# Environmental Effects on the Stellar Mass Function in a $z\sim 3.3$
Overdensity of Galaxies in the COSMOS Field111Some of the data presented
herein were obtained at Keck Observatory, which is a private 501(c)3 non-
profit organization 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.

Ben Forrest Department of Physics and Astronomy, University of California
Davis, One Shields Avenue, Davis, CA, 95616, USA  Brian C. Lemaux Gemini
Observatory, NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, HI, 96720, USA
Department of Physics and Astronomy, University of California Davis, One
Shields Avenue, Davis, CA, 95616, USA  Ekta A. Shah Department of Physics and
Astronomy, University of California Davis, One Shields Avenue, Davis, CA,
95616, USA  Priti Staab Department of Physics and Astronomy, University of
California Davis, One Shields Avenue, Davis, CA, 95616, USA  Roy R. Gal
University of Hawai’i, Institute for Astronomy, 2680 Woodlawn Drive, Honolulu,
HI 96822, USA  Lori M. Lubin Department of Physics and Astronomy, University
of California Davis, One Shields Avenue, Davis, CA, 95616, USA  M. C. Cooper
Department of Physics and Astronomy, University of California, Irvine, 4129
Frederick Reines Hall, Irvine, CA 92697, USA  Olga Cucciati INAF Osservatorio
di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3,
40129 Bologna, Italy  Denise Hung Gemini Observatory, NSF’s NOIRLab, 670 N.
A’ohoku Place, Hilo, HI, 96720, USA  University of Hawai’i, Institute for
Astronomy, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Ian McConachie
Department of Physics & Astronomy, University of California Riverside, 900
University Ave., Riverside, CA, 92521, USA  Adam Muzzin Department of Physics
and Astronomy, York University, 4700, Keele Street, Toronto, ONMJ3 1P3, Canada
Gillian Wilson Department of Physics, University of California Merced, 5200
North Lake Rd., Merced, CA 95343, USA  Sandro Bardelli INAF Osservatorio di
Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129
Bologna, Italy  Letizia P. Cassarà INAF-IASF Milano, Via Alfonso Corti 12,
20133, Milano, Italy  Wenjun Chang Department of Physics & Astronomy,
University of California Riverside, 900 University Ave., Riverside, CA, 92521,
USA  Finn Giddings University of Hawai’i, Institute for Astronomy, 2680
Woodlawn Drive, Honolulu, HI 96822, USA  Emmet Golden-Marx Department of
Astronomy, Tsinghua University, Beijing 100084, People’s Republic of China
Nimish Hathi Space Telescope Science Institute, Baltimore, MD 21218, USA
Stephanie M. Urbano Stawinski Department of Physics and Astronomy, University
of California, Irvine, 4129 Frederick Reines Hall, Irvine, CA 92697, USA
Elena Zucca INAF Osservatorio di Astrofisica e Scienza dello Spazio di
Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

###### Abstract

We present an analysis of the number density of galaxies as a function of
stellar mass (i.e., the stellar mass function, SMF) in the COSMOS field at
$z\sim 3.3$, making a comparison between the SMF in overdense environments and
the SMF in the coeval field. In particular, this region contains the Elentári
proto-supercluster, a system of 6 extended overdensities spanning $\sim 70$
cMpc on a side. A clear difference is seen in the high-mass slope of these
SMFs, with overdense regions showing an increase in the ratio of high-mass
galaxies to low-mass galaxies relative to the field, indicating a more rapid
build-up of stellar mass in overdense environments. This result qualitatively
agrees with analyses of clusters at $z\sim 1$, though the differences between
protocluster and field SMFs at $z\sim 3.3$ are smaller. While this is
consistent with overdensities enhancing the evolution of their member
galaxies, potentially through increased merger rates, whether this enhancement
begins in protocluster environments or even earlier in group environments is
still unclear. Though the measured fractions of quiescent galaxies between the
field and overdense environments do not vary significantly, implying that this
stellar mass enhancement is ongoing and any starbursts triggered by merger
activity have not yet quenched, we note that spectroscopic observations are
biased towards star-forming populations, particularly for low-mass galaxies.
If mergers are indeed responsible, high resolution imaging of Elentári and
similar structures at these early epochs should then reveal increased merger
rates relative to the field. Larger samples of well-characterized
overdensities are necessary to draw broader conclusions in these areas.

Galaxy evolution, High-redshift galaxy clusters

††software:  Astropy (Robitaille et al., 2013; Price-Whelan et al., 2018; The
Astropy Collaboration et al., 2022), FAST++ (Schreiber et al., 2018b), IPython
(Pérez & Granger, 2007), LePhare (Arnouts et al., 1999; Ilbert et al., 2006),
Matplotlib (Hunter, 2007), NumPy (Oliphant & Millma, 2006).

##  1 Introduction

The environment in which a galaxy resides plays an important role in its
evolution. Obvious differences exist in the local Universe between the
populations of galaxies in massive, evolved clusters and populations of
galaxies in the field across a wide range of properties including stellar
mass, star formation rate, age, color, morphology, velocity dispersion, and
metallicity (e.g., Dressler, 1984; Kauffmann et al., 2004; Thomas et al.,
2005). These differences are consistent with cluster galaxies having a faster
and/or earlier evolutionary timescale than field galaxies and this signal is
seen in the most overdense environments out past $z\gtrsim 1$ (e.g.,
Kawinwanichakij et al., 2017; Papovich et al., 2018; Mei et al., 2023). The
strength of this signal begins to decrease or perhaps reverse by $z\gtrsim
1.5$ (Tran et al., 2010; Nantais et al., 2016; Pérez-Martínez et al., 2022;
Taamoli et al., 2023; Edward et al., 2023), though some systems with elevated
quenched fractions do still appear at earlier epochs (e.g., Zavala et al.,
2019; McConachie et al., 2022; Ito et al., 2023). In fact, at very early
epochs, many galaxies in protoclusters, the progenitors of today’s clusters,
appear to have enhanced star formation rates (SFRs) relative to the field
(e.g., Capak et al., 2011; Hatch et al., 2011; Wang et al., 2016; Pérez-
Martínez et al., 2023; Staab et al., 2024), suggesting that the effect of an
overdense environment is to increase SFRs at early times. This may
subsequently deplete the molecular gas content of these galaxies, as seen in
low redshift galaxies (e.g., Fumagalli et al., 2009), thus inhibiting future
star formation and leaving the galaxy more massive and with older stellar
populations than galaxies which continue forming stars. This is consistent
with findings of enhanced molecular gas reservoirs and gas fractions in
clusters, protoclusters, and groups relative to the field at high redshift
(e.g., Noble et al., 2019; Jin et al., 2021; Shen et al., 2021a), a trend
which also disappears around $z\sim 1.5$ (e.g., Alberts et al., 2022; Williams
et al., 2022). However, the specific physical mechanisms responsible for any
such environmental effects to take place and whether there is a particular
density threshold or timescale required for these effects is unclear.

The combined effects of these processes can be seen by analyzing the number
density of galaxies as a function of their stellar mass, which is an integral
of the SFR of a galaxy across cosmic time. The shape of this stellar mass
function (SMF) between nearby galaxies in clusters and in the field varies
significantly, with galaxies in overdense regions showing a larger ratio of
high-mass to low-mass galaxies (e.g., Blanton & Moustakas, 2009). Some
evidence suggests that this variation in shape may be entirely due to changes
in shape and/or normalization of the SMF of red / early-type / quiescent
populations, with the shape of the star-forming galaxy SMF staying relatively
similar between field and cluster environments (e.g., Peng et al., 2010),
though this is not universally found (e.g., Annunziatella et al., 2014, 2016).

Evidence is mixed as to whether or not this is the case in higher redshift
overdensities. Field surveys at $z\sim 1$ have shown that the SMF varies with
environmental density (Bundy et al., 2006; Cooper et al., 2010b; Papovich et
al., 2018). Targeted spectroscopic observations of cluster environments at
$z\sim 1$ such as those in the ORELSE (Lubin et al., 2009), GCLASS (Muzzin et
al., 2012), and GOGREEN (Balogh et al., 2017, 2020) surveys have found
differences between cluster and field population SMFs as well. The results
from GCLASS (van der Burg et al., 2013) and GOGREEN (van der Burg et al.,
2020) suggest that these differences are due to changes in the relative
fraction of quenched galaxies, however the shapes of the quiescent SMFs in
both overdensity and field are statistically the same, as are the shapes of
the star-forming SMFs. However, results from ORELSE (Tomczak et al., 2017)
instead show evolution of shape in both the quiescent and star-forming SMFs
with environmental overdensity. While narrowband imaging of $\rm{H}\alpha$
emitters in two protoclusters at $z=2.16$ (Shimakawa et al., 2018a) and
$z=2.53$ (Shimakawa et al., 2018b) show differences in SMF shape relative to
the field, a compilation of results at $z\gtrsim 2$ found a combined
protocluster SMF with shape consistent with that of the field for star-forming
galaxies, while the shape of quiescent galaxy SMFs between environments showed
minor differences (Edward et al., 2023).

While SMF analyses of field populations $z>3$ are numerous (e.g., Marchesini
et al., 2009; Stefanon et al., 2015; Marsan et al., 2022; Weaver et al.,
2023), similar analyses of overdense environments are lacking. This stems from
the difficulty of identification and characterization of high redshift
overdensities, which is several-fold. Photometric identification of candidate
overdensities at these epochs requires deep multiband imaging, in particular
in the near-infrared, in order to identify stellar-mass limited samples of
faint galaxies, to infer the location of features such as the Balmer break
which aid in constraining photometric redshifts, and to cover the large
projected sizes of these structures ($\sim 10-15$ comoving Mpc, and in some
cases larger; Muldrew et al., 2015; Chiang et al., 2017; Cucciati et al.,
2018). The low density contrast of these structures with the coeval field
combined with significant photometric redshift uncertainties means that
significant spectroscopic follow-up is also required to obtain precise galaxy
redshifts, confirm these structures, and allow for accurate density mapping of
the systems and their surroundings.

Similarly, simulations have had some success replicating quenched fractions
and SMFs in the Universe over a range of redshifts (Pillepich et al., 2018; De
Lucia et al., 2024), though some disagreement in the SMF for high stellar mass
galaxies at $z\gtrsim 2.5$ has been noted (e.g., Steinhardt et al., 2016;
Sherman et al., 2020). Cluster SMFs can also be well replicated out to $z\sim
1.5$, though the quenched fractions of satellite galaxies are often severely
different from observations (e.g., Bahé et al., 2017; Kukstas et al., 2023).
Some of this mismatch can be attributed to slightly different definitions of
e.g., star-forming vs. quiescent galaxies (Donnari et al., 2021). Recent
results from the GAEA models (De Lucia et al., 2024) appear to replicate the
observed quenched fraction from GOGREEN clusters at $z\sim 1$ (van der Burg et
al., 2020).

An assumption often made in attempting to understand the environmental effects
on galaxy evolution is that the cluster satellite galaxies are drawn from same
population as the field, and have simply fallen into a massive halo which
proceeds to influence member galaxies. Many works have also suggested that
such influences begin even before infall into a massive cluster, in the
earlier proto-cluster or group environments in what has been termed ‘pre-
processing’ (Balogh et al., 2000; Fujita, 2004; De Lucia et al., 2012; Donnari
et al., 2020). However, a recent analysis of the dark matter halos in
simulations has suggested that the population of cluster galaxies may not in
fact be drawn from the same parent population as field galaxies which would
allow for intrinsic halo properties to be responsible for observed population
differences between field and cluster environments (Ahad et al., 2024).

Exploring whether there are environmental effects on the stellar mass function
in protocluster environments at $z>3$ can lead to increased understanding of
the mechanisms in overdense environments which contribute to galaxy evolution.
To that end, in this work we build a stellar mass function based on galaxies
in the COSMOS field around the Elentári proto-supercluster at $z\sim 3.3$
(Forrest et al., 2023). To our knowledge, this is the first time such an
analysis has been performed at this early epoch and is only possible due to a
wealth of deep photometric and spectroscopic data as described in Section 2.
We discuss the analysis methodology and results in Section 3 before presenting
conclusions (Section 4). Throughout this work we use the AB magnitude system
(Oke & Gunn, 1983) and assume a $\Lambda$CDM cosmology with with $H_{0}=70$
km/s/Mpc, $\Omega_{M}=0.3$, and $\Omega_{\Lambda}=0.7$.

##  2 Data

###  2.1 Parent Photometric Catalogs

This work relies upon the considerable investment of observing time focused on
the COSMOS field (Scoville et al., 2007; Koekemoer et al., 2007). The
ultraviolet, optical, and near-infrared imaging in this field have been
compiled most recently in the COSMOS2020 catalogs (Weaver et al., 2022), which
contain over 1.5 million sources observed in up to 40 bandpasses over $\sim
1.5$ deg2. This includes space-based observations from GALEX (ultraviolet;
Zamojski et al., 2007), HST/ACS (optical; Leauthaud et al., 2007) and
Spitzer/IRAC (near-infrared Ashby et al., 2013, 2015, 2018; Steinhardt et al.,
2014). Ground based data includes ultraviolet CFHT/MegaCam observations
(Sawicki et al., 2019), optical data from Subaru/Suprime-Cam (Taniguchi et
al., 2007, 2015) and Hyper Suprime-Cam (Aihara et al., 2019), and near-
infrared observations from VISTA/VIRCAM (McCracken et al., 2012; Moneti et
al., 2019).

The depth of the imaging involved in construction of the COSMOS2020 catalogs
as well as associated derived properties, including well-characterized
photometric redshifts ($z_{\textrm{phot}}$) and their probability
distributions ($p(z)$), rest-frame colors, stellar masses, and SFRs are
critical to this work. Unless otherwise stated, we use the COSMOS2020 Classic
catalog, and the associated properties derived using LePhare (Arnouts et al.,
1999; Ilbert et al., 2006). These characterizations use the same process as
described in Ilbert et al. (2013), and include galaxy templates from Polletta
et al. (2007), Bruzual & Charlot (2003), and Onodera et al. (2012), and
stellar templates from Pickles (1998), with additional templates for white and
brown dwarfs as well as AGN. Allowed dust attenuation curves include Small
Magellanic Cloud (Prevot et al., 1984), starburst (Calzetti et al., 2000), and
starburst+2175Å profiles (Fitzpatrick & Massa, 1986), and a Chabrier (2003)
initial mass function is assumed.

###  2.2 Spectroscopy

####  2.2.1 Field Surveys

The COSMOS field has also been the target of many spectroscopic surveys,
several of which are included in this work. The VIMOS Ultra-Deep Survey (VUDS;
Le Fèvre et al., 2015), targeted $\sim$104 objects across the COSMOS, ECDFS,
and VVDS-2h fields with the VIMOS instrument on ESO-VLT (Le Fèvre et al.,
2003). This survey preferentially selected targets for follow-up which had
$z_{\textrm{phot}}$$\gtrsim 2$ and was deep enough to reliably detect
continuum for $i\sim 25$ objects.

The zCOSMOS survey (Lilly et al., 2007) also used the VIMOS spectrograph on
the VLT and consisted of two sub-samples. The zCOSMOS-bright subsample
targeted $\sim 2\times 10^{4}$ galaxies with $I<22.5$ and thus mainly
confirmed galaxies across $0.1<z<1.2$ over the entire COSMOS ACS field. The
zCOSMOS-deep subsample targeted $\sim$104 galaxies in the central portion of
the field believed to have $1.4<z<3.0$ based on their colors (Daichi, K. et
al., in preparation).

The DEIMOS 10k Spectroscopic Survey (Hasinger et al., 2018) similarly targeted
$\sim$104 objects, using the DEIMOS instrument on the Keck II telescope (Faber
et al., 2003). While the entirety of this survey was in the COSMOS field,
there was no photometric redshift cut applied and thus the majority of objects
with spectroscopic redshifts are at $z<2$. Sample selection was heterogenous,
with several subsamples of galaxies, including (amongst others) Spitzer/MIPS
sources, high-redshift candidates, and optical counterparts of X-ray sources.

These surveys have also used similar spectroscopic redshift quality flagging
systems. The base flag for each object is one of the following: 0 - no
redshift measured, 1 - low confidence redshifts, 2, 3, 4, 9 - secure redshifts
(estimated $\gtrsim 75\%$ reliability; Lilly et al., 2007; Le Fèvre et al.,
2013; Cassata et al., 2015). Each flag may also prepended with a number X,
indicating that the target either has broad lines observed in the spectrum
(X=1), the target is a serendipitous detection (X=2), or the target is a
serendipitous detection at location of target (i.e.,chance alignment or
merger; X=3).

Table 1: C3VO Keck/MOSFIRE Observations in COSMOS. $H$-band exposures were 120s each, $K$-band exposures were 180s each. The slitwidth was 0.7″. Target ($z$) | Mask | Bandpass | Date(s) Observed | Total Exp.Time (m) | Avg. Seeing(″)
---|---|---|---|---|---
Hyperion (2.45) | Hyperion1 | H | 2020.03.09 | 150 | 0.71
| Hyperion2 | H | 2020.03.09 | 112 | 0.69
| Hyperion3 | H | 2020.03.10 | 106 | 0.66
| Hyperion4 | H | 2020.03.11 | 104 | 0.55
| Hyperion5 | H | 2020.03.11 | 106 | 0.55
| Hyperion6 | H | 2020.11.30 | 118 | 0.79
| Hyperion7 | H | 2020.11.30 | 164 | 0.86
|  |  |  2021.01.06 |  |
|  |  |  2021.12.25 |  |
Elentàri (3.33) | DONGOCps23n24_1 | K | 2021.12.26 | 102 | 0.77
| DONGOCps23n24_2 | K | 2021.12.26 | 102 | 0.68
| DONGOCps23n24_3 | K | 2022.10.15 | 48 | 0.86
| NEb_1 | K | 2023.02.03 | 90 | 0.86
| NEc_1 | K | 2023.03.30 | 60 | 0.67
| NEd_1 | K | 2023.03.30 | 42 | 0.81
| Bridge1 | K | 2023.02.03 | 84 | 0.89
|  |  |  2023.03.30 |  |
| Bridge2 | K | 2023.03.31 | 72 | 0.70
| SWa_1 | K | 2023.02.03 | 84 | 1.00
|  |  |  2023.03.30 |  |
| SWc_1 | K | 2023.03.31 | 48 | 0.93
Table 2: C3VO Keck/DEIMOS Observations in COSMOS. The 600ZD grating (600 lines/mm) was used for all observations. Target ($z$) | Mask | Filter | Central Wavelength (Å) | Date(s) Observed | Total Exp.Time (m) | Avg. Seeing(″)
---|---|---|---|---|---|---
Taralay (4.57) | dongN1C | GG400 | 6500 | 2017.12.26 | 210 | 0.8
| dongS1B | GG400 | 6500 | 2016.12.22 | 275 | 0.8
| dongD1 | GG455 | 7200 | 2017.12.26 | 320 | 0.94
|  |  |  |  2019.02.05 |  |
|  |  |  |  2019.12.24 |  |
|  |  |  |  2020.12.23 |  |
| dongD2 | GG455 | 7200 | 2020.02.02 | 360 | 0.78
|  |  |  |  2020.12.10 |  |
|  |  |  |  2022.12.23 |  |
| dongA1 | GG455 | 7200 | 2021.01.17 | 299 | 0.84
|  |  |  |  2022.01.10 |  |
| dongA2 | GG455 | 7200 | 2022.01.10 | 240 | 0.59
|  |  |  |  2022.01.101 |  |
PCl J1000+0200 (2.90) | dongC2D1 | GG400 | 6500 | 2022.01.11 | 145 | 0.82
| dongC2N1 | GG400 | 6500 | 2020.02.02 | 309 | 1.15
| dongC2S1 | GG400 | 6500 | 2019.02.25 | 268 | 0.97
|  |  |  |  2020.12.10 |  |
|  |  |  |  2020.12.23 |  |
|  |  |  |  2021.01.17 |  |

####  2.2.2 Targeted Surveys - C3VO

The Charting Cluster Construction with VUDS (Le Fèvre et al., 2015) and ORELSE
(Lubin et al., 2009) Survey (C3VO; Lemaux et al., 2022) has used the
Keck/DEIMOS and Keck/MOSFIRE (McLean et al., 2010, 2012) instruments on the
Keck telescopes to follow-up candidate overdensities identified in density
maps constructed from a combination of spectroscopic and photometric data
across the CFHTLS-D1, ECDFS, and COSMOS fields (see Sections 3.1 and 3.2 for a
description of these maps and candidate overdensity identification). The
survey has observed $\sim 2000$ galaxies across the three fields,
approximately half with MOSFIRE and half with DEIMOS. Targeted regions
included Hyperion ($z=2.45$; Casey et al., 2015; Cucciati et al., 2018), PCl
J1000+0200 ($z=2.90$; Cucciati et al., 2014), PCl J0227-0421 ($z=3.31$; Lemaux
et al., 2014; Shen et al., 2021b), Elentári ($z=3.33$; McConachie et al.,
2022; Forrest et al., 2023), Smruti ($z=3.47$; Forrest et al., 2017; Shah et
al., 2024), and Taralay ($z=4.57$; Lemaux et al., 2018; Staab et al., 2024).

All C3VO COSMOS observations used in this work are shown in Tables 1 & 2.
MOSFIRE masks targeting Hyperion as well as the first three masks targeting
Elentári used photometric redshifts and magnitudes from the COSMOS2015 catalog
(Laigle et al., 2016) for target selection. Subsequent masks targeting
Elentári (observed in 2023) selected objects based on $p(z)$, stellar masses,
and rest-frame colors from the COSMOS2020 Classic catalog. DEIMOS masks
prioritized targeting star-forming galaxies down to $i_{AB}<25.3$ with
photometric redshifts near that of the overdensity in question, as detailed in
Lemaux et al. (2022).

In this work we focus on density maps constructed from data including VUDS and
zCOSMOS spectroscopy, photometry from COSMOS2015 and COSMOS2020, and C3VO
spectroscopic data taken prior to fall 2021 (the 2021B semester).
Spectroscopic redshifts from other masks listed in Tables 1 & 2 are
incorporated into subsequent pieces of the analysis, and are important for
confirming redshifts of objects whose membership in Elentári is inconclusive
from $p(z)$ alone.

####  2.2.3 Targeted Surveys - MAGAZ3NE

The Massive Ancient Galaxies at $z>3$ Near-Inrared Survey (MAGAZ3NE; Forrest
et al., 2020) has used Keck/MOSFIRE to spectroscopically follow-up ultra-
massive galaxies (UMGs; $\log(M_{*}/\rm{M}_{\odot})$$>11$ at $z>3$) and
investigate their environments. It has thus far targeted $\sim 1000$ galaxies
across the UltraVISTA (COSMOS), VIDEO-XMM, and VIDEO-CDFS fields. This survey
selected targets in the COSMOS field for follow-up based on observed galaxy
spectral energy distributions (SEDs), $p(z)$, stellar masses, and SFRs from
the UltraVISTA DR1 and DR3 catalogs (Muzzin et al., 2013a, A. Muzzin, private
communication).

This paper focuses on a set of six structures (S1-S6) at $z\sim 3.3$ named
Elentári (Forrest et al., 2023). While it is unlikely that all six will
collapse into a single system at $z=0$, there are multiple pairs of structures
which may do so. This system as a whole has over 100 spectroscopically-
confirmed members, and the best characterized structure (S1) has an estimated
$z=0$ mass of $1.3\times 10^{14}$ M⊙. Two of these (S1, S4) were
spectroscopically confirmed via MAGAZ3NE spectroscopy (McConachie et al.,
2022) as they contain UMGs, and the larger region was independently identified
and then spectroscopically followed-up with C3VO.

####  2.2.4 Spectroscopic Data Reduction

Details on the data reduction process and redshift assignment for zCOSMOS
(Lilly et al., 2007), VUDS (Le Fèvre et al., 2015), and DEIMOS 10k (Hasinger
et al., 2018) data can be found in the publications of those surveys. However,
all surveys used a combination of automated initial redshift assignment
followed by visual inspection and checking of results.

We reduced the C3VO MOSFIRE spectra using the MOSDEF 2D data reduction
pipeline (Kriek et al., 2015). This pipeline was also used to re-reduce the
MAGAZ3NE MOSFIRE data, which were initially reduced using the Keck-supported
MOSFIRE Data Reduction Pipeline (DRP; Version 2018). The MOSDEF pipeline
subtracts the sky background noise, masks both cosmic rays and bad pixels, and
rectifies each frame. It also identifies the trace of a star on a science
slit, which is used to measure atmospheric seeing and throughput, as well as
to account for any drift in telescope pointing by shifting individual frames
to match the location of the star spectrum, which is particularly important
when targeting the same mask for long periods without realigning due to
flexure of the system (Hutchison et al., 2020). The program weights each
exposure according to the seeing and throughput values before coadding the
frames and applying a telluric correction and flux calibration. Combined with
the weighting of individual frames, this method returns 2D spectra with
increases in SNR of $\sim 5\%$ relative to the MOSFIRE DRP. The resultant 2D
spectrum was collapsed in a narrow range around either the strongest emission
line or along the entire wavelength axis for continuum sources. This was fit
with a Gaussian which was subsequently used for weighting the 1D spectral
extraction (optimal extraction; Horne, 1986).

A modified version of the spec2D pipeline (Cooper et al., 2012) was used to
reduce C3VO DEIMOS spectra. This program performs wavelength fitting,
background sky subtraction, and 1D spectral extraction. Additional
modifications are detailed in Lemaux et al. (2019) and include improvements in
interpolation over the DEIMOS chip gap, throughput correction, and wavelength
solution.

####  2.2.5 Spectroscopic Redshift Determination

The MOSFIRE spectra were visually inspected to identify galaxies with emission
lines. At the redshifts considered in this work, emission lines from
$\rm{H}\beta$ and the [Oiii]$\lambda\lambda$4959,5007 doublet are the most
obvious features and when seen, a model consisting of three Gaussians is used
to obtain a spectroscopic redshift. This model has four parameters - the
redshift, the amplitudes of $\rm{H}\beta$ and [Oiii]$\lambda 5007$, and the
width of the lines. The level of stellar continuum is assumed to be constant
over the spectral range of the observations, and is taken to be the weighted
average flux outside of regions with emission lines. The amplitude of
[Oiii]$\lambda 4959$ is fixed to 30% that of [Oiii]$\lambda 5007$ (e.g.,
Schreiber et al., 2018a). In this work we are not concerned with the
quantification of line velocity widths, velocity offsets, or any broad line
components beyond obtaining a redshift as pertains to MOSFIRE spectra. A small
number of galaxies at lower redshifts, which had $\rm{H}\alpha$, [N
II]$\lambda\lambda 6548,6584$, and [S II]$\lambda\lambda 6718,6733$ in the
wavelengths probed by the MOSFIRE observations were fit with a similar multi-
Gaussian model. Each spectroscopic observation is additionally given a quality
flag in the style of the zCOSMOS, VUDS, and DEIMOS10k surveys described above
which denotes the confidence in the assigned spectroscopic redshift (see e.g.,
Le Fèvre et al., 2015; Lemaux et al., 2022, for more details). Additionally,
emission spatially offset from targeted galaxies that serendipitously fell in
MOSFIRE slits (or in DEIMOS slits, see below) was re-extracted and the same
redshift measurement and quality assessment process was performed on such
detections.

The DEIMOS spectra were interactively assigned spectroscopic redshifts by
using a modified version of the zspec environment (Newman et al., 2013) as
described in Lemaux et al. (2022). The modified version of the zspec software
incorporates empirical high-redshift galaxy templates from the VUDS and VVDS
(Le Fèvre et al., 2004, 2013) surveys as well as high-resolution empirical
Ly$\alpha$ templates from Lemaux et al. (2009). The quality flagging for these
data follow a DEEP2 style flag (Newman et al., 2013). Similar to the VUDS
flagging system, flags of 3 and 4 represent high confidence redshifts ($>95\%$
accurate). For example, the observation of a single emission line skewed
redward indicative of Ly$\alpha$ would result in flag 3, and the observation
of multiple spectral features would result in flag 4. Flags of 1 and 2
indicate low confidence redshifts. For consistency with the MOSFIRE data and
redshifts from the field surveys, C3VO-DEIMOS objects with a quality flag of 2
are changed to a quality flag of 1 when creating the master spectroscopic
catalog (next section). All spectra were independently inspected and flagged
by two of the authors (ES and BCL) and any objects receiving disparate
redshifts/flags were reconciled via a re-inspection of the spectra and
associated photometry (when available).

Figure 1: The process for determining the spread in voxel overdensity values
for a given redshift slice. Left: Histograms of all voxel overdensity values
(median set equal to zero) in redshift slices of $z=3.0772$ (top) and
$z=3.3485$ (bottom). A Gaussian model is fit to the distribution at each
slice, which produces a fit mean ($\mu$) and standard deviation ($\sigma$).
Right: The plot of the fit $\mu$ (top) and $\sigma$ (bottom) values for each
slice of the VMC map considered in this work. A polynomial is then fit to this
distribution to smooth out the effects of any large scale structures on these
values, and these polynomial values are used to determine the overdensity
significance ($\sigma_{\delta}$) of a given voxel. Herein we use the value of
a $5^{\rm th}$-order polynomial (green), though using a $2^{\rm nd}$ order
polynomial (red) for example does not effect the results. The redshifts of the
two slices shown on the left are given by dashed vertical lines.

###  2.3 Catalog Matching and Remodeling SEDs

While target selection for the various spectroscopic surveys used in this work
came from different parent photometric catalogs, we compare the spectroscopic
redshifts, sky coordinates, and $i$\- and $K$-band magnitudes from the
spectroscopic survey catalogs to the photometric redshifts, coordinates and
magnitudes in the same bandpasses from the COSMOS2020 Classic photometric
catalog to find the best match. For galaxies targeted in multiple surveys,
only the highest quality flag entry was kept. See Appendix A for more details
regarding the matching process. Of the 40008 final combined spectroscopic
catalog entries, 37771 (94.4%) have a match in the COSMOS2020 Classic catalog.
Additionally, 26676 (66.7%) spectroscopic targets have moderate-high quality
spectroscopic redshift measurements $0<z<7$ (quality flags X2, X3, X4, or X9).

With confirmed redshifts of these galaxies, it is necessary to remodel their
physical properties, which will change from those given in COSMOS2020 unless
the photometric redshift was identical to the spectroscopic redshift. While
there are many programs used to model galaxy spectral energy distributions
(SEDs), in this work we use LePhare (Arnouts et al., 1999; Ilbert et al.,
2006), as this program is used in the COSMOS2020 catalogs. We remodel all
spectroscopically confirmed galaxies using the same setup as in COSMOS2020
with the redshift now fixed to the spectroscopic redshift. Detailed
descriptions of these choices can be found in the catalog publications above,
as well as Ilbert et al. (2009).

As will be described shortly, we also perform a Monte Carlo resampling of the
$p(z)$ for all galaxies without a high confidence spectroscopic redshift. For
each such galaxy we run LePhare with the redshift fixed to values from
$3.0<z<3.7$ (the redshift range considered in this work) with $\Delta z=0.05$.
The results from this grid are then interpolated to the redshift of a galaxy
determined in an individual MC iteration. We found that the differences in the
fit stellar mass and SFR between adjacent redshift runs for a given galaxy
differ by $>0.1$ dex in less than 0.3% and 2.3% of cases, respectively, more
than sufficient for the studies herein, which validates this interpolation.

##  3 Analysis

###  3.1 Voronoi Tesselation Monte Carlo Mapping

We use the Voronoi Tesselation Monte Carlo (VMC) mapping technique to
determine galaxy environmental density, a method which has been extensively
tested and used to find overdense structures previously (Lemaux et al., 2017;
Tomczak et al., 2017; Cucciati et al., 2018; Lemaux et al., 2018; Hung et al.,
2020; Shen et al., 2021b; Lemaux et al., 2022; Forrest et al., 2023). This
method uses a combination of spectroscopic redshifts and photometric redshift
probability distributions to statistically determine density in three-
dimensional space.

####  3.1.1 Density maps

Voronoi cells are generated by drawing boundaries that are equidistant from
the two nearest galaxies in projected space. This strategy cannot be
effectively extended to the redshift dimension due to the redshift
uncertainties of objects in photometric catalogs as well as the uncertain
contributions of peculiar velocities for spectroscopically confirmed galaxies.
While high spectroscopic completeness could minimize effects of the former,
the spectroscopy in this work is too sparse to do so. As a result of these
uncertainties along the line of sight, the volume of interest is divided into
redshift slices and only galaxies within such a slice are considered. The
slice width is determined from a combination of photometric redshift
uncertainties and a consideration of overdensity sizes. Structures can be
missed either if slices are too narrow - when associated galaxies are not
grouped together - or if slices are excessively wide, which results in a
decrease in overdensity signal. Similar to previous work, slices of 7.5 pMpc
in depth are used ($\delta z\sim 0.036$ at $z=3.35$) with an oversampling
factor of $10\times$, that is the distance between central redshifts in
adjacent slices is 0.75 pMpc.

We perform 100 Monte Carlo (MC) iterations, in which the $p(z)$ of every
photometric galaxy is resampled to minimize the effect of photometric redshift
uncertainties. A statistical treatment of spectroscopic redshifts is also
included, in which the quality flag of the spectroscopic redshift determines
how often the spectral redshift is used as compared to a draw from that
galaxy’s $p(z)$ (see Appendix B of Lemaux et al., 2022). In practice, the
spectroscopically targeted galaxies with redshift quality flags of 3 or 4 have
their spectroscopic redshift used in $\sim$99.4% of all iterations (high
confidence), galaxies with redshift quality flags 2 or 9 have their
spectroscopic redshift used in $\sim$70.0% of all iterations, and galaxies
with redshift quality flags 0 or 1 do not have their spectroscopic redshifts
used at all. In such iterations where the spectroscopic redshift is not used,
the redshift of a galaxy for that iteration is determined via a draw from the
galaxy’s $p(z)$.

For each of the 100 iterations, Voronoi tesselation is performed on all
objects with magnitude $\left[3.6\right]<24.8$ that fall into a given redshift
slice for a given iteration. The results for each iteration are then regridded
onto a regular grid of size $75\times 75$ pkpc, with the median density at a
grid point in all iterations assigned to each voxel, $\Sigma_{{\rm
VMC},\alpha,\delta,z}$. Figure 3 of Tomczak et al. (2017) provides a
visualization of this process.

####  3.1.2 Overdensity maps

The typical density of the Universe evolves with time, and the measurement of
the average density from the VMC method is subject to differences in data
quality, detection bands, magnitude cuts, etc. As a result we are more
concerned with the relative overdensity of a galaxy’s environment rather than
a pure density value. This overdensity value is calculated by normalizing each
density in a redshift slice by the median density of all voxels in the map at
the same redshift, $\log(1+\delta_{{\rm VMC},\alpha,\delta,z})$=
log(1+$\Sigma_{{\rm VMC},\alpha,\delta,z}$/ $\tilde{\Sigma}_{{\rm VMC},z}$).
Additionally, given the extended nature of high-redshift protoclusters, the
possibility exists that the entire field may be over- or underdense in a
particular redshift slice, which could bias our overdensity calculations. To
account for this, we fit a Gaussian to the distribution of
$\log(1+\delta_{{\rm VMC},\alpha,\delta,z})$ values in each redshift slice, to
obtain the average and standard deviation of the overdensity values therein
(left panels of Figure 1). A $5^{\rm th}$-order polynomial is then fit to the
average overdensities as a function of redshift, removing any effects of
field-filling over- or underdensities and obtaining a smoothed overdensity
distribution, $\log(1+\delta_{f^{5},\alpha,\delta,z})$ (right panels of Figure
1). We note that the differences between these two measures of overdensity,
$\log(1+\delta_{{\rm VMC},\alpha,\delta,z})$ and
$\log(1+\delta_{f^{5},\alpha,\delta,z})$, are on the order of several parts in
one thousand, which is $\sim 10\times$ smaller than the spread of values at a
given redshift, and thus in general does not have a significant effect on our
results.

Finally, the overdensity of a galaxy $\log(1+\delta_{\rm gal})$ is simply the
fit overdensity value $\log(1+\delta_{f^{5},\alpha,\delta,z})$ of the voxel
which contains the galaxy’s three-dimensional position in space in a given
iteration. We also calculate the number of standard deviations of a galaxy’s
overdensity value, $\sigma_{\delta}$, above or below the fit median using the
fit standard deviation value at the redshift of interest. This value will be
the primary overdensity metric used in this work.

Figure 2: The relative numbers of photometric and spectroscopic galaxies in
COSMOS in 3′$\times$3′ bins across $3.0<z<3.7$ near the VUDS footprint (black
dashed outline). Top: The number of galaxies from the COSMOS2020 catalog in
3′$\times$3′ bins with photometric redshifts $3.0<z<3.7$. The structures
associated with Elentári (Forrest et al., 2023) are shown as contours
representing $2\sigma$ and $5\sigma$ overdensities collapsed over $3.0<z<3.7$.
Middle: Similar to the top panel, but showing the spectroscopic sampling rate
(SSR). Bottom: Similar to the top panel, but showing the spectroscopic
redshift fraction (SzF).

###  3.2 Structure Identification

As described in Cucciati et al. (2018); Shen et al. (2021b), we identify
overdense structures by finding all contiguous voxels with $\sigma_{\delta}>2$
($>5$ for peak regions). The volume enclosed within these envelopes can then
be converted to a total mass based on the average comoving matter density,
average overdensity of voxels within the envelope, and the galaxy sampling
bias. Following this process, a set of coeval structures with enclosed masses
$\log(M_{\rm tot}/$M${}_{\odot})\gtrsim 14$ in close proximity at
$3.20<z<3.45$ were identified in Forrest et al. (2023). While that work
focused on characterization of the structures themselves, in this work we
analyze the galaxy populations therein.

In many studies of overdense structures, members are defined as being within
some spherical radius of a central point in the structure. However at early
epochs such as this, protocluster systems are not necessarily spherically
symmetric in nature, and the VMC maps allow for accounting and inclusion of
some of these asymmetries. This lack of symmetry also means that an accurate
determination of the extent and overdensity of these structures is critical to
drawing accurate conclusions about the effects such environments have on their
component galaxies.

####  3.2.1 Effects of Uneven Spectroscopic Sampling

To this end, analyzing the dependence of overdensity significance on
spectroscopic completeness is a critical test. Using the above VMC method, a
real overdensity with all members spectroscopically confirmed will have a
stronger signal (higher $\sigma_{\delta}$) than the same overdensity with no
spectroscopically confirmed members as the latter will have the total signal
spread out in redshift space due to the width of the $p(z)$ for member
galaxies. Alternatively, if a region has little to no spectroscopically
confirmed galaxies, it is possible that the VMC data may identify an
overdensity when none is truly there. Such a situation occurs when the $p(z)$
distributions of many galaxies in a small projected area, potentially
including background and foreground objects, overlap significantly in redshift
space.

We attempt to quantify these effects by considering galaxies with
$\left[3.6\right]<24.8$ and analyzing the spatial variance of: 1) the
spectroscopic sampling rate (SSR) - the number of galaxies photometrically
within a given volume which have been spectroscopically targeted divided by
the total number of galaxies with a photometric redshift within that same
volume, and 2) the spectroscopic redshift fraction (S$z$F), which we define
here as the number of galaxies which have a high confidence spectroscopic
redshift within some volume divided by the number of galaxies with a
photometric redshift within that same volume. We calculate these fractions in
spatial bins of $3\arcmin\times 3\arcmin$ over the full $3.0<z<3.7$ redshift
range considered for Elentári and the associated field. This is shown in
Figure 2 along with the number of objects with photometric redshifts in each
bin.

As can be seen in the bottom two panels of Figure 2, the SSR and S$z$F both
fall off significantly outside of the VUDS footprint (dashed line) while the
number of photometric targets stays roughly constant across the same boundary
(top panel). Overdensities identified in regions with low S$z$F have an
increased probability of being false detections as the signal may be dominated
by broad photometric redshift probability distributions, e.g., S6 from Forrest
et al. (2023), shown by the very extended gray contour in the NE. However,
some regions with low S$z$F may still be real if there are significant
spectroscopic confirmations, e.g., the extension of S1 from Forrest et al.
(2023) (red contours) outside of the VUDS footprint. This particular region
has 14 confirmed spectroscopic members from targeted follow-up with MAGAZ3NE
(McConachie et al., 2022). Clearly, further spectroscopic observations of
potential overdensities in such regions can resolve this issue.

The possibility also exists that overdensities identified in regions with high
SzF and SSR, while real, are less overdense in reality than the VMC maps would
suggest. To ensure this effect is not influencing our results significantly,
we rerun the VMC mapping analysis ignoring the spectroscopic redshifts from
C3VO and MAGAZ3NE. Removing this spectroscopy from our sample limits the
effects of intentional spectroscopic targeting of overdense regions as all
other surveys targeted galaxies across the COSMOS field as a whole. Rerunning
the VMC mapping and overdensity detection in this manner produces the results
shown in Figure 3, where new structure overdensity contours of +2$\sigma$ and
+5$\sigma$ are shown as filled cyan and magenta regions, respectively, and the
original Elentári overdensities as reported in Forrest et al. (2023) are shown
as open colored contours.

Using the same structure identification routine, the centers of commonly
identified structures differ by medians of 78″ (0.58 pMpc) in projection and
0.002 in redshift. However, this can be split into those structures mostly
within the VUDS footprint (S2 - orange contour on Fig. 3 \- and S3 in green)
with projected offsets of 8.1″ (0.06 pMpc) and 22″ (0.16 pMpc), and those
which extend outside (S1 in red and S6 in gray) with projected offsets of 133″
(0.99 pMpc) and 160″ (1.2 pMpc). For the former two structures the two maps
result in volume differences of 8.0% and 0.7% and mass differences of 0.04 dex
and 0.01 dex, in remarkable agreement. The overdensity-weighted central three-
dimensional locations for commonly identified +5$\sigma$ peaks differ in the
two cases by similar amounts, with median differences of 18″ (0.13 pMpc) in
projection and 0.002 in redshift. Noting that the typical systematic
uncertainty for determining the stellar mass of a galaxy at similar epochs is
estimated to be $\sim 0.2$ dex (Mobasher et al., 2015; Leja et al., 2019), the
characterization of these structures’ masses and positions is robust to the
effects of targeted spectroscopic followup at the levels obtained. Regions
extending beyond the VUDS outline without significant additional spectroscopy
may be difficult to characterize accurately without additional data however.
On the whole, we conclude that the targeted spectroscopic followup has not
significantly biased our characterization of the Elentári system, and for the
remainder of this work consider the structure extends as in Forrest et al.
(2023).

Figure 3: The recovery of overdensities in the field of interest with targeted
follow-up spectroscopy (empty colored contours at +2$\sigma$ and +5$\sigma$)
and without targeted follow-up spectroscopy (filled cyan and magenta contours
at +2$\sigma$ and +5$\sigma$). The former set are as presented in Forrest et
al. (2023).

###  3.3 The Stellar Mass Function

In order to investigate environmental effects on galaxy evolution, we
construct stellar mass functions (SMFs) based on the overdensities derived
from the VMC maps. Similar to the generation of the VMC maps, we run 100
realizations drawing from the $p(z)$ of galaxies without reliable
spectroscopic redshifts and determine the significance of the overdensity in
which each galaxy resides, $\sigma_{\delta}$, from the VMC map at the galaxy’s
redshift in the realization. All galaxies are subsequently refit using LePhare
with the same methodology as when refitting the spectroscopically confirmed
galaxies, but instead using the redshifts drawn from the $p(z)$ and the
interpolated fits with $\delta z=0.05$. The resultant galaxy stellar masses
are then used to construct SMFs. The volume associated with a SMF is the
volume of the VMC map within the associated redshift and $\sigma_{\delta}$
cuts.

For each realization, SMFs are constructed over $3.20<z<3.45$ from galaxies in
bins of $\sigma_{\delta}$: $-5<\sigma_{\delta}<2$ (field),
$2<\sigma_{\delta}<3$, $3<\sigma_{\delta}<4$, and $\sigma_{\delta}>4$. There
are insufficient galaxies at $\sigma_{\delta}>5$ to recover a SMF in this
regime with a large enough signal-to-noise ratio (SNR) to make significant
conclusions. Similarly, considering only galaxies within each structure of
Elentári separately leads to small numbers of high-mass galaxies which make
the uncertainties too large to justify drawing strong conclusions. Consistent
results are found from constructing a combined SMF for all galaxies in all
regions of Elentári and from calculating the SMF based on overdensity values
of $\log(1+\delta_{\rm gal})$ as well. We confirm that the field SMF is
insensitive to other possible definitions, for example averaging galaxies with
$-5<\sigma_{\delta}<2$ at $3.0<z<3.2$ and $3.5<z<3.7$ and that the field SMF
is also in very good agreement with those over $3<$$z_{\textrm{phot}}$$<4$
based on the COSMOS2015 (Davidzon et al., 2017) and COSMOS2020 (Weaver et al.,
2023) catalogs.

Figure 4: The stellar mass function in several bins of overdensity at
$3.20<z<3.45$. Left: The SMF of the field from COSMOS2020 over $3.0<z<3.5$
(Weaver et al., 2023) is shown as a series of pink squares, while the field as
measured in this work is shown as a series of black points. The SMFs of
galaxies in bins of $2<\sigma_{\delta}<3$, $3<\sigma_{\delta}<4$, and
$\sigma_{\delta}>4$ are shown as blue, periwinkle, and gold points,
respectively. Error bars from this work represent the range of 16th to 84th
percentiles from MC iterations added in quadrature to Poisson noise. Note that
this does not include uncertainty due to cosmic variance, which is the
dominant source of error in the COSMOS2020 analysis, and thus the error bars
between the two works should not be compared. Masses below the stellar mass
completeness limits at $z=3.3$ for the COSMOS2015 and COSMOS2020 catalogs are
shaded. Right: The best-fit Schechter function to each measured SMF is shown
as a solid line with the same color scheme. Another fit to each SMF performed
fixing $\alpha$=-1.3 is shown as a dashed curve.

The median SMFs in each overdensity bin from all realizations are shown in
Figure 4, with error bars representing the 16th-84th percentile range. In
addition to the vertical offset that is a result of the selected regions being
overdense, a difference in the shape of the SMFs is also apparent and can be
seen in Figure 5, in which the ratio of each SMF with that of the field is
displayed. In all overdense regions, there is a trend of increasingly elevated
SMF relative to the field with increasing stellar mass, a pattern also seen in
lower redshift cluster SMFs (Tomczak et al., 2017; van der Burg et al., 2020),
as well as in individual protoclusters at $z=2.16$ (Shimakawa et al., 2018a)
and $z=2.53$ (Shimakawa et al., 2018b). This higher ratio of high-mass to low-
mass galaxies in overdense regions is consistent with galaxies in protocluster
environments undergoing, or having previously undergone, increased stellar
mass build-up relative to field galaxies.

We compare our results to those from the $z\sim 1$ ORELSE survey (Tomczak et
al., 2017), which used a similar methodology for determination of overdensity.
The qualitative trends seen in the $z\sim 1$ cluster sample are similar to
those in this work, with the ratio of high-mass to low-mass galaxies
increasing with increasing overdensity. Additionally, as shown in Figure 5,
when converting our SMFs from $\sigma_{\delta}$ to $\log(1+\delta_{\rm gal})$
we find that the SMF for galaxies at similar overdensities appears the same at
both $z\sim 1$ and $z\sim 3.3$. The field of interest in this work and those
in Tomczak et al. (2017) have different photometric bandpasses and depths, as
well as different spectroscopic depths and SSR/SzF, which add uncertainty to
such a direct comparison. However, this similarity of SMFs at similar
overdensities at different redshifts would be consistent with the hypothesis
that group environments, galaxy associations with lower total masses ($\sim
10^{13}$ M⊙) than protoclusters, are host to evolutionary effects (e.g.,
mergers) which ‘pre-process’ galaxies before their eventual residence in
cluster environments (Zabludoff et al., 1996; McGee et al., 2009; De Lucia et
al., 2012; Bahé et al., 2019; Reeves et al., 2021).

Additionally, we fit a single-Schechter function (Schechter, 1976) to each
SMF, first allowing the characteristic turnover mass ($M^{*}$), faint-end
slope ($\alpha$), and normalization ($\phi^{*}$) parameters to vary, and then
again fixing $\alpha=-1.3$, in rough agreement with previous results (e.g.,
Marchesini et al., 2009; Muzzin et al., 2013b; Tomczak et al., 2014). The
best-fit parameterizations are given in Table 3. We compare the characteristic
turnover mass and faint-end slope values to those from studies of $z\sim 1$
cluster SMFs (Tomczak et al., 2017; van der Burg et al., 2020) shown in Figure
6. In general, we find that $M^{*}$ decreases and $\alpha$ becomes shallower
with increasing overdensity. This is perhaps not so much due to the stellar
mass of the average galaxy decreasing, but is instead a result of
environmental processes increasing the number of galaxies around or just below
the characteristic mass. This increase may be due to increased merger rates in
overdense environments (Tomczak et al., 2017), preferential enhancement of SFR
in high mass galaxies in overdense environments, increased numbers of
quiescent galaxies (Nantais et al., 2016; van der Burg et al., 2018, 2020), or
an underlying bias in galaxies in overdense environments relative to those in
the field (Ahad et al., 2024).

Finally, we confirm that the observed difference in SMF shape is not due to
preferential scattering of low mass galaxies with broader $p(z)$ out of the
overdensity. We use a toy model to resample redshifts, stellar masses, and
overdensity membership of 1000 galaxies 1000 times in a mock region of sky,
and then reconstruct SMFs (details in Appendix B). No evidence for a mass-
dependent bias is observed.

Figure 5: The ratio of the stellar mass function at different overdensities to that observed in the field. The gold, periwinkle, and blue points are as in Fig. 4 and represent galaxies in regions with overdensities of roughly $0.23<\log(1+\delta)<0.34$, $0.34<\log(1+\delta)<0.45$, and $\log(1+\delta)>0.45$ at $z\sim 3.3$. Similar points from Tomczak et al. (2017) at $z\sim 1$ are shown as squares for comparison. SMFs of similar overdensity seem to scale to the field in similar manners at both redshifts. Figure 6: Comparison of the characteristic mass ($M^{*}$) and faint-end slope ($\alpha$) fit values from studies of the SMF in overdense environments. Values from this work are shown as circles of the same colors as in Fig. 4, values from $z\sim 1.2$ GOGREEN clusters van der Burg et al. (2020) are grayscale triangles, and values from $z\sim 0.9$ ORELSE clusters Tomczak et al. (2017) are cyan to magenta squares. A simple weighted linear fit for each dataset is shown in gold, gray, and magenta, respectively. Table 3: The parameters of Schechter function fits to the SMFs at varying densities. The best-fit values for varying $M*$, $\alpha$, and $\phi*$ are shown as are the results for fixing $\alpha=-1.3$. Density bin | $\log(M^{*}/{\rm M}_{\odot})$ | $\alpha$ | $\phi^{*}/(10^{-3}\rm{\ Mpc}^{-3})$
---|---|---|---
$\sigma_{\delta}<2$ | 10.86$\pm$0.10 | -1.63$\pm$0.04 | 0.16$\pm$0.04
| 10.20$\pm$0.05 | =-1.3 | 0.87$\pm$0.07
$2<\sigma_{\delta}<3$ | 10.58$\pm$0.03 | -1.42$\pm$0.01 | 0.66$\pm$0.04
| 10.40$\pm$0.03 | =-1.3 | 1.07$\pm$0.05
$3<\sigma_{\delta}<4$ | 10.08$\pm$0.10 | -0.86$\pm$0.09 | 4.83$\pm$0.78
| 10.58$\pm$0.19 | =-1.3 | 1.49$\pm$0.33
$\sigma_{\delta}>4$ | 10.38$\pm$0.14 | -0.86$\pm$0.17 | 6.57$\pm$2.00
| 11.10$\pm$0.20 | =-1.3 | 1.40$\pm$0.35

###  3.4 Quiescent Fractions

The fraction of galaxies with SFRs below the main sequence of star formation
(i.e., quenched) at a given epoch is significantly increased in cluster
environments relative to the coeval field out to $z\gtrsim 1$ (van der Burg et
al., 2013; Tomczak et al., 2017; van der Burg et al., 2020), though the
majority of massive satellite galaxies at this epoch appear to have been
quenched before cluster infall (Baxter et al., 2022; Werner et al., 2022).
High-redshift protocluster environments at $z\gtrsim 2$ do not generally show
these same quenched fractions, but some counterexamples appear to exist, at
least with regards to high mass galaxies (Chartab et al., 2020; Shi et al.,
2021; Ito et al., 2023), which has been seen in one of the peaks of Elentári
(McConachie et al., 2022). Analyzing how the SMFs of such quenched galaxies
vary relative to the field environments can help uncover the mechanisms
responsible for accelerated evolution of galaxies in overdense systems (e.g.,
Tomczak et al., 2017; Papovich et al., 2018).

For each of the 100 $p(z)$ sampling realizations, we calculate the number of
quiescent and star-forming galaxies over $3.20<z<3.45$ in two ways. First, we
use the popular comparison of $(U-V)$ and $(V-J)$ rest-frame colors (e.g.,
Williams et al., 2009; Muzzin et al., 2013a; Straatman et al., 2016) as
modeled by LePhare and the wedge location specified for $2.0<z<3.5$ from
Whitaker et al. (2011). We also fit the relation between SFR and stellar mass
(e.g., Daddi et al., 2007; Noeske et al., 2007; Salmon et al., 2015) by
finding the median SFR in overlapping bins of width 0.2 dex with centers
separated by 0.01 dex, smoothing via a first-order Savitzsky-Golay filter, and
fitting with a quadratic polynomial. Galaxies with SFRs more than 1 dex below
this ‘star-forming main sequence’ (SFMS) are then considered quiescent. The
resultant numbers of galaxies with $\log(M_{*}/\rm{M}_{\odot})$$>9.1$, the
mass completeness of the COSMOS2020 Classic catalog at this redshift, are
given in Table 4.

While the numbers of identified quiescent galaxies in the overdense regions
are too small to construct SMFs from, we can compute quiescent fractions,
which we plot in the right panel of Figure 7, along with quiescent/star-
forming selections for an example MC iteration in the left and middle panels.
No statistically significant differences between field and overdense
environments are seen, though the uncertainties are significant. The two
methodologies also seem to be in general agreement, with the $UVJ$ color
selection identifying more quiescent galaxies than the SFMS cut, particularly
for galaxies with $\log(M_{*}/\rm{M}_{\odot})$ $<10$.

We do note however, that while the COSMOS2020 photometric catalog is complete
down to $\log(M_{*}/\rm{M}_{\odot})$ $\sim 9.1$ at $z\sim 3.3$, most of the
spectroscopy used for construction of the VMC maps is biased toward the
detection of star-forming galaxies, which may artificially decrease the
quenched fractions seen here. The follow-up observations with MOSFIRE are less
sensitive to this bias, but still no enhancement in quenched fraction relative
to the field is seen in the overdense environments which were targeted with
MOSFIRE.

Table 4: The number of star-forming ($N_{SF}$) and quiescent galaxies ($N_{Q}$) and the associated quenched fractions (QF) in the field and overdensity samples across $3.20<z<3.45$ identified using $UVJ$ colors and the SFMS. Two sets of results are shown, one only considering galaxies with masses $\log(M_{*}/\rm{M}_{\odot})$ $>10.0$ and one considering galaxies with masses $\log(M_{*}/\rm{M}_{\odot})$ $>9.1$.  | $UVJ_{\rm M>9.1}$ | $UVJ_{\rm M>10}$ | SFMSM>9.1 | SFMSM>10
---|---|---|---|---
$N_{\rm SF,field}$ | 3593${}^{+129}_{-137}$ | 463.0${}^{+37.0}_{-38.0}$ | 3688${}^{+131}_{-136}$ | 477.0${}^{+39.0}_{-36.0}$
$N_{\rm Q,field}$ | 130.0${}^{+40.0}_{-29.0}$ | 50.0${}^{+23.0}_{-14.0}$ | 37.0${}^{+17.0}_{-12.0}$ | 37.0${}^{+15.0}_{-12.0}$
$N_{\rm SF,od}$ | 398.0${}^{+81.0}_{-71.1}$ | 61.5${}^{+24.0}_{-22.1}$ | 398.0${}^{+88.6}_{-65.1}$ | 59.0${}^{+29.0}_{-18.9}$
$N_{\rm Q,od}$ | 7.5${}^{+13.8}_{-7.1}$ | 4.0${}^{+6.3}_{-4.0}$ | 2.0${}^{+5.4}_{-1.7}$ | 2.0${}^{+5.4}_{-1.7}$
$QF_{\rm field}$ | 3.49${}^{+1.07}_{-0.78}$ | 9.75${}^{+4.48}_{-2.73}$ | 0.99${}^{+0.46}_{-0.32}$ | 7.20${}^{+2.92}_{-2.33}$
$QF_{\rm od}$ | 1.85${}^{+3.40}_{-1.74}$ | 6.11${}^{+9.66}_{-6.11}$ | 0.50${}^{+1.34}_{-0.43}$ | 3.28${}^{+8.77}_{-2.84}$
Figure 7: The identification of star-forming and quiescent galaxies at
$3.20<z<3.45$. Left: The restframe $UVJ$ color-color plane for a single MC
iteration. Red symbols above/left of the dividing wedge are considered
quiescent, with squares indicating those galaxies in overdense environments
and circles indicating galaxies in the field. Blue symbols below/right of the
dividing wedge are classified as star-forming. Center: The SFR-stellar mass
plane for a single MC iteration. The solid black curve is the median relation
termed the star-forming main sequence (SFMS), while the dashed curve is 1 dex
below the SFMS and is used to distinguish between star-forming and quiescent
galaxies. The symbol colors and shapes remain the same. Right: The quenched
fraction as a function of stellar mass averaged over all 100 MC iterations.
Orange circles represent the field quenched fraction identified using the
$UVJ$ selection. Green circles represent the field quenched fraction
identified using the SFMS selection. Purple squares represent the overdensity
quenched fraction identified using the $UVJ$ selection. Turquoise squares
represent the overdensity quenched fraction identified using the SFMS
selection. Downward-facing arrows indicate upper limits. While an increasing
trend with stellar mass is seen, the sample sizes are insufficient to
distinguish between the quenched fractions in field and overdense
environments.  Figure 8: Comparison of stellar mass, stellar age, and
environmental overdensity from SED fitting for spectroscopically confirmed
galaxies at $3.0<z<3.7$ in COSMOS shown in three different projections. Median
values are shown by the large circles, with the error bars representing the
uncertainty on the calculated median. The Spearman $\rho$ coefficient and
$p$-value are shown in each panel for the set of parameters on the ordinate
and abcissa.

###  3.5 Relations between Stellar Mass, Age, and Overdensity

Observed increases in the masses of galaxies residing in overdense
environments relative to the field population could be caused by factors such
as enhanced SFRs due to gas inflows or bursts of star formation as a result of
increased merger rates. Depending on when these effects occur, it is possible
that the ages of galaxies of a given mass will have a dependence upon their
environment as seen at lower redshifts (e.g., Cooper et al., 2010a), though
these appear small at $z\sim 1.3$ (Webb et al., 2020). While in theory stellar
ages can be discerned from spectral absorption features and the shape of the
SED, the spectra of the vast majority of sources in this work do not have the
requisite SNR to measure ages precisely, having spectral detections of
emission lines only. In an attempt to discern age differences between the
field and structure populations, we fit the photometry of each
spectroscopically-confirmed galaxy with the redshift fixed to the
spectroscopic redshift using the LePhare (Arnouts et al., 1999; Ilbert et al.,
2006) and FAST++ (Schreiber et al., 2018b) programs. We then compare the
stellar mass and age derived from these fits to the $\sigma_{\delta}$ of each
galaxy and perform a Spearman correlation test (Figure 8).

As seen in the SMF analysis, we find a weak ($\rho=0.105$), though significant
($p=0.008$) correlation between massive galaxies and overdense environments,
similar to that found over $2<z<5$ in Lemaux et al. (2022). A commonly found
correlation between stellar mass and age is also recovered ($\rho=0.476$,
$p<0.0001$). However, there is no significant trend for this sample between
age and overdensity. This could indicate that gas-rich mergers which trigger
bursts of star formation are not responsible for the increased stellar masses
of galaxies in these overdense environments, although some studies suggest
that such bursts are not as pronounced at higher redshifts(Shah et al., 2022).
In this case, mergers could build high stellar mass galaxies without adding a
significant younger stellar population. Some other intrinsic difference
between galaxies in overdense and field environments may also be responsible
(Ahad et al., 2024). It should be noted though that age determinations from
SED fitting have significant uncertainties as well as degeneracies with
stellar mass and dust extinction (e.g., Mobasher et al., 2015), and thus
drawing strong conclusions from these tests is not supported.

##  4 Conclusions

In this work we construct and compare stellar mass functions and quiescent
fractions in several bins of environmental overdensity in the COSMOS field
centered on the Elentári overdensity at $z\sim 3.33$. Such an analysis is only
possible at these epochs with the extensive amounts of photometry and
spectroscopy available in well-studied fields such as COSMOS. These are used
to build a three-dimensional density map to accurately estimate the
environmental density field in which a galaxy resides. We consider in this
work galaxies above the approximate stellar mass completeness of the
COSMOS2020 catalog at $z\sim 3.3$, $\log(M_{*}/\rm{M}_{\odot})$ $\sim 9.1$.

We observe distinct shapes of the stellar mass function between galaxies in
overdense environments and galaxies in the field at $3.20<z<3.45$, with the
densest regions having number densities $\sim 6\times$ that of the field for
galaxies with $\log(M_{*}/\rm{M}_{\odot})$ $\sim 10.0$, compared to only $\sim
3\times$ that of the field for galaxies with $\log(M_{*}/\rm{M}_{\odot})$
$\sim 9.5$. This distinction clearly indicates that the environment in which a
galaxy resides begins to have an effect on its evolution prior to the galaxy
entering a cluster environment. The increased number of high mass galaxies in
dense environments is suggestive of the long-theorized ‘pre-processing’, in
which the masses of such galaxies are enhanced in proto-cluster or even group
systems via mergers and/or increased in situ SFRs before infall into proper
clusters, eventually resulting in the quenching of star formation in these
overdense systems before quenching in field galaxies. The quiescent fractions
of galaxies in field and overdense environments do not differ, peaking at
$\sim 20-30$% for galaxies with $\log(M_{*}/\rm{M}_{\odot})$ $\sim 11.0$. This
may suggest that while processes of mass enhancement in overdense environments
have begun, processes which enhance the quenched fraction in these same
environments have not yet had significant effects. We note however, that the
uncertainties on these measurements are large and that the spectroscopic
surveys in this work are in general more sensitive to star forming
populations. More dedicated observations of quiescent candidates identified
from photometry are required for stronger conclusions.

Finally, we compare the relationship between stellar mass, stellar age, and
environmental overdensity of spectroscopically-confirmed galaxies. We find
statistically significant positive correlations between stellar mass and
stellar age, as well as between stellar mass and environmental overdensity.
This again suggests that the overdense structure of the Elentári proto-
supercluster may be affecting the evolution of member galaxies through
enhanced stellar mass growth, but is inconclusive on the matter of enhanced
quenching of member galaxies. Further observations, particularly of the
densest protocluster cores in Elentári are necessary to uncovering the extent
and significance of these effects.

##  5 Acknowledgements

The authors wish to recognize and acknowledge the very significant cultural
role and reverence that the summit of Maunakea has always had within the
indigenous Hawaiian community. We are most fortunate to have the opportunity
to conduct observations from this mountain. This work is also based on
observations collected at the European Southern Observatory under ESO
programmes 175.A-0839, 179.A-2005, and 185.A-0791, as well as work supported
by the National Science Foundation under Grant No. 1908422. GW gratefully
acknowledges support from the National Science Foundation through grant
AST-2205189 and from HST program number GO-16300.

This work has relied heavily upon code developed by other people, for which we
are quite thankful.

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##  Appendix A Object Matching

We use observations of galaxies from the zCOSMOS (Lilly et al., 2007), VUDS
(Le Fèvre et al., 2015), and DEIMOS10k (Hasinger et al., 2018) spectroscopic
surveys, as well as observations taken with Keck/MOSFIRE as part of the C3VO
(Lemaux et al., 2022) and MAGAZ3NE (Forrest et al., 2020) surveys to construct
a master spectroscopic catalog. The targets in these samples are drawn from
various observational catalogs in the COSMOS field and here we detail the
process of matching these observations to galaxies in the COSMOS2020
photometric catalog (Weaver et al., 2022).

###  A.1 Astrometric Correction

For each spectroscopic survey, each spectroscopic entry ($s_{i}$) is matched
to the nearest photometric catalog member ($p_{j0}$) in projected space. The
coordinates for spectroscopic entries are then updated based on the median
positional offsets between the data sets, median($\Delta\alpha_{i,j0}$) and
median($\Delta\delta_{i,j0}$), providing a first-order astrometric correction.
These median offsets are $\lesssim 0.1^{\prime\prime}$ arcseconds in all
cases.

###  A.2 Positional Threshold

Catalog matching is performed again to find the nearest photometric catalog
member ($p_{j}$). We then use the distribution of distances between matches to
calculate our matching tolerance, considering that this distribution is
composed of a combination of correct matches and random nearest matches in
cases where the spectroscopic target is not in the photometric catalog. These
two components become clear by analyzing the histogram of logarithmic distance
separations (Figure A.1).

We fit a Gaussian to each of these distributions and take the $3\sigma$ upper
limit for the main peak (assumed to be correct matches) to be the distance
threshold within which to search for a given spectroscopic survey.
Alternatively taking the $3\sigma$ limit from fitting a single Gaussian to the
entire distribution or by choosing the distance at which the contribution of
the two Gaussians are equal, while changing the number of galaxies matched,
does not result in differences to the scientific conclusions of this work. For
objects in the VUDS, C3VO, zCOSMOS, and DEIMOS10k surveys, this search radius
threshold is 0.70”, 0.53”, 0.49”, and 1.35”, respectively, which successfully
matches 91.0%, 94.2%, 95.0%, and 92.7% of entries.

Figure A.1: Determination of matching thresholds. The distribution of
distances from each spectroscopic object to the nearest photometric catalog
member after a bulk astrometric correction is plotted as a gray histogram. A
two Gaussian model is fit, with the green representing ‘true’ matches and the
red representing random matches. A green vertical line shows the $+3\sigma$
value of the ‘true’ Gaussian fit, with the associated separation, percentage
of matches within that separation, and the ratio of amplitude of the two
Gaussian components at that distance given.

###  A.3 Single Matches

If there is a single photometric match to a spectroscopic object within the
$3\sigma$ radius threshold of a survey, we take the two entries to be matches
to the same object.

###  A.4 Multiple Matches

Many of the spectroscopic entries in the catalog have more than one
photometric catalog member which satisfies both the distance and magnitude
threshold cuts above. In these cases, comparisons are also made between the
spectroscopic redshift and the photometric redshifts of potential matches, as
well as differences in their total $i$\- and $K$-band magnitudes, resulting in
a four-parameter comparison. If no other spectroscopically-confirmed galaxies
are nearby, the photometric member with the better weighted combination of
values is determined to be the correct match. If another spectroscopic entry
is also nearby, the photometric and spectroscopic entries are paired based on
closest positional match.

###  A.5 No Matches

There are 2237 spectroscopic entries in the catalog which have no photometric
catalog members that satisfy the distance threshold cuts above. These objects
are retained in the final spectroscopic catalog and are not considered when
generating the VMC maps or further analyses as they do not have the requisite
photometry for performing SED fitting to determine stellar mass, SFR, etc.

###  A.6 Duplicates

At this point, each spectroscopic object is considered to be matched to the
correct photometric catalog object. As such, photometric catalog objects with
multiple spectroscopic matches exist and are given a true multi-spec flag. If
these spectroscopic entries (which have a quality flag of 3, 4, or 9) have the
same redshift, this is considered the spectroscopic redshift. When discrepant
spectroscopic redshifts with identical good quality flags exist, the
instrument and survey are used to determine the correct redshift. In order of
priority, these are: C3VO, MAGAZ3NE, VUDS, DEIMOS-10k, zCOSMOS (updated
catalog), zCOSMOS (original catalog).

##  Appendix B SMF Significance Testing

It is possible that the observed difference in the SMF of members of the
Elentári protostructure and the coeval field could be partially or entirely
due to differential effects related to large photometric redshift
uncertainties. More specifically, assuming that lower mass galaxies have
broader $p(z)$, they are more likely to scatter in and out of different
environmental bins than high mass galaxies. If both the field and overdensity
SMF have the same intrinsic shape and are simply different in normalization,
then due to the fairly small redshift extent of the higher density bins
presented in this work, a broader $p(z)$ for lower mass galaxies relative to
their more massive counterparts would potentially lead to a differential loss
of such galaxies within the highest density bins as they will scatter out of
the volumes associated with the higher density environments and into those
associated with the lower density environments more frequently than higher
mass galaxies. Under such a scenario the SMF in higher density bins would then
appear to have a lower ratio of low-mass to high-mass galaxies than the field.

We use a toy model to test whether such an effect can reproduce the observed
results. We start by assuming that the only difference in the field and
overdensity SMFs is the normalization (factor of 10 difference) and that
overdensities have a volume filling factor of $\sim 3\%$ (Chiang et al.,
2017), and then populate a mock region of sky with 1000 galaxies. The
probability of a random galaxy residing in the field/overdensity will then be

$\displaystyle p_{f}$ $\displaystyle=$ $\displaystyle\frac{0.97\times
1}{0.03\times 10+0.97\times 1}\times 100\%=76.4\%$ (B1) $\displaystyle p_{o}$
$\displaystyle=$ $\displaystyle\frac{0.03\times 10}{0.03\times 10+0.97\times
1}\times 100\%=23.6\%$ (B2)

Field galaxies are distributed randomly across the mock projected area and
assigned a random redshift in the range $3.0<z<3.7$. Overdensity members are
assigned positions based on random draw from a Gaussian in each dimension such
that the $\pm 2\sigma$ values encompass 3% of the total volume. The centers
and widths of these Gaussians are $\mu_{\alpha}=\mu_{\delta}=0$,
$\mu_{z}=3.325$, $\sigma_{\alpha}$=$\sigma_{\delta}$=0.14,
$\sigma_{z}$=0.0625. Each galaxy is then assigned a stellar mass drawing from
the SMF.

With each galaxy assigned a ‘true’ position, redshift, and stellar mass, we
now assign redshift probability distributions based on uncertainties from the
COSMOS2020 catalog. Each galaxy is assigned a $p(z)$ which is an asymmetrical
Gaussian. The center of this Gaussian is drawn from a Gaussian characterized
by the mean and standard deviation of the offset between spectroscopic and
photometric redshifts at $3.0<z<3.7$ ($0.09\pm 0.29$). Similarly, the width of
each side of the Gaussian is drawn from a Gaussian characterized by the mean
and standard deviation of the $16^{\rm th}$ and $84^{\rm th}$ percentiles of
the $p(z)$ of galaxies at similar stellar mass at $3.0<z<3.7$.

We then run 1000 Monte Carlo iterations, in each one randomly drawing a
‘measured’ redshift from the $p(z)$ of each galaxy. A ‘measured’ stellar mass
is determined from the difference between ‘measured’ and ‘true’ redshifts
combined with an uncertainty of 0.2 dex (e.g., Mobasher et al., 2015; Wang et
al., 2023). The overdensity or field membership of a galaxy is then determined
based on the three dimensional position of the galaxy relative to the known
overdensity extent. A SMF is then constructed for the field and the overdense
regions using the medians of all 1000 iterations with uncertainties given by
the 16th and 84th percentile values.

This process is run ten times to remove any bias due to assignment of galaxy
locations. In all runs, the ratio between the overdensity and field SMF shows
no evidence of the increased high-mass to low-mass galaxy ratio seen the
observations. The result of an example run is shown in Figure B.1. We note
that this test does not include consideration of spectroscopic redshifts which
would reduce the size of uncertainties further.

Figure B.1: The result of an example run of the model to test for the effect
of biases on the SMF ratios. Left: The generating SMFs for field and
overdensity are shown as blue and orange dashed curves, respectively, and the
recovered SMFs are plotted as red and black lines. Right: The ratio of the
generating SMFs (orange dashed line) and recovered SMFs (red line). No bias
toward higher SMF ratios at higher masses is observed.