# COSMOS-Web: Unraveling the Evolution of Galaxy Size and Related Properties at 2 < z < 10

Lilan Yang, Jeyhan S Kartaltepe, Maximilien Franco, Xuheng Ding, Mark J

Achenbach, Rafael C Arango-Toro, Caitlin M Casey, Nicole E Drakos,

Andreas L Faisst, Steven Gillman, et al.

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## ► To cite this version:

Lilan Yang, Jeyhan S Kartaltepe, Maximilien Franco, Xuheng Ding, Mark J Achenbach, et al.,

COSMOS-Web: Unraveling the Evolution of Galaxy Size and Related Properties at 2 < z < 10.

The Astrophysical Journal Supplement Series, 2025, 281 (2), pp.68. 10.3847/1538-4365/ae0e1b.

hal-05470236

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Submitted on 21 Jan 2026

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
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# COSMOS-Web: Unraveling the Evolution of Galaxy Size and Related Properties
at $2 < z < 10$

Lilan Yang<fnref n="1" />, Jeyhan S. Kartaltepe<fnref n="1" />, Maximilien Franco<fnref n="2" />,<fnref n="3" />, Xuheng Ding<fnref n="4" />, Mark J. Achenbach<fnref n="5" />, Rafael C. Arango-Toro<fnref n="6" />, Caitlin M. Casey<fnref n="3" />,<fnref n="7" />,<fnref n="8" />, Nicole E. Drakos<fnref n="9" />, Andreas L. Faisst<fnref n="10" />, Steven Gillman<fnref n="8" />,<fnref n="11" />, Ghassem Gozalias<fnref n="12" />,<fnref n="13" />, Marc Huertas-Company<fnref n="14" />,<fnref n="15" />,<fnref n="16" />, Shuowen Jin<fnref n="8" />,<fnref n="11" />,<fnref n="29" />, Daizhong Liu<fnref n="17" />, Georgios Magdis<fnref n="8" />,<fnref n="11" />,<fnref n="18" />, Richard Massey<fnref n="19" />, John D. Silverman<fnref n="20" />,<fnref n="21" />, Takumi S. Tanaka<fnref n="22" />,<fnref n="23" />,<fnref n="24" />, Si-Yue Yu<fnref n="20" />,<fnref n="21" />, Hollis B. Akins<fnref n="3" />, Natalie Allen<fnref n="8" />,<fnref n="18" />, Olivier Ilbert<fnref n="6" />, Anton M. Koekemoer<fnref n="25" />, Henry Joy McCracken<fnref n="26" />, Louise Paquereau<fnref n="26" />, Jason Rhodes<fnref n="27" />, Brant E. Robertson<fnref n="28" />, Marko Shuntov<fnref n="8" />,<fnref n="18" />, and Sune Toft<fnref n="8" />,<fnref n="18" />

## Abstract

We measure galaxy sizes from $2 < z < 10$ using COSMOS-Web, the largest-area JWST imaging survey to date, covering ~0.54 deg<fnref n="2" />. We analyze the rest-frame optical (~5000 Å) size evolution and its scaling relation with stellar mass ($R_e \propto M_*^\alpha$) for star-forming and quiescent galaxies. For star-forming galaxies, the slope $\alpha$ remains approximately 0.20 at $2 < z < 8$, showing no significant evolution over this redshift range. At higher redshifts, the slopes are $-0.13 \pm 0.15$ and $0.37 \pm 0.36$ for $8 < z < 9$ and $9 < z < 10$, respectively. At fixed galaxy mass, the size evolution for star-forming galaxies follows $R_e \propto (1+z)^{-1.21\pm0.05}$. For quiescent galaxies, the size-mass relation is steeper with $\alpha \sim 0.5-0.8$ at $2 < z < 5$, and size evolves as $R_e \propto (1+z)^{-0.81\pm0.26}$. We find that the size-mass relation is consistent between UV and optical at $z < 8$ for star-forming galaxies. However, we observe a decrease in the slope from UV to optical at $z > 8$, with a tentative negative slope in the optical at $8 < z < 9$, suggesting a complex interplay between intrinsic galaxy properties and observational effects such as dust attenuation. We discuss the ratio between galaxies' half-light radius and underlying halos' virial radius, $R_{vir}$, and find the median value of $R_e/R_{vir} = 2.7\%$. The star formation rate surface density evolves as $\log(\Sigma_{SFR}/(M_{\odot}/\text{yr}/\text{kpc}^2)) = (0.20 \pm 0.08)z + (-0.65 \pm 0.51)$, and the $\Sigma_{SFR}-M_*$ relation remains flat at $2 < z < 10$. Lastly, we identify a threshold in stellar mass surface density $\log(\Sigma_e/(M_{\odot}/\text{kpc}^2)) \sim 9.5-10$ marking the transition to compact, quenched galaxies from extended, star-forming progenitors. In summary, our

<figure><img src="image_4.png" /></figure>

<footnote n="1">¹ Laboratory for Multiwavelength Astrophysics, School of Physics and Astronomy, Rochester Institute of Technology, 84 Lomb Memorial Drive, Rochester, NY 14623, USA</footnote>

<footnote n="2">² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France</footnote>

<footnote n="3">³The University of Texas at Austin, 2515 Speedway Boulevard, Stop C1400, Austin, TX 78712, USA</footnote>

<footnote n="4">⁴School of Physics and Technology, Wuhan University, Wuhan 430072, People's Republic of China</footnote>

<footnote n="5">⁵ Department of Physics and Astronomy, University of Hawaii at Manoa, 2505 Correa Road, Honolulu, HI 96822, USA</footnote>

<footnote n="6">⁶ Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France</footnote>

<footnote n="7">⁷ Department of Physics, University of California, Santa Barbara, Santa Barbara, CA 93109, USA</footnote>

<footnote n="8">⁸ Cosmic Dawn Center (DAWN), Denmark</footnote>

<footnote n="9">⁹ Department of Physics and Astronomy, University of Hawaii, Hilo, 200 W Kawili Street, Hilo, HI 96720, USA</footnote>

<footnote n="10">¹⁰ Caltech/IPAC, MS 314-6, 1200 E. California Boulevard, Pasadena, CA 91125, USA</footnote>

<footnote n="11">¹¹ DTU-Space, Technical University of Denmark, Elektrovej 327, DK-2800 Kgs. Lyngby, Denmark</footnote>

<footnote n="12">¹² Department of Computer Science, Aalto University, P.O. Box 15400, FI-00076 Espoo, Finland</footnote>

<footnote n="13">¹³ Department of Physics, University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland</footnote>

<footnote n="14">¹⁴ Instituto de Astrofísica de Canarias, La Laguna, Tenerife, Spain</footnote>

<footnote n="15">¹⁵ Universidad de la Laguna, La Laguna, Tenerife, Spain</footnote>

<footnote n="16">¹⁶ Université Paris-Cité, LERMA - Observatoire de Paris, PSL, Paris, France</footnote>

<footnote n="17">¹⁷ Purple Mountain Observatory, Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, People's Republic of China</footnote>

<footnote n="18">¹⁸ Niels Bohr Institute, University of Copenhagen, Jagtvej 128, DK-2200, Copenhagen, Denmark</footnote>

<footnote n="19">¹⁹ Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road, Durham DH1 3LE, UK</footnote>

<footnote n="20">²⁰ Kayli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba 277-8583, Japan</footnote>

<footnote n="21">²¹ Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan</footnote>

<footnote n="22">²² Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan</footnote>

<footnote n="23">²³ Kayli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan</footnote>

<footnote n="24">²⁴ Center for Data-Driven Discovery, Kayli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan</footnote>

<footnote n="25">²⁵ Space Telescope Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA</footnote>

<footnote n="26">²⁶ Institut d'Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, F-75014 Paris, France</footnote>

<footnote n="27">²⁷ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91001, USA</footnote>

<footnote n="28">²⁸ Department of Astronomy and Astrophysics, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA</footnote>

<footnote>Received 2025 April 4; revised 2025 September 23; accepted 2025 September 29; published 2025 December 12</footnote>

<footnote n="29">²⁹ Marie Curie Fellow.</footnote>
findings show that the extensive COSMOS-Web dataset at $z > 3$ provides new insights into galaxy size and related properties in the rest-frame optical.

*Unified Astronomy Thesaurus concepts: Galaxy evolution (594); Galaxy structure (622)*

# 1. Introduction

In the standard Lambda cold dark matter (ΛCDM) cosmology, galaxy structure forms hierarchically. In the early Universe, there are small density fluctuations in the overall matter distribution, where small dark matter halos form first and then aggregate into larger systems. Baryonic gas falls into the dark matter halos, undergoing processes such as cooling and condensation, leading to the formation of galaxies. Larger dark matter halos are expected to carry a larger amount of baryonic gas, hence corresponding to more massive galaxies (for details, see a review by R. H. Wechsler & J. L. Tinker 2018). Additionally, both dark matter and diffuse gas acquire their angular momentum via tidal torques and galaxy mergers; therefore, the structure of galaxies follows the properties of dark matter to a certain degree.

Examining the evolution of galaxy size and its correlation with other physical parameters is vital to studying the fundamental physics of their growth. Over the past several decades, observations from both ground- and space-based telescopes have obtained fruitful results (S. Shen et al. 2003; R. J. Williams et al. 2010; M. Mosleh et al. 2012; A. van der Wel et al. 2014; T. Shibuya et al. 2015; L. Kawinwanichakij et al. 2021; L. Yang et al. 2021; R. J. Bouwens et al. 2022; L. Yang et al. 2022a). For example, in the local Universe, S. Shen et al. (2003) utilized Sloan Digital Sky Survey data and found that the size distribution at a given luminosity is well described by a lognormal function at $z \lesssim 0.3$. Later, the Hubble Space Telescope (HST) pushed our understanding to new frontiers. A. van der Wel et al. (2014) found that at $0 < z < 3$ galaxy size evolves as $R_e \propto (1+z)^{-0.75}$ at a fixed stellar mass for star-forming galaxies (SFGs), and the size-mass relation follows $R_e \propto M^{0.22}$. Their measurements were performed at rest-frame 5000 Å.

At $z > 3$, the wavelength range of Hubble limits the investigation of the evolution of galaxy size to the rest-frame ultraviolet (UV; P. A. Oesch et al. 2010; T. Shibuya et al. 2015; R. J. Bouwens et al. 2017; R. A. A. Bowler et al. 2017; L. Yang et al. 2022a). For example, T. Shibuya et al. (2015) report that the size of Lyman break galaxies evolves as $R_e \propto (1+z)^{-1.1}$ at $z = 0-10$ at a given luminosity. The UV size-luminosity relation at these high redshifts not only is important for understanding galaxy formation and evolution but also has implications for the UV luminosity function and, hence, the properties of galaxies at the epoch of reionization (A. Grazian et al. 2012; E. Curtis-Lake et al. 2016; R. J. Bouwens et al. 2017).

The assembly history of quiescent galaxies (QGs) is distinct from that of SFGs. The size evolution at a given mass occurs faster, and the slope of the size-mass relation is steeper. For example, A. van der Wel et al. (2014) found that QG size evolves with redshift as $R_e \propto (1+z)^{-1.48}$ and its correlation with mass is $R_e \propto M^{0.75}$, at $0 < z < 3$ in the rest-frame optical. Unlike SFGs, the size growth of QGs is primarily driven by galaxy mergers. Theoretically, two possible merger scenarios are each linked to the mass ratio of progenitor galaxies (see derivation in T. Naab et al. 2009). Minor mergers contribute size growth proportional to the increase in stellar mass,

$\Delta R \propto \Delta M_*$, and major mergers between gas-poor galaxies of similar stellar mass produce size growth $\Delta R \propto \Delta M_*^2$.

Overall, the evolution of galaxy size in SFGs and QGs, along with its scaling relation with mass and luminosity, has been well characterized in the rest-frame optical using HST data at $z < 3$, and up to $z \sim 10$ for SFGs but in the rest-frame UV (e.g., T. Shibuya et al. 2015). However, galaxies' size measured from the rest-frame UV is not a good tracer of the overall stellar mass. The UV light is emitted from young massive short-lived stars that may be distributed differently than the bulk of the stellar mass (older stars) and may also suffer from significant dust extinction. Longer-wavelength emission traces a galaxy's mass distribution more effectively because it is dominated by older, low-mass stars that constitute most of the galaxy's stellar mass. It is also less affected by dust extinction, providing a clearer view of the galaxy's true mass (N. M. Förster Schreiber & S. Wuyts 2020). Before the launch of the James Webb Space Telescope (JWST), simulations offered testable predictions for the rest-frame optical size of galaxies and its scaling relations with mass/luminosity at high redshifts ($z > 3$), as well as size as a function of wavelength (X. Ma et al. 2018; X. Wu et al. 2020; G. Popping et al. 2021; M. A. Marshall et al. 2022; W. J. Roper et al. 2022; X. Shen et al. 2024), and we are able now to test that.

JWST is now revolutionizing our understanding of galaxies by providing broad wavelength coverage, unprecedented depth, and high spatial resolution across a broad wavelength range. At $z > 3$, the NIRCam instrument (e.g., with the F448W filter) enables us to probe the rest-frame optical size of galaxies out to $z \sim 7$ at a similar angular resolution to that provided by HST WFC3-IR in the rest-frame UV (i.e., F160W). In addition, multiple NIRCam filters sampling the rest-frame optical (e.g., covering the 4000 Å break) benefit the determination of galaxies' stellar populations and their properties, such as stellar mass. Many recent JWST studies focus on galaxy structures in the rest-frame optical, examining their relationship with luminosity or stellar mass and comparing these findings with those obtained from rest-frame UV observations or simulations. For instance, L. Yang et al. (2022b) explored galaxy size and its wavelength-dependent correlation with luminosity at $z > 7$, finding that the median size in the rest-frame optical is compatible with but slightly larger than that in the UV. Several studies have investigated the evolution of the size-mass relation of SFGs at $z > 3$ (T. Morishita et al. 2024; K. Ormerod et al. 2024; E. Ward et al. 2024; N. Allen et al. 2025; T. B. Miller et al. 2025). The number of observed QGs at $z > 3$ has also increased significantly, enabling more robust statistical analyses (K. Ito et al. 2024; L. Wright et al. 2024). However, these studies are based on relatively small sample sizes. To enable an unbiased statistical analysis, a larger sample of both SFGs and QGs is required.

The COSMOS-Web survey, the largest survey selected in JWST Cycle 1 (PIs: J. Kartaltepe & C. Casey; C. M. Casey et al. 2023), covering ~0.6 deg², provides an extensive dataset for this study. The primary goals of this work are to (1) investigate the size-mass relation of both SFGs and QGs at
$z = 2–10$ and how their properties vary as a function of wavelength, (2) validate the predictions made by cosmological simulations, and (3) gain insights into galaxy growth and quenching mechanisms through the evolution of the star formation rate (SFR) surface density. In summary, we analyze the evolution of galaxy sizes and related properties to gain insights into galaxy growth and quenching processes.

This paper is organized as follows: The data and sample selection for this study are described in Section 2. In Section 3, we present the methodology of our morphological measurements and size-mass relation fitting. In Section 4, we report the results of the size-mass relation and its evolution with redshift for SFGs and QGs, as well as its variation as a function of wavelength in Section 6. We also study the size distribution histogram in different mass bins as a complementary analysis of the size-mass relation in Section 5. Lastly, we discuss and summarize our results in Sections 7 and 8, respectively. Throughout this work, we adopt the standard $\Lambda$CDM cosmology with $\Omega_m = 0.3$, $\Omega_\Lambda = 0.7$, and $H_0 = 70 \text{ km s}^{-1} \text{ Mpc}^{-1}$; AB system magnitudes (J. B. Oke & J. E. Gunn 1983); and a G. Chabrier (2003) initial mass function for computing stellar masses.

## 2. Data

### 2.1. The COSMOS-Web Survey

The COSMOS-Web survey is the largest survey selected for observations during JWST Cycle 1 and consists of 0.54 deg² Near-Infrared Camera (NIRcam) observations in four filters (F115W, F150W, F277W, and F444W) and 0.2 deg² Mid-Infrared Imager (MIRI) observations in F770W (PIs: Kartaltepe & Casey; C. M. Casey et al. 2023). The depth of the NIRCam data is measured to be 26.6–27.3 mag (F115W), 26.9–27.7 mag (F150W), 27.5–28.2 mag (F277W), and 27.5–28.2 mag (F444W) for 5$\sigma$ point sources calculated within 0.15-radius apertures. The depths of the MIRI observations are 25.33–25.98 mag calculated within 0.3-radius apertures. The full details of the NIRCam and MIRI data reduction are presented by M. Franco et al. (2024, 2025) and S. Harish et al. (2025), respectively.

The COSMOS-Web data were obtained during three observing windows, 2023 January, 2023 April, and 2023 December/2024 January, with a handful of pointings observed during 2024 April/May. The final NIRcam mosaics<fnref n="30" /> are created with two different pixel scales, 30 and 60 mas. In this paper, we use the 30 mas pixel scale mosaic.

### 2.2. COSMOS-Web Photometric Catalog

Details of the multiwavelength photometry extraction and catalog construction are fully described by M. Shuntov et al. (2025). Here we summarize key relevant features.

#### 2.2.1. SE++ Photometry

M. Shuntov et al. (2025) performed source extraction across 33 ground- and space-based filters using a multiband model-fitting approach with SOURCEXTRACTOR++ (SE++; E. Bertin et al. 2020; M. Kümmel et al. 2020), which is an updated version of the widely used SExtractor package (E. Bertin & S. Arnouts 1996). SE++ fits Sérsic parametric models to extract source photometry for all detected sources

across available filters. For each source, the structural parameters are kept the same for all filters; thus, the structural parameters correspond to the averaged morphology over a wide wavelength range. For the purpose of this work and also to maximize the scientific application of the catalog, i.e., investigating galaxy structure as a function of wavelength, we provide an alternative morphology catalog (L. Yang et al. 2025, in preparation) that models each galaxy with separate Sérsic profiles across the four NIRCam bands, as described in Section 3.

#### 2.2.2. SED Fitting

The template spectral energy distribution (SED) fitting code LEPHARE (S. Arnouts et al. 2002; O. Ilbert et al. 2006) is used to derive photometric redshifts and physical parameters from the SE++-model-based photometry for each source in the full catalog (M. Shuntov et al. 2025). The template fitting is based on G. Bruzual & S. Charlot (2003) models with diverse star formation histories, ages, and dust attenuation curves (D. Calzetti et al. 2000; S. Arnouts et al. 2013; S. Salim et al. 2018). Emission lines and intergalactic medium absorption are modeled following S. Saito et al. (2020) and P. Madau (1995), respectively. LEPHARE provides the probability density function (pdf) of the photometric redshift for each source, and the median value is adopted in this work. The physical parameters (e.g., stellar mass, SFR, etc.) are then calculated using this fixed redshift.

Based on a comparison with available spectroscopic redshifts in the field (A. A. Khostovan et al. 2025), the photometric redshifts computed via LEPHARE have a high level of confidence. The scatter $\sigma_{NMAD}$ is approximately 0.013 for galaxies with $m_{F444} < 25$, where $\sigma_{NMAD} = 1.48 \times \text{median}[(|\Delta z - \text{median}(\Delta z)|)/(1 + z_{\text{spec}})]$, $\Delta z = z_{\text{phot}} - z_{\text{spec}}$; see Table 1 in M. Shuntov et al. (2025). Additional assessment of stellar mass estimates is delivered by comparison with results measured by CIGALE (M. Boquien et al. 2019), employing nonparametric star formation history modeling and alternative dust attenuation laws. Detailed comparisons between LEPHARE and CIGALE are also provided by M. Shuntov et al. (2025). In this work, we adopt the stellar mass obtained by LEPHARE.

### 2.3. Sample Selection

We initially selected our sample at $2 < z < 10$ in eight redshift bins with bin width $\Delta z = 1$ from the parent COSMOS-Web SE++ galaxy catalog. Following M. Shuntov et al. (2025), we apply the bright star mask to remove sources near bright stars and an F444W magnitude cut ($m_{F444W} = 27.5$) to ensure that the flux in the rest-frame optical is robustly measured. We adopt the median value of the redshift pdf as the photometric redshift in this work, and we remove sources with poorly constrained photo-z, specifically those with a 68% confidence level width greater than the width of our redshift bins. After these selections, the sample contains 84,820 galaxies. Additionally, we remove stars and brown dwarfs using the $\chi^2_{\text{star}}$ of the star/brown dwarf SED templates fit by LEPHARE, resulting in the removal of 0.6% of the sample.

We also exclude potential active galactic nuclei (AGN) to avoid contamination in the measurement of galaxy physical properties. We remove sources with X-ray counterparts by

<footnote n="30">³⁰ https://cosmos.astro.caltech.edu/page/cosmosweb</footnote>
cross-matching within 1" with the catalog of F. Civano et al. (2016) or those listed in the little red dot (LRD) catalog of H. B. Akins et al. (2025). LRDs are very red compact sources identified at high redshift that potentially host strong AGN (e.g., D. D. Kocevski et al. 2023; J. Matthee et al. 2024). We identify further AGN candidates by requiring that $\chi^2_{AGN} < \chi^2_{gal}$ and that the size is smaller than 60 mas (corresponding to half the FWHM of the F277W point-spread function (PSF)). This step removed a further 0.3% of the sample.

To ensure that our galaxy sample is above the completeness limit at all redshifts, we select galaxies with stellar mass $log M_*/M_\odot > 9$. This mass cut is chosen because, as demonstrated in M. Shuntov et al. (2025), the COSMOS-Web survey achieves 95% stellar mass completeness down to $log M_*/M_\odot = 7.5 - 8.8$ at $0.2 < z < 12$. The galaxies with $log M_*/M_\odot > 9$ are well above the completeness threshold for the entire redshift range of $2 < z < 10$. This mass cut removed 63.8% of the sample, yielding 30,300 galaxies for analysis.

One of our main goals is to study the size-mass relation of SFGs and QGs. The next step is to separate galaxies into those two classes. Following the approach of O. Ilbert et al. (2013), we utilize the near-UV (NUV) $-r-J$ $^{31}$color diagram to separate the sample into QGs and SFGs. Galaxies with criteria

$$M_{\text{NUV}} - M_r > 3(M_r - M_J) + 1 \\ \text{and } M_{\text{NUV}} - M_r > 3.1 \qquad (1)$$

are classified as QGs. Figure 1 shows the distribution of our sample in NUV $-r-J$ space and color coded by their specific SFR (sSFR). The magenta lines in each panel mark the division, with galaxies in the upper-left corner considered to be quiescent and the rest classified as star-forming.

The sSFR is also commonly used to separate QGs and SFGs. QGs are often defined as having $log(sSFR) < log(0.2/t_{obs})$, where $t_{obs}$ is the age of the Universe at the corresponding redshift (C. Pacifici et al. 2016; A. C. Carnall et al. 2023). Galaxy counts classified by the color-color criteria and with the sSFR criteria are also labeled in Figure 1. For example, at $2 < z < 3$, we identify 469 galaxies as quiescent in the NUV $-r-J$ diagram, with 356 (76%) of these also satisfying the threshold $log(sSFR/\text{yr}^{-1}) < -10.1$. Within a redshift bin, we adopt the same threshold that is calculated via the center redshift value. In our work, to select a conservative sample of QGs, we require that galaxies pass both the color-color and sSFR criteria. For SFGs, we also impose the condition that $log(sSFR) > log(0.2/t_{obs})$. Galaxies that pass the color-color criteria but do not satisfy the sSFR criterion are excluded. These galaxies may correspond to transitioning systems (green valley galaxies) that appear blue but have low sSFR, representing galaxies in the process of quenching (W. Chang et al. 2022). Alternatively, they could be dust-reddened SFGs with relatively high sSFR, where the red colors are due to dust attenuation rather than true quiescence (Y.-H. Hwang et al. 2021). Our sample now comprises 29,874 galaxies, including 29,395 SFGs and 479 QGs.

The sample size of QGs can vary based on the selection method—whether using NUV $-r-J$, the traditional UVJ, or methods utilizing NIRCam filters (A. S. Long et al. 2024), which could introduce potential systematic uncertainties. NUV $-r-J$ is a modified version of the UVJ diagram proposed by R. J. Williams et al. (2009). We have also tested the UVJ

selection criteria and compared them with sSFR. Our results indicate that QGs selected using the NUV $-r-J$ criteria better match the sSFR selection, whereas only about 50% of UVJ-selected galaxies meet the sSFR threshold at $2 < z < 3$. Therefore, we adopt the NUV $-r-J$ method in this work.

### 3. Size Measurement

To measure the size of the galaxies in our sample, we use the 2D Sérsic model to fit the surface brightness profile of galaxies (J. L. Sersic 1968),

$$I(r) = I_0 \exp \left[ -b_n \left( \frac{R}{R_e} \right)^{\frac{1}{n_{\text{sérsic}}} - 1} \right], \qquad (2)$$

where $I_0$ is the surface brightness amplitude at the half-light radius $R_e$, $n_{\text{sérsic}}$ is the Sérsic index, and $b_n$ is a parameter dependent on $n_{\text{sérsic}}$. $R = \sqrt{x^2 + y^2/q^2}$, where $(x, y)$ are the coordinates of the image and $q$ is the axis ratio. We utilize the Python software package Galight (X. Ding et al. 2020) to perform the surface brightness profile fitting, $^{32}$ which inherits the image modeling capabilities of Lenstronomy (S. Birrer et al. 2021).

The detailed process of size measurement and uncertainty assessment will be described by L. Yang et al. (2025, in preparation), but here we provide a summary. Before fitting the surface brightness profile, it is necessary to determine the appropriate image cutout size, which should balance computational efficiency while being large enough to encompass the entire galaxy. We use a cutout radius of 5 times the size of the galaxy as measured in the parent SE++ catalog, with a minimum radius of 30 pixels and a maximum radius of 200 pixels. A corresponding noise map, i.e., the ERR extension in the i2d fits file, of the same size is also created. The noise map is computed as the square root of the total variance, which includes contributions from background noise, readout noise, and Poisson noise. In some cases, the image cutout may include emissions from nearby sources. We either mask out or model the contaminating sources using additional Sérsic models, depending on their proximity to the central galaxy. For the Sérsic parameters, we set the range of $R_e$ to be between 0.01 and the size of the cutout image, $n_{\text{sérsic}}$ between 0.3 and 9, and the axis ratio $q$ between 0.1 and 1. Disklike galaxies typically have $n_{\text{sérsic}} \sim 1$, while some diffuse galaxies can have even lower values. To accommodate these cases while preventing unphysically shallow profiles, we set the lower boundary of $n_{\text{sérsic}}$ to 0.3. Elliptical galaxies typically have $n_{\text{sérsic}} \sim 4$, and some highly concentrated systems such as brightest cluster galaxies can have extremely high values; therefore, we set the upper limit to 9. For the axis ratio $q$, edge-on disk galaxies have $q \sim 0.2-0.3$, while $q = 1$ indicates a perfect circular system. To ensure reasonable fits, we set $q$ to 0.1-1. The PSF is also crucial for accurate surface brightness profile fitting. The PSF for each filter used in this work is constructed using PSFEx$^{33}$ (E. Bertin 2011); see details in M. Shuntov et al. (2025).

One of the main goals of this work is to study size-related properties as a function of wavelength. To measure the sizes of galaxies in the rest-frame optical and UV, we need to identify the corresponding NIRCam images observed in the appropriate filters.

<footnote>$^{31}$ The effective wavelengths of NUV, $r$, and $J$ are 2306.5, 6231.8, and 12444.1 Å, respectively (O. Ilbert et al. 2009).</footnote>

<footnote>$^{32}$ https://github.com/dartoon/galight</footnote>

<footnote>$^{33}$ https://github.com/astromatic/psfex</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 1.** Rest-frame NUV $r-J$ color–color diagram for galaxies at $2 < z < 10$. Data points are color coded according to their sSFR. The magenta line indicates the NUV $r-J$ criteria (see Equation (1)), separating QGs (top left) from SFGs (bottom right). Additionally, galaxies are required to meet the sSFR criterion, e.g., $\log(\text{sSFR}) < \log(0.2/t_{\text{obs}})$ for QGs, where $t_{\text{obs}}$ is the observed Universe age. In each panel, the numbers of QGs and SFGs classified using the color–color diagram are labeled in black, while those further classified with the additional sSFR criterion are labeled in blue and red inside the bracket.</figcaption></figure>

We select the rest-frame wavelength range 2000–4000 Å (4000–6000 Å) to represent the UV (optical). As shown in Figure 2, the appropriate filters for each rest-frame wavelength range vary between different redshift bins. For example, we select F277W (F444W) to measure the rest-frame UV (optical) at $6 < z < 10$.

We apply the above strategy to fit each of the galaxies in the rest-frame UV and optical. We discard the results if any of the parameters hit the boundaries of the provided ranges, or have a catastrophic fitting performance, i.e., reduced $\chi^2 > 15$. After removing these sources, our final galaxy sample consists of 28,274 galaxies in total, including 27,861 SFGs and 413 QGs.

# 4. Results

## 4.1. Size–Mass Distribution at $2 < z < 10$

We present the size–mass distribution of galaxies in the rest-frame optical as a function of redshift in Figure 3. Intuitively, more massive galaxies tend to have larger sizes across most redshift bins, a trend observed for both SFGs (blue) and QGs (red). However, at a given stellar mass, the scatter in size is substantial. On average, QGs are smaller than their star-forming counterparts. Following earlier work by S. Shen et al. (2003) and A. van der Wel et al. (2014), in each redshift bin we fit a linear relation between the logarithm of stellar mass
<figure><img src="image_6.png" /><figcaption>Figure 2. The rest-frame wavelength probed by each of the COSMOS-Web filters as a function of redshift. The shaded background purple (red) regions indicate the rest-frame UV (optical) range, i.e., 2000–4000 Å (4000–6000 Å) for UV (optical). For example, at 6 < z < 10, the F277W (F444W) filter probes the rest-frame UV (optical) properties of galaxies.</figcaption></figure>

($M_*$) and effective radius ($R_e$)

$$ \log \frac{R_e}{\text{kpc}} = \log(A) + \alpha \log \frac{M_*}{5 \times 10^{10} M_{\odot}}, \quad (3) $$

where $log(A)$ is the y-intercept at the characteristic stellar mass $5 \times 10^{10} M_{\odot}$ and $\alpha$ is the slope. At a given stellar mass, the effective radius obeys a lognormal distribution $N(\log R_e(M_*), \sigma_{\log R_e}^2)$, where $\sigma_{\log R_e}$ is the intrinsic scatter.

We then use a standard Bayesian approach to derive the posterior distributions for the parameters, the y-intercept $log(A)$, slope $\alpha$, and $\sigma_{\log R_e}$. Our analysis incorporates both statistical uncertainties from the Markov Chain Monte Carlo fitting process and systematic uncertainties arising from variations in initial settings and from different software measurements, i.e., SE++ and Galight (see L. Yang et al. 2025, in preparation, for details). The total uncertainty in $log R_e$ is ~0.1–0.2 dex, depending on the filter wavelength and redshift, with systematic uncertainties dominating.

Additionally, following A. van der Wel et al. (2014), we account for size uncertainties related to the stellar mass measurements. The median $log M_*$ uncertainty is 0.09–0.24 dex at $z = 2.5–9.5$, and we use $\alpha = 0.7$ and 0.2 to convert these into size uncertainties for QGs and SFGs, respectively. It has been noted that the scaling relation for QGs flattens for stellar masses below $2 \times 10^{10} M_{\odot}$ (A. van der Wel et al. 2014; S. E. Cutler et al. 2024). Therefore, we restrict our fitting to QGs above this mass threshold. Figure 3 displays the fitting results (see also Table 1), with solid black lines and shaded regions representing the best-fit relations and their $1\sigma$ uncertainty range, respectively. The horizontal black dotted lines indicate the PSF size (FWHM/2), and the fitting results at $2 < z < 3$ are shown as dashed lines in each panel for reference. For comparison with previous HST results, we also include the best-fit line from A. van der Wel et al. (2014) at $z \sim 2.75$, as shown by the lime dashed line.

## 4.2. Size Evolution

The evolution of the rest-frame optical size at a given mass, characterized by the y-intercept $log(A)$, for SFGs and QGs is shown in the top panel of Figure 4. The sizes of both SFGs and QGs decrease toward higher redshifts. We parameterize this size evolution as a function of the cosmological scale factor ($1+z$). We find that the size evolution of SFGs follows $R_e \propto (1+z)^{-1.21 \pm 0.05}$, with the blue solid line showing the fitting result and the shaded region indicating the $1\sigma$ uncertainty. We compare our results to those from recent JWST studies (T. Morishita et al. 2024; K. Ormerod et al. 2024; R. G. Varadaraj et al. 2024; E. Ward et al. 2024; N. Allen et al. 2025) and a previous HST study (A. van der Wel et al. 2014). Our fitting result suggests a faster size evolution than previous results, while these previous works found more moderate evolution with $R_e \propto (1+z)^\beta$, with $\beta$ ranging from -0.26 to -0.81. At $2 < z < 3$, where measurements in the rest-frame optical from both HST and JWST are available, our measured size ($log R_e/\text{kpc} \sim 0.47$) is consistent with other JWST results (e.g., E. Ward et al. 2024 report $log R_e/\text{kpc} \sim 0.48$) but slightly smaller than HST results (e.g., A. van der Wel et al. 2014 obtained $log R_e/\text{kpc} \sim 0.51 \pm 0.01$ at $z \sim 2.75$). We speculate that this subtle offset arises from the higher resolution of NIRCam F150W imaging compared to the HST $H_{\text{F160W}}$ band, which covers a similar wavelength range.

At $z > 3$, our sizes inferred from the size–mass scaling relation are smaller than those reported by E. Ward et al. (2024) and N. Allen et al. (2025), resulting in faster size evolution. This discrepancy possibly arises from several factors. First, both studies have limited sample sizes and use broader redshift bins at high redshifts. Although N. Allen et al. (2025) have sufficient data at $5 < z < 6$, the number of high-mass galaxies ($log(M_*/M_{\odot}) > 9.5$) is limited. Second, differences in slope determination for the size–mass relation can lead to variations in inferred sizes (see the bottom left panel of Figure 4). For example, at $7 < z < 8$ we obtain a slope $\alpha = 0.10$, which is very flat compared to the slope obtained in N. Allen et al. (2025). Furthermore, the COSMOS-Web survey is conducted with four NIRCam filters, while other JWST surveys have coverage with more filters (e.g., E. Ward et al. 2024 use imaging in seven NIRCam filters from CEERS; S. L. Finkelstein et al. 2025), enabling those studies to select bands more closely aligned with rest-frame 5000 Å for analysis. However, since galaxy sizes do not vary significantly over this narrow wavelength range, especially at $z > 2$, we do not expect this to be the primary source of the observed differences.

The size evolution trends discussed by E. Ward et al. (2024) and N. Allen et al. (2025) are derived for galaxies at a characteristic stellar mass of $5 \times 10^{10} M_{\odot}$, enabling a fair comparison across studies. However, some other studies use different stellar mass ranges or quoted sizes when deriving size evolution. For example, R. G. Varadaraj et al. (2024) analyzed the evolution of the average size with $log(M_*/M_{\odot}) > 9$ at $z = 3–5$ and found $(1+z)^{-0.60 \pm 0.22}$ across the sample. K. Ormerod et al. (2024) analyzed ~1400 galaxies with stellar mass $log(M_*/M_{\odot}) > 9.5$ at $0.5 < z < 8$, reporting an average rest-frame optical size evolution, $(1+z)^{-0.71 \pm 0.19}$. Additionally, T. Morishita et al. (2024) obtained a much slower rate of
<figure><img src="image_7.png" /><figcaption>**Figure 3.** The rest-frame optical size–mass distribution of SFGs (blue) and QGs (red) presented in redshift bins at $2 < z < 10$. The black solid lines indicate the best-fit size–mass relation of SFGs and QGs (see also Table 1). The thick black and lime dashed lines show the fitting results at $2 < z < 3$ in this work and $z \sim 2.75$ obtained by A. van der Wel et al. (2014), respectively. The horizontal black dotted line in each panel indicates the PSF size (FWHM/2) of the filter that is closest to the rest-frame optical in each redshift bin. The numbers of galaxy data points are labeled in the lower-left corner in each redshift bin.</figcaption></figure>

size evolution, $(1+z)^{-0.26\pm0.19}$, using ~400 galaxies with stellar mass as low as $\log(M_*/M_\odot) \sim 7$.

While the size evolution of SFGs provides insights into the growth of actively forming systems, the trends for QGs offer a complementary perspective on the structural changes in galaxies that have ceased significant star formation. For QGs, the red data points in Figure 4 show the y-intercepts $\log(A)$ at $2 < z < 5$. The red solid line represents the fitting result, $R_e \propto (1+z)^{-0.81\pm0.26}$. Due to the fact that there are fewer QG samples and we only have results in three redshift bins, the $1\sigma$ uncertainty for the slope of the size evolution is relatively large, as shown by the shaded region. At $2 < z < 3$, our results are consistent with recent JWST results from K. Ito et al. (2024; lime pentagons), as well as HST results from A. van der Wel et al. (2014; dark-red squares). At $z > 3$, our data points are also consistent with the results extrapolated

from the size evolution of $(1+z)^{-1.48}$ derived from A. van der Wel et al. (2014).

### 4.3. Evolution of the Slope of the Size–Mass Relation

In the bottom left panel of Figure 4, we show the evolution of the slope, $\alpha$, for both SFGs and QGs. For SFGs $\alpha$ ranges from 0.10 to 0.20 at $2 < z < 8$, showing no significant variation across these redshift bins. At the highest two redshift bins ($8 < z < 9$ and $9 < z < 10$), the slopes are $-0.13 \pm 0.15$ and $0.37 \pm 0.36$, respectively. These values are poorly constrained owing to the limited number of data points and large scatter. We compare our findings with other works. At $2 < z < 3$, our results are consistent with A. van der Wel et al. (2014), who reported an average slope of $0.22$ at $z < 3$ (dark-blue squares). Their measured slope of $0.18 \pm 0.02$ at $z \sim 2.75$ agrees well with our result of $0.20 \pm 0.01$ at $z = 2.5$, as well as
<table><caption>**Table 1**
The Fitting Results for the Size–Mass Distribution, Expressed as $log(R_e/kpc) = log(A) + \alpha log(M_*/5 \times 10^{10} M_\odot)$, for Star-forming and Quiescent Galaxies at $2 < z < 10$ in Both the Rest-frame Optical and UV</caption><thead><tr><th rowspan="2">z</th><th colspan="3">Star-forming Galaxies</th><th colspan="3">Quiescent Galaxies</th></tr><tr><th>α</th><th>log(A)</th><th>σ(log R<sub>e</sub>)</th><th>α</th><th>log(A)</th><th>σ(log R<sub>e</sub>)</th></tr></thead><tbody><tr><td colspan="7" style="text-align: center; font-weight: bold;">Optical</td></tr><tr><td>2.5</td><td>0.20 ± 0.01</td><td>0.47 ± 0.01</td><td>0.19 ± 0.01</td><td>0.52 ± 0.06</td><td>-0.05 ± 0.01</td><td>0.16 ± 0.01</td></tr><tr><td>3.5</td><td>0.15 ± 0.01</td><td>0.33 ± 0.01</td><td>0.21 ± 0.01</td><td>0.78 ± 0.11</td><td>-0.13 ± 0.03</td><td>0.24 ± 0.03</td></tr><tr><td>4.5</td><td>0.18 ± 0.01</td><td>0.27 ± 0.02</td><td>0.22 ± 0.01</td><td>0.64 ± 0.26</td><td>-0.31 ± 0.12</td><td>0.25 ± 0.15</td></tr><tr><td>5.5</td><td>0.14 ± 0.02</td><td>0.16 ± 0.03</td><td>0.21 ± 0.01</td><td></td><td></td><td></td></tr><tr><td>6.5</td><td>0.19 ± 0.04</td><td>0.16 ± 0.05</td><td>0.17 ± 0.01</td><td></td><td></td><td></td></tr><tr><td>7.5</td><td>0.10 ± 0.06</td><td>-0.19 ± 0.09</td><td>0.25 ± 0.02</td><td></td><td></td><td></td></tr><tr><td>8.5</td><td>-0.13 ± 0.15</td><td>-0.61 ± 0.21</td><td>0.26 ± 0.04</td><td></td><td></td><td></td></tr><tr><td>9.5</td><td>0.37 ± 0.36</td><td>0.10 ± 0.50</td><td>0.28 ± 0.10</td><td></td><td></td><td></td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">UV</td></tr><tr><td>2.5</td><td>0.19 ± 0.01</td><td>0.41 ± 0.01</td><td>0.22 ± 0.01</td><td>0.61 ± 0.05</td><td>-0.10 ± 0.01</td><td>0.15 ± 0.01</td></tr><tr><td>3.5</td><td>0.19 ± 0.01</td><td>0.35 ± 0.01</td><td>0.23 ± 0.01</td><td>0.94 ± 0.04</td><td>-0.10 ± 0.03</td><td>0.20 ± 0.02</td></tr><tr><td>4.5</td><td>0.18 ± 0.01</td><td>0.20 ± 0.02</td><td>0.25 ± 0.01</td><td>0.31 ± 0.34</td><td>-0.27 ± 0.10</td><td>0.07 ± 0.11</td></tr><tr><td>5.5</td><td>0.12 ± 0.03</td><td>0.06 ± 0.04</td><td>0.25 ± 0.01</td><td></td><td></td><td></td></tr><tr><td>6.5</td><td>0.25 ± 0.04</td><td>0.21 ± 0.05</td><td>0.19 ± 0.01</td><td></td><td></td><td></td></tr><tr><td>7.5</td><td>0.13 ± 0.06</td><td>-0.17 ± 0.09</td><td>0.24 ± 0.02</td><td></td><td></td><td></td></tr><tr><td>8.5</td><td>0.17 ± 0.11</td><td>-0.18 ± 0.15</td><td>0.22 ± 0.04</td><td></td><td></td><td></td></tr><tr><td>9.5</td><td>0.70 ± 0.20</td><td>0.50 ± 0.26</td><td>0.09 ± 0.08</td><td></td><td></td><td></td></tr></tbody></table>

with the slope reported by E. Ward et al. (2024; magenta triangles). At higher redshifts ($3 < z < 8$), we observe slightly flatter slopes in some bins ($3 < z < 4$, $5 < z < 6$, and $7 < z < 8$), with the flattest slope being $α = 0.10 ± 0.06$ at $7 < z < 8$; however, this is still consistent with $0.20$ within $2σ$. N. Allen et al. (2025; green diamonds) also found a relatively constant slope of $\sim 0.2$ over $3 < z < 8$. However, much flatter slopes at $3 < z < 5$ have been reported by R. G. Varadaraj et al. (2024; cyan squares), though their sample size is smaller.

For QGs, the slopes are $0.52 ± 0.06$, $0.78 ± 0.11$, and $0.64 ± 0.26$ at three redshift bins between $z = 2$ and $z = 5$, respectively. At $2 < z < 3$, our result aligns with the results of K. Ito et al. (2024; lime pentagons), who recently analyzed two dozen QGs at $2.8 < z < 4.6$ and found slopes of $α \sim 0.4 - 0.55$. However, our result is slightly shallower than the average value of $α \sim 0.75$ (dark-red dashed line) reported by A. van der Wel et al. (2014) at lower redshift. One possible explanation for this difference are the selection criteria for QGs. We use the NUV – r – J diagram with an additional sSFR requirement, while A. van der Wel et al. (2014) adopted the UVJ diagram. Other contributing factors include the increasing fraction of green valley galaxies and changes in the stellar mass distribution (see the discussion of K. Ito et al. 2024 for more details). At $3 < z < 4$ and $4 < z < 5$, our result is consistent with that of A. van der Wel et al. (2014), but the uncertainties are relatively large owing to the limited sample size.

### 4.4. Evolution of Intrinsic Scatter

The evolution of intrinsic scatter, $σ_{log R_e}$, is shown in the bottom right panel of Figure 4. For SFGs, $σ_{log R_e}$ remains

around $\sim 0.2$ dex at $2 < z < 7$ and increases to $\sim 0.25$ dex at $7 < z < 10$ with large uncertainties. Our result at $2 < z < 3$ is consistent with those of A. van der Wel et al. (2014) and E. Ward et al. (2024). R. G. Varadaraj et al. (2024) measured intrinsic scatter values of $0.21–0.25$ dex in F356W for galaxies at $z = 3–5$ (cyan points), which generally agree with our results, though their values are slightly higher at $z \sim 3$. Similarly, N. Allen et al. (2025) found $σ_{log R_e} \lesssim 0.2$ dex at $3 < z < 8$, which is also in general agreement with our results but is slightly lower at $z \sim 7.5$. For QGs, $σ_{log R_e}$ is $0.16 ± 0.01$ dex at $2 < z < 3$ and smaller than that of SFGs, which is consistent with the results reported by A. van der Wel et al. (2014). It increases to $0.24 ± 0.03$ dex and $0.25 ± 0.25$ dex at higher redshifts, where the values are comparable to those for SFGs. Large intrinsic scatters have also been reported by K. Ito et al. (2024) at $3 < z < 5$.

The properties of intrinsic scatter are closely related to the spin of dark matter halos. If we assume that SFGs follow the characteristics of disk galaxies, their growth is expected to align with the evolution of their dark matter halos. Consequently, the intrinsic scatter in galaxy sizes should resemble the scatter in dark matter halo spin parameters. A. V. Macciò et al. (2008) presented the distribution of halo spin parameters, $log λ$, finding a $1σ$ scatter of $\sim 0.24$ dex, which is independent of halo mass and the choice of cosmological models. The distribution of spin parameters also does not change significantly as a function of redshift (J. C. Muñoz-Cuartas et al. 2011). Our findings show a consistent size scatter across a wide redshift range ($2 < z < 7$), albeit with slightly lower values than the spin parameter. This suggests that the sizes of disk galaxies are generally determined by the properties of their underlying dark matter halos. At $z > 7$, the $σ_{log R_e}$
<figure><img src="image_8.png" /><figcaption>**Figure 4.** Top: the evolution of rest-frame optical sizes for SFGs (blue circles) and QGs (red circles) at a fixed stellar mass $5 \times 10^{10} M_{\odot}$ at $2 < z < 10$, with comparisons to previous studies. The fitting results for SFGs and QGs are shown by the blue and red solid lines, respectively, corresponding to $R_e \propto (1+z)^{-1.21 \pm 0.05}$ and $R_e \propto (1+z)^{-0.81 \pm 0.26}$, with the shaded regions representing the $1\sigma$ uncertainties. Utilizing recent JWST data, the results of SFGs from K. Ormerod et al. (2024), R. G. Varadaraj et al. (2024), E. Ward et al. (2024), T. Morishita et al. (2024), and N. Allen et al. (2025) are illustrated by brown, cyan, magenta, orange, and green colors, respectively. Lime pentagons display results for QGs (K. Ito et al. 2024). The dark blue and dark red represent HST results of SFGs and QGs, respectively, from A. van der Wel et al. (2014). Bottom: the evolution of the slope $\alpha$ (left) and intrinsic scatter $\sigma_{\log R_e}$ (right), with colors the same as in the top panel.</figcaption></figure>

increase, and it is possibly because of the higher galaxy interaction rate at an earlier time. For QGs, the intrinsic scatter at higher redshifts is ~0.25 dex. We speculate that this similarity in scatter with SFGs implies some shared characteristics with disk galaxies (see more discussion in Section 7.3), possibly reflecting a common dependence on dark matter halo properties.

## 5. Size Distribution as a Function of Mass

### 5.1. Size Distribution

We present a complementary analysis of the evolution of the size-mass relation by examining size evolution as a function of stellar mass. Figure 5 shows histograms of the size distributions categorized into various stellar mass and redshift bins. The five mass bins are $9 < \log(M_*/M_{\odot}) < 9.5$, $9.5 < \log(M_*/M_{\odot}) < 10$, $10 < \log(M_*/M_{\odot}) < 10.5$, $10.5 < \log(M_*/M_{\odot}) < 11$, and $11 < \log(M_*/M_{\odot}) < 11.5$. The size distributions are asymmetric. The distribution of SFGs skews toward the small side, and the skewness is more obvious for more massive galaxies and higher redshifts. However, in some of the highest-redshift bins (e.g., $z > 8$) and in some of the most massive bins (e.g., $\log(M_*/M_{\odot}) > 10.5$), the sample size

is too small to clearly establish this skewness. Meanwhile, the distribution of QGs skews toward the large side. We characterize these size distributions by fitting a skew-normal distribution using the Python code `scipy.stats.skewnorm`. The pdf is

$$f(x; a, \mu_m, \sigma_m) = \frac{2}{\sigma_m} \phi\left(\frac{x - \mu_m}{\sigma_m}\right) \Phi\left(a \frac{x - \mu_m}{\sigma_m}\right), \quad (4)$$

where $\phi$ is the standard normal pdf; $\Phi$ is the standard normal cumulative distribution function; $\mu_m$ and $\sigma_m$ are the modeled mean and scatter, respectively; and $a$ quantifies the skewness of the distribution. The fitting results are shown as blue and red curves for SFGs and QGs, respectively, with the corresponding modeled parameters displayed within each panel. The parameter $a$ determines the direction and magnitude of skewness, and the positive value suggests that the right tail of the distribution is heavier and the peak of the distribution shifts leftward. In some high-mass or high-redshift bins, fitting results are unavailable owing to the limited sample sizes.

First, we show the evolution of the modeled mean size $\mu_m$ in different stellar mass bins in Figure 6. For SFGs, we also fit the
<figure><img src="image_9.png" /><figcaption>**Figure 5.** Size distribution histograms for SFGs (blue) and QGs (red) in bins of stellar mass and redshift. The distributions are fit with a skewed normal distribution, and the mean size $\mu_m$, scatter $\sigma_m$, and skewness parameter $a$ are labeled inside each panel.</figcaption></figure>

size evolution as $(1+z)^{\beta_m}$, and fitting results are shown as dotted lines. $\beta_m$ ranges from −0.97 to −1.31 and does not depend strongly on stellar mass. The size evolution in different mass bins is consistent with the size evolution inferred from the size–mass relation. For QGs, we did not fit the size evolution owing to the limited sample size. Second, we find that the scatter $\sigma_m$ is approximately 0.2–0.35

in most bins but reaches $\gtrsim 0.5$ at $z > 6$ for mass bin $9.5 < \log(M^*/M_\odot) < 10$. Meanwhile, the skewness $a$ becomes more significantly negative compared to lower redshifts. The above characteristics suggest that our sample contains an additional larger fraction of small galaxies at high redshift compared to lower redshifts; see further discussion in the following section.
<figure><img src="image_10.png" /><figcaption>**Figure 6.** Evolution of the modeled mean size, $\mu_m$, in different mass bins. Fitting results for SFGs in the form of $\mu_m \propto (1+z)^{\beta_m}$ are shown by dashed lines.</figcaption></figure>

## 5.2. Tiny Blue Sources at $z > 5$

For the lower-redshift bins $z < 5$, SFGs skew toward smaller size, which may be partly due to potential contamination from the QG populations. This is because there is no strict bimodality between the two populations, whether in the color-color diagram or the sSFR criteria, as also pointed out in A. van der Wel et al. (2014). However, this skewness still exists at $z > 5$, where there are almost no significant effects from QGs. This excess of small galaxies may either reflect intrinsic differences in galaxy structure in the early Universe or possible contamination from AGN, despite our exclusion of X-ray AGN and LRDs. T. Morishita et al. (2024) also reported a number of blue compact sources in the size-mass plane, and those sources are suspected to be AGN candidates. We further examine the properties of these small galaxies, particularly those sources that are unresolved. We test the possible AGN nature of unresolved sources by performing a decomposition of their surface brightness profiles, assuming a point source for the central AGN and a Sérsic model for the extended host galaxy, following X. Ding et al. (2020). We find that some unresolved sources exhibit morphological features indicative of AGN as presented in X. Ding et al. (2020), such as source ID=24154 ($z = 7.9$) as shown in Figure 7. Further investigation is required to confirm the nature of these sources, which we will address in future work.

# 6. The Wavelength Dependence of Size and Its Relation to Mass

Investigating the variation in galaxy size across different wavelengths offers valuable insights into the history of galaxy formation and the distribution of stellar populations. For example, observations at lower redshifts ($z < 2$) indicate that galaxy sizes tend to appear smaller at longer wavelengths, suggesting an inside-out growth pattern where the inner regions of galaxies age first (K. A. Suess et al. 2022). Meanwhile, the central regions are more metal-rich because of prolonged star formation and chemical enrichment, which could reinforce the color gradients (M. Montes et al. 2014). The distribution of dust can also amplify this effect. At higher redshifts ($z > 2$), due to the short cosmic time, a smaller stellar age difference and flat metallicity gradients are expected (A. Pallottini et al. 2022), hence the smaller offsets between sizes at different wavelengths.

At $z > 3$, observations of galaxies' sizes in the rest-frame optical have only become feasible recently with the advent of JWST. Before this, many simulation studies made falsifiable predictions about the size evolution as a function of wavelength, mass, and luminosity (X. Ma et al. 2018; X. Wu et al. 2020; M. A. Marshall et al. 2022; W. J. Roper et al. 2022; L. Costantin et al. 2023).

## 6.1. $\Delta \log R_e$ as a Function of Stellar Mass

In Figure 8, we show the size difference, $\Delta \log R_e$, between the rest-frame optical and UV for SFGs with secure measurements at both wavelengths as a function of stellar mass. We divide the galaxy sample into five mass bins as we did for studying size distribution; see Section 5.1. The squares represent the median value, while error bars represent the $1\sigma$ distribution and the dashed line represents $\Delta \log R_e = 0$.

Generally, the optical sizes are comparable to the UV sizes. This is consistent with many JWST studies at $z > 3$, which probe a similar or lower stellar mass range. Earlier work by L. Yang et al. (2022a) investigated the size as a function of wavelength at $z > 7$ for galaxies with stellar mass $\sim \log(M_*/M_\odot) = 8-9$ and found the size ratio to be almost unity. Similar results have also been reported by T. Morishita et al. (2024), Y. Ono et al. (2024), K. Ormerod et al. (2024), and N. Allen et al. (2025). Simulations have also found similar results. For example, L. Costantin et al. (2023) measured the size for galaxies at $3 < z < 6$ in F200W and F365W from the TNG50 cosmological simulation (D. Nelson et al. 2019) and found that the size ratio does not vary significantly at each mass bin.

In some cases, we find that the optical sizes are slightly larger than UV toward the low-mass end for some redshift bins, such as $4 < z < 5$ and $5 < z < 6$. One reason could be that UV light is heavily obscured by dust, such as observed in dusty SFGs (L. Colina et al. 2023). Another reason could be due to the fact that UV emission traces star-forming regions, which usually consist of smaller-scale clumpy structures as demonstrated by FIRE simulation (X. Ma et al. 2018).

Interestingly, we find that at some redshift bins the more massive galaxies tend to have $\Delta \log R_e < 0$, meaning that their optical sizes are smaller than their UV sizes. The median value of $\Delta \log R_e$ is negative for massive galaxies with $\log(M_*/M_\odot) > 10$ at $3 < z < 4$, as well as for the most massive galaxies at $8 < z < 9$. Our findings are qualitatively consistent with many simulations (M. A. Marshall et al. 2022; X. Shen et al. 2024) at high $z$. For example, M. A. Marshall et al. (2022) presented the observed images of high-$z$ galaxies across different mass ranges and multiple bands (far-UV (FUV), V, and H), using the BLUETIDES cosmological hydrodynamical simulation. They found that the intrinsic morphologies across different bands are similar and show no strong dependence on stellar mass. However, for more massive galaxies the observed FUV images are more extended than their intrinsic counterparts. This is because dust is concentrated in more massive galaxies, causing the observed dust-attenuated FUV sizes to appear more extended. As a result, the observed FUV sizes are larger than the optical sizes.

The size difference, $\Delta \log R_e$, varies as a function of stellar mass, indicating that galaxies follow different growth tracks depending on their mass (X. Shen et al. 2024). In massive galaxies, the central regions are significantly affected by dust, which correlates with young stellar populations. This suggests
<figure><img src="image_11.png" /><figcaption>Figure 7. Surface brightness profile fitting of an example unresolved source at $7 < z < 8$. This source is modeled by a Sérsic profile plus a central point-like profile.</figcaption></figure>

that these galaxies undergo a compaction process, driven by rapid gas inflow toward the center, ultimately leading to a more compact structure and effective quenching. Further discussion of different evolutionary paths will be presented in Section 7.3.

## 6.2. Size–Mass Relation as a Function of Wavelength

We further investigate the variation of the size–mass relation as a function of wavelength. We adopt the same method used to derive the size–mass relation in the rest-frame UV as in optical, and the fitting results are presented in Table 1. In Figure 9, we compare the best-fit scaling relation for SFGs derived from the UV (solid blue line) and optical (red line) at $2 < z < 10$. We find no significant differences between these two relations at $z < 8$. This result is consistent with L. Costantin et al. (2023), who predicted the size–mass relation at $z = 3–6$ using the TNG50 simulation dataset. Their predictions, shown as magenta (using the F356W filter for the optical) and green (using the F200W filter for the UV) dashed lines, align well with our observations. They also found that the observed slopes transition from positive to negative at $z \sim 5$ for both wavelengths.

Despite their broad agreement, we find a discrepancy between the UV and optical, emerging at $z > 8$, where the slope of the size–mass relation differs between rest-frame optical and UV wavelengths. Specifically, the slope is negative in the optical but positive in the UV. The negative slope for the size–mass relation is counterintuitive. Interestingly, negative slopes in the size–mass relation have been reported from several simulations (M. A. Marshall et al. 2022; W. J. Roper et al. 2022; L. Costantin et al. 2023; X. Shen et al. 2024). For example, W. J. Roper et al. (2022) analyzed the intrinsic and observed sizes of galaxies at $z > 5$ using the FLARES simulation. They found that the intrinsic UV size–luminosity relation has a negative slope, conflicting with observational results (T. Shibuya et al. 2015; L. Yang et al. 2022a). This discrepancy is mitigated when dust attenuation is taken into account, as dust tends to be concentrated in galaxy cores, affecting observed sizes. After including the dust effect, the observed UV size will be much larger than its intrinsic value.

W. J. Roper et al. (2022) also present that the observed size–luminosity slopes decrease toward redder wavelengths including the effects of dust (see their Figure 11). This trend is also supported by M. A. Marshall et al. (2022). We observe a similar trend in our highest-redshift bins, at $z > 8$, though the sample size is limited in this range. A more straightforward comparison can be made with X. Shen et al. (2024), who derived scaling relations in the UV (with and without dust effects) and optical V band at $z > 5$. Their results demonstrate that dust attenuation increases observed UV sizes and has a

more pronounced impact on massive galaxies, explaining the slope discrepancies.

# 7. Discussion

## 7.1. Size Ratio between the Half-light Radius of a Galaxy and the Virial Radius of a Halo

The angular momentum of the gas has long been considered one of the most important factors for regulating galaxy morphology (H. J. Mo et al. 1998; A. B. Romeo et al. 2023). Both dark matter and diffuse gas acquire their angular momentum through the same process, tidal torques and mergers. Similar to the stellar-to-halo mass relation (SHMR), there exists a stellar-to-halo radius relation, which describes the ratio between the half-mass or half-light radius of galaxies and the virial radius of the underlying dark matter halo (A. V. Kravtsov 2013). The halo virial mass, $M_{vir}$, and radius, $R_{vir}$, are defined as that within the overdensity, $\Delta_{vir}$, times the critical density $\rho_{crit}$; therefore, the virial radius is calculated by

$$R_{vir} = \left( \frac{3M_{vir}}{4\Delta_{vir}\rho_{crit}} \right)^{1/3}, \qquad (5)$$

where $\Delta_{vir} = 18\pi^2 + 82x - 39x^2$, $x = \Omega_m(z) - 1$, and critical density $\rho_{crit} = 3H(z)^2/8\pi G$. Following the disk formation model (H. J. Mo et al. 1998), the size of disk galaxies is proportional to the radius of the dark matter halo,

$$R_e/R_{vir} = \frac{1.68}{\sqrt{2}} \lambda f_j, \qquad (6)$$

where $\lambda$ is the dark matter halo spin parameter and $f_j$ is the ratio of the specific angular momentum of the disk to that of the halo.

Following previous work, such as T. Shibuya et al. (2015), for a galaxy with a certain stellar mass, we infer its underlying halo mass, $M_{vir}$, from the SHMR relation and subsequently calculate its virial radius. In this work, we adopt the SHMR relation from M. Shuntov et al. (2025) using the COSMOS-Web dataset, which performed abundance matching to estimate the relation across a large redshift range $0.2 < z < 12$ consistently, for the first time. In Figure 10, we show the ratio between the half-light radius of the galaxy and virial radius of its host halo, $R_e/R_{vir}$, at $5 \times 10^{10} M_{\odot}$ as a function of redshift. The $R_e/R_{vir}$ of SFGs is almost constant at $z \sim 2–7$, with a median value $\sim 2.7\%$. The radius ratio decreases to $\sim 1\%$ at $7 < z < 8$ and $8 < z < 9$ and then increases to a larger value, albeit with large uncertainties.

We compare our results with those of other studies. A. V. Kravtsov (2013) found the radius ratio to be $1.5\%$ at $z \sim 0$, and R. S. Somerville et al. (2018) found a similar
<figure><img src="image_12.png" /><figcaption>**Figure 8.** Size difference, $\Delta \log R_e$, of SFGs between the rest-frame optical and UV as a function of stellar mass in different redshift bins at $2 < z < 10$. The blue squares and error bars show the median value and its $1\sigma$ distribution. The dark dashed lines indicate the reference line $\Delta \log R_e = 0$.</figcaption></figure>

result at $z = 0.1$. K.-H. Huang et al. (2017) reported that the ratio is 2.3% at $0 < z < 3$, and it remains unchanged using different SHMR functions, which is consistent with our results at $2 < z < 3$. Similar results are also reported by T. Shibuya et al. (2015) and R. Kawamata et al. (2015) up to $z \sim 9.5$, though their size at high $z$ is measured in rest-frame UV. Y. Ono et al. (2025) recently reported ratio $\sim 0\% - 4\%$ at $z > 10$.

The radius ratio can also be inferred from the spin parameter, as shown in Equation (6). Based on simulations, the spin parameter is $\lambda \sim 0.035$ and remains almost constant as a function of redshift, as demonstrated by A. Rodríguez-Puebla et al. (2016). If we simply assume that the disk and halo have the same specific angular momentum, $f_j = 1$, we obtain

$R_e/R_{vir} \sim 0.04$, as shown by the black dashed line in Figure 10. The observed radius ratio of SFGs is smaller than this theoretical expectation, indicating $f_j < 1$. We also note that $R_e/R_{vir}$ tentatively decreases toward lower redshift since $z < 7$. This result could suggest that, at early times, the angular momentum of galaxies is closer to that of their dark matter halos but decreases at lower redshifts. The growth of galaxies may even decouple from the growth of dark matter, as also speculated by A. V. Kravtsov (2013).

## 7.2. SFR Surface Density

The SFR surface density, $\Sigma_{SFR}$, is defined as $\Sigma_{SFR} = 0.5 \times SFR / (\pi R_e^2)$. This parameter is directly linked to the surface
<figure><img src="image_13.png" /><figcaption>**Figure 9.** The size–mass relation for SFGs in several bins across a range of redshifts, $2 < z < 10$, comparing observations at rest-frame UV and optical wavelengths with results from the cosmological simulations TNG50 (L. Costantin et al. 2023) and THESAN-1 (X. Shen et al. 2024).</figcaption></figure>

density of gas, making $\Sigma_{SFR}$ a direct tracer of the local gas reservoir available for star formation (R. C. Kennicutt 1998). Additionally, stellar feedback (e.g., from supernovae, stellar winds, and radiation) plays a critical role in regulating star formation by heating or expelling gas. Feedback efficiency depends on the local $\Sigma_{SFR}$. Studying the evolution of $\Sigma_{SFR}$ is crucial for understanding how efficiently galaxies convert gas into stars across cosmic time.

### 7.2.1. $\Sigma_{SFR}$ Evolution

In Figure 11, we present the evolution of $\Sigma_{SFR}$ as a function of redshift at $2 < z < 10$. All SFGs are shown as blue points, with their median values represented by black diamonds, while unresolved sources are highlighted by magenta crosses. We find that the median value of $\log(\Sigma_{SFR}/(M_{\odot}/\text{yr}/\text{kpc}^2))$

increases from −0.5 to 1.5 at $2 < z < 10$. We fit a linear relation to $\log \Sigma_{SFR}$ and redshift, and the best-fit result is $\log(\Sigma_{SFR}/(M_{\odot}/\text{yr}/\text{kpc}^2)) = (0.20 \pm 0.08)z + (-0.65 \pm 0.51)$ as shown by the black solid line. Our result agrees well with the best-fit results of the median $\log \Sigma_{SFR}$ reported by A. Calabrò et al. (2024), as shown by the lime dashed line. A. Calabrò et al. (2024) include a sample with lower stellar mass reaching to $\log(M_*/M_{\odot}) \sim 8-8.6$, and we will discuss the dependence of $\log \Sigma_{SFR}$ on stellar mass later in this section.

Furthermore, we observe a fraction of galaxies with a very high value of $\log(\Sigma_{SFR}/(M_{\odot}/\text{yr}/\text{kpc}^2)) > 1.5$ in Figure 11. Most of these extreme cases are unresolved sources, especially at $z > 7$; this could be due to those sources either having efficient compact SFRs or hosting AGN as suggested by
<figure><img src="image_14.png" /><figcaption>**Figure 10.** Evolution of the ratio of the galaxy half-light radius to halo virial radius $R_e/R_{vir}$ for SFGs. The blue data points represent data in this work, with the blue dashed line indicating the median value of the size ratio, $R_e/R_{vir} = 2.7\%$ at $z \sim 2-7$. The results obtained at lower redshifts are shown with a red square (A. V. Kravtsov 2013), green square (R. S. Somerville et al. 2018), and magenta dashed line (A. V. Kravtsov 2013). The black dashed line shows the theoretical prediction assuming $f_j = 1$; see Equation (6).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 11.** Evolution of the SFR surface density, $\Sigma_{SFR}$. Blue points represent individual SFGs, while magenta crosses highlight unresolved sources. Black diamonds show the median $\Sigma_{SFR}$ in redshift bins, with error bars representing the $1\sigma$ error. The solid black line shows the best-fit linear relation, while the lime dashed line shows a comparison from A. Calabrò et al. (2024) for $4 < z < 10$.</figcaption></figure>

several works (T. Morishita et al. 2024; Y. Harikane et al. 2025; Y. Ono et al. 2025). Some of those compact sources have high-ionization emission lines (Y. Harikane et al. 2025), which can be a strong hint of the existence of AGN, while our morphological decomposition also provides supportive evidence; see Section 5.2.

### 7.2.2. $\Sigma_{SFR}-M_*$ Relation

Compared to the classical (s)SFR-$M_*$ relation, the $\Sigma_{SFR}-M_*$ provides a more direct probe of local star formation, since $\Sigma_{SFR}$ traces the SFR per unit area and is thus more directly tied to local gas density and star formation

efficiency. This avoids the ambiguity of integrated SFR, which averages over the entire galaxy and can obscure the spatial variation. For instance, S. Salim et al. (2023) showed the $\Sigma_{SFR}$ versus stellar mass $M_*$ plane at $0 < z < 2$, and they found that the relation is flat locally, meaning that local main-sequence galaxies exhibit similar $\Sigma_{SFR}$ values across a wide range of stellar masses, whereas the classical (s)SFR-$M_*$ relation is tilted. At higher redshift, $z \sim 2$, the relation slightly steepens toward the high-mass end but remains relatively flat.

In this work, we explore the $\Sigma_{SFR}-M_*$ relation across eight redshift bins up to $z = 10$ as shown in the top panel of Figure 12. We find a weak positive linear correlation between $\Sigma_{SFR}$ and $M_*$ at all redshift bins, with best-fit slopes of $0.12 \pm 0.31$, $0.31 \pm 0.31$, $0.36 \pm 0.56$, $0.28 \pm 0.73$, $0.28 \pm 0.56$, $0.40 \pm 0.64$, and $2.27 \pm 1.81$ for redshift bins between $z = 2$ and $z = 9$. While the slopes appear to increase toward higher redshifts, the large uncertainties make them consistent with zero within errors. At $9 < z < 10$, only one effective data point is available, preventing a reliable fit. These results are consistent with the flat $\Sigma_{SFR}-M_*$ relation observed at $z \sim 0$ (S. Salim et al. 2023; gray dashed line) and the mild positive trends reported by A. Calabrò et al. (2024) at $4 < z < 6$ and $6 < z < 10$, as shown with magenta and red dashed lines, respectively. Interestingly, some simulations suggest a strong evolution of the $\Sigma_{SFR}-M_*$ relation. For example, J. Nadolny et al. (2025) report that the slope of $\Sigma_{SFR}-M_*$ decreases rapidly from $z = 4$ to $z = 1$ and suggest that this is driven by a rapid decrease in SFR for the most massive galaxies in this redshift range. We further investigate the evolution of $\Sigma_{SFR}$ in different mass bins, shown in the bottom panel of Figure 12, comparing with the best-fit results of the median value of the entire sample and the result from A. Calabrò et al. (2024), as also shown in Figure 11. The evolution does not show a strong dependence on stellar mass.

### 7.3. Compaction and Quenching

From the size-mass distribution shown in Figure 3, at a given stellar mass, QGs are smaller, leading to higher stellar mass surface densities than SFGs, suggesting a link between structural change and star formation quenching as part of galaxy evolution. G. Barro et al. (2017) found that SFGs and QGs follow distinct and tight correlations in stellar mass surface density, $\Sigma_e$, as a function of stellar mass. They suggested an evolutionary pathway where main-sequence SFGs grow inside out, with both size and central density increasing over time while maintaining disklike structures. Subsequently, galaxies undergo a compaction process that significantly enhances their central density, driving a transition toward bulge-like morphologies. Eventually, the SFR declines, leading to galaxy quenching. In this scenario, compaction is so tightly correlated with quenching that the galaxies will be quenched when reaching a $\Sigma_e$ threshold.

In Figure 13, we show the distribution of log(sSFR) and log$\Sigma_e$ to link star formation activity and mass distribution for SFGs and QGs at $2 < z < 5$. We show the threshold log(sSFR) > log(0.2/$t_{obs}$) with a red dashed line that separates SFGs and QGs and a blue dashed line for log(sSFR) > log(0.2/$t_{obs}$) + 1, indicating that the galaxies in between are at a transition phase, such as green valley galaxies. The data points are colored by their Sérsic index, $n_{sérsic}$. The $n_{sérsic}$ parameter describes the shape of a galaxy's surface brightness profile, where lower $n_{sérsic}$ values indicate disk-dominated
<figure><img src="image_16.png" /><figcaption>**Figure 12.** Top: $\Sigma_{SFR}-M_*$ relation across eight redshift bins at $z=2-10$. The gray dashed line shows the relation at $z \sim 0$ (S. Salim et al. 2023), and magenta and red dashed lines represent the fitting results from A. Calabrò et al. (2024) at $4 < z < 6$ and $6 < z < 10$, respectively. Bottom: the evolution of $\Sigma_{SFR}$ in different redshift bins. The fitting results from this work (solid black line) and from A. Calabrò et al. (2024; lime dashed line) are as shown in Figure 11.</figcaption></figure>

galaxies and higher values indicate compact and bulge-dominated galaxies.

We observe the characteristic L-shaped evolutionary track as described by G. Barro et al. (2017). SFGs have lower $\Sigma_e$ and a disklike morphology, i.e., the median value is $n_{\text{sérsic}} \sim 1$. Galaxies then become compact, with $\log(\Sigma_e/(M_{\odot}/\text{kpc}^2))$ reaching $\sim 9.5-10$; after that, galaxies become quenched. A similar threshold of compaction and quenching is also found at higher redshift $z > 6$ as reported by simulations (X. Shen et al. 2024). We consider galaxies with $n_{\text{sérsic}} > 2.5$ as bulge-dominated galaxies. To quantify the structural variation, we label the fraction of bulge-like galaxies at three phases, star-forming (blue), transitioning (green), and quenching (red), in each panel.

In all three redshift bins, the SFGs are dominated by disklike morphologies and only a small fraction (10%–11%) have bulge-like structure. The fraction of bulge-like galaxies then increases to approximately 25% at the transition phase. Those compact SFGs are likely to be quenching imminently, acting as progenitors of QGs, which implies that the corresponding quenching mechanism is accompanied by the emergence of bulge-like structure in SFGs (see also P. Lang et al. 2014).

Finally, QGs are dominated by bulge-like features, consisting of $\sim 70\%$ at $2 < z < 3$ and $3 < z < 4$. However, it is interesting that at $4 < z < 5$ only 14% of QGs have $n_{\text{sérsic}} > 2.5$. The variation of bulge fraction in QGs is compatible with the results of M. Huertas-Company et al. (2024), where their galaxy morphologies are classified by a convolutional neural network. A similarly low value is also reported by A. C. Carnall et al. (2023), who found a spectroscopically confirmed QG at $z = 4.658$ with measured Sérsic index $n_{\text{sérsic}} \sim 2.3$. Additionally, the lower $n_{\text{sérsic}}$ value likely indicates that a fraction of QGs have more disk-dominated structures, though other factors, such as an extended envelope surrounding the bulge, may also contribute. K. Ito et al. (2024) also investigated the Sérsic index distribution of QGs at $z > 3$, and they found that QGs in their sample have lower Sérsic index $n_{\text{sérsic}} < 2$. Our findings suggest that it is likely that the first generation of the QG population consists of a significant fraction of disklike galaxies.

The mechanisms driving compaction and quenching likely leave distinct morphological imprints. Simulations by X. Shen et al. (2024) also found the prevalence of disklike morphologies at high redshifts as demonstrated in this work. They suggested that internal processes, such as disk instabilities, dominate over external triggers like mergers. They further show that gas inflow, driven by disk instability, enhances central density and triggers central star formation. This process is accompanied by a temporary increase in SMBH accretion and leads to eventual quenching, and the AGN host galaxies will remain disklike. M. Onoue et al. (2025) analyzed two quasar host galaxies at $z > 6$ and found that one of them exhibits little ongoing star formation while another is transitioning to a quiescent phase. However, determining AGN host galaxy morphology is still challenging, and we will further investigate this topic in future work.

## 8. Summary and Conclusion

In this work, we analyze the evolution of galaxy sizes and their scaling relations with mass for SFGs and QGs across a wide redshift range ($2 < z < 10$). The data used for this analysis come from COSMOS-Web, the largest area imaging survey conducted with JWST to date. We summarize our main findings as follows:

1. *Parameterized size-mass relation at the rest-frame optical up to z = 10.* We parameterize the scaling relation between the half-light radius ($R_e$) and stellar mass ($M_*$) of galaxies as $\log(R_e/\text{kpc}) = \log(A) + \alpha \log(M_*/5 \times 10^{10}M_{\odot})$. For SFGs, the slope $\alpha$ at $2 < z < 8$ is approximately 0.20, showing no significant evolution with redshift. At higher redshifts, the sample size is limited and we obtain the slopes $-0.13 \pm 0.15$ and $0.37 \pm 0.36$ at $8 < z < 9$ and $9 < z < 10$, respectively. The y-intercept $\log(A)$ decreases with
<figure><img src="image_17.png" /><figcaption>**Figure 13.** The relation between stellar mass surface density ($\Sigma_e$) and sSFR (log sSFR), with points color coded by Sérsic index $n_{\text{sérsic}}$. The red dashed line marks the threshold log(sSFR) > log(0.2/t<sub>obs</sub>) separating SFGs and QGs. The blue dashed line indicates log(sSFR) > log(0.2/t<sub>obs</sub>) + 1, with galaxies between the two lines considered to be in a transition phase. Galaxies with $n_{\text{sérsic}}$ > 2.5 are considered bulge dominated. The fractions of bulge-dominated galaxies in the star-forming, quiescent, and transition phases are labeled in blue, red, and green, respectively.</figcaption></figure>

redshift, following $R_e \propto (1+z)^{-1.21\pm0.05}$. The intrinsic scatter $\sigma_{\log R_e}$ ranges between 0.2 and 0.3 dex for SFGs. For QGs, the slope $\alpha$ is steeper than that of SFGs, with values ranging from 0.5 to 0.8 at $2<z<5$. The y-intercept $\log(A)$ follows $R_e \propto (1+z)^{-0.81\pm0.26}$, and the intrinsic scatter ranges between 0.15 and 0.25 dex.

2. *Size and its relation with mass as a function of wavelength.* We have compared the size and its relation with mass in the rest-frame UV and optical. In summary, our findings indicate that the size–mass relation for SFGs is consistent between rest-frame UV and optical wavelengths at $z<8$. However, at $z>8$ the slope decreases from UV to optical, with a negative slope observed in the optical at $8<z<9$. Unlike predictions from cosmological simulations, we do not find an evident negative optical slope since $z>5$, which indicates the complex interplay between intrinsic galaxy properties and observational effects such as dust attenuation.

3. *Size ratio between galaxy and halo.* We have investigated the size ratio, $R_e/R_{vir}$, between stellar light and its underlying dark matter halo using the latest SHMR result from COSMOS-Web, and we find that $R_e/R_{vir}$ is almost consistent at $2<z<7$, with a median value of 2.7%, and slightly decreases at $z>7$.

4. *SFR surface density as a function of redshift and stellar mass.* We find that $\Sigma_{SFR}$ increases monotonically with redshift following $\log(\Sigma_{SFR}/(M_{\odot} \text{ yr}^{-1} \text{ kpc}^{-2})) = (0.20 \pm 0.08)z + (-0.65 \pm 0.51)$ at $2<z<10$. We also investigate the $\Sigma_{SFR}-M_{*}$ relation and find a weak positive correlation at all redshift bins.

5. *Galaxy quenching and morphological transformation.* We have also explored the link between galaxy structural changes and star formation quenching at $2<z<5$. We find a threshold in stellar mass surface density $\log(\Sigma_e/(M_{\odot}/\text{kpc}^2))= 9.5-10$, beyond which galaxies become compact and eventually quench. Interestingly, QGs at higher redshifts consist of a larger sample fraction with $n_{\text{sérsic}} < 2.5$.

## Acknowledgments

We thank the anonymous referee for careful reading and constructive comments, which helped to improve the paper significantly. This work is based on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations are associated with program No. 1727. Support for this work was provided by NASA through grant JWST-GO-01727 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101148925. This work was made possible by utilizing the CANDIDE cluster at the Institut d'Astrophysique de Paris. The cluster was funded through grants from the PNCG, CNES, DIM-ACAV, the Euclid Consortium, and the Danish National Research Foundation Cosmic Dawn Center (DNRF140). It is maintained by Stephane Rouberol. Some of the measurements in this work are supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.

**Facility:** JWST (NIRCAM).

**Software:** Galight (X. Ding et al. 2020; S. Birrer et al. 2021), SourceXtractor++ (E. Bertin et al. 2020; M. Kümmel et al. 2020), SAOImage DS 9 (W. A. Joye & E. Mandel 2003), Numpy (C. R. Harris et al. 2020), Matplotlib (J. D. Hunter 2007), Scipy (P. Virtanen et al. 2020), Astropy (Astropy Collaboration et al. 2013).

## ORCID iDs

Lilan Yang https://orcid.org/0000-0002-8434-880X

Jeyhan S. Kartaltepe https://orcid.org/0000-0001-9187-3605

Maximilien Franco https://orcid.org/0000-0002-3560-8599
Xuheng Ding https://orcid.org/0000-0001-8917-2148

Mark J. Achenbach https://orcid.org/0009-0000-7385-3539

Rafael C. Arango-Toro https://orcid.org/0000-0002-0569-5222

Caitlin M. Casey https://orcid.org/0000-0002-0930-6466

Nicole E. Drakos https://orcid.org/0000-0003-4761-2197

Andreas L. Faisst https://orcid.org/0000-0002-9382-9832

Steven Gillman https://orcid.org/0000-0001-9885-4589

Ghassem Gozaliasl https://orcid.org/0000-0002-0236-919X

Marc Huertas-Company https://orcid.org/0000-0002-1416-8483

Shuowen Jin https://orcid.org/0000-0002-8412-7951

Daizhong Liu https://orcid.org/0000-0001-9773-7479

Georgios Magdis https://orcid.org/0000-0002-4872-2294

Richard Massey https://orcid.org/0000-0002-6085-3780

John D. Silverman https://orcid.org/0000-0002-0000-6977

Takumi S. Tanaka https://orcid.org/0009-0003-4742-7060

Si-Yue Yu https://orcid.org/0000-0002-3462-4175

Hollis B. Akins https://orcid.org/0000-0003-3596-8794

Natalie Allen https://orcid.org/0000-0001-9610-7950

Olivier Ilbert https://orcid.org/0000-0002-7303-4397

Anton M. Koekemoer https://orcid.org/0000-0002-6610-2048

Henry Joy McCracken https://orcid.org/0000-0002-9489-7765

Louise Paquereau https://orcid.org/0000-0003-2397-0360

Jason Rhodes https://orcid.org/0000-0002-4485-8549

Brant E. Robertson https://orcid.org/0000-0002-4271-0364

Marko Shuntov https://orcid.org/0000-0002-7087-0701

Sune Toft https://orcid.org/0000-0003-3631-7176

## References

Akins, H. B., Casey, C. M., Lambrides, E., et al. 2025, ApJ, 991, 37

Allen, N., Oesch, P. A., Toft, S., et al. 2025, A&A, 698, A30

Arnouts, S., Le Floc'h, E., Chevallard, J., et al. 2013, A&A, 558, A67

Arnouts, S., Moscardini, L., Vanzella, E., et al. 2002, MNRAS, 329, 355

Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33

Barro, G., Faber, S. M., Koo, D. C., et al. 2017, ApJ, 840, 47

Bertin, E. 2011, in ASP Conf. Ser. 442, Astronomical Data Analysis Software and Systems XX, ed. I. N. Evans et al. (San Francisco, CA: ASP), 435

Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393

Bertin, E., Schefer, M., Apostolakos, N., et al. 2020, in ASP Conf. Ser. 527, Astronomical Data Analysis Software and Systems XXIX, ed. R. Pizzo et al. (San Francisco, CA: ASP), 461

Birrer, S., Shajib, A., Gilman, D., et al. 2021, JOSS, 6, 3283

Boquien, M., Burgarella, D., Roehlly, Y., et al. 2019, A&A, 622, A103

Bouwens, R. J., Illingworth, G. D., Oesch, P. A., et al. 2017, ApJ, 843, 41

Bouwens, R. J., Illingworth, G. D., van Dokkum, P. G., et al. 2022, ApJ, 927, 81

Bowler, R. A. A., Dunlop, J. S., McLure, R. J., & McLeod, D. J. 2017, MNRAS, 466, 3612

Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000

Calabrò, A., Pentericci, L., Santini, P., et al. 2024, A&A, 690, A290

Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682

Carnall, A. C., McLure, R. J., Dunlop, J. S., et al. 2023, Natur, 619, 716

Casey, C. M., Kartaltepe, J. S., Drakos, N. E., et al. 2023, ApJ, 954, 31

Chabrier, G. 2003, PASP, 115, 763

Chang, W., Fang, G., Gu, Y., et al. 2022, ApJ, 936, 47

Civano, F., Marchesi, S., Comastri, A., et al. 2016, ApJ, 819, 62

Colina, L., Crespo Gómez, A., Álvarez-Márquez, J., et al. 2023, A&A, 673, L6

Costantin, L., Pérez-González, P. G., Vega-Ferrero, J., et al. 2023, ApJ, 946, 71

Curtis-Lake, E., McLure, R. J., Dunlop, J. S., et al. 2016, MNRAS, 457, 440

Cutler, S. E., Whitaker, K. E., Weaver, J. R., et al. 2024, MNRAS, 967, L23

Ding, X., Silverman, J., Treu, T., et al. 2020, ApJ, 888, 37

Finkelstein, S. L., Bagley, M. B., Arrabal Haro, P., et al. 2025, ApJL, 983, L4

Förster Schreiber, N. M., & Wuyts, S. 2020, ARA&A, 58, 661

Franco, M., Akins, H. B., Casey, C. M., et al. 2024, ApJ, 973, 23

Franco, M., Casey, C. M., Koekemoer, A. M., et al. 2025, arXiv:2506.03256

Grazian, A., Castellano, M., Fontana, A., et al. 2012, A&A, 547, A51

Harikane, Y., Inoue, A. K., Ellis, R. S., et al. 2025, ApJ, 980, 138

Harish, S., Kartaltepe, J. S., Liu, D., et al. 2025, ApJ, 992, 45

Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Natur, 585, 357

Huang, K.-H., Fall, S. M., Ferguson, H. C., et al. 2017, ApJ, 838, 6

Huertas-Company, M., Iyer, K. G., Angeloudi, E., et al. 2024, A&A, 685, A48

Hunter, J. D. 2007, CSE, 9, 90

Hwang, Y.-H., Wang, W.-H., Chang, Y.-Y., et al. 2021, ApJ, 913, 6

Ilbert, O., Arnouts, S., McCracken, H. J., et al. 2006, A&A, 457, 841

Ilbert, O., Capak, P., Salvato, M., et al. 2009, ApJ, 690, 1236

Ilbert, O., McCracken, H. J., Le Fèvre, O., et al. 2013, A&A, 556, A55

Ito, K., Valentino, F., Brammer, G., et al. 2024, ApJ, 964, 192

Joye, W. A., & Mandel, E. 2003, in ASP Conf. Ser. 295, Astronomical Data Analysis Software and Systems XII, ed. H. E. Payne, R. I. Jedrzejewski, & R. N. Hook (San Francisco, CA: ASP), 489

Kawamata, R., Ishigaki, M., Shimasaku, K., Oguri, M., & Ouchi, M. 2015, ApJ, 804, 103

Kawinwanichakij, L., Silverman, J. D., Ding, X., et al. 2021, ApJ, 921, 38

Kennicutt, R. C., Jr. 1998, ApJ, 498, 541

Khostovan, A. A., Kartaltepe, J. S., Salvato, M., et al. 2025, arXiv:2503.00120

Kocevski, D. D., Onoue, M., Inayoshi, K., et al. 2023, ApJL, 954, L4

Kravtsov, A. V. 2013, ApJL, 764, L31

Kümmel, M., Bertin, E., Schefer, M., et al. 2020, in ASP Conf. Ser. 527, Astronomical Data Analysis Software and Systems XXIX, ed. R. Pizzo et al. (San Francisco, CA: ASP), 29

Lang, P., Wuyts, S., Somerville, R. S., et al. 2014, ApJ, 788, 11

Long, A. S., Antwi-Danso, J., Lambrides, E. L., et al. 2014, ApJ, 970, 68

Ma, X., Hopkins, P. F., Boylan-Kolchin, M., et al. 2025, MNRAS, 477, 219

Macciò, A. V., Dutton, A. A., & van den Bosch, F. C. 2008, MNRAS, 391, 1940

Madau, P. 1995, ApJ, 441, 18

Marshall, M. A., Wilkins, S., Di Matteo, T., et al. 2022, MNRAS, 511, 5475

Matthee, J., Naidu, R. P., Brammer, G., et al. 2024, ApJ, 963, 129

Miller, T. B., Suess, K. A., Setton, D. J., et al. 2025, ApJ, 988, 196

Mo, H. J., Mao, S., & White, S. D. M. 1998, MNRAS, 295, 319

Montes, M., Trujillo, I., Prieto, M. A., & Acosta-Pulido, J. A. 2014, MNRAS, 439, 990

Morishita, T., Stiavelli, M., Chary, R.-R., et al. 2024, ApJ, 963, 9

Mosleh, M., Williams, R. J., Franx, M., et al. 2012, ApJL, 756, L12

Muñoz-Cuartas, J. C., Macció, A. V., Gottlöber, S., & Dutton, A. A. 2011, MNRAS, 411, 584

Naab, T., Johansson, P. H., & Ostriker, J. P. 2009, ApJL, 699, L178

Nadolny, J., Michałowski, M. J., Parente, M., et al. 2025, A&A, 693, L6

Nelson, D., Pillepich, A., Springel, V., et al. 2019, MNRAS, 490, 3234

Oesch, P. A., Bouwens, R. J., Carollo, C. M., et al. 2010, ApJL, 709, L21

Oke, J. B., & Gunn, J. E. 1983, ApJ, 266, 713

Ono, Y., Harikane, Y., Ouchi, M., et al. 2024, PASJ, 76, 219

Ono, Y., Ouchi, M., Harikane, Y., et al. 2025, ApJ, 991, 222

Onoue, M., Ding, X., Silverman, J. D., et al. 2025, NatAs, 9, 1541

Ormerod, K., Conselice, C. J., Adams, N. J., et al. 2024, MNRAS, 527, 6110

Pacifici, C., Kassin, S. A., Weiner, B. J., et al. 2016, ApJ, 832, 79

Pallottini, A., Ferrara, A., Gallerani, S., et al. 2022, MNRAS, 531, 5621

Popping, G., Pillepich, A., Calistro Rivera, G., et al. 2021, MNRAS, 510, 3321

Rodríguez-Puebla, A., Behroozi, P., Primack, J., et al. 2016, MNRAS, 462, 893

Romeo, A. B., Agertz, O., & Renaud, F. 2023, MNRAS, 518, 1002

Roper, W. J., Lovell, C. C., Vijayan, A. P., et al. 2022, MNRAS,

Saito, S., de la Torre, S., Ilbert, O., et al. 2020, MNRAS, 494, 199

Salim, S., Boquien, M., & Lee, J. C. 2018, ApJ, 859, 11

Salim, S., Tacchella, S., Osborne, C., et al. 2023, ApJ, 958, 183

Sersic, J. L. 1968, Atlas de Galaxias Australes (Cordoba: Observatorio Astronomico)

Shen, S., Mo, H. J., White, S. D. M., et al. 2003, MNRAS, 343, 978

Shen, X., Vogelsberger, M., Borrow, J., et al. 2024, MNRAS, 534, 1433

Shibuya, T., Ouchi, M., & Harikane, Y. 2015, ApJS, 219, 15

Shuntov, M., Akins, H. B., Paquereau, L., et al. 2025, arXiv:2506.03243

Shuntov, M., Ilbert, O., Toft, S., et al. 2025, A&A, 695, A20

Somerville, R. S., Behroozi, P., Pandya, V., et al. 2018, MNRAS, 473, 2714

Suess, K. A., Bezanson, R., Nelson, E. J., et al. 2022, ApJL, 937, L33

van der Wel, A., Franx, M., van Dokkum, P. G., et al. 2014, ApJ, 788, 28

Varadaraj, R. G., Bowler, R. A. A., Jarvis, M. J., et al. 2024, MNRAS, 533, 3724

Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, NatMe, 17, 261
Ward, E., de la Vega, A., Mobasher, B., et al. 2024, ApJ, 962, 176

Wechsler, R. H., & Tinker, J. L. 2018, ARA&A, 56, 435

Williams, R. J., Quadri, R. F., Franx, M., et al. 2010, ApJ, 713, 738

Williams, R. J., Quadri, R. F., Franx, M., van Dokkum, P., & Labbé, I. 2009, ApJ, 691, 1879

Wright, L., Whitaker, K. E., Weaver, J. R., et al. 2024, ApJL, 964, L10

Wu, X., Davé, R., Tacchella, S., & Lotz, J. 2020, MNRAS, 494, 5636

Yang, L., Leethochawalit, N., Treu, T., et al. 2022a, MNRAS, 514, 1148

Yang, L., Morishita, T., Leethochawalit, N., et al. 2022b, ApJL, 938, L17

Yang, L., Roberts-Borsani, G., Treu, T., et al. 2021, MNRAS, 501, 1028