi et al., 2017, 2021).
However, a major limitation of the overdensity mapping is the line-of-sight
projection (e.g. Chen et al., 2023). In this regard, advanced techniques that
include colour and redshift information, for example red IRAC colours
(Wylezalek et al., 2013, 2014; Mei et al., 2023), narrowband emitters (Koyama
et al., 2013; Shimakawa et al., 2014; Hu et al., 2021), and photometric or
spectroscopic redshifts (e.g. Cucciati et al., 2018; Sillassen et al., 2022;
Helton et al., 2023; Jin et al., 2024), have significantly improved the
efficiency and robustness of the selection. Second, far-infrared (FIR) and
(sub-)millimetre-bright dusty star-forming galaxies have been used to detect
high-$z$ protocluster candidates, which were later confirmed by follow-up
observations, for example GN20 (Daddi et al., 2009), AzTEC3 (Capak et al.,
2011), the SCUBA2-selected HDF850.1 (Walter et al., 2011), the Herschel-
selected DRC (Oteo et al., 2018) and HerBS-70 (Bakx et al., 2024), and the
millimetre-selected SPT2349-56 (Miller et al., 2018). Third, extended X-ray
emission from hot plasma in the intracluster medium (ICM) can be used to trace
mature clusters (e.g. Stanford et al., 2006). Fourth, Sunyaev-Zel’dovich (SZ)
emission (Sunyaev & Zeldovich, 1970) is a sign of a collapsed massive
structure, where cosmic microwave background photons are accelerated by the
host ICM in clusters via inverse Compton scattering (e.g. Staniszewski et al.,
2009). Finally, extended Ly$\alpha$ emission (Ly$\alpha$ blobs), stemming from
cool gas in dense regions associated with overdensities of galaxies, can be
used to trace actively star-forming massive groups (e.g. Prescott et al.,
2008). A new technique that uses Ly$\alpha$ absorption has recently been
exploited to search for galaxy groups missed by other surveys: Ly$\alpha$
tomography (Lee et al., 2018; Newman et al., 2022).

Overdensity mapping and dusty star-forming galaxy (DSFG) tracers are widely
used to search for massive structures at $z>2$, for which the other methods
are either infeasible (e.g. SZ and X-ray) or require prohibitively time-
consuming observations. Therefore, a combined search of FIR-luminous objects
and overdensities of optical/NIR galaxies provides an efficient and powerful
tool for selecting massive galaxy groups and protoclusters. However, this
method still suffers from projection effects, and high quality photometric
redshifts are required to associate the FIR emission with the candidate
overdensities. Recently, the advent of deep, wide, and panchromatic
extragalactic survey fields, such as the Cosmic Evolution Survey (COSMOS), and
the construction of state-of-the-art, multi-band photometric catalogues (e.g.
COSMOS2020; Weaver et al. 2022) have made this cluster selection method more
viable than ever before. The efficiency of this combined search method has
been verified by some pilot projects; they successfully selected the cluster
CLJ1001, which was later spectroscopically confirmed to reside at $z=2.51$
(Wang et al., 2016), as well as three massive groups at $z\sim 3$ (Daddi et
al., 2021, 2022b). These discoveries demonstrated the potential of building
large, homogeneously selected samples of massive groups and protoclusters in
large and deep survey fields.

The dark matter halo mass is a vital parameter of these identified groups and
protoclusters, and an accurate estimate of halo masses is crucial to assessing
their dynamical and evolutionary states (Chiang et al., 2013; Ata et al.,
2022; Montenegro-Taborda et al., 2023). To date, various methods have been
exploited to estimate the dark matter halo mass of galaxies and galaxy groups,
including (1) the stellar-to-halo mass relation (SHMR; e.g. Behroozi et al.,
2013; Shuntov et al., 2022), (2) dynamical constraints of member galaxies
(e.g. Wang et al., 2016; Miller et al., 2018), (3) X-ray emission from the hot
ICM (e.g. Gobat et al., 2011; Wang et al., 2016), and (4) the SZ effect from
the inverse Compton scattering of cosmic microwave background photons (e.g.
Gobat et al., 2019; Di Mascolo et al., 2023). However, constraining the dark
matter halo mass of structures in the early Universe remains a challenging
task. This is because (1) optical data are often too shallow to allow for
accurate stellar mass measurements (Daddi et al., 2021), (2) spectroscopic
surveys of high-$z$ structures are too incomplete for membership
identification, (3) X-ray observations from current facilities are not deep
enough to probe the hot ICM (Overzier, 2016), and (4) the SZ effect is a
powerful tool but one that is very demanding in terms of observing time, and
only a couple of structures have been detected at $z\gtrsim 2$ (Gobat et al.,
2019; Di Mascolo et al., 2023). Recently, Wang et al. (2016) found that the
stellar mass density profile of the $z=2.5$ X-ray-detected cluster CLJ1001 can
be fitted by a projected Navarro-Frenk-White (NFW) profile (Navarro, Frenk, &
White, 1997), suggesting that the structure is virialized and that the halo
has a relatively high concentration (Sun et al., 2024). The similar shape of
the two profiles implies that the halo mass can be estimated from the stellar
mass density profile, which provides an efficient and powerful approach to
constraining the halo mass of collapsed structures. However, this novel method
has yet to be tested with a statistically robust sample at high redshifts and
still suffers from limitations (1) and (2).

Another open question concerns the growth of galaxies residing in massive
structures. Theoretically, structures with dark matter halo masses above
$M_{\rm shock}\simeq 10^{12}\,{\rm M_{\odot}}$ would generate shocks and heat
the infalling gas of the intergalactic medium to the temperature of the ICM
(Birnboim & Dekel, 2003), preventing further star formation and the growth of
cluster galaxies. However, advanced simulations predict a mechanism of gas
inflow in which cold streams travelling along intersections of dense filaments
are able to penetrate the halo without being shock-heated (Dekel & Birnboim,
2006; Dekel et al., 2009; Rosdahl & Blaizot, 2012; Mandelker et al., 2020).
This regime of cold gas inflow in a hot environment is defined by a redshift-
dependent theoretical upper limit of the host halo mass where these streams
can efficiently occur, $M_{\rm stream}$, and a theoretical lower limit of the
host halo mass where shock heating occurs, $M_{\rm shock}$ (Dekel et al.,
2013). Nevertheless, observational evidence for this picture is lacking. The
model from Goerdt et al. (2010) predicted that this mode of cold accretion
would be detectable via collision-driven Ly$\alpha$ emission. This idea is
supported by the recent discovery of giant Ly$\alpha$ nebulae in massive
galaxy groups at $1.9<z<3.3$ by Daddi et al. (2021, 2022b). The rate of
accretion of both cold and warm gas can be quantified with the baryonic
accretion rate (BAR), which is predicted to scale with the dark matter halo
mass (Goerdt et al., 2010) and the total SFR it feeds (Daddi et al., 2022b).
To further verify and observationally constrain this picture of cold
accretion, a large sample of homogeneously selected massive galaxy groups and
protoclusters is needed.

Finally, the fate of massive structures in the early Universe remains
unresolved. Whether massive groups of galaxies at high-$z$ will form present-
day clusters, a proposition that is fundamental for precisely defining the
term ‘protocluster’, remains an open question. Currently, there are no direct
observables that can offer a robust characterization and accurate
classification of protoclusters (Overzier, 2016). Instead, comparisons between
the observables and cosmological simulations provide a feasible approach to
inferring the evolutionary stage and final fate of structures (e.g. Chiang et
al., 2013; Miller et al., 2018; Ata et al., 2022; Jin et al., 2023, 2024).

In this paper we report spectroscopic confirmation of eight galaxy groups from
the NOrthern Extended Millimeter Array (NOEMA) formIng Cluster survEy (NICE)
in the COSMOS field and study their integrated stellar, gas, dust, and dark
matter properties. The paper is organized as follows: We describe the sample
and selection in Section 2. In Section 3 we describe the observations and data
reduction. In Section 4 we explain in detail our analysis methods. We present
our results in Section 5, discuss the corresponding science in Section 6, and
summarize this study in Section 7. We adopt a flat cosmology with parameters
$H_{0}=70\,{\rm km\,s^{-1}\,Mpc^{-1}}$, $\Omega_{m}=0.27$, and
$\Omega_{\Lambda}=0.73$, and use a Chabrier (2003) initial mass function.
Magnitudes are in the AB system (Oke, 1974).

##  2 NOEMA formIng Cluster survEy (NICE)

NICE is a 159 hours NOEMA large programme (ID:M21AA, PIs: E. Daddi and T.
Wang) targeting 48 massive galaxy group candidates in the COSMOS, Lockman
Hole, Elais-N1, Boötes, and XMM-LSS fields. This programme is complemented by
a 40 hours Atacama Large submillimeter Array (ALMA) programme (ID:
2021.1.00815.S, PI: E. Daddi) targeting 25 candidates in the southern sky in
the ECDFS, COSMOS, and XMM-LSS fields. Four candidates are observed with both
NOEMA and ALMA. Overall, 69 targets are selected in a total of 46 deg2 sky
area. The first discovery of NICE is a $z=3.95$ star-bursting group in the
Lockman Hole field, which was recently reported in Zhou et al. (2024). In this
paper, we focus on the eight candidates in the COSMOS field (Table 1), of
which four are observed with NOEMA, three are observed with ALMA, and one is
observed with both facilities.

In Table 1 we list the eight massive galaxy group candidates of this study:
seven of them (i.e. COS-SBC3, COS-SBC4, COS-SBC6, COS-SBCX1, COS-SBCX3, COS-
SBCX4, and COS-SBCX7) were selected as a significant overdensity of red IRAC
sources with red Herschel colours, following the identical selection method
utilized by Zhou et al. (2024). The selection is described in detail in Zhou
et al. (2024), and we briefly list the selection criteria below:

(1) Overdensity of red IRAC sources:

$\displaystyle[3.6]-[4.5]>0.1$ $\displaystyle 20<[4.5]<23$ (1)
$\displaystyle{\Sigma_{N}>5\sigma,}$

where [3.6] and [4.5] are IRAC channel 1 and 2 magnitudes from the COSMOS2020
catalogue (Weaver et al., 2022). We used the distance to the $N$-th nearest
neighbour $r_{N}$ to quantify the local galaxy density, and constructed a
galaxy surface density map of $\Sigma_{N}=N/(\pi r^{2}_{N})$. We selected
overdensities with either $\Sigma_{5}$ or $\Sigma_{10}$ that are $5\sigma$
above the field levels in log scale (e.g. Wang et al. 2016).

(2) Herschel detection with red colours:

$\displaystyle S_{500\,{\rm\mu m}}>30\,{\rm mJy}$ $\displaystyle
S_{350\,{\rm\mu m}}/S_{250\,{\rm\mu m}}>1.07$ (2) $\displaystyle
S_{500\,{\rm\mu m}}/S_{350\,{\rm\mu m}}>0.72.$

Additionally, the target HPC1001 was originally selected by Sillassen et al.
(2022) using the overdensity of COSMOS2020 sources at $z_{\rm phot}\sim 3.7$
and an overdensity of ALMA sources. We note that HPC1001 has red IRAC colours
as in Eq. 1 but was not selected as an IRAC overdensity. This is because
HPC1001 is extremely compact, and the members are severely blended in the low-
resolution IRAC images. However, the $\Sigma_{5}$ of $z\sim 3.7$ sources in
HPC1001 is 6.8$\sigma$ above the average, which is one of the strongest
overdensities in the COSMOS field at $z>3$ (Sillassen et al., 2022).
Furthermore, HPC1001 satisfies the criteria of Herschel selection (Eq. 2) and
shows even redder colours. Therefore, the eight candidates share a consistent
selection, constituting a homogeneous sample. Benefiting from the rich multi-
wavelength datasets and well-established catalogues in the COSMOS field, the
eight high-$z$ group candidates are entitled to the best data quality in the
NICE sample, constituting an ideal sample for this initial statistical study
of the NICE programme.

Table 1: Observations presented in this work.

Target name | RA | Dec. | $z_{\rm spec}$ | Programme ID | Sensitivitya | Beam | Ancillary ID | Sens.b | Ang. Res.c
---|---|---|---|---|---|---|---|---|---
| [deg] | [deg] |  |  | [mJy/beam] | [arcsec] |  | [mJy/beam] | [arcsec]
(NOEMA) |  |  |  |  |  |  |  |  |
HPC1001 | 150.4656 | 2.6359 | $3.613$ | M21AA | $0.13$ | $4.7\times 3.7$ | 2013.1.00034.S | 0.06 | 0.4
COS-SBCX3 | 150.3113 | 2.4511 | $3.031$ | M21AA | $0.15$ | $5.4\times 4.5$ | 2016.1.00463.S | 0.26 | 0.8
COS-SBCX4 | 150.7509 | 2.4132 | $2.646$ | M21AA | $0.13$ | $4.2\times 1.8$ | 2016.1.00463.S | 0.27 | 0.8
COS-SBCX7 | 149.9898 | 1.7978 | $2.415$ | M21AA | $0.14$ | $4.7\times 3.8$ | 2015.1.00137.S | 0.12 | 1.0
(ALMA) |  |  |  |  |  |  |  |  |
COS-SBC3 | 150.7196 | 2.6995 | $2.365$ | 2021.1.00815.S | $0.13$ | $0.84\times 0.55$ | 2021.1.00246.S | 0.02 | 1.6
COS-SBC6 | 149.7057 | 2.2160 | $2.323$ | 2021.1.00815.S | $0.13$ | $0.87\times 0.53$ | 2016.1.00463.S | 0.27 | 0.8
COS-SBC4 | 150.0364 | 2.2177 | $1.65^{b}$ | 2021.1.00815.S | $0.13$ | $0.72\times 0.57$ | 2016.1.00463.S | 0.27 | 0.8
(NOEMA + ALMA) |  |  |  |  |  |  |  |  |
COS-SBCX1 | 150.3492 | 2.7619 | $2.422$ | M21AA | 0.14 | $4.8\times 3.8$ | 2016.1.00463.S | 0.26 | 0.8
|  |  |  | 2021.1.00815.S | $0.23$ | $0.83\times 0.66$ |  |  |

Notes: aline sensitivity over $500\,{\rm kms^{-1}}$. bThe redshift is measured
from Subaru/FMOS observations (Kashino et al., 2019). bContinuum sensitivity
of the ancillary ALMA data. cAngular resolution of the ancillary ALMA data.

##  3 Data

The eight galaxy group candidates in the COSMOS field are observed with the
NOEMA and ALMA interferometers. A summary of our observations is provided in
Table 1, and we describe them in detail below.

###  3.1 NOEMA

As a part of the NICE large programme, five targets were observed with NOEMA
(Table 1). The observations were designed with two frequency setups of two
sidebands each in NOEMA Band 1, covering CO(3-2) and CO(4-3) in the redshift
ranges $2<z<4$ and $z>3$, respectively. The first setup covered the
frequencies of the most probable CO lines. If lines were detected with the
first setup, the second setup was not executed. The observations were
conducted in October 2022 with a total on-source time of 10.8h for the five
targets in track sharing mode with array configurations C and D. The data were
reduced and calibrated using the institut de radioastronomie millimétrique
(IRAM) software package111https://www.iram.fr/IRAMFR/GILDAS. The final data
products were generated in uv tables, reaching an average continuum
sensitivity of $17\,{\rm\mu Jy/beam}$ and line sensitivity ${\rm
0.13\leavevmode\nobreak\ mJy/beam}$ over a 500 km s-1 line width at $\sim$100
GHz, with an average angular resolution of $\sim 4.1"$ (see details in Table
1).

###  3.2 ALMA

ALMA Band 4 and 5 observations of four targets were carried out in Cycle 8. We
designed four frequency tunings that cover one or multiple CO and CI lines
based on the estimated redshift of the groups. The four tunings cover the
frequency range $135-183\,{\rm GHz}$, but leave two gaps at 157.5–168.5 GHz
and 170–178 GHz. The observations were conducted in August 2022, reaching an
rms sensitivity of ${\rm 0.13\leavevmode\nobreak\ mJy/beam}$ over a 500 km s-1
line width at $\sim 150$ GHz. The raw data were reduced and calibrated using
the Common Astronomy Software Application (CASA; McMullin et al. 2007)
pipeline. Following our standard pipeline (e.g. Coogan et al. 2018; Jin et al.
2019, 2022; Zhou et al. 2024), we converted the calibrated measurement sets to
uvfits format for further analysis with the GILDAS/mapping software. In each
ALMA tuning, we achieved an average continuum sensitivity of $16\,{\rm\mu
Jy/beam}$ and an angular resolution of $\sim 0.7"$.

###  3.3 Spectrum extraction pipeline

The extraction of NOEMA and ALMA spectra is carried out with the pipeline
adopted in Zhou et al. (2024). Briefly, we extracted spectra in the $uv$ space
(visibility) using the uvfit routine of GILDAS. The uvfit run was performed on
the original uv tables at all frequencies, where we adopted a point source
model for the sources, using prior positions from the COSMOS2020 catalogue or
ALMA continuum images. To enhance the sensitivity in overlapping frequency
ranges, we combined all spectral windows of ALMA into a single 1D spectrum for
each source.

###  3.4 Ancillary data

We utilized the rich multi-wavelength data and catalogues in the COSMOS field.
In the optical and NIR, we adopted the COSMOS2020 photometric catalogue
(Weaver et al., 2022), along with the provided photometric redshifts and
stellar masses that were crucial for the identification of spectral lines in
our data and for characterization of the physical properties of the member
galaxies. At FIR and sub-millimetre wavelengths, we made use of the MIPS 24
$\mu$m (Le Floc’h et al., 2009), Herschel 100–500 $\mu$m (Lutz et al., 2011),
SCUBA-2 850 $\mu$m (Simpson et al., 2019), and AzTEC 1.1 mm maps (Aretxaga et
al., 2011), and we measured the integrated fluxes of this sample by performing
the super-deblending technique (Liu et al., 2018b; Jin et al., 2018). For
radio bands, we used the low-resolution MeerKAT-DR1 image with a beam size of
$8.9^{\prime\prime}\times 8.9^{\prime\prime}$ and frequency range 1.15–1.35
GHz (Jarvis et al. 2016; Heywood et al. 2022; Hale et al. in prep.). We also
used the archival ALMA data (ID: 2016.1.00463.S, PI: Y. Matsuda; ID:
2021.1.00246.S, PI: C. Chen; ID: 2015.1.00137.S, PI: N. Scoville;
2013.1.00034.S, PI: N. Scoville) for the dust continuum imaging in Band 6 and
7, and ALMA photometry from the A3COSMOS catalogue (Liu et al., 2019) where
available.

##  4 Methodology

In this section we describe the methods adopted to determine the redshifts and
group membership, as well as the integrated FIR properties, the BAR, and the
halo mass of the groups.

###  4.1 Line detection and redshift determination

Following Zhou et al. (2024), we ran a line-searching algorithm as in Coogan
et al. (2019) and Jin et al. (2019) to search for the highest integrated
signal-to-noise ratio (S/N) emission lines in the 1D NOEMA/ALMA spectra. We
fit the line-free continuum emission as a power-law with a fixed slope of 3.7
in frequency, assuming modified blackbody emission with $\beta\sim 1.7$
(Magdis et al., 2012), by masking out channels where significant ($P_{\rm
chance}<5\%$, Jin et al. 2019) emission lines are detected. The continuum-
subtracted spectra are then fitted with a Gaussian line-profile using
MPFIT222http://cow.physics.wisc.edu/~craigm/idl/idl.html, at the frequencies
identified by the line searching algorithm. The redshift can be robustly
identified if two or more lines are detected on one source. For sources only
detected with a single line, we determined their redshifts by comparing them
to the photo-z redshift probability density function (PDF(z)) from the
COSMOS2020 catalogue. As an example, in Fig. 23, we determined the best
$z_{\rm spec}$ solution by comparing all possible redshift solutions for each
object with optical/NIR photometric PDF(z) from the Classic LePhare version of
COSMOS2020. For galaxies with a broad PDF(z) and an emission line detection
close to the frequency of the structure as determined by other secure members,
it is assumed that its redshift is closest to the redshift of the structure.
Such cases only occur on two sources (HPC1001 ID1272853 and SBCX4 ID1049929),
and one of them (ID1272853) has been recently confirmed with our ALMA [CI]
observation (ID: 2023.1.00652.S, PI: N. Sillassen), which further validates
our identification method.

###  4.2 Candidate member selection

With the photometric redshifts in the COSMOS2020 catalogue (Weaver et al.,
2022), we selected candidate group members with $|z_{\rm phot}-z_{\rm
spec,group}|<0.1(1+z_{\rm spec,group})$ within the virial projected radius
from the group centres (see Table 4), where $z_{\rm spec,group}$ is the
spectroscopic redshift of the central galaxy. This redshift range is defined
by the representative uncertainty at the faint end of the COSMOS2020 catalogue
of $\sim 10\%$ (Weaver et al., 2022). The virial radius limit ensures that we
were only probing the inner region of these structures. We note there is a
radial- and stellar-mass-dependent expected interloper fraction (Fig.
32-right); that is, low stellar mass candidate members far from the centre
have a higher chance of being interlopers. We discuss implications of
interlopers in detail in Section 6.4.

###  4.3 Integrated FIR spectral energy distributions

A deblended FIR catalogue of the COSMOS field is publicly available (Jin et
al., 2018); however, it is not directly applicable for individual galaxies in
crowded group and protocluster environments. Due to the overdense nature and
the large Herschel and SCUBA2 beams (15–36′′), in the group centre tens of
galaxies can be present in one beam, which leads to severe blending of
sources. Given the high compactness of the eight groups, we applied the super-
deblending technique (Jin et al., 2018; Liu et al., 2018a) with improved
priors to measure the integrated fluxes in Herschel and SCUBA2 images,
following the same method applied in Daddi et al. (2021) and Zhou et al.
(2024).

In detail, for each group, we defined one prior at the peak position of the
SCUBA2 850 $\mu$m detection (Simpson et al., 2019) to represent the whole
structure. In the prior list, we excluded sources within a $10^{\prime\prime}$
radius of the prior to reduce the crowding (Liu et al., 2018a). Then we
subtracted faint foreground and background sources by convolving the point
spread function (PSF) of each instrument to the corresponding image, and ran
PSF fitting on the fixed prior positions together with other sources from
COSMOS2020 that are beyond the $10^{\prime\prime}$ radius of the group centre.
We note that nearly all ALMA and NOEMA continuum sources in the groups are
spectroscopically confirmed to be group members; hence, the contamination of
dusty interlopers is negligible, and the fitting is straightforward. The PSF
fitting is performed for Herschel 100-500$\mu$m, SCUBA2 850$\mu$m, and MeerKAT
images, and the measured fluxes and their uncertainties are then calibrated by
Monte Carlo simulations performed on the maps (see Jin et al. 2018 for
details). Finally, we checked the residual images and find that a few groups
are resolved in the MeerKAT map (beam size $\sim 9^{\prime\prime}$); hence, we
adopted aperture photometry for these. Due to its relatively high resolution
(6′′), the MIPS 24$\mu$m image cannot be fit with a single PSF. We thus
adopted the total weighted 24$\mu$m photometry of individual members in the
Jin et al. (2018) catalogue. The resultant photometry is summarized in Table
15.

To infer the integrated physical properties of these groups, we fit the
integrated FIR spectral energy distribution (SED) using STARDUST (Kokorev et
al., 2021) with the above FIR photometry, as well as the integrated ALMA and
NOEMA continuum fluxes where available. The fitting was performed at the
spectroscopic redshift of each group (Table 1). Only photometric points with a
significant detection ($>3\sigma$) were considered in the fitting, and the
rest were treated as $3\sigma$ upper limits (Kokorev et al., 2021). We note
that the radio photometry is not included in the fitting. Instead, we
extrapolated a radio component based on the IR luminosity using the stellar
mass-dependent IR-radio relation from Delvecchio et al. (2021), assuming the
average stellar mass of spectroscopically confirmed ALMA continuum-detected
sources. This allows us to identify potential radio excess by comparing the
IR-derived radio model with the measured radio flux.

###  4.4 Estimate of dark matter halo mass

Based on literature studies (e.g. Wang et al., 2016; Daddi et al., 2021,
2022b; Sillassen et al., 2022), we adopted and developed in total six methods
for estimating the dark matter halo mass333We use $M_{\rm h}(n)$ as a
shorthand to refer to the n-th method for halo mass estimation.. Our six
methods are split into three main techniques; the first three methods employ
the simple SHMR with the peak stellar mass and the total stellar mass,
respectively, the fourth method employs overdensity with clustering bias, and
the final two use projected stellar mass surface density profile fitting. We
briefly summarize the six halo mass methods in Table 2, and refer the details
as follows:

Table 2: Halo mass estimate methods in this work.

Method | Input | SHMR | SMF | Overdensity | NFW fit | Assumption
---|---|---|---|---|---|---
(Stellar mass scaling with SHMR)
$M_{\rm h}(1)$ | $M_{\rm\ast,BCG}$ | Behroozi et al. 2013 | – | – | – | –
$M_{\rm h}(2a)$ | $M_{\rm\ast,tot}$ | Shuntov et al. 2022 | Muzzin et al. 2013 | – | – | Virialization
$M_{\rm h}(2b)$ | $M_{\rm\ast,tot}$ | van der Burg et al. 2014 | Muzzin et al. 2013 | – | – | Virialization
(Galaxy overdensity-based)
$M_{\rm h}(3)$ | – | – | – | This work | – | Virialization
($M_{*}$ surface density profile fitting)
$M_{\rm h}(4)$ | $\Sigma_{M_{*}}(R)$ | – | – | – | This work | NFW profile
$M_{\rm h}(5)$ | $\Sigma_{M_{*}}(R)$ | – | – | – | This work | NFW profile & fixed $c^{*}$

Note: The details are described in Sect. 4.4, and the results are presented on
Table 4. ${}^{*}c$ is the concentration parameter of the dark matter halo.

(1) We derived a halo mass by scaling the stellar mass of the most massive
central group member with the SHMR in Behroozi et al. (2013);

(2a) Following the methodology in Daddi et al. (2021, 2022b) and Sillassen et
al. (2022), we computed the mass-complete total stellar mass of members within
the radius $R<{R_{\rm vir}}$. $R$ selected from mass-complete COSMOS2020
(Weaver et al., 2022), where the expected contamination from the background is
$<10\%$ (e.g. Fig. 32-left). We then extrapolated the mass down to
$10^{7}\,{\rm M_{\odot}}$ assuming the field stellar mass function (SMF) from
Muzzin et al. (2013). We subtracted the contamination of the background from
the recovered total mass. This background-corrected total stellar mass was
then scaled to the redshift-dependent central and satellite stellar mass
($M_{\rm\ast,cent}+M_{\rm\ast,satellite}$) SHMR in the COSMOS2020 catalogue
from Shuntov et al. (2022). This recovered halo mass was corrected for the
measuring stellar mass within a radius smaller than virial, by assuming a NFW
density profile (Navarro, Frenk, & White, 1997).

(2b) Using the total stellar mass in $M_{\rm h}(2a)$, we derived a halo mass
by scaling the total stellar mass with the SHMR of $z\sim 1$ clusters from van
der Burg et al. (2014).

(3) We estimated halo mass based on the overdensity of the groups above the
field level, following the methodology presented in Sillassen et al. (2022). A
stellar mass cut, selected where the interloper fraction at the virial radius
of the group was $<10\%$ (e.g. Fig. 32-right), was applied to the entire
catalogue. First, we measured the average number density of the photo-z-
selected galaxies ($|z_{\rm phot}-z_{\rm spec,group}|<0.1(1+z_{\rm
spec,group})$) in the mass cut COSMOS2020 Classic LePhare catalogue, and
obtained the group core density by measuring the number density within the
virial radius centred on the core. The depth difference between the field and
the group selection was accounted for by assuming a group velocity dispersion
$\Delta v=400\,{\rm km/s}$, which is the velocity dispersion of a virialized
group with $M_{\rm h}\sim 2\times 10^{13}\,{\rm M_{\odot}}$ at $z\sim 2.5$
(Ferragamo et al., 2021). We then calculated the mass of a sphere with
comoving virial radius $R_{\rm 200}$, defined as the radius within which the
average density is 200 times the critical density of the universe with initial
halo mass from $M_{\rm h}(2a)$:

$M_{\rm h}=\frac{\rho\leavevmode\nobreak\
{\rm\delta}}{b}\frac{4}{3}\leavevmode\nobreak\ \pi(R_{\rm 200}(1+z))^{3}.$ (3)

Here $\delta=(\Sigma_{\rm group}-\Sigma_{\rm field})/\Sigma_{\rm field}$ is
the overdensity and $\rho$ is the average matter density at $z$
$\left(\rho=\rho_{c}\Omega_{m},\leavevmode\nobreak\
\rho_{c}=\frac{3H(z)^{2}}{8\pi G},\leavevmode\nobreak\
H(z)=H_{0}\sqrt{\Omega_{m}(1+z)^{3}+\Omega_{\Lambda}}\right)$, where
$\rho_{c}$ is the critical density of the universe at $z$, $H(z)$ is the
Hubble parameter at $z$, $H_{0}$ is the Hubble parameter at $z=0$,
$\Omega_{m}$ and $\Omega_{\Lambda}$ are the fraction of matter and vacuum
energy of the total energy in the Universe, respectively, and $b$ is a
clustering bias calculated with the Tinker et al. (2010) formalism. Using the
halo mass from $M_{\rm h}(2a)$ as an initial guess on the halo mass, we
recalculated the bias in an iterative fashion from the result of this method
until convergence.

(4) Inspired by the stellar mass density profile of the $z=2.5$ X-ray detected
cluster CLJ1001 being consistent with a NFW profile (Wang et al., 2016), we
explored fitting the projected stellar mass density of each group using a NFW
dark matter halo profile (Navarro, Frenk, & White, 1997). We assumed that the
structures are virialized, their stellar mass density profiles can be
described by a NFW profile, and the stellar mass profile follows the
underlying dark matter profile. We first sampled the projected NFW profiles
with a range of halo mass and concentration parameter values at a fixed
redshift (see Appendix I). The radial bins are annuli with increasing radius
$R$ from $R\sim 10$ pkpc out to $\sim 2\,{\rm pMpc}$. We calculated a
characteristic mass, $M_{0,i}=(\delta
M_{{\rm\ast,total},i})^{2}/M_{{\rm\ast,total,}i}$, and background stellar mass
density in each annulus, for the mass-complete $z$-phot selected COSMOS2020
catalogue in 10000 randomly placed annuli. Combining the model and background,
we estimated the expected number of galaxies in each radial bin, $N_{{\rm
model},i}$. The observed characteristic number in each radial bin was
calculated as $N_{{\rm obs,}i}=M_{{\rm\ast,total},i}/M_{0,i}$. We found the
best model by maximizing the combined probability of finding $N_{\rm obs}$
when expecting $N_{\rm model}$; $p_{\rm combined}=\Pi_{i}(p_{i})$ where
$p_{i}=p(N_{\rm obs,i}\leq N_{{\rm model,}i})$ when $N_{{\rm model,}i}>N_{{\rm
obs,}i}$ and $p_{i}=p(N_{{\rm obs,}i}\geq N_{{\rm model,}i})$ when $N_{{\rm
model,}i}\leq N_{{\rm obs,}i}$ assuming a Poisson distribution. The projected
stellar mass surface density was calculated within the annuli (i.e.
$\Sigma(R)$) centred on the mass and distance to FIR peak weighted barycentre
of spectroscopically confirmed member galaxies. The best-fit profile yields a
total baryonic mass $M_{\rm b,total}$. We adopted a dark matter to baryonic
mass ratio of $\Omega_{m}/\Omega_{b}-1\approx 5.4$ from PLANCK cosmology
(Planck Collaboration et al., 2020) to convert $M_{\rm b,total}$ to halo mass
$M_{\rm h}(4)$.

(5) Assuming that the stellar mass density profiles largely follow NFW models,
we further explored deriving halo mass solely based on the shape of the
density profiles, independent of a scaling with stellar mass. We fit the
stellar mass surface density profiles and their background levels using a NFW
model with scale radius ($R_{\rm s}$) as a variable. Unlike with $M_{\rm
h}(4)$, we fixed the concentration parameter, $c,$ of the halos using the
predictions from Ludlow et al. (2016), assuming a prior halo mass from the
average of $M_{\rm h}(2a)$, $M_{\rm h}(3)$, and $M_{\rm h}(4)$. The best-fit
$R_{s}$ value allowed us to obtain a virial radius $R_{200}=R_{s}c$. This
virial radius is directly correlated with the halo mass, and hence we obtained
the halo mass using the redshift-dependent $M_{\rm h}-R_{\rm 200}$ relation
from Goerdt et al. (2010).

##  5 Results

In this section we report the results of our analyses adopting the
methodologies presented in Section 4. We produced colour images and spectra
for confirmed and candidate members (Figs. 1, 12, 13, 14, 8, 9, 10 and 11) and
multi-wavelength cutouts (Figs. 20, 21, 22, 16, 17, 18, 19 and 15).
Coordinates and physical properties of confirmed and candidate members are
shown in Tables C1 to C8.

Figure 1: Colour images and NOEMA spectra of HPC1001. Photometrically selected
galaxies with $3.15<z_{\rm phot}<4.07$ are shown in cyan circles.
Spectroscopically confirmed galaxies are shown in green circles, with the
spec-z labelled. Cyan plus signs indicate where 1D 3mm spectra have been
extracted. Top left: Red-green-blue image corresponding to IRAC/4.5 and
3.6$\,\mu$m, and UVISTA/Ks overlaid with yellow SPIRE/350${\rm\mu m}$ contours
at $10,20,\ {\rm and}\ 30\,{\rm mJy}$ levels. Magenta contours show ALMA Band
6 1.2 mm dust continuum at $3,5,\ {\rm and}\ 7\sigma$ levels. Top right: Red-
green-blue image corresponding to UVISTA/Ks, J, and ACS/i. The yellow contours
show CO(J=4-3) line emission at $3,5,\ {\rm and}\ 7\,\sigma$ levels. Bottom:
NOEMA Band 1 spectra in the HPC1001 core. The continuum level is marked with a
red line, and significant ($P_{\rm chance}<5\%$) emission lines are marked in
yellow. The dotted blue line shows the flux uncertainty (1$\sigma$) per
channel. The structure name, bin velocity width, ID, and redshift are
provided. Corresponding plots for the seven other fields are shown in Figs.
12, 13, 14, 8, 9, 10 and 11.

###  5.1 Emission lines and redshifts

We detect robust ($\sigma>7$,$p_{\rm chance}<0.001$) emission lines in seven
out of the eight pointings, with no significant lines detected in COS-SBC4. To
identify the lines and determine the redshift, we calculated all possible
redshift solutions of CO and [CI] lines allowed by the observed frequencies,
and compared them with the PDF(z) in the COSMOS2020 catalogue. As shown in
Fig. 23 to 29, the best redshift solution is determined as the one that is
closest to the peak of PDF(z). In cases where the group frequency is
significantly offset from the peak of the PDF(z), for example ID1272853 in
Fig. 23, we reject solutions closer to the peak as one or more bright lines
would be covered but none are detected. In total, we identify 22 emission
lines of CO(3-2), CO(4-3), CO(5-4), and [CI](1-0) for 20 sources. A summary of
the detected lines is presented in Table 3. We detect a single emission line
from 18 galaxies, and two sources are detected with two or more lines. For 58%
(95%) of the sources, the best $z_{\rm spec}$ solution lies within the
1$\sigma$ (2$\sigma$) uncertainty of the $z_{\rm phot}$ estimates (Figs. 23,
28, 29, 24, 25, 26 and 27). The mean $z_{\rm spec}$ solution is $-0.57\sigma$
in the PDF(z).

Table 3: Significant emission lines detected with NICE.

Structure | ID | RA | Dec. | $\nu_{\rm obs}$ | Line | $S_{\rm line}$ | WidthFWZI | S/N | ${P_{\rm chance}}^{a}$
---|---|---|---|---|---|---|---|---|---
|  | [deg] | [deg] | [GHz] |  | [${\rm Jy\,km/s}$] | [${\rm km/s}$] |  |
HPC1001 | – | 150.4659 | 2.6362 | 99.957 | CO(4-3) | $1.03\pm 0.09$ | $1824\pm 167$ | 10.9 | ¡0.001
HPC1001 | 1272853 | 150.4618 | 2.6294 | 100.004 | CO(4-3) | $0.38\pm 0.08$ | $1036\pm 266$ | 3.9 | 0.001b
HPC1001 | 1274387 | 150.4647 | 2.6307 | 100.130 | CO(4-3) | $0.36\pm 0.08$ | $1288\pm 300$ | 4.3 | 0.019b
COS-SBCX3 | 1088787 | 150.3105 | 2.4515 | 85.803 | CO(3-2) | $0.90\pm 0.08$ | $571\pm 49$ | 11.6 | ¡0.001
COS-SBCX3 | 1088927 | 150.3117 | 2.4510 | 85.768 | CO(3-2) | $0.62\pm 0.07$ | $428\pm 45$ | 9.5 | ¡0.001
COS-SBCX4 | 1050531 | 150.7504 | 2.4129 | 94.805 | CO(3-2) | $1.71\pm 0.06$ | $653\pm 27$ | 26.8 | ¡0.001
COS-SBCX4 | 1049510 | 150.7512 | 2.4124 | 94.947 | CO(3-2) | $0.38\pm 0.07$ | $653\pm 112$ | 5.8 | ¡0.001
COS-SBCX4 | 1049929 | 150.7522 | 2.4140 | 94.789 | CO(3-2) | $0.30\pm 0.05$ | $392\pm 62$ | 6.3 | ¡0.001
COS-SBCX1 | 1408110 | 150.3480 | 2.7611 | 168.415 | CO(5-4) | $0.59\pm 0.08$ | $554\pm 70$ | 7.9 | ¡0.001
| ” | ” | ” | 143.797 | [CI](1-0) | $0.43\pm 0.06$ | $557\pm 82$ | 6.8 | ¡0.001
| ” | ” | ” | 134.686 | CO(4-3) | $0.80\pm 0.13$ | $1145\pm 182$ | 6.3 | ¡0.001
| ” | ” | ” | 101.046 | CO(3-2) | $0.98\pm 0.15$ | $859\pm 133$ | 6.5 | ¡0.001
COS-SBCX7 | 394609 | 149.9896 | 1.7977 | 101.228 | CO(3-2) | $0.79\pm 0.09$ | $675\pm 74$ | 9.1 | ¡0.001
COS-SBCX7 | 394944 | 149.9882 | 1.7980 | 101.221 | CO(3-2) | $0.57\pm 0.07$ | $491\pm 63$ | 7.8 | ¡0.001
COS-SBCX7 | 392257 | 149.9910 | 1.7967 | 101.247 | CO(3-2) | $0.54\pm 0.09$ | $675\pm 113$ | 6.0 | ¡0.001
COS-SBCX7 | 392639 | 149.9816 | 1.7960 | 101.310 | CO(3-2) | $0.75\pm 0.20$ | $491\pm 132$ | 3.7 | 0.028b
COS-SBC3 | 1345246 | 150.7193 | 2.6998 | 154.812 | CO(5-4) | $1.00\pm 0.08$ | $725\pm 55.3$ | 13.1 | ¡0.001
COS-SBC3 | 1340799 | 150.7226 | 2.6963 | 137.021 | CO(4-3) | $0.72\pm 0.11$ | $308\pm 49$ | 6.4 | ¡0.001
| ” | ” | ” | 146.305 | [CI](1-0) | $0.62\pm 0.15$ | $390\pm 95$ | 4.1 | 0.022b
COS-SBC6 | 835289 | 149.7053 | 2.2153 | 138.757 | CO(4-3) | $0.94\pm 0.10$ | $909\pm 98$ | 9.3 | ¡0.001
COS-SBC6 | 839791 | 149.7053 | 2.2171 | 138.718 | CO(4-3) | $1.05\pm 0.12$ | $1044\pm 116$ | 9.0 | ¡0.001
COS-SBC6 | 838104 | 149.7074 | 2.2140 | 168.253 | CO(4-3) | $0.39\pm 0.07$ | $305\pm 57$ | 5.4 | ¡0.001

Notes: achance probability over the entire spectrum as defined in Jin et al.
(2019). bchance probability when limiting the line search to $\pm 2000\,{\rm
km/s}$ from the brightest line (Zhou et al., 2024).

The $z=3.61$ HPC1001 is the most distant group in this sample, in which we
detect three CO lines. Notably, the emission line from the core region has a
velocity width of $1824\pm 167\,{\rm km/s}$. This large width suggests a
blending of multiple sources in the low resolution NOEMA beam ($\sim
4^{\prime\prime}$, Fig. 1), consistent with the fact that three ALMA 1.2 mm
continuum sources are detected (at 0.4” resolution) within the NOEMA beam. As
the photometric redshifts of the two i, J, and Ks-detected galaxies in the
core are consistent with the CO redshift (see Fig. 23), we suspect the three
galaxies to be at the same redshift $z=3.613$. Similarly, Gómez-Guijarro et
al. (2019) studied Herschel selected sources blended at similar scales, and
found all blended candidate member galaxies at the same redshift, if this is
also true for HPC1001, this would result in a total of five $z_{\rm spec}$
confirmed members. Our ongoing high-resolution ALMA observations (ID:
2023.1.00652.S, PI: N. Sillassen) will reveal the members in the compact core.
Interestingly, we spectroscopically confirm the nearby DSFG (HPC1001.m) at
$z=3.610$ (i.e. at a velocity difference of just $-141\,{\rm km/s}$ from the
core). At a projected distance of $\sim 204\,{\rm kpc}$, the nearby DSFG is
outside the expected virial radius of the dark matter halo (Table 4),
indicating that the DSFG HPC1001.m is in a larger structure at the same
redshift.

In the other groups, we can separate individual members without blending
issues. We confirm two members in COS-SBCX3, three members in COS-SBCX4, four
members in COS-SBCX7, one member in COS-SBC3, and two members in COS-SBC6. In
the pointing COS-SBCX1, we confirmed a member with four emission lines
CO(3-2), CO(4-3), [CI](1-0), and CO(5-4) all with S/N$>$6\. Though no line was
detected in COS-SBC4 with ALMA, we confirm three members with Subaru/FMOS
(Kashino et al., 2019). All emission lines at the redshift of COS-SBC4,
$z=1.65$, would fall out of the frequency coverage of our ALMA observations.

###  5.2 Integrated FIR properties

In Fig. 2 we present the best-fit of the integrated FIR photometry with
STARDUST based on dust templates from Magdis et al. (2012). We obtain FIR
properties of the integrated dust emission of the groups, including total IR
luminosity ($L_{\rm IR}$), SFR, dust mass ($M_{\rm dust}$) and mean radiation
field ($\langle U\rangle$). As summarized in Table 5, we obtain integrated
SFRs in the range ${\rm SFR_{IR}}=(262-1319)\,{\rm M_{\odot}/yr}$, dust masses
in the range ${\rm M_{\rm dust}}=(1.0-5.2)\times 10^{9}\,{\rm M_{\odot}}$
(optically thin model), and dust-weighted mean starlight intensity scale
factors in the range $\langle{\rm U}\rangle=(9-50)$ (Fig. 2).

Remarkably, seven of the eight FIR SEDs are well fit by pure dust emission,
that is, they need no mid-IR or radio active galactic nucleus (AGN)
contribution to fit the data. As shown in Fig. 2, they closely follow the IR-
radio correlation with a dispersion of 0.11 dex (inter quartile range),
indicating that they are powered predominantly by star formation. However,
COS-SBC6 exhibits clear radio excess that suggests the presence of a radio-
loud AGN. Adding a mid-IR AGN component to the fit of COS-SBC6 yields a mid-IR
AGN contribution of $\sim 10\%$ to the total IR luminosity. We recall that the
radio part of the model is not part of the fit but extrapolated using the
Delvecchio et al. (2021) IR-radio correlation. By including the radio excess
found in the $z=3.95$ LH-SBC3 presented in Zhou et al. (2024), this gives a
radio-loud AGN fraction of 2/9 (i.e. 22%) in the NICE sample of massive galaxy
groups at $1.6<z<4$. This low fraction of radio-loud AGNs implies that this
massive group population is primarily in star formation mode, and they are not
significantly affected by AGN activity.

Figure 2: Integrated FIR SEDs of our sample of high-$z$ structures, which are
fitted with dust models (grey curve; Magdis et al. 2012) and, in the case of
COS-SBC6, a mid-IR AGN template (yellow; Mullaney et al. 2011) (see Section
5.2). We show the best-fit SFR, dust mass, and radiation field $\langle{\rm
U}\rangle$ in each panel. We note that the radio photometry is not included in
the fitting; instead we extrapolated a radio component from IR luminosity
using the IR-radio relation from Delvecchio et al. (2021).

###  5.3 Dark matter halos

Using the methods described in Section 4.4, we estimated halo masses of
$\log(M_{\rm h}/{\rm M_{\odot}})=12.8-13.7$ as listed in Table 4. In Fig. 3 we
compare $M_{\rm h}(2a)$, $M_{\rm h}(3)$, and $M_{\rm h}(4),$ which represent
the three main techniques of stellar mass scaling, projected galaxy
overdensity, and NFW profile fitting, respectively. We calculated the standard
deviation and mean offset from a 1:1 relation between each two methods (Fig.
3). We find that the results from different methods agree within 0.2–0.3 dex
with systematic offsets $\lesssim 0.4$ dex, which are consistent with the
expected uncertainty of lower-mass halos ($M_{\rm h}<4\times 10^{13}\,{\rm
M_{\odot}}$) at high redshifts ($z>2$; Looser et al., 2021; Daddi et al.,
2021, 2022b). The mean offset is in all cases $\lesssim 2\sigma$, and thus
with this limited sample size we are unable to detect significant systematic
offsets. We adopted an average of methods $M_{\rm h}(2a)$, $M_{\rm h}(3)$, and
$M_{\rm h}(4)$ as the median of the best estimate, and the uncertainty is
conservatively adopted as 0.3 dex, based on the scatter between methods (see
Fig. 3).

Figure 3: Comparison between dark matter halo estimate methods $M_{\rm h}(2)$,
$M_{\rm h}(4)$, $M_{\rm h}(5)$, and $M_{\rm h}(6)$. The standard deviation,
$\sigma,$ and the mean offset from the 1:1 relation, $\mu,$ are provided in
each panel. The solid and dashed lines correspond to the 1:1 relation and
1$\sigma$, respectively.

Figure 4: Projected density profiles of the eight structures. We fit a NFW
profile to the radial stellar mass density. Green circles mark the projected
stellar mass density, with the field level shown as a dashed black line. The
red curve shows the best-fit NFW profile with uncertainty as the red shaded
area, and the blue line indicates the derived virial radius (Goerdt et al.,
2010) with uncertainty as the blue shaded area. The name of the structure,
$z_{\rm spec}$, fitted halo mass, and fitted concentration parameters are
indicated in each panel. Upper limits are at $3\sigma$ significances. Table 4:
Dark matter halo mass results for all groups.

Structure |  $\sigma_{\rm OD}$a |  $M_{\rm\ast,max}$b | Total $M_{\ast}$ | $M_{\rm h}(2a)$ | $M_{\rm h}(3)$ |  $M_{\rm h}$(4) |  $M_{\rm h}$ Bestc |  $R_{\rm vir}$d | $M_{\rm h}(1)$ | $M_{\rm h}(2b)$ |  $M_{\rm h}$(5)
---|---|---|---|---|---|---|---|---|---|---|---
|  | [$10^{11}{\rm M_{\odot}}$] | [$10^{11}{\rm M_{\odot}}$] | ${\rm log\,M_{\odot}}$ | ${\rm log\,M_{\odot}}$ | ${\rm log\,M_{\odot}}$ | ${\rm log\,M_{\odot}}$ | [${\rm pkpc}$] | ${\rm log\,M_{\odot}}$ | ${\rm log\,M_{\odot}}$ | ${\rm log\,M_{\odot}}$
HPC1001 | 7.7 | $1.0\pm 0.2$ | $2.4\pm 0.2$ | $13.0^{+0.3}_{-0.2}$ | $13.4^{+0.3}_{-0.2}$ | $13.6^{+0.2}_{-0.3}$ | $13.3\pm 0.3$ | $181\pm 42$ | $>12.8$ | $12.8\pm 0.3$ | $12.9^{+0.9}_{-1}$
COS-SBCX3 | 6.0 | $0.5\pm 0.1$ | $1\pm 0.1$ | $12.6^{+0.5}_{-0.2}$ | $12.8^{+0.2}_{-0.3}$ | $13.1^{+0.3}_{-0.5}$ | $12.8\pm 0.3$ | $141\pm 33$ | $12.3^{+0.4}_{-0.1}$ | $12.2\pm 0.4$ | $12.8^{+2.4}_{-1.3}$
COS-SBCX4 | 6.0 | $1.6\pm 0.4$ | $4.4\pm 0.6$ | $13.1^{+0.3}_{-0.2}$ | $13.3^{+0.2}_{-0.3}$ | $13.6^{+0.2}_{-0.1}$ | $13.3\pm 0.3$ | $229\pm 53$ | $>13.1$ | $13.2\pm 0.3$ | $13.2^{+1.3}_{-1}$
COS-SBCX1 | 7.0 | $2.5\pm 0.6$ | $8.6\pm 0.6$ | $>13.6$ | $13.7^{+0.3}_{-0.3}$ | $13.9^{+0.1}_{-0.2}$ | $13.7\pm 0.3$ | $331\pm 70$ | $>13.8$ | $13.7\pm 0.2$ | $13.4^{+2.6}_{-1.3}$
COS-SBCX7 | 5.6 | $1.3\pm 0.3$ | $4.5\pm 0.6$ | $13.6^{+0.5}_{-0.3}$ | $13.4^{+0.2}_{-0.3}$ | $13.7^{+0.1}_{-0.1}$ | $13.6\pm 0.3$ | $308\pm 71$ | $13.5^{+1.4}_{-0.4}$ | $13.3\pm 0.2$ | $13.3^{+0.8}_{-0.8}$
COS-SBC3 | 4.6 | $3.2\pm 0.7$ | $5.2\pm 0.7$ | $13.7^{+0.5}_{-0.3}$ | $13.4^{+0.2}_{-0.3}$ | $13.9^{+0.2}_{-0.1}$ | $13.7\pm 0.3$ | $337\pm 71$ | $>14.1$ | $13.3\pm 0.2$ | $13.3^{+1.7}_{-1.3}$
COS-SBC6 | 4.6 | $1.3\pm 0.3$ | $2.5\pm 0.2$ | $13.2^{+0.9}_{-0.3}$ | $13.3^{+0.2}_{-0.3}$ | $13.6^{+0.1}_{-0.3}$ | $13.4\pm 0.3$ | $271\pm 57$ | $13.5^{+1.4}_{-0.4}$ | $12.9\pm 0.3$ | $13.0^{+1.7}_{-1.3}$
COS-SBC4 | 7.4 | $1.6\pm 0.6$ | $7.9\pm 0.4$ | $>13.5$ | $13.7^{+0.3}_{-0.4}$ | $13.9^{+0.1}_{-0.2}$ | $13.7\pm 0.3$ | $429\pm 90$ | $>13.0$ | $13.8\pm 0.2$ | $13.4^{+0.7}_{-0.6}$

Notes: Lower limits are at $1\sigma$ significance. aPeak significance of
overdensity. b$M_{\rm\ast,max}$ is the stellar mass of the most massive
central spectroscopically confirmed member galaxy. cThe best estimate halo
mass is the average of $M_{\rm h}(2a)$, $M_{\rm h}(3)$, and $M_{\rm h}(4)$,
and the uncertainty is estimated by the average scatter between the methods
(Fig. 3). dVirial radius of $M_{\rm h}$ Best, using the $M_{\rm h}-R_{\rm
vir}$ relation from Goerdt et al. (2010).

Uniquely, as shown in Fig. 4, the best fit of $M_{\rm h}(4)$ shows that all
stellar mass density profiles can be fitted by a NFW profile. This suggests
that these structures are likely already collapsed and hosted by a single dark
matter halo. Furthermore, $M_{\rm h}(4)$ allows us to constrain the
concentration parameter $c$ of the dark matter halos (see Table 16). In Fig.
31 we compare the measured concentrations with the predicted values $c(M,z)$
from simulations (Ludlow et al., 2016). The comparison shows a standard
deviation from the 1:1 relation of 0.28 dex, and our measured mean
concentration is 0.4 dex higher than the predictions from simulations.

###  5.4 Baryonic accretion rate

Following the procedure in Daddi et al. (2022b) and using Eq. (5) in Goerdt et
al. (2010), we estimated the total BAR:

${\rm BAR}\simeq 137\left(\frac{M_{\rm h}}{10^{12}{\rm
M_{\odot}}}\right)^{1.15}\left(\frac{1+z}{1+3}\right)^{2.25}\,{\rm
M_{\odot}\,yr^{-1}}.$ (4)

Based on the best estimate of halo masses (Table 4), we calculated the BAR
using Eq. 4, yielding ${\rm BAR}=(1200-8400)\,{\rm M_{\odot}/yr}$ (Table 5).
The SFR arising from cold accretion can be generalized as follows:

${\rm SFR}=C_{\rm SFR}\times\left\\{\begin{array}[]{l l}\left(\frac{M_{\rm
stream}}{M_{\rm h}}\right)^{\alpha_{\rm SFR}}{\rm BAR}&M_{\rm h}>M_{\rm
stream}\\\ {\rm BAR}&M_{\rm h}\lesssim M_{\rm stream}\end{array}\right.,$ (5)

where $M_{\rm stream}$ is the theoretical upper limit halo mass, where cold
streams efficiently occur (Dekel & Birnboim, 2006; Daddi et al., 2022b).

Using the BAR and the fitted values of $\log C_{\rm SFR}=-0.54\pm 0.23$ and
$\alpha=0.78\pm 0.28$ from Daddi et al. (2022b) with Eq. 5, the expected SFR
derived by the BAR are ${\rm SFR}=(100-1700)\,{\rm M_{\odot}/yr}$ (Table 5).
In six of the eight groups, the BAR-derived SFRs are consistent with our
measured IR SFRs within the uncertainties, only the least massive COS-SBCX3
and the lowest redshift COS-SBC4 groups have a higher SFR than expected from
the BAR. Although tentative, this rough consistency supports the baryon
accretion models.

In Fig. 5 we show this sample on the diagrams of gas accretion from Daddi et
al. (2022b) and Dekel et al. (2013). Interestingly, the two most distant
groups, HPC1001 and COS-SBCX3, occupy the regime of cold streams in hot media,
suggesting cold gas inflow. As HPC1001 has a similar halo mass to the group
RO-1001 (Daddi et al., 2021), the cold streams should be detectable via
Ly$\alpha$ emission. Given that the dark matter halo estimates are prone to
large uncertainties, future observations of Ly$\alpha$ will be ideal to
robustly constrain the BAR and reveal possible cold gas accretion.

As shown in Fig. 5, our sample enlarges the sample size of massive groups in
Daddi et al. (2022b) by a factor of two. By including the sample in Daddi et
al. (2022b) and Zhou et al. (2024), we fit a quasi-linear model to the
SFR/BAR-${\rm M_{stream}/M_{\rm h}}$ relation, where the theoretical upper
limit halo mass of cold gas streams ${\rm M_{stream}}$ is adopted from Eq. (2)
in Daddi et al. (2022a). The best fit gives $\alpha_{\rm SFR}=0.71\pm 0.16$,
$\log C_{\rm SFR}=-0.46\pm 0.22$ (Fig. 5) with a scatter of $0.38\,{\rm dex}$
assuming a linear relation, and $0.40\,{\rm dex}$ assuming flattening at ${\rm
M_{stream}/M_{\rm h}}>1$. As discussed in Coogan et al. (2023), this group in
the CEERS field is a strong outlier, and we therefore excluded it from the
fitting. Our fit result is in excellent agreement with the result from Daddi
et al. (2022b), and is improved with $2\times$ better statistics. Adopting
instead the definition of $M_{\rm stream}$ from (Dekel & Birnboim, 2006), does
not significantly change the fitting results, but slightly increases the
scatter to 0.43 dex assuming a single relation.

In the hot-accretion regime, where the estimate of $M_{\rm DM}$ is less
important (Daddi et al., 2022b), we find a 0.30 dex scatter from the relation.
In the cold-stream regime, we find a scatter of $0.53$ dex and mean offset of
$0.12$ dex from the flattening model, and scatter of $0.45$ dex and mean
offset of $-0.35$ dex from the linear relation. Adopting the linear relation
would result in two structures with a $\sim 1.1$ dex deviation from the model,
where the bending model results in one $\sim 0.8$ dex outlier.

Table 5: Baryonic accretion rate (BAR) and integrated FIR properties (${\rm L}_{\rm IR}$,${\rm SFR}_{\rm IR}$,$\langle{\rm U}\rangle$, and dust mass $M_{\rm dust}$). Name | $z$ |  $M_{\rm h}$ Best | BAR | SFRBAR | ${\rm L_{\rm IR}}$ | ${\rm SFR_{IR}}$ | $\langle{\rm U}\rangle$ | ${\rm M_{dust}}$
---|---|---|---|---|---|---|---|---
|  | ${\rm log\leavevmode\nobreak\ M_{\odot}}$ | [${\rm M_{\odot}\,yr^{-1}}$] | [${\rm M_{\odot}\,yr^{-1}}$] | [${\rm 10^{12}L_{\odot}}$] | [${\rm M_{\odot}\,yr^{-1}}$] |  | [$10^{9}{\rm M_{\odot}}$]
HPC1001 | 3.613 | $13.3\pm 0.3$ | $6000\pm 5000$ | $1700\pm 1600$ | $7.18\pm 0.04$ | $718\pm 4$ | $35\pm 1$ | $1.7\pm 0.2$
COS-SBCX3 | 3.031 | $12.8\pm 0.3$ | $1200\pm 900$ | $300\pm 300$ | $9.79\pm 0.02$ | $979\pm 2$ | $50\pm 1$ | $1.6\pm 0.2$
COS-SBCX4 | 2.646 | $13.3\pm 0.3$ | $3500\pm 2800$ | $800\pm 900$ | $13.2\pm 0.4$ | $1319\pm 45$ | $26\pm 1$ | $4.1\pm 0.5$
COS-SBCX1 | 2.422 | $13.7\pm 0.3$ | $7700\pm 6900$ | $600\pm 700$ | $4.1\pm 0.1$ | $408\pm 13$ | $33\pm 1$ | $1.0\pm 0.7$
COS-SBCX7 | 2.415 | $13.6\pm 0.3$ | $6600\pm 5300$ | $600\pm 600$ | $6.1\pm 0.2$ | $606\pm 21$ | $23\pm 1$ | $2.1\pm 0.7$
COS-SBC3 | 2.365 | $13.7\pm 0.3$ | $8400\pm 6700$ | $500\pm 600$ | $5.93\pm 0.03$ | $593\pm 3$ | $9\pm 1$ | $5.2\pm 1.6$
COS-SBC6 | 2.323 | $13.4\pm 0.3$ | $3700\pm 2900$ | $400\pm 400$ | $7.4\pm 0.1$ | $743\pm 2$ | $27\pm 1$ | $2.2\pm 0.3$
COS-SBC4 | 1.65 | $13.7\pm 0.3$ | $4900\pm 3900$ | $100\pm 100$ | $2.62\pm 0.01$ | $262\pm 1$ | $9\pm 1$ | $2.3\pm 1.0$

Figure 5: Baryonic accretion in massive galaxy groups and (proto-)clusters.
Left: SFRIR/BAR fraction versus ${\rm M_{stream}/M_{\rm h}}$ ratio for massive
galaxy groups in this work (green dots), Daddi et al. (2022b, black dots),
Zhou et al. (2024, red dot), and Coogan et al. (2023, orange dot). Black lines
mark the fit from Daddi et al. (2022b). We fit the SFR/BAR$-{\rm
M_{stream}/M_{\rm h}}$ relation with all data points and show the best-fit as
a green line. The black cross in the top-left corner shows representative
errors. The solid lines show a model with bending at $M_{\rm stream}>M_{\rm
h}$, and the dashed lines show a model with a single trend. The dotted blue
line shows the separation between the hot accretion and cold stream regimes.
Right: Dark matter halo mass versus redshift for this sample and the samples
from Daddi et al. (2022b), Zhou et al. (2024), and Coogan et al. (2023),
overlaid with dotted and dashed lines separating the three regimes of gas
inflow from Dekel & Birnboim (2006), Mandelker et al. (2020), and Daddi et al.
(2022a).

##  6 Discussion

###  6.1 Dark matter halo mass estimates: Prospects and caveats

Accurate estimates of halo masses are vital to inferring the evolutionary
state and eventual fate of massive structures; however, it remains a
challenging task especially at high redshifts. In this work, we applied three
methods based on SHMR $M_{\rm h}(1),(2a),(2b)$, a method based on galaxy
overdensity $M_{\rm h}(3)$, and developed two methods based on NFW profile
fitting $M_{\rm h}(4),(5)$. Every method has its strengths and limitations, we
discuss the details in the following.

$M_{\rm h}(1)$ is widely used in the literature (e.g. Ito et al., 2023; Brinch
et al., 2024; Helton et al., 2024; Jin et al., 2024), and is solely based on
the stellar mass of the most massive member galaxy. However, it is a very
simplified assumption that the stellar mass of the central galaxy is solely
correlated with halo mass, with a large dispersion between BCG mass and halo
mass (e.g. Montenegro-Taborda et al., 2023). The accuracy of the halo mass
derived with this approach can be severely affected by uncertainties in the
stellar mass and redshift of the central galaxy, where the situation is even
worse if the central galaxies are DSFGs, as the stellar mass estimate can be
very uncertain (e.g. Long et al., 2023). Furthermore, since the relation is
derived for establishing expected stellar masses given a halo mass, this
results in stellar mass saturation, that is, the SHMR is almost constant at
$M_{\rm h}\gtrsim 3\times 10^{12}\,{M_{\odot}}$ (Behroozi et al., 2013).
Comparing with results from other methods, the resultant mass is inconsistent
with the other methods, yielding mainly lower limits, which is rather risky
when it is applied to high redshift groups. With these points in mind, we
caution against the use of this method for massive galaxy groups, and massive
individual galaxies.

Method $M_{\rm h}(2a)$ scales to the total stellar mass and is clearly more
advanced than $M_{\rm h}(1)$. It assumes that all members are in a collapsed
structure hosted by a single dark matter halo. However, it is difficult to
assess whether the structure is already collapsed. The SHMR scaling is
redshift dependent and has been calibrated for a high redshift ($z\sim 5$;
Shuntov et al., 2022). Nevertheless, it is not calibrated to real clusters as
no massive clusters exist in the COSMOS field, where this SHMR is measured.
$M_{\rm h}(2b)$ shares similar benefits and risks as $M_{\rm h}(2a)$. This
method has been applied in several studies (e.g. Daddi et al., 2022b; Ito et
al., 2023; Coogan et al., 2023). However, the scaling relation is calibrated
to $z\sim 1$ clusters, which might not persist, and might evolve, at higher
redshift, and might not be applicable to lower-mass halos. In this work, the
most massive members are all spectroscopically confirmed, and only low-mass
members are identified using photometric redshifts. Although some foreground
and background interlopers could be included, their low masses are not
expected to significantly impact the inferred total stellar mass, and by
extension the halo mass (see Section 6.4).

Unlike the above discussed methods, $M_{\rm h}(3)$ is not directly dependent
on the stellar mass of the cluster galaxies, instead relying solely on their
spatial density. A big advantage is that it is independent of uncertainties in
stellar mass measurements. On the other hand, the clustering bias of the halo
is not well constrained, and we simply assumed a bias value from the Tinker et
al. (2010) formalism, which adds another layer of uncertainty in the estimate.
Because the bias value is dependent on the halo mass, and we used the bias to
calculate a halo mass, this method is circularly defined; however, we avoided
this circularity by iteratively calculating the bias using $M_{\rm h}(2a)$ as
an initial guess. The bias is not 1:1 with halo mass, and the iterative
approach converges quickly.

Method $M_{\rm h}(4)$ assumes that the stellar mass density profile traces the
dark matter density profile, and that they both follow a NFW model at high
redshifts. With this method, we derived a total baryonic mass and inferred a
halo mass using a dark matter-to-baryon mass ratio. This assumption has been
validated in low redshift clusters, for example Annunziatella et al. (2014)
and Palmese et al. (2016) find both the stellar mass density and number
density profiles of the clusters MACS J1206.2-0847 (Biviano et al., 2013) and
RXC J2248.7-4431 can be fitted by a NFW profile, and further at cosmic noon in
CLJ1449 (Strazzullo et al., 2013). Andreon (2015) find that the stellar-to-
total mass ratio is radially constant in three $z\sim 0.45$ clusters. Caminha
et al. (2017) find that dark matter and hot gas asymmetry of the $z=0.44$ MACS
1206 closely follows the asymmetric distribution of the stellar component.
Accordingly, if the stellar mass density profile of a high-$z$ group is found
consistent with a NFW profile, it would suggest that the structure is likely
collapsed. Uniquely, this method can constrain the halo mass and its
concentration parameter simultaneously, which is a significant advance in
characterizing dark matter halos of collapsed structures. As a proof of this
method at high redshifts ($z>2$), we applied it to the most distant X-ray
detected cluster CLJ1001 (Wang et al., 2016, see Fig. 30). CLJ1001 is uniquely
suited for this, as it is at a high redshift of $z=2.5$ and has both an X-ray
and velocity dispersion calibrated halo mass. Our NFW fitting yields a halo
mass of $M_{\rm h}=(8\pm 2)\times 10^{13}\,M_{\odot}$, with concentration
$c=54^{+25}_{-46}$ and scale radius $R_{s}=7^{+3}_{-6}\,{\rm kpc}$ (Fig. 30).
The recovered halo mass is in excellent agreement with the X-ray and velocity
dispersion halo masses of $M_{\rm h}=(5.0\pm 2.3)\times 10^{13}\,M_{\odot}$,
and, the scale radius is consistent with the one reported in Wang et al.
(2016) $R_{s}=0^{+8}_{-0}\,{\rm kpc}$. Nevertheless, similarly to $M_{\rm
h}(1)$, (2a) and (2b), this method suffers from the uncertainty on stellar
masses and membership, and requires an accurate constraint on the background
density level. Moreover, $M_{\rm h}(4)$ is also impacted by the uncertainty on
the dark matter-to-baryonic mass ratio and possible inconsistency between
stellar mass density profile and dark matter halo profile at high-$z$. We also
tested two methods for finding the exact centre of the group: (1) using the
position of the most massive central galaxy; and (2) randomly shifting the
centre position by up to a few arcseconds, instead of calculating the distance
to FIR-peak-weighted barycentre. We find no significant changes in either the
recovered halo masses or recovered concentrations, nor in the uncertainties of
either values.

Method $M_{\rm h}(5)$ is a variant of $M_{\rm h}(4)$. It shares with $M_{\rm
h}(4)$ the assumption of the consistency between stellar mass density profile
and halo mass density profile. However, it is totally independent of the
stellar masses, as it purely relies on the shape of the profile. This is a
significant advantage with respect to other methods. Notably, adopting this
method with the number density profile would further reduce the bias
introduced by the stellar mass estimate of the central galaxy, as the halo
mass would be solely based on the distribution of member galaxies. However,
this method has two major drawbacks: (1) it must assume a fixed concentration
parameter to break the degeneracy between scale radius and concentration,
while the fixed concentration is based on simulation results with a prior halo
mass, and neither are fully tested by observations; (2) the profile fitting to
the stellar mass density is dominated by the central galaxy, fitting to the
number density can remove this bias but requires a larger sample of confirmed
memberships. Another problem with both $M_{\rm h}(4)$ and $M_{\rm h}(5)$ is
the degeneracy between $M_{\rm h}$, $c$, and $R_{\rm s}$ as they are all co-
dependent and influence the shape and scaling of the density profile (Appendix
I). We tried to limit this degeneracy by fixing the concentration and purely
fitting the scale radius without directly incorporating the halo mass;
however, this adds another layer of uncertainty as the true concentration is
unknown.

Overall, the self-consistency between different methods shows encouraging
prospects in halo mass estimates for high redshift structures like these.
Among these methods, the NFW profile fitting $M_{\rm h}(4)$ and (5) are
exploited for high-$z$ groups for the first time, showing potential for state-
of-the-art in characterizing dark matter halos. Nevertheless, thorough
analyses and tests with a large sample of low-z clusters are required to fully
explore the prospects of the profile fitting techniques, and then exploit it
towards high redshift, which is beyond the scope of this paper.

###  6.2 Nature and fate: Are these structures clusters in formation?

To understand the nature and fate of these structures, following Jin et al.
(2024), we compared our observations with cosmological simulations. First, we
compared the estimated halo masses with simulations of Coma- and Fornax-like
clusters from Chiang et al. (2013). We find all groups to have halo masses
consistent with progenitors of clusters with present day halo masses of at
least $M_{\rm h}(z=0)>10^{14}\,{\rm M_{\odot}}$ (Fig. 6). We also compared the
halo masses of this sample to clusters from the TNG300 simulation (Montenegro-
Taborda et al., 2023, Fig. 6); again, we find that the halo masses of all
groups are consistent with those of the progenitors of $z=0$ clusters ($M_{\rm
h}(z=0)>10^{14}\leavevmode\nobreak\ M_{\odot}$). Furthermore, we compared the
stellar masses of the most massive group galaxies with that of BCG progenitors
in the TNG300 simulation (Montenegro-Taborda et al., 2023), and again find
they are consistent (Fig. 6). This supports the idea that the eight groups are
real forming clusters, and their central galaxies are likely proto-BCGs (Jin
et al., 2024).

Figure 6: Dark matter halo mass (upper black points) and stellar mass of BCG
(lower grey points) versus redshift. Overlaid are the halo mass of simulated
progenitors of Fornax- and Coma-type clusters from Chiang et al. (2013) and
halo and BCG masses from the TNG300 simulation (Montenegro-Taborda et al.,
2023). The black and grey diamonds show halo masses and (proto-)BCG stellar
masses from the NICE COSMOS sample. Other points show halo and (proto-)BCG
masses from literature (proto-)clusters as identified in the figure (Jee et
al., 2009; Rosati et al., 2009; Brodwin et al., 2016; Newman et al., 2014;
Trudeau et al., 2022; Gobat et al., 2019; Strazzullo et al., 2018; Wang et
al., 2016; Miller et al., 2018; Rotermund et al., 2021; Coogan et al., 2023)

Another approach assessing the fate of massive structures is the
observationally constrained large-scale simulations, which has been recently
performed by Ata et al. (2022) on the $z=2.5$ large-scale structure Hyperion
(Cucciati et al., 2018). This simulation requires a highly complete
spectroscopic survey of cluster members (Ata et al., 2022); hence, deep
spectroscopic follow-up observations on both the cores and large-scale
structure are essential. On the other hand, dedicated cluster simulations have
been achieved, for example Cluster-EAGLE (Barnes et al., 2017), Magneticum
(Remus et al., 2023), FLAMINGO (Schaye et al., 2023), and TNG-Cluster (Nelson
et al., 2024). Further work comparing a large sample with these simulations
would provide new insights into galaxy and cluster formation.

###  6.3 Baryonic accretion: Flattening or not?

In Fig. 5 we fit the BAR using both a quasi-linear single trend and assuming
flattening at $M_{\rm stream}>M_{\rm h}$. With double sample size compared to
Daddi et al. (2022b), we now find a significant ($4.5\sigma$) slope compared
with their $2.5\sigma$ fit. We excluded the group from Coogan et al. (2023) as
it remains a strong outlier from the expected SFR from the BAR. The group is
also a strong outlier in terms of the proportions of stellar mass and SFR in
the BCG, suggesting that it might be caught in a short-lived starburst
connected to the formation of the BCG, or might signal a cooling flow (Coogan
et al., 2023). The scatter of our fit ($0.40$ dex) is somewhat lower from
$0.45$ dex in Daddi et al. (2022b). The data do not prefer the bending model
or the linear model, with nearly identical scatter of $0.40$ dex and $0.38$
dex, respectively. Instead of using the updated $M_{\rm stream}$ definition in
Daddi et al. (2022a), adopting the $M_{\rm stream}$ definition from Dekel &
Birnboim (2006), does not change the scatter significantly. Because the
scatter in the cold-stream regime is more dependent on the halo mass (Daddi et
al., 2022b), we calculated the scatters in the hot (Fig. 5-left, $M_{\rm
stream}/M_{\rm h}<1$) versus cold-stream (Fig. 5-left, $M_{\rm stream}/M_{\rm
h}>1$) regimes and find a scatter of 0.30 dex in the hot and 0.53 dex in the
cold-stream regime. The expected scatter in the BAR at fixed halo mass is 0.2
dex (Correa et al., 2015), and the scatter arising from the fraction of cold
gas to total gas, $f_{\rm cold}$, is 0.1 dex (Correa et al., 2018), adding
these in quadrature yields 0.3 dex in excellent agreement with our scatter in
the hot regime. In the cold-stream regime, the scatter from $f_{\rm cold}$ is
negligible as all accreted gas is cold, leaving a scatter from the BAR of 0.2
dex and from $M_{\rm h}$ of 0.3 dex, adding these in quadrature yields 0.36
dex, significantly lower than the observed scatter. This increased observed
scatter is only from six points and would require a larger sample to confirm;
however, if real, this could indicate that there is some intrinsic
stochasticity, inefficiencies in converting accreted baryonic matter into SFR,
feedback mechanisms, or a combination of these processes.

###  6.4 Interlopers in candidate members

Given the majority of candidate members are selected with photometric
redshifts, it is common that foreground and background interlopers can be
included in the candidate members. We quantified the contamination of possible
interlopers in two ways: (1) we measured the background number count in the
mass-complete photo-$z$ selection in COSMOS2020 Classic LePhare and calculated
the expected number of interlopers that can appear by chance in an aperture
around the groups. We find possible mass-complete interloper fractions of
$4-36\%$ (${\rm median}=11.9\%$) within a $r=10^{\prime\prime}$ aperture, and
the fractions increase with larger aperture, which is $23-73\%$ (${\rm
median}=45.8\%$) within 30” (see Fig. 32-left). (2) We tested our candidate
selection method in CLJ1001 (Wang et al., 2016) using the COSMOS2020 photo-z,
and compare with the highly complete spectroscopic redshift sample of Sun et
al. (2024). We find two clear interlopers and a total interloper fraction of
$17-35\%$ in a $r=30^{\prime\prime}$ aperture, which is largely consistent
with the result of method (1). Furthermore, we also tested the interloper
contamination in the total stellar mass budgets. We measured the background
stellar mass in the COSMOS2020 catalogue and compared it with the total
stellar mass of the groups, finding mass-complete fractions of $2-10\%$ (${\rm
median}=3.7\%$) within $r=10^{\prime\prime}$ and $11-42\%$ (${\rm
median}=17.3\%$) within $r=30^{\prime\prime}$, respectively (see Fig.
32-right). We note that the interloper contamination were accounted for by
subtracting them from the total stellar masses or overdensity when deriving
halo masses.

###  6.5 Line-of-sight projection: Chance probabilities

To understand the probability of finding two line-of-sight projected groups,
we calculated the chance probability of finding two halos of $M_{\rm h}/2$
within $R_{\rm vir}/2$ and indistinguishable $z$-phot distributions (i.e. the
redshift selection for halos are overlapping), using halo mass functions
calculated with hmf444https://github.com/halomod/hmf (Murray et al., 2013). We
multiplied this chance probability by the total number of expected halos of
mass $M_{\rm h}/2$ in the entire COSMOS field. The highest chance probability
of this sample is the lowest redshift COS-SBC4, with $p_{\rm
chance,los}=2\times 10^{-4}$, as seen in Table 6. This is only assuming the
case of twin halos, and possible combinations of triples or more halos are not
considered; however, this would not change the ballpark probabilities
considerably.

In general, we find decreasing chance probability with increasing redshift and
halo mass. We explored the halo mass limits in the COSMOS field (assuming a
full redshift dispersion in the structure of $\Delta z=0.1$), where the chance
probability of being a line-of-sight projection is $<1\%$ and $<0.1\%$, as
shown in Fig. 7. At low redshift (z¡1.5) only massive halos with $\log(M_{\rm
h}/{\rm M_{\odot}})>13.5$ are unlikely to be line-of-sight projection of two
lower mass halos, whereas at $z\sim 3.5$ the mass limit decreases to
$\log(M_{\rm h}/{\rm M_{\odot}})\sim 12$. As shown in (Fig. 7), the NICE
sample and Daddi et al. (2022b) sample are all above the limits, with the
majority of them significantly above the limits by $\sim$0.8 dex, indicating
that they are unlikely line-of-sight projections, further supporting their
massive group nature.

Structure | $p_{\rm chance,los}$
---|---
HPC1001 | $9\times 10^{-16}$
COS-SBCX3 | $3\times 10^{-7}$
COS-SBCX4 | $8\times 10^{-8}$
COS-SBCX1 | $1\times 10^{-8}$
COS-SBCX7 | $3\times 10^{-8}$
COS-SBC3 | $3\times 10^{-6}$
COS-SBC6 | $6\times 10^{-6}$
COS-SBC4 | $2\times 10^{-4}$
Table 6: Chance probabilities of a line-of-sight projection of two $M_{\rm
h}/2$ halos. Figure 7: Halo mass limits as a function of redshift. The limits
correspond to the chance probability of finding two overlapping halos of mass,
$M_{\rm h}/2$: $p_{\rm chance,los}=1\%$ and $p_{\rm chance,los}=0.1\%$. We
overplot the halo masses of this work and the sample from Daddi et al.
(2022b).

##  7 Summary and conclusions

We selected eight high-$z$ group candidates based on the overdensity of red
IRAC sources that have red Herschel colours. As part of the NICE large
programme, we followed up on these candidates with NOEMA and ALMA
observations. We summarize the results as follows:

(1) We spectroscopically confirmed a sample of eight massive galaxy groups in
the redshift range $1.65\leq z\leq 3.61$ in the COSMOS field, in which 21
members were detected with CO lines or H$\alpha$ line emission (Kashino et
al., 2019). Using photometric redshifts in the COSMOS2020 catalogue, we
selected a total of $\sim$250 candidate members in these structures.

2) Utilizing Herschel and SCUBA2 data, we measured the integrated FIR-to-radio
photometry of the eight structures and performed FIR SED fitting using dust
and mid-IR AGN models. Seven of the eight group SEDs are well fitted by a
single dust template. Only the group COS-SBC6 exhibits a significant radio
excess and a mid-IR AGN component, yielding a radio excess fraction of 22% in
the total NICE sample. This indicates that these massive groups are presumably
dominated by star formation and that strong AGN activity does not play a major
role.

(2) We applied six methods for estimating the dark matter halo mass of each
structure, including the SHMR, galaxy overdensity with bias, and the NFW
profile fitting technique. The results from the different methods are overall
consistent within 0.2–0.3 dex. Adopting the average results from different
methods, our best estimate of the halo masses is $\log(M_{\rm h}/{\rm
M_{\odot}})=12.8-13.7$. Using the NFW profile fitting technique, we found that
the stellar mass densities of the eight groups can be fitted by a NFW profile,
suggesting they are likely collapsed structures. We tentatively constrained
the concentration parameters of the halos, and the most massive groups are
overall consistent with predictions from the simulations (Ludlow et al.,
2016), albeit with a large scatter.

(3) Using scaling relations between dark matter halo masses, the BAR, and the
SFR, we calculated the expected BAR for each structure. The expected SFRs from
baryonic accretion in all structures are in good agreement with the FIR-
measured integrated SFRs. Together with literature samples, we derive a quasi-
linear relation between SFR/BAR and Mstream/Mh, with ${\rm
SFR/BAR}=10^{-0.46\pm 0.22}({\rm M_{stream}/M_{h}})^{0.71\pm 0.16}$ and a
scatter of $\sim 0.4$ dex. This supports the idea that the star formation in
these structures is fed by gas accretion. Specifically, HPC1001 and COS-SBCX3
occupy the regime of cold gas streams in hot media, which could make them
ideal laboratories for studying cold gas accretion in dense, $z\gtrsim 3$
environments.

(4) By comparing these massive groups with simulations (Chiang et al., 2013;
Montenegro-Taborda et al., 2023), we find that the former have halo masses and
proto-BCG stellar masses that are consistent with them being the progenitors
of $z=0$ clusters. This suggests that these structures are likely forming
clusters in the early Universe and that their central galaxies are forming
BCGs.

All these results point to these structures being forming clusters and groups
in the early Universe that, in turn, are growing their masses via gas
accretion. Future spectroscopic observations of the large-scale and central
cores, combined with comprehensive complementary simulations, are essential to
confirming their nature and further assessing their evolution. This work
serves as a pilot study of the NICE sample. In the near future we will expand
studies in this work with the full NICE sample and investigate the properties
of individual group galaxies to shed light on the formation of structures and
galaxies in dense environments.

###### Acknowledgements.

We thank the anonymous referee for helpful and constructive comments. We thank
Camila Correa for useful discussions on baryonic accretion. The Cosmic Dawn
Center (DAWN) is funded by the Danish National Research Foundation under grant
DNRF140. SJ acknowledges the financial support from the European Union’s
Horizon Europe research and innovation program under the Marie Skłodowska-
Curie Action grant No. 101060888. TW acknowledges support by National Natural
Science Foundation of China (Project No. 12173017 and Key Project No.
12141301), National Key R&D Program of China (2023YFA1605600), and the China
Manned Space Project (No. CMS-CSST-2021-A07). LZ is supported by the National
Natural Science Foundation of China (NSFC grant 13001103) and the National Key
R&D Program of China No. 2022YFF0503401. This work is based on observations
carried out under project number M21AA with the IRAM NOEMA Interferometer.
IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). We are
grateful for the help received from IRAM staff during observations and data
reduction. This paper makes use of the following ALMA data: ADS/JAO.ALMA
2021.1.00815.S, 2021.1.00246.S, 2016.1.00463.S, 2015.1.00137.S, and
2013.1.00034.S. ALMA is a partnership of ESO (representing its member states),
NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA
(Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of
Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.

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##  Appendix A Colour images and spectra

Figure 8: Colour images overlaid with ALMA Band 7 dust continuum, and ALMA
(top) and NOEMA (bottom) spectra of COS-SBCX1. Photometrically selected
galaxies with $2.10<z_{\rm phot}<2.78$ are marked with cyan circles. See the
caption of Fig. 1.

Figure 9: Colour images overlaid with ALMA Band 7 dust continuum and NOEMA
spectra of COS-SBCX3. Photometrically selected galaxies with $2.73<z_{\rm
phot}<3.33$ are shown as cyan circles. See the caption of Fig. 1.

Figure 10: Colour images overlaid with ALMA Band 7 dust continuum and NOEMA
spectra of COS-SBCX4. Photometrically selected galaxies with $2.28<z_{\rm
phot}<3.01$ are marked by cyan circles. See the caption of Fig. 1.

Figure 11: Colour images overlaid with ALMA Band 6 dust continuum and NOEMA
spectra of COS-SBCX7. Photometrically selected galaxies with $2.17<z_{\rm
phot}<2.68$ are marked by cyan circles. See the caption of Fig. 1.

Figure 12: Colour images overlaid with ALMA Band 3 dust continuum and ALMA
spectra of COS-SBC3. Photometrically selected galaxies with $2.03<z_{\rm
phot}<2.70$ are marked by cyan circles. See the caption of Fig. 1.

Figure 13: Colour images overlaid with ALMA Band 7 dust continuum of COS-SBC4.
Photometrically selected galaxies with $1.39<z_{\rm phot}<1.92$ are marked
with cyan circles. ALMA spectra are not shown, as no emission lines fall
within the frequency coverage. See the caption of Fig. 1.

Figure 14: Colour images overlaid with ALMA Band 7 dust continuum and ALMA
spectra of COS-SBC6. Photometrically selected galaxies with $1.99<z_{\rm
phot}<2.66$ are marked with cyan circles. See the caption of Fig. 1.

##  Appendix B Multi-wavelength cutouts

Figure 15: $90^{\prime\prime}\times 90^{\prime\prime}$ size cutouts of
HPC1001.  Figure 16: $90^{\prime\prime}\times 90^{\prime\prime}$ size cutouts
of COS-SBCX1. Figure 17: $90^{\prime\prime}\times 90^{\prime\prime}$ size
cutouts of COS-SBCX3. Figure 18: $90^{\prime\prime}\times 90^{\prime\prime}$
size cutouts of COS-SBCX4. Figure 19: $90^{\prime\prime}\times
90^{\prime\prime}$ size cutouts of COS-SBCX7. Figure 20:
$90^{\prime\prime}\times 90^{\prime\prime}$ size cutouts of COS-SBC3. Figure
21: $90^{\prime\prime}\times 90^{\prime\prime}$ size cutouts of COS-SBC4.
Figure 22: $90^{\prime\prime}\times 90^{\prime\prime}$ size cutouts of COS-
SBC6.

##  Appendix C Physical properties of individual galaxies

Table 7: Physical properties of HPC1001 members from COSMOS2020 Classic
LePhare.

Name | ID | RA | Dec. | $z_{\rm phot}$ | $z_{\rm spec}$ | $\log(M_{\ast}/{\rm M_{\odot}})$ | SFR | $d_{\rm core}$
---|---|---|---|---|---|---|---|---
|  | [deg] | [deg] |  |  |  | [${\rm M_{\odot}\,yr^{-1}}$] | [arcsec]
(Confirmed members) |  |  |  |  |  |  |  |
HPC1001.a | – | 150.4659 | 2.6362 | – | 3.613b | $10.3^{+0.2}_{-0.2}$ | $429^{+20}_{-20}$ | $1.5$
HPC1001.b | 1281317 | 150.4656 | 2.6360 | $3.48^{+0.10}_{-0.09}$ | 3.613b | $11.0^{+0.1}_{-0.1}$ | $152^{+30}_{-29}$ | $0.2$
HPC1001.d | 1279885 | 150.4661 | 2.6361 | $3.66^{+0.14}_{-0.17}$ | 3.613b | $10.6^{+0.1}_{-0.1}$ | $81^{+15}_{-17}$ | $1.9$
HPC1001.la | 1274387 | 150.4647 | 2.6307 | $3.75^{+0.26}_{-0.16}$ | 3.604$\pm 0.001$ | $10.3^{+0.1}_{-0.1}$ | $68^{+69}_{-20}$ | $19.1$
HPC1001.ma | 1272853 | 150.4618 | 2.6294 | $4.38^{+0.41}_{-0.35}$ | 3.610$\pm 0.001$ | $11.3^{+0.1}_{-0.2}$ | $496^{+290}_{-241}$ | $27.3$
(Candidate members) |  |  |  |  |  |  |  |
HPC1001.c | 1279884 | 150.4652 | 2.6361 | $3.65^{+0.11}_{-0.15}$ | – | $10.0^{+0.1}_{-0.1}$ | $18^{+15}_{-5}$ | $1.6$
HPC1001.e | 1280959 | 150.4652 | 2.6366 | $3.76^{+0.25}_{-0.18}$ | – | $10.3^{+0.1}_{-0.1}$ | $57^{+37}_{-37}$ | $2.9$
HPC1001.f | 1280265 | 150.4654 | 2.6370 | $3.82^{+0.29}_{-0.31}$ | – | $10.0^{+0.1}_{-0.2}$ | $18^{+15}_{-6}$ | $3.9$
HPC1001.g | 1278992 | 150.4650 | 2.6353 | $3.62^{+0.11}_{-0.13}$ | – | $10.1^{+0.1}_{-0.1}$ | $18^{+4}_{-3}$ | 3.1
HPC1001.hc | – | 150.4655 | 2.6356 | $3.79^{+0.37}_{-0.34}$ | – | $10.0^{+0.2}_{-0.2}$ | $77^{+65}_{-42}$ | $1.1$
HPC1001.i | 1277620 | 150.4665 | 2.6344 | $3.26^{+0.53}_{-0.60}$ | – | $9.9^{+0.1}_{-0.2}$ | $20^{+16}_{-14}$ | $6.2$
HPC1001.j | 1282867 | 150.4637 | 2.6384 | $3.76^{+0.15}_{-0.12}$ | – | $10.7^{+0.1}_{-0.1}$ | $109^{+26}_{-79}$ | $11.2$
HPC1001.ka | 1280828 | 150.4673 | 2.6370 | $3.15^{+0.14}_{-0.11}$ | – | $9.4^{+0.2}_{-0.1}$ | $14^{+4}_{-12}$ | 7.3
| 1271738 | 150.4664 | 2.6284 | $3.95^{+0.20}_{-0.26}$ | – | $9.5^{+0.1}_{-0.2}$ | $11^{+6}_{-7}$ | $27.2$
| 1271880 | 150.4628 | 2.6283 | $3.64^{+0.11}_{-0.13}$ | – | $9.6^{+0.1}_{-0.1}$ | $15^{+3}_{-2}$ | $29.2$
| 1273801 | 150.4611 | 2.6305 | $3.69^{+0.23}_{-3.39}$ | – | $8.4^{+0.2}_{-0.2}$ | $3^{+1}_{-2}$ | $25.2$
| 1273919 | 150.4676 | 2.6300 | $3.84^{+0.24}_{-0.26}$ | – | $10.0^{+0.1}_{-0.2}$ | $23^{+21}_{-6}$ | $22.5$
| 1274349 | 150.4646 | 2.6304 | $3.85^{+0.13}_{-0.13}$ | – | $9.6^{+0.1}_{-0.1}$ | $15^{+2}_{-2}$ | $20.2$
| 1275202 | 150.4629 | 2.6318 | $3.81^{+0.34}_{-0.17}$ | – | $9.4^{+0.2}_{-0.1}$ | $16^{+4}_{-4}$ | $17.5$
| 1278508 | 150.4686 | 2.6352 | $4.00^{+0.10}_{-0.11}$ | – | $9.0^{+0.1}_{-0.2}$ | $4^{+4}_{-1}$ | $11.0$
| 1278832 | 150.4713 | 2.6356 | $2.96^{+0.12}_{-0.12}$ | – | $8.6^{+0.2}_{-0.2}$ | $4^{+1}_{-3}$ | $20.5$
| 1282347 | 150.4695 | 2.6390 | $3.02^{+0.15}_{-0.15}$ | – | $8.8^{+0.4}_{-0.4}$ | $1^{+1}_{-1}$ | $17.9$
| 1282620 | 150.4688 | 2.6393 | $4.06^{+0.30}_{-0.37}$ | – | $8.9^{+0.2}_{-0.2}$ | $4^{+1}_{-3}$ | $16.9$
| 1286318 | 150.4700 | 2.6427 | $3.72^{+0.24}_{-0.18}$ | – | $9.6^{+0.1}_{-0.2}$ | $15^{+15}_{-4}$ | $29.1$
| 1286772 | 150.4657 | 2.6426 | $3.04^{+0.06}_{-0.04}$ | – | $9.6^{+0.1}_{-0.1}$ | $17^{+3}_{-3}$ | $24.0$
| 1282703 | 150.4654 | 2.6393 | $0.45^{+3.23}_{-0.26}$ | – | $7.2^{+0.2}_{-0.2}$ | $<1$ | 12.1
Total | – | 150.4656 | 2.6359 | $3.65\pm 0.07$ | $3.613\pm 0.001$ | $11.6\pm 0.1$ | $1194^{+306}_{-260}$ | –

Notes: aNewly discovered members, not previously reported in Sillassen et al.
(2022). bSources are completely blended in the $4.5"$ NOEMA beam (Fig. 1),
with a strong (S/N=10.9) and broad (Width=1824${\rm km/s}$) emission line
(Table 3). cSource is not in the COSMOS2020 catalogue, parameters adopted from
COSMOS2015 (Laigle et al. 2016; Sillassen et al. 2022).

Table 8: Physical properties of COS-SBCX1 members from COSMOS2020 Classic LePhare. ID | RA | Dec. | $z_{\rm phot}$ | $z_{\rm spec}$ | $\log(M_{\ast}/{\rm M_{\odot}})$ | SFR | $d_{\rm core}$
---|---|---|---|---|---|---|---
| [deg] | [deg] |  |  |  | [${\rm M_{\odot}\,yr^{-1}}$] | [arcsec]
(Confirmed members) |  |  |  |  |  |  |
1408110 | 150.3480 | 2.7611 | $2.38^{+0.12}_{-0.17}$ | 2.422$\pm 0.001$ | $11.4^{+0.1}_{-0.1}$ | $156^{+30}_{-31}$ | 4.9
(Candidate members) |  |  |  |  |  |  |
–* | 150.3497 | 2.7619 | – | – | $10.8^{+0.2}_{-0.2}$ | – | 1.9
1398871 | 150.3534153 | 2.7532749 | $2.18^{+0.85}_{-0.64}$ | – | $9.1^{+0.2}_{-0.2}$ | $3^{+2}_{-2}$ | 34.3
1399225 | 150.3483456 | 2.7530453 | $2.76^{+0.09}_{-0.11}$ | – | $9.7^{+0.1}_{-0.2}$ | $17^{+6}_{-14}$ | 29.1
1399474 | 150.3479133 | 2.7530239 | $2.45^{+0.09}_{-0.08}$ | – | $9.3^{+0.1}_{-0.1}$ | $15^{+2}_{-2}$ | 29.1
1399745 | 150.3487553 | 2.7523927 | $2.50^{+0.03}_{-0.06}$ | – | $9.9^{+0.1}_{-0.1}$ | $62^{+10}_{-10}$ | 31.5
1399984 | 150.3541567 | 2.7542877 | $2.12^{+0.47}_{-0.91}$ | – | $8.5^{+0.5}_{-0.4}$ | $1^{+0}_{-0}$ | 33.0
1400213 | 150.3415066 | 2.7543926 | $2.71^{+0.12}_{-0.17}$ | – | $8.8^{+0.2}_{-0.2}$ | $2^{+2}_{-0}$ | 33.7
1400229 | 150.3470434 | 2.7545470 | $2.15^{+0.47}_{-1.62}$ | – | $8.1^{+0.2}_{-0.2}$ | $1^{+0}_{-1}$ | 23.9
1400635 | 150.3417414 | 2.7547666 | $2.61^{+0.09}_{-0.11}$ | – | $9.7^{+0.1}_{-0.1}$ | $22^{+5}_{-18}$ | 32.2
1401156 | 150.3540867 | 2.7554773 | $1.98^{+0.34}_{-0.25}$ | – | $9.0^{+0.1}_{-0.2}$ | $1^{+1}_{-0}$ | 29.8
1401256 | 150.3502810 | 2.7545819 | $2.76^{+0.07}_{-0.07}$ | – | $9.5^{+0.1}_{-0.2}$ | $34^{+6}_{-7}$ | 24.9
1401272 | 150.3395136 | 2.7556119 | $2.19^{+0.41}_{-0.44}$ | – | $8.8^{+0.1}_{-0.2}$ | $1^{+1}_{-0}$ | 36.5
1401354 | 150.3515443 | 2.7550129 | $2.63^{+0.13}_{-0.16}$ | – | $9.5^{+0.1}_{-0.2}$ | $10^{+9}_{-2}$ | 25.4
1401671 | 150.3472055 | 2.7559690 | $2.59^{+0.38}_{-0.52}$ | – | $9.1^{+0.2}_{-0.2}$ | $3^{+1}_{-2}$ | 18.8
1401759 | 150.3431070 | 2.7559796 | $2.40^{+0.23}_{-0.43}$ | – | $8.8^{+0.1}_{-0.1}$ | $3^{+0}_{-1}$ | 25.6
1401866 | 150.3403186 | 2.7561221 | $2.24^{+0.19}_{-0.18}$ | – | $9.5^{+0.1}_{-0.1}$ | $1^{+0}_{-0}$ | 33.1
1401922 | 150.3439038 | 2.7551156 | $2.09^{+0.09}_{-0.06}$ | – | $9.6^{+0.1}_{-0.2}$ | $33^{+7}_{-27}$ | 26.2
1402490 | 150.3503583 | 2.7558268 | $2.17^{+0.19}_{-0.16}$ | – | $10.2^{+0.2}_{-0.2}$ | $62^{+51}_{-64}$ | 20.8
1402700 | 150.3389536 | 2.7568049 | $1.99^{+0.22}_{-0.22}$ | – | $8.7^{+0.2}_{-0.2}$ | $2^{+0}_{-1}$ | 36.2
1402958 | 150.3452583 | 2.7569484 | $2.77^{+0.21}_{-0.28}$ | – | $8.8^{+0.2}_{-0.1}$ | $2^{+0}_{-2}$ | 18.0
1403375 | 150.3393030 | 2.7569974 | $2.33^{+0.11}_{-0.11}$ | – | $9.3^{+0.1}_{-0.1}$ | $7^{+1}_{-1}$ | 34.7
1404385 | 150.3465587 | 2.7584031 | $2.49^{+0.13}_{-0.17}$ | – | $8.7^{+0.1}_{-0.1}$ | $1^{+0}_{-0}$ | 11.1
1404606 | 150.3524059 | 2.7583128 | $2.68^{+0.15}_{-0.22}$ | – | $9.5^{+0.1}_{-0.1}$ | $18^{+4}_{-6}$ | 18.7
1404729 | 150.3519759 | 2.7575986 | $2.30^{+0.08}_{-0.15}$ | – | $10.7^{+0.1}_{-0.1}$ | $217^{+39}_{-43}$ | 19.1
1404945 | 150.3447842 | 2.7582966 | $2.64^{+0.56}_{-1.78}$ | – | $9.3^{+0.1}_{-0.2}$ | $12^{+10}_{-3}$ | 15.5
1405016 | 150.3467285 | 2.7591544 | $2.76^{+0.24}_{-0.30}$ | – | $10.1^{+0.1}_{-0.1}$ | $9^{+7}_{-3}$ | 8.5
1405330 | 150.3412585 | 2.7584464 | $2.66^{+0.06}_{-0.14}$ | – | $10.0^{+0.1}_{-0.1}$ | $58^{+11}_{-18}$ | 26.2
1405903 | 150.3473917 | 2.7600336 | $2.33^{+0.37}_{-0.38}$ | – | $8.9^{+0.2}_{-0.2}$ | $3^{+1}_{-2}$ | 4.5
1406026 | 150.3419379 | 2.7597845 | $2.01^{+0.24}_{-0.17}$ | – | $9.6^{+0.1}_{-0.2}$ | $13^{+4}_{-13}$ | 22.4
1406132 | 150.3487067 | 2.7592945 | $2.31^{+0.27}_{-0.30}$ | – | $10.7^{+0.0}_{-0.0}$ | $0^{+0}_{-0}$ | 7.0
1406593 | 150.3444680 | 2.7606627 | $2.33^{+0.37}_{-0.46}$ | – | $8.9^{+0.1}_{-0.2}$ | $1^{+1}_{-0}$ | 12.9
1406826 | 150.3496448 | 2.7606866 | $2.41^{+0.50}_{-0.34}$ | – | $10.2^{+0.1}_{-0.2}$ | $40^{+39}_{-24}$ | 6.0
1406877 | 150.3437063 | 2.7608204 | $2.59^{+0.21}_{-0.31}$ | – | $9.1^{+0.1}_{-0.1}$ | $2^{+0}_{-0}$ | 15.6
1407283 | 150.3481033 | 2.7607376 | $1.88^{+0.12}_{-0.10}$ | – | $10.6^{+0.1}_{-0.1}$ | $14^{+9}_{-3}$ | 1.4
1407341 | 150.3534620 | 2.7613525 | $2.64^{+0.20}_{-0.25}$ | – | $9.3^{+0.1}_{-0.2}$ | $6^{+3}_{-4}$ | 19.6
1407342 | 150.3397290 | 2.7614006 | $2.41^{+0.58}_{-1.79}$ | – | $8.5^{+0.2}_{-0.2}$ | $1^{+1}_{-0}$ | 29.9
1407673 | 150.3477238 | 2.7616945 | $2.62^{+0.30}_{-0.35}$ | – | $9.5^{+0.1}_{-0.2}$ | $6^{+5}_{-2}$ | 2.3
1407983 | 150.3500725 | 2.7614637 | $2.37^{+0.66}_{-0.75}$ | – | $9.5^{+0.2}_{-0.2}$ | $11^{+6}_{-9}$ | 7.5
1408029 | 150.3475805 | 2.7619215 | $2.54^{+0.63}_{-0.44}$ | – | $10.2^{+0.1}_{-0.2}$ | $40^{+32}_{-31}$ | 3.3
1408242 | 150.3542594 | 2.7620097 | $2.70^{+0.29}_{-0.35}$ | – | $10.1^{+0.1}_{-0.2}$ | $29^{+23}_{-13}$ | 22.7
1408284 | 150.3480351 | 2.7617402 | $2.66^{+0.21}_{-0.29}$ | – | $9.9^{+0.1}_{-0.2}$ | $15^{+12}_{-5}$ | 2.2
1408512 | 150.3457383 | 2.7623290 | $2.68^{+0.07}_{-0.09}$ | – | $8.9^{+0.1}_{-0.1}$ | $7^{+1}_{-1}$ | 9.3
1408732 | 150.3522480 | 2.7618868 | $2.07^{+0.24}_{-0.17}$ | – | $9.8^{+0.2}_{-0.2}$ | $28^{+7}_{-29}$ | 15.5
1409126 | 150.3457790 | 2.7631643 | $2.47^{+0.35}_{-0.46}$ | – | $8.4^{+0.2}_{-0.2}$ | $1^{+0}_{-1}$ | 10.9
1409304 | 150.3524976 | 2.7633564 | $2.25^{+0.39}_{-0.40}$ | – | $9.4^{+0.1}_{-0.2}$ | $3^{+2}_{-1}$ | 18.0
1409685 | 150.3470603 | 2.7637415 | $2.63^{+0.21}_{-0.32}$ | – | $8.9^{+0.1}_{-0.1}$ | $3^{+0}_{-2}$ | 10.1
1409707 | 150.3496428 | 2.7630066 | $2.15^{+0.21}_{-0.23}$ | – | $11.1^{+0.1}_{-0.1}$ | $125^{+20}_{-20}$ | 9.0
1409806 | 150.3532777 | 2.7638843 | $2.74^{+0.48}_{-2.28}$ | – | $8.8^{+0.5}_{-0.5}$ | $1^{+1}_{-0}$ | 21.4
1410423 | 150.3554314 | 2.7638052 | $2.52^{+0.07}_{-0.05}$ | – | $9.6^{+0.1}_{-0.1}$ | $14^{+11}_{-3}$ | 28.4
1410451 | 150.3502562 | 2.7637331 | $2.01^{+0.40}_{-0.35}$ | – | $10.0^{+0.1}_{-0.1}$ | $19^{+11}_{-6}$ | 12.4
1410521 | 150.3419140 | 2.7645586 | $2.30^{+0.23}_{-0.38}$ | – | $8.5^{+0.1}_{-0.2}$ | $2^{+0}_{-0}$ | 25.2
1412364 | 150.3508360 | 2.7661634 | $2.52^{+0.48}_{-0.45}$ | – | $10.9^{+0.1}_{-0.1}$ | $108^{+72}_{-54}$ | 20.8
1412370 | 150.3461119 | 2.7664528 | $2.43^{+0.24}_{-1.19}$ | – | $8.7^{+0.1}_{-0.1}$ | $2^{+0}_{-1}$ | 20.4
1412651 | 150.3538193 | 2.7667801 | $2.65^{+0.27}_{-0.41}$ | – | $8.7^{+0.1}_{-0.1}$ | $2^{+0}_{-0}$ | 29.2
1412702 | 150.3517594 | 2.7665658 | $2.63^{+0.15}_{-0.19}$ | – | $9.2^{+0.2}_{-0.1}$ | $11^{+3}_{-9}$ | 23.8
1412826 | 150.3524741 | 2.7663713 | $2.41^{+0.26}_{-0.24}$ | – | $11.0^{+0.1}_{-0.1}$ | $144^{+116}_{-108}$ | 24.8
1413261 | 150.3450722 | 2.7673326 | $2.02^{+0.44}_{-0.29}$ | – | $9.0^{+0.1}_{-0.2}$ | $1^{+1}_{-0}$ | 24.8
1413740 | 150.3536237 | 2.7679074 | $2.39^{+0.32}_{-1.21}$ | – | $8.8^{+0.1}_{-0.1}$ | $1^{+0}_{-0}$ | 31.7
1415067 | 150.3523728 | 2.7691123 | $2.69^{+0.20}_{-0.34}$ | – | $8.5^{+0.1}_{-0.1}$ | $3^{+0}_{-0}$ | 32.8
1415067 | 150.3523728 | 2.7691123 | $2.69^{+0.20}_{-0.34}$ | – | $8.5^{+0.1}_{-0.1}$ | $3^{+0}_{-0}$ | 32.8
Total | 150.3492 | 2.7619 | $2.48\pm 0.03$ | $2.422\pm 0.001$ | $12.0\pm 0.1$ | $1438^{+170}_{-165}$ | –

Notes:*source not in the COSMOS2020 catalogue or in previous versions of
COSMOS catalogues.

Table 9: Physical properties of COS-SBCX3 members from COSMOS2020 Classic LePhare. ID | RA | Dec. | $z_{\rm phot}$ | $z_{\rm spec}$ | $\log(M_{\ast}/{\rm M_{\odot}})$ | SFR | $d_{\rm core}$
---|---|---|---|---|---|---|---
| [deg] | [deg] |  |  |  | [${\rm M_{\odot}\,yr^{-1}}$] | [arcsec]
(Confirmed members) |  |  |  |  |  |  |
1088787 | 150.3105 | 2.4515 | $2.98^{+0.21}_{-0.20}$ | 3.030$\pm 0.001$ | $10.7^{+0.1}_{-0.1}$ | $53^{+40}_{-12}$ | 2.7
1088927 | 150.3117 | 2.4510 | $3.15^{+0.28}_{-0.67}$ | 3.032$\pm 0.001$ | $10.5^{+0.1}_{-0.2}$ | $100^{+45}_{-90}$ | 1.8
(Candidate members) |  |  |  |  |  |  |
1088602 | 150.3144 | 2.4515 | $2.71^{+0.13}_{-0.21}$ | – | $8.5^{+0.2}_{-0.2}$ | $1^{+1}_{-0}$ | 11.5
1088952 | 150.3092 | 2.4516 | $2.77^{+0.12}_{-0.15}$ | – | $8.6^{+0.1}_{-0.2}$ | $1^{+1}_{-0}$ | 7.3
1089223 | 150.3112 | 2.4511 | $1.94^{+0.48}_{-0.43}$ | – | $9.9^{+0.1}_{-0.2}$ | $15^{+12}_{-10}$ | 0.5
1089223 | 150.3112 | 2.4511 | $1.94^{+0.48}_{-0.43}$ | – | $9.9^{+0.1}_{-0.2}$ | $15^{+12}_{-10}$ | 0.5
1089511 | 150.3155 | 2.4522 | $3.09^{+0.14}_{-0.12}$ | – | $8.4^{+0.1}_{-0.2}$ | $1^{+1}_{-0}$ | 15.8
1089759 | 150.3105 | 2.4518 | $3.12^{+0.11}_{-0.12}$ | – | $10.1^{+0.1}_{-0.1}$ | $13^{+10}_{-4}$ | 3.3
1090209 | 150.3099 | 2.4529 | $3.01^{+0.27}_{-0.39}$ | – | $9.3^{+0.1}_{-0.2}$ | $3^{+2}_{-0}$ | 8.0
1090976 | 150.3119 | 2.4537 | $2.74^{+0.11}_{-0.13}$ | – | $9.1^{+0.1}_{-0.1}$ | $7^{+1}_{-1}$ | 9.4
Total | 150.3113 | 2.4511 | $2.89\pm 0.08$ | $3.031\pm 0.001$ | $11.1\pm 0.1$ | $213^{+63}_{-92}$ | –

Table 10: Physical properties of COS-SBCX4 members from COSMOS2020 Classic LePhare. ID | RA | Dec. | $z_{\rm phot}$ | $z_{\rm spec}$ | $\log(M_{\ast}/{\rm M_{\odot}})$ | SFR | $d_{\rm core}$
---|---|---|---|---|---|---|---
| [deg] | [deg] |  |  |  | [${\rm M_{\odot}\,yr^{-1}}$] | [arcsec]
Core members |  |  |  |  |  |  |
(Confirmed members) |  |  |  |  |  |  |
1049510 | 150.7512 | 2.4124 | $2.93^{+0.35}_{-0.38}$ | 2.642$\pm 0.001$ | $11.1^{+0.1}_{-0.1}$ | $257^{+83}_{-186}$ | 2.2
1049929 | 150.7521 | 2.4140 | $3.85^{+0.66}_{-0.92}$ | 2.648$\pm 0.001$ | $10.9^{+0.2}_{-0.2}$ | $195^{+120}_{-101}$ | 5.5
1050531 | 150.7504 | 2.4130 | $2.67^{+0.08}_{-0.12}$ | 2.647$\pm 0.001$ | $11.2^{+0.1}_{-0.1}$ | $416^{+135}_{-265}$ | 1.8
(Candidate members) |  |  |  |  |  |  |
1042545 | 150.7528 | 2.4067 | $2.35^{+0.16}_{-1.13}$ | – | $8.6^{+0.1}_{-0.1}$ | $7^{+1}_{-1}$ | 23.4
1042632 | 150.7517 | 2.4069 | $2.50^{+0.43}_{-0.80}$ | – | $8.5^{+0.2}_{-0.2}$ | $1^{+0}_{-1}$ | 21.7
1044106 | 150.7463 | 2.4083 | $2.53^{+0.21}_{-0.26}$ | – | $9.1^{+0.1}_{-0.1}$ | $3^{+0}_{-1}$ | 23.3
1044704 | 150.7447 | 2.4088 | $2.54^{+0.21}_{-0.31}$ | – | $9.2^{+0.1}_{-0.1}$ | $3^{+0}_{-0}$ | 26.6
1045961 | 150.7463 | 2.4097 | $2.42^{+0.22}_{-0.63}$ | – | $8.8^{+0.1}_{-0.1}$ | $6^{+1}_{-1}$ | 20.0
1046616 | 150.7468 | 2.4107 | $2.72^{+0.46}_{-2.53}$ | – | $8.7^{+0.4}_{-0.4}$ | $2^{+1}_{-1}$ | 16.6
1047063 | 150.7557 | 2.4108 | $3.03^{+0.10}_{-0.07}$ | – | $9.0^{+0.2}_{-0.2}$ | $6^{+6}_{-1}$ | 19.3
1048929 | 150.7519 | 2.4124 | $2.74^{+0.15}_{-0.14}$ | – | $9.5^{+0.1}_{-0.1}$ | $8^{+7}_{-1}$ | 4.5
1049031 | 150.7508 | 2.4131 | $2.74^{+0.17}_{-0.13}$ | – | $10.4^{+0.1}_{-0.1}$ | $24^{+4}_{-4}$ | 0.8
1049700 | 150.7550 | 2.4138 | $2.71^{+0.25}_{-0.41}$ | – | $8.6^{+0.2}_{-0.2}$ | $2^{+0}_{-2}$ | 15.4
1049920 | 150.7499 | 2.4134 | $2.65^{+0.25}_{-0.19}$ | – | $10.6^{+0.1}_{-0.1}$ | $41^{+17}_{-24}$ | 3.8
1049965 | 150.7511 | 2.4141 | $2.66^{+0.44}_{-1.34}$ | – | $8.7^{+0.1}_{-0.2}$ | $2^{+0}_{-0}$ | 4.3
1050218 | 150.7547 | 2.4143 | $3.00^{+0.35}_{-0.40}$ | – | $9.5^{+0.1}_{-0.2}$ | $7^{+6}_{-2}$ | 15.0
1050855 | 150.7533 | 2.4143 | $3.18^{+0.07}_{-0.12}$ | – | $9.7^{+0.1}_{-0.1}$ | $15^{+2}_{-2}$ | 10.4
1050901 | 150.7528 | 2.4150 | $2.00^{+0.56}_{-0.47}$ | – | $9.1^{+0.1}_{-0.2}$ | $2^{+1}_{-1}$ | 10.2
1051433 | 150.7561 | 2.4155 | $2.30^{+0.76}_{-0.81}$ | – | $8.8^{+0.2}_{-0.2}$ | $1^{+1}_{-1}$ | 21.3
1053106 | 150.7552 | 2.4169 | $2.73^{+0.26}_{-0.49}$ | – | $9.1^{+0.1}_{-0.1}$ | $4^{+3}_{-1}$ | 21.5
1053892 | 150.7502 | 2.4173 | $1.95^{+0.33}_{-0.19}$ | – | $9.2^{+0.1}_{-0.2}$ | $4^{+4}_{-1}$ | 16.1
1055135 | 150.7515 | 2.4190 | $2.57^{+0.53}_{-2.20}$ | – | $8.4^{+0.2}_{-0.2}$ | $1^{+0}_{-1}$ | 22.2
Total | 150.7509 | 2.4132 | $2.85\pm 0.09$ | $2.646\pm 0.001$ | $11.7\pm 0.1$ | $1017^{+200}_{-341}$ | –

Table 11: Physical properties of COS-SBCX7 members from COSMOS2020 Classic LePhare. ID | RA | Dec. | $z_{\rm phot}$ | $z_{\rm spec}$ | $\log(M_{\ast}/{\rm M_{\odot}})$ | SFR | $d_{\rm core}$
---|---|---|---|---|---|---|---
| [deg] | [deg] |  |  |  | [${\rm M_{\odot}\,yr^{-1}}$] | [arcsec]
(Confirmed memebers) |  |  |  |  |  |  |
392257 | 149.9910 | 1.7967 | $2.91^{+0.63}_{-0.58}$ | 2.415$\pm 0.001$ | $10.7^{+0.1}_{-0.1}$ | $91^{+61}_{-49}$ | 6.0
392639 | 149.9816 | 1.7960 | $2.70^{+0.04}_{-0.07}$ | 2.413$\pm 0.001$ | $10.3^{+0.1}_{-0.1}$ | $114^{+25}_{-112}$ | 30.2
394609 | 149.9897 | 1.7977 | $2.36^{+0.13}_{-0.14}$ | 2.416$\pm 0.001$ | $10.8^{+0.1}_{-0.1}$ | $14^{+11}_{-4}$ | 0.6
394944 | 149.9883 | 1.7980 | $2.38^{+0.15}_{-0.14}$ | 2.416$\pm 0.001$ | $11.1^{+0.1}_{-0.1}$ | $92^{+70}_{-25}$ | 5.5
(Candidate members) |  |  |  |  |  |  |
384203 | 149.9855 | 1.7889 | $1.83^{+0.17}_{-0.16}$ | – | $8.8^{+0.1}_{-0.2}$ | $0^{+0}_{-0}$ | 33.8
385317 | 149.9929 | 1.7900 | $2.23^{+0.27}_{-0.29}$ | – | $9.5^{+0.1}_{-0.1}$ | $2^{+0}_{-0}$ | 30.8
385439 | 149.9936 | 1.7900 | $2.13^{+0.18}_{-0.22}$ | – | $8.9^{+0.1}_{-0.1}$ | $3^{+0}_{-0}$ | 32.1
385916 | 149.9957 | 1.7907 | $2.01^{+0.30}_{-0.26}$ | – | $8.6^{+0.1}_{-0.2}$ | $1^{+0}_{-0}$ | 34.8
386678 | 149.9966 | 1.7911 | $1.99^{+0.13}_{-0.13}$ | – | $9.2^{+0.1}_{-0.1}$ | $5^{+0}_{-0}$ | 35.9
389851 | 149.9848 | 1.7938 | $2.73^{+0.07}_{-0.07}$ | – | $9.4^{+0.2}_{-0.1}$ | $23^{+5}_{-20}$ | 20.6
390151 | 149.9969 | 1.7944 | $2.75^{+0.04}_{-0.05}$ | – | $8.6^{+0.2}_{-0.2}$ | $5^{+1}_{-1}$ | 30.7
390263 | 149.9957 | 1.7947 | $2.48^{+0.13}_{-0.17}$ | – | $9.7^{+0.1}_{-0.1}$ | $13^{+2}_{-2}$ | 26.4
390843 | 149.9926 | 1.7944 | $2.30^{+0.18}_{-0.12}$ | – | $9.9^{+0.1}_{-0.1}$ | $19^{+15}_{-4}$ | 17.4
391472 | 149.9889 | 1.7953 | $2.41^{+0.12}_{-0.10}$ | – | $9.5^{+0.1}_{-0.2}$ | $9^{+8}_{-3}$ | 8.4
392030 | 149.9945 | 1.7965 | $2.31^{+0.28}_{-0.36}$ | – | $8.6^{+0.2}_{-0.2}$ | $1^{+0}_{-1}$ | 20.1
392370 | 149.9939 | 1.7968 | $2.59^{+0.24}_{-0.31}$ | – | $8.5^{+0.1}_{-0.1}$ | $2^{+0}_{-0}$ | 17.8
393623 | 149.9822 | 1.7968 | $2.22^{+0.05}_{-0.06}$ | – | $10.8^{+0.1}_{-0.1}$ | $289^{+59}_{-73}$ | 24.6
393835 | 149.9879 | 1.7982 | $2.24^{+0.48}_{-2.15}$ | – | $8.1^{+0.2}_{-0.2}$ | $1^{+0}_{-0}$ | 4.7
394391 | 149.9917 | 1.7981 | $2.85^{+0.19}_{-0.29}$ | – | $11.1^{+0.1}_{-0.1}$ | $245^{+193}_{-76}$ | 9.8
396033 | 149.9907 | 1.8003 | $2.64^{+0.20}_{-0.23}$ | – | $9.1^{+0.1}_{-0.2}$ | $3^{+2}_{-0}$ | 11.2
396633 | 149.9834 | 1.8002 | $2.08^{+0.04}_{-0.05}$ | – | $8.8^{+0.1}_{-0.1}$ | $14^{+3}_{-3}$ | 22.2
397066 | 149.9847 | 1.8012 | $2.48^{+0.49}_{-0.61}$ | – | $8.7^{+0.2}_{-0.2}$ | $2^{+0}_{-1}$ | 20.3
397363 | 149.9816 | 1.8016 | $2.71^{+0.18}_{-0.20}$ | – | $9.7^{+0.1}_{-0.1}$ | $5^{+4}_{-1}$ | 30.2
397795 | 149.9903 | 1.8010 | $2.79^{+0.23}_{-0.20}$ | – | $10.9^{+0.1}_{-0.1}$ | $132^{+93}_{-33}$ | 13.0
397953 | 149.9958 | 1.8021 | $2.51^{+0.15}_{-0.17}$ | – | $9.1^{+0.1}_{-0.1}$ | $4^{+0}_{-0}$ | 29.2
398018 | 149.9815 | 1.8022 | $2.52^{+0.38}_{-0.56}$ | – | $9.5^{+0.1}_{-0.2}$ | $4^{+4}_{-1}$ | 31.5
398599 | 149.9917 | 1.8027 | $2.83^{+0.27}_{-0.55}$ | – | $9.1^{+0.2}_{-0.2}$ | $5^{+2}_{-3}$ | 20.7
398634 | 149.9882 | 1.8018 | $2.61^{+0.14}_{-0.14}$ | – | $9.4^{+0.1}_{-0.2}$ | $8^{+7}_{-2}$ | 15.2
398787 | 149.9821 | 1.8019 | $2.37^{+0.12}_{-0.09}$ | – | $10.8^{+0.1}_{-0.1}$ | $50^{+7}_{-7}$ | 29.3
399896 | 149.9934 | 1.8040 | $2.54^{+0.27}_{-0.32}$ | – | $8.7^{+0.1}_{-0.2}$ | $1^{+0}_{-0}$ | 27.8
400170 | 149.9961 | 1.8043 | $2.84^{+0.38}_{-0.54}$ | – | $9.3^{+0.2}_{-0.2}$ | $7^{+3}_{-5}$ | 34.8
400185 | 149.9890 | 1.8042 | $2.49^{+0.16}_{-0.22}$ | – | $8.6^{+0.2}_{-0.2}$ | $1^{+1}_{-0}$ | 23.5
400413 | 149.9956 | 1.8042 | $1.84^{+0.36}_{-0.31}$ | – | $8.7^{+0.2}_{-0.2}$ | $2^{+1}_{-2}$ | 33.5
400526 | 149.9865 | 1.8041 | $2.97^{+0.18}_{-0.18}$ | – | $9.1^{+0.1}_{-0.2}$ | $4^{+3}_{-1}$ | 25.0
401372 | 149.9923 | 1.8054 | $1.83^{+0.56}_{-0.37}$ | – | $8.3^{+0.2}_{-0.2}$ | $0^{+0}_{-0}$ | 30.3
401840 | 149.9904 | 1.8053 | $2.49^{+0.20}_{-0.16}$ | – | $9.7^{+0.1}_{-0.2}$ | $13^{+12}_{-3}$ | 27.8
Total | 149.9898 | 1.7978 | $2.57\pm 0.03$ | $2.415\pm 0.001$ | $11.8\pm 0.1$ | $1097^{+244}_{-169}$ | –

Table 12: Physical properties of COS-SBC3 members from COSMOS2020 Classic LePhare. ID | RA | Dec. | $z_{\rm phot}$ | $z_{\rm spec}$ | $\log(M_{\ast}/{\rm M_{\odot}})$ | SFR | $d_{\rm core}$
---|---|---|---|---|---|---|---
| [deg] | [deg] |  |  |  | [${\rm M_{\odot}\,yr^{-1}}$] | [arcsec]
(Confirmed members) |  |  |  |  |  |  |
1340799 | 150.7226 | 2.6963 | $3.48^{+0.80}_{-0.84}$ | 2.365$\pm 0.001$ | $11.5^{+0.1}_{-0.1}$ | $190^{+90}_{-61}$ | 0.0
(Candidate members) |  |  |  |  |  |  |
1334731 | 150.7227768 | 2.6905261 | $2.28^{+0.48}_{-0.99}$ | – | $8.7^{+0.2}_{-0.2}$ | $2^{+2}_{-0}$ | 20.9
1335919 | 150.7306877 | 2.6917006 | $2.87^{+0.05}_{-0.05}$ | – | $8.9^{+0.1}_{-0.1}$ | $4^{+0}_{-0}$ | 33.6
1337358 | 150.7297781 | 2.6932095 | $2.41^{+0.38}_{-0.66}$ | – | $9.2^{+0.1}_{-0.2}$ | $4^{+1}_{-3}$ | 28.2
1337546 | 150.7273308 | 2.6934159 | $2.38^{+0.22}_{-0.25}$ | – | $9.1^{+0.1}_{-0.1}$ | $2^{+0}_{-2}$ | 20.0
1337712 | 150.7234355 | 2.6935964 | $2.03^{+0.61}_{-0.50}$ | – | $8.4^{+0.2}_{-0.2}$ | $0^{+0}_{-0}$ | 10.3
1337749 | 150.7271582 | 2.6936214 | $2.36^{+0.24}_{-0.54}$ | – | $9.0^{+0.1}_{-0.2}$ | $2^{+0}_{-1}$ | 19.1
1338883 | 150.7310329 | 2.6941766 | $2.52^{+0.19}_{-0.16}$ | – | $10.6^{+0.1}_{-0.0}$ | $0^{+0}_{-0}$ | 31.4
1338945 | 150.7233826 | 2.6943064 | $3.02^{+0.12}_{-0.11}$ | – | $9.6^{+0.1}_{-0.2}$ | $9^{+8}_{-2}$ | 7.8
1338973 | 150.7240954 | 2.6945682 | $2.70^{+0.19}_{-0.15}$ | – | $10.2^{+0.1}_{-0.1}$ | $23^{+15}_{-15}$ | 8.3
1339741 | 150.7217645 | 2.6943989 | $2.60^{+0.28}_{-0.25}$ | – | $11.1^{+0.1}_{-0.1}$ | $100^{+36}_{-1044}$ | 7.5
1339910 | 150.7245508 | 2.6957013 | $2.92^{+0.12}_{-0.15}$ | – | $9.0^{+0.2}_{-0.2}$ | $3^{+1}_{-2}$ | 7.4
1340398 | 150.7227948 | 2.6957280 | $2.07^{+0.31}_{-0.33}$ | – | $10.3^{+0.1}_{-0.2}$ | $30^{+24}_{-22}$ | 2.3
1342336 | 150.7172687 | 2.6947672 | $3.01^{+0.17}_{-2.80}$ | – | $9.7^{+0.1}_{-0.1}$ | $28^{+6}_{-6}$ | 19.9
1343209 | 150.7207002 | 2.6986974 | $3.04^{+0.18}_{-0.20}$ | – | $9.4^{+0.1}_{-0.1}$ | $4^{+3}_{-1}$ | 10.9
1345593 | 150.7217632 | 2.7006506 | $2.79^{+0.31}_{-0.35}$ | – | $10.0^{+0.1}_{-0.2}$ | $27^{+13}_{-20}$ | 15.9
1345985 | 150.7173665 | 2.7015039 | $2.70^{+0.06}_{-0.07}$ | – | $9.8^{+0.1}_{-0.1}$ | $24^{+4}_{-3}$ | 26.5
1346174 | 150.7183122 | 2.7007088 | $3.05^{+0.29}_{-0.22}$ | – | $10.1^{+0.1}_{-0.2}$ | $26^{+13}_{-19}$ | 22.1
1350310 | 150.7214095 | 2.7048155 | $2.85^{+0.06}_{-0.05}$ | – | $9.7^{+0.1}_{-0.1}$ | $57^{+12}_{-14}$ | 30.9
1332724 | 150.7252518 | 2.6887611 | $2.32^{+0.31}_{-0.30}$ | – | $9.1^{+0.1}_{-0.2}$ | $3^{+3}_{-0}$ | 28.9
1334717 | 150.7259156 | 2.6906676 | $2.15^{+0.30}_{-0.61}$ | – | $9.1^{+0.1}_{-0.1}$ | $4^{+0}_{-1}$ | 23.6
1336266 | 150.7228321 | 2.6917998 | $2.07^{+0.29}_{-0.53}$ | – | $8.5^{+0.2}_{-0.2}$ | $2^{+1}_{-0}$ | 16.3
1336604 | 150.7225462 | 2.6921015 | $1.82^{+0.18}_{-0.14}$ | – | $9.2^{+0.1}_{-0.2}$ | $4^{+4}_{-1}$ | 15.2
1337924 | 150.7219464 | 2.6937675 | $2.27^{+0.50}_{-1.41}$ | – | $8.4^{+0.2}_{-0.2}$ | $2^{+0}_{-0}$ | 9.5
1343661 | 150.7188833 | 2.6993108 | $1.95^{+0.30}_{-0.26}$ | – | $8.9^{+0.1}_{-0.2}$ | $1^{+1}_{-0}$ | 17.1
1344343 | 150.7199699 | 2.6994621 | $2.29^{+0.78}_{-0.67}$ | – | $10.1^{+0.2}_{-0.2}$ | $44^{+29}_{-29}$ | 14.7
1344398 | 150.7190970 | 2.6982136 | $2.10^{+0.10}_{-0.25}$ | – | $10.5^{+0.1}_{-0.1}$ | $166^{+29}_{-39}$ | 14.3
1345139 | 150.7153071 | 2.7000313 | $2.04^{+0.15}_{-0.15}$ | – | $9.5^{+0.1}_{-0.2}$ | $13^{+3}_{-11}$ | 29.4
1345894 | 150.7270190 | 2.7014442 | $2.20^{+0.61}_{-0.45}$ | – | $9.3^{+0.1}_{-0.2}$ | $3^{+2}_{-2}$ | 24.4
1344398 | 150.7190970 | 2.6982136 | $2.10^{+0.10}_{-0.25}$ | – | $10.5^{+0.1}_{-0.1}$ | $166^{+29}_{-39}$ | 14.3
Total | 150.7196 | 2.6995 | $2.72\pm 0.04$ | $2.365\pm 0.001$ | $11.8\pm 0.1$ | $955^{+116}_{-1048}$ | –
(Rejected members) |  |  |  |  |  |  |
1345246 | 150.7193 | 2.6998 | $3.18^{+0.55}_{-0.48}$ | 2.723$\pm 0.001$ | $11.8^{+0.1}_{-0.1}$ | $243^{+158}_{-65}$ | 15.6

Table 13: Physical properties of COS-SBC4 members from COSMOS2020 Classic LePhare. ID | RA | Dec. | $z_{\rm phot}$ | $z_{\rm spec}$ | $\log(M_{\ast}/{\rm M_{\odot}})$ | SFR | $d_{\rm core}$
---|---|---|---|---|---|---|---
| [deg] | [deg] |  |  |  | [${\rm M_{\odot}\,yr^{-1}}$] | [arcsec]
(Confirmed members) |  |  |  |  |  |  |
840072 | 150.0368 | 2.2178 | $1.82^{+0.04}_{-0.09}$ | $1.6543\pm 0.0006^{a}$ | $11.4^{+0.1}_{-0.1}$ | $100^{+18}_{-18}$ | 1.4
840456 | 150.0366 | 2.2192 | $1.64^{+0.05}_{-0.03}$ | $1.6381\pm 0.0006^{a}$ | $10.2^{+0.1}_{-0.1}$ | $52^{+8}_{-9}$ | 5.4
840660 | 150.0325 | 2.2195 | $1.65^{+0.04}_{-0.03}$ | $1.6388\pm 0.0006^{a}$ | $10.4^{+0.1}_{-0.1}$ | $76^{+14}_{-14}$ | 15.6
(Candidate members) |  |  |  |  |  |  |
824041 | 150.0366923 | 2.2061331 | $1.74^{+0.25}_{-0.18}$ | – | $8.7^{+0.1}_{-0.1}$ | $3^{+0}_{-0}$ | 42.1
824902 | 150.0356076 | 2.2068429 | $1.35^{+0.08}_{-0.11}$ | – | $8.8^{+0.1}_{-0.1}$ | $1^{+1}_{-0}$ | 39.8
825606 | 150.0349940 | 2.2077652 | $1.39^{+0.43}_{-0.19}$ | – | $8.2^{+0.1}_{-0.2}$ | $0^{+0}_{-0}$ | 36.8
826524 | 150.0388680 | 2.2086292 | $1.81^{+0.05}_{-0.04}$ | – | $9.1^{+0.1}_{-0.1}$ | $22^{+4}_{-4}$ | 34.0
826583 | 150.0294105 | 2.2087104 | $1.90^{+0.40}_{-0.37}$ | – | $8.9^{+0.1}_{-0.2}$ | $0^{+0}_{-0}$ | 42.2
828463 | 150.0318645 | 2.2093383 | $1.88^{+0.11}_{-0.12}$ | – | $9.1^{+0.1}_{-0.1}$ | $11^{+2}_{-2}$ | 35.3
830066 | 150.0394925 | 2.2117027 | $1.78^{+0.20}_{-0.28}$ | – | $8.5^{+0.1}_{-0.1}$ | $1^{+0}_{-0}$ | 24.2
830220 | 150.0379440 | 2.2119681 | $1.69^{+1.66}_{-1.21}$ | – | $7.9^{+0.2}_{-0.2}$ | $0^{+0}_{-0}$ | 21.6
830689 | 150.0275325 | 2.2092421 | $1.89^{+0.13}_{-0.16}$ | – | $9.4^{+0.2}_{-0.2}$ | $19^{+5}_{-18}$ | 45.4
830722 | 150.0437771 | 2.2118636 | $1.39^{+0.04}_{-0.04}$ | – | $9.1^{+0.1}_{-0.1}$ | $3^{+0}_{-0}$ | 33.2
831134 | 150.0363399 | 2.2124207 | $1.29^{+0.16}_{-0.21}$ | – | $9.2^{+0.1}_{-0.2}$ | $2^{+1}_{-2}$ | 19.6
832008 | 150.0422681 | 2.2131902 | $1.62^{+0.10}_{-0.11}$ | – | $8.7^{+0.1}_{-0.1}$ | $2^{+0}_{-0}$ | 25.9
832093 | 150.0353196 | 2.2132796 | $1.83^{+0.18}_{-0.11}$ | – | $9.3^{+0.2}_{-0.2}$ | $8^{+2}_{-7}$ | 17.2
832129 | 150.0385824 | 2.2128016 | $1.91^{+0.20}_{-0.22}$ | – | $9.5^{+0.1}_{-0.1}$ | $7^{+6}_{-1}$ | 19.3
833467 | 150.0429095 | 2.2139294 | $1.45^{+0.01}_{-0.02}$ | – | $9.0^{+0.1}_{-0.1}$ | $5^{+0}_{-0}$ | 26.2
835280 | 150.0353156 | 2.2155435 | $1.37^{+0.08}_{-0.34}$ | – | $9.5^{+0.1}_{-0.1}$ | $12^{+8}_{-5}$ | 9.8
835641 | 150.0353282 | 2.2149129 | $1.51^{+0.18}_{-0.13}$ | – | $10.7^{+0.1}_{-0.1}$ | $22^{+7}_{-25}$ | 11.7
835706 | 150.0422240 | 2.2167433 | $1.77^{+0.12}_{-0.13}$ | – | $9.0^{+0.1}_{-0.1}$ | $0^{+0}_{-0}$ | 20.1
835713 | 150.0446451 | 2.2168417 | $1.43^{+1.10}_{-0.40}$ | – | $8.3^{+0.2}_{-0.2}$ | $0^{+0}_{-0}$ | 28.6
836069 | 150.0440213 | 2.2165815 | $1.81^{+0.18}_{-0.15}$ | – | $9.2^{+0.1}_{-0.2}$ | $3^{+1}_{-2}$ | 26.5
836257 | 150.0366450 | 2.2172921 | $1.89^{+0.19}_{-0.19}$ | – | $9.4^{+0.1}_{-0.2}$ | $6^{+5}_{-4}$ | 2.0
836352 | 150.0349150 | 2.2173707 | $1.87^{+2.54}_{-0.99}$ | – | $8.3^{+0.2}_{-0.2}$ | $0^{+0}_{-0}$ | 6.8
836436 | 150.0339463 | 2.2167755 | $1.74^{+0.14}_{-0.31}$ | – | $9.4^{+0.1}_{-0.1}$ | $8^{+3}_{-1}$ | 10.8
838011 | 150.0360963 | 2.2180155 | $1.91^{+0.07}_{-0.09}$ | – | $10.1^{+0.1}_{-0.1}$ | $22^{+16}_{-5}$ | 2.5
838016 | 150.0430325 | 2.2189057 | $1.86^{+0.27}_{-0.24}$ | – | $8.1^{+0.1}_{-0.2}$ | $0^{+0}_{-0}$ | 22.9
838184 | 150.0356083 | 2.2176223 | $1.87^{+0.16}_{-0.23}$ | – | $11.0^{+0.0}_{-0.0}$ | $26^{+7}_{-20}$ | 4.2
838627 | 150.0353935 | 2.2170824 | $1.56^{+0.04}_{-0.08}$ | – | $10.5^{+0.1}_{-0.1}$ | $33^{+16}_{-6}$ | 5.6