A Bending in the Size-mass Relation of Star-forming Galaxies across $0.5 < z < 6.0$ at a Critical Stellar Mass of $10^{10}M_\odot$ Revealed by JWST

Avishai Dekel; David Elbaz; Emanuele Daddi; Hanwen Sun; Houjun Mo; Ke Xu; Longyue Chen; Luwenjia Zhou; Mauro Giavalisco; Maxime Tarrasse

REVIEW 2 major objections 5 minor 3 cited by

Star-forming galaxies bend in size at a fixed mass of 10 billion suns, and the compact ones can build the quiescent population at high redshift.

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2026-07-13 20:19 UTC pith:2UBDMHDF

load-bearing objection Solid JWST result: SFGs show a stable broken size-mass relation at ~10^10 M⊙ across 0.5<z<6; the cSFG-to-QG number-density claim is the soft interpretive step, not the observation. the 2 major comments →

arxiv 2603.22239 v3 pith:2UBDMHDF submitted 2026-03-23 astro-ph.GA

A Bending in the Size-mass Relation of Star-forming Galaxies across 0.5 < z < 6.0 at a Critical Stellar Mass of 10¹⁰M_odot Revealed by JWST

Longyue Chen , Tao Wang , Hanwen Sun , Ke Xu , Luwenjia Zhou , Tiancheng Yang , Maxime Tarrasse , Houjun Mo

show 7 more authors

Zhaozhou Li Yangyao Chen Avishai Dekel Emanuele Daddi Xuheng Ding Mauro Giavalisco David Elbaz

This is my paper

classification astro-ph.GA

keywords galaxy size-mass relationstar-forming galaxiesquiescent galaxiescompact star-forming galaxiesJWSThigh-redshift galaxiesgalaxy quenchingcompaction

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Using deep JWST imaging, this paper maps how galaxy size scales with stellar mass from cosmic noon back almost to the first billion years. Star-forming galaxies do not follow one smooth power law: below about 10 billion solar masses size tracks mass (and likely halo growth) as before, but above that mass the relation flattens because a large population of compact massive star-formers appears. Those compact objects have sizes, shapes, light profiles and number densities that match the massive quiescent galaxies that accumulate at z greater than 2. The authors therefore argue that the dominant route to high-redshift massive quiescent galaxies is compaction of already-compact star-formers, not major mergers of extended disks. A sympathetic reader cares because the result rewrites the high-mass end of galaxy structural evolution and supplies a concrete progenitor population that earlier HST work largely missed.

Core claim

Across 0.5 < z < 6, star-forming galaxies follow a broken power-law size-mass relation whose pivot mass stays near 10^10 solar masses while the high-mass slope flattens; the compact subset of these galaxies has the masses, surface-brightness profiles, morphologies and cumulative number densities needed to account for the observed buildup of massive quiescent galaxies at z > 2 via a compaction pathway.

What carries the argument

The smoothly broken power-law size-mass fit for star-forming galaxies (pivot mass Mp, low-mass slope alpha, high-mass slope beta), together with the offset-defined compact-star-forming sample whose gas-depletion times are used to predict the cumulative number density of quenched descendants.

Load-bearing premise

The claim that compact star-formers can supply the observed quiescent population rests on every such galaxy quenching after a fixed gas-depletion-time recipe and on no large competing channels changing the count.

What would settle it

A complete census of compact star-forming galaxies whose measured gas fractions or quenching times leave their cumulative number density well below the observed number density of massive quiescent galaxies at z greater than 2 would break the progenitor argument.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Solid JWST result: SFGs show a stable broken size-mass relation at ~10^10 M⊙ across 0.5<z<6; the cSFG-to-QG number-density claim is the soft interpretive step, not the observation.

read the letter

The new result is clean: with a mass-complete PRIMER NIRCam+MIRI sample they show that SFGs follow a broken power-law size-mass relation at every redshift from 0.5 to 6, with a nearly constant pivot near 10^10 M⊙ and a high-mass slope that flattens (even to ~0 at z>2). That is the part that sticks. Earlier HST work and a few simulations had hinted at high-mass flattening; this paper makes the pivot stable and the compact massive SFG population hard to ignore, and Appendix B shows why HST systematically overestimated Re for the compact systems.

What they do well is the observational scaffolding. Size recovery tests, residual-flux and Sérsic-boundary cleaning, BIC comparison of single vs broken models, UVJ vs sSFR classification, and the HST-JWST cross-match are all documented. The mixture model for QGs and the rising QG pivot with redshift are sensible secondary results. The stacked profiles, b/a and n for the compact SFGs look intermediate between extended SFGs and QGs without being forced by the definition.

The soft spot is exactly the one the reader flagged: the cumulative number-density argument that cSFGs can supply the high-z QG buildup assumes every cSFG quenches after a fixed Tacconi depletion time with no rejuvenation or other channels. That is a reasonable order-of-magnitude check, not a closed proof, and they present it as such. Defining cSFGs relative to the single-power-law fit is a bit circular on paper, but the independent morphology and surface-brightness comparisons still hold, so it does not sink the claim. Free parameters (Mp, α, β, mixture W, depletion coefficients) are standard for this kind of fit; nothing load-bearing is invented.

This is for people working on structural evolution, quenching, and the SHMR peak. The math and citation pattern look solid; the data volume and wavelength coverage are the real advance. I would send it to peer review without hesitation and would cite the broken-relation result myself. Engage with it.

Referee Report

2 major / 5 minor

Summary. The paper measures rest-frame optical size–stellar mass relations for field galaxies at 0.5<z<6.0 with PRIMER JWST/NIRCam+MIRI imaging (plus multiwavelength ancillary data). Using galight single-Sérsic fits and sSFR-based SFG/QG separation on a mass-, magnitude-, and S/N-complete sample of ~65k galaxies, the authors find that SFGs are better described by a smoothly broken power-law (Eq. 5) with a nearly constant pivot mass Mp~10^10 M⊙ and a high-mass slope that flattens with redshift, while QGs are better described by a two-component mixture model (Eqs. 6–7) whose transition mass rises with z. They interpret the SFG bend as two size-growth modes (halo-coupled below Mp; compaction/bulge growth above Mp), define compact SFGs (cSFGs) relative to the single power-law residual, and argue from stacked profiles, morphologies, and a cumulative number-density calculation that cSFGs can supply the observed buildup of massive QGs at z≳2 via compaction rather than major mergers of extended disks.

Significance. If the broken SFG relation and nearly constant Mp hold, the result is a clear observational advance over HST-era single power-law fits and directly constrains mass-dependent size growth and quenching pathways out to z~6. Strengths include a large mass-complete sample, MIRI-informed SED masses/redshifts, documented size-recovery tests (Appendix A), HST–JWST cross-checks that explain why the high-mass flattening was previously underrepresented (Appendix B), UVJ vs sSFR robustness (Appendix C), and BIC model comparison (Table 2). The cSFG progenitor interpretation is a falsifiable, high-impact claim for high-z massive QG formation, even though it rests on a simplified depletion-time accounting.

major comments (2)

Section 5.3 and left panel of Figure 6: the claim that cSFG number densities “can account for” the observed QG buildup assumes every cSFG quenches after its Tacconi et al. (2018) gas-depletion time with fixed coefficients (At=0.9, Bt=−0.62, Ct=−0.44, Dt=Et=0, δMS=1) and that rejuvenation, environmental quenching, or other channels do not materially change the count. This is load-bearing for the “compaction dominates” conclusion. Please add a sensitivity test (vary At/Bt/Ct or δMS within published ranges; allow a non-unity quenching efficiency or a modest rejuvenation fraction) and report how the cumulative cSFG curve shifts relative to the QG points, or else reframe the statement as an order-of-magnitude consistency check rather than a dominant-channel demonstration.
Section 5.2 / definition of cSFGs: compact SFGs are defined as ΔlogR < −1σ relative to the single power-law fit of Section 4.1, yet the same single-power-law residual is used both to identify the population that drives the broken-power-law bend and to argue that those objects are the QG progenitors. The stacked profiles, b/a, and n (Figure 6, Figure E2) are independent and supportive, but the paper should state explicitly that the morphological similarity is not circular with the size cut, and should show that the number-density match is robust to a modest change in the ΔlogR threshold (e.g., −0.5σ vs −1.5σ) or to defining cSFGs relative to the broken-law high-mass branch instead.

minor comments (5)

Table 2: for 0.5<z<1.0 and 4.0<z<6.0, ΔBIC is negative (favoring the single power-law). The text already notes sample-size and evolutionary reasons; a short quantitative statement of how much the high-mass slope β is still constrained in those bins would help readers judge whether the “all redshifts” claim is uniform or strongest at 1<z<4.
Equation 5: δ is fixed to 6 “to reduce degeneracy.” Please cite the prior (Kawinwanichakij et al. 2021) more explicitly for this choice and note whether free-δ fits change Mp or β at a level that affects the constant-pivot conclusion.
Section 3.2: exclusion of 2414 COSMOS SFGs at 2.2<z<2.8 is justified by the supercluster and Appendix D; state the fractional change in the high-mass slope when they are retained so readers can assess residual field-to-field variance.
Figure 3 insets and the last-panel definition of ΔlogR are useful; ensure the caption fully defines the mirrored KDE and the 1σ threshold used later for cSFGs so the figure stands alone.
Minor typos/consistency: “Draft version May 26, 2026” and arXiv date line; “A vishai Dekel” spacing; occasional “size-mass” vs “size–mass”; confirm that F277W/F356W assignment for 4<z<6 is stated once in the main text as well as in the figure caption.

Circularity Check

1 steps flagged

No load-bearing circularity: broken power-law and Mp are data-driven fits; cSFG definition uses single-power-law residuals but morphological/number-density comparisons remain independent measurements.

specific steps

other [Section 5.2 (classification of cSFGs/eSFGs)]
"We classify massive SFGs into two populations based on their offsets from the best-fit single power-law size–mass relation (i.e., ∆ logR, as illustrated in the last panel of Figure 3): •Compact star-forming galaxies (cSFGs): SFGs with ∆ logR <−1σ, i.e., galaxies lying more than 1σ below the best-fit single power-law size–mass relation."

cSFGs are defined as the 1σ under-size tail relative to the single power-law that the broken model later improves upon; this makes the existence of a compact excess partly definitional. However, the subsequent stacked profiles, axis ratios, Sérsic indices, and number-density matching are independent measurements, so the progenitor argument is not forced by construction and the circularity is only minor.

full rationale

The central observational claim (broken power-law size–mass relation for SFGs with nearly constant fitted Mp ≈ 10^10 M⊙ and high-mass flattening) is obtained by maximizing likelihood on the mass-complete JWST sample (Eqs. 3–5, Tables 1–2, BIC comparison), with recovery tests, HST–JWST re-analysis, and UVJ/sSFR robustness checks that do not presuppose the bend. The numerical coincidence of Mp with the SHMR peak is noted after the fit, not imposed. cSFGs are defined via residuals from the single power-law (Section 5.2), which is a classification choice that highlights the excess already visible in the data; their stacked surface-brightness profiles, b/a, Sérsic indices, and the cumulative number-density comparison (using an external Tacconi et al. 2018 depletion-time formula with fixed parameters) are independent observables, not forced by that definition. Self-citations (Wang et al. 2025, Sun et al. 2026) supply data products and photo-z/mass methods, not uniqueness theorems or the size–mass result itself. No equation reduces a claimed prediction to its own fitted input by construction, and no ansatz or uniqueness is smuggled via overlapping-author citation. Score 1 reflects only the mild residual-based classification step; the derivation chain is otherwise self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 1 invented entities

The central claims rest on standard cosmological and stellar-population assumptions plus a set of fitted broken-power-law and mixture-model parameters; no new physical entities are postulated beyond the observationally defined cSFG population.

free parameters (5)

pivot mass Mp (SFGs) = ~10^9.5–10^10.2 M⊙
Fitted freely in each redshift bin of the smoothly broken power-law (Eq. 5); reported values cluster near 10^10 M⊙ but are not fixed a priori.
low- and high-mass slopes α, β (SFGs) = α≈0.16–0.23, β≈0.01–0.19
Free parameters of the broken power-law; β is allowed to flatten with redshift.
mixture transition mass Mp and width W (QGs) = Mp rises from ~10^10.0 to ~10^10.5 M⊙
Free parameters of the logistic mixture model (Eqs. 6–7).
Tacconi depletion-time coefficients = At=0.9, Bt=-0.62, Ct=-0.44, Dt=Et=0, δMS=1
Fixed to literature values (At=0.9, Bt=-0.62, …) when converting cSFG counts into predicted QG number densities; not re-fitted but load-bearing for the progenitor claim.
smoothing factor δ = 6
Hard-set to 6 in the broken power-law to reduce degeneracy.

axioms (5)

domain assumption Flat ΛCDM cosmology with Ωm=0.3, ΩΛ=0.7, H0=70 km s^-1 Mpc^-1
Stated in Section 1; converts angular sizes and redshifts into physical kpc and comoving volumes.
domain assumption Kroupa IMF and Bruzual & Charlot 2016 SPS models with delayed-τ SFH and Calzetti dust
Used for all stellar-mass and sSFR estimates (Section 2.2).
domain assumption Single-component Sérsic profile adequately recovers Re for the magnitude and size cuts adopted
Validated by injection-recovery tests in Appendix A; multi-component or non-parametric sizes are not used.
domain assumption sSFR100 < 0.2 / tage(z) cleanly separates quiescent from star-forming galaxies
Primary classification (Eq. 1); UVJ alternative tested in Appendix C and yields consistent size-mass results.
domain assumption Log-normal intrinsic size scatter about the mean size-mass relation
Likelihood construction following van der Wel et al. (2014) (Section 4.1).

invented entities (1)

compact star-forming galaxies (cSFGs) independent evidence
purpose: Operationally defined population (Δlog R < -1σ from single power-law) used to argue for a compaction-driven quenching channel.
Definition is relative to the authors’ own single-power-law fit; independent morphological and number-density checks are provided, but the entity itself is introduced by the paper.

pith-pipeline@v1.1.0-grok45 · 31852 in / 3318 out tokens · 30546 ms · 2026-07-13T20:19:11.076009+00:00 · methodology

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read the original abstract

We investigate the rest-frame optical size-stellar mass relation of galaxies at $0.5<z<6.0$ using deep JWST/NIRCam and MIRI imaging from the PRIMER survey. We find that star-forming galaxies (SFGs) exhibit a broken power-law relation at all redshifts, with a nearly constant pivot mass ($M_{\rm p}$) of $\sim 10^{10} M_\odot$, and a slope flattening above $M_{\rm p}$. This highlights the prevalence of a population of compact, massive SFGs that was underrepresented in previous studies. The size distribution of quiescent galaxies (QGs) is well described by a mixture power-law model, with a pivot mass that increases from $M_{\rm p} \sim 10^{10.0} M_\odot$ at $z =0.75$ to $M_{\rm p} \sim 10^{10.5} M_\odot$ at $z = 2.6$, suggesting that the minimum halo mass required to quench high-mass galaxies increases with redshift. The bending in the size-mass relation of SFGs supports two distinct size growth modes. At $M_{\star} < M_{\rm p}$, size growth is closely coupled to halo growth, while at $M_{\star} > M_{\rm p}$, an increasing fraction of SFGs decouple from halo growth and become compact, likely associated with rapid bulge (and black hole) growth in $M_{\rm h} \gtrsim 10^{12} M_{\odot}$ halos. These compact SFGs are promising progenitors of massive QGs, as evidenced by their similar masses, surface brightness profiles, and morphologies. Their high number densities can account for the observed buildup of massive QGs at $z > 2$, suggesting that the compaction pathway, rather than major mergers of extended SFGs, dominates the formation of high-z massive QGs.

discussion (0)

Forward citations

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