The Structural Anatomy of Galaxies: Environmental Dependence of Morphological and Quenching Evolution at 0.1 < z < 0.5

Email: [email protected],[email protected]

Introduction

Understanding how environment regulates galaxy evolution is a central problem in extragalactic astronomy. Galaxies are embedded within the large-scale cosmic web, a network of clusters, filaments, and voids [25], and their star-formation activity, stellar populations, and morphology depend systematically on the surrounding environment [59, 21]. Quantifying these environmental dependencies is therefore essential for disentangling the interplay between internal secular evolution and externally driven processes.

The galaxy population exhibits a well-known bimodality, separating into a “red sequence” dominated by quiescent, bulge-dominated galaxies (QGs) and a “blue cloud” populated primarily by star-forming, disk-dominated galaxies (SFGs) [148, 10]. This dichotomy is closely linked to quenching processes that suppress star formation and move galaxies away from the star-forming sequence. Environmental mechanisms are widely regarded as important contributors to this transformation, particularly in high-density regions [127, 162] (R. F. J. van der Burg et al. 2018).

Galaxy clusters, which occupy the densest nodes of the cosmic web, provide powerful laboratories for studying environmental influences on galaxy evolution. A variety of physical processes operate within clusters, including ram-pressure stripping by the hot intracluster medium (ICM; [69] (A. Boselli & G. Gavazzi 2006)), high-velocity gravitational encounters commonly referred to as harassment [110], and tidal interactions with other galaxies and the cluster potential [108]. These mechanisms can remove or redistribute gas, suppress star formation, and alter galaxy structure and morphology (e.g., [28]). Their efficiency depends on galaxy properties and orbital history, including stellar mass, infall time, and trajectory through the host halo, naturally producing a diversity of evolutionary responses within cluster populations [80, 120].

Because environmental processes can affect star formation, stellar populations, and galaxy structure on different timescales, their signatures need not emerge simultaneously or with equal strength across different observables. A joint analysis of multiple galaxy properties and scaling relations therefore provides a powerful framework for characterizing environmental effects and for distinguishing changes in star-formation activity from structural transformation. The stellar mass–size ($M_\star$–$R_{\rm e}$) relation is a particularly important diagnostic of galaxy structural evolution. Star-forming galaxies and quiescent galaxies occupy distinct mass–size sequences, both of which evolve with redshift, with especially strong evolution among massive systems. At $z \gtrsim1$–2, massive galaxies are substantially more compact than their present-day counterparts [143, 49, 156, 95] (A. van der Wel et al. 2014).

However, whether environment systematically alters the stellar mass–size relation remains unsettled. Some studies find little or no residual size dependence after controlling for stellar mass, morphology, or star-formation state [78, 87, 93], whereas others report significant environmental size differences [129, 131, 51, 64] (T. Valentinuzzi et al. 2010). The sign and strength of these differences are not uniform across the literature. At higher redshift, some studies of massive galaxies report larger sizes in dense environments, potentially associated with accelerated merger-driven evolution [123, 96], while other studies find smaller galaxies or weaker environmental differences. These apparently conflicting results span different redshifts, stellar-mass ranges, population selections, membership criteria, environmental definitions, and structural measurements, making direct comparison difficult.

Environmental structural effects may also depend strongly on stellar mass. Several studies suggest that the magnitude of cluster–field structural differences varies across the stellar-mass distribution [38, 152], indicating that a single population-averaged mass–size relation may obscure differential environmental responses. More generally, galaxy size alone provides only one projection of structural evolution and cannot determine whether an observed environmental difference is accompanied by changes in star formation, central light concentration, or stellar populations. A more complete picture therefore requires complementary observables that trace these different aspects of galaxy evolution.

Furthermore, the bulge-to-total light ratio ($B/T$) provides a measure of the relative prominence of bulge and disk components and is closely connected to galaxy morphology and star-formation state [59, 161, 22]. Emission-line SFRs provide a comparatively direct tracer of ongoing star formation, while the 4000 Å break strength ($D_{\rm n}4000$) is sensitive to recent star-formation history and stellar-population properties [84, 114]. Jointly examining $R_{\rm e}$, $B/T$, SFR, and $D_{\rm n}4000$ therefore enables environmental differences in star formation, stellar populations, and structure to be characterized within a common framework and across different stellar-mass regimes.

The combination of recent wide-area surveys makes such a joint analysis possible. The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) provides deep optical imaging suitable for structural measurements, while the Dark Energy Spectroscopic Instrument (DESI) survey supplies precise spectroscopic redshifts together with emission-line and stellar-population diagnostics ([53]). The eROSITA X-ray survey identifies galaxy clusters through extended emission from their hot intracluster gas, providing a complementary and physically motivated selection of dense environments [35, 91, 98]. Their overlapping coverage therefore enables structural and spectroscopic environmental trends to be studied for spectroscopically confirmed galaxies associated with X-ray-selected clusters.

In this work, we combine HSC-SSP PDR3 imaging, DESI DR1 spectroscopy, and eROSITA X-ray cluster catalogs to investigate environmental galaxy evolution at $0.1 \le z \le0.5$. Using spectroscopically confirmed cluster satellites and a field control sample matched in stellar mass and redshift, we compare SFR, $R_{\mathrm{e}}$, $B/T$, and $D_{n4000}$ as functions of stellar mass, projected cluster-centric radius, and galaxy population. In addition to UVJ star-forming and quiescent galaxies, we isolate an H$\alpha$-low UVJ-star-forming transition population to examine where environmental effects are most strongly expressed. We further quantify the joint environmental displacement using a multivariate framework based on matched cluster–field residuals, allowing us to assess whether star-formation and structural responses show the same dependence on stellar mass and projected cluster-centric radius.

This paper is organized as follows. § 2 describes the datasets and sample construction, and § 3 presents the measurements of galaxy properties and the validation of the structural analysis. § 4 presents the environmental trends, which are interpreted in § 5. Our main conclusions are summarized in § 6. Throughout this work, we adopt a flat $\Lambda$CDM cosmology with $\Omega_{\mathrm{m}} = 0.3$, $\Omega_{\Lambda} = 0.7$, and $h = 0.67$. Stellar masses and SFRs are derived assuming a Chabrier (2003) initial mass function.

Data

Photometry: HSC-SSP Public Data Release 3

Our primary source of optical photometry and morphological measurements is the third Public Data Release (PDR3) of the HSC-SSP survey [2]. The HSC-SSP utilizes the wide-field prime-focus camera ($1.77\ \mathrm{deg}^{2}$; [109]) on the 8.2 m Subaru Telescope to conduct a deep, multi-band imaging survey in five broad bands ($g$, $r$, $i$, $z$, $Y$; [85]). We adopt data from the Wide field of PDR3. The PDR3 imaging achieves excellent median seeing conditions ($\sim0.6''$–$0.8''$ FWHM in the $i$-band; [2]) and reaches nominal $5\sigma$ point-source depths of $i \sim26.2$ mag. This unique combination of depth and image quality enables precise structural measurements—such as effective radii ($R_{\mathrm{e}}$) and bulge–disk decompositions (yielding B/T ratios)—particularly for bright galaxies ($i < 21$ mag). All imaging data are processed with the dedicated hscPipe reduction pipeline [27], which performs astrometric and photometric calibration tied to the Pan-STARRS1 system [139, 155].

Following procedures similar to those in [86], we construct our parent sample from HSC-PDR3 by requiring galaxies to have $i_{\mathrm{cmodel}} < 23$ mag. This ensures sufficiently high signal-to-noise ratios for reliable morphological analyses and is well matched to the typical magnitude limit of the DESI spectroscopic sample used in this work. We further restrict our selection to primary detections (detect_is_primary=True) located in regions covered by all five grizy filters (verified via the corresponding countinputs flags). To avoid sources with problematic measurements, we exclude objects flagged for saturation (flags_pixel_saturated_any), proximity to bright stars (flags_pixel_bright_object_center), image edges (flags_pixel_edge), or poor deblending (cmodel_flux_flags). These criteria yield a high-quality photometric sample suitable for robust structural and cross-survey analyses.

Spectroscopy: DESI Data Release 1

Spectroscopic redshifts, essential for determining cluster membership and deriving physical parameters such as $D_{n4000}$ and star-formation rates (SFRs), are obtained from the first Data Release (DR1) of the DESI survey [55]. DESI employs a robotic multi-fiber positioner at the prime focus of the Mayall 4-m telescope at Kitt Peak National Observatory, capable of simultaneously observing 5000 targets over an 8 deg$^{2}$ field of view [52, 144]. The fibers feed ten three-arm spectrographs covering 3600–9800 Å, with a spectral resolution of $R = \lambda/\Delta\lambda\sim2000$–5200 [52, 70].

DESI DR1 comprises data from the Survey Validation (SV) phases [54, 71] and the first 13 months of the main survey (May 2021–June 2022), providing reliable redshifts for over 18 million unique objects [55]. We primarily use redshifts and spectral measurements from the Bright Galaxy Survey (BGS) component [72], specifically the BGS_BRIGHT sample ($r < 19.5$) and the BGS_FAINT sample ($19.5 < r < 20.175$), which overlaps significantly with our HSC photometric sample at $z \lesssim0.5$.

We cross-match the HSC PDR3 catalog with the DESI DR1 “Iron” spectroscopic production. Following the DESI DR1 definition of unique objects with confident redshifts, we adopt catalog entries with ZCAT_PRIMARY=True and ZWARN=0 [55]. The former identifies the recommended best redshift determination for each target, while the latter indicates that no known issues are flagged in the spectroscopic data or the redshift fit.

Notes. Galaxies are divided into high-mass and low-mass populations using a stellar mass threshold of $\log_{10}(M_{\ast}/M_{\odot}) = 10.5$. High-mass galaxies satisfy $\log_{10}(M_{\ast}/M_{\odot}) > 10.5$, while low-mass galaxies have $\log_{10}(M_{\ast}/M_{\odot}) \le10.5$. For cluster galaxies, regions are defined by the projected cluster-centric radius in units of $R_{500}$.

Cluster Catalogs: eROSITA eFEDS and eRASS1

We identify cluster environments using X-ray-selected galaxy clusters detected by eROSITA aboard the Spectrum-Roentgen-Gamma (SRG) mission ([151] (P. Predehl et al. 2021)). Our cluster sample combines systems from the eROSITA Final Equatorial-Depth Survey (eFEDS; [32, 98]) and the first eROSITA All-Sky Survey (eRASS1; [35, 91]). The deeper eFEDS observations cover $\sim140\ \mathrm{deg}^{2}$ overlapping the HSC Wide footprint and yielded 542 X-ray-selected cluster candidates with extent likelihood $\mathcal{L}_{\mathrm{ext}} > 6$ and detection likelihood $\mathcal{L}_{\mathrm{det}} > 5$ in the $0.2$–$2.3$ keV band. The deep X-ray coverage and overlap with HSC make eFEDS ideal for detailed studies (e.g., [89, 42, 86, 8, 9]). To increase the sample size and sky coverage, we supplement eFEDS with the eRASS1 primary catalog, comprising 12,247 optically identified clusters and groups over $\sim13,100\ \mathrm{deg}^{2}$. The eRASS1 catalog adopts a lower extent likelihood threshold ($\mathcal{L}_{\mathrm{ext}} > 3$), allowing the inclusion of lower-significance X-ray sources and expanding the discovery space toward low-mass groups and higher-redshift clusters ([35]). We additionally require a contamination probability of $P_{\mathrm{cont}} < 0.1$ to reduce the contribution from spurious or incorrectly associated systems. Optical identification and redshift estimates are obtained using the eROMAPPER algorithm applied to the DESI Legacy Imaging Surveys ([56, 91]).

We restrict the combined catalog to $0.1 \le z \le0.5$ and $10^{14} \le M_{500}/M_{\odot} \le10^{15}$. To ensure that each system can be used for our galaxy analysis, we further require overlap with the HSC-SSP PDR3 and DESI DR1 galaxy catalogs and at least two DESI spectroscopic members within $R_{500}$. After these selections, our final sample contains 348 clusters.

Figure 1 summarizes the cluster selection. The left panel shows the parent eROSITA systems in the $M_{500}$–redshift plane, with the final sample highlighted after applying the redshift and halo-mass cuts together with the HSC–DESI coverage and spectroscopic-member requirements. The right panel shows the sky distribution of the selected clusters, color-coded by redshift. The higher surface density of selected clusters in the eFEDS region mainly reflects its deeper X-ray coverage relative to the surrounding eRASS1 survey area.

We adopt the catalog $M_{500}$ measurements, which are based on eROSITA X-ray observables and calibrated using weak-lensing measurements [42, 68, 90, 118]. The corresponding $R_{500}$, enclosing a mean overdensity 500 times the critical density of the Universe at $z_{\mathrm{cl}}$, is calculated from

where $\rho_{\mathrm{c}}(z)$ is the critical density of the Universe at the cluster redshift.

Methodology and Sample Selection

In this section, firstly we describe the criteria for establishing spectroscopic cluster membership and the construction of the field control sample. And we describe the methodology used to derive galaxy physical properties and define our representative samples of cluster and field galaxies, building upon the multi-wavelength datasets introduced in § 2. We first outline the derivation of rest-frame colors and the subsequent classification of galaxies into quiescent and star-forming populations. This is followed by a description of the estimation of stellar masses and star formation rates (SFRs). We then detail the measurement of structural parameters, including a dedicated suite of image simulations designed to assess the reliability and systematic uncertainties of our bulge-to-total ($B/T$) decompositions.

Sample Selection and Environmental Classification

Our final parent galaxy sample comprises all objects satisfying the HSC photometric quality criteria (§ 2.1) and possessing secure DESI spectroscopic redshifts (§ 2.2) within the redshift range $0.1 < z < 0.5$. This range ensures substantial overlap with the DESI BGS sample and the redshift distribution of eROSITA-detected clusters (see Figure 1), while providing a sufficiently large cosmological volume and lookback time baseline. Additionally, all galaxies in the final sample are required to have valid measurements for the key physical properties used in our analysis, as described in the preceding subsections.

We classify galaxies into cluster and field according to their large-scale environment using the eROSITA cluster catalogs (§ 2.3). A galaxy is considered a cluster member if it lies within twice the projected virial radius ($2R_{500}$) of an eROSITA-detected cluster and has a line-of-sight velocity relative to the cluster systemic redshift, $z_{\mathrm{cl}}$, consistent with gravitational association to the cluster halo. Specifically, following established practice [134 R. Capasso] et al. 2019), we define cluster members as galaxies satisfying both

We divide members into $R_{\mathrm{proj}} < 0.5R_{500}$, $0.5 \le R_{\mathrm{proj}}/R_{500} < 1$, and $1 \le R_{\mathrm{proj}}/R_{500} < 2$. Brightest cluster galaxies are excluded, so the cluster sample analyzed below is dominated by satellites. The fixed $\pm2000\ \mathrm{km\ s^{-1}}$ window is deliberately inclusive but can admit interlopers, especially at large projected radius; such contamination would generally dilute rather than create a cluster–field difference.

Figure 3 illustrates the X-ray morphology and the projected distribution of selected members for one system. It is an example rather than a membership validation: association is set by the projected-radius and spectroscopic-velocity cuts above. Galaxies out to $2R_{500}$ are retained to probe the core, intermediate region, and outskirts consistently.

Galaxies in the parent sample that do not satisfy the membership criteria for any eROSITA cluster are considered as potential field candidates. To minimize contamination from cluster environments, we exclude all galaxies located within $4R_{500}$ of any eROSITA cluster center within the surveyed area. From the remaining galaxies, we construct a field control sample matched to the cluster sample in stellar mass and redshift, retaining only objects with well-constrained stellar masses. This procedure ensures that the field sample is largely free from cluster contamination and provides a fair comparison sample with similar mass and redshift distributions, without imposing additional selection cuts on other galaxy properties.

The properties of the cluster sample are shown in Figure 2, and the environmental differences are illustrated in the UVJ diagrams presented in Figure 4. The galaxy number counts of the cluster and field samples are listed in Table 1.

Environment	Region	Total	High-mass SF	High-mass GV	High-mass QG	Low-mass SF	Low-mass GV	Low-mass QG
Cluster	$< 0.5\ R_{500}$	877	31	145	455	66	51	129
Cluster	$0.5$–$1\ R_{500}$	1328	114	159	596	167	88	204
Cluster	$1$–$2\ R_{500}$	2425	269	316	1040	414	138	248

Rest-frame Colors and Galaxy Classification

Rest-frame properties are essential for classifying galaxies and comparing their intrinsic characteristics. We derive rest-frame magnitudes in standard filters (e.g., $U$, $V$, and $J$) from the observed HSC $grizy$ photometry using the EAZY code (G. B. Brammer et al. [31]). The code fits spectral templates to the observed fluxes while fixing each redshift to its DESI spectroscopic value. Following R. J. Williams et al. [164], A. Muzzin et al. [115], and L. Kawinwanichakij et al. [86], the rest-frame UVJ diagram first separates quiescent galaxies (QGs) from the UVJ star-forming population, including dust-reddened star-forming systems.

Within the UVJ-star-forming population with reliable H$\alpha$ and H$\beta$ detections, we make a second, operational split at $\mathrm{sSFR}_{\mathrm{H}\alpha} = 10^{-10.5}\ \mathrm{yr^{-1}}$. Objects above this threshold are labeled actively star-forming (SF), while those below it are labeled H$\alpha$-low UVJ-SF galaxies. For brevity we call the latter the “green-valley” (GV) sample throughout this paper. This is our analysis-specific definition, not a claim that every object lies in a conventional optical-color green valley: it identifies UVJ-SF galaxies whose dust-corrected nebular emission is weak relative to their stellar mass. Figure 4 shows the parent UVJ classification.

Stellar Mass and Star Formation Rate Estimation

Stellar masses ($M_\ast$) and star formation rates (SFRs) are estimated through spectral energy distribution (SED) fitting using CIGALE (Code Investigating GALaxy Emission; M. Boquien et al. [26]; G. Yang et al. [169]; G. Yang et al. [170]). The SED-derived SFRs are used only for galaxies classified as quiescent based on the UVJ diagram.

Our fitting incorporates the five HSC optical bands ($grizy$) combined with mid-infrared photometry from the unWISE catalog ($W1$ at $3.4\ \mu\mathrm{m}$ and $W2$ at $4.6\ \mu\mathrm{m}$; E. F. Schlafly et al. [138]), which helps constrain both older stellar populations and dust emission, improving the robustness of $M_\ast$ and SFR estimates, especially for dusty or quiescent systems. Redshifts are fixed to the DESI spectroscopic values.

We adopt a delayed-$\tau$ star formation history,

stellar population synthesis models from G. Bruzual & S. Charlot [33] with a Chabrier initial mass function, and dust attenuation following D. Calzetti et al. [36]. Dust emission is modeled using the templates of D. A. Dale et al. [50], and possible AGN contributions are accounted for using the templates of J. Fritz et al. [62].

For each galaxy, CIGALE outputs the full posterior probability distribution function (PDF) for each parameter. We adopt the median of the PDF as the best estimate for $M_\ast$ and SFR, with uncertainties derived from the 16th and 84th percentiles. While CIGALE provides SFR estimates for all galaxies, only those for the QG sample are used in the subsequent analysis. For SFGs, we instead adopt SFRs derived from the H$\alpha$ emission line, as described in the following section.

Structural Parameter Measurements

Galaxy structural parameters are derived from HSC $i$-band imaging using GALIGHT (Galaxy Light Profile Analysis; X. Ding et al. [57]), a Python package built on lenstronomy (S. Birrer et al. [20]; S. Birrer & A. Amara [19]). The $i$ band offers the best combination of depth and seeing in HSC Wide (H. Aihara et al. [2]) and probes approximately rest-frame 5100–7000 Å over $0.1 < z < 0.5$. For each galaxy we extract a $12^{\prime\prime} \times12^{\prime\prime}$ image cutout and adopt the position-dependent PSF model provided by the HSC-SSP PDR3 data reduction pipeline, which are constructed using PSFEx (E. Bertin [18]) based on nearby stars.

We first perform a single-component Sérsic fit (J. L. Sersic [141]), convolved with the PSF, to obtain the major-axis effective radius ($R_{\mathrm{e}}$), Sérsic index, axis ratio, and position angle. To account for wavelength-dependent variations in galaxy size, we correct the measured $R_{\mathrm{e}}$ to a common rest-frame wavelength of 5000 Å following the description of A. van der Wel et al. (2014). We then fit a two-component model with a de Vaucouleurs-like bulge ($n_{\mathrm{bulge}} \equiv4$) and exponential disk ($n_{\mathrm{disk}} \equiv1$). Fixing the indices stabilizes a large-sample decomposition and makes $B/T$ comparisons uniform, but it does not represent bars, pseudo-bulges, tidal features, or arbitrary Sérsic shapes; accordingly, $B/T$ is treated as a model-dependent light-concentration proxy rather than a unique physical bulge mass fraction. It is computed as

serving as a quantitative morphological measure that correlates well with visual classifications (L. Simard et al. [145]; A. Meert et al. [107]).

Simulated Galaxies

To quantify the robustness of our bulge–disk decomposition, we generate realistic mock galaxy cutouts using GalSim ([133]), designed to mimic the HSC PDR3 $i$-band observations. We create 3000 simulated galaxies with bulge-to-total light ratios uniformly distributed between 0 and 1. For each mock galaxy, the structural parameters of the Sérsic components are drawn from uniform distributions within the ranges listed in Table 2; we allow the Sérsic indices of both the bulge and disk to vary (rather than fixing them), thereby spanning a broad diversity of intrinsic light profiles. The total flux and effective radius ($R_{\mathrm{e}}$) are chosen to match the distributions of HSC galaxies at $z \sim0.3$.

Component Name	Sérsic Index	Half-Light Radius (arcsec)	Flux (ADUs)	Axis Ratio	Position Angle (degrees)
Single-Component Galaxies
	0.8–1.2 − 3.5–5.0	0.1–5.0	900–1.35 × $10^{5}$	0.25–1.0	−90.0 – 90.0
		($m_g \sim18$–23)
Double-Component Galaxies
Disk	0.8–1.2	0.1–5.0	0.0–1.0	0.25–1.0	−90.0 – 90.0
Bulge	3.5–5.0	0.1–3.0	1.0–Disk Comp	0.25–1.0	Disk Comp. ±[0, 15]

To reproduce observational systematics, we convolve each model with a PSF randomly selected from a set of 100 empirical HSC PDR3 Wide-field PSFs. We also add sky noise constructed from 100 sky cutouts drawn from the same data release. After confirming visually that these regions are free of detectable sources, we pool their pixel values to build an empirical noise distribution. We then generate a noise image for each simulation by randomly sampling this distribution into a two-dimensional array with the same dimensions as the mock cutout and add it to the PSF-convolved model.

Each simulated cutout has a size of 178 × 178 pixels, corresponding to approximately 30″ × 30″ for the HSC pixel scale of 0.168″ pixel$^{-1}$. Figure 6 presents an example of a mock galaxy after PSF convolution and sky-noise addition.

Figure 7 compares the input and recovered $B/T$. Recovery is tightest for $i \le21$, which contains most of the spectroscopic sample, and degrades toward fainter magnitudes. These simulations incorporate representative PSFs and blank-sky noise, but they do not explicitly stratify recovery by cluster-centric radius, local surface brightness, crowding, blending with neighbors, or intracluster light. Dust-corrected H$\alpha$ fluxes address attenuation in the emission-line measurement, not these imaging systematics. Excluding BCGs and analyzing primarily satellites reduces the most extreme background and profile-complexity cases, but does not by itself eliminate a radius-dependent structural bias. We therefore interpret $B/T$ and $R_{\mathrm{e}}$ trends jointly with the spectroscopic indicators and avoid treating small structural offsets as definitive in isolation.

Spectroscopic Parameters

Complementary physical parameters related to stellar populations are derived directly from the DESI spectra using the publicly available fastspecfit value-added catalog associated with DESI DR1 ([55, 112]). fastspecfit performs rapid fitting of stellar population synthesis models combined with emission-line templates to the DESI spectra.

From these fits, we utilize measurements of the $D^*_{n4000}$ index, defined as the ratio of the average flux density in the 4000–4100 Å and 3850–3950 Å rest-frame bands [34, 12]. $D^*_{n4000}$ is a robust tracer of the mean stellar age of the population dominating the optical light (G. Kauffmann et al. [84]).

In addition to the SFR derived from SED fitting, we estimate the instantaneous SFR corrected for dust attenuation using the Balmer decrement for galaxies where both Hα and Hβ emission lines are reliably detected. We adopt emission-line fluxes from the fastspecfit catalog. Following standard procedures (D. E. Osterbrock & G. J. Ferland [121]; A. Domínguez et al. [58]), we select galaxies with Hα and Hβ detected at signal-to-noise ratio (SNR) $\geq3$. The observed flux ratio,

is compared to the intrinsic Case B recombination ratio, $R_{\mathrm{int}} = 2.86$, appropriate for typical H ii regions ($T = 10^{4}$ K and $n_{\mathrm{e}} = 100$ cm$^{-3}$; D. E. Osterbrock & G. J. Ferland [121]).

The color excess due to dust attenuation is then

where $k(\lambda)$ is the extinction curve value at the corresponding wavelength. For cases where $R_{\mathrm{obs}} < R_{\mathrm{int}}$—typically due to measurement uncertainties or residual stellar absorption corrections—we set $E(B-V) = 0$.

The intrinsic Hα flux is then

The Hα luminosity is calculated using the spectroscopic redshift and adopted cosmology:

Finally, the dust-corrected star formation rate, SFR(Hα), is computed using the calibration of R. C. Kennicutt [88], converted to a Chabrier IMF following C.-N. Hao et al. [74] and E. J. Murphy et al. [113]:

This spectroscopically derived, dust-corrected SFR traces recent star formation within the DESI fiber. Throughout this work, we use it for the UVJ-SF Balmer-line-detected sample, including both the SF and operational GV subsets.

Results

We present the empirical results in the order in which the samples are defined: the Hα SFR–mass plane, actively star-forming galaxies, the Hα-low UVJ-SF subset, and UVJ-quiescent galaxies. We compare each cluster subsample with a field reference matched in stellar mass and redshift. The word “field” therefore denotes the non-cluster control defined in § 3.1, not an isolated or void population; it may include galaxies in groups, filaments, and other large-scale structures.

We first use the $M_{*}$–SFR plane only within the UVJ-SF, Balmer-line-detected sample. The split at sSFR$_{\mathrm{H}\alpha}$ = $10^{-10.5}\ \mathrm{yr}^{-1}$ separates actively star-forming galaxies from the H$\alpha$-low UVJ-SF subset that we call GV for brevity. UVJ-QGs are classified separately and are not defined by this H$\alpha$ threshold. Consequently, SF, GV, and QG are useful analysis categories, but they should not automatically be read as a unique temporal sequence for individual galaxies.

This classification provides an evolutionary framework for the remainder of the analysis. In the following sections, we first investigate environmental trends in star formation activity through the SFR–$M_\ast$ relation and the transition fraction. We then examine how structural properties, including effective radius ($R_{\mathrm{e}}$) and bulge-to-total ratio ($B/T$), vary among SFGs, GVs, and QGs as a function of environment. By comparing these populations, we aim to identify when structural transformation occurs relative to the suppression of star formation and to constrain the physical mechanisms responsible for environmentally driven galaxy evolution.

SFR–$M_\ast$ Relation and Transition Fraction

Figure 8 presents the H$\alpha$ SFR–$M_\ast$ relation and the fraction below our operational threshold within the UVJ-SF, Balmer-line-detected sample. We emphasize that “GV” here means H$\alpha$-low UVJ-SF; it is a compact label for this paper rather than a conventional color selection or proof that each object is caught in transition.

The left panel of Figure 8 shows that the star-forming main sequence is present in both cluster and field environments over the full stellar mass range probed by our sample. However, subtle environmental differences are evident. At fixed stellar mass, cluster SFGs exhibit systematically lower SFRs than their field counterparts, particularly within the innermost regions ($R_{\mathrm{proj}} < 0.5\,R_{500}$). The suppression is modest, typically below 0.2 dex, but becomes increasingly pronounced toward higher stellar masses. Such behavior is consistent with previous studies reporting environmentally driven reductions in star formation activity prior to complete quenching [127, 162, 114].

The residual trends shown in the lower panel further illustrate this environmental dependence. While galaxies beyond $R_{500}$ display SFRs comparable to those of field galaxies, systems located within the cluster core exhibit significantly reduced SFRs, with the strongest suppression occurring at intermediate and high stellar masses. This radial dependence suggests that environmental processes become increasingly effective toward the cluster center.

The two-dimensional distributions in the $M_\ast$–SFR plane provide additional insight into this trend. In the outer cluster regions ($R_{\mathrm{proj}}/R_{500} \gtrsim1$), the galaxy distribution closely resembles that of the field population and is dominated by low-mass galaxies with relatively high star formation rates. Toward smaller cluster-centric radii, the peak of the distribution shifts toward higher stellar masses and lower SFRs. This evolution indicates that massive galaxies are preferentially found in dense environments and experience stronger suppression of star formation activity. Such behavior is broadly consistent with environmental quenching mechanisms, including ram-pressure stripping, starvation, and the removal of gas reservoirs, which progressively reduce star formation before galaxies become fully quiescent [97, 13, 163].

The right panel quantifies the frequency of the operationally defined H$\alpha$-low subset,

Cluster galaxies show a larger $f_{\mathrm{GV}}$ than the field over much of the sampled mass range, with the clearest enhancement toward small projected radius. This is consistent with an environmental contribution to suppressed recent star formation, although the Balmer-line selection, fiber aperture, and projection effects prevent a direct conversion of $f_{\mathrm{GV}}$ into a quenching timescale. The mass dependence can reflect both mass-related and environmental selection effects [127, 126].

UVJ Star-forming Population: Active and H$\alpha$-low Subsamples

Figures 9–11 use a common three-panel layout. The first panel compares SF and H$\alpha$-low UVJ-SF galaxies within the field control itself; the second isolates the cluster–field difference for active SF galaxies; and the third shows the analogous difference for the H$\alpha$-low subset. This ordering prevents the intrinsic SF–GV contrast in the control sample from being conflated with an environmental residual.

Actively Star-forming Galaxies

Having classified galaxies into star-forming (SFG), green-valley (GV), and quiescent (QG) populations based on their locations in the $M_{*}$–SFR plane and UVJ color space, we first examine the structural and stellar population properties of SFGs.

As the least evolved population in our classification scheme, SFGs provide a baseline for assessing the earliest environmental influences on galaxy evolution. Although these galaxies remain actively star-forming, the results of Section 4.1 indicate that cluster SFGs already exhibit modestly suppressed star formation activity relative to their field counterparts. An important question is therefore whether this suppression is accompanied by measurable changes in galaxy structure or stellar populations.

To address this issue, we investigate the size–mass relation, $B/T$–mass relation, and D$_{\mathrm{n}}4000$-mass relation for SFGs in different environments. These diagnostics probe complementary aspects of galaxy evolution, including structural growth, bulge assembly, and stellar population aging. Comparing cluster and field SFGs allows us to determine whether environmental processes first affect star formation activity alone or whether structural transformation has already begun before galaxies enter the transition phase.

Size–mass relation. —Figure 9 shows the size-mass relation for SFGs in the field and in different cluster-centric radial bins. Field SFGs follow the expected positive correlation between stellar mass and effective radius, consistent with the well-established size–mass relation of star-forming disk galaxies [143] (A. van der Wel et al. 2014). Cluster SFGs broadly follow the same relation, indicating that galaxies that remain actively star-forming have not yet experienced a strong global structural transformation in size.

The residual panel shows that the size offsets of cluster SFGs relative to field SFGs are generally small, typically within $\sim0.1$ dex over most of the stellar mass range. This suggests that the modest SFR suppression, described in Section 4.1, is not accompanied by a comparably strong change in galaxy size. The innermost cluster SFGs show a mild enhancement in $R_{\mathrm{e}}$ at some masses, but this trend is weak compared to the offset between field GV galaxies and field SFGs, shown by the black dashed curve and further discussed below. Therefore, the size evolution associated with the transition from SFGs to GVs is substantially larger than the environmental size offset among SFGs alone.

These results suggest that environmental processes can begin to suppress star formation in SFGs before producing a strong change in their global size. This behavior is consistent with a scenario in which environmental mechanisms such as starvation or partial gas stripping first reduce the gas supply and star formation activity, while leaving the stellar structure largely intact during the early stages of quenching [97, 13, 163].

Bulge-to-total ratio–mass relation. —Figure 10 presents the stellar $B/T$–mass relation for SFGs. Field SFGs are dominated by low $B/T$ systems across most of the stellar mass range, as expected for disk-dominated star-forming galaxies. Cluster SFGs show a broadly similar distribution, with most objects remaining at low $B/T$, indicating that the actively star-forming population in clusters is still predominantly disk dominated.

The residual panel shows that the $B/T$ offsets between cluster and field SFGs are small at most stellar masses and cluster-centric radii. In contrast, the black dashed curve, which represents the offset between field GV galaxies and field SFGs, shows a substantially larger increase in $B/T$. This comparison indicates that the morphological difference between SFGs and GVs is much larger than the environmental difference among SFGs themselves.

The absence of a strong $B/T$ enhancement among cluster SFGs suggests that significant bulge growth is not yet widespread in galaxies that remain actively star-forming. Thus, while environmental effects may already be reducing the SFRs of cluster SFGs, the corresponding morphological transformation appears to occur later, or more gradually, as galaxies move into the transition population. This result is broadly consistent with studies showing that quenching and morphological transformation are related but not necessarily simultaneous processes [84, 17, 22].

D$_{\mathrm{n}}4000$–mass relation. —Figure 11 shows the D$_{\mathrm{n}}4000$–mass relation for SFGs. The D$_{\mathrm{n}}4000$ index traces the strength of the 4000 Å break and is commonly used as an indicator of the luminosity-weighted stellar population age, with larger values corresponding to older stellar populations and/or lower recent star formation activity [12, 84]. Field SFGs exhibit low $D_{\mathrm{n}4000}$ values, consistent with young stellar populations and ongoing star formation.

Cluster SFGs occupy a similar region of the $M_\ast$–$D_{\mathrm{n}4000}$ plane as field SFGs. The residual panel shows only weak $D_{\mathrm{n}4000}$ offsets between cluster and field SFGs over most of the stellar mass range. These offsets are much smaller than the difference between field GV galaxies and field SFGs, shown by the black dashed curve. Therefore, although cluster SFGs show modest SFR suppression, their stellar populations remain broadly consistent with those of actively star-forming field galaxies.

This result suggests that the environmental effect on SFGs is still at an early stage. The current star formation activity may already be reduced, but the integrated stellar population has not yet aged enough to produce a strong increase in $D_{\mathrm{n}4000}$. In this interpretation, SFGs in clusters represent a pre-transition population, in which environmental quenching has begun but has not yet produced the stellar population aging characteristic of GV or QG systems.

H-low UVJ-SF (“GV”) Galaxies

The active SF results provide the baseline against which we now compare the H$\alpha$-low UVJ-SF subset. These objects occupy an intermediate location in our H$\alpha$ SFR–mass classification, but the cross-sectional selection does not establish that every object will evolve directly from SF through this subset into the present QG sample.

Such H$\alpha$-weak but UVJ-SF systems are plausible candidates for recent or ongoing suppression and therefore provide a useful window on transformation [102, 137]. They can nevertheless include dust- or aperture-affected systems and galaxies with non-monotonic star-formation histories; we therefore report population offsets rather than assigning an evolutionary fate to each galaxy.

To investigate this transition phase, we examine the size–mass relation, $B/T$–mass relation, and D$_{\mathrm{n}}$4000–mass relation for GVs in different environments. Comparing cluster and field GVs allows us to determine whether environmental quenching is accompanied by structural growth, bulge buildup, and stellar population aging as galaxies evolve toward the quiescent population.

Size–mass relation. —Figure 9 shows the stellar size–mass relation for green-valley galaxies. In contrast to the SFG population, cluster GVs exhibit a more pronounced environmental dependence. At fixed stellar mass, cluster GVs are systematically smaller than field GVs, particularly at intermediate stellar masses ($10^{10.2} \lesssim M_{*}/M_{\odot} \lesssim10^{11}$). The strongest size deficit is observed in the innermost cluster regions, where the median size offset reaches $\sim0.2$–$0.3$ dex.

The comparison with the field SFG relation further illustrates this trend. While field GVs already lie below the field SFG size sequence, cluster GVs occupy an even more compact region of the parameter space. This result suggests that structural evolution becomes increasingly important once galaxies enter the transition phase.

The emergence of smaller sizes among cluster GVs is consistent with scenarios in which environmental quenching preferentially removes star-forming material from the outer disk or suppresses the growth of extended stellar components, thereby increasing the central concentration of stellar mass [128, 92, 43]. The stronger effect observed toward smaller cluster-centric radii further supports an environmental origin.

Bulge-to-total ratio–mass relation. —Figure 10 presents the $B/T$–mass relation for green-valley galaxies. Unlike the SFG population, cluster GVs exhibit systematically elevated $B/T$ values across nearly the entire stellar mass range. The enhancement is particularly significant within $R_{\mathrm{proj}} < 0.5R_{500}$, where the median $B/T$ exceeds the field relation by up to $\sim0.3$–$0.5$.

The increased fitted bulge prominence indicates that structural differences are most evident in this subsample. Compared with field SF galaxies, cluster GVs occupy a more centrally concentrated region of parameter space. This may reflect morphological evolution, preferential quenching of already concentrated galaxies, or both.

This trend is consistent with previous studies showing that galaxies undergoing quenching frequently develop enhanced central mass concentrations and larger bulge fractions [84, 60, 22]. The strong environmental dependence observed here implies that cluster-specific processes either accelerate bulge growth or preferentially quench galaxies that already possess more concentrated stellar structures.

D$_{\mathrm{n}}$4000–mass relation. —Figure 11 shows the D$_{\mathrm{n}}$4000–mass relation for green-valley galaxies. In contrast to the weak environmental dependence observed among SFGs, cluster GVs exhibit systematically larger D$_{\mathrm{n}}$4000 values than field GVs at nearly all stellar masses. The offset is typically $\sim0.2$–$0.4$, with the strongest enhancement occurring in the innermost cluster regions.

The elevated D$_{\mathrm{n}}$4000 values indicate older luminosity-weighted stellar populations and reduced recent star formation activity. Together with the enhanced $B/T$ ratios and reduced sizes, these results suggest that cluster GVs represent a more advanced stage of the quenching process than their field counterparts.

The simultaneous population-level offsets in size, fitted $B/T$, and D$_{\mathrm{n}}$4000 show that the selected H$\alpha$-low cluster sample differs from its field counterpart in several correlated observables [12, 84, 137]. The data alone do not determine whether structural change precedes, follows, or is selected together with declining star formation; this covariance is quantified explicitly in § 5.1.

Quiescent Galaxies

We finally examine the quiescent galaxy (QG) population, which represents the endpoint of the evolutionary sequence considered in this work. The analyses of SFGs and GVs suggest that environmental effects first manifest as a suppression of star formation and subsequently become associated with significant structural transformation during the transition phase. An important remaining question is whether these environmental signatures persist once galaxies have become fully quenched. Since QGs have largely ceased forming stars, any remaining environmental dependence is expected to reflect differences in their quenching histories, structural assembly, or the timescales over which they entered the quiescent population.

Size–Mass Relation

Figure 12 presents the stellar size–mass relation for quiescent galaxies. In contrast to the clear environmental dependence observed among GVs, cluster and field QGs follow remarkably similar size–mass relations across the full stellar mass range. The residual panel shows that the size offsets remain within $\sim0.05$ dex and are generally consistent with zero within the uncertainties.

This result suggests that the structural differences that emerge during the transition phase do not continue to grow after galaxies become fully quiescent. Instead, the size–mass relation appears to converge toward a common sequence largely independent of environment. The agreement with the relation reported by L. Kawinwanichakij et al. [86] further supports the robustness of this result.

The disappearance of the environmental size dependence among QGs implies that the dominant structural transformation likely occurs before or during the transition phase, rather than after quenching is complete.

Bulge-to-Total Ratio–Mass Relation

Figure Figure 12 shows the $B/T$–mass relation for quiescent galaxies. Both cluster and field QGs occupy a strongly bulge-dominated region of parameter space, with typical $B/T$ values substantially larger than those observed for SFGs and comparable to those of GVs.

The residual panel indicates only weak environmental differences. Although the lowest-mass cluster QGs exhibit slightly elevated $B/T$ values relative to the field population, the offsets rapidly diminish toward higher stellar masses and remain consistent with zero within the uncertainties over most of the mass range.

The absence of a strong environmental dependence suggests that once galaxies become fully quenched, their bulge-dominated structures are largely established. Therefore, the substantial increase in $B/T$ observed in the GV population likely represents the primary phase of morphological transformation, while subsequent evolution within the quiescent population is comparatively modest.

Dn4000–Mass Relation

Figure Figure 12 presents the Dn4000–mass relation for quiescent galaxies. Unlike the mass–size and $B/T$–mass relations, a clear environmental dependence remains visible in Dn4000. At fixed stellar mass, cluster QGs exhibit systematically larger Dn4000 values than field QGs, with typical offsets of $\sim0.1$–$0.2$.

The enhanced Dn4000 values indicate older luminosity-weighted stellar populations and imply that cluster QGs were quenched earlier than their field counterparts. The strongest offsets are observed at low and intermediate stellar masses, suggesting that environmental quenching is particularly effective in accelerating the cessation of star formation among satellite galaxies in dense environments.

Combined with the weak environmental trends in size and $B/T$, these results indicate that the primary difference between cluster and field QGs lies not in their present-day structures but in their quenching histories. Cluster QGs appear to have reached the quiescent phase earlier, resulting in older stellar populations at fixed stellar mass. This interpretation is consistent with previous studies showing that galaxies in dense environments tend to experience earlier formation and quenching epochs than comparable field galaxies [154, 127, 163].

Discussion

Coupled and Multivariate Environmental Effects

The environmental signatures in star formation, stellar-population age, and galaxy structure are correlated, and therefore cannot be interpreted independently. We first examine the joint structure of the matched cluster–field residuals directly, and then quantify the total multivariate displacement with a Mahalanobis metric. These two diagnostics address complementary questions: the residual maps show which combinations of galaxy properties change together, whereas the Mahalanobis distance measures the overall amplitude of the multivariate displacement.

For each cluster satellite, we construct a field reference matched in stellar mass and redshift. In the residual-map analysis, each satellite is compared with the mean of up to five field controls satisfying

and at least three acceptable controls are required. For an observable $X$, we define

where $F(i)$ denotes the matched field controls of satellite $i$. Thus, $\Delta X = 0$ corresponds to no difference from field galaxies of comparable stellar mass and redshift. Sources with the flagged $B/T = 0.5$ value are excluded before matching.

Figure Figure 13 visualizes these residuals for the full satellite population, without conditioning on SF, GV, or QG classification. The horizontal and vertical coordinates are $\Delta\log\mathrm{SFR}$ and $\Delta D_{n4000}$, respectively, and the color in each occupied cell gives the cluster-weighted mean $\Delta(B/T)$. The sample is divided at $\log(M_\ast/M_\odot) = 10.5$, and the two panels use identical coordinate ranges and color normalization. Cells containing fewer than two galaxies are omitted. The figure should therefore be interpreted in terms of coherent trends across multiple neighboring cells rather than individual low-occupancy cells.

The residual maps show that galaxies with more strongly suppressed star formation tend to exhibit more positive $B/T$ residuals. We quantify this trend separately in the two stellar-mass intervals using cluster-weighted linear regressions,

where the tildes denote the median within the corresponding stellar-mass interval. Each host cluster is given equal total weight, and the coefficient uncertainties quoted here are cluster-robust standard errors with host cluster as the clustering unit.

For the low-mass sample, we obtain

whereas the high-mass sample gives

Thus, in both stellar-mass regimes, stronger suppression of star formation relative to the matched field population is associated with a systematically larger $B/T$ residual. In practical terms, a decrease of 1 dex in $\Delta\log\mathrm{SFR}$ corresponds to an increase of approximately 0.1 in $\Delta(B/T)$ at fixed $\Delta D_{n4000}$, stellar mass, and redshift.

By contrast, the coefficient of $\Delta D_{n4000}$ is positive but not independently significant:

at low mass and

at high mass. The color structure in Figure 13 therefore does not imply that $D_{n4000}$ independently predicts the structural residual once the correlated SFR residual is taken into account. Rather, the apparent association between older stellar populations and enhanced bulge prominence is largely embedded in the same population that exhibits suppressed star formation.

Within the high-mass interval, residual trends with stellar mass and redshift remain detectable ($\beta_M = 0.128 \pm0.057$, $p = 0.024$ and $\beta_z = -0.408 \pm0.133$, $p = 0.002$), whereas neither control term is significant in the low-mass interval. We therefore retain both stellar mass and redshift in the regression rather than assuming that the initial matching removes all within-bin dependence. These residual trends do not imply a failure of the matching: matching removes systematic differences between each cluster galaxy and its field controls, while the regression tests whether the environmental residual itself varies continuously with galaxy mass or redshift.

We next compress the correlated residuals into a single multivariate effect-size statistic. For this purpose, we use the four-dimensional vector

Stellar mass is not included as a coordinate of the distance because it is already controlled through the matching and is used separately for stratification.

For the Mahalanobis analysis, we use the matched cluster–field residuals from the production multivariate pipeline. The residual vector is

with the field counterpart selected under the same $\lvert\Delta\log M_\ast\rvert< 0.05$ and $\lvert\Delta z \rvert< 0.01$ criteria. A unique field control is assigned within each matched sample so that the same field galaxy does not contribute repeatedly to the group centroid.

The reference covariance, $\Sigma_{\mathrm{FF}}$, is estimated from matched field–field residuals constructed with the same matching procedure. The mean field–field residual is subtracted as a zero-point correction. Importantly, within a given evolutionary-stage and stellar-mass stratum, the same $\Sigma_{\mathrm{FF}}$ is used for all three radial bins. Radial changes in the metric therefore reflect changes in the cluster–field centroid displacement rather than changes in the covariance used to measure it.

To prevent rich clusters from dominating the measurement, galaxy residuals are first averaged within each host cluster and the host centroids are subsequently given equal weight. If $K$ host clusters contribute to a bin,

The multivariate environmental offset is then

where $\boldsymbol{\Sigma}_{\mathrm{FF}}^{+}$ denotes the inverse covariance, evaluated with a Moore–Penrose pseudoinverse when necessary. $D_{\mathrm{env}}\geq0$ is dimensionless and quantifies how far the cluster centroid is displaced from the matched field reference after accounting for the covariance among SFR, size, $B/T$, and $D_{n4000}$. It is therefore a standardized multivariate effect size, rather than a physical force, evolutionary timescale, or causal “environmental intensity.”

Uncertainties on $D_{\mathrm{env}}$ are estimated from 3000 hierarchical-bootstrap realizations. Host clusters are resampled first, followed by resampling of galaxies within the selected hosts. Statistical significance is assessed with 10,000 cluster-block sign-flip permutations, and the resulting probabilities are corrected with the Benjamini–Hochberg false-discovery-rate procedure across the 18 stage–mass–radius combinations.

Figure 14(a) shows that the strongest radial variation is associated with the GV population. Low-mass GV satellites exhibit the largest inner-region multivariate displacement and a strong decrease toward larger projected radius. The corresponding high-mass GV population shows a substantially smaller displacement. The QG population exhibits a more moderate radial trend, while the SF population shows a weaker multivariate offset overall.

Because the field–field covariance is defined separately for each evolutionary-stage and stellar-mass stratum, the most direct interpretation of $D_{\mathrm{env}}$ is the radial change within a fixed stratum. Differences in the absolute values of $D_{\mathrm{env}}$ between distinct populations should be interpreted as differences in standardized effect size relative to the field scatter appropriate to each population, rather than as measurements made with a single universal covariance scale.

The decomposition in Figure 14(b) provides physical context for the GV signal. The SFR residual remains negative over a broader range in projected radius than the strongest residuals in $R_{\mathrm{e}}$ and $B/T$, whereas the largest structural offsets occur preferentially at smaller $R/R_{500}$. This spatial ordering is consistent with a scenario in which suppression of the gas supply affects star formation over a broader radial range than the strongest changes in the stellar-light distribution [163, 61].

However, projected cluster-centric radius is not an evolutionary clock. Orbital mixing, backsplash, pre-processing, and rejuvenation can place galaxies with substantially different accretion and star-formation histories at the same projected radius. We therefore interpret the radial ordering as evidence that different galaxy properties respond over different spatial scales, rather than as a direct measurement that one physical transformation necessarily precedes another in time.

Taken together, Figure 13 and Figure 14 provide complementary views of the environmental response. Figure 13 shows that, after controlling for stellar mass and redshift through field matching, suppressed star formation is systematically associated with enhanced bulge prominence. The regression analysis confirms that this relation remains significant after additionally controlling for $D_n4000$, stellar mass, and redshift. Figure 14 then shows that the total multivariate displacement is strongest for low-mass GV satellites in the inner cluster regions and declines outward.

These results are consistent with environmental quenching accompanied by structural transformation, but they do not establish a unique evolutionary pathway. The observed covariance can arise from transformation after infall, differences already present among the progenitor population, pre-processing before cluster entry, or preferential survival and selection of structurally distinct galaxies. The similarity of the fitted $\Delta(B/T)$–$\Delta\log\mathrm{SFR}$ slopes in the two broad mass intervals further suggests that the coupling between star-formation suppression and structural residuals may operate in both regimes, even though the overall magnitude of the environmental displacement is more strongly mass dependent.

A Coherent Picture of Environmentally Driven Galaxy Transformation

The results reveal a coherent population-level ordering, but not a unique evolutionary track. Star-formation residuals appear over a broader radial range than the strongest structural residuals; the largest joint offset is found for low-mass H$\alpha$-low UVJ-SF galaxies; and QGs retain a clearer $D_n4000$ than structural difference. Figure 15 summarizes one interpretation while explicitly retaining alternative pathways. This distinction is important because projected radius mixes first-infall, virialized, and backsplash populations, and the three galaxy classes are not progenitor-matched.

The earliest environmental signature is seen in the SFR–$M_\ast$ relation. Cluster SFGs exhibit systematically lower SFRs than field SFGs at fixed stellar mass, with the strongest suppression occurring toward smaller cluster-centric radii. However, these galaxies still remain on or near the star-forming sequence, and their sizes, bulge-to-total ratios, and $D_n4000$ values remain broadly similar to those of field SFGs. This suggests that environmental processes initially act on the gas supply rather than immediately altering the stellar structure. Such behavior is consistent with mechanisms such as starvation, strangulation, or partial gas stripping, in which the gas reservoir available for future star formation is reduced before the existing stellar distribution is significantly modified [97, 13, 163] (A. Boselli & G. Gavazzi 2006).

The enhanced H$\alpha$-low fraction in clusters is consistent with the environment increasing the incidence of suppressed recent star formation at fixed mass. It is not, by itself, a direct transition rate: the denominator is restricted to UVJ-SF galaxies with measurable Balmer lines, and galaxies can enter or leave the selection through dust, aperture effects, stochasticity, or renewed star formation. We therefore interpret the fraction together with $D_n4000$ and structure rather than as a standalone clock [127, 126].

The H$\alpha$-low UVJ-SF population is nevertheless central to the empirical result because its SFR, size, fitted $B/T$, and $D_n4000$ residuals are simultaneously displaced. This makes it the clearest observational window on where suppressed recent star formation and structural differences coexist. It does not prove that bulges grew during quenching: preferential quenching of compact or bulge-dominated progenitors, disk fading, and environment-dependent measurement bias remain possible contributors [171, 167, 165].

The radial ordering is qualitatively consistent with delayed-then-rapid satellite quenching [163, 61], yet cluster entry need not be the beginning of environmental processing. Galaxies can lose gas or be morphologically altered in groups, filaments, and infalling substructure before crossing $R_{500}$—the “pre-processing” channel [136]. Large-scale gas flows and cosmic-web detachment can also reduce fuel supply outside the nominal halo boundary [4, 63]. These channels naturally help explain an SFR signal in the outskirts without requiring the present cluster core to have acted there.

The $D_n4000$ measurements add a longer-timescale stellar-population constraint. Their persistence among QGs, when size and $B/T$ residuals are weaker, is consistent with earlier average quenching in the cluster population. However, $D_n4000$ also depends on metallicity and detailed star-formation history; it should not be converted directly into an age difference without spectral modeling.

The covariance-aware $D_{\rm env}$ strengthens the mass-dependent result without double-counting correlated residuals. The larger low-mass offset is physically plausible because shallow potentials are less able to retain gas, whereas high-mass evolution can be more strongly regulated by internal or halo-related processes [84, 60, 22, 166]. Yet $D_{\rm env}$ describes a standardized displacement rather than a causal susceptibility; different covariance widths and selection functions across classes are handled within the stated strata but still limit comparisons.

Taken together, the data favor a picture in which suppression of recent star formation can be visible before the strongest structural residuals, with the H$\alpha$-low UVJ-SF population marking where these observables overlap most strongly. Pre-processing, backsplash and orbit mixing, progenitor selection, and rejuvenation broaden that pathway (C. Mancini et al. [101]). The schematic therefore encodes a set of allowed channels rather than a conveyor belt with a single direction or timescale.

Reconciling Previous Environmental Studies

The environmental trends identified in this work can be placed in the broader context of studies of star formation, stellar populations, and galaxy structure. A broad observational consensus is that galaxies in dense environments, and satellites in particular, are more frequently quenched than comparable field or central galaxies (e.g., [83, 11, 76, 162, 163, 126, 48] (A. Boselli & G. Gavazzi 2006)). The environmental dependence of structural properties is less uniform, however, and depends on stellar mass, evolutionary state, redshift, the definition of environment, rest-frame wavelength, and the adopted structural metric.

Our star-formation results are broadly consistent with this picture. Beyond the well-known enhancement of the quenched fraction, several studies have found reduced star-formation activity among galaxies that have not yet become fully quiescent. HSC measurements, for example, find modestly lower specific star-formation rates for star-forming galaxies in groups and clusters, with stronger environmental quenching toward lower stellar mass (H.-Y. Jian et al. [81]). Studies of nearby clusters likewise favor quenching histories that include a period of reduced gas supply or slow decline followed by more rapid suppression, with pre-processing contributing before final cluster accretion ([163, 73]). Our detection of negative SFR residuals among galaxies that remain on the star-forming side of our classification is therefore consistent with environmental processing beginning before complete quiescence.

The abundance of transition or “green-valley” galaxies requires more care. Its inferred environmental dependence is sensitive to the transition definition and to the population used for normalization. Some studies identify an enhanced transition population in groups or clusters ([46, 82]), whereas the SDSS satellite analysis of A. R. Wetzel et al. [162] found no excess in the intermediate-SSFR population despite a strong enhancement of the quenched fraction. At $z \sim1$, K. McNab et al. [106] found only a modest cluster excess of transition galaxies, concentrated primarily below $\log(M_\ast/M_\odot) \simeq10.5$, with little evidence for an excess at higher stellar mass. We therefore interpret the radial behavior of our operational transition class as evidence for a population associated with environmental quenching, rather than assuming that a green-valley fraction is a universal or model-independent measure of the quenching rate.

The stellar-population trends point in the same general direction. Stronger 4000-Å breaks and older luminosity-weighted stellar populations have been reported in denser environments over a broad range of redshift ([12, 83, 124, 147]). We likewise find positive $D_{n4000}$ residuals for the transition and quiescent populations. Because $D_{n4000}$ depends on recent star-formation history and, particularly for older populations, on metallicity, we do not interpret it as a unique age clock. The persistence of a $D_{n4000}$ residual when some structural offsets become weak is therefore most conservatively interpreted as evidence that stellar-population differences remain detectable, not as a direct measurement that stellar-population transformation necessarily precedes or outlasts structural evolution.

The environmental dependence of galaxy size is considerably less settled. Several studies report little or no environmental difference in the stellar-mass–size relation once stellar mass, morphology, or color is controlled ([100, 132, 78, 87, 111, 150]). In contrast, larger characteristic sizes in dense environments have been reported for massive, often quiescent, galaxies at intermediate and high redshift ([47, 123, 96, 51, 41, 3]). Other studies instead find smaller sizes or truncated outer structures in clusters and other overdense regions ([39, 103, 104, 40, 64] (C. Xu et al. 2023)). These results are not necessarily mutually exclusive: the studies span different redshifts, stellar-mass ranges, morphological selections, cluster definitions, rest-frame wavelengths, and size estimators. In particular, recent work illustrates that environmental size differences can depend on whether one uses conventional effective radii, low-surface-brightness galaxy edges, or different rest-frame wavelengths ([40, 64]).

Our results suggest that evolutionary state provides an additional source of heterogeneity. Within our sample, the size residual is weak for the star-forming and fully quiescent populations but becomes more pronounced for the transition population. Differences in the relative mixture of these populations can therefore dilute or amplify the ensemble environmental size signal. We do not argue that population mixing alone reconciles the literature; redshift evolution, progenitor bias, sample selection, rest-frame wavelength, and the adopted size definition remain important. Rather, separating galaxies by evolutionary state reveals a structural signal that would be substantially less apparent in an undivided population. The cluster post-starburst results of J. Matharu et al. [103, 104, 105] provide a particularly relevant comparison. At $z \sim1$, recently quenched cluster galaxies occupy an intermediate locus between the star-forming and quiescent mass–size relations, and models in which the outer stellar populations fade after outside-in suppression can produce both an apparent reduction in light-weighted effective radius and an increase in bulge prominence without requiring an equally large redistribution of stellar mass (J. Matharu et al. [104]). Spatially resolved $H\alpha$ measurements provide additional evidence for outside-in suppression of star formation in recently quenched cluster systems (J. Matharu et al. [105]). These results are qualitatively consistent with our finding that the strongest coupled star-formation and structural residuals occur in the transition population, although the redshift ranges, observables, and sample definitions differ and therefore do not require an identical physical mechanism. The compact, evolved star-forming population identified in a $z = 2.51$ cluster by C. Xu et al. (2023) provides a higher-redshift example in which environmental star-formation and structural evolution appear to be coupled.

Our morphology results should be interpreted with the same distinction between association and causation. The classical morphology–density relation establishes a strong population-level connection between galaxy structure and environment (A. Dressler [59]), but studies controlling for stellar mass and star-formation activity generally find that residual morphology–environment trends are weaker than the corresponding color or star-formation trends ([15, 146]). Bulge prominence is itself strongly connected to quiescence at fixed stellar mass, while satellites retain an additional environmental contribution to their quenching and structure ([23, 24]). Bulge–disc decompositions also show that environmental effects can act on discs without requiring substantial changes in the bulge component ([94]). At $z \sim0.8$, A. Paulino-Afonso et al. [125] similarly find that morphology depends on both stellar mass and environment, while environmental correlations weaken substantially when star-forming and quiescent populations are considered separately. More recently, M. Oxland et al. [122] find evidence that satellite quenching and morphological transformation both proceed with environmental processing, with particularly strong effects at low stellar mass, but need not share the same characteristic timescale.

These results motivate a deliberately conservative interpretation of our $B/T$ measurements. Our cluster-weighted regression shows that $\Delta(B/T)$ is independently associated with $\Delta\log\mathrm{SFR}$ in both stellar-mass intervals, whereas $\Delta D_{n4000}$ is not independently significant once SFR, stellar mass, and redshift are controlled. We therefore describe the observed trend as enhanced bulge prominence or structural transformation associated with suppressed star formation, rather than as direct evidence for bulge growth. A larger light-based $B/T$ may arise from genuine growth of the bulge, fading or truncation of the disc, or some combination of these effects.

A key strength of the present work is the combination of spectroscopic galaxy redshifts with X-ray-selected cluster catalogs. The eFEDS cluster catalog is based on extended eROSITA detections and subsequent optical characterization ([99, 89]), while the eRASS1 catalog similarly combines extended X-ray detections with optical confirmation and characterization ([35, 91]). This substantially reduces the projection ambiguity associated with purely photometric overdensity selections, but does not produce a mass-complete or selection-neutral cluster sample. The probability of detecting an extended X-ray source depends on source flux, apparent extent, redshift, exposure, background, and source morphology, and simulations are required to characterize completeness and contamination ([140]). Our permissive extent-likelihood selection should therefore be viewed as broadening the parent candidate set rather than guaranteeing completeness. The final 348-cluster subset additionally inherits the HSC imaging footprint and DESI spectroscopic targeting selection. Within these limits, the combined HSC–DESI–eROSITA sample enables the environmental trends to be separated by stellar mass, operational evolutionary class, and projected cluster-centric radius. In particular, the strongest multivariate offset is found for the $H\alpha$-low UVJ-SF transition class, which would be mixed into the broader star-forming population in a purely UVJ-based division.

Conclusions

Using HSC imaging, DESI spectroscopy, and eROSITA-selected clusters, we compared matched cluster satellites and non-cluster controls in SFR, size, fitted $B/T$, and $D_{n4000}$. Within the UVJ-SF population we call objects below $\mathrm{SFR}_{H\alpha} = 10^{-10.5}\,\mathrm{yr}^{-1}$ “GV” for brevity; this is an operational $H\alpha$-low definition, distinct from a conventional color-selected green valley. Our main conclusions are as follows.

1. Environmental effects are strongest among low-mass galaxies and become progressively weaker toward higher stellar masses.

Using a covariance-aware Mahalanobis distance in SFR, effective radius, $B/T$, and $D_{n4000}$, after matching in mass and redshift, we find larger cluster–field displacements at low mass than at high mass. This is consistent with greater environmental susceptibility of shallow-potential systems, although the metric is an effect size rather than a causal measure.

2. The cluster environment exerts its strongest influence within the cluster core and weakens with increasing cluster-centric radius. The multivariate offset and several individual residuals are largest inside $0.5R_{500}$ and generally decline outward. Because projected radius mixes orbital histories and backsplash populations, this is a radial association rather than a direct measurement of processing time or local three-dimensional density.

3. Star formation suppression appears to precede the strongest structural transformation. Cluster SF galaxies show SFR suppression with weaker structural residuals, whereas the H$\alpha$-low UVJ-SF sample shows joint offsets in size, fitted $B/T$, and D$_{\mathrm{n}}4000$. This ordering is consistent with star-formation suppression preceding the strongest changes in the stellar-light distribution, but it does not exclude progenitor bias, disk fading, or non-monotonic star-formation histories.

4. The strongest environmental signatures emerge in the green-valley population. Among the three operational classes, low-mass GV galaxies have the largest covariance-normalized cluster–field offset. This population is therefore the most sensitive tracer in our selection of the coexistence of suppressed recent star formation, older luminosity-weighted populations, and structural differences.

5. Quiescent galaxies retain a stronger memory of environmental history in their stellar populations than in their present-day structures. Cluster and field QGs have relatively weak residual differences in size and fitted $B/T$, while the D$_{\mathrm{n}}4000$ offset is clearer. This is consistent with different average quenching histories even after present-day structural relations have largely converged, subject to the metallicity dependence of D$_{\mathrm{n}}4000$.

Taken together, these results support—but do not uniquely establish—a pathway in which gas-supply suppression can begin in cluster outskirts or pre-processing environments before the strongest structural differences appear. Orbital mixing, backsplash, rejuvenation, and preferential selection of compact progenitors remain viable. The main empirical conclusion is therefore narrower and more robust: after matching in stellar mass and redshift, the strongest joint cluster–field displacement is associated with low-mass H$\alpha$-low UVJ-SF satellites.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 12533003, 12192222, 12192220, and 12121003). This work made extensive use of the following software and analysis tools: Astropy ( [5, 6, 7]), NumPy ( [75]), SciPy ( [160]), Matplotlib ( [79]), TOPCAT ( [153]), CIGALE ( [26]), EAZY ( [31]), GALIGHT ( [57]), and GalSim ( [133]). The analysis presented in this work was primarily performed using Python and its scientific computing ecosystem.

Appendix

Magnitude-dependent Calibration of the Bulge-to-total Ratio

The reliability of a two-component bulge–disk decomposition depends on the signal-to-noise ratio and therefore on apparent magnitude. At progressively fainter magnitudes, the surface-brightness distribution becomes less well constrained and the recovered bulge-to-total light ratio, $B/T$, can become systematically biased. Because $B/T$ is used throughout this work as one of the primary structural diagnostics, we quantify this magnitude dependence with image simulations and derive an empirical calibration that is applied to the science catalog.

The simulated galaxies are analyzed with the same structural-fitting procedure adopted for the observed sample.

We divide the simulations into five one-magnitude intervals spanning

and examine the relation between the input (true) and recovered (measured) $B/T$ independently in each interval. Only structural fits satisfying the adopted fit-quality criterion,

are used to determine the calibration relation. Figure A1 shows the resulting recovery tests. The horizontal axis is the measured value returned by the fitting pipeline, $(B/T)_{\mathrm{meas}}$, while the vertical axis is the true input value of the simulation, $(B/T)_{\mathrm{true}}$. The gray dashed line marks perfect recovery,

The color coding indicates the median reduced $\chi^2$ of the simulated fits, and the solid red line shows the best-fitting empirical calibration relation for the subset satisfying $\chi^2_\nu\le2$. The dotted red curves indicate the measured $1\sigma$ scatter about this relation.

Within each magnitude interval $m$, we fit

Because the regression is explicitly performed with true $B/T$ as the dependent variable and measured $B/T$ as the independent variable, Equation A4 can be applied directly to the observed measurements. The calibrated value used in the science analysis is therefore

where the coefficients corresponding to the galaxy’s apparent-magnitude interval are adopted. No inversion of the fitted relation is required.

The best-fitting calibration coefficients are listed in Table A1. At the bright end, the relation remains close to one-to-one. For $18 \le i < 19$, we find

and for $19 \le i < 20$,

Thus, for the brightest simulated galaxies, the fitted slope is statistically consistent with unity and the mean recovery bias is small.

The calibration becomes progressively stronger toward fainter magnitudes. In the $20 \le i < 21$ interval, the fitted slope decreases to $0.83 \pm0.02$, with an intercept of $0.13 \pm0.01$. At $21 \le i < 22$, the slope decreases further to $0.60 \pm0.03$, while the intercept increases to $0.29 \pm0.01$. In the faintest interval, $22 \le i < 23$, the recovered $B/T$ values show substantial compression relative to the true dynamic range, with

The increasing deviation from the one-to-one relation demonstrates that a single global correction would not provide an adequate description over the full magnitude range.

The mean recovery offset,

increases from approximately 0.04 at $i < 20$ to 0.19 in the faintest magnitude interval. At the same time, the scatter about the calibration relation increases from $\simeq0.11$ at $i < 20$ to 0.16, 0.19, and 0.25 in the progressively fainter bins. This increasing scatter is important: Equation A5 removes the mean magnitude-dependent bias, but it does not remove the object-to-object uncertainty in the recovered structural parameters. Consequently, the calibrated $B/T$ values are most reliable for population-level statistical comparisons rather than for interpreting small differences in individual faint galaxies.

The behavior in Figure A1 also illustrates why the calibration must be interpreted as a statistical correction rather than an exact recovery of the intrinsic morphology. At bright magnitudes, the fitted slopes are close to unity and the scatter is comparatively small. At faint magnitudes, however, the fitted slope becomes substantially shallower than unity and the range of recoverable $B/T$ values becomes increasingly compressed. The correction therefore restores the mean relation between measured and true $B/T$, but the information content of an individual faint-galaxy decomposition remains limited by the substantially larger scatter.

The calibration also addresses only those biases represented by the simulations. In particular, it captures the magnitude-dependent recovery bias within the adopted parametric model family and under the image conditions represented by the mock sample. It does not explicitly calibrate structural errors caused by bars, spiral arms, tidal features, asymmetric components, or other deviations from the assumed bulge–disk model. Similarly, it does not isolate possible environment-dependent effects associated with crowding, blending, local sky subtraction, or diffuse intracluster light.

These limitations are relevant for the environmental analysis because the most crowded and highest-background regions may preferentially occur toward smaller projected cluster-centric radii. A magnitude-dependent calibration alone therefore cannot demonstrate that the structural measurements are completely independent of environment. For this reason, we interpret the corrected $B/T$ measurements primarily through population-level trends and in conjunction with the independent size, star-formation, and spectroscopic diagnostics. A more direct future assessment would inject mock galaxies into real cluster images over a controlled range of local background surface brightness, crowding, and projected cluster-centric radius. Finally, Equation (26) should not be interpreted as reducing the random uncertainty quoted in Table A1. The systematic mean mapping and the object-to-object scatter are distinct components of the recovery performance. The former is corrected empirically in the science catalog, whereas the latter remains part of the uncertainty budget and motivates caution when interpreting small $B/T$ differences, particularly at $i \gtrsim21$.

$i$ range	$a_m$	$b_m$	Avg. offset	$\sigma$	$N_{\mathrm{fit}}$
$18 \le i < 19$	$1.03 \pm0.02$	$0.03 \pm0.01$	$+0.041$	$0.109$	$405$
$19 \le i < 20$	$0.99 \pm0.02$	$0.04 \pm0.01$	$+0.039$	$0.112$	$480$
$20 \le i < 21$	$0.83 \pm0.02$	$0.13 \pm0.01$	$+0.060$	$0.162$	$488$
$21 \le i < 22$	$0.60 \pm0.03$	$0.29 \pm0.01$	$+0.124$	$0.189$	$462$
$22 \le i < 23$	$0.34 \pm0.04$	$0.45 \pm0.02$	$+0.186$	$0.250$	$338$

Central Stellar-Mass Density as an Additional Structural Diagnostic

The main analysis uses the bulge-to-total light ratio, $B/T$, as one measure of structural transformation. Because a two-component bulge–disk decomposition is model dependent, we perform an additional test using the central stellar-mass surface density within 1 kpc, $\Sigma_{1\,\mathrm{kpc}}$. This quantity provides a complementary measure of central concentration that does not rely explicitly on separating the galaxy into bulge and disk components. Previous studies have shown that central stellar-mass density is closely related to galaxy compactness and star-formation state and can provide a useful structural diagnostic of galaxies undergoing or having undergone quenching (e.g., [60, 16]).

We estimate $\Sigma_{1\,\mathrm{kpc}}$ from the best-fitting single-Sérsic structural model. The projected Sérsic surface-brightness profile is written as

where $R_{\mathrm{e}}$ is the effective radius, $n$ is the Sérsic index, and $b_n$ is defined such that $R_{\mathrm{e}}$ encloses one half of the total Sérsic luminosity ([141, 44, 67]). Specifically,

where $\Gamma$ and $\gamma$ are the complete and lower incomplete gamma functions, respectively ([44, 45, 67]).

For a Sérsic profile, the fraction of the projected luminosity enclosed within radius $R$ is

Assuming that stellar mass follows the fitted light profile with a spatially constant mass-to-light ratio for an individual galaxy, the stellar mass enclosed within 1 kpc is therefore

and the corresponding projected central stellar-mass surface density is

We use $\log\Sigma_{1\ \mathrm{kpc}}$ in units of $M_\odot\ \mathrm{kpc}^{-2}$ throughout the analysis. This definition follows the commonly adopted central-density measure used in studies of galaxy structure and quenching [e.g. 60, 16].

Figure A2 presents the $\Sigma_{1\ \mathrm{kpc}}$–stellar-mass relation separately for the SF, transition (GV), and quiescent populations. The gray distributions show the matched field reference, while the cluster samples are divided into the same three projected radial intervals used in the main analysis: $R < 0.5R_{500}$, $0.5 < R/R_{500} < 1$, and $1 < R/R_{500} < 2$. The marginal distributions above and to the right of the main panels illustrate the corresponding stellar-mass and central-density distributions, while the lower panels show the cluster-minus-field residual,

after the same stellar-mass and redshift matching adopted in the main analysis.

The central-density trends provide a useful cross-check on the $B/T$ results presented in the main text. The transition population shows the clearest positive $\Delta\log\Sigma_{1\ \mathrm{kpc}}$ signal, particularly at small and intermediate projected cluster-centric radii. The magnitude of the offset is weaker and less coherent for the SF population, while the quiescent population is generally much closer to the matched field relation. Thus, the population for which we find the strongest environmental enhancement in $B/T$ also tends to exhibit the largest enhancement in central stellar-mass density.

This qualitative agreement is important because $B/T$ and $\Sigma_{1\ \mathrm{kpc}}$ probe structure in different ways. The former is derived from an explicit bulge–disk decomposition and measures the relative contribution of the fitted bulge component to the total galaxy light. In contrast, $\Sigma_{1\ \mathrm{kpc}}$ measures the total projected stellar mass inferred to lie within a fixed physical aperture and does not require assigning the central light to a separate bulge component. The consistent behavior of the two diagnostics therefore argues against the environmental $B/T$ trend being produced solely by a peculiarity of the two-component decomposition.

At the same time, the two measurements are not statistically or physically independent. Both ultimately depend on the galaxy surface-brightness distribution, and $\Sigma_{1\ \mathrm{kpc}}$ additionally relies on the assumption that the stellar mass-to-light ratio does not vary strongly with radius. Strong stellar-population or dust gradients could therefore cause the true stellar-mass profile to differ from the fitted light profile. Moreover, because $\Sigma_{1\ \mathrm{kpc}}$ is inferred from the best-fitting Sérsic model, the measurement can be affected by uncertainties in $n$ and $R_e$, particularly when the physical 1-kpc aperture approaches or falls below the effective spatial resolution.

We therefore regard $\Sigma_{1\ \mathrm{kpc}}$ as a complementary structural consistency check rather than as a fully independent measurement of central stellar mass. Within these limitations, the fact that the strongest positive central-density residuals occur in the same transition population that exhibits the strongest $B/T$ offsets supports the interpretation that the environmental structural signal is associated with enhanced central concentration of the stellar-light distribution. It does not, however, by itself demonstrate physical bulge mass growth: an increase in central concentration can also arise through changes in the relative prominence of the disk and central component, including disk fading or truncation.

Comparison with Previous Environmental Studies

The observational literature on environmental galaxy evolution is heterogeneous by construction: studies use different definitions of environment (e.g., cluster membership, host-halo mass, projected density, or cosmic-web class), different population selections, and different structural estimators and rest-frame wavelengths. The tables below are therefore intended as a structured comparison of representative results rather than as a formal meta-analysis. In particular, apparently different size results need not be mutually inconsistent when the samples differ in redshift, stellar mass, star-formation state, morphology, or size definition. This point is especially important for the present work, where the environmental signal changes substantially when galaxies are separated by evolutionary state and stellar mass.

Environmental dependence of galaxy size

Table B1 summarizes representative measurements of the environmental dependence of galaxy size. We group the studies by their reported result, but retain the principal qualification in the final column. This avoids treating conditional results—for example, a trend confined to low-mass disks or to very massive early-type galaxies—as universal statements about all galaxies.

Reference	$z$	Environment	Population	Size measure	Reported environmental trend	Important qualification
No significant or weak dependence for the quoted population
D. T. Maltby et al. [100]	$\sim0.17$	Cluster/field	E, S0, spirals	$R_e$	No trend for E/S0 and high-$M_\ast$ spirals	Low-$M_\ast$ spirals show a possible cluster-size reduction
M. Huertas-Company et al. [77]	$\sim0$	Halo mass; central/satellite	ETGs	$R_e$	No significant dependence at fixed $M_\ast$	Rules out large ($\gtrsim30$–$40\%$) offsets for massive ETGs
F. Shankar et al. [142]	$<0.3$	Host-halo mass	ETGs	$R_e$	Observed SDSS sizes show no dependence at fixed $M_\ast$	Used primarily to test hierarchical-model predictions
A. Rettura et al. [132]	$\sim1.2$	Cluster/field	Massive ETGs	$R_e$	Similar mass–size relations	Cluster and field stellar populations also compared
K. Kelkar et al. [87]	$0.4$–$0.8$	Cluster/field	Morphology- or color-matched	$R_e$	No significant difference	Average differences $\gtrsim10$–$20\%$ are disfavored
A. B. Newman et al. [116]	$1.80$	Cluster/field	QGs	$R_e$	No significant difference after morphology mix is considered	JKCS 041; mean QG ages also similar to field
P. Saracco et al. [135]	$1.2$–$1.4$	Cluster/field	Ellipticals	$R_e$, $\Sigma$	Same structural relations at fixed $M_\ast$	Field lacks the most massive/large ellipticals
V. Strazzullo et al. [150]	$1.4$–$1.7$	Cluster/field comparison	Massive cluster galaxies	$R_e$, Sérsic structure	No compelling cluster-specific size offset at fixed population	Very massive SPT-SZ clusters; central regions
Weak or conditional dependence
Y.-C. Zhang & X.-H. Yang (2019)	$\lesssim0.2$	Halo mass; central/satellite; cosmic web	Mixed	$R_e$	Weak halo/central–satellite dependence	Satellites slightly smaller at $9 \lesssim\log M_\ast\lesssim10.5$; cosmic-web trend nearly negligible
Larger sizes in denser environments for the quoted population
Y. Yoon et al. [172]	$0.10$–$0.15$	Large-scale density	ETGs	Non-parametric radius	Dense-region ETGs larger	Trend appears for $M_\ast\gtrsim10^{11.2}M_\odot$; amplitude $\sim20$–$40\%$
M. C. Cooper et al. [47]	$0.4$–$1.2$	Local overdensity	Massive ETGs	$R_e$	Larger in denser regions	Interpreted in connection with earlier assembly
C. Lani et al. [96]	$0.5$–$2.0$	Local density	QGs and SFGs	$R_e$	Positive size–density relation mainly for QGs	Strength depends on redshift and environment
C. Papovich et al. [123]	$1.62$	Cluster/field	Quiescent galaxies	$R_e$	Cluster QGs larger on average	High-redshift single-cluster comparison
L. Delaye et al. [51]	$0.8$–$1.5$	Cluster/field	Passive Q/ETGs	$R_e$	Mean cluster sizes larger	Cluster proximity as high-z sample; median difference is weaker
V. Strazzullo et al. [149]	$\sim2$	Cluster/field	Passive ETGs	$R_e$	Cluster passive ETGs larger than field analogs	Cluster galaxies remain much smaller than local ETGs
J. C. C. Chan et al. [41]	$1.39$–$1.61$	Cluster/field	Massive passive galaxies	$R_e$	Passive galaxies in evolved clusters are larger	Significant cluster-to-cluster variation
S. Andreon [3]	$\lesssim2$	Cluster/field	Red-sequence ETGs	$R_e$	Faster early size growth in clusters	Environmental difference decreases toward low $z$
E. Annunziatella et al. (2022)	$1.98$	Cluster/field	Bulge-like QGs	$R_e$	Cluster QGs larger	$6^{+2}_{-1}$ larger in mass $M_\ast\lesssim10^{11.5}M_\odot$
A. V. Afanasiev et al. [1]	$1.4$–$2.8$	Cluster/field	Passive ETGs	$R_e$	Massive cluster ETGs larger	Main signal at $\log(M_\ast/M_\odot)>10.5$
A. Ghosh et al. [65]	$\sim0.7$	Projected density	Mixed; morphology/SF split	Radius	Dense-region galaxies larger	Up to $\sim25\%$; weakens with redshift and depends on mass/morphology
Smaller sizes in denser environments for the quoted population
M. Cebrián & L. Trujillo (2014b)	$<0.12$	Local density	Early- and late-type	$R_e$	Dense-environment galaxies slightly smaller	Stronger for low-mass late types
J. H. Harker et al. (2019)	$0.86$–$1.34$	Cluster/field	SFGs and QGs	$R_e$	Cluster galaxies smaller	Effects of order $\sim0.07$–$0.08$ dex for the quoted populations
C. Xu et al. (2023)	$2.51$	Cluster/field comparison	Massive cluster galaxies	$R_e$-morphology	Cluster galaxies more compact	High-$z$ starbursting cluster; different evolutionary regime
N. Chamba et al. [40]	$\leq0.02$	Faint?	Broad mass range, including dwarfs	Galaxy-edge radius	Faint galaxies smaller	Uses an edge-based size metric rather than conventional $R_e$
A. George et al. [64]	$0.1$–$0.85$	Cluster/field	QGs	$V$-proportional $R_e$	Cluster QGs smaller	Difference is stronger in rest-UV than rest-optical

The diversity in Table B1 motivates caution when reducing the size literature to a single “cluster versus field” sign. For example, D. T. Maltby et al. [100] found no measurable environmental dependence for ellipticals, S0s, and high-mass spirals, while finding tentative evidence that low-mass cluster spirals are smaller. Conversely, the high-mass ETG signal reported by Y. Yoon et al. [172] appears only above $M_\ast\sim10^{11.2}M_\odot$. At high redshift, several studies report larger passive galaxies in dense environments (e.g., [123, 51, 149, 117, 1]), whereas other work finds no significant difference (e.g., [116, 135]) or smaller systems in clusters for different populations and redshift ranges (e.g., [103] (C. Xu et al. 2023)). More recent work further shows that the inferred environmental signal can depend on the adopted size definition and rest-frame wavelength ([40, 64]). Our evolutionary-stage split should therefore be viewed as one additional axis that helps organize this heterogeneous literature, not as a unique explanation for all previous discrepancies.

Star formation, quenching, and transition populations

The environmental dependence of star formation is considerably more robust than that of size, but even here it is important to distinguish a change in the fraction of star-forming galaxies from a shift in the SFR distribution within the star-forming population. This distinction is directly relevant to our detection of residual SFR suppression among galaxies that have not yet entered the fully quiescent class. Reviews of gas-removal and satellite-quenching processes are given by A. Boselli & G. Gavazzi (2006) and [48].

An important nuance is provided by M. L. Balogh et al. [14]: the fraction of star-forming systems changes strongly with density, while the H$\alpha$ equivalent-width distribution among galaxies that remain star forming is approximately independent of environment in their low-redshift sample. The literature therefore does not require a universal continuous SFR suppression within every star-forming sample. Our residual result should instead be stated as an additional observational constraint for our particular mass, redshift, environment, and SFR selection. Likewise, transition-galaxy fractions are definition dependent ([46, 82, 106]); we therefore interpret our operational H$\alpha$-low UVJ-SF class as a useful transition tracer rather than a unique or model-independent quenching stage.

Stellar-population indicators

These studies support using $D_{n}4000$ as a tracer of differences in recent star-formation history, but not as a one-parameter age clock. In particular, $D_{n}4000$ is sensitive to both stellar age and metallicity, and its interpretation becomes increasingly degenerate for older populations. We therefore describe positive cluster–field $D_{n}4000$ residuals as evidence for systematically different, typically more evolved recent SFHs, rather than converting them directly into a unique age offset or quenching timescale.

Morphology, bulge prominence, and structural transformation

The terminology is important for the interpretation of our $B/T$ result. A larger light-based $B/T$ can reflect genuine growth of the bulge, fading or truncation of the disk, or both. We therefore use “enhanced bulge prominence” or “structural transformation” rather than treating $\Delta(B/T)>0$ as direct evidence for bulge stellar-mass growth. This conservative interpretation is consistent with studies showing that star-formation state, stellar mass, and morphology are strongly covariant and that residual environmental effects can remain for satellites [15, 146, 24, 122].

Reference	$z$	Environment/sample	Principal SF result	Population-level implication	Relevance/caveat
G. Kauffmann et al. [83]	Low $z$	SDSS; local density	SFH indicators vary strongly with environment at fixed $M_\ast$	Dense regions host more evolved populations	Structural indicators show weaker residual trends
M. L. Balogh et al. [14]	$0.05$–$0.2$	SDSS+2dFGRS; density/groups	SF fraction declines with density	Strong population-mix effect	H$\alpha$ distribution of the SF population is nearly environment-independent
Y.-J. Peng et al. [127]	$0$–$1$	SDSS+COSMOS; density	Mass- and environment-quenching are statistically separable	Environment preferentially raises passive fraction	Framework rather than a cluster-specific mechanism
Y.-J. Peng et al. [126]	Low $z$	SDSS; centrals/satellites	Satellite quenching drives much of the environmental signal	Satellites are the environmentally affected population	Useful for interpreting our satellite-only analysis
A. R. Wetzel et al. [162]	Low $z$	SDSS group/cluster	Satellite quenched fraction is enhanced	Broad SF distribution persists in satellites	Active satellites need not show a large continuous SFR shift
A. R. Wetzel et al. [163]	Low $z$	SDSS satellites	Delayed-then-rapid quenching histories	Environmental effects depend on time since infall	Projected radius is not itself a clock
C. F. Haines et al. [73]	$\sim0.15$–$0.30$	LoCuSS clusters	Slow suppression plus pre-processing is required	Quenching begins beyond the core for some systems	Supports a broad radial response
H. Y. Jian et al. [81]	$0.2$–$1.1$	HSC groups/clusters	Environment enhances quenching relative to field	Strong mass dependence	Directly relevant HSC-based comparison
V. Coenda et al. [46]	Low $z$	Field/groups/$R_{\rm vir}$ clusters	GV properties and abundance depend on environment	Transition populations depend on environment	GV definition is selection-dependent
H.-Y. Jian et al. [82]	$0.2$–$1.1$	HSC environments	GV evolution depends on environment and redshift	Transition statistics depend on environmental/sf history	Avoids treating GV fraction as a universal quenching-rate proxy
K. McNab et al. [106]	$\sim1$	GOGREEN clusters/field	Transition excess is strongest at lower stellar mass	Environmental transition population is mass dependent	High-mass excess can be weak/absent
A. Paulino-Afonso et al. (2022)	$\sim0.8$	VIMOS/GOODS-CDFS field	Spectral SFH indicators vary with environment	Denser environments host more evolved SFHs	Connects emission lines and $D_{4000}$ ordering temporally
K. Oomann et al. (2024)	Low $z$	SDSS+ALFALFA groups/clusters	Gas stripping produces observable SF quenching	Different phases respond on different timescales	Supports caution in interpreting radial ordering
P. H. Goubert et al. [66]	Low $z$	SDSS + hydrodynamical simulations	Environment is most predictive for low-mass satellite quenching	Intrinsic predictors dominate centrals/high-mass satellites	Closely related to our mass-dependent environmental response

Reference	$z$	Indicator(s)	Environment/sample	Reported result	Interpretation relevant here
M. L. Balogh et al. [12]	$0.18$–$0.55$	$D_{4000}$, H$\delta$, [O II]	CNOC1 clusters/field	Spectral populations vary with cluster radius/environment	Direct evidence for environmentally varying recent SFHs
G. Kauffmann et al. [83]	Low $z$	$D_{4000}$, SFR and structure	SDSS local density	SFH indicators show strong residual environment dependence	Spectral response can exceed structural response
A. Paulino-Afonso et al. [124]	$\sim0.8$	$D_{4000}$, H$\delta$, [O II]	VIS$^3$COS density field	Spectral indices vary systematically with environment	Directly comparable to our $D_{4000}$ analysis
D. Sobral et al. [147]	$\sim0.6$–$1.0$	$D_{4000}$, H$\delta$	LEGA-C environments; QGs	Environment-dependent stellar-population assembly histories	Demonstrates that different age-sensitive indices need not respond identically
A. B. Newman et al. [116]	$1.80$	Composite absorption-line spectra/ages	JKCS 041 cluster/field QGs	Mean QG ages are similar to field comparison	Useful high-$z$ null result; environment can change fractions without shifting mean QG age

Reference	$z$	Structural diagnostic	Environment/sample	Main result	Relevance/caveat
A. Dressler [59]	Low $z$	Visual morphology	Rich-cluster projected density	Early-type fraction rises with density	Classical morphology–density relation
G. Kauffmann et al. [83]	Low $z$	Concentration/structure	SDSS local density	Structural residuals are weaker than SFH residuals at fixed $M_\ast$	Environment acts strongly through population/SFH changes
S. P. Bamford et al. [15]	Low $z$	Galaxy Zoo morphology + color	Density/group-centric distance	Both color and morphology depend on environment	Color–density relation remains stronger at fixed mass
R. A. Skibba et al. [146]	Low $z$	Galaxy Zoo morphologies	Marked correlations	Residual morphology–environment relation weak after controlling for color	Highlights covariance between SF state and morphology
C. N. A. K. B. et al. (2013)	Low $z$	Bulge–disc decomposition	SDSS environment	Environment affects disc/bulge populations differently	A change in light-based $B/T$ need not imply pure bulge mass growth
A. F. L. Bluck et al. [23]	Low $z$	Central structure + quenching diagnostics	SDSS central/satellites	Internal and environmental predictors differ for central/satellite	Motivates separating satellite-specific environmental effects
A. F. L. Bluck et al. [24]	Low $z$	Sérsic/$R_e$ and other structure	SDSS/VLS environment	SFR and $M_\ast$ are the strongest predictors of $B/T$	Directly relevant to multivariate interpretation
A. Paulino-Afonso et al. [125]	$\sim0.8$	Size, Sérsic index, morphology	VISTA/UDS density field	Structure depends on both nature and nurture, with strong mass/SF covariance	Relevant intermediate-$z$ comparison
E. N. Oesch et al. (2021)	$1.98$	Sérsic index + size	XLSS J1221 cluster/field	Excess bulge-like QGs and larger QGs in the cluster	Demonstrates coupled population/structural differences at high $z$
M. Oxland et al. [122]	Low $z$	Morphology + SFR after infall	Groups/clusters	Quenching and morphological transformation both evolve after infall	Their characterizations of morphology and SF may not be synchronous; strongest environmental effects at low mass

Studies jointly connecting star formation and structure

Table B5 collects a smaller set of studies that are particularly useful for interpreting our multivariate analysis because they explicitly connect more than one of star formation, stellar populations, and structure. We intentionally omit nonenvironmental age–size studies from this table; such work can inform physical interpretation but is not a direct environmental comparison.

Reference	$z$	Environment/sample	Star-formation/stellar-population result	Structural result	Main interpretation	Connection to this work
G. Kauffmann et al. [83]	Low $z$	SDSS local density	Strong environmental differences in SFH indicators	Weaker structural residuals at fixed $M_{\ast}$	SFH is highly environment sensitive	Supports treating SFH and structure as correlated but non-equivalent responses
S. P. Bamford et al. [15]	Low $z$	Galaxy Zoo + SDSS	Color strongly environment dependent	Morphology also environment dependent	Color and morphology respond differently	Motivates avoiding a single-property environmental interpretation
A. F. L. Bluck et al. [24]	Low $z$	SDSS/MaNGA; centrals/satellites	$\Delta\mathrm{SFR}$ is a dominant predictor	$B/T$ tightly coupled to $\Delta\mathrm{SFR}$ and $M_{\ast}$	Structure–quenching coupling exceeds most direct environment predictors	Closely parallels our significant $\Delta\mathrm{SFR}$–$\Delta(B/T)$ relation
A. Paulino-Afonso et al. [125]	$\sim0.8$	VIS3COS density field	SF state covaries with environment	Size/Sérsic/morphology studied versus density	Nature and nurture both contribute	Structural companion to the VIS3COS spectral analysis
A. Paulino-Afonso et al. [124]	$\sim0.8$	VIS3COS density field	[O II], H$\delta$, and $D_n4000$ vary with environment	Interpreted together with morphology work	Environment modifies recent SFHs	Direct comparison for our spectroscopic residuals
J. Matharu et al. [103]	0.86–1.34	GCLASS cluster/field	Galaxies separated by SF state	Cluster SFGs and QGs are smaller than field analogs	Environment-dependent size evolution is population dependent	Relevant to our stage-dependent $R_{\mathrm{e}}$ residuals
J. Matharu et al. [104]	0.86–1.34	Cluster post-starbursts	PSBs identify recently quenched systems	PSB sizes are intermediate between SFGs and QGs	Fading/quenching can alter light-weighted structure	Relevant to the strong structural signal in our transition population
J. Matharu et al. [105]	$\sim1$	Cluster/field; resolved H$\alpha$	Recently quenched systems show rapid environmental suppression	H$\alpha$ spatial extent is truncated relative to stellar continuum	Supports outside-in quenching of star formation	Physical analogue for spatially ordered SF suppression, not a direct continuum-size measurement
E. Noordeh et al. [117]	1.98	XLSSC 122 cluster/field	Strongly enhanced QG fraction	Enhanced large-size QG fraction	Population mix and structure are jointly environment dependent	Directly supports our cautions about composition-driven structural offsets
M. Choi et al. (2022)	2.51	High-$z$ cluster/field comparison	Enhanced quiescent fraction in dense environments	Morphological transformation accompanies quenching	Quenching and morphology evolve together in dense environments	Provides a high-redshift analogue for our joint interpretation

Taken together, the literature supports three conservative conclusions that are directly relevant to our analysis. First, environmental quenching is robust at the population level, but the amount of SFR suppression within galaxies that remain formally star forming is sample dependent ([14, 162, 81]). Second, the sign and amplitude of the environmental size residual depend on population selection, mass, redshift, and measurement definition ([100, 87, 51, 103, 1, 65, 40, 64]). Third, morphology and star-formation state are tightly covariant, so an environmental $B/T$ residual should not be interpreted independently of the accompanying SFR and stellar-population residuals ([15, 146, 24, 122]). These considerations motivate the matched, stage-resolved, and multivariate analysis adopted in the main text.