# Enhanced star formation and metallicity deficit in the USS 1558–003 forming
protocluster at z=2.53

J. M. Pérez-Martínez,1 T. Kodama,1 Y. Koyama,2 R. Shimakawa,3,4 T. L. Suzuki,5
K. Daikuhara,1 K. Adachi,1 M. Onodera,2,6 I. Tanaka2
1 Astronomical Institute, Tohoku University, 6-3, Aramaki, Aoba, Sendai,
Miyagi, 980-8578, Japan.
2 Subaru Telescope, National Astronomical Observatory of Japan, National
Institutes of Natural Sciences (NINS), 650 North A’ohoku Place, Hilo, HI
96720, USA.
3 Waseda Institute for Advanced Study (WIAS), Waseda University, 1-21-1,
Nishi-Waseda, Shinjuku, Tokyo 169-0051, Japan.
4 National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo,
181-8588, Japan.
5 Kavli Institute for the Physics and Mathematics of the Universe (WPI),
University of Tokyo, Kashiwa, Chiba, 277-8583, Japan.
6 Department of Astronomical Science, SOKENDAI (The Graduate University for
Advanced Studies), Osawa 2-21-1, Mitaka, Tokyo, 181-8588, Japan
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We use K-band multi-object near-infrared spectroscopy with Keck/MOSFIRE to
search for environmental imprints on the gas properties of 27 narrow-band
selected H$\alpha$ emitters (HAEs) across the three major clumps of the
assembling USS1558–003 protocluster at $z=2.53$. We target the H$\alpha$ and
[Nii]$\lambda$6584 emission lines to obtain star-formation rates (SFR) and
gas-phase oxygen abundances for our sources, confirming the membership of 23
objects. HAEs belonging to this protocluster display enhanced SFRs with
respect to the main sequence of star formation at the same cosmic epoch. This
effect is more prominent for low-mass galaxies ($\mathrm{\log
M_{*}/M_{\odot}<10.0}$), which may be experiencing a vigorous phase of mass
assembly shortly after they were formed. We compute the individual and stacked
gas-phase metallicities for our sources finding a metallicity deficit for low-
mass objects when compared against the field mass-metallicity relation and the
massive Spiderweb protocluster at $z=2.16$. These results suggest that HAEs
within USS1558–003 may be less evolved than those in the Spiderweb
protocluster. Finally, we explore the gas metallicity - gas fraction relation
for a small sample of five galaxies with CO(3-2) molecular gas information.
Assuming our objects are in equilibrium, we obtain a relatively wide range of
mass loading factors ($\mathrm{\lambda=0.5-2}$) matching field samples at the
cosmic noon but in contrast with our previous results in the Spiderweb
protocluster. We speculate that these discrepancies between protoclusters may
be (partly) driven by differences in their current dynamical and mass assembly
stages, hinting at the co-evolution of protoclusters and their galaxy
populations at $2<z<3$.

###### keywords:

galaxies: clusters: individual: USS1558-003 – galaxies: evolution – galaxies:
high-redshift – galaxies: abundances – galaxies: star formation – galaxies:
molecular gas.

††pubyear: 2022††pagerange: Enhanced star formation and metallicity deficit in
the USS 1558–003 forming protocluster at z=2.53–B

##  1 Introduction

In the framework of the hierarchical growth of large-scale structures in the
Universe, mass is assembled inhomogeneously along walls and filaments creating
a "cosmic web" (Bond et al. 1996). Galaxy clusters are formed at intersections
of such filaments and, in the local universe, they are dominated by old
quiescent massive early-type galaxies (with $>10$ Gyrs stellar ages)
indicating that the majority of their stellar components were formed in the
early universe ($z>2$, Thomas et al. 2010) when clusters were still being
assembled (i.e., protoclusters, see Overzier 2016 and Alberts & Noble 2022 for
a review). Thus, while clusters represent an important component of the total
stellar mass content of the universe (5-10%), protoclusters are thought to
vigorously contribute to the star formation rate density (SFRD) at high
redshifts (Chiang et al. 2017), e.g., 20-50% at $z>2$. Simulations predict
that cold gas streams along the filaments of the cosmic web supply the
required fuel to galaxies and drive their elevated SFRs at high-z (e.g., Kereš
et al. 2005; Dekel & Birnboim 2006; Genel et al. 2008). It is expected that
the channeling of cold gas streams towards the center of galaxies, the effect
of dynamical friction, and the onset of environmental effects contribute to
compressing/altering the gas distribution (Tacchella et al. 2016) of
protoclusters members, possibly triggering central starburst (Gómez-Guijarro
et al. 2019) and supporting their inside out mass growth (van Dokkum et al.
2015). Thus, galaxies populating high-redshift protoclusters are expected to
be sites of exceptionally vigorous (though short-lived) star formation (Hickox
et al. 2012). At times, this star formation may be detectable in the rest-
frame UV/optical, but during intense starburst ($\mathrm{SFR\approx
10^{2}-10^{3}\,M_{\odot}/yr}$) it can be heavily obscured by dust, emitting
mainly in the rest-frame infrared (Riechers et al. 2013). Therefore, unlike
galaxy clusters in the local universe which are dominated by their passive
population, young forming high-z protoclusters are observed as strong
overdensities of gas-rich dusty starbursts (e.g., Dannerbauer et al. 2014;
Popesso et al. 2015; Casey 2016; Casey et al. 2017; Chiang et al. 2017; Oteo
et al. 2018; Long et al. 2020; Zhang et al. 2022) which may be triggered by
mergers and are believed to be the predecessors of the red ellipticals that
dominate the clusters cores by $z=0$ (e.g., Ivison et al. 2013; Smail et al.
2014). It is for these reasons that the epoch between $2<z<3$ represents not
only the peak epoch of star-formation and black hole activity (Madau &
Dickinson 2014) but also a crucial stage in the evolutionary pathway of
protocluster galaxy populations, setting the (pre-)conditions for the start of
environmental effects both as a consequence of changes in the gas accretion
due to their rapid dark matter halo growth (Dekel et al. 2009; Kereš et al.
2009) as well as due to enhanced galaxy-galaxy interactions (e.g., Gottlöber
et al. 2001; Genel et al. 2014; Hine et al. 2016; Coogan et al. 2018; Watson
et al. 2019).

As such, numerous studies have been carried out during the last decade to
determine the interplay between the protocluster environment and the
accelerated evolution of the galaxy populations therein in terms of star-
formation activity, metal enrichment, and molecular gas content (see Alberts &
Noble 2022 for a review). However, a unified picture depicting how the cluster
assembly process affects the early evolution of galaxies is still missing,
with contradicting results between protoclusters at similar cosmic epochs.
Some works suggest the enhancement of star formation relative to the field in
high-z dense environments both as a result of higher gas accretion and merging
rate (Alberts et al. 2014; Shimakawa et al. 2018a; Lemaux et al. 2022; Monson
et al. 2021; Shi et al. 2023), which would contribute to an accelerated mass
assembly compared to their field counterparts. However, others report no such
differences (e.g. Toshikawa et al. 2014; Cucciati et al. 2014; Shi et al.
2021; Sattari et al. 2021; Koyama et al. 2021; Polletta et al. 2021; Pérez-
Martínez et al. 2023). A similar situation is found regarding the metal
enrichment of galaxies in protoclusters. Some authors claim that the early
development of an intracluster medium (ICM) in massive protoclusters (e.g.,
Willis et al. 2020; Tozzi et al. 2022b; Di Mascolo et al. 2023) would
contribute to detach infalling galaxies from the cosmic web, progressively
hampering their gas accretion and forcing them to enrich their ISM via
strangulation (Maier et al. 2019) and by recycling of already processed gas
due to the external pressure of an overdense IGM (e.g. Kulas et al. 2013;
Shimakawa et al. 2015; Pérez-Martínez et al. 2023). On the other hand, various
levels of metallicity deficiency have been reported in other protoclusters at
similar redshifts (Valentino et al. 2015; Chartab et al. 2021; Sattari et al.
2021). Paradoxically, the proposed physical scenario to explain such results
involves the powerful accretion of cold gas in very young and not massive
($\mathrm{\log\,M_{cl}/M_{\odot}<13.5}$) high-z protoclusters, which would
contribute to both fuel star formation and dilute the metal content with
respect to the general field. Conversely, some other studies have not observed
significant environmental dependence of the mass-metallicity relation during
this epoch (e.g. Tran et al. 2015; Kacprzak et al. 2015; Namiki et al. 2019).

Furthermore, the molecular gas properties of protocluster galaxies at $z>2$,
which are key to understanding the gas feeding and consumption processes
fueling star formation, have been traced by a significant number of studies
albeit over relatively small sample sizes (Dannerbauer et al. 2017; Coogan et
al. 2018; Wang et al. 2018; Tadaki et al. 2019; Zavala et al. 2019; Champagne
et al. 2021; Jin et al. 2021; Aoyama et al. 2022; Ikeda et al. 2022). In
Pérez-Martínez et al. (2023) the authors proposed a co-evolution scenario
where the total mass of different protoclusters could play a key role in the
physical properties of the galaxies inhabiting them due to the predicted
changes on their accretion mode (cold vs hot, Dekel et al. 2009) as a
consequence of the protocluster dark matter halo growth and early
virialization (Overzier et al. 2008; Toshikawa et al. 2014). However, this
scenario requires further observational support and a number of potential
biases may also play a role in explaining some of the aforementioned
contradictions. For example, the different selection criteria for the parent
samples of protocluster galaxies under scrutiny, the lack of statistics due to
small sample size, the use of a diverse set of star-formation, metal
enrichment, and molecular gas tracers, the difficulties in precisely defining
environmental variables in this forming structures, and the presence of AGNs
and the relevance of their fraction (e.g., Macuga et al. 2019; Monson et al.
2021; Tozzi et al. 2022a) in the recent past and future protocluster
evolution.

Among the many attempts to establish an unbiased and systematic census of
star-formation activities in high-z protoclusters, the MAHALO-Subaru project
(MApping H-Alpha and Lines of Oxygen with Subaru) led by Kodama et al. 2013
stands as one of the most successful and prolific environmental surveys over
the last decade. It has carried out a series of narrow-band observations
targeting H$\alpha$ and Oxygen emission lines tracing the star formation
activity within the cores of 10 overdensities at $0.5<z<2.5$ (e.g. Hayashi et
al. 2010, 2011, 2012, 2016; Koyama et al. 2010, 2013, 2014; Tanaka et al.
2011; Tadaki et al. 2012; Shimakawa et al. 2018a, b). In this work, we
spectroscopically follow up one of these structures, the USS 1558–003
protocluster at $z=2.53$ (hereafter USS1558), to investigate the effect of the
environment over the star formation activity, gas-phase metallicity, and
molecular gas properties of narrow-band selected H$\alpha$ emitters (HAEs).
USS1558 was first discovered as an overdensity of distant red galaxies (DRGs)
around the radio galaxy 4C-00.62 (Kajisawa et al. 2006; Kodama et al. 2007;
Galametz et al. 2012; Hayashi et al. 2012). The MAHALO-Deep NB imaging
observations targeting H$\alpha$ emission at $z=2.53$ identified $>100$
H$\alpha$ emitters (HAEs) in an area of $\mathrm{3\times 2\,pMpc^{2}}$ around
the radio galaxy (Hayashi et al. 2012, 2016; Shimakawa et al. 2018a; Suzuki et
al. 2019). The membership of a significant number of them have been
spectroscopically confirmed by rest-frame optical emission lines and ALMA
combined CO and dust continuum observations (Shimakawa et al. 2014, 2015;
Tadaki et al. 2019; Aoyama et al. 2022), with most sources being distributed
in a filamentary structure made of three dense clumps (Hayashi et al. 2012)
dominated by relatively low mass galaxies
($\mathrm{M_{*}<10^{10.5}M_{\odot}}$, Shimakawa et al. 2018a), yielding a
total protocluster mass of $\mathrm{M_{USS1558}\lesssim 10^{14}M_{\odot}}$
(Shimakawa et al. 2014). Given the group-like structure, and the lack of a
diffuse X-ray emission detection in this field (Macuga et al. 2019), USS1558
is considered to be an immature system at the stage of vigorous assembly and
thus the ideal test site to search for environmental effects in a rapidly
growing protocluster at the cosmic noon.

In this manuscript we will investigate the star-forming activity, metal
enrichment, and gas reservoir of HAEs within USS1558 and compare our results
with our recent findings in the Spiderweb protocluster (hereafter PKS1138),
which is a more mature coeval system (Pérez-Martínez et al. 2023), following
the same approach. The manuscript is structured in the following way: Sect. 2
describes our Keck/MOSFIRE spectroscopic campaign and the archival data
available within this field. Sect. 3 outlines the methods used to analyze the
star formation, metal enrichment, and gas reservoir of the USS1558
protocluster members as well as the parametrization we use to define the
environment. Sect. 4 and 5 present our main results and the discussion of
their physical interpretation in the context of galaxy evolution respectively.
Finally, Sect. 6 outlines the major conclusions of this study. Throughout this
article, we assume a Chabrier (2003) initial mass function (IMF), and adopt a
flat cosmology with $\Omega_{\Lambda}$=0.7, $\Omega_{m}$=0.3, and $H_{0}$=70
km s-1Mpc-1. All magnitudes quoted in this paper are in the AB system (Oke &
Gunn 1983).

##  2 Observations

###  2.1 Keck/MOSFIRE spectroscopy

We carried out multi-object spectroscopy observations of a sample of narrow-
band selected HAEs in the USS1558 protocluster (Hayashi et al. 2012, 2016;
Shimakawa et al. 2018a) to obtain H$\alpha$ and [Nii]$\lambda 6584$ emission
line fluxes and study the galaxies’ star-formation activity, gas-phase
metallicities and their relation with the surrounding environment. Our
spectroscopic targets encompass the three densest clumps across the large
scale structure of USS1558 (Fig. 1) and were selected to have narrow-band flux
excess above $\mathrm{F_{NB}\geq 1.5\times 10^{-17}}$ ergs s-1 cm-2 (Fig. 2).
The observations were carried out using the NIR multi-object spectrograph
MOSFIRE (McLean et al. 2010, 2012) installed at the Cassegrain focus of the
Keck I telescope in Mauna Kea, Hawaii (Program ID: S20A-075; PI: T. Kodama)
using $0.7\arcsec$ wide slits. We used a single mask configuration targetting
27 objects previously identified by Hayashi et al. (2012, 2016) and Shimakawa
et al. (2018a), plus one star to monitor the sky conditions during the night.
Out of these 27 targets, Shimakawa et al. (2018a) classified 20 of them as
confirmed HAEs (magenta circles in Fig. 1) and constitute our primary sample.
The remaining 7 objects were labeled as candidate HAEs by the same authors due
to the lack of color-color diagram (e.g.,
$\mathrm{r^{\prime}JK_{s}\,and\,Br^{\prime}K_{s}}$) or spectroscopic
confirmation. These targets were included in our mask design either as fillers
or as companion galaxies within the same slit assigned to one of our primary
targets. Finally, eight objects within our USS1558 sample have ALMA molecular
gas information available either through CO(3-2) emission (Tadaki et al. 2019)
or from dust continuum observations (Aoyama et al. 2022).

The observing run was carried out during the night of June 25th 2021 following
an ABA’B’ dithering pattern of individual exposures consisting of 180s each in
K-band ($19540-23970$ Å). This configuration yields a nominal spectral
resolution of R$\sim$3600 around the central wavelength of the grating
enabling us to resolve H$\alpha$ and [Nii]$\lambda 6584$ at $z=2.53$, and a
spatial sampling of $0.2\arcsec$ per pixel. We integrated for 174 min under
average $0.6-0.7\arcsec$ seeing conditions (FWHM) and airmass value of 1.5.
The spectra were reduced using the MOSFIRE Data Reduction Pipeline (MOSFIRE-
DRP, Steidel et al. 2014) following standard reduction procedures (i.e., bias
subtraction, flat-field normalization, sky subtraction, wavelength
calibration) producing a final 1D science and error spectra for each target
using the Horne (1986) algorithm. We carry out the flux calibration of our
sample by using the slit star (RA=16:01:19.26, DEC=-00:30:35.49) within our
mask. First, we identify the spectral type of the star based on the G-band
absolute magnitude and effective temperature ($\mathrm{t_{eff}}$) reported by
the Gaia DR3 survey (Gaia Collaboration et al. 2016, 2023). This yields
$\mathrm{t_{eff}=5096^{+35}_{-42}\,K}$ and $\mathrm{G\approx 6.8\,mag}$ which
correspond to a main sequence K1 star. The continuum emission of K stars is
affected by strong features in the optical regime, usually compromising their
utility as flux calibrators. However, these features are relatively weak in
the K-band. Thus, we retrieve a model of such spectral type (Pickles 1998) and
re-scale it to match the 2MASS NIR broad-band photometry of the star
(Skrutskie et al. 2006), thus modeling the intrinsic spectrum. By dividing the
modeled and observed stellar spectra we obtain the transmission function which
includes the conversion from raw units to physical flux, the slit loss
correction, and all instrumental and atmospheric effects present during our
observing run. Finally, we apply the same transmission function to all our
targets.

Figure 1: Distribution of narrow-band HAEs in the field of the USS1558
protocluster. Orange circles show the sample of Keck/MOSFIRE targets studied
in this work. Magenta small circles depict the parent sample of confirmed
narrow-band HAEs from Shimakawa et al. (2018a). Empty squares highlight a
small overlapping sample of ALMA CO(3-2) sources from Tadaki et al. (2019) and
dust continuum emitters from Aoyama et al. 2022. Blue crosses display the
position of X-ray emitters from Macuga et al. (2019). The big yellow cross
shows the position of the radio galaxy 4C-00.62 (Kajisawa et al. 2006). All
targets are overlaid over the HST/WFC3 F160W mosaic. Figure 2: Main diagram:
Stellar-mass and narrow-band flux excess properties of our 27 Keck/MOSFIRE
targets (orange circles) and their parent sample of 107 confirmed HAEs
(magenta circles) from Shimakawa et al. (2018a). Side panels: Distribution
(histograms) and median values (dashed lines) of the MOSFIRE and parent
samples. Colors follow the same scheme applied in the main diagram.

###  2.2 Archival Photometry

Over the last decade, the USS1558 protocluster field has been surveyed by
several optical to NIR photometric campaigns (Hayashi et al. 2012, 2016. These
observations include the Subaru/Suprime-Cam B, r’, z’ bands and the
Subaru/MOIRCS J, H, Ks bands and the NB2315 narrow-band filter (Program IDs:
S10B-028 and S15A-047, PI: T. Kodama). In addition, this field is almost
completely covered by a Hubble Space Telescope (HST) WFC3 program in H-band
(i.e, F160W; Program ID: GO-13291, PI: M. Hayashi). In this work, we make use
of the reprocessed mosaics in each band (Shimakawa et al. 2018a) to compute
the stellar mass and dust extinction of our main targets. Even though the
characteristics of these observations have been extensively described in
detail in previous publications (Hayashi et al. 2016; Shimakawa et al. 2018a),
we provide a brief summary of their main features in Table 1.

Table 1: Optical to NIR photometric bands available for the USS1558 protocluster field. Integration times, FWHM, pixel size, and galactic extinction reproduced from Shimakawa et al. (2018a). Ellipsis are placed to avoid repetitions in the instrument and reference columns. Instrument | Filter | Int. Time | FWHM | Pixel-size | $\mathrm{A_{\lambda}}$ | Reference
---|---|---|---|---|---|---
|  | (min) | ($\arcsec$) | ($\arcsec$) | (mag) |
Suprime-Cam/Subaru | B | 80 | 0.70 | 0.200 | 0.55 | Hayashi et al. 2012
… | r’ | 90 | 0.67 | 0.200 | 0.35 | …
… | z’ | 55 | 0.67 | 0.200 | 0.19 | …
MOIRCS/Subaru | J | 191 | 0.67 | 0.116 | 0.11 | Hayashi et al. 2012, 2016
… | H | 45 | 0.67 | 0.116 | 0.07 | …
… | Ks | 207 | 0.67 | 0.116 | 0.05 | …
… | NB2315 | 583 | 0.67 | 0.116 | 0.05 | …
WFC3/HST | F160W | 87 | 0.21 | 0.130 | 0.08 | …

##  3 Methods

###  3.1 Emission line fitting

Our Keck/MOSFIRE program aims at obtaining information from the H$\alpha$ and
[Nii]$\lambda 6584$ emission lines for HAEs at $z\approx 2.5$. We will carry
out the emission line fitting by making use of a self-written code written in
python (Astropy library, Astropy Collaboration et al. 2013, 2018) which was
previously utilized to fit the same spectral features in HAEs belonging to
PKS1138 at similar redshift (Pérez-Martínez et al. 2023). We present a brief
summary of its most important features in the following paragraph.

First, we visually inspect the flux-calibrated spectrum of each HAE searching
for emission lines within the width of the NB2315 narrow-band filter (i.e.,
$\sim 23000-23300$ Å). Our sample is initially selected to be made of 27
confirmed and candidate HAEs at $z\approx 2.5$ from Shimakawa et al. (2018a),
based both on narrow-band excess and color-color selection throughout the
r’JKs and Br’Ks diagrams, which separate interlopers at lower and higher
redshift respectively. Only two objects (IDs 9 and 84) displayed no detectable
emission within the inspected wavelength range. ID 84 was classified as a non-
emitter by the parent sample and it is a filler in our spectroscopic campaign.
On the other hand ID 9 was identified as HAE candidate by Shimakawa et al.
(2018a) albeit it was not possible to discard it as a background galaxy due to
its dim colors in the Br’Ks diagram. However, no emission could be detected
for this object. In addition, two [Oiii]$\lambda 5007$ emitters at $z\approx
3.6$ were spectroscopically confirmed in our observing run (IDs 25 and 151).
These objects were classified as HAE candidates in Shimakawa et al. (2018a)
due to their narrow-band flux excess although their interloper nature could
not be discarded for the same reasons applied to ID 9. This represents
contamination of $\sim 12\%$ within the emitting candidates (i.e. 3 out of 26
objects) or a $\sim 88\%$ success rate in the spectroscopic identification of
narrow-band selected emitters at $z\approx 2.5$. This rate is in line with
previous narrow-band studies suggesting a contamination rate by fore- and
background sources of $\sim 10\%$ (e.g., Sobral et al. 2013, Pérez-Martínez et
al. 2023). These four objects have been removed from subsequent analyses
yielding a final sample composed of 23 confirmed HAEs.

Once an emission line is identified, we proceed to fit and subtract a local
continuum consisting of several windows free from skyline contamination and
encompassing a few hundred angstroms left and right of the detected line.
Then, we perform a simultaneous triple Gaussian fit for the H$\alpha$ line and
[Nii]$\lambda\lambda 6548,6584$ doublet while tying the center of the [Nii]
lines to their expected value based on the H$\alpha$ fit and fixing the flux
ratio $F_{\lambda 6584}/F_{\lambda 6548}=3$ (Storey & Zeippen 2000).
Furthermore, we also couple the H$\alpha$ and [Nii] line widths since they
originate in the same star-forming region while their amplitude remains a free
parameter. The radio galaxy (ID 138) displays an extremely broad H$\alpha$
profile ($\sigma>1000$ km/s) characteristic of type-1 AGN activity and it is
the only X-ray emitter from Macuga et al. (2019) within our sample. This
object is flagged in all subsequent analyses due to the difficulty to separate
its AGN and star-forming components. Another target (ID 38) also displays a
broad emission line component ($\sigma\approx 700$ km/s) suggesting the
presence of an AGN in spite of not being detected in X-rays. In these two
cases, we use an additional free gaussian component to account for the broad
H$\alpha$ emission in addition to the three narrower H$\alpha$ \+
[Nii]$\lambda\lambda 6548,6584$ components (see Fig. 3).

In total, we spectroscopically confirm the protocluster membership of 23
H$\alpha$ emitters (including the two broad-component objects) with 7 of them
being new sources unknown to previous spectroscopic studies in this
protocluster (Shimakawa et al. 2014, 2015; Tadaki et al. 2019). Finally, we
estimate the uncertainties over the fitting procedure by using the Montecarlo
approach. The fitting procedure outlined above is repeated 1000 times allowing
for random gaussian variations on every spectral data point with a maximum
amplitude equal to the value found in the 1D noise spectra. The mean fitted
values are then used to compute the total flux for the H$\alpha$ and [Nii]
emission lines. We use the standard deviation over the 1000 realizations as
the formal uncertainty of our measurements. Finally, we consider a line to be
detected if the ratio between the total flux and the flux error measured in
the way described above is higher than two. This constraint applies both to
H$\alpha$ and [Nii]. In total, we identify 10 dual H$\alpha$ \+ [Nii]$\lambda
6584$ detections at $>2\sigma$ level. Flux upper limits can be derived for 3
extra cases while the remaining 10 objects without [Nii] estimates will be
only used for the stacking analysis. Figure 3 displays the spectral fitting
results for every object within our sample.

###  3.2 Stellar masses and dust extinction

The USS1558 protocluster field has extensive optical to NIR photometry (see
Table 1) that can be used to obtain reliable stellar mass values for our
targets via SED fitting. To this end, we first homogenized the pixel size and
FWHM of our available bands to that of the narrow-band filter. Then, we use
the NB2315 image for source detection while running SExtractor (Bertin &
Arnouts 1996) in dual-image mode thus obtaining the observed magnitudes
(MAG_AUTO) for each object in every other band available. This approach
ensures that the targets’ fluxes are measured consistently over the same area
at different wavelengths. We carry out the SED fitting over the multi-band
photometric measurements (excluding NB2315) we have gathered for every object
with the Code Investigating GALaxy Emission (CIGALE, Boquien et al. 2019).
This code incorporates the stellar, nebular, and dust attenuation and re-
emission into a grid of models while conserving the energy balance between its
different components. CIGALE then applies Bayesian statistics to compute the
physical properties of each object based on the probability distribution
function (PDF) of models with respect to the best fit. Thus, the physical
properties are statistically derived as the likelihood-weighted mean of the
PDF and standard deviations represent the uncertainties taking into account
both the goodness of the fit as well as the intrinsic degeneracies between
physical parameters.

CIGALE offers great flexibility to customize the grid of models used during
the SED fitting through its different modules. In this work, we assume the
stellar population synthesis models of Bruzual & Charlot (Bruzual & Charlot
2003) applied to an exponentially delayed star formation history with the
following functional form:

$\mathrm{SFR(t)\propto\frac{t}{\tau^{2}}\times\exp{(-t/\tau)}}$ (1)

with e-folding times ($\tau$) ranging between 0.1 and 8 Gyr, stellar
population ages constraint to be younger than the age of the Universe at
$z=2.5$ (i.e., $\sim 2.5$ Gyr), and allowing for the possibility of a recent
minor star-forming burst accounting for up to 1, 5, or 10% of the mass
fraction with age not older than 300 Myrs. The reason behind this choice lies
in the higher interaction rate expected during the formation and maturing
phases of young protoclusters, which could increase the frequency of starburst
events within their members. In addition, we assume a Chabrier IMF (Chabrier
2003) and subsolar metallicity (i.e $Z=0.004$) for the stellar component. We
constrain the ionization parameter ($U$) between $-2.4<\log(U)<-2.8$ for the
nebular emission, which encompasses the typical values for star-forming
galaxies at $z\sim 2$ (Cullen et al. 2016). Finally, the dust extinction is
modeled throughout Calzetti’s attenuation law (Calzetti et al. 2000) with
reddening values ranging $\mathrm{E(B-V)=0-1\,mag}$ in steps of 0.1 mag. Most
objects display reasonable fits with average reduced $\chi^{2}=1.7$ within a
range of $0.2\leq\chi^{2}\leq 7.9$. The average accuracy of the derived
stellar masses is 0.2 dex. All fitted SEDs as well as their reduced $\chi^{2}$
values are shown in the Appendix. This combination of parameters was
previously used by Pérez-Martínez et al. (2023) to describe a sample of HAEs
in PKS1138 at $z=2.16$, except for the maximum age of stellar populations
which matched the age of the universe at that cosmic epoch (i.e., 3 Gyrs). We
decided to follow exactly the same approach for consistency in our
environmental analysis (Sect. 4).

Figure 3: Keck/MOSFIRE 1D reduced spectra and emission line fitting modeling.
We use a black solid line for the aperture extracted signal spectrum, a red
solid line for the noise, and an orange solid line for the H$\alpha$ and [Nii]
fit. The 23 spectroscopically confirmed protocluster objects are ordered in
four columns following the ID numbering given in Table 2.

Figure 4: continued

###  3.3 Star-formation activity

Our Keck/MOSFIRE spectroscopic campaign allows us to trace the H$\alpha$
emission line of protocluster members at $z\approx 2.53$. We follow a standard
approach to compute the star-formation rate (SFR) of our sources by applying
the calibration developed by Kennicutt (1998) modified for a Chabrier IMF (Eq.
2). This calibration has proven to be one of the most reliable both at local
and high redshift (e.g. Moustakas et al. 2006, Wisnioski et al. 2019):

$\mathrm{SFR(H\alpha)\ [M_{\odot}/{yr}]=4.65\times 10^{-42}L(H\alpha)\ [ergs\
s^{-1}]}$ (2)

where $\mathrm{L(H\alpha)}$ is the luminosity of the H$\alpha$ emission-line.
We estimate the value of this quantity by measuring the H$\alpha$
spectroscopic fluxes of our targets and assuming a Calzetti’s extinction law
($\mathrm{R_{v}}$=4.05, Calzetti et al. 2000) to account for the dust
attenuation. SED extinction ($\mathrm{A_{v}}$) values are used to correct for
the diffuse dust attenuation in the galaxy’s continuum following:
$\mathrm{A_{cont}=0.82A_{v,SED}}$ (Wuyts et al. 2013; Wisnioski et al. 2019).
However, the nebular contribution produced in the active star-forming regions
of the galaxy remains unaccounted for at this stage. To tackle this problem,
Wuyts et al. (2013) add an extra extinction term ($\mathrm{A_{extra}}$) that
can be parametrized as $\mathrm{A_{extra}=0.9A_{cont}-0.15A_{cont}^{2}}$ and
is in good agreement with the previous extinction estimates made by Calzetti
et al. (2000) in the local universe. Thus, the total extinction applied to the
measured H$\alpha$ fluxes is $\mathrm{A(H\alpha)=A_{cont}+A_{extra}}$. This
method is also applied by Pérez-Martínez et al. (2023) in PKS1138 and by the
KMOS3D team in Wisnioski et al. (2019), which we will use as our main field
comparison sample in Sect. 4. Two objects (IDs 38 and 138) display very broad
H$\alpha$ line widths suggesting the presence of type 1 AGNs. In these two
cases, the SFR values were computed by using only the H$\alpha$ narrow
component in Eq. 2. The final SFR and reddening values of our protocluster
sample can be found at the end of this work in Table 2.

###  3.4 Gas phase metallicities

The ISM metal enrichment of galaxies is frequently computed as a function of
the Oxygen to Hydrogen ratio. However, the difficulties to obtain a
simultaneous and direct measurement of auroral and nebular Oxygen line
intensities, such as [Oiii]$\lambda$4363/$\lambda$5007 Oxygen species in the
optical rest-frame (i.e., direct or $t_{e}$ method, Aller 1984; Stasińska
2005; Izotov et al. 2006) led to the development of empirical calibrations
that uses either a reduced set of these Oxygen lines or different species such
as Nitrogen and Sulfur to indirectly trace the Oxygen enrichment based on
stellar evolution physics (see Kewley & Ellison 2008 for a review of different
methods). At $z>1$ the access to these diagnostics shifts to the NIR and thus
empirical calibrations are the most common tracer of metallicities due to the
difficulty to obtain multi-band spectroscopy. In this work, we apply the N2
calibration developed by Pettini & Pagel (2004) which involves the
[Nii]$\lambda$6584/H$\alpha$ ratio:

$\mathrm{12+log(O/H)=8.90+0.57\times N2}$ (3)

where N2 is equivalent to $\log$(F[Nii]/F(H$\alpha$)). This approach has been
successfully applied for field galaxies up to $z\sim 3$ (Erb et al. 2006,
Wuyts et al. 2016, Sanders et al. 2021) albeit it was calibrated locally.
However, the accuracy of its absolute values at high redshift is still under
debate (Steidel et al. 2014) with an estimated systematic scatter of $<0.1$
dex (Curti et al. 2017). The aim of this work, however, is to compare the
relative metal enrichment of USS1558 protocluster members with those belonging
to PKS1138 (Pérez-Martínez et al. 2023) and the coeval field. Thus calibration
uncertainties do not play a role in our analysis as long as we consistently
apply the same empirical calibration at a fixed cosmic time. Furthermore, we
consider the effect of AGN contamination by splitting our sample in objects
below and above $\log$([Nii]/H$\alpha$)$\geq-0.35$. This threshold effectively
separates the purely star-forming from the composite and AGN regions in the
BPT diagram (Baldwin et al. 1981) even at relatively low [Oiii]/H$\beta$
ratios (e.g. $\log$([Oiii]/H$\beta$)$\,\leq-0.2$, Agostino et al. 2021). Thus,
we use $\log$([Nii]/H$\alpha$)$\geq-0.35$ as an upper limit beyond which the
ionization source of most objects is either composite or dominated by the AGN
contribution and label such objects as AGN candidates in our subsequent
analyses.

Only 10 out of the 23 inspected objects yielded [Nii]$\lambda$6584 fluxes
above the $2\sigma$ level and thus, we resort to the stacking analysis
(excluding AGN candidates) to trace the mean metal enrichment of our sample in
two mass bins ($\mathrm{9.3<\log M_{*}/M_{\odot}<10.0\,and\,10.0<\log
M_{*}/M_{\odot}<10.8}$). Only three galaxies have stellar masses above this
limit and are thus excluded from the stacking analysis: IDs 38 and 138 (radio
galaxy) which display broad emission line components and ID 59 which lies just
above the limit with $\mathrm{\log M_{*}/M_{\odot}=10.88}$. The spectral
stacking is performed following the approach outlined in Shimakawa et al.
(2015):

$\mathrm{F_{stack}=\sum_{i}^{n}\frac{F_{i}(\lambda)}{\sigma_{i}(\lambda)^{2}}\Bigg{/}\sum_{i}^{n}\frac{1}{\sigma_{i}(\lambda)^{2}}}$
(4)

where $F_{i}(\lambda)$ is the flux density of an individual spectrum and
$\sigma_{i}(\lambda)$ is the noise as a function of wavelength. Within a given
bin, the galaxies’ spectrum is summed up using a median sigma clipping
algorithm to reduce the contamination by sky residuals. In addition, we use
bootstrapping, thus resampling the number of spectra within our stellar mass
bins over a thousand realizations, to limit the impact of emission line flux
variability between individual sources during the stacking process. After
this, we take the mean bootstrapped spectrum as the final one for each bin,
and one standard deviation as the new spectral error. These two quantities are
used to fit and measure the N2 ratio following the same procedure applied to
every individual spectrum (see Sect. 3.1). Finally, based on the values
reported in Table 2 we estimate the median uncertainties for our gas-phase
abundances to be of the order of 0.10 dex for the individual measurements
across our stellar mas range, while we report $<0.10$ dex for the stacking
analysis measurements after bootstrapping. Figure 5 displays the stacked
spectrum for each bin and their best fit.

Figure 5: Mean bootstrapped rest-frame spectra (black), 1$\sigma$ confidence
interval (grey), and fit around the H$\alpha$ and
[Nii]$\mathrm{\lambda\lambda}$6548, 6584 emission lines (orange) for the two
inspected stellar-mass bins.

###  3.5 Molecular gas masses

USS1558 has been subject to deep multiwavelength observations including the
submillimeter/radio regime with ALMA (e.g., CO(3-2) from Tadaki et al. 2019
and dust continuum at $\sim 1.1$ mm from Aoyama et al. 2022). In this work, we
will make use CO(3-2) measurements to estimate the molecular gas mass of a
small subsample of our targets. In order to minimize the systematics between
different molecular gas tracers we will focus solely on the available CO(3-2)
measurements published by Tadaki et al. (2019). In total, we share 6
overlapping targets with 4 of them being detected in CO at more than $5\sigma$
level and two upper limits. In order to convert the CO(3-2) luminosity,
$L^{\prime}_{\mathrm{CO(3-2)}}$, to a molecular gas mass estimate we assume a
conversion factor, $\alpha_{\mathrm{CO(3-2)}}$, between the CO(3-2) and the
CO(1-0) luminosity, which better trace the amount of molecular gas from
optically thick virialized clouds (Dickman et al. 1986, Solomon et al. 1987):

$M_{\mathrm{mol,CO}}=\alpha_{\mathrm{CO(3-2)}}\times
L^{\prime}_{\mathrm{CO(3-2)}}$ (5)

$\alpha_{\mathrm{CO(3-2)}}=\alpha_{\mathrm{CO(1-0)}}\times\frac{1}{r_{\mathrm{31}}}\times\mathrm{f_{corr}}$
(6)

However, the estimates of $r_{\mathrm{31}}$ for high-z star-forming galaxies
reported in the literature show large variations with some works suggesting
values close to those reported in the local universe ($r_{\mathrm{31}}\approx
0.5$, Genzel et al. 2012; Aravena et al. 2014; Daddi et al. 2015), while
others suggest higher values as a consequence of the expected high star
formation activity at this cosmic epoch ($r_{\mathrm{31}}\approx 0.8-0.9$,
Sharon et al. 2016; Riechers et al. 2020). Interestingly, Aoyama et al. (2022)
found that the molecular gas masses computed for USS1558 objects both from
CO(3-2) and from dust continuum observations achieve a higher degree of
agreement when the Riechers et al. (2020) prescription
($r_{\mathrm{31}}\approx 0.9\pm 0.14$) is assumed. However, we will assume
$r_{\mathrm{31}}\approx 0.56\pm 0.14$ (Genzel et al. 2012) for our own
molecular gas computation in order to be consistent with the calibrations of
our field comparison samples (e.g., Sanders et al. 2023). In addition,
$\alpha_{\mathrm{CO(1-0)}}$ is found to be approximately constant for nearby
galaxies with solar gas-phase metallicities
($\alpha_{\mathrm{CO(1-0)}}=4.36\pm 0.90$, Bolatto et al. 2013). At lower
metallicities, the conversion factor inversely correlates with metallicity.
Therefore, we compute our molecular gas masses by assuming the metallicity
dependent conversion factor, $\mathrm{f_{corr}}$, outlined in Genzel et al.
(2015) and later revisited by Tacconi et al. (2018):

$\mathrm{f_{corr}=\sqrt{0.67\times\exp{(0.36\times 10^{-(Z_{gas}-8.67)}\times
10^{-1.27\times(Z_{gas}-8.67)})}}}$ (7)

where $\mathrm{Z_{gas}=12+log(O/H)}$ assuming the Pettini & Pagel (2004)
metallicity calibration. This conversion factor is based on the geometric sum
of the metallicity corrections proposed by Genzel et al. (2012) and Bolatto et
al. (2013). However, both methods strongly diverge in the low metallicity
regime. Thus, we constrain the range of application of this prescription to
galaxies with $\mathrm{12+log(O/H)}>8.44$, which corresponds to a maximum
offset between methods of 0.2 dex. Given the distribution of our galaxies in
the mass-metallicity relation (see Sect. 4.2), this approximation allows us to
constrain the molecular gas fraction
($\mathrm{f_{gas}=M_{Mol}/(M_{*}+M_{Mol})}$) of 6 targets with CO(3-2)
emission although only 5 of them have individual metallicity estimates in this
work.

###  3.6 Environment quantification

The accurate quantification of the environment around a given object is a
recurrent problem in galaxy evolution studies. Two main paths have been
developed to answer this question although any of them can only offer an
incomplete picture due to projection effects and the difficulties to trace all
galaxy populations within a given region. First, global environmental
indicators such as clustercentric distance or phase-space variables require
the pre-identification and physical characterization (in terms of $M_{200}$,
$R_{200}$, and $\sigma_{cl}$, Carlberg et al. 1997) of strong overdensities
within the field of view studied. This method is usually applied to massive
virialized clusters but it is not appropriate when the structure under
scrutiny is made up of several clumps or groups lacking virialization, as is
the case of USS1558.

In addition, the environment can be measured locally, as a number density of
objects within a given projected area (e.g. Dressler 1980). This is a very
common environmental tracer because it does not require the pre-identification
of any kind of overdensity (group, cluster, or protocluster) in a given area
to be applied, and its accuracy is only limited by the number and type of
objects identified within a sufficiently narrow redshift range. Its main
weakness resides in the simultaneous identification of different galaxy
populations (e.g., star-forming vs passive) at a given cosmic epoch so that we
can obtain a complete picture of the density field. Protoclusters such as
USS1558 at $z=2.53$ are overwhelmingly populated by star-forming galaxies
(e.g., Overzier 2016; Chiang et al. 2017; Remus et al. 2023; Alberts & Noble
2022) which are easily identified by their emission lines using deep NB
surveys such as the MAHALO-Subaru project (Kodama et al. 2013). This approach,
however, may miss a population of heavily obscured star-forming galaxies whose
main emission is concentrated in the far infrared and (sub-)millimeter. In the
case of USS1558, this has been ruled out by the ALMA CO(3-2) and dust
continuum studies of Tadaki et al. (2019) and Aoyama et al. (2022)
respectively, who found that most ALMA sources are also identified as narrow-
band HAEs. Similarly, the NB approach misses potential protocluster members
without detectable emission lines (i.e., quenched objects). Even though this
population is expected to be a minority within protoclusters, previous
observational works in this field have identified an overdensity of distant
red objects (DRGs) close to the radio galaxy and to the main clump in the
bottom right corner of Fig. 1 using color diagnostics (Kodama et al. 2007;
Galametz et al. 2012; Hayashi et al. 2012). This means that the distribution
of DRGs is largely consistent with the overdensities depicted by the HAEs
alone. It is for these reasons that we decided to use the catalog of
Subaru/MOIRCS narrow-band confirmed HAEs in USS1558 published by Shimakawa et
al. (2018a) to compute the local density of every object. This catalog
contains 107 sources and represents the parent sample of our spectroscopic
campaign. The spectroscopic confirmation of narrow-band selected HAES in this
and previous works related to MAHALO-Subaru yields a $>90\%$ success rate
(e.g., Shimakawa et al. 2014, 2015; Pérez-Martínez et al. 2023), which allow
us to assume that all remaining HAEs without spectroscopic confirmation have a
high chance of belonging to USS1558. The position of every HAE is projected
into a plane where distances between objects are measured by their sky angular
separation and transformed to the physical scale using a fixed cosmology with
the scale factor ($a$) corresponding with the redshift of the cluster (e.g.
$a=8.050$ kpc/″at $z=2.53$). This way we define a number surface density in
the following way:

$\Sigma_{N}=\frac{N}{\pi r^{2}_{N-1}}$ (8)

For consistency with previous works in this protocluster (Shimakawa et al.
2018a), we will use $\Sigma_{5}$, i.e. the local density defined by the
minimum radius enclosing five neighboring galaxies. The determination of
galaxy positions is carried out during the source detection (Sect. 3.2) by
fitting a 2D surface brightness profile to each object. Typical uncertainties
are of $\pm 1$ pixel, which results on
$\mathrm{\sigma_{\Sigma_{5}}<0.01\,Mpc^{-2}}$. The values of $\Sigma_{5}$ for
each member of our sample can be found in Table 2. This choice enables us to
trace the local density gradient inside each of the three densest clumps as
well as identify additional small compact galaxy groups representing local
density peaks outside the main structures.

Figure 6: Left: Star-forming main sequence diagram. Orange circles show the
distribution of our Keck/MOSFIRE sample in USS1558. Blue circles display
protocluster HAEs within PKS1138 (Pérez-Martínez et al. 2023). Empty circles
depict the field comparison sample from the KMOS3D survey (Wisnioski et al.
2019). This dataset consists of 192 field galaxies at a similar mean redshift
to the USS1558 sample. The black solid line represents the star-forming main
sequence parametrized for $z=2.2$ (Speagle et al. 2014), while the grey shaded
region marks the 3$\mathrm{\sigma}$ scatter around it. Right: Cumulative
distribution function of the offsets with respect to the main sequence for the
three inspected samples after matching their minimum SFR to
$\mathrm{25M_{\odot}/yr}$

. Vertical dashed lines display the median offset for each dataset. The colors
remain the same as in the left-hand panel.

Figure 7: Residuals from the main sequence of galaxies as a function of the
local number density of objects, which is defined as the minimum area to
enclose five neighboring galaxies. The horizontal solid line and grey area
depict the position and 3$\mathrm{\sigma}$ scatter of the main sequence
(Speagle et al. 2014). Vertical dashed lines separate the three density
regimes outlined in Sect. 3.6. The radio galaxy (cross) and AGN candidates
(empty circles) are flagged using different symbols.

##  4 Results

###  4.1 Star formation in the assembling USS1558 protocluster

In this section, we trace the star formation activity of our sample of HAEs
belonging to the USS1558 protocluster and compare our results with previous
studies in massive protoclusters (Pérez-Martínez et al. 2023) and the coeval
field (Speagle et al. 2014; Wisnioski et al. 2019). Figure 6 (left) shows the
distribution of our targets within the SFR-$\mathrm{M_{*}}$ and along the so-
called "Main Sequence" of star formation at $z=2.53$. USS1558 galaxies are
preferentially located above the main sequence, with at least one-third of the
sample displaying an SFR enhancement of $\mathrm{\sim 0.3\,dex}$. This effect
becomes ever clearer when inspecting the low-mass end of the sample. Eight out
of the nine objects at $\mathrm{\log M_{*}/M_{\odot}<10.0}$ lie above the
$3\sigma$ scatter of the main sequence suggesting that low-mass galaxies are
going through a rapid phase of mass build-up. This effect was previously
reported by Hayashi et al. (2016) who analyzed a larger sample of HAEs in this
very same structure relying only on narrow-band photometry for computing SFRs.
On the other hand, a recent study by Pérez-Martínez et al. (2023) (blue in
Fig. 6) found that HAEs belonging to the massive PKS1138 protocluster at
$z=2.16$ agree well with the main sequence prescription parametrized for the
protocluster redshift.

However, Fig. 6 also shows a clear mismatch between the minimum typical SFR
between USS1558 and PKS1138. In fact, $>90\%$ of the USS1558 sample lies at
$\mathrm{\log SFR>1.4}$ (i.e., $\mathrm{SFR>25M_{\odot}/yr}$) while PKS1138
objects trace the star formation activity down to
$\mathrm{SFR>10M_{\odot}/yr}$. This may be the result of different flux cuts
applied over their respective narrow-band parent samples coupled with the
effects of spectroscopic sampling during our observations. For these reasons,
we decide to compute the cumulative distribution function of the offsets with
respect to the main sequence (i.e, $\Delta\mathrm{MS=SFR-SFR_{MS}}$) for the
three samples previously discussed after imposing an
$\mathrm{SFR>25M_{\odot}/yr}$ cut on them (right panel of Fig. 6) Our results
show that the USS1558 (orange) distribution is shifted towards higher offsets
in comparison with both the PKS1138 (blue) and the KMOS3D (black) samples,
which are consistent with their respective main sequences. In the case of
PKS1138, we have computed its $\Delta\mathrm{MS}$ by parametrizing the main
sequence of Speagle et al. (2014) to $z=2.16$, thus avoiding possible biases
due to the expected evolution of star formation with cosmic time. The median
values for each sample are represented by vertical dashed lines confirming the
SFR enhancement of the USS1558 sample ($\mathrm{\Delta\mathrm{MS}\approx
0.26\pm 0.07\,dex}$). In addition, we have performed a Kolmogorov-Smirnov test
between our samples to investigate if these differences are statistically
significant. We choose $\mathrm{p<0.05}$ as the threshold to test if a given
distribution is significantly different with respect to the reference sample,
which in this case is USS1558. The results of the KS-test suggest that the
differences found between USS558 and PKS1138 are statistically significant
($\mathrm{p=2\times 10^{-3}}$) as well as those with respect to the KMOS3D
sample ($\mathrm{p=4\times 10^{-5}}$). On the other hand, the KMOS3D sample
and PKS1138 are statistically indistinguishable ($\mathrm{p=0.502}$). These
results suggest that HAEs from different protoclusters at approximately the
same cosmic epoch may be experiencing different phases of their stellar-mass
build-up which could potentially be related to the evolutionary stage of the
large-scale structure they belong to.

Finally, we investigate the influence of the protocluster environment over the
star formation activity of USS1558 HAEs. We decide to trace the local density
across the protocluster structure by computing the minimum area to enclose
five neighboring galaxies (i.e., $\Sigma_{5}$) from the position of each of
our targets. In Figure 7 we show the distribution of main sequence offsets
(i.e., $\Delta\mathrm{MS}$) as a function of $\Sigma_{5}$ and compute the
median offset within each density bin. The SFR enhancement detected for the
USS1558 sample is approximately constant ($\mathrm{\approx 0.25\,dex}$) across
different density regimes. However, given the limited size of our sample, we
can not discard that particularly overdense regions within the protocluster
play a role in boosting star formation, as suggested by Shimakawa et al.
(2018a).

###  4.2 Gas-phase metallicities

Figure 8: Mass-metallicity relation (MZR) diagrams. Left: Individual gas-phase
metallicity measurements for USS1558 (this work) and PKS1138 (Pérez-Martínez
et al. 2023) displayed by orange and blue circles respectively. Right: Stacked
metallicity results for USS1558 and PKS1138. Horizontal error bars display the
stellar mass standard deviation within each bin. In both panels, the solid
line depicts the field MZR using a second-order polynomial fit over the
combined results of the Erb et al. (2006) sample, the KMOS3D sample of Wuyts
et al. (2016) and the MOSDEF sample of Sanders et al. (2021) at $z\sim 2.3$.
The grey area shows the mean metallicity uncertainty for the samples used to
define the field MZR at $z\sim 2.3$. The dashed line marks the position of the
local MZR (Kewley & Ellison 2008) assuming the Pettini & Pagel (2004)
metallicity calibration but adjusted to the Chabrier (2003) IMF. Figure 9:
Main panel: Offsets from the field MZR as a function of local density values,
which is defined as the minimum area to enclose five neighboring galaxies. The
horizontal dashed line shows the position of the field MZR from Fig. 8.
Vertical dashed lines separate the density regimes outlined in Sect. 3.6.
Upper panel: Local density cumulative distribution functions for the [Nii]
detected (orange) and non-detected (black) samples. Dashed vertical lines
display the median values for each sample.

This section investigates the mass-metallicity relation (MZR) for HAEs
belonging to USS1558 and the impact of the environment on their ISM
enrichment. We derive gas-phase metallicities from the H$\alpha$ and
[Nii]$\lambda 6584$ emission lines based on the N2 calibration developed by
Pettini & Pagel (2004). We extract individual metallicity measurements for 10
sources (plus 3 upper limits) which are represented by orange circles in
Figure 8 (left). We compare our results with those obtained in PKS1138 by
Pérez-Martínez et al. (2023) (blue circles) and with a coeval field MZR
constructed by combining the $2<z<3$ samples of Erb et al. (2006), Wuyts et
al. (2016) (KMOS3D) and Sanders et al. (2021) (MOSDEF) as it is explained in
Sect. 3.4. Prior to the comparison, we have homogenized all samples to the
same IMF (Chabrier 2003) and the same metallicity diagnostic (N2 following
Sect. 3.4) using the empirical calibration transformations of Curti et al.
(2017) when needed.

Our results suggest that most of the individual metallicity measurements
performed for the USS1558 sample lie on or above the field MZR, albeit
displaying lower metallicities than the PKS1138 counterparts. However, the
[Nii] emission line was not detected in approximately half of the sample thus
biasing any comparison with the field. Thus our individual measurements only
trace the metal-rich end of the distribution of HAEs and the lack of metal-
poor galaxies may be just a reflection of our [Nii] detection limit. Thus, we
resort to the stacking analysis to recover all the [Nii] non-detections
objects and present its results in the right diagram of Figure 8. Both USS1558
and PKS1138 stacked measurements are compatible with each other at
$\mathrm{10.0<\log M_{*}/M_{\odot}<10.8}$ displaying the following offsets
with respect to the field relation: $\mathrm{\Delta MZR(USS1558)=0.02\pm
0.07\,dex}$ and $\mathrm{\Delta MZR(PKS1138)=0.06\pm 0.03\,dex}$. However, in
the low-mass regime, we find a marginally significant offset between these two
samples with USS1558 being more metal-poor compared to PKS1138:
$\mathrm{\Delta MZR(USS1558)=-0.14\pm 0.08\,dex}$ and $\mathrm{\Delta
MZR(PKS1138)=0.00\pm 0.04\,dex}$. This result and the SFR enhancement detected
in Fig. 6 within the same mass regime are qualitatively consistent with the
expectations of the fundamental metallicity relation (FMR, Mannucci et al.
2010) which predicts that the star-forming activity and the metal enrichment
are anti-correlated.

We note, however, that previous work in the same field by part of our team
(Shimakawa et al. 2015) reported a $\mathrm{\sim 0.1dex}$ metallicity
enhancement with respect to the field across a similar mass regime even when
accounting for the IMF differences. Several factors may explain this
discrepancy: First, the lower sensitivity and spectral resolution ($R\sim
500$) of their observations with Subaru/MOIRCS hinder the precision of their
measurements, yielding only metallicity upper limits for stacked results in
the mid-to-low mass regime ($\mathrm{\log M_{*}/M_{\odot}<10.5}$). In
addition, they derive the stellar mass of their objects relying on the
relationship between $J-K_{s}$ color and the $M_{*}/L_{K_{s}}$ using the
stellar population synthesis models of Kodama et al. (1998, 1999). This
approach systematically underestimates the stellar masses by $\mathrm{\sim
0.1dex}$ when compared with the SED fitting carried out in this work, although
this difference increases towards lower mass objects. A possible explanation
for this effect is that this approach becomes less accurate for fainter
objects in these bands (i.e. lower mass galaxies at a fixed redshift), while
Ks-band and $J-K_{s}$ color remain a suitable proxy to estimate the stellar
mass of massive galaxies at $z=2.5$. Finally, the field MZR in Shimakawa et
al. (2015) is based on the UV-selected galaxies alone (Erb et al. 2006). UV
selection tend to be biased towards objects with relatively young stellar
populations while excluding some dust and metal rich galaxies (e.g., Steidel
et al. 2004; Stott et al. 2013). This combined effect naturally bias the field
MZR towards lower metallicities, albeit the contribution of missing dusty
objects may be only marginal according to Shimakawa et al. (2015) after
comparing the metallicity offset of a subsample of SDSS galaxies selected in a
similar manner than the HAEs with their measured extinctions. Nevertheless, we
highlight that this work in USS1558 and that of Pérez-Martínez et al. (2023)
in PKS1138 have applied exactly the same methods to the derivation of stellar
masses, SFRs, and gas-phase metallicities and thus, any comparison between
protoclusters remains fair within the statistical limitations of the samples
studied.

Finally, we explore the relation of diverse local density regimes within the
protocluster with the metallicity offsets (i.e.,
$\mathrm{\Delta\,MZR=12+\log(O/H)-12+\log(O/H)_{MZR}}$) present in the objects
lying therein. Figure 9 summarizes our results with the main panel displaying
the distribution of the individual metallicity measurements as a function of
$\Sigma_{5}$. The median values (empty diamonds) for each local density bin
display a flat trend. However, the distribution of [Nii] non-detections is
also of interest for the environmental analysis as this group is
representative of objects with lower metallicities (e.g., lower [Nii] emission
line flux) than their counterparts at fixed stellar-mass. The upper panel of
Figure 9 displays the cumulative distribution function of metallicity offsets
for the [Nii] detected and non-detected samples as a function of local
density. Intriguingly, the non-detections (ND) tend to lie at lower density
regimes than the [Nii] detected (D) sample, which traces the metal-rich end of
the metallicity distribution, thus suggesting a relation between the denser
areas of the protocluster and higher metal enrichment. The median values
(dashed lines in the figure) for each sample also support this description
with $\mathrm{\log\Sigma_{5}(ND)=1.42\pm 0.21\,Mpc^{-2}}$ and
$\mathrm{\log\Sigma_{5}(D)=1.78\pm 0.18\,Mpc^{-2}}$. However, we should take
this result with caution as the KS-test dims these two distributions as
statistically indistinguishable ($\mathrm{p=0.14}$). Furthermore, more massive
galaxies (typically more metal-rich too) tend to reside in the denser areas of
overdensities. This behavior is certain within both the [NII] detected and
undetected samples, albeit objects within the latter have overall lower
stellar masses than the detected sample which could also explain why they lie
in less dense environments.

###  4.3 Molecular gas fractions

In the context of the gas regulator model (Peng et al. 2010; Peng & Maiolino
2014), galaxies are progressively metal-enriched throughout successive
episodes of star formation. Thus, their gas reservoir is gradually depleted
(Bothwell et al. 2013; Hunt et al. 2015) due to gas consumption and the
contribution of outflows expelling gas from the galaxy disk via supernova or
AGN feedback. The lack of cold gas diminishes the efficiency of star formation
and eventually quenches the galaxy unless additional pristine gas is accreted
from the cosmic web compensating for such consumption (Dekel & Birnboim 2006).
Therefore, the gas regulator model can be parameterized by four simple
parameters: the star formation efficiency, the gas inflow rate, the mass-
loading factor which controls the balance between star-formation and outflows
($\lambda$=outflows/SFR), and the return mass fraction, which is assumed to be
constant. The mass loading factor is a parameter of special relevance for us
as it can be described as a function of the gas fraction and gas phase
metallicity, as it was shown by Suzuki et al. (2021).

Figure 10: Molecular gas fraction versus gas-phase metallicity. The solid
lines show the tracks of constant mass-loading factor (outflows/SFR) assuming
equilibrium in the context of the gas regulator model (Peng et al. 2010; Peng
& Maiolino 2014). Filled orange and blue circles display our subsamples of
HAEs with measured molecular gas fractions in the USS1558 (this work) and
PKS1138 protoclusters (Pérez-Martínez et al. 2023). Blue-edged squares show
the distribution of field galaxies at $z=3.3$ from Suzuki et al. (2021).
Brown-edged diamons display the field sample from Sanders et al. (2023).
Violet-edged triangles depict the field sample of Seko et al. (2016) at
$z=1.5$. The local field comparison sample is composed of galaxies from the
XCOLD GASS (Saintonge et al. 2017; Catinella et al. 2018) and the ALLSMOG
(Bothwell et al. 2014) surveys. The grey area would require negative values
for the outflow parameter and thus it is labeled as unphysical according to
the gas regulator model.

In this section, we aim to investigate the relation between the molecular gas
fraction and the metallicity of five of our spectroscopically confirmed
protocluster HAEs for which we have obtained metallicity measurements in this
work and CO(3-2) information from Tadaki et al. (2019). We derive molecular
gas fractions for these five objects following the procedure outlined in Sect.
3.5. Figure 10 displays the distribution of our targets in the gas fraction vs
gas metallicity plane in comparison with objects from PKS1138 and four
different field samples at $0<z<3.3$. For reference, we overplot the tracks of
constant mass-loading factor for $\mathrm{\lambda=0-3}$ (solid black lines)
from the origin to the current estimated age of the universe (i.e, 13.6 Gyrs).
Star formation proceeds in a more vigorous and short-lived way at high-z than
in the local universe (Thomas et al. 2010) and thus we expect to find higher
mass-loading factors during this cosmic epoch as a consequence of enhanced
outflows (Suzuki et al. 2021). As we move towards lower redshifts, star
formation proceeds more gradually thus yielding lower mass loading factors as
we can see from the Sanders et al. (2023) sample at $z=2.3$, the Seko et al.
(2016) sample at $z=1.5$, and the xCOLD-GASS (Saintonge et al. 2017; Catinella
et al. 2018) and ALLSMOG (Bothwell et al. 2014) samples in the local universe.
The metallicity calibrations used by the different works presented in Figure
10 have been rescaled to the N2 method of Pettini & Pagel (2004) following the
empirical prescriptions provided in Curti et al. (2017). This ensures a fair
comparison between samples at different cosmic epochs and environments in
terms of metallicity. Finally, the grey-shaded area of Figure 10 depicts the
locus where a negative value for the outflow parameter would be required, and
thus it is deemed as unphysical within the gas regulator model. Thus, objects
lying within this region may have overestimated values for $\mathrm{M_{mol}}$,
or underestimated values for $\mathrm{M_{*}}$ assuming their metallicities are
reliable. The five USS1558 objects scatter around $0.5\lesssim\lambda\lesssim
2$ similarly to the $z=2.3$ and at $z=1.5$ field samples but in contrast with
higher redshift galaxies of Suzuki et al. (2021). The six objects part of the
PKS1138 sample were previously published in Pérez-Martínez et al. (2023) and
made use of a sample of CO(1-0) emitters presented in Jin et al. (2021) as
part of the COALAS project (large program ID: C3181, PI: H. Dannerbauer) with
the Australia Telescope Compact Array (ATCA). This dataset was analyzed
following the exact same methods quoted in Sect. 3 albeit making use of a
lower CO transition. Some objects in both USS1558 and PKS1138 overlap around
very low $\lambda$ values albeit the USS1558 sample displays in general lower
gas fractions and metallicities. Only one object in the USS1558 sample lies
within the unphysical region although its uncertainties in $\mathrm{f_{gas}}$
and gas metallicity make it compatible with several of the mass-loading factor
tracks.

Finally, Pérez-Martínez et al. (2023) argued that the low mass-loading factors
displayed by the PKS1138 sample may be (at least partly) caused by the
suppression of outflows in those objects, as their SFRs are representative of
the Main sequence. This would be the result of the external pressure exerted
by an overdense IGM over the gas halo of the protocluster members, preventing
the outflows from star formation to leave the gravitational potential of the
galaxy and forcing the HAEs to recycle their already enriched gas. This
scenario looks less clear in USS1558 given the variety of $\mathrm{\lambda}$
values displayed by this sample, sharing a similar locus with other field
samples at similar redshift in Fig. 10. However, the limited number of objects
both in USS1558 and PKS1138 prevent us from drawing firm conclusions at this
stage. We will discuss different scenarios of environmentally driven galaxy
evolution in Sect. 5.

##  5 Discussion

###  5.1 Enhanced star formation activities in USS1558

This work has investigated the relationship between the protocluster
environment of USS1558 at $z=2.53$ and the physical properties of their star-
forming protocluster members. In particular, we focused on the star formation
activity, the metal enrichment and the gas reservoir of our objects, three
quantities that are entangled with each other and, together with the
environment, regulate the evolution of the galaxies’ ISM (Peng et al. 2010;
Peng & Maiolino 2014). Sect. 4.1 showed that the majority of our spectroscopic
targets display enhanced SFR with respect to the field and to other
protocluster samples at similar cosmic epochs, with this enhancement being
especially prominent in the low-mass regime ($\mathrm{\log
M_{*}/M_{\odot}<10.0}$). This effect is of special interest for environmental
studies, as most works below $z=1.5$ report an anti-correlation between the
star formation activity of galaxies and the number density of objects in their
surroundings (e.g., Balogh et al. 1998; Lewis et al. 2002; Quadri et al. 2012;
Muzzin et al. 2012; Old et al. 2020; Reeves et al. 2021). The reversal of the
star formation-density relation would point towards drastic changes in the
physical properties of overdense regions in the high-z universe (e.g.
protoclusters) compared to their lower redshift counterparts (clusters), thus
pointing towards the joint evolution of galaxy populations and the large scale
structures they inhabit over cosmic time. Several works have found evidence of
this reversal by inspecting large high-z samples covering a wide range of
local densities (Lemaux et al. 2022; Shi et al. 2023) and by focusing on
particularly overdense regions such as protoclusters (Hayashi et al. 2016;
Wang et al. 2016; Shimakawa et al. 2018a; Shi et al. 2020; Monson et al.
2021). However, this picture is not yet unanimous as many others find no
significant differences between protoclusters and field in terms of SFR (e.g.,
see Koyama et al. 2013; Shimakawa et al. 2018b; Pérez-Martínez et al. 2023 in
PKS1138, or Sattari et al. 2021 in the CC2.2 protocluster at $z=2.2$).

Gravitational interactions between protocluster members are one of the
possible mechanisms to explain higher star formation activity with respect to
the field. These events are expected to be more frequent in high-z
protoclusters due to the higher number density of objects in protoclusters,
their yet low relative velocities which favor close encounters (Hine et al.
2016), and their gas-rich nature (Gottlöber et al. 2001; Genel et al. 2014).
Thus we would expect that the densest protocluster regions host a larger
fraction of merging starbursting galaxies. Luminous dusty star-forming
galaxies (DSFG) fit well into this description and have been usually found in
protoclusters (e.g., Dannerbauer et al. 2014; Zeballos et al. 2018; Harikane
et al. 2019; Long et al. 2020; Zhang et al. 2022; Calvi et al. 2023), albeit
these objects often are a minority among the protocluster galaxy populations
and tend to be representative of the high end of the stellar-mass
distribution. However, not all DSFGs are produced through merging events, with
several works reporting remarkably disk-like morphologies and a high degree of
rotational support for less extreme DSFGs in the field at $z\gtrsim 2$ (e.g.,
Hodge et al. 2015, 2016, 2019; Fujimoto et al. 2018; Rizzo et al. 2021;
Gillman et al. 2023).

The environmental analysis presented in Fig. 7 yields a flat SFR enhancement
trend across low-to-high density regimes within USS1558, arguing against
gravitational interactions as the sole mechanism behind the SFR enhancement.
Thus, we must consider possible environmental effects related to the growth of
the large-scale structure and the accretion of fresh gas from the cosmic web
as candidates to explain this effect. Simulations predict that cold gas
streams along the filaments of the cosmic web supply the required fuel to feed
and sustain the elevated SFRs of high-z massive galaxies (e.g., Kereš et al.
2005; Dekel & Birnboim 2006; Genel et al. 2008). Beyond a certain mass limit,
however, the supply of cold gas in an otherwise hot medium would progressively
become inefficient until it is shut down completely as we expect for massive
virialized galaxy clusters (Dekel et al. 2009). In fact, cold accretion not
only helps massive galaxies to sustain their star-forming activities (Daddi et
al. 2007; Béthermin et al. 2014) but could also provide an extra supply of gas
to lower mass satellite galaxies, thus enhancing their star formation. Such an
effect would be widespread across the whole protocluster as it acts as a node
of the cosmic web, and would offer a suitable explanation for the SFR
enhancement we report for HAEs within USS1558. Recently, Wang et al. (2022)
also suggested a similar accretion scenario to explain the enhancement of star
formation in the low mass regime ($\mathrm{\log M_{*}/M_{\odot}<10.0}$) within
their sample while Valentino et al. (2015) found a similar enhancement at
slightly higher masses albeit with limited statistics. Conversely, other
spectroscopic works found no such signs of SFR enhancement (i.e., Sattari et
al. 2021; Pérez-Martínez et al. 2023) suggesting that the specific
evolutionary mechanisms at play may significantly differ between protoclusters
at the cosmic noon. Future studies particularly focusing on the star formation
of very low-mass galaxies in protoclusters will be able to explore this
scenario in greater depth.

###  5.2 Metal deficit for low-mass protocluster galaxies

The metallicity analysis of USS1558 protocluster HAEs (Sect. 4.2) yielded a
metallicity deficit for low mass galaxies ($\mathrm{\log
M_{*}/M_{\odot}<10.0}$) of approximately 0.1 dex with respect to both our
coeval field MZR and our previous results in PKS1138 at $z=2.16$ at the same
stellar mass bin (Fig. 8). On the other hand, this discrepancy disappears at
higher masses ($\mathrm{\log M_{*}/M_{\odot}>10.0}$). The ISM metal enrichment
is a byproduct of sustained star formation over a period of time. In the
general field, the fundamental metallicity relation (FMR, Mannucci et al.
2010, Sanders et al. 2018, 2021) predicts that star formation and gas-phase
metallicity are anticorrelated quantities, as the gas consumption required to
produce metals from successive generations of stars will eventually exhaust
the gas reservoir of their host galaxy. Thus, it is expected that vigorous
star-forming galaxies present relatively low metallicity values with
additional processes such as mergers contributing to this scenario,
particularly at $z>2$ (Bustamante et al. 2018; Rodríguez Montero et al. 2019;
Horstman et al. 2021; Calabrò et al. 2022). Similarly, enhanced cold gas
accretion as proposed in Sect. 5.1 would further foster these trends. The
extra supply of pristine gas from the cosmic web will naturally dilute the ISM
of satellite galaxies while promoting their star formation, thus accelerating
the process of mass assembly in these objects. In this context, the FMR is
able to qualitatively explain the results we have obtained for USS1558 in
terms of SFR and metal enrichment, with low-mass metal-poor galaxies forming
stars at a greater pace than the coeval field.

Contradicting results on the metal enrichment of cosmic noon protocluster
galaxies have been reported in recent years (e.g., Kulas et al. 2013;
Valentino et al. 2015; Kacprzak et al. 2015; Sattari et al. 2021; Chartab et
al. 2021; Wang et al. 2022; Pérez-Martínez et al. 2023). Selection biases of
different kinds may surely play a role in this puzzling situation. However,
the cosmic noon is as crucial for the evolution of galaxies as it is for the
development of the large-scale structures that host them. Thus, diverse stages
of protoclusters mass assembly may be an important factor driving the onset,
strength, and type of environmental effects in overdense regions. If the
transition between different gas accretion regimes as a consequence of the
dark matter halo growth (Dekel & Birnboim 2006; Dekel et al. 2009) is the
dominant factor driving these changes, we would expect that protoclusters made
of several clumpy lower-mass substructures such as USS1558 are first born as
sites of vigorous star formation and low metallicity due to the surplus of
fresh gas, then evolve towards less active and more metal-rich structures as
the halo growth shock heats the IGM and suppress the gas inflows, which will
be shut down once the protocluster achieves virialization. It is during this
last phase, that the overdense environment (now a full-fledged cluster of
galaxies) deprives galaxies of external gas supply and actively removes their
existing gas reservoir through ram-pressure stripping (see Boselli et al. 2022
for a review). Interestingly, individual [Nii] detections within our sample,
which trace its metal-rich end, tend to lie in slightly more overdense regions
than the non-detections, associated with lower metallicity values (Fig 9).
This may hint at different accretion regimes between the outskirts and the
denser areas of the four protocluster clumps where the mass assembly has been
going on for a longer time and the gas inflows may be starting to lose
efficiency. However, the KS-test yields no statistical significance between
the spatial distribution of both groups. Thus, a larger (and more complete)
sample would be needed to explore this possibility in an unbiased way.

###  5.3 Molecular gas fractions and mass-loading factors

Finally, we have used the gas regulator model (Peng & Maiolino 2014) to
investigate the relation between the metal enrichment of our galaxies and the
status of their molecular gas reservoir ($\mathrm{f_{gas}}$). USS1558
protocluster galaxies occupy a similar locus than the field samples at $z=2.3$
(Sanders et al. 2023) and $z=1.5$ (Seko et al. 2016) reaching up to
$\lambda=2$. However, our analysis is limited by the small number of galaxies
with both metallicity and $\mathrm{M_{Mol}}$ estimates. Field galaxies at
$z=3.3$ display higher mass-loading factors ($\lambda\approx 3$, Suzuki et al.
2021) suggesting the presence of higher outflow activity. On the other hand,
the main sequence star-forming galaxies from PKS1138 (Pérez-Martínez et al.
2023) lie at even lower $\lambda$ values, hinting at the suppression of
outflows in these objects. The authors speculate that this effect may be the
result of the increased external pressure of the IGM in this massive cluster,
forcing the galaxies to recycle their gas as proposed by Kulas et al. (2013),
thus yielding higher metallicity values at a fixed molecular gas fraction.
However, statistical limitations prevent them to draw firm conclusions, as is
also our case for USS1558. A direct comparison between the distribution of
USS1558 and PKS1138 protocluster galaxies in Fig. 10 hints at USS1558 being
less metal enriched at intermediate gas fractions, thus confirming its less
evolved nature compared with PKS1138. Nevertheless, larger number statistics
are required to quantitatively explore possible environmental imprints into
the gas metallicity gas fraction plane.

##  6 Conclusions

In this work, we have analyzed new Keck/MOSFIRE NIR spectroscopy to measure
the star-formation and gas-phase metallicity of a sample of HAEs belonging to
the USS1558 protocluster at $z=2.53$. Archival spectrophotometric observations
encompassing the rest-frame UV to submillimeter regime complemented our
analysis thus providing stellar and molecular gas masses and fractions.
Finally, we have examined the physical properties of 23 protocluster members
as a function of environment and discussed the implications of these results
on different scenarios of environmentally driven galaxy evolution during the
early stages of protocluster assembly. In the following paragraphs, we
summarize the main conclusions of this work:

  1. 1.

We have spectroscopically confirmed the protocluster membership of 23 narrow-
band selected HAEs out of an initial sample composed of 27 objects, thus
yielding a success rate of $\sim 88\%$ and including eight new sources
unconfirmed by previous spectroscopic campaigns (Shimakawa et al. 2015; Tadaki
et al. 2019). In addition, we report two foreground galaxies at $z\approx 3.6$
and two non-detections.

  2. 2.

HAEs in USS1558 at $z=2.53$ display enhanced SFRs with respect to the main
sequence of star formation fixed for that cosmic epoch (Speagle et al. 2014).
Furthermore, this enhancement is statistically significant when compared with
protocluster HAEs belonging to PKS1138 at $z=2.16$ (Pérez-Martínez et al.
2023) and with the coeval field sample of KMOS3D galaxies (Wisnioski et al.
2019). Galaxies with enhanced SFRs tend to display low stellar masses
($\mathrm{\log M_{*}/M_{\odot}<10.0}$) and are homogeneously distributed
across different density regimes within the protocluster. This suggests that
USS1558 is experiencing a phase of vigorous star formation possibly driven by
protocluster-wide effects such as increased accretion of pristine gas, and
disfavors alternative channels such as galaxy-galaxy interactions which are
expected to predominately occur within the densest areas of the protocluster.

  3. 3.

We extract individual and stacked [Nii] metallicity values for USS1558
protocluster members. The 10 individual metallicity measurements represent the
metal-rich end of our distribution and tend to lie in slightly more overdense
areas than [Nii] non-detected objects, which trace the low-metallicity end of
our distribution. The stacking analysis yielded similar metallicity values to
those found in PKS1138 and the field for $\mathrm{10.0<\log
M_{*}/M_{\odot}<10.8}$, but lower metallicity values at $\mathrm{\log
M_{*}/M_{\odot}<10.0}$: $\mathrm{\Delta MZR(USS1558)=-0.14\pm 0.08\,dex}$ vs
$\mathrm{\Delta MZR(PKS1138)=0.00\pm 0.04\,dex}$. We propose this metallicity
deficit together with the SFR enhancement at low stellar masses may suggest
that this regime is dominated by young galaxies still in the process of
forming the bulk of their mass and whose gas reservoir may be fed by
environmentally enhanced gas inflows.

  4. 4.

We obtain molecular gas fraction for a subsample of 5 protocluster members by
making use of the CO(3-2) measurements from Tadaki et al. (2019). After
exploring the gas-phase metallicity gas fraction relation, and in the context
of the gas regulator model (Peng & Maiolino 2014), we find that HAEs in
USS1558 are distributed along mass-loading factor tracks
($\mathrm{\lambda\approx 0.5-2}$) comparable with those of field samples at
$1.5<z<2.3$ in contrast with previous studies at $z\approx 3$
($\mathrm{\lambda\approx 3}$) arguing for higher outflow activity (Suzuki et
al. 2021), but also contrary to the environmentally suppressed outflows
scenario proposed in Pérez-Martínez et al. (2023) for the PKS1138 protocluster
sample ($\mathrm{\lambda\approx 0-1}$). However, a larger sample of deeper
metallicity and gas fraction estimates is required to further explore this
scenario.

## Acknowledgements

We thank the anonymous referee for his/her constructive feedback, which has
contributed to improving this manuscript. Part of the data presented herein
were obtained at the W. M. Keck Observatory, which is operated as a scientific
partnership among the California Institute of Technology, the University of
California, and the National Aeronautics and Space Administration. The
Observatory was made possible by the generous financial support of the W. M.
Keck Foundation. The observations were carried out within the framework of
Subaru-Keck/Subaru-Gemini time exchange program which is operated by the
National Astronomical Observatory of Japan. We are honored and grateful for
the opportunity of observing the Universe from Maunakea, which has the
cultural, historical, and natural significance in Hawaii. This research is
based in part on data collected at the Subaru Telescope, which is operated by
the National Astronomical Observatory of Japan (NAOJ). This research is based
in part on observations made with the NASA/ESA Hubble Space Telescope obtained
from the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5–26555. This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2015.1.00395.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. The Australia Telescope Compact Array is part of the Australia Telescope
National Facility (https://ror.org/05qajvd42) which is funded by the
Australian Government for operation as a National Facility managed by CSIRO.
We acknowledge the Gomeroi people as the Traditional Owners of the Observatory
site. This research made use of Astropy,111http://www.astropy.org a community-
developed core Python package for Astronomy (Astropy Collaboration et al.,
2013, 2018). JMPM is grateful for the support from T. Kodama and Tohoku
University in the development of this work. JMPM also thanks H. Dannerbauer
for providing access to the COALAS datasets for the PKS1138 comparison sample.
TK acknowledges the support of Grant-in-Aid for Scientific Research (A)
(KAKENHI #18H03717). MO acknowledges the support by JSPS KAKENHI Grant Number
JP21K03622. Kavli IPMU is supported by the World Premier International
Research Center Initiative (WPI), MEXT, Japan.

## Data Availability

The spectroscopic data used within this article belong to the Subaru-Keck
exchange program ID: S20A-075 (PI: T. Kodama) and it is publicly available
throughout the Keck Observatory Archive (KOA). The ground-based photometric
data used in this work belongs to the Subaru programs S10B-028 and S15A-047
(PI: T. Kodama) and it is publicly available throughout the Subaru Mitaka
Okayama Kiso Archive (SMOKA) system. The HST photometry used in this work
belongs to the program GO-13291 (PI: M. Hayashi) and it is publicly available
through the Hubble Legacy Archive. The ALMA CO(3-2) quoted in this work and
used to derive molecular gas masses for the USS1558 sample belongs to the ALMA
program 2015.1.00395.S (PI: T. Kodama). The ATCA CO(1-0) quoted in this work
and used to derive molecular gas masses for the PKS1138 sample belongs to the
ATCA large program COALAS (ID: C3181, PI: H. Dannerbauer). Enhanced data
products from these datasets may be shared on reasonable request.

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##  Appendix A SED fitting results

Figure 11: The black solid line for each panel displays the Cigale SED model.
Orange circles and blue-edged diamonds respectively show the broad-band
observed and modeled fluxes for each protocluster member within our sample.

##  Appendix B Summary Table

Table 2: Physical properties of our USS1558 protocluster sample. Coordinates
(RA and DEC) are shown in degrees. The redshifts (z) are based on the
H$\alpha$ measurements of this work. The molecular masses have been computed
following the metallicity-dependent calibration by Tacconi et al. (2018) and
making use of the ALMA CO(3-2) information published by Tadaki et al. (2019).
(see Sect. 3.5). $\mathrm{A_{V}}$ represents the extinction extracted from the
SED modelling assuming the Calzetti et al. (2000) extinction law (see Sect.
3.3).

ID | RA | DEC | z | $\mathrm{\log\,M_{*}/M_{\odot}}$ | SFR | $\mathrm{12+\log(O/H)}$ | $\mathrm{\log\,M_{mol}/M_{\odot}}$ | $\mathrm{A_{V}}$ | $\Sigma_{5}$
---|---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) |  |  | ($\mathrm{M_{\odot}/yr}$) |  |  | $\mathrm{(mag)}$ | ($\mathrm{Mpc^{-2}}$)
16 | 240.2826584 | -0.5308889 | 2.5410 | $9.82^{+0.16}_{-0.26}$ | $42\pm 9$ | $8.46\pm 0.13$ | - | $0.82\pm 0.21$ | 29.92
18 | 240.2831295 | -0.5255959 | 2.5247 | $9.35^{+0.20}_{-0.37}$ | $10\pm 4$ | - | - | $0.71\pm 0.24$ | 40.27
34 | 240.2915811 | -0.5269186 | 2.5251 | $10.51^{+0.14}_{-0.20}$ | $63\pm 29$ | - | - | $1.86\pm 0.22$ | 104.31
38a | 240.2924994 | -0.5211665 | 2.5237 | $11.12^{+0.12}_{-0.17}$ | $189\pm 5$ | - | $<10.45$ | $2.11\pm 0.24$ | 135.18
39 | 240.2931181 | -0.5239965 | 2.5244 | $9.49^{+0.15}_{-0.23}$ | $34\pm 8$ | - | - | $0.71\pm 0.22$ | 135.51
59 | 240.2976694 | -0.5220065 | 2.5134 | $10.88^{+0.14}_{-0.20}$ | $266\pm 85$ | $8.66\pm 0.13$ | $11.10\pm 0.06$ | $2.66\pm 0.48$ | 350.95
64 | 240.2987622 | -0.5199375 | 2.5294 | $10.11^{+0.12}_{-0.16}$ | $35\pm 15$ | $<8.60$ | $10.76\pm 0.12$ | $0.74\pm 0.23$ | 550.95
73 | 240.3020857 | -0.5148570 | 2.5260 | $10.57^{+0.13}_{-0.18}$ | $311\pm 45$ | $8.57\pm 0.10$ | $10.73\pm 0.09$ | $1.78\pm 0.22$ | 82.71
74 | 240.3019612 | -0.4821418 | 2.5344 | $10.18^{+0.13}_{-0.19}$ | $115\pm 27$ | $8.45\pm 0.13$ | - | $1.37\pm 0.23$ | 17.79
79 | 240.3039954 | -0.5211177 | 2.5092 | $10.72^{+0.14}_{-0.21}$ | $179\pm 33$ | $8.45\pm 0.10$ | $<10.78$ | $1.67\pm 0.23$ | 243.28
88 | 240.3056859 | -0.5060703 | 2.5185 | $9.42^{+0.14}_{-0.20}$ | $43\pm 5$ | $<8.30$ | - | $0.63\pm 0.19$ | 121.26
91 | 240.3079703 | -0.5108609 | 2.5178 | $9.96^{+0.14}_{-0.21}$ | $82\pm 22$ | - | - | $1.53\pm 0.23$ | 201.22
94 | 240.3080466 | -0.4968055 | 2.5268 | $10.70^{+0.18}_{-0.33}$ | $192\pm 29$ | $8.54\pm 0.10$ | - | $1.87\pm 0.32$ | 25.5
112 | 240.3143353 | -0.5083207 | 2.5246 | $9.68^{+0.16}_{-0.25}$ | $72\pm 13$ | $8.47\pm 0.12$ | - | $1.39\pm 0.26$ | 30.25
134 | 240.3249030 | -0.4846260 | 2.5352 | $10.41^{+0.15}_{-0.23}$ | $102\pm 33$ | - | - | $1.70\pm 0.22$ | 89.5
137 | 240.3247461 | -0.4756063 | 2.5267 | $10.64^{+0.14}_{-0.21}$ | $94\pm 28$ | $<8.57$ | $10.66\pm 0.11$ | $2.00\pm 0.24$ | 53.03
138a,b,c | 240.3222771 | -0.4795241 | 2.5345 | $11.83^{+0.11}_{-0.15}$ | $90\pm 15$ | $8.59\pm 0.06$ | - | $0.26\pm 0.25$ | 84.18
139 | 240.3266295 | -0.4931553 | 2.5262 | $9.77^{+0.14}_{-0.20}$ | $43\pm 9$ | - | - | $0.73\pm 0.20$ | 15.69
144 | 240.3290271 | -0.4616180 | 2.5332 | $10.20^{+0.13}_{-0.20}$ | $55\pm 13$ | - | - | $1.73\pm 0.23$ | 48.61
154 | 240.3312181 | -0.4995278 | 2.5278 | $9.36^{+0.16}_{-0.25}$ | $30\pm 4$ | - | - | $0.39\pm 0.20$ | 9.05
167 | 240.3382885 | -0.4621250 | 2.5332 | $10.28^{+0.14}_{-0.20}$ | $115\pm 19$ | $8.55\pm 0.09$ | - | $1.45\pm 0.22$ | 13.22
168a | 240.3392922 | -0.4609448 | 2.5358 | $10.62^{+0.13}_{-0.18}$ | $19\pm 4$ | $8.82\pm 0.09$ | - | $0.20\pm 0.17$ | 10.75
173 | 240.3479611 | -0.4806875 | 2.5213 | $9.84^{+0.16}_{-0.24}$ | $74\pm 24$ | - | - | $1.47\pm 0.32$ | 5.78

  * a

These objects are labeled as AGN candidates due to displaying
$\log$([Nii]/H$\alpha$)$\geq-0.35$ or broad H$\alpha$ profiles ($\sigma>700$
km s-1).

  * b

Confirmed X-ray emission (Macuga et al. 2019).

  * c

Radio galaxy 4C-00.62 (Kajisawa et al. 2006).