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# EPOCHS paper – X. Environmental effects on Galaxy formation and protocluster Galaxy candidates at 4.5 < z < 10 from JWST observations

Qiong Li, Christopher J. Conselice, Florian Sarron, Thomas Harvey, Duncan Austin, Nathan Adams, James A. A. Trussler, Qiao Duan, Leonardo Ferreira, Lewi Westcott, et al.

► To cite this version:

Qiong Li, Christopher J. Conselice, Florian Sarron, Thomas Harvey, Duncan Austin, et al., EPOCHS paper - X. Environmental effects on Galaxy formation and protocluster Galaxy candidates at 4.5 < z < 10 from JWST observations. Monthly Notices of the Royal Astronomical Society, 2025, 539, pp.1796-1819. 10.1093/mnras/staf543. insu-05100388

HAL Id: insu-05100388

https://insu.hal.science/insu-05100388v1

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# EPOCHS paper – X. Environmental effects on Galaxy formation and protocluster Galaxy candidates at $4.5 < z < 10$ from JWST observations

Qiong Li<sup>1,1*</sup> Christopher J. Conselice,<sup>1</sup> Florian Sarron,<sup>2,3,★</sup> Thomas Harvey<sup>1,†</sup>, Duncan Austin,<sup>1</sup> Nathan Adams<sup>1,‡</sup>, James A. A. Trussler<sup>1,§</sup>, Qiao Duan,<sup>1</sup> Leonardo Ferreira,<sup>4</sup> Lewi Westcott,<sup>1</sup> Honor Harris,<sup>1</sup> Hervé Dole,<sup>5</sup> Norman A. Grogin,<sup>6</sup> Brenda Frye,<sup>7</sup> Anton M. Koekemoer<sup>1,6</sup>, Clayton Robertson,<sup>8</sup> Rogier A. Windhorst,<sup>9</sup> Maria del Carmen Polletta<sup>1,10,11</sup>, Nimish P. Hathi<sup>7,6</sup> and Rolf A. Jansen<sup>9</sup>

Accepted 2025 April 1. Received 2025 March 25; in original form 2024 May 24

## ABSTRACT

In this paper, we describe our search for galaxy protocluster candidates at $4.5 < z < 10$ and explore the environmental and physical properties of their member galaxies identified through JWST wide-field surveys within the CEERS (Cosmic Evolution Early Release Science), JADES (JWST Advanced Deep Extragalactic Survey), and PEARLS (Prime Extragalactic Areas for Reionization and Lensing Science) NEP-TDF (North Ecliptic Pole Time-Domain Fields). Combining with *Hubble Space Telescope* (HST) data, we identify 2948 robust $z > 4.5$ galaxy candidates within an area of 185.4 arcmin$^2$. We determine nearest neighbour statistics and galaxy environments. We find that high-$z$ galaxies in overdense environments exhibit higher star formation activity compared to those in underdense regions. Galaxies in dense environments have a slightly increased star formation rate (SFR) at a given mass compared with galaxies in the lower density environments. At the high-mass end, we also find a gradual flattening of the $M_\star$-SFR slope. We find that galaxies in high-density regions often have redder ultraviolet slopes than those in low-density regions, suggesting more dust extinction, weaker Ly$\alpha$ emission, and/or a higher damped Ly$\alpha$ absorption. The mass–size relation shows a weak positive correlation between galaxy size and local density. Furthermore, we quantitatively assess the probability of a galaxy belonging to a protocluster candidate. In total, we identified 26 overdensities at $z = 5–7$ and estimate their dark matter halo masses. We find that all proto-cluster candidates could evolve into clusters with $M_{\text{halo}} > 10^{14} M_\odot$ at $z = 0$, thereby supporting the theoretical and simulation predictions of cluster formation. Notably, this marks an early search for protocluster candidates in JWST wide field based on photometric data, providing valuable candidates to study cosmic structure formation at the early stages.

**Key words:** galaxies: formation – galaxies: general – galaxies: high-redshift – galaxies: photometry – galaxies: star formation.

## 1 INTRODUCTION

Galaxy clusters, along with their high-redshift progenitor structures, have played a prominent role throughout the history of cosmology.

Many observational and theoretical studies show out these objects have been central to discussions on diverse cosmological models, structure formation scenarios, and the nature of dark matter (e.g. Overzier 2016; Chiang et al. 2017; Alberts & Noble 2022). As unique laboratories, they provide valuable insights into cosmic mass assembly, the intricate interplay between galaxy and structure

<footnote n="1"><sup>1</sup>Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road, Manchester M13 9PL, UK</footnote>

<footnote n="2"><sup>2</sup>IRAP, Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, UPS-OMP, CNRS, CNES, 14 Avenue E. Belin, F-31400 Toulouse, France</footnote>

<footnote n="3"><sup>3</sup>Institut de Recherche en Informatique de Toulouse (IRIT) et Centre de Biologie Intégrative (CBI), Laboratoire MCD, CNRS, Université de Toulouse, F-31400 Toulouse, France</footnote>

<footnote n="4"><sup>4</sup>School of Physics and Astronomy, University of Victoria, Finnerty Road, Victoria, British Columbia, V8P 1A1, Canada</footnote>

<footnote n="5"><sup>5</sup>Institut d'Astrophysique Spatiale, CNRS, Université Paris-Saclay, F-91405 Orsay, France</footnote>

<footnote n="6"><sup>6</sup>Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA</footnote>

<footnote n="7"><sup>7</sup>Department of Astronomy/Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ 85721-0009, USA</footnote>

<footnote n="8"><sup>8</sup>Department of Physics, University of Louisville, Natural Science Building 102, Louisville KY 40292, USA</footnote>

<footnote n="9"><sup>9</sup>School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-6004, USA</footnote>

<footnote n="10"><sup>10</sup>INAF – Istituto di Astrofisica Spaziale e Fisica Cosmica Milano, Via A. Corti 12, I-20133 Milano, Italy</footnote>

<footnote n="11"><sup>11</sup>Department of Astronomy & Astrophysics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA</footnote>

<footnote>*E-mail: qiong.li@manchester.ac.uk (QL); florian.sarron@irit.fr (FS)</footnote>
formation, and the complex interactions between galaxies and the intergalactic medium.

However, studying cluster formation using standard galaxy surveys is challenging due to their rarity and the need for extensive surveys to find their progenitors. To identify overdense regions in the early universe, researchers have employed a variety of strategies. In addition to surveys at X-ray and sub-mm wavelengths through the Sunyaev–Zeldovich (SZ) effect, the optical and near-infrared (NIR) remain a powerful way to find clusters through the distribution of their galaxies. This includes conducting spectroscopic and photometric redshift surveys centred around rare and luminous objects believed to be associated with overdense structures. Numerous successful discoveries of overdense regions have been made using this approach. Notable examples include the studies around quasi-stellar objects (QSOs; e.g. Morselli et al. 2014; Li et al. 2023), high-redshift radio galaxies (HzRGs; e.g. Miley & De Breuck 2008; Wylezalek et al. 2013; Shimakawa et al. 2018), and submillimetre galaxies (SMGs; e.g. Chapman et al. 2009; Umehata et al. 2015; Oteo et al. 2018; Harikane et al. 2019; Li et al. 2021; Polletta et al. 2021). Overall, these studies have provided insights into the formation and evolution of galaxy clusters and their precursor structures, significantly advancing our understanding of structure formation.

Protoclusters have been discovered in certain fields using techniques such as rest-frame ultraviolet (UV) spectroscopy and through the Lyα emitters/Lyman break galaxies (LAEs/LBGs) selection (e.g. Ouchi et al. 2005; Steidel et al. 2005; Lee et al. 2014; Dey et al. 2016; Toshikawa et al. 2016; Shimakawa et al. 2018; Toshikawa et al. 2018; Harikane et al. 2019; Brinch et al. 2024). To accelerate this process, pre-selection of overdense regions from photometric surveys has been employed, followed by spectroscopic confirmation of the most significant overdensities (e.g. Cucciati et al. 2014; Lemaux et al. 2014; Chiang et al. 2015; Diener et al. 2015; Wang et al. 2016). Examples of successful protocluster surveys include the Subaru Deep Field ($z \simeq 4.86$ and $z \simeq 6.01$, Shimasaku et al. 2003; Toshikawa et al. 2012), the Subaru/XMM–Newton Deep Field ($z \simeq 5.7$, Ouchi et al. 2005), and the Canada–France–Hawaii Telescope Legacy Survey ($z \sim 3–6$, Toshikawa et al. 2016).

The JWST stands as a transformative telescope for addressing this problem in new ways, offering a broad wavelength range, high sensitivity, and advanced imaging and spectroscopy (Gardner et al. 2006; Rigby et al. 2023) particularly adept for finding distant cluster/groups and proto-clusters. JWST/NIRCam, with two neighbouring $2 \times 2$ arcmin detectors, despite its small size can likely efficiently identify substantial samples of high-redshift galaxy clusters and their progenitors, facilitating large-scale statistical studies of galaxy clustering in the early universe. Furthermore, JWST’s deep observations extend the exploration of galaxies to unprecedented redshifts of perhaps $z \sim 15$ (e.g. Castellano et al. 2022; Finkelstein et al. 2023; Harikane et al. 2023; Robertson et al. 2024; Hainline et al. 2024). Its high spatial resolution of $\sim 0.03$ arcmin per pixel enables us to also resolve individual galaxies within dense environments, supplying detailed information about their morphology and spatial distribution, including discerning merger events and galaxy interactions.

Recently, there have been some notable successes in the search for galaxy protocluster candidates at $z \sim 6$ utilizing the powerful capabilities of JWST. For instance, the deep imaging and wide-field slitless spectroscopy (WFSS) provided by JWST/NIRCam has already uncovered extensive galaxy overdensities around ultraluminous QSOs such as J0100 + 2802 at $z \simeq 6.3$ (Kashino

et al. 2023) and J0305–3150 at $z \simeq 6.6$ (Wang et al. 2023). Additionally, noteworthy discoveries include the identification of an overdensity around a well-known dusty star-forming galaxy (DSFG), HDF850.1, at $z \simeq 5.2$ (Herard-Demanche et al. 2023; Sun et al. 2024), and in a blank region of the sky near the Hubble Ultra Deep Field (HUDF) at $z \simeq 5.4$ (Helton et al. 2023). Furthermore, at higher redshifts, researchers have utilized the Near-Infrared Spectrograph (NIRSpec; Ferruit et al. 2022) to reveal the highest redshift spectroscopically confirmed protocluster to date at $z \simeq 7.9$ (Morishita et al. 2023), a lensed protocluster candidate at $z \simeq 7.66$ (Laporte et al. 2022) and the identification of a candidate protocluster core surrounding GN-z11 at $z \simeq 10.6$ (Scholtz et al. 2023).

In this paper, we use recent photometric surveys conducted by the JWST to probe the impact of environment on galaxy evolution at high redshifts. Here, we have selected regions with relatively contiguous observations by JWST, including Cosmic Evolution Early Release Science (CEERS) Survey, North Ecliptic Pole (NEP), and JWST Advanced Deep Extragalactic Survey (JADES). The total surveyed area we study spans 185 arcmin². The main emphasis of this investigation lies in the discrimination between high-density and low-density environments. Furthermore, we investigate the physical properties of galaxies in different environments, including mass, morphology, and star formation activity. Additionally, our analysis includes the search for potential protocluster candidates and the quantitative assessment of the probability that a galaxy belongs to a specific galaxy cluster. We then discuss how the overdense areas relate to these proto-clusters.

The organizational structure of this paper is as follows: In Section 2, we provide an overview of the JWST data used in this study and the relevant *Hubble Space Telescope (HST)* data acquisition. Section 3 delves into the establishment of our high-redshift sample, discussing the reliability of photometric redshifts and discussing the completeness of our sample. In Section 4, we categorize the sample into dense and under dense regions, comparing galaxy mass and star-forming activity. We explore the impact of galaxy environments on the physical properties of galaxies. In Section 5, we detail our search for galaxy clusters in early-universe using JWST and *HST* photometric data. We employ Bayesian methods to quantitatively assign group galaxy membership probabilities within these clusters. In Section 6, we compare our findings with relevant spectroscopic studies at these redshifts, and discuss the process of cluster assembly by integrating simulations and previous observational data at lower redshifts. Finally, in Section 7, we summarize our findings and outline the challenges faced in our exploration of high-redshift galaxy protocluster candidates. Additionally, we discuss future plans and directions for further research in this field.

Throughout this paper, we assume a flat cosmological model with $\Omega_{\Lambda} = 0.7$, $\Omega_{m} = 0.3$ and $H_0 = 70 \text{ km s}^{-1} \text{ Mpc}^{-1}$. All magnitudes used in this paper are in the AB system (Oke & Gunn 1983).

## 2 OBSERVATIONS AND DATA REDUCTIONS

In this study, we selected data from continuous deep fields imaged by the NIRCam instrument of three JWST observation programmes: JADES (Eisenstein et al. 2023; Rieke et al. 2023), CEERS (Bagley et al. 2023), and PEARLS/NEP-TDF (Windhorst et al. 2023), as shown in Fig. 1. These fields offer a contiguous area, enabling a more comprehensive investigation of the galactic environment at the Mpc scale compared to other existing JWST observations. The combined
<figure><img src="image_4.png" /><figcaption>**Figure 1.** NIRCam/F444W images of the three fields (CEERS, JADES, and NEP) analysed in this work. We have created masks to avoid diffraction spikes from bright stars, image artefacts, and field edges. These masks are used throughout the analysis in this article. CEERS field has 10 NIRCam pointings and covers ~94 arcmin<fnref n="2" /> in total; JADES GOODS-S DR1 has 4 pointings, ~27 arcmin<fnref n="2" /> and NEP has 8 pointings, ~64 arcmin<fnref n="2" />.</figcaption></figure>

area of these fields reaches 185.4 arcmin<fnref n="2" />. Additionally, to study objects at lower redshifts (z ~ 4.5–6), we incorporated data sets from HST imaging. Specifically, the HST CANDELS survey (Grogin et al. 2011; Koekemoer et al. 2011) includes the fields: GOODS-S (Guo et al. 2013), GOODS-N (Barro et al. 2019), COSMOS (Nayyeri et al. 2017), and EGS (Stefanon et al. 2017a). This section provides an overview of the observational details for each programme.

## 2.1 CEERS JWST NIRCam and HST Imaging

We use data from JWST/NIRCam observing runs of the CEERS (Bagley et al. 2023; ID: 1345, PI: S. Finkelstein) conducted in 2022 July and 2022 December. This survey involves 10 NIRCam pointings that were mosaiced over the Extended Groth Strip field (EGS) area covered by CANDELS (Grogin et al. 2011; Koekemoer et al. 2011). JWST/NIRCam observations in this field span seven photometric bands: F115W, F150W, F200W, F277W, F356W, F410M, and F444W. In our JWST observations, CEERS field provided the largest single area, about 94.32 square arcminutes.

We processed the CEERS JWST data utilizing the STScI JWST Pipeline<fnref n="1" /> v1.9.6 (Bushouse et al. 2022) and CRDS<fnref n="2" /> using the calibration

files v1084 independently ourselves with a bespoke reduction. The final resolution of the drizzled images is 0.03 arcsec pixel⁻<fnref n="1" />. We calculate that the average photometric depth in this field is 28.6 AB magnitudes using 0.32 arcsec circular apertures, corresponding to a 5σ detection limit. More detailed calibration process and data products can be found in our EPOCHS paper II (Adams et al. 2023).

To complement our photometry for lower redshift systems, we also collect HST Advanced Camera for Surveys (ACS) images from the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011; Koekemoer et al. 2011). The HST ACS observations we used include the F606W and F814W filters and were part of the CANDELS survey. Notably, the CEERS team has refined the astrometric alignment of these HST ACS observations to the Gaia Early Data Release 3 (EDR3). Detailed information regarding this can be found on the CEERS team's website.<fnref n="3" /> The average 5σ local depth is about 28.8–28.3 mag. The pixel scale of the processed data was 0.03 arcsec.

The inclusion of these HST F606W and F814W observations in our data set serves as a valuable complement, particularly in compensating for the absence of observations in the F090W filter within the CEERS survey. This data also expands our sample's lower redshift range to z ~ 4.5. However, it is important

<footnote n="1">¹https://github.com/spacetelescope/jwst</footnote>

<footnote n="2">²https://jwst-crds.stsci.edu/</footnote>

<footnote n="3">³https://ceers.github.io/hdr1.html</footnote>
to note that redshift measurements for sources in the range of
$7<z<7.5$ have larger uncertainties due to the Ly$\alpha$ line falling
between the ACS/F814W and NIRCam/F115W filters. Similarly,
sources in the range of $9<z<10$ have larger uncertainties due to
their position between the NIRCam/F115W and NIRCam/F150W
filters.

## 2.2 JADES JWST NIRCam and HST Imaging

The JADES NIRCam imaging observation (Rieke et al. 2023) covers 25 arcmin² in and around the Hubble Ultra Deep Field (HUDF), and both the GOODS-S and GOODS-N fields. Here, we use the JADES DR1 Release data of the GOODS-S field (PI: Eisenstein, N. Lützgendorf, ID:1180, 1210). There are data in nine filters in JADES: F090W, F115W, F150W, F200W, F277W, F335M, F356W, F410M, and F444W for these fields.

We process the images with the JWST Calibration Pipeline (version 1.9.6, CRDS v1084) with our custom steps, as described in EPOCHS II (Adams et al. 2023). We have considered various issues, including flat-field inaccuracies, cosmic ray, dark, distortion, bad pixel masks. This results in 5σ depths reaching as faint as 29.8–29.6 mag for aperture sizes of 0.32 arcsec. The final image resolution for this data is 0.03 arcsec pixel⁻¹.

To extend the wavelength coverage, we use imaging data from the CANDELS (Grogin et al. 2011; Koekemoer et al. 2011), which covers a broader area in GOODS-S. We use the Hubble Legacy Fields reduction<fnref n="4" /> for the ACS images in F435W, F606W, F775W, F814W, and F850LP, as well as WFC3 images in F105W, F125W, and F160W. It is noteworthy that we typically combine JWST NIRCam data with HST ACS data in our analyses. These images, derived from the CANDELS programme, provide optical photometric coverage for the JADES sources.

## 2.3 NEP-TDF NIRCam Imaging

The North Ecliptic Pole Time-Domain Fields (NEP-TDFs; Windhorst et al. 2023) is part of the JWST PEARLS observational programme. PEARLS, the Prime Extragalactic Areas for Reionization and Lensing Science project (Diego et al. 2023; Frye et al. 2023; Windhorst et al. 2023), is a JWST Guaranteed Time Observation (GTO) programme (PID 1176, 2738, PI: Rogier Windhorst). The NEP-TDF observations involve imaging in eight filter bands: F090W, F115W, F150W, F200W, F277W, F356W, and F444W, along with one medium band: F410M. The total area for the four TDF epochs is 64 arcmin². We process the images with the JWST Calibration Pipeline (version 1.9.6, CRDS v1084) independently, as described in Adams et al. (2023). The 5σ depths reach 28.7–28.5 mag in aperture sizes of 0.32 arcsec in diameter. The final image resolution is 0.03 arcsec pixel⁻¹.

We obtained deep HST observations with WFC3/UVIS F275W and ACS/WFC F435W and F606W through GO programmes 15 278 (PI: R. Jansen) and 16252 + 16793 (PI: R. Jansen & N. Grogin) from October 2017 to October 2022. Details of these observations will be presented in Jansen et al. in preparation.

## 2.4 Source extraction

We carry out source identification and extraction using the code SEXTRACTOR (Bertin & Arnouts 1996). We run this in dual-image mode

with the weighted stack of the F277W + F356W + F444W bands used for object selection, from which we carry out forced aperture photometry for multiband measurements. For source detection, we require a minimum of 9 contiguous pixels with a signal-to-noise ratio (SNR) threshold of 1.8. The deblending process was managed with 32 subthresholds and a minimum contrast parameter of 0.005. To reduce spurious detections, we apply a cleaning efficiency of 1.0. We estimate the background locally with a mesh size of 64 pixels. This photometry is calculated within 0.32 arcsec diameter circular apertures, and we include an aperture correction derived from simulated WebbPSF point spread functions for each band used (Perrin et al. 2012, 2014). We use 5σ local depth as the error of the photometry to avoid the known underestimate of the photometric errors. We calculate local depths by placing apertures across the ‘empty’ regions of our images. We use the normalized mean absolute deviation of the nearest 200 apertures for each source. The details can be found in our EPOCHS paper I (Conselice et al. 2025) and paper II (Adams et al. 2023).

# 3 PHOTOMETRIC REDSHIFTS AND SED FITTING

In this section, we outline our methodology for fitting galaxy SEDs using EAZY and Bagpipes and selecting a high-redshift galaxy sample. We also discuss the differences between our photometric redshifts and the measured spectroscopic redshifts to ensure the accuracy of our photometric data. Additionally, we conduct a statistical analysis of number counts in each field and calculate both detection and selection completeness to assess the reliability of our data set.

## 3.1 SED fitting

To obtain our photometric redshift measurements, we first use the EAZY-PY photometric redshift code (Brammer, van Dokkum & Coppi 2008). We use the default EAZY templates (tweak_fspS_QSF_12_v3, Conroy & Gunn 2010), along with Sets 1 and 4 of the SED templates generated by Larson et al. (2023), for a total of 18 templates. These additional templates have bluer rest-frame UV colours compared with the default templates, as well as stronger emission lines, both of which have been observed in high-redshift galaxies (Finkelstein et al. 2022; Nanayakkara et al. 2023; Withers et al. 2023; Cullen et al. 2023a). These templates have young stellar populations with ages (10⁶–10⁷ yr), at low metallicities (5 per cent Z⊙) and have been shown by Larson et al. (2023) to improve the accuracy of photo-z estimates at high redshift. The Larson et al. (2023) templates were generated using BPASS v2.2.1 (Stanway & Eldridge 2018) and reprocessed to include nebular emission with CLOUDY v17.0 (log U = −2, 5 per cent Z⊙). This is consistent with the configuration used in previous papers of the EPOCHS series (e.g. Adams et al. 2023). We apply an intergalactic medium (IGM) attenuation derived from Madau (1995). We set a minimum error of 10 per cent to our measured photometry to take into account potential zero-point offsets and inaccuracies in our theoretical templates.

To compute the probability density functions for redshift and stellar mass, we employ the photometric redshifts obtained with EAZY as input values for each galaxy candidate. These redshifts contain uncertainties, modelled using a Gaussian redshift prior, and input into the Bayesian SED fitting code Bayesian Analysis of Galaxies for Physical Inference and Parameter Estimation Bagpipes (Carnall et al. 2018). Bagpipes leverages a Bayesian approach and SED

<footnote n="4">⁴https://archive.stsci.edu/prepds/hlf/</footnote>
templates to infer the most likely properties of galaxies, including their star formation history (SFH), stellar mass, stellar population age, metallicities, among other properties.

We utilize BC03 stellar population models (Bruzual & Charlot 2003) with a Kroupa Initial Mass Function (IMF, Kroupa 2001) in our fits using Bagpipes. The fitting process of Bagpipes we use the lognormal SFH parametrization, a well-established model used in various other studies (e.g. Carnall et al. 2023; Whitler et al. 2023). The lognormal SFH is parametrized by two parameters; the age of the Universe at maximum star formation, and the FWHM of star formation. We parametrize both parameters with a broad prior range of [0.01, 10] Gyr. Bagpipes requires that no star-formation can occur before the age of the Universe at the best-fitting redshift and so the SFH will be truncated if this occurs with a given lognormal SFH.

Additionally, we include the emission lines and nebular continuum based on CLOUDY models (Ferland et al. 2013). We apply Log10 priors for dust and metallicity, considering the expectation of young, less dusty, and lower metallicity galaxies at high redshifts. The fitting process incorporates the Calzetti et al. (2000) dust attenuation model. We set prior ranges for metallicity in the range of [10⁻³, 3] Z☉ and for the dust in the range of [0.0001, 10] in A_V, ionization parameter Log₁₀(U) in the range [-3, -1].

## 3.2 A robust high-z galaxy sample

In this section we list our selection criteria for locating $z > 4.5$ galaxies. Our sample closely align with those utilized in other papers of the EPOCH series, including a detailed breakdown in previous papers (e.g. Adams et al. 2024; Harvey et al. 2025). In summary these criteria are as follows:

(i) The source must not be detected ≥ 3σ in band(s) bluewards of the Lyman break; it also must have ≥ 5σ detections in the two bands directly redwards of the Lyman break, and ≥ 2σ detections in all other redward bands. This insures a strong detection of the Lyman-break for these systems, as well as a strong detection for measuring accurate redshifts and other galaxy properties based on the spectrum redwards of the break.

(ii) We require that the integration of the photometric redshift place the galaxy with high certainty at high redshift. The mathematical express for this is $\int_{0.90 \times z_{phot}}^{1.10 \times z_{phot}} P(z) dz \ge 0.6$, which ensures the majority of the redshift PDF is located within the primary peak. Here, $z_{phot}$ is the maximum likelihood redshift from the PDF.

(iii) We required a good fit, such that $\chi^2_{reduced} < 6$ for a best-fitting SED to be classed into the ‘good’ sample.

(iv) We also require that the secondary photometric redshift solution $P(z_{sec}) < 0.5 \times P(z_{phot})$ to ensure the low probability of a secondary peak, if it exists, is less than 50 per cent of the high-z solution.

(v) We remove contamination sources by checking the morphology and SED fitting by eye, e.g. hot pixels, artefacts, blended features. 98 per cent are kept in our final sample.

High-redshift galaxies with strong emission lines, such as Hβ + OIII, can exhibit excess flux in the corresponding photometric bands, often leading to elevated $\chi^2$ values when fitting with standard templates. To ensure a more inclusive and consistent selection, we perform visual inspection on all galaxies with reduced $\chi^2 < 6$. This approach allows us to identify and retain galaxies where photometric excess may cause template mismatches, ensuring a more robust sample. The fitting results for these galaxies are carefully

examined to confirm their reliability. EAZY-py calculates a redshift PDF for each galaxy, from which we approximate the one sigma uncertainties from the 84–50th and 50–16th percentiles. The median value of the photometric redshift uncertainty from SED fitting is $\Delta z \sim 0.14$.

By incorporating HST bands F606W and F814W using the Lyman break method, we can identify galaxies with $z > 4.5$. However, due to the incomplete wavelength coverage across the full optical spectrum, our high-redshift sample may not be complete in the redshift direction. We will discuss the implications of this incompleteness for our work in Section 3.5.

## 3.3 Comparison between photometric and spectroscopic redshifts

To investigate how well the photometric redshifts we have determined compare to the spectroscopic redshifts, we conducted a matching process involving all galaxies within our sample. There are 86 galaxies at $z > 4.5$ with a reliable spectroscopic redshift measurement matched within the projected distance of $\Delta < 0.3''$, 34 from JADES and 52 from CEERS. As described above in Section 3.1, the photometric redshifts were obtained via EAZY. For spectroscopic redshifts, within CEERS, we combine catalogues obtained from NIRSpec prism data of the publicly DAWN JWST Archive<fnref n="5" /> (Heintz et al. 2023), the DEEP2 survey (Newman et al. 2013), 3D-HST (Momcheva et al. 2016) and MOSDEF/MOSFIRE surveys (Kriek et al. 2015) of the Extended Goth Strip (EGS). Within JADES, we use JADES DR1 spectroscopy PRISM catalogue released from the JADES collaboration (Bunker et al. 2023).

The results of our redshift comparison of 86 matched galaxies are represented in Fig. 2. The photometric redshift data predominantly fall within 15 per cent of the spectroscopic redshifts. We assess photometric quality using two statistical measures, the outlier fraction $\eta$, and the normalized median absolute deviation (NMAD). The fraction of outliers $\eta$, defined as the fraction of the photometric redshifts differing from the spectroscopic redshifts by more than 15 per cent in $(1+z)$, $(|\Delta z|/(1+\text{spec-z})) > 0.15)$, is given by

$$ \eta = \frac{N_{115} + N_{85}}{N_{\text{total}}}, \qquad (1) $$

where $N_{115}$ and $N_{85}$ represent the counts of points lying above the line $z_{phot} = 1.15 \times (z_{spec} + 1)$ and below the line $z_{phot} = 0.85 \times (z_{spec} + 1)$, respectively.

The NMAD is the quantification of the dispersion in the redshift variances, normalized for scale, defined by the following expression:

$$ \text{NMAD} = 1.48 \times \text{med} \left| \frac{z_{\text{spec}} - z_{\text{phot}}}{1 + z_{\text{spec}}} \right|, \qquad (2) $$

All the statistical measurement values for these parameters are detailed in Table 1. The diagnostic of photometric versus spectroscopic redshift (Fig. 2) shows that the fraction of outliers $\eta$ is 7.0 per cent for the combined high-z galaxies, and the NMAD of the whole sample is 0.038. This suggests a good agreement between our photometric and spectroscopic redshift measurements. The values of $\mu$ and $\sigma$ denote the average and standard deviation, respectively, of the relative difference distribution between the photometric redshifts derived from our EAZY-py fits and the spectroscopic redshifts in $(1+z_{spec})$. Although the proximity of $\mu$ values to 0 and their low standard deviation suggest good overall accuracy of the photometric

<footnote n="5">⁵https://dawn-cph.github.io/dja/</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Left: Diagnostic plot showing the comparison of spectroscopic redshifts with photometric redshifts for all the sample at $z > 4$. The spectroscopic redshifts are from the observations of Subaru, VLT/MUSE, JWST/NIRISS, and JWST/NIRSpec (e.g. Bunker et al. 2023; Heintz et al. 2024). The black solid line shows the one-to-one relation; the dashed lines show 15 per cent offsets in $(1+z)$. Right: the histogram of the relative difference between the photometric redshifts from our EAZY-py fits and the spectroscopic redshift in $(1+z_{spec})$. The labelled scatter indicates the median of the relative difference, respectively. The error bars show the range of the 16th–84th percentiles.</figcaption></figure>

<table><caption>**Table 1.** Accuracy of our photometric redshift measurements for the JADES, CEERS, and combined data at $z > 4.5$. The outlier fraction, $\eta$ quantifies the proportion of outliers in the redshift comparison. The NMAD, serves as a measure of the scatter in the redshift differences, adjusted for scale. The low values observed for both $\eta$ and NMAD across the data sets affirm the precision and accuracy of our photometric redshift measurements. $\mu$ and $\sigma$ represent the median and standard deviation, respectively, of the relative difference between the photometric redshifts obtained from our EAZY fits and the spectroscopic redshifts in $(1+z_{spec})$.</caption><thead><tr><th>Parameters</th><th>JADES</th><th>CEERS</th><th>Combined</th></tr></thead><tbody><tr><td>η</td><td>2.9 per cent</td><td>9.6 per cent</td><td>7.0 per cent</td></tr><tr><td>NMAD</td><td>0.031</td><td>0.044</td><td>0.038</td></tr><tr><td>μ</td><td>0.056</td><td>0.064</td><td>0.061</td></tr><tr><td>σ</td><td>0.273</td><td>0.127</td><td>0.198</td></tr></tbody></table>

redshift measurements, we acknowledge a systematic tendency for photometric redshifts to overestimate spectroscopic values. This effect, which is consistent with findings in recent studies (e.g. Fujimoto et al. 2023; Haro et al. 2023; Helton et al. 2023; Hainline et al. 2024), is often attributed to limitations in the photometric template fitting process, especially in cases where strong emission lines can affect the redshift estimates.

Our photometric redshift determination demonstrates their reliability. It is crucial to note that the spectroscopic observations of high-redshift objects are insufficient for mapping galaxy environments on scales of several Mpc, e.g. these detect only <10 kpc scale protocluster cores around GN-z11 (Scholtz et al. 2023). In contrast, Tacchella et al. (2023) previously identified a photometric candidate overdensity surrounding GN-z11 within a radius of ~5 Mpc, corresponding to ~430 pkpc at $z = 10.6$. Our analysis, based on precise photometric redshift data, provides an effective approach for identifying protocluster galaxy candidates while minimizing selection bias. Subsequent redshift facilities, such as JWST or ALMA spectroscopic observations, will further validate whether these galaxies indeed reside within an interacting proto-cluster or a larger-scale structure.

<table><caption>**Table 2.** The high-$z$ samples used in this work, with their main properties: the unmasked region area, the $5\sigma$ depth in rest frame UV bands, the number counts at $z > 4.5$. The unmasked region area refers to the area remaining after applying a mask, where we have excluded regions at the edges of observations, gaps, and portions of the data with noticeably poor quality. $C_{p\ 90\ per\ cent}$ is the 90 per cent selection completeness; $N$ is the total galaxy number at $z > 4.5$ in each unmasked fields.</caption><thead><tr><th>Fields</th><th>Sky area<br>(arcmin<sup>2</sup>)</th><th>5σ depth<br>UV<sub>rest</sub><br>(mag)</th><th>C<sub>p\ 90\ per cent</sub><br>(mag)</th><th>N</th></tr></thead><tbody><tr><td>CEERS</td><td>94.32</td><td>28.8–28.3</td><td>28.9</td><td>926</td></tr><tr><td>JADES</td><td>26.88</td><td>29.8–29.6</td><td>29.8</td><td>932</td></tr><tr><td>NEP</td><td>64.21</td><td>28.7–28.5</td><td>28.9</td><td>1090</td></tr><tr><td>Combined</td><td>185.41</td><td></td><td></td><td>2948</td></tr></tbody></table>

## 3.4 Number counts

In Table 2, we provide a summary of the galaxy catalogues in each field mentioned above, covering most of the protocluster footprint compared to the typical scale we expect protoclusters to subtend at these high redshifts. Fig. 3 displays the redshift distribution $N(z)$ for each catalogue, spanning a redshift range $z = 4.5–14.0$. However, due to issues related to the gaps in the photometry bands, the galaxy density is underestimated at certain redshifts (e.g. $z \sim 9.5$). This results in a potential underestimation of density for high-density regions already identified. To address this, we implement a simple redshift mask as follows:

$$ \mathcal{M}^z(z) = \begin{cases} 0 & \text{if } z[z_{i,\text{lower},68 \text{ per cent}}, z_{i,\text{upper},68 \text{ per cent}}] \in z_{\text{masked}} \\ 1 & \text{otherwise} \end{cases}. \quad (3) $$

where $z_{i,\text{lower},68 \text{ per cent}, z_{i,\text{upper},68 \text{ per cent}}}$ are the lower and upper limit of 68 per cent confidence interval on PDF($z$), respectively. $z_{\text{masked}}$ is the redshift masked region. It is important to note that this effect is attributed to the limitations arising from the discontinuous redshift of photometric data. The absence of specific HST bands, which are crucial for detecting galaxies at these lower redshifts, resulted in an underestimation of galaxy counts in the $z = 4.5–5.5$ range. However, our primary focus in this paper is on high-redshift
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Redshift distribution of the high-z galaxies in the CEERS, JADES, NEP fields, in bins of $z = 0.5$. The black histogram combines all the data we used in this paper. These samples are those galaxies with a high probability of existing at high redshifts (Adams et al. 2024; Harvey et al. 2025).</figcaption></figure>

galaxies. We have corrected for galaxy incompleteness, ensuring that this does not affect our main conclusions regarding high-redshift populations.

We limit the sample to $z < 9.5$, by masking galaxies whose 68 per cent integral of the $P(z)$ falls at $z > 9.5$, totalling 128 galaxies (3.9 per cent). These galaxies are distributed over a wide redshift range from $9.5 < z < 16$. Due to limitations in observational depth, the number of galaxies in these redshift bins is too small to conduct a meaningful analysis of the galaxy environment. In the future, observations from even deeper JWST fields can extend this work to higher redshifts. Here, we set $z_{\text{masked}}$ as $[9.5, \infty]$.

## 3.5 Detection and selection completeness

In this section, we briefly describe how we calculate the completeness and selection completeness measures and their impact on our results. We use the same methods with the EPOCHS II and IV papers, for more detailed methods, please refer to these papers (Adams et al. 2023; Harvey et al. 2025).

To assess JWST data detection completeness, we carry out completeness simulations by inserting simulated galaxies with an exponential light profile and absolute UV magnitudes ranging from $M_{UV} = -16$ to $-24$ into the detection image. Using the same SEXTRACTOR configuration as our catalogue pipeline, we measured the recovery fraction as a function of apparent magnitude. Magnitudes were sampled in 0.2 steps, with 1000 sources added per run to avoid artificial overdensities. We assume a size-luminosity relation of $r \propto L^{0.5}$ (Grazian et al. 2012), with scatter modelled with a lognormal distribution calibrated from the results of Yang et al. (2022). We simulated redshifts from $z = 4$ to $z = 13.5$ in steps of $\delta z = 0.5$ to account for the changes in angular diameter distance and to obtain a 2D dependence of completeness on redshift and absolute magnitude. This process was repeated for all fields in the study. An example of detection completeness in CEERS is shown in Table 3. Our detection completeness is > 90 per cent across the redshift ranges and apparent magnitudes of our high-z sample, which has a relatively minor impact on our results.

<table><caption>**Table 3.** An example of detection completeness in CEERS. We list the corresponding $M_{UV}$ values in different redshift bins for completeness of 25 per cent, 50 per cent, and 75 per cent. The completeness for the other fields are described in more detail in Adams et al. (2024) and Harvey et al. (2025).</caption><thead><tr><th>Redshift bins</th><th>&gt;25 per cent</th><th>&gt;50 per cent</th><th>&gt;75 per cent</th></tr></thead><tbody><tr><td>4-5</td><td>-18.87</td><td>-18.50</td><td>-18.21</td></tr><tr><td>5-6</td><td>-19.26</td><td>-18.73</td><td>-18.33</td></tr><tr><td>6-7</td><td>-19.50</td><td>-18.95</td><td>-18.54</td></tr><tr><td>7-8</td><td>-19.63</td><td>-19.12</td><td>-18.75</td></tr><tr><td>8-9</td><td>-19.53</td><td>-19.09</td><td>-18.55</td></tr><tr><td>9-10</td><td>-19.78</td><td>-19.31</td><td>-18.85</td></tr></tbody></table>

For the selection completeness, we used JAGUAR<fnref n="6" /> version 1.2 (Williams et al. 2018), a synthetic galaxy catalogue at $z \le 10$ (Tomczak et al. 2014; Bouwens et al. 2015; Stefanon et al. 2017b) based on observational constraints. We match the $10^6$ mock sources to the sources which are detectable given the depths of our observations. Realistic observations were simulated by perturbing catalogue photometry based on $1\sigma$ local depth errors. Our same selection procedure is then applied to assess redshift recovery. Using Bagpipes, we tested the reconstruction of stellar masses for JAGUAR galaxies. Completeness and contamination are estimated for each redshift and mass bin, revealing a strong dependence on galaxy stellar mass. For masses above $\approx 10^8 M_{\odot}$, we achieved $\ge 50$ per cent completeness in most areas. Fig. 4 shows the selection completeness results in all three fields.

# 4 GALAXY LOCAL ENVIRONMENT

To study the local environments of high-z galaxies, we utilized the k-dimensional tree (KDTree) data structure to search for nearest neighbours. We investigate the properties of galaxies as a function of their local environment (number of neighbours/local density), and compare this to the physical parameters exhibited by galaxies residing in overdense and underdense regions. Through this analysis, we aim to not only discern the existing disparities but also to shed light on the potential redshift evolution characterizing the galaxy environment. By examining these aspects, we can gain insights into the complex interplay and evolution between the galaxy and its surroundings across cosmic time.

## 4.1 Galaxies in underdense and overdense environments

To ensure a robust evaluation of the galaxy environment, accounting for variations in the selected surrounding area, we employ the nearest neighbour method to measure the local environment of the galaxy, and select possible galaxy group members (Lopes et al. 2016).

Specifically, we utilize KDTree data structure to facilitate nearest neighbour queries. For each galaxy in our data set, we calculate its projected distance, denoted as $d_n$, to the nth nearest neighbouring galaxy, considering a maximum velocity offset relative to the velocity of the galaxy under investigation. The velocity offset mask is defined as

$$M^v(z) = \begin{cases} 1 & \text{if } \Delta z < 0.1 \\ 0 & \text{otherwise} \end{cases}. \qquad (4)$$

Here, we chose galaxies within a $\Delta z < 0.1$ redshift cube, in order to better match our photometric redshift uncertainty constraints. We

<footnote n="6">⁶https://fenrir.as.arizona.edu/jwstmock/</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 4.** The stellar masses and redshifts of simulated JAGUAR galaxies in all three fields (CEERS, JADES, NEP), shown with their completeness values. We include only the brighter galaxies with completeness $CP(z, M_*) > 20$ per cent in our calculations. White region show where no galaxies exist in the simulation.</figcaption></figure>

tested thresholds of $\Delta z < 0.15$ and $\Delta z < 0.2$ and found that the local galaxy density values for some galaxies do change with these larger thresholds. However, these variations are independent of redshift because the photometric redshift uncertainties remain consistent across the redshift range. Additionally, according to the predictions by Chiang, Overzier & Gebhardt (2013) and Muldrew, Hatch & Cooke (2015), the effective diameter of protoclusters, defined as $2 \times$ the effective radius (2Re), is about 20 cMpc at $z = 5$. Hence, selecting galaxies with $\Delta z < 0.1$ conveniently covers the entire overdensity region.

The local galaxy density, $\Sigma_n(z)$ is denoted as defined as

$$ \Sigma_n(z) = n/\pi d_n^2, \qquad (5) $$

where $d_n$ is the projected distance in Mpc of the nth neighbour, $\Sigma_n$ is expressed in units of galaxies/Mpc$^2$. The choice of the parameter n, representing the rank of the density-defining neighbour, is crucial. It is imperative to ensure that n is not greater than the number of galaxies within the halo, as this could lead to a loss of sensitivity in our environmental analysis. Consequently, we adopt the $\Sigma_5$, local galaxy density estimator with $n = 5$. This choice is often preferred in the literature, as it tends to be smaller than the number of galaxies typically found in a cluster, ensuring a robust and commonly used estimate (e.g. Santos et al. 2014; Lopes et al. 2016).

We also examined how changing the value of n influences our results. Using a similar approach, we calculated $\Sigma_3$ and $\Sigma_{10}$ for comparison and found that the values are positively correlated. This indicates that our results remain consistent and are not significantly influenced by this parameter choice. A minor potential impact is observed when using $n = 5$ instead of $n = 3$, as it may overlook some small-scale dense regions, such as cases where four galaxies are closely clustered but isolated from others. Nevertheless, this does not affect our main conclusions.

### 4.1.1 Completeness due to image borders

For galaxies located in the proximity to image boundaries or masked regions (e.g. bright stars), there is a tendency to underestimate their $\Sigma_5$. While this impact may not significantly alter the classification of galaxies in dense regions, it can have a substantial effect on galaxies situated in underdense areas, necessitating careful consideration.

The simplest approach is to exclude galaxies significantly affected by the boundaries. For each galaxy, we calculate its distance to the boundary, denoted as $d_{\text{edge}}$. We define a mask for galaxies affected by the boundary as follows:

$$ \mathcal{M}_{\text{edge}} = \begin{cases} 0 & \text{if } \Sigma_5 \le \Sigma_{5,16 \text{ per cent}} \text{ and } d_{\text{edge}} < 1 \text{cMpc}, \\ 1 & \text{otherwise} \end{cases}, \qquad (6) $$

where $d_5$ is the distance to the fifth-nearest galaxy from the central galaxy. For galaxies already situated within dense regions, adjusting for boundary effects would only further accentuate their overdensity, thus having no impact on the classification of overdense galaxies. Therefore, we are solely addressing boundary effects for underdense galaxies. We apply the mask to galaxies in the 16 percentile lower density regions that is the galaxies in the most underdense regions. We do not apply this correction for the highest density systems, given that these are very compact and would only increase the over densities of these regions.

### 4.1.2 Completeness cut from JAGUAR simulation

The galaxy number counts in our study are flux-limited and affected by the depths of the observations. Thus, density estimations are primarily derived for galaxies falling within a specific luminosity range. In this section, we employ a set of simulated JAGUAR galaxies to assess the completeness of CEERS, JADES, and NEP, and subsequently remove faint galaxies from our density estimates. JAGUAR is a simulation of the spectral energy distributions of galaxies as observed with JWST. These mock catalogues can then be used to determine how well we are able to retrieve galaxies of various types and at various redshifts.

The photometric selection completeness, denoted as $CP(z, M_*)$, is determined as the selection proportion of JAGUAR simulated galaxies, which is a function of redshift and stellar mass as shown in Fig. 4. In this mock selection process, we introduce photometric noise to the measurements of each JAGUAR galaxy to mimic our observations. The noise levels set to match the actual median NIRCam F444W depths, which are 29.8–28.3 mag deep based on observations in Table 2. However, we also apply the depths of the similar fields to determine how these findings might change.

Our analysis reveals that for galaxies with apparent rest-UV magnitudes of $M_{\text{UV}} = -18.50, -18.95, -19.31$ at $z = 4, 6$, and
9, over 50 per cent of them are accurately selected to fall within the correct photometric redshift range. The JAGUAR simulation data corroborates that by restricting our analysis to galaxies brighter than these specified magnitudes, we effectively control the contamination fraction for low-redshift galaxies, maintaining it at reasonably low values (<15 per cent). As a result, we choose to include only the brightest galaxies with completeness exceeding 20 per cent in our density calculations. We thus define a selection completeness mask as follows:

$$M_{CP} = \begin{cases} 0 & \text{if } CP(z, M_{*}) < 20 \text{ per cent} \\ 1 & \text{otherwise} \end{cases}, \qquad (7)$$

The completeness mask we selected here is a compromise for subsequent analysis. We aimed to correct for incompleteness while ensuring sufficient data for statistical analysis. We also experimented with a $CP(z, M_{*}) < 50$ per cent mask, finding that the overall conclusions remained unchanged. However, the differences are diluted due to increased statistical uncertainty.

### 4.1.3 Selection of overdense and underdense galaxies

The measurements of $\Sigma_5$ are influenced by variations in galaxy counts at different redshifts. When galaxies are scarce, it leads to a lower estimate of $\Sigma_5$. The number of galaxies is limited by the flux detection limits and selection biases. At highest redshifts, typically, only the bright end of the luminosity function is sampled, resulting in the detection of only a small number of galaxies. Another limitation arises from the presence of transmission gaps between the filters, which leads to the omission of galaxies with redshift tracers (e.g. strong emission lines) falling into the gaps.

To mitigate the influence of redshift on the galaxy environment, we have divided galaxies into different redshift bins from $z = [4.5, 9.5]$ with the bins having a width of 0.5 that are chosen large enough to compensate against biases in certain redshifts. Within each redshift bin, we classify galaxies in the distribution of $\Sigma_5$ as ‘overdense galaxies’ if $\Sigma_5$ is in the >84 per cent percentile of overdensities, and as ‘underdense galaxies’ if in the < 16 per cent percentile, as shown in Fig. 5, given by

$$\begin{cases} \Sigma_{5,i} \ge \Sigma_{5, 84 \text{ per cent (z}_{\text{bin}})} & \text{overdense galaxies} \\ \Sigma_{5,i} \le \Sigma_{5, 16 \text{ per cent (z}_{\text{bin}})} & \text{underdense galaxies} \end{cases} \qquad (8)$$

where $\Sigma_{5,84 \text{ per cent (z}_{\text{bin}})}$ and $\Sigma_{5,16 \text{ per cent (z}_{\text{bin}})}$ are the 84 per cent and 16 per cent confidence interval on $\Sigma_5$ at a given redshift bin, respectively.

Here, we consider several key factors influencing this measurement, and we apply corresponding masks to remove certain biases, which are as follows:

(i) $M^z(z)$: the mask of redshift selection bias, described in Section 3.4.

(ii) $M^v(z)$: the mask of the velocity offset (redshift offset), which restricts galaxies that are too distant along the line of sight to avoid contamination from foreground/background objects, described in Section 4.1.

(iii) $M^{\text{edge}}(z)$: the mask for the galaxies close to image boundaries or masked regions, see Section 4.1.1.

(iv) $M^{\text{CP}}(z, M_*)$: the mask of the selection completeness, described in Section 4.1.2.

Finally, we calculate the local galaxy density $\Sigma_5(z, M_*)$ for each galaxy at a given redshift and stellar mass.

$$\Sigma_{5,i}(z, M_*) = \Sigma_{5,i} \times M^{\text{edge}}(z) \times M^{\text{CP}}(z, M_*) \qquad (9)$$

<figure><img src="image_8.png" /><figcaption>**Figure 5.** An example of selecting overdense and underdense galaxies using $\Sigma_5$, based on galaxies in the CEERS field at $5.5 < z < 6$. The green and red dashed lines are the 84 per cent and 16 per cent confidence interval on $\Sigma_5$ at given redshift bin respectively. Within each redshift bin, we classify galaxies in the distribution of $\Sigma_5$ as ‘overdense galaxies’ if $\Sigma_5$ fall within the > 84 per cent and as ‘underdense galaxies’ if they fall within the < 16 per cent, refer to Section 4.1.3. This plot has not been corrected for any observational selection effects or incompleteness corrections. It appears similar across all of the redshift bins being considered.</figcaption></figure>

The redshift selection bias and velocity offset masks were applied before calculating $\Sigma_5$ to ensure that only truly overdense galaxies along the line of sight were considered. The mask for selection completeness and the borders mask were applied afterward to remove the influence of galaxies with low completeness and those near the border. Following the classification criteria in equation (8), we select 1006 (34 per cent) ‘overdense galaxies’ in overdense regions, and ‘underdense galaxies’ in underdense regions combined from all redshift bins from $z = 4$ to 10, which we define as the parent sample. After applying the masking criteria (equation (9)), we end up with 376 overdense galaxies and 199 underdense galaxies in our final catalogue across the CEERS, JADES, and NEP fields.

To ensure the robustness of our methodology, we further examine the impact of mask application order in defining overdense and underdense galaxies. The application of the border mask necessarily occurs after $\Sigma_5$ computation. Removing galaxies near the edges of the image before measuring $\Sigma_5$ would introduce an artificial bias by prematurely excluding sources that should contribute to the calculation of the local density. This effect is particularly significant for underdense galaxies; in contrast, the impact on overdense galaxies is minimal due to their inherently higher local densities.

To evaluate the potential influence of this application over the completeness mask, we compared the classification of overdense and underdense galaxies when the completeness mask was applied before, versus after, computing $\Sigma_5$. We used the CEERS field at $z = 5.5 - 6.0$ as a test. Our analysis shows that 11 out of 13 (85 per cent) underdense galaxies, and 25 out of 33 (75 per cent) overdense galaxies were consistently identified across both methods. The Jaccard Index values for underdense and overdense galaxies are 0.58 and 0.62, respectively, indicating a high level of agreement. Additionally, the Kolmogorov-Smirnov (KS) test yields a test statistic of 0.13 with a p-value of 0.18, suggesting that while there are minor systematic differences, the two methods produce broadly comparable distributions of $\Sigma_5$. These results show that although there is some variation between the two approaches, the differences are relatively small and do not impact the general conclusions of our
study. Given this consistency, our current approach remains robust while we acknowledge its limitations.

## 4.2 Star formation rate and stellar mass

We use Bagpipes to perform Bayesian SED fitting for each individual galaxy and derive its stellar mass, star formation rate (SFR) and the specific star formation rates (sSFRs), see Section 3 and Harvey et al. (2025). Additionally, Bagpipes provides the probability distribution for each parameter of interest for every galaxy in the analysis.

However, Bagpipes gives rise to issues with a maximum sSFR upper limit. This is a consequence of the time-scale on which Bagpipes measures SFRs, which by default is 100 Myr. We attempted to address this issue by changing the time-scale on which Bagpipes calculates the SFR, with ages = [10, 50, 100] Myr to provide more flexibility. Given the implied rapid growth of many of our galaxies within 10–20 Myr of observation, the default Bagpipes SFR time-scale of 100 Myr is not appropriate for estimating average SFRs. We thus also infer the SFR averaged over 10 and 50 Myr in order to better quantify the recent SFH of our galaxies. However, setting the time-scale too small is impractical, as all galaxies would need to rapidly form within this time-scale, resembling a ‘burst’.

Bursty star formation histories can result in situations where the light-weighted SFR (traced by UV) is significantly higher than the time-averaged SFR inferred from stellar mass growth over longer time-scales (Tacchella et al. 2022; Harvey et al. 2025; McClymont et al. 2025). The assumption of a 100 Myr SFH time-scale is an approximation, and that our sample likely includes galaxies experiencing bursty star formation, leading to deviations from this assumption. To solve this issue, we also derived SFRs from observed UV rest-frame photometry by employing a power-law approximation to fit the photometric points within the 1250–3000 Å spectral range. We applied the Meurer, Heckman & Calzetti (1999) relation to estimate the extinction necessary for correcting the 1600 Å luminosity. Subsequently, the dust-corrected luminosity is transformed into an SFR estimate using the factor in Kennicutt & Evans (2012). The SFR calculations using both Bagpipes and UV methods exhibit strong consistency between the two approaches. However, UV-derived SFRs are subject to systematic uncertainties related to SFH variability, dust correction, and SFR conversion factors. Nonetheless, this approach mitigates the degeneracy of SED parameters. In the discussion of this section, the SFR values are derived using this method.

Fig. 6 shows the relationship between SFR and stellar mass for both overdense and underdense galaxies. The histograms of stellar mass and SFR are displayed in the top and right panels, respectively. We use the bootstrapping method to determine the median values and errors represented by the data points in the plot. We apply a linear fit to the relation from the full sample and in three separate redshift bins, and the resulting parameters are presented in Table 4. While the slope of overdense galaxies appears slightly steeper, the difference is not significant within the error bars. We conducted a KS test, yielding a *p*-value of 0.04 for SFR, indicating distinct distributions with a significance of ~2σ. However, the *p*-value for stellar mass is 0.20, suggesting no statistically significant difference in the stellar mass distribution between overdense and underdense galaxies. These findings suggest that overdense galaxies exhibit more active star-forming activity, although the latter trend is less pronounced.

Fig. 7 shows the relation between SFR and stellar mass across various redshift bins in our sample, ranging from *z* = 4 to *z* = 10. The data set undergoes a 2σ clipping process to exclude outliers,

<figure><img src="image_9.png" /><figcaption>**Figure 6.** The relationship between the SFR and stellar mass for our whole sample at *z* = 4.5 – 10. The greyscale background on the (SFR, M<sub>⋆</sub>) plane represents the source density on a linear scale. The red and blue represent the overdense and underdense galaxies, respectively. The circles are the median values and the errors in the stellar mass bins are derived through a bootstrapping method. The solid coloured lines are the best linear least-squares regression fits, with the parameters shown in the Table 4. The shaded regions represent the 1σ uncertainties around the best-fitting linear relations. The top and right panels show the probability density of each stellar mass and SFR bin, respectively. The *p* value of K-S test for SFR is 0.04, showing different distributions; while *p* value for stellar mass is 0.20, showing that these are probably not significantly different.</figcaption></figure>

<table><caption>**Table 4.** The best fits of the slope (α) and intercept (β) from the linear least-squares regression (see equation 10) for the relationship between SFR and stellar mass across various redshift bins, ranging from *z* = 4 to *z* = 10.</caption><thead><tr><th>Redshift bins</th><th>α</th><th>β</th></tr></thead><tbody><tr><td colspan="3" style="text-align: left;">Overdense galaxies</td></tr><tr><td>4–6</td><td>0.50 ± 0.02</td><td>-3.54 ± 0.17</td></tr><tr><td>6–8</td><td>0.48 ± 0.03</td><td>-3.30 ± 0.22</td></tr><tr><td>8–10</td><td>0.45 ± 0.10</td><td>-3.00 ± 0.79</td></tr><tr><td>All</td><td>0.49 ± 0.01</td><td>-3.39 ± 0.11</td></tr><tr><td colspan="3" style="text-align: left;">Underdense galaxies</td></tr><tr><td>4–6</td><td>0.46 ± 0.03</td><td>-3.34 ± 0.24</td></tr><tr><td>6–8</td><td>0.43 ± 0.04</td><td>-2.92 ± 0.32</td></tr><tr><td>8–10</td><td>0.37 ± 0.12</td><td>-2.40 ± 0.96</td></tr><tr><td>All</td><td>0.43 ± 0.02</td><td>-3.00 ± 0.17</td></tr></tbody></table>

and within each stellar mass bin, we compute the median and its corresponding error using the bootstrap method. We fit the data with the linear relation:

$$ \log(\text{SFR}) = \alpha\log(M_{\star}) + \beta. \quad (10) $$

The best fits are shown in the coloured lines in Fig. 7 and Table 4.

The lower panel of Fig. 7 displays the median SFRs within various stellar mass bins at different redshifts. Our findings reveal that galaxies at higher redshifts demonstrate elevated levels of star formation activity when compared to their lower-redshift
<figure><img src="image_10.png" /><figcaption>**Figure 7.** The relationship between log₁₀SFR and log₁₀M* in different redshift bins. The greyscale background on the (SFR, M*) plane represents the source density on a linear scale. The open boxes are the median values in the stellar mass bins, with error bars determined through a bootstrapping method. The solid coloured lines are the best linear fits. The shaded regions represent the 1σ uncertainties around the best-fitting linear relations. The dashed vertical lines are the observational mass completeness limit for the sample at the central redshift in each bin. Bottom panel: The median values and main-sequence relations are displayed for all redshift bins, with colour-coding corresponding to each bin.</figcaption></figure>

counterparts, as has long been known. We observe a subtle rise with increasing redshift and a gentle flattening of the slope. It is important to note that the highest redshift bin has limitations and

is more susceptible to poor number statistics. Overall, we observe this trend extended up to z = 10, which is rarely probed in previous studies (e.g. Magnelli et al. 2014; Whitaker et al. 2014; Schreiber
et al. 2015; Tasca et al. 2015; Tomczak et al. 2016; Santini et al. 2017; Popesso et al. 2023).

The left and the middle panels show these relationships for
overdense and underdense galaxies. Notably, overdense galaxies
consistently exhibit higher SFRs across the entire redshift range
studied. Furthermore, the overdense galaxies display around > 1σ
slightly steeper slope (Table 4), suggesting that the environment may
indeed influence the stellar formation activity of galaxies, although
this impact does not appear to be very pronounced, also see Fig. 6.

4.3 Star formation activities and quenching

Cluster galaxies are often associated with quiescence at low redshift, but at high-z a significant portion of systems in clusters/groups continue to display active star-forming behaviour. In our sample, sSFRs of all selected galaxies fall within the range [log(sSFR/yr⁻¹) = −9.5, −7], while their stellar masses span the range log(M<sub>⋆</sub>/M<sub>☉</sub>) = [6.5, 10.6]. Although this mass range suggests that most galaxies are star forming, it is possible that some may be post-starburst or mini-quenched, particularly as the threshold for quiescence at high redshifts is often set at log(sSFR/yr⁻¹) < −9.7 at z = 5 and log(sSFR/yr⁻¹) < −9.3 at z = 10 (e.g. Pacifici et al. 2016). Within the redshift range z = [4.5, 10], we do not detect any massive galaxies (M<sub>⋆</sub> > 10<sup>10</sup>M<sub>☉</sub>) exhibiting strong quiescent behaviour. Instead, the galaxies appear to be actively star-forming, consistent with the empirical star-forming main sequence observed at these high redshifts (Speagle et al. 2014; Salmon et al. 2015). This finding aligns with predictions from models of cosmic evolution (Somerville & Davé 2015), as during this early epoch, near the time of the epoch of reionization, galaxies in both overdense environments and the field were highly active in terms of star formation.

Fig. 8 displays the sSFR of the overdense and underdense galaxies as a function of stellar mass. Remarkably, from Fig. 8 bottom panel, ΔsSFR = sSFR<sub>over|under</sub> - <sSFR>, we find that overdense galaxies exhibited significantly higher sSFRs, exceeding those of field galaxies by ~0.13 dex at all stellar masses. We use the Markov Chain Monte Carlo (MCMC) method to sample the posterior distribution of the median sSFR using a likelihood function based on the observed sSFR values for the two galaxy populations. The median sSFR of overdense galaxies is 3σ higher than that of underdense galaxies. Statistical tests, such as the KS test, confirm the differences between these populations, with a *p*-value of 0.01, showing a statistically significant difference.

During cosmic youth when the universe was less populated by
massive galaxies, likely nearly all galaxies are star forming galaxies
and the sSFRs are well above the quenching value. Fig. 9 shows
the sSFR of all high-z galaxies in CEERS on the Σ<sub>5</sub> - stellar mass
plane. We find that the mass factor is the one dominating whether a
system is star forming or not. The quenching mechanisms related to
environmental factors do not seem as pronounced at these redshifts.
In contrast, cluster galaxies exhibited higher sSFRs, due to the
perhaps higher mass accretion rate of gas which is likely present
at these epochs (Overzier 2016). The gravitational mass assembly
of baryonic matter within some massive dark matter halos seems
to enhance star formation activity among overdense galaxies. For
example, Chiang et al. (2017) explored cluster evolution using N-
body simulations and semi-analytic models. They point out that
from z ~ 5 to z ~ 1.5, there exists a prolonged star formation phase
responsible for about 65 per cent of the final stellar mass in present-
day clusters. Protoclusters might harbour massive cores by the end of
this epoch, marking the onset of widespread galaxy quenching and

<figure><img src="image_11.png" /></figure>

**Figure 8.** The sSFR of the overdense and underdense galaxies as a function of stellar mass at *z* = 4–10. The red and blue represent the overdense and underdense galaxies, respectively. The grey line is for the whole sample. The value of the differences in sSFR (ΔsSFR) is shown in the bottom panel, which is calculated as ΔsSFR = (sSFR<sub>over|under</sub> - <sSFR>). Error bars are calculated with the bootstrap method.

<figure><img src="image_12.png" /></figure>

**Figure 9.** The sSFR of all *z* = 4–10 galaxies on the Σ<sub>5</sub> - stellar mass plane. The colour of the various bins show the value of the sSFR in that region of this parameter space. The black dashed lines show the locations of the sSFR = [−8.0, −7.5] contour lines. From this there is a clear indication that stellar mass is the driving mechanism for producing galaxies with low sSFR values.

the build-up of the intracluster medium (ICM). Additionally, several
studies at high redshifts also indicate that star formation in dense
environments is enhanced compared to field galaxies, attributed
to the increased rates of gas accretion and mergers (Alberts et al.
2014; Monson et al. 2021; Lemaux et al. 2022; Pérez-Martínez
et al. 2024). However, we can show that this increase continues
<figure><img src="image_13.png" /><figcaption>Figure 10. The UV slope $\beta$ of under and overdense galaxies in different stellar mass bins. The lines and the shallow regions are their median and the median errors, derived from the bootstrap method. The bottom panel is $\Delta\beta = \beta_{\text{over|under}} - \beta$.</figcaption></figure>

to increase at the highest redshifts where these proto-clusters can be identified.

## 4.4 Effect of the environment on UV slope

The rest-frame UV continuum slope, $\beta$, is commonly used as a diagnostic tool to probe the characteristics of the stellar continuum (Calzetti, Kinney & Storchi-Bergmann 1994). It serves as an indicator of massive O/B-type main sequence stars and the associated H II nebular regions, and it is also a main indicator of dust in high-redshift galaxies as well as for any unusual stellar populations, such as Pop III star dominated galaxies. We use a Bayesian MCMC methods to fit a power-law form of the UV continuum, as $f_{\lambda} \propto \lambda^{\beta}$. This fitting is conducted using the rest-frame UV photometric data within the wavelength range $1250 < \lambda_{\text{rest}} / \AA < 3000$ (e.g. Rogers et al. 2014; Cullen et al. 2023b). We use the Meurer et al. (1999) relation to infer the UV dust attenuation as $A_{\text{UV}} = 4.43 + 1.99\beta$, which assumes an intrinsic $\beta_{\text{int}} = -2.23$. A comparison with the dust attenuation results from Bagpipes shows a general consistency, although some deviations are noted due to differences in modelling assumptions. Following a visual inspection of sources with extreme UV slope values, we remove sources with $\beta > -1$ or $\beta < -3.5$, primarily attributed to noisy photometry. For additional details on this fitting, refer to EPOCHS-III (Austin et al. 2024).

Fig. 10 shows the variation of $\beta$ in different stellar mass bins for galaxies in diverse environments. The value of $\beta$, denoted as $\beta(z, M_*)$, correlates with both redshift ($z$) and stellar mass ($M_*$), with a predominant strong dependence on stellar mass. Our analysis distinctly reveals that galaxies located in overdense regions consistently exhibit higher and thus redder $\beta$ values across all stellar mass bins. The average deviation is substantial, with ($\beta_{\text{over}} - \beta_{\text{under}}$) ~ 0.15. Using MCMC method, the median slope $\beta$ of overdense galaxies are $2\sigma$ higher than the underdense galaxies. Employing the KS test on the two data sets yields a $p$-value of 0.03, indicating a high likelihood that they originate from distinct distributions.

The UV $\beta$ is influenced by stellar age, stellar population, and dust attenuation. Since young stars are mostly located in proximity of dusty molecular clouds, star formation activity is usually associated with high extinction values. Galaxies in overdensities are characterized by enhanced star formation activity, it is thus plausible that their redder UV slope is due to higher dust attenuation rather than to an older stellar population, indicating that the cause may be dust. It is consistent with the presence of neighbouring galaxies that produce dust, which may be expelled from the host galaxy through outflows but remain within the CGM, potentially falling back onto nearby galaxies. This process is supported by studies such as Tumlinson, Peeples & Werk (2017), which discuss how feedback processes, like supernova-driven winds, can expel dust into the CGM and subsequently return enriched material to other galaxies in the vicinity.

Another plausible explanation is the influence of Ly$\alpha$ emission. Large Ly$\alpha$ EWs result in a decrease in the UV slope $\beta$ due to the biases present in wide-band photometric studies (Rogers, McLure & Dunlop 2013; Austin et al. 2024), suggesting that galaxies in underdense environments may exhibit stronger Ly$\alpha$ emission. There is also an alternative explanation involving Damped Ly$\alpha$ systems (DLAs). Austin et al. (2024) suggested that galaxies with high neutral Hydrogen column densities ($N_{\text{HI}} > 2 \times 10^{20} \text{ cm}^{-2}$) along the line-of-sight could result in higher $\beta$ values in wide-band photometric studies (Heintz et al. 2024), indicating that galaxies in denser regions may exhibit stronger DLA absorption (e.g. Cen & Ostriker 1999; Heintz et al. 2024). It appears that overdense regions tend to host a greater abundance of metal-rich objects such as damped Ly$\alpha$ systems or exhibit stronger absorption (Chen et al. 2024; Heintz et al. 2025). The details of the unbiased continuum slope measurements obtained using various methods can be found in the Epochs III paper (Austin et al. 2024), where we also simulate the impact of rest-UV line emission (including Ly$\alpha$) and damped Ly$\alpha$ systems on our measured $\beta$ value (see Figs 6 and 7 in the paper). Further spectroscopic observations will be essential to investigate this idea in the future.

## 4.5 Effect of the environment on the mass-size relation

To investigate the mass–size relation in different environments, we first use GALFIT version 3.0.5 (Peng et al. 2002, 2010) to fit a single Sersic light profile to each galaxy. GALFIT in a least-squares-fitting algorithm that finds the best-fitting model by minimizing the reduced chi-squared statistic ($\chi^2$). We choose filters that closely match the rest-frame optical wavelength of the sources to minimize the morphological $k$-correction effect (Taylor-Mager et al. 2007). Extreme cases are filtered out based on the criteria that the half-light radius should be within $0.01 < R_e(\text{pixels}) < 100$ and the fitted Sersic index lies within the range $0.05 < n < 10$. For more details, please refer to Ormerod et al. (2023) and Westcott et al. in preparation.

Fig. 11(a) shows the median of the stellar mass–size relation for the underdense and overdense galaxies. We find the stellar mass–size relation is universal within the mass ranges we probe ($\log M_*/M_{\odot} = 7-10$). Here, we perform a linear fitting on their respective medians in each stellar mass bins using a procedure similar to that described by Newman et al. (2012):

$$R_e = \gamma \left( \frac{M_*}{M_{11}} \right)^{\beta} \qquad (11)$$

where $M_{11}$ is $10^{11} M_{\odot}$. This expression can be written as follows:

$$\log(\gamma) = \log_{10}(R_e) + \beta(11 - \log_{10} M_*). \qquad (12)$$
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 11.** Mass–size relations in different environments. (a) Median stellar mass-size relation for overdense and underdense galaxies at different stellar masses. Error bars are computed through the bootstrapping method. (b) The normalized size ($\gamma$) of galaxies as a function of $\Sigma_5$. $<\gamma>$ is defined as equation (12). Values have been normalized to the median size in the $\Sigma_5$ bin $\Sigma_5 = 10^{0.5-1.0}$. Errors on the median values are computed through bootstrapping.</figcaption></figure>

The linear fitting results in a slope of $\beta = 0.12 \pm 0.01$ and an intercept of $C = -1.14 \pm 0.08$ for the overdense galaxies, and a slope of $\beta = 0.07 \pm 0.04$ and an intercept of $C = -0.74 \pm 0.33$ for the underdense galaxies. These best-fitting parameters are listed in Table 5. We find that the mass–size relation does not show a significant trend with environment; there are similar mass–size relations regardless of the host’s mass. Our results are consistent with the findings of the study in the local universe, indicating no evidence of a dependence of the mass–size relation of galaxies on environment (Weinmann et al. 2009; Huertas-Company et al. 2013).

Despite the observation from Fig. 11(a) that galaxies of similar mass exhibit similar size distributions regardless of their environment, there remains the possibility of some intrinsic environmental dependence (Bernardi et al. 2010). To investigate this further, we examine the $\Sigma_5-R_e$ relation, which characterizes the median size at a fixed stellar mass as a function of environment. Given the

<table><caption>**Table 5.** The best linear fits of the mass–size relation in equation (12).</caption><thead><tr><th>Redshift bins (total)</th><th>γ</th><th>β</th></tr></thead><tbody><tr><td>4 &lt; z &lt; 6</td><td>0.102 ± 0.056</td><td>0.088 ± 0.007</td></tr><tr><td>6 &lt; z &lt; 8</td><td>0.018 ± 0.047</td><td>0.081 ± 0.005</td></tr><tr><td>8 &lt; z &lt; 10</td><td>-0.160 ± 0.003</td><td>0.049 ± 0.001</td></tr></tbody><thead><tr><th>Environment subsets</th><th>γ</th><th>β</th></tr></thead><tbody><tr><td>Overdense</td><td>0.155 ± 0.079</td><td>0.117 ± 0.009</td></tr><tr><td>Underdense</td><td>0.074 ± 0.333</td><td>0.073 ± 0.039</td></tr><tr><td>All</td><td>0.075 ± 0.033</td><td>0.089 ± 0.003</td></tr></tbody></table>

correlation between environment and stellar mass, it is expected that more massive galaxies, and therefore larger galaxies, are more likely to be found in overdense regions. To account for this effect, we normalize the sizes ($\gamma$) using a procedure similar to that described by Newman et al. (2012). Here, $\beta$ is the slope of the stellar mass–size relation within the specified mass range, and $R_e$ denotes the effective radius. We adopt a standard value of $\beta = 0.83$, which corresponds to the slope measured across the entire galaxy sample.

In Fig. 11(b), we present the relative differences across different environments by normalizing all sizes to the median size in the $\Sigma_5$ bin $\Sigma_5 = 10^{0.5-1.0}$. The uncertainties associated with the median values are estimated using bootstrapping. The most notable finding is that the $\gamma-\Sigma_5$ relation appears essentially flat. Upon closer examination of the $\gamma-\Sigma_5$ relation in the lower panel of Fig. 11(b), excluding the two extreme points reveals a potential positive trend. A linear fit to the remaining data suggests a weak positive correlation between $\gamma$ and $\Sigma_5$, with a slope of $0.11 \pm 0.03$ and an intercept of $[0.87 \pm 0.03]$. To further assess the significance of this trend, we performed a Spearman correlation test, which yields a coefficient of $\rho = 0.89$ with a p-value of 0.007, indicating a strong and statistically significant relationship. These results hint at a potential environmental dependence of galaxy sizes that may become more apparent with larger samples or improved error constraints. Future studies with expanded data sets will be critical to validating this observation and understanding its physical implications.

## 5 GALAXY PROTOCLUSTER CANDIDATES

To further describe the global environment of our galaxy sample, we search for protocluster candidates in the JWST photometric data using the DETECTIFz algorithm<fnref n="7" /> (Sarron & Conselice 2021) to detect extended overdensities. In particular, we assess the probability of individual galaxies to belong to protocluster candidates and study the most probable members properties. This is related to but different from the efforts earlier in the paper where we have determined the properties of galaxies as a function of local density. Here, we investigate whether any of these overdense regions would qualify as being clusters or proto-clusters.

The DETECTIFz algorithm utilizes the Delaunay Tessellation Field Estimator (DTFE), previously used to detect cosmic web filaments (Sousbie 2011), to find extended galaxy overdensities in redshift slices. The approach is empirical and model-free, relying solely on galaxy sky coordinates and samples from joint photometric redshift and stellar mass probability distribution. We review the

<footnote n="7">⁷https://github.com/fsarron/detectifz</footnote>
main steps of the algorithm relevant to this work in the next sections, focusing on the adjustment made for JWST data. We refer to Sarron & Conselice (2021) for a more detailed description of the algorithm and the establishment of the DETECTIFz method.

## 5.1 Overdensity detection

### 5.1.1 Overview of the detection process

To search for galaxy protocluster candidates, we proceed with the estimation of the 2D galaxy density in redshift slices. The slice width is based directly on the uncertainty associated with photometric redshifts such that the galaxy population sampled in the slice is representative of the underlying galaxy population at the slice central redshift.

In each slice centred at $z_i$, we estimate the 2D galaxy density using 100 Monte Carlo realization of each galaxy's redshift probability distribution. For each realization $mc_j$, we build the 2D density $\Sigma_{gal}(mc_j, z_i)$ distribution using the DTFE method. The final surface density map is taken as the logarithmic average over all Monte Carlo realizations:

$$ \log \Sigma_{gal}^{mc}(z_i) = \frac{1}{N_{mc}} \sum_j \log \Sigma_{gal}(mc_j, z_i). \quad (13) $$

The 2D overdensity maps in each slice can then be written in Cucciati et al. (2018) as follows:

$$ \log(1 + \delta_{gal})(z_i) = \frac{\Sigma_{gal}^{mc}(z_i)}{\langle \Sigma_{gal}^{mc}(z_i) \rangle}, \quad (14) $$

where $\langle \Sigma_{gal}^{mc}(z_i) \rangle$ is the mean $3\sigma$ clipped mean surface density map. After obtaining an overdensity map for each slice $z_i$, we smooth the 3D data cube (RA, Dec, z) along the redshift dimension. This is achieved through convolution with a one-dimensional normal distribution with a standard deviation of $\sigma_z = 0.02$.

We then search for peaks in each slice with a minimum signal-to-noise ratio ($S/N$)$_{min} > 1.5$ in the 2D overdensity maps using the PHOTUTILS PYTHON package (Bradley et al. 2019), as follows:

$$ S/N = \frac{\log(1 + \delta_{gal}^{mc}) - \mu_{\delta}}{\sigma_{\delta}}, \quad (15) $$

where $\mu_\delta$ and $\sigma_\delta$ are, respectively, the mean and standard deviation of the $3\sigma$ clipped distribution of $\log(1 + \delta_{gal}^{mc})$. For each detection, we record the bounding-box (RA$_{min}$, RA$_{max}$, Dec$_{min}$, Dec$_{max}$) encompassing the region with pixel values above the ($S/N$)$_{min}$ threshold.

To remove multiple detection of the same protocluster in different adjacent slices and/or with multiple substructures, we merge detected peaks that are contiguous in the line-of-sight direction (i.e. redshift direction) and whose peaks are separated by less than 2 comoving Mpc or have overlapping bounding boxes. These selected regions are our final galaxy protocluster candidates. The sky coordinates of the peak with the highest $S/N$ ratio, with its corresponding redshift, are recorded as the centre of the galaxy protocluster candidate are listed in Table A1.

### 5.1.2 Adjustment made for protocluster detection

Due to the scarcity of galaxies at high redshifts ($z>7$), we are interested in detecting protocluster candidates at $5<z<7$, we had to make a few adjustments to the DETECTIFz algorithm that was originally devised to detect galaxy groups at $0<z<3$.

First of all, given the lower spatial density of the JWST data compared to lower redshift deep photometric surveys, we elect to detect the overdensities using the galaxy density rather than the stellar-mass density. Indeed, our test with stellar mass densities turned out to be biased towards detecting overdensities centred on very massive galaxies, even with relatively few neighbours. The galaxy density is more robust in this regard. Thus, in this set-up, we did not use samples from the 2D probability density PDF($M_*$, z) to compute the stellar mass surface density, but instead worked with the galaxy surface density, and thus only used samples from the 1D $p(z)$.

We also modified the way we merge individual peaks detected in adjacent slices to get rid of multiple detections of the same overdensity. Here, we are interested in detecting protoclusters i.e. very extended unvirialized structures, rather than more compact galaxy groups at lower redshift. Protoclusters also typically present several substructures. We focused on larger scales by merging peaks further away and considered the extent of each individual peak in the merging process. Thus, while the DETECTIFz method merges overdensities that are closer than 500 physical kpc, in our approach, we merge peaks that are closer than 2 comoving Mpc or have overlapping bounding boxes, to capture smaller-scale structures while ensuring their continuity to identify extended protoclusters with multiple substructures. The bounding-box of each candidate protocluster is defined as the union of the bounding-boxes of all merged individual detections.

Finally, in the original DETECTIFz, we made sure to have a 90 per cent stellar-mass complete sample of galaxies in each slice in order to have a very robust estimate of the expected density fluctuations and in turn of the $S/N$. For this study, we fixed the lower limiting stellar mass of the sample to be close to the 50 per cent stellar-mass completeness estimated from the JAGUAR simulations. This lower limiting was chosen to be redshift independent and fixed, respectively, to $M_{lim} = 10^{8.5}M_\odot$ for CEERS and NEP and $M_{lim} = 10^{7.5}M_\odot$ for JADES. This choice was a necessary trade-off in order to have a sufficient galaxy density, but this could impact the purity of the output protocluster catalogues.

We note that we were not able to test these different changes on simulations to assess how they impact in detail the selection function of our JWST protocluster catalogue. Given the novelty and exploratory nature of our results, we however defer this effort to future work.

## 5.2 Group membership probability and cluster mass

For individual galaxies within the bounding-box of each protocluster candidate, we compute their probability to be protocluster members. This probability is calculated in a Bayesian method following Sarron & Conselice (2021), similar to the approaches outlined in George et al. (2011) and Castignani & Benoist (2016). It involves the convolution of the redshift PDFs of galaxies and that of the protocluster with a prior based on excess number counts in the protocluster region. We refer to Sarron & Conselice (2021) for a more thorough description of the method and outline here the main modifications that we adopted for JWST data.

We write the probability membership $P_{mem} = P(\text{gal} \in \text{PC}|\text{PDF}_{gal}(z), \text{PDF}_{PC}(z), M_*^{gal})$ in a given protocluster (PC) and use Bayes rule

$$ P_{mem} \propto \int P(\text{PDF}_{gal}(z)|\text{gal} \in G, \text{PDF}_{PC}(z), M_*^{gal})(z) \times P(\text{gal} \in G | \text{PDF}_{PC}(z), M_*^{gal})(z) dz, \quad (16) $$
where $P(\text{PDF}_{\text{gal}}(z)|\text{gal} \in G, \text{PDF}_{\text{PC}}(z), M_{*}^{\text{gal}})(z)$ is the likelihood of observing the data ($\text{PDF}_{\text{gal}}(z)$) evaluated at redshift $z$ given the galaxy belong to the protocluster, while $P(\text{gal} \in G | \text{PDF}_{\text{PC}}(z), M_{*}^{\text{gal}})(z)$ is the prior probability that a galaxy with stellar mass $M_{*}^{\text{gal}}$ belongs to the protocluster evaluated at a redshift $z$.

The main difference with Sarron & Conselice (2021) resides in our use of the stellar mass information in the computation of the prior. Due to number counts in the JWST data being quite low, the method proposed in Sarron & Conselice (2021), where the prior was based on number counts excess in bins of redshift and stellar-mass was simplified by using only bins of redshifts, to prevent number counts excess estimate to be shot noise dominated. Thus we were able to use directly the DETECTIFz overdensity maps that allows us to compute number count excess at any (RA, Dec, $z$) and deduce our prior as follows:

$$P_{\text{Prior}}(z) = 1 - \frac{\langle n^{\text{DETECTIFz}}(z) \rangle_{\text{notPC}}}{n^{\text{DETECTIFz}}(z)(\text{RA}_{\text{gal}}, \text{Dec}_{\text{gal}})}, \quad (17)$$

where $n^{\text{DETECTIFz}}$ are surface densities given by DETECTIFz 3D overdensity maps $n \propto 10^{(1+\delta_{\text{gal}}^{\text{DETECTIFz}})}$. In the numerator, the surface density estimate are averaged over pixels outside any protocluster bounding-box at redshift $z$ ('notPC'). In the denominator, we take the surface densities at the pixel in which the galaxy falls.

Further details of the definition of likelihood and the rescaling of probabilities can be found in Sarron & Conselice (2021). We note that while probabilities calibration was thoroughly checked using simulations in Sarron & Conselice (2021), there is no guarantee here that the absolute $P_{\text{mem}}$ values are good estimators of the probability of a galaxy to belong to the protocluster. In particular, since protoclusters are unvirialized clusters, we expect $P_{\text{mem}}$ to behave differently than what was presented in Sarron & Conselice (2021) for the case of groups and clusters at lower redshifts. However, our probability membership definition is well motivated by probability theory, so we expect our probability memberships to be informative in a relative sense. This is reflected in the following, where we use $P_{\text{mem}}$ to select a quantile of the most probable protocluster galaxies for further analysis of their properties.

We use the $P_{\text{mem}}$ values to compute the cluster's total stellar mass, which can be written as follows:

$$M_{*,\text{PC}} = \sum_{\substack{\text{gal} \in \text{PC} \\ P_{\text{mem}} \in Q_4}} M_{*}^{\text{gal}} \quad (18)$$

where $Q_4$ is the upper quartile of probability memberships, $M_{*}^{\text{gal}}$ is the galaxy's stellar mass. The final protocluster candidate catalogue is listed in Table A1.

We estimated the cluster size $R_{200}$ in our catalogue following the methodology of Hansen et al. (2005) and Sarron & Conselice (2021). This size is the radius of a sphere in which an average mass density is 200 times the critical density of the Universe.

## 5.3 Protocluster detected in DETECTIFz

In total, we find 26 protocluster candidates using DETECTIFz at $5<z<7$, of which 12 are at $z>6$. There are 10, 10, and 6 in CEERS, JADES, and NEP, respectively. The total stellar mass of these protoclusters ranges $\log(M_{*}/\text{M}_{\odot}) = 9.2-10.6$. Fig. 13 shows examples of the largest photometric protocluster candidate in JADES field and its probable member galaxies (with $P_{\text{mem}} \in Q_4$). The member probabilities $P_{\text{mem}}$ are coloured in the right panel. The

point size shows the galaxy's stellar mass at the group redshift. The overdensity $\log \delta_{\text{gal}} = 0.59$, is shown in the blue shaded regions.

We tested whether the results obtained from different SED fitting codes would impact our search for protocluster candidates. For this purpose, we conducted an alternative run using EAZY Larson PDF($z$) instead of the Bagpipes ones. In this alternative run, we identified 6 protocluster candidates. Remarkably, 5 of these 6 protocluster candidates are also detected in the reference run, while the two were merged into a single entity in the reference run. This merging is likely due to the use of a smoothed version of the slice width in the reference run, which helps the merging process following detection. However, 5/10 protoclusters identified in the reference run were not recovered in the alternative run. This discrepancy arise most likely because the EAZY PDF($z$) estimates are approximate, and estimated on a coarser redshift binning, when compared to the Bayesian analysis of the redshift posterior conducted with Bagpipes. Moreover, these missing protoclusters are those within the sample which have the lower masses and fewer member galaxies, suggesting our reference run is more sensitive thanks to the finer sampling of the redshift PDF($z$) from Bagpipes. A more complete analysis of the effects of the SED fitting tool or templates on photometric protocluster identification is left for future work.

Encouragingly, we have detected a novel overdensity located at the periphery, absent in the previous run. However, in the alternative run, its significance is at $S/N = 1.8$, indicating that it may have narrowly missed the $S/N = 1.5$ threshold in the reference run. On average, the $S/N$ for detections are higher in the recent run. This uptrend could be attributed to the smoothing of the slice width and/or the consistent stellar-mass input across all 100 Monte Carlo realizations of the redshift. Nonetheless, this difference does not cause significant concern and does not affect our main detections and conclusions here.

## 5.4 Dark matter halo mass

The estimated comoving number density of protocluster candidates in this study is $5 \times 10^{-7} \text{Mpc}^{-3}$, which is higher than predictions from several other studies. The comoving number density of massive protoclusters at $z > 2$ is previous work is found to be $\sim 1 \times 10^{-7} \text{Mpc}^{-3}$ (e.g. Chiang et al. 2013; Mul-drew et al. 2015, $M_{\text{halo}} \gtrsim 13.5 \text{M}_{\odot}$). The higher number density in this study suggests that the sample may include a relatively rich population of protoclusters, or that the selection criteria used may identify a greater number of candidates compared to previous studies. Additionally, it is possible that only a fraction of these candidates are true progenitors of massive galaxy clusters by $z = 0$. Further investigation into the mass and evolution of these candidates is necessary to assess whether they are likely to evolve into massive galaxy clusters by $z = 0$.

We estimated dark matter halo masses for these protoclusters and compared these with simulations to infer their properties and evolution. This estimate assumes a scenario where each galaxy originates within the same dark matter halo. Consequently, we derived the dark matter halo mass from the total stellar mass of the clusters, leveraging the $M_{\text{halo}} - M_{*}$ scaling relation outlined by Behroozi et al. (2013). By summing the stellar masses of individual galaxies constituting the overdensity and converting them to a halo mass, our analysis yields a total halo mass of $\log10 (M_{\text{halo}}/\text{M}_{\odot}) = (11.2 - 13.9) \pm 0.6$ for most systems.

Fig. 12 illustrates the distribution of dark matter halo masses across various representative groups and protoclusters at $z<8$, with simulation data from Chiang et al. (2013) and TNG300 simulations from Montenegro-Taborda et al. (2023). Chiang et al. (2013)
<figure><img src="image_16.png" /><figcaption>**Figure 12.** The dark matter halo mass distribution for protocluster candidates at $z = 1.3–8.0$ compared with simulations. The red points are the photometrically identified protocluster candidates from this work. The blue and green lines are the simulated halo mass evolution of ‘Coma’($> 10^{15}M_{\odot}$) and ‘Fornax’((1.37–3) × $10^{14}M_{\odot}$) type clusters in Chiang et al. (2013), respectively. The grey shaded region is from the TNG300 simulation of $M_{200} \le 10^{14}M_{\odot}$ systems at $z = 0$ in Montenegro-Taborda et al. (2023).</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Figure 13.** Left: The photometric and spectroscopic galaxies identified in a protocluster at $z = 5.51–5.85$ in the JADES field as shown by open circles and filled squares, respectively. The colours for each system show their redshifts. Right: the member galaxies in the protocluster candidate with $P_{\text{mem}} \in Q_4$ colour-coded by their probability of being at the group redshift. The point size is proportional to the galaxy stellar mass at the group redshift. The yellow star is the centre of the protocluster candidate. The blue shaded regions present the overdensity level as indicated by the colour bars.</figcaption></figure>

employed a semi-analytical galaxy formation model (Guo et al. 2011) applied to the dark matter-only N-body simulation Millennium (Springel et al. 2005), tracking the evolution of both dark matter and galaxies across approximately 3000 clusters from $z = 7$ to $z = 0$. The blue and green shaded regions denote the simulated halo mass evolution of ‘Coma’ ($> 10^{15}M_{\odot}$) and ‘Fornax’ (1.37–3) × $10^{14}M_{\odot}$) type clusters in Chiang et al. (2013), respectively. In contrast, Montenegro-Taborda et al. (2023) identified 280 systems with $M_{200} \le 10^{14}M_{\odot}$ at $z = 0$ in the TNG300 simulation (Pillepich et al.

2018) and traced their progenitors at high redshift, represented by the grey shaded areas.

Our findings indicate that the confirmed halo mass aligns with the theoretical prediction in Chiang et al. (2013) and the progenitor of the TNG300 simulations, even when considering the uncertainty in halo mass. This suggests that most of the confirmed clusters would evolve into clusters with $M_{\text{halo}} > 10^{14}$ at $z = 0$, with some (8/26) potentially evolving into Coma-like clusters with $\log10(M_{\text{halo}}/M_{\odot}) > 15$ by $z = 0$ (e.g. Ruel et al. 2014; Buddendiek et al. 2015). We
also plot the halo and stellar masses of other massive proto-clusters at 1.3<z<8.0 that also exhibit consistency with simulations (e.g. Rosati et al. 2009; Stanford et al. 2012; Gobat et al. 2013; Andreon et al. 2014; Wang et al. 2016; Mantz et al. 2018; Miller et al. 2018; Shimakawa et al. 2018; Laporte et al. 2022; Sillassen et al. 2022; Coogan et al. 2023; Di Mascolo et al. 2023; Jin et al. 2024; Pérez-Martínez et al. 2024), further supporting the forming cluster scenario of the theoretical and simulation prediction.

It is worth noting that our sample may lack additional overdensity members characterized by low levels of star formation or heavy obscuration (e.g. DSFGs and/or obscured AGNs). Consequently, our total halo mass range is likely an underestimation of the true halo mass. However, considering the uncertainties in our halo mass calculations, these factors do not significantly impact the main conclusions of our study.

## 5.5 Galaxy environment of protocluster candidates

To validate whether the identified protocluster candidate members align with the findings on galaxy environments discussed in Section 4, we compare the members of protocluster candidates with a control sample. The control sample are selected from the lower quartile of probability membership within each protocluster candidate. Some galaxies, although having a low probability within a specific protocluster, may be associated with another protocluster; these are also excluded from the sample. Ultimately, 401 galaxies are selected, providing a representation of galaxies in underdense regions.

We examine the Σ<sub>5</sub> values, where the median Σ<sub>5</sub> of the protocluster members was found to be 2.6 times higher than that of the control sample, with errors estimated using the bootstrap method. Employing the MCMC approach, the median Σ<sub>5</sub> for cluster members is determined to be significantly higher than that of the control sample, supporting the consistency between different methods in identifying overdense and underdense galaxies. We conduct the further analysis on their physical characteristics such as mass, SFR, and UV slope. We find that the median UV slope (β) values for cluster members and the control sample were -2.28 ± 0.04 and -2.38 ± 0.05, respectively, indicating that cluster members were significantly redder, consistent with our previous findings. Similarly, the SFR for cluster members was also marginally higher by ~2σ compared to the control sample. The median stellar masses for cluster members and the control sample are 8.22 ± 0.08M<sub>☉</sub> and 7.95 ± 0.03M<sub>☉</sub>, respectively, showing a significant difference of about 3 sigma; the difference in sSFR is not as pronounced.

We note that 32 per cent of the overdense galaxies identified by Σ<sub>5</sub> values overlap with cluster members identified by the DETECTIFz algorithm. The selection by Σ<sub>5</sub> is based on individual redshift bins, hence it still identifies relatively overdense galaxies at high redshifts. However, due to the limitations in the number of high-redshift galaxies available, it is very challenging for the DETECTIFz algorithm at z>7 to produce meaningful density maps. Furthermore, while the proxy may work in a relative sense (i.e. a higher number indicates larger mass structures), it may be a poor absolute measure of the number of protocluster galaxies. These factors can lead to biases in the selection of overdense galaxies.

## 6 DISCUSSION

In this study, we have conducted an analysis of high-z galaxies within the CEERS, JADES, and NEP field at z > 4, utilizing high-resolution broad-band imaging data from the HST and using JWST NIRCam

data. Our investigation quantitatively examines the members of protoclusters within the range z = 4.5–10. By leveraging the three wide-field data sets, we have illuminated the crucial role of environment in galaxy evolution at z > 4. In this section, we compare our findings with relevant studies on the clustering properties of galaxies at these redshifts. We explore how environmental factors influence the formation and evolution of galaxy clusters at these early cosmic epochs. By integrating simulations and previous observational data at lower redshifts, we can analyse the process of cluster assembly.

### 6.1 Association between photometric and spectroscopic overdensity

In theory, there should be a correlation between photometric and spectroscopic overdensities because they trace the same dark matter halo or structure. However, previous studies on overdensities at z = 2–5 have shown that different tracer galaxies (e.g. LAE, LBG, or SMG) exhibit different distributions when describing the same dark matter halo. In this section, we compare the overdensities identified through our photometric analysis with those confirmed by spectroscopic observations to assess their consistency and provide a more comprehensive study of large-scale structure.

Fig. 13 shows one of our protocluster candidates in the GOODS-S field, JADES-ID1-5.68, with a total of 66 galaxies ($P_{mem} > 0.32$). Fig. 14 presents the three-dimensional spatial distribution of these galaxies, providing a clearer view of their locations within the overdense region. This overdensity holds the distinction of being the largest in terms of the total number of galaxies identified in JADES DR1, and it also ranks as one of the most massive inferred halo mass within these fields. The average overdensity value within a central circle of 250 kpc radius is $\delta\text{gal} = 3.9$. These photometric sources exhibit potential associations with the overdensity studies of JADES-GS-OD-5.386 reported in Helton et al. (2023). The latter identified 42 spectroscopic sources at redshifts $z = 5.2–5.5$, although they were labelled as ‘field galaxies’ potentially due to limitations in spectroscopic data coverage. Spectroscopic follow-up observations are imperative to confirm the true association of the photometric sources with the overdensity. Notably, JADES-ID1-5.68 is in close proximity to JADES-GS-OD-5.386. The latter exhibits an average overdensity value of $\delta\text{gal} = 9.134$ (Helton et al. 2023). This makes JADES-GS-OD-5.386 the most significant overdensity characterized by $H\alpha$ emitters within the redshift range of $4.9 < z_{spec} < 6.6$. The central redshift of JADES-ID 1 is 5.68, with a photometric redshift range from $z = 5.25$ to $z = 6.23$. The protocluster identified in (Helton et al. 2023) has a spectroscopic redshift of approximately $z = 5.386$, which falls within the structure we have identified. Additionally, the protocluster’s position in JADES-ID-1 is located near Helton et al.’s overdensity. It is plausible that our photometric sources and these overdensities are situated within a larger, intricate filamentary structure.

While some photometrical confirmed overdensities exhibit concordance with spectroscopically confirmed counterparts, others do not. This discrepancy can be attributed to various factors. Spectroscopic surveys frequently prioritize the observation of brighter sources to ensure robust detection rates. However, this strategy may inadvertently neglect fainter sources. Such dimmer sources may nevertheless be detected through JWST broad-band surveys, particularly at higher redshifts, where galaxies with magnitudes around $m \sim 30$ become accessible.

Even overdensities confirmed using narrow-band selected emission-line galaxies such as $H\alpha$ and [O III], or even $Ly\alpha$, may also contain bias. This is because some high-z galaxies may exhibit
<figure><img src="image_18.png" /><figcaption>**Figure 14.** A 3D plot of the largest galaxy overdense environment at $5.51 < z_{\text{photo}} < 5.85$ in the JADES data set. Each photometric selected galaxy is colour-coded based on its probability of cluster membership, with the point size indicating the galaxy's stellar mass, the same as in Fig. 13. Spectroscopy-confirmed galaxies are denoted by the grey squares and circles in the plot. The yellow star is the centre of the protocluster candidate. This figure shows that these galaxy overdensities are situated within a complex environment characterized by possible interconnected filamentary structures.</figcaption></figure>

weak emission lines, which can introduce uncertainties in the overdensity identification process (e.g. Lemaux et al. 2018). Additionally, insights from UNCOVER spectra shed light on why Ly$\alpha$ emission is not detected in many galaxies within the overdensity identified by Morishita et al. (2023). Many observations have indicated evidence of damped Ly$\alpha$ absorption, which can significantly attenuate any Ly$\alpha$ emission that may be present. Consequently, the density of Ly$\alpha$ emitters may be underestimated, potentially leading to the oversight of genuinely dense regions within the overdensity.

It is worth noting that the uncertainties in redshift measurements for galaxies confirmed through photometry, typically ranging from 0.1 to 0.3. At a redshift of approximately $z \sim 6$, this corresponds to uncertainties of about 30 to 90 h$^{-1}$ Mpc. This can result a lack of sensitivity in identifying structures with scales smaller than 30 h$^{-1}$ Mpc in the overdensity regions. Another significant effect of redshift measurement uncertainty is the contamination introduced by $\Delta z$ when measuring excess surface density. As $\Delta z$ increases, it smoothies the density field, reduces scatter within each bin, and largely underestimates the proto-cluster overdensity. This effect was also pointed by Chiang et al. (2013) in Fig. 13, that find at $z = 3$ a drop of approximately 40 per cent in the surface density of protoclusters ($1 + \delta_{\text{gal}}$), when using a narrow-band filter with a typical FWHM of $\sim 60$ Å (corresponding to a $\Delta z \sim 0.05$ and the comoving length $d_c \sim 50$ h$^{-1}$ Mpc) compared to a 15 Mpc cubic window. Therefore, protoclusters identified through our photometric methods may underestimate the surface density and provide the lower limit densities. Follow-up spectroscopic data from JWST will be instrumental in confirming their densities.

## 6.2 When were the first mature clusters virialized?

The evidence for galaxy clusters typically relies on the observation that these entities are virialized, distinguishing them from protoclusters. This virialization requirement necessitates detection through emission from ICM, either in X-rays (e.g. Rosati, Borgani &

Norman 2002; Rosati et al. 2004, 2009; Gobat et al. 2011; Wang et al. 2016) or at submillimetre wavelengths via the SZ effect (e.g. Staniszewski et al. 2009; Williamson et al. 2011; Reichardt et al. 2013; Bleem et al. 2015; Hilton et al. 2021). But current sensitivity in X-ray and submillimetre observations remains insufficient to detect galaxy clusters at early cosmic epochs, beyond $z = 2 - 3$ (e.g. Tozzi et al. 2022; Di Mascolo et al. 2023). Additionally, early galaxy clusters may not have undergone virialization, as their halos are undergoing rapid mass accretion. We aim to facilitate subsequent multiwavelength studies to better understand when these structures begin to virialize, a crucial aspect of cosmic evolution.

In Fig. 12, we find that some extremely large-scale structures with halo masses exceeding $10^{13} M_{\odot}$ are predicted to have already formed as early as $z \sim 6$. Similar structures have also been identified at high redshift in previous studies (e.g. Shimasaku et al. 2003; Matsuda et al. 2005; Brinch et al. 2024). Although the central regions of these structures may evolve into massive virialized clusters by $z = 0$, the outer structures are not necessarily destined to virialize, it is improbable that the collapse of the entire structure will be completed by that time. This can explain why their mass is larger compared to clusters or simulations evolved to $z = 0$.

Most galaxies within $z = 4.5-10$ exhibit significant star formation activity regardless of their environment. Notably, as shown in Fig. 8, the galaxies in high-density environments exhibit even stronger star formation activity compared to those in low-density environments. In contrast, observational studies have demonstrated that during the epoch of $1 < z < 4$ certain galaxies in high-density environments generally display suppressed star formation activity relative to their counterparts in underdense regions (e.g. Gómez et al. 2003; von der Linden et al. 2010; Nantais et al. 2017; Lemaux et al. 2019; Tomczak et al. 2019; Sarron & Conselice 2021).

In protoclusters at $z \sim 2$, there is evidence of most members being on the main sequence, so they are not more star forming than typical galaxies (Polletta et al. 2021; Pérez-Martínez et al. 2024). The observation of an overabundance of massive quiescent galaxies in
overdense environments during these redshift epochs (e.g. Davidzon et al. 2016; Tomczak et al. 2017) suggests that rapid stellar mass growth occurred during the early stages of cluster assembly, likely through a combination of in situ star formation processes and *ex situ* galaxy–galaxy merging activity. We therefore expect there to be a heightened levels of star formation activity in the high redshift to align with the characteristics of low- and intermediate-redshift cluster populations.

## 7 CONCLUSIONS

In this paper, we investigate the environment of galaxies at $z = 4.5 - 10$ using JWST photometric data. Utilizing data sets from JWST and HST wide-field broad-band surveys (CEERS, JADES, and NEP), totalling ~185 arcmin² in area, we carefully selected a sample of 2948 high-redshift galaxies falling within the redshift range of $4.5<z<10$. The photometric data obtained from these surveys exhibit well constraints and exhibit close agreement with spectroscopic redshift measurements.

Our primary scientific goal is to analyse whether galaxies inhabiting distinct environments exhibit varying physical characteristics and whether these attributes undergo evolutionary changes with redshifts. Furthermore, we conduct a comprehensive survey for the first time utilizing JWST photometry data to find galaxy protocluster candidates that emerged during the cosmic dawn. Our findings include the following:

I. We employed the KDTree data structure to facilitate the nearest neighbour measurement, to effectively estimate the local environment of galaxies and to select potential galaxy cluster members. Simultaneously, we curated a control sample consisting of underdense galaxies for comparative analysis. Our selection process meticulously accounts for various factors that could influence sample selection, such as redshift selection bias, velocity offsets along the line of sight, image boundaries, and selection completeness.

II. We find that overdense galaxies consistently have higher star formation activity across all studied redshifts at $z>4.5$. These galaxies also display a slightly steeper slope in the relation of SFR and $M_*$, suggesting a possible influence of the environment on their stellar formation activity, though this is not very pronounced. Galaxies at higher redshifts in overdensities exhibit increased star formation activity compared to their lower redshift counterparts. It has a subtle rise with increasing redshift, followed by a gentle flattening of the $M_*$-SFR slope.

III. The sSFR of both overdense and underdense galaxies indicates that overdense galaxies have higher sSFRs, surpassing those of field galaxies by 0–0.5 dex. We find, during the early universe when massive galaxies were less common, the effect of mass dominates the sSFR, while the quenching mechanisms related to environmental factors appeared less pronounced. In contrast, overdense galaxies exhibit higher sSFRs due to their higher mass accretion rates.

IV. Our study also reveals that galaxies situated in dense regions of consistently redder in terms of UV slope $\beta$ values across all stellar mass bins. One possible explanation is that galaxies in dense environments may exhibit redder UV slopes due to higher dust extinction. Additionally, they may have weaker or even absent Ly$\alpha$ emission or stronger damped Ly$\alpha$ absorption, or a higher prevalence of DLAs. Other factors, such as stellar age and stellar population, could also contribute.

V. We use the DETECTIFz algorithm, a Bayesian approach tailored for quantitatively identifying cosmic web filaments and galaxy clusters/groups using photometric data, to evaluate the probability of

a galaxy’s membership in a galaxy group. Our analysis yields a total of the control sample are selected from t 26 candidate overdensities. Of these, one candidate has been confirmed through spectroscopic observations. The remaining candidates require further spectroscopic follow-up to confirm their association. Additionally, we conduct tests to ensure that variations in the results obtained from different SED fitting codes did not significantly impact our cluster detection efforts.

VI. We estimate the dark matter halo mass of our proto-clusters and compared these with other protoclusters identified at $z = 1.3 - 7.0$, as well as with N-body simulations and TNG300 simulation. The close correspondence observed lends support that some of these protocluster candidates are likely to evolve into clusters with $M_{halo} > 10^{14}$ at $z=0$, thereby reinforcing the theoretical and simulation predictions of forming clusters.

Our study represents one of the first searches for protocluster candidates in JWST wide field regions based on photometric data, offering valuable insights into the early phases of cosmic structure formation. Looking ahead, future work with advanced telescopes such as new JWST, ALMA, or similar instruments offers the potential to advance our understanding of protoclusters in the early Universe by providing in-depth, multiple-band and/or spectroscopy observations and analyses. Utilizing the spectroscopic capabilities of JWST, for instance, would allow for detailed investigations of the chemical composition and physical properties of galaxies within these protocluster candidates. Additionally, ALMA’s sensitivity to submillimetre wavelengths could unveil crucial information about the cold gas and dust content, shedding light on the early stages of galaxy formation within these cosmic structures. This work serves as a crucial reference for future observations of galaxy clusters. As we move forward, combining the power of such advanced tools with spectroscopic observations promises to enhance our comprehension of the intricate processes shaping the universe and structure formation at the earliest stages.

## ACKNOWLEDGEMENTS

We acknowledge support from the ERC Advanced Investigator Grant EPOCHS (788113) and support from STFC studentships. This work is based on observations made with the NASA/ESA HST and NASA/ESA/CSA JWST obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST, and NAS 5-26555 for HST. The observations used in this work are associated with JWST programme 1345, 1180 1176, and 2738. The authors thank all involved in the construction and operations of the telescope as well as those who designed and executed these observations. RAW and RAJ acknowledge support from NASA JWST Interdisciplinary Scientist grants NAG5-12460, NNX14AN10G, and 80NSSC18K0200 from GSFC. MP acknowledges financial support from INAF mini-grant 2023 (1.05.23.04.01). FS acknowledges support from a CNES Postdoctoral Fellowship in the early stage of this research project.

The authors thank Anthony Holloway and Sotirios Sanidas for their providing their expertise in high performance computing and other IT support throughout this work. The authors also thank Shuowen Jin and Yi-Kuan Chiang for their support with the data and simulations. This work makes use of ASTROPY (Astropy Collaboration 2013, 2018, 2022), MATPLOTLIB (Hunter 2007), REPROJECT, DRIZZLEPAC (Hoffmann et al. 2021), SciPY (Virtanen et al. 2020), and PHOTUTILS (Bradley et al. 2022).
DATA AVAILABILITY

The JWST data used in this work are available in the CEERS Survey (ID: 1345, PI: S. Finkelstein, Bagley et al. 2023), the JADES (ID: 1180 and 1210, PI: Eisenstein, N. Lützgendorf, Rieke et al. 2023) and the NEP-TDF (Windhorst et al. 2023) in JWST PEARLS observational programme (JWST GTO programme, PID 1176, 2738, PI: Rogier Windhorst, Diego et al. 2023; Frye et al. 2023; Windhorst et al. 2023), through the Mikulski Archive for Space Telescopes (https://mast.stsci.edu/). HST data is from the the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011; Koekemoer et al. 2011), which be shared on reasonable request to the CANDELS team. Additional data products will be shared on reasonable request to the first author.

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## APPENDIX A: CATALOGUE OF THE HIGH-Z PROTOCLUSTER IN DETECTIFZ

In Section 5, we describe our systematic approach utilizing the DETECTIFz to quantitatively assess the probability of a galaxy being associated with a particular galaxy cluster. Our investigation spans the contiguous regions of CEERS, JADES, and NEP fields, encompassing a cumulative area of ~185 arcmin². Within these expanses, we have identified 26 galaxy protocluster candidates at $5<z<7$. Below, we present the spatial locations and the properties of the protocluster candidates. Table A1 is the catalogue of the high-z protocluster candidates found in this work. Table A2 is the catalogue illustrating group membership.
<table><caption>**Table A1.** The catalogue of the clusters candidates found in CEERS, JADES, and NEP using DETECTIFz. The sky coordinates and group redshift are measured at the peak of the highest S/N detection in the group. $z_{group}$ is the redshift of the centre of the protocluster. $z_{inf}$ and $z_{sup}$ are the minimum and maximum redshift of detection at S/N > 1.5. It is important to note that these values do not necessarily indicate the full redshift range of the protoclusters themselves; they include all detected galaxies above this threshold, some of which may not have a clear association with the protocluster candidate. The group membership probability of these galaxies is generally low, as discussed in Section 5.2. log $\delta_{gal}$ is the number density contrast in a circle of 250 kpc radius. The definition of $R_{200}$ is in Section 5.2, measured in the highest SNR single slice in Mpc unit. $n_{dets}$ is the number of members with $P_{mem} \in Q_4$ in the galaxy cluster, where $Q_4$ is the upper quartile of probability memberships. $M_{*,PC}$ is the total cluster stellar mass by adding galaxy members. $M_{halo}$ is the total halo mass of clusters using $M_{halo} - M_{*}$ scaling relation in Behroozi, Wechsler & Conroy (2013), described in Section 5.4.</caption><thead><tr><th>Group ID</th><th>RA J2000</th><th>Dec J2000</th><th>z<sub>group</sub></th><th>z<sub>inf</sub></th><th>z<sub>sup</sub></th><th>log δ<sub>gal</sub></th><th>R<sub>200</sub> Mpc</th><th>M<sub>*,PC</sub></th><th>M<sub>halo</sub></th><th>n<sub>dets</sub></th></tr></thead><tbody><tr><td>CEERS - ID 1</td><td>214.98271</td><td>52.87480</td><td>5.16</td><td>5.01</td><td>5.91</td><td>0.37</td><td>0.78</td><td>10.48<sup>+0.15</sup><sub>-0.16</sub></td><td>12.27<sup>+0.52</sup><sub>-0.29</sub></td><td>32</td></tr><tr><td>CEERS - ID 2</td><td>214.95095</td><td>52.91322</td><td>5.19</td><td>5.04</td><td>5.53</td><td>0.26</td><td>0.31</td><td>10.40<sup>+0.15</sup><sub>-0.17</sub></td><td>12.12<sup>+0.40</sup><sub>-0.24</sub></td><td>9</td></tr><tr><td>CEERS - ID 3</td><td>214.80541</td><td>52.73319</td><td>5.40</td><td>5.12</td><td>5.68</td><td>1.01</td><td>0.41</td><td>9.95<sup>+0.13</sup><sub>-0.25</sub></td><td>11.63<sup>+0.10</sup><sub>-0.16</sub></td><td>6</td></tr><tr><td>CEERS - ID 4</td><td>214.92576</td><td>52.94283</td><td>5.40</td><td>5.10</td><td>5.84</td><td>0.37</td><td>0.30</td><td>10.73<sup>+0.14</sup><sub>-0.22</sub></td><td>13.57<sup>+0.83</sup><sub>-1.07</sub></td><td>20</td></tr><tr><td>CEERS - ID 5</td><td>214.94564</td><td>52.91242</td><td>5.42</td><td>5.25</td><td>5.61</td><td>0.34</td><td>0.33</td><td>9.82<sup>+0.19</sup><sub>-0.17</sub></td><td>11.54<sup>+0.13</sup><sub>-0.10</sub></td><td>5</td></tr><tr><td>CEERS - ID 6</td><td>214.80659</td><td>52.79719</td><td>5.47</td><td>5.19</td><td>5.76</td><td>0.35</td><td>0.19</td><td>9.68<sup>+0.11</sup><sub>-0.21</sub></td><td>11.45<sup>+0.06</sup><sub>-0.12</sub></td><td>5</td></tr><tr><td>CEERS - ID 7</td><td>214.95629</td><td>52.93801</td><td>5.79</td><td>5.53</td><td>6.07</td><td>0.39</td><td>0.32</td><td>9.94<sup>+0.16</sup><sub>-0.16</sub></td><td>11.61<sup>+0.15</sup><sub>-0.12</sub></td><td>10</td></tr><tr><td>CEERS - ID 8</td><td>214.98669</td><td>52.87240</td><td>5.93</td><td>5.68</td><td>6.15</td><td>0.35</td><td>0.25</td><td>10.45<sup>+0.11</sup><sub>-0.16</sub></td><td>12.65<sup>+0.55</sup><sub>-0.58</sub></td><td>6</td></tr><tr><td>CEERS - ID 9</td><td>214.83161</td><td>52.87481</td><td>6.29</td><td>5.78</td><td>6.62</td><td>0.63</td><td>0.49</td><td>9.85<sup>+0.17</sup><sub>-0.17</sub></td><td>11.52<sup>+0.17</sup><sub>-0.13</sub></td><td>25</td></tr><tr><td>CEERS - ID 10</td><td>214.92044</td><td>52.91803</td><td>6.76</td><td>6.21</td><td>7.01</td><td>0.36</td><td>0.47</td><td>9.58<sup>+0.14</sup><sub>-0.18</sub></td><td>11.28<sup>+0.11</sup><sub>-0.12</sub></td><td>12</td></tr><tr><td>NEP - ID 1</td><td>260.69501</td><td>65.77955</td><td>5.34</td><td>5.00</td><td>5.60</td><td>0.46</td><td>0.26</td><td>10.23<sup>+0.18</sup><sub>-0.21</sub></td><td>11.88<sup>+0.29</sup><sub>-0.20</sub></td><td>14</td></tr><tr><td>NEP - ID 2</td><td>260.73205</td><td>65.76115</td><td>5.50</td><td>5.00</td><td>5.88</td><td>0.46</td><td>0.41</td><td>10.46<sup>+0.16</sup><sub>-0.22</sub></td><td>12.40<sup>+0.69</sup><sub>-0.48</sub></td><td>37</td></tr><tr><td>NEP - ID 3</td><td>260.69490</td><td>65.90675</td><td>5.57</td><td>5.16</td><td>5.87</td><td>0.45</td><td>0.16</td><td>9.19<sup>+0.18</sup><sub>-0.20</sub></td><td>11.17<sup>+0.10</sup><sub>-0.10</sub></td><td>5</td></tr><tr><td>NEP - ID 4</td><td>260.73008</td><td>65.72515</td><td>5.74</td><td>5.33</td><td>6.03</td><td>0.45</td><td>0.46</td><td>10.44<sup>+0.11</sup><sub>-0.16</sub></td><td>12.46<sup>+0.50</sup><sub>-0.45</sub></td><td>29</td></tr><tr><td>NEP - ID 5</td><td>260.81414</td><td>65.82672</td><td>6.08</td><td>5.61</td><td>6.34</td><td>0.37</td><td>0.40</td><td>10.68<sup>+0.10</sup><sub>-0.13</sub></td><td>13.92<sup>+0.48</sup><sub>-0.63</sub></td><td>41</td></tr><tr><td>NEP - ID 6</td><td>260.43907</td><td>65.82410</td><td>6.29</td><td>6.06</td><td>6.48</td><td>0.44</td><td>0.34</td><td>9.96<sup>+0.19</sup><sub>-0.18</sub></td><td>11.61<sup>+0.27</sup><sub>-0.16</sub></td><td>12</td></tr><tr><td>NEP - ID 7</td><td>260.95675</td><td>65.82736</td><td>6.41</td><td>6.04</td><td>6.70</td><td>0.46</td><td>0.58</td><td>10.16<sup>+0.15</sup><sub>-0.16</sub></td><td>11.94<sup>+0.51</sup><sub>-0.27</sub></td><td>37</td></tr><tr><td>NEP - ID 8</td><td>260.68717</td><td>65.81155</td><td>6.69</td><td>6.47</td><td>6.85</td><td>0.19</td><td>0.33</td><td>10.07<sup>+0.15</sup><sub>-0.14</sub></td><td>11.83<sup>+0.46</sup><sub>-0.23</sub></td><td>13</td></tr><tr><td>NEP - ID 9</td><td>260.65784</td><td>65.83154</td><td>6.75</td><td>6.65</td><td>6.87</td><td>0.20</td><td>0.26</td><td>9.59<sup>+0.18</sup><sub>-0.17</sub></td><td>11.29<sup>+0.14</sup><sub>-0.11</sub></td><td>5</td></tr><tr><td>NEP - ID 10</td><td>260.77117</td><td>65.83474</td><td>6.90</td><td>6.75</td><td>7.02</td><td>0.32</td><td>0.31</td><td>9.98<sup>+0.24</sup><sub>-0.28</sub></td><td>11.70<sup>+0.78</sup><sub>-0.34</sub></td><td>20</td></tr><tr><td>JADES - ID 1</td><td>53.12985</td><td>-27.78021</td><td>5.68</td><td>5.25</td><td>6.23</td><td>0.59</td><td>0.41</td><td>10.62<sup>+0.07</sup><sub>-0.07</sub></td><td>13.28<sup>+0.37</sup><sub>-0.34</sub></td><td>66</td></tr><tr><td>JADES - ID 2</td><td>53.17325</td><td>-27.75462</td><td>5.84</td><td>5.69</td><td>5.99</td><td>0.21</td><td>0.11</td><td>9.21<sup>+0.13</sup><sub>-0.20</sub></td><td>11.16<sup>+0.07</sup><sub>-0.10</sub></td><td>4</td></tr><tr><td>JADES - ID 3</td><td>53.11175</td><td>-27.80421</td><td>6.02</td><td>5.89</td><td>6.16</td><td>0.39</td><td>0.15</td><td>9.36<sup>+0.13</sup><sub>-0.14</sub></td><td>11.22<sup>+0.07</sup><sub>-0.08</sub></td><td>12</td></tr><tr><td>JADES - ID 4</td><td>53.19043</td><td>-27.77381</td><td>6.02</td><td>5.86</td><td>6.20</td><td>0.26</td><td>0.13</td><td>9.51<sup>+0.14</sup><sub>-0.15</sub></td><td>11.30<sup>+0.09</sup><sub>-0.09</sub></td><td>10</td></tr><tr><td>JADES - ID 5</td><td>53.15517</td><td>-27.74182</td><td>6.17</td><td>5.99</td><td>6.38</td><td>0.31</td><td>0.22</td><td>9.94<sup>+0.09</sup><sub>-0.09</sub></td><td>11.60<sup>+0.10</sup><sub>-0.08</sub></td><td>19</td></tr><tr><td>JADES - ID 6</td><td>53.16421</td><td>-27.77302</td><td>6.34</td><td>6.11</td><td>6.50</td><td>0.26</td><td>0.17</td><td>9.53<sup>+0.16</sup><sub>-0.15</sub></td><td>11.29<sup>+0.10</sup><sub>-0.09</sub></td><td>13</td></tr></tbody></table>

<table><caption>**Table A2.** The example catalogue of the group membership found in CEERS using DETECTIFz. The redshift, stellar mass and SFR are from Bagpipes. $M_{UV}$ and UV slope $\beta$ are calculated in Section 4.4. $P_{mem}$ is the group membership probability for each individual galaxies in a group. The full catalogue can be accessed in the online version. The complete catalogue is available in the online version.</caption><thead><tr><th>Group ID</th><th>Galaxy ID</th><th>RA J2000</th><th>Dec J2000</th><th>z<sub>photo</sub></th><th>log M<sub>*</sub><sup>gal</sup><br>M<sub>☉</sub></th><th>SFR<sub>UV</sub><br>M<sub>☉</sub>/yr</th><th>M<sub>UV</sub><br>mag</th><th>β</th><th>P<sub>mem</sub></th></tr></thead><tbody><tr><td>CEERS - ID 1</td><td>5699</td><td>214.95790</td><td>52.85781</td><td>5.47<sup>+0.08</sup><sub>-0.26</sub></td><td>8.33<sup>+0.25</sup><sub>-0.18</sub></td><td>2.82<sup>+0.53</sup><sub>-0.39</sub></td><td>-19.35<sup>+0.20</sup><sub>-0.18</sub></td><td>-2.72<sup>+0.52</sup><sub>-0.54</sub></td><td>0.99</td></tr><tr><td>CEERS - ID 1</td><td>5938</td><td>214.94327</td><td>52.84919</td><td>5.48<sup>+0.08</sup><sub>-0.27</sub></td><td>8.57<sup>+0.18</sup><sub>-0.13</sub></td><td>7.02<sup>+8.81</sup><sub>-2.47</sub></td><td>-19.71<sup>+0.20</sup><sub>-0.19</sub></td><td>-1.88<sup>+0.54</sup><sub>-0.54</sub></td><td>0.86</td></tr><tr><td>CEERS - ID 1</td><td>8811</td><td>214.98093</td><td>52.88148</td><td>5.54<sup>+0.14</sup><sub>-0.51</sub></td><td>8.89<sup>+0.13</sup><sub>-0.18</sub></td><td>3.87<sup>+0.83</sup><sub>-0.57</sub></td><td>-19.68<sup>+0.21</sup><sub>-0.20</sub></td><td>-2.81<sup>+0.66</sup><sub>-0.70</sub></td><td>0.82</td></tr><tr><td>CEERS - ID 1</td><td>7240</td><td>214.93700</td><td>52.91066</td><td>5.35<sup>+0.09</sup><sub>-0.28</sub></td><td>9.34<sup>+0.06</sup><sub>-0.06</sub></td><td>3.48<sup>+1.83</sup><sub>-0.51</sub></td><td>-19.43<sup>+0.21</sup><sub>-0.20</sub></td><td>-2.58<sup>+0.54</sup><sub>-0.53</sub></td><td>0.73</td></tr><tr><td>CEERS - ID 1</td><td>6018</td><td>214.94368</td><td>52.85008</td><td>5.52<sup>+0.09</sup><sub>-0.15</sub></td><td>9.31<sup>+0.14</sup><sub>-0.18</sub></td><td>24.58<sup>+30.74</sup><sub>-13.98</sub></td><td>-20.26<sup>+0.20</sup><sub>-0.18</sub></td><td>-1.72<sup>+0.53</sup><sub>-0.54</sub></td><td>0.71</td></tr><tr><td>CEERS - ID 1</td><td>7653</td><td>214.96547</td><td>52.87933</td><td>5.47<sup>+0.22</sup><sub>-0.14</sub></td><td>9.44<sup>+0.07</sup><sub>-0.14</sub></td><td>5.18<sup>+1.95</sup><sub>-0.70</sub></td><td>-19.90<sup>+0.20</sup><sub>-0.19</sub></td><td>-2.28<sup>+0.54</sup><sub>-0.53</sub></td><td>0.71</td></tr><tr><td>CEERS - ID 1</td><td>8812</td><td>214.98087</td><td>52.88110</td><td>5.59<sup>+0.13</sup><sub>-0.08</sub></td><td>9.46<sup>+0.11</sup><sub>-0.13</sub></td><td>12.49<sup>+2.42</sup><sub>-1.65</sub></td><td>-20.94<sup>+0.19</sup><sub>-0.18</sub></td><td>-2.77<sup>+0.54</sup><sub>-0.54</sub></td><td>0.70</td></tr><tr><td>CEERS - ID 1</td><td>8505</td><td>214.95318</td><td>52.91579</td><td>5.40<sup>+0.21</sup><sub>-0.25</sub></td><td>8.81<sup>+0.08</sup><sub>-0.09</sub></td><td>4.36<sup>+0.91</sup><sub>-0.77</sub></td><td>-19.85<sup>+0.21</sup><sub>-0.21</sub></td><td>-3.90<sup>+0.60</sup><sub>-0.63</sub></td><td>0.70</td></tr><tr><td>CEERS - ID 1</td><td>5719</td><td>214.88850</td><td>52.90485</td><td>5.62<sup>+0.08</sup><sub>-0.25</sub></td><td>7.87<sup>+0.13</sup><sub>-0.20</sub></td><td>4.36<sup>+1.06</sup><sub>-0.54</sub></td><td>-19.76<sup>+0.19</sup><sub>-0.17</sub></td><td>-2.42<sup>+0.52</sup><sub>-0.53</sub></td><td>0.69</td></tr></tbody></table>
<table><caption>Table A2 – continued</caption><thead><tr><th>Group ID</th><th>Galaxy ID</th><th>RA<br>J2000</th><th>Dec<br>J2000</th><th>z<sub>photo</sub></th><th>log M<sub>☉</sub><sup>gal</sup><br>M<sub>☉</sub></th><th>SFR<sub>UV</sub><br>M<sub>☉</sub>/yr</th><th>M<sub>UV</sub><br>mag</th><th>β</th><th>P<sub>mem</sub></th></tr></thead><tbody><tr><td>CEERS – ID 1</td><td>8933</td><td>214.94735</td><td>52.91899</td><td>5.46<sup>+0.22</sup><sub>-0.11</sub></td><td>8.41<sup>+0.17</sup><sub>-0.26</sub></td><td>3.63<sup>+0.69</sup><sub>-0.62</sub></td><td>-19.65<sup>+0.20</sup><sub>-0.19</sub></td><td>-3.49<sup>+0.54</sup><sub>-0.53</sub></td><td>0.68</td></tr><tr><td>CEERS – ID 1</td><td>6255</td><td>214.94998</td><td>52.85578</td><td>5.48<sup>+0.12</sup><sub>-0.21</sub></td><td>8.96<sup>+0.25</sup><sub>-0.26</sub></td><td>4.36<sup>+1.50</sup><sub>-0.60</sub></td><td>-19.72<sup>+0.20</sup><sub>-0.19</sub></td><td>-2.37<sup>+0.54</sup><sub>-0.53</sub></td><td>0.66</td></tr><tr><td>CEERS – ID 1</td><td>5844</td><td>214.94942</td><td>52.90788</td><td>5.32<sup>+0.14</sup><sub>-0.41</sub></td><td>9.47<sup>+0.18</sup><sub>-0.16</sub></td><td>18.18<sup>+3.62</sup><sub>-2.92</sub></td><td>-21.39<sup>+0.21</sup><sub>-0.20</sub></td><td>-3.09<sup>+0.55</sup><sub>-0.53</sub></td><td>0.65</td></tr><tr><td>CEERS – ID 1</td><td>8984</td><td>214.98532</td><td>52.95874</td><td>4.94<sup>+0.47</sup><sub>-0.03</sub></td><td>7.64<sup>+0.28</sup><sub>-0.19</sub></td><td>2.46<sup>+0.64</sup><sub>-0.45</sub></td><td>-19.20<sup>+0.26</sup><sub>-0.25</sub></td><td>-3.02<sup>+0.60</sup><sub>-0.62</sub></td><td>0.64</td></tr><tr><td>CEERS – ID 2</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>NEP – ID 1</td><td>1716</td><td>260.69784</td><td>65.78069</td><td>5.46<sup>+0.44</sup><sub>-0.11</sub></td><td>9.84<sup>+0.18</sup><sub>-0.22</sub></td><td>34.71<sup>+51.00</sup><sub>-19.15</sub></td><td>-20.12<sup>+0.21</sup><sub>-0.17</sub></td><td>-1.34<sup>+0.58</sup><sub>-0.51</sub></td><td>0.52</td></tr><tr><td>NEP – ID 1</td><td>8048</td><td>260.72580</td><td>65.77226</td><td>5.44<sup>+0.46</sup><sub>-0.31</sub></td><td>8.10<sup>+0.17</sup><sub>-0.19</sub></td><td>13.24<sup>+26.43</sup><sub>-9.12</sub></td><td>-18.02<sup>+0.28</sup><sub>-0.27</sub></td><td>-0.90<sup>+0.73</sup><sub>-0.76</sub></td><td>0.50</td></tr><tr><td>NEP – ID 1</td><td>1912</td><td>260.68502</td><td>65.76349</td><td>5.63<sup>+0.25</sup><sub>-0.18</sub></td><td>9.42<sup>+0.10</sup><sub>-0.25</sub></td><td>9.41<sup>+12.38</sup><sub>-3.17</sub></td><td>-20.08<sup>+0.19</sup><sub>-0.16</sub></td><td>-1.97<sup>+0.54</sup><sub>-0.52</sub></td><td>0.46</td></tr><tr><td>NEP – ID 1</td><td>7527</td><td>260.71876</td><td>65.76629</td><td>5.50<sup>+0.41</sup><sub>-0.23</sub></td><td>8.77<sup>+0.18</sup><sub>-0.31</sub></td><td>3.32<sup>+2.27</sup><sub>-0.45</sub></td><td>-19.37<sup>+0.19</sup><sub>-0.17</sub></td><td>-2.31<sup>+0.53</sup><sub>-0.54</sub></td><td>0.45</td></tr><tr><td>NEP – ID 1</td><td>1988</td><td>260.68919</td><td>65.76916</td><td>5.20<sup>+0.29</sup><sub>-0.10</sub></td><td>7.71<sup>+0.12</sup><sub>-0.15</sub></td><td>0.96<sup>+0.80</sup><sub>-0.13</sub></td><td>-18.06<sup>+0.11</sup><sub>-0.09</sub></td><td>-2.42<sup>+0.42</sup><sub>-0.42</sub></td><td>0.45</td></tr><tr><td>NEP – ID 1</td><td>9678</td><td>260.73132</td><td>65.76976</td><td>6.29<sup>+0.17</sup><sub>-0.17</sub></td><td>7.12<sup>+0.13</sup><sub>-0.08</sub></td><td>8.38<sup>+13.98</sup><sub>-5.42</sub></td><td>-18.54<sup>+0.18</sup><sub>-0.15</sub></td><td>-1.44<sup>+0.61</sup><sub>-0.63</sub></td><td>0.40</td></tr><tr><td>NEP – ID 1</td><td>5891</td><td>260.72108</td><td>65.77939</td><td>6.31<sup>+0.09</sup><sub>-0.09</sub></td><td>8.17<sup>+0.07</sup><sub>-0.08</sub></td><td>6.80<sup>+2.56</sup><sub>-0.67</sub></td><td>-20.25<sup>+0.13</sup><sub>-0.12</sub></td><td>-2.40<sup>+0.56</sup><sub>-0.51</sub></td><td>0.38</td></tr><tr><td>NEP – ID 1</td><td>1969</td><td>260.68427</td><td>65.76288</td><td>5.94<sup>+0.15</sup><sub>-0.17</sub></td><td>7.26<sup>+0.18</sup><sub>-0.14</sub></td><td>1.58<sup>+1.16</sup><sub>-0.21</sub></td><td>-18.60<sup>+0.16</sup><sub>-0.15</sub></td><td>-2.37<sup>+0.59</sup><sub>-0.62</sub></td><td>0.35</td></tr><tr><td>NEP – ID 1</td><td>2249</td><td>260.69600</td><td>65.77503</td><td>5.47<sup>+0.29</sup><sub>-0.10</sub></td><td>8.51<sup>+0.26</sup><sub>-0.23</sub></td><td>3.66<sup>+1.04</sup><sub>-0.46</sub></td><td>-19.55<sup>+0.21</sup><sub>-0.18</sub></td><td>-2.44<sup>+0.53</sup><sub>-0.55</sub></td><td>0.29</td></tr><tr><td>NEP – ID 1</td><td>3021</td><td>260.71007</td><td>65.78709</td><td>6.38<sup>+0.10</sup><sub>-0.10</sub></td><td>7.66<sup>+0.10</sup><sub>-0.06</sub></td><td>5.66<sup>+5.16</sup><sub>-0.68</sub></td><td>-19.98<sup>+0.13</sup><sub>-0.11</sub></td><td>-2.09<sup>+0.50</sup><sub>-0.52</sub></td><td>0.25</td></tr><tr><td>NEP – ID 1</td><td>9512</td><td>260.74154</td><td>65.78315</td><td>5.50<sup>+0.34</sup><sub>-0.09</sub></td><td>8.51<sup>+0.22</sup><sub>-0.20</sub></td><td>5.88<sup>+6.94</sup><sub>-1.23</sub></td><td>-19.80<sup>+0.19</sup><sub>-0.18</sub></td><td>-2.16<sup>+0.51</sup><sub>-0.53</sub></td><td>0.24</td></tr><tr><td>NEP – ID 1</td><td>8426</td><td>260.73253</td><td>65.77678</td><td>6.37<sup>+0.10</sup><sub>-0.18</sub></td><td>9.74<sup>+0.22</sup><sub>-0.19</sub></td><td>85.83<sup>+122.07</sup><sub>-51.79</sub></td><td>-20.28<sup>+0.15</sup><sub>-0.11</sub></td><td>-1.02<sup>+0.53</sup><sub>-0.55</sub></td><td>0.24</td></tr><tr><td>JADES – ID 1</td><td>17226</td><td>53.15477</td><td>-27.80651</td><td>6.21<sup>+0.08</sup><sub>-0.30</sub></td><td>10.54<sup>+0.05</sup><sub>-0.05</sub></td><td>30.93<sup>+37.83</sup><sub>-17.82</sub></td><td>-18.57<sup>+0.14</sup><sub>-0.12</sub></td><td>-0.38<sup>+0.50</sup><sub>-0.52</sub></td><td>0.82</td></tr><tr><td>JADES – ID 1</td><td>35742</td><td>53.13047</td><td>-27.77824</td><td>5.75<sup>+0.17</sup><sub>-0.16</sub></td><td>8.92<sup>+0.10</sup><sub>-0.10</sub></td><td>2.32<sup>+1.49</sup><sub>-0.27</sub></td><td>-19.03<sup>+0.18</sup><sub>-0.14</sub></td><td>-2.27<sup>+0.52</sup><sub>-0.52</sub></td><td>0.80</td></tr><tr><td>JADES – ID 1</td><td>24313</td><td>53.14078</td><td>-27.80217</td><td>5.95<sup>+0.05</sup><sub>-0.05</sub></td><td>8.23<sup>+0.19</sup><sub>-0.16</sub></td><td>3.49<sup>+0.47</sup><sub>-0.40</sub></td><td>-19.58<sup>+0.16</sup><sub>-0.14</sub></td><td>-2.63<sup>+0.54</sup><sub>-0.54</sub></td><td>0.77</td></tr><tr><td>JADES – ID 1</td><td>23748</td><td>53.14398</td><td>-27.79874</td><td>5.83<sup>+0.11</sup><sub>-0.13</sub></td><td>8.47<sup>+0.13</sup><sub>-0.14</sub></td><td>3.17<sup>+3.24</sup><sub>-0.47</sub></td><td>-19.29<sup>+0.17</sup><sub>-0.15</sub></td><td>-2.22<sup>+0.56</sup><sub>-0.54</sub></td><td>0.72</td></tr><tr><td>JADES – ID 1</td><td>18093</td><td>53.15205</td><td>-27.80828</td><td>5.75<sup>+0.14</sup><sub>-0.15</sub></td><td>8.37<sup>+0.12</sup><sub>-0.20</sub></td><td>1.37<sup>+0.32</sup><sub>-0.16</sub></td><td>-18.51<sup>+0.18</sup><sub>-0.16</sub></td><td>-2.56<sup>+0.56</sup><sub>-0.53</sub></td><td>0.71</td></tr><tr><td>JADES – ID 1</td><td>37202</td><td>53.12705</td><td>-27.78887</td><td>5.48<sup>+0.02</sup><sub>-0.03</sub></td><td>6.93<sup>+0.14</sup><sub>-0.11</sub></td><td>0.77<sup>+0.64</sup><sub>-0.12</sub></td><td>-17.75<sup>+0.19</sup><sub>-0.18</sub></td><td>-2.48<sup>+0.56</sup><sub>-0.54</sub></td><td>0.70</td></tr><tr><td>JADES – ID 1</td><td>24376</td><td>53.14189</td><td>-27.80025</td><td>5.94<sup>+0.13</sup><sub>-0.24</sub></td><td>8.63<sup>+0.11</sup><sub>-0.12</sub></td><td>4.93<sup>+6.52</sup><sub>-2.91</sub></td><td>-17.36<sup>+0.17</sup><sub>-0.15</sub></td><td>-1.08<sup>+0.55</sup><sub>-0.55</sub></td><td>0.70</td></tr><tr><td>JADES – ID 1</td><td>35460</td><td>53.12954</td><td>-27.77736</td><td>5.99<sup>+0.13</sup><sub>-0.12</sub></td><td>7.77<sup>+0.07</sup><sub>-0.05</sub></td><td>10.12<sup>+3.51</sup><sub>-1.10</sub></td><td>-20.68<sup>+0.17</sup><sub>-0.13</sub></td><td>-2.44<sup>+0.54</sup><sub>-0.53</sub></td><td>0.67</td></tr><tr><td>JADES – ID 1</td><td>27143</td><td>53.13600</td><td>-27.79848</td><td>5.94<sup>+0.04</sup><sub>-0.05</sub></td><td>7.76<sup>+0.08</sup><sub>-0.08</sub></td><td>3.01<sup>+3.53</sup><sub>-0.53</sub></td><td>-19.16<sup>+0.16</sup><sub>-0.15</sub></td><td>-2.20<sup>+0.51</sup><sub>-0.53</sub></td><td>0.65</td></tr><tr><td>JADES – ID 1</td><td>36154</td><td>53.12488</td><td>-27.78412</td><td>5.70<sup>+0.20</sup><sub>-0.05</sub></td><td>8.23<sup>+0.15</sup><sub>-0.16</sub></td><td>2.14<sup>+0.37</sup><sub>-0.28</sub></td><td>-19.05<sup>+0.18</sup><sub>-0.16</sub></td><td>-2.83<sup>+0.50</sup><sub>-0.52</sub></td><td>0.60</td></tr><tr><td>JADES – ID 1</td><td>30094</td><td>53.12870</td><td>-27.79826</td><td>5.48<sup>+0.03</sup><sub>-0.03</sub></td><td>7.26<sup>+0.23</sup><sub>-0.23</sub></td><td>0.78<sup>+0.12</sup><sub>-0.12</sub></td><td>-17.98<sup>+0.18</sup><sub>-0.16</sub></td><td>-3.22<sup>+0.52</sup><sub>-0.50</sub></td><td>0.59</td></tr><tr><td>JADES – ID 1</td><td>17532</td><td>53.15530</td><td>-27.80555</td><td>5.83<sup>+0.12</sup><sub>-0.07</sub></td><td>7.11<sup>+0.11</sup><sub>-0.13</sub></td><td>0.72<sup>+0.98</sup><sub>-0.17</sub></td><td>-17.49<sup>+0.16</sup><sub>-0.16</sub></td><td>-2.13<sup>+0.53</sup><sub>-0.51</sub></td><td>0.59</td></tr><tr><td>JADES – ID 1</td><td>37094</td><td>53.13005</td><td>-27.77839</td><td>5.60<sup>+0.26</sup><sub>-0.02</sub></td><td>8.22<sup>+0.15</sup><sub>-0.20</sub></td><td>3.94<sup>+0.67</sup><sub>-0.52</sub></td><td>-19.69<sup>+0.18</sup><sub>-0.17</sub></td><td>-2.60<sup>+0.53</sup><sub>-0.48</sub></td><td>0.57</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

This paper has been typeset from a *TEX/LATEX* file prepared by the author.