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This paper claims that the observed mass–SFR–size relation — the tendency for galaxies to become more compact as they move away from the star-forming main sequence — is reproduced by two independent cosmological simulations, and that its st

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2026-08-02 19:31 UTC pith:LMV6K4UJ

load-bearing objection Useful, honest comparison of the joint mass–SFR–size relation in EAGLE and TNG100; the reported EAGLE-vs-observed slope difference is plausible but rests on an untested half-mass-to-half-light proxy and no error bars. the 3 major comments →

arxiv 2603.01726 v2 pith:LMV6K4UJ submitted 2026-03-02 astro-ph.GA

The Galaxy Stellar Mass-SFR-Size Relation in EAGLE, TNG100, and Observations

Jiani Chu , Dandan Xu , Enci Wang , Stijn Wuyts This is my paper
classification astro-ph.GA
keywords galaxy stellar mass–size relationstar-forming main sequencegalaxy star formation rategalaxy sizeEAGLE simulationIllustrisTNGgalaxy evolutioncosmological hydrodynamical simulations
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.

The paper sets out to show that the joint mass–SFR–size relation — the observed tendency for galaxies to become smaller and more compact as they drift away from the ridge of the star-forming main sequence (SFMS) — is not an accidental feature of one dataset but an emergent outcome of cosmological galaxy formation. By comparing SDSS and CANDELS galaxies with the EAGLE and TNG100 simulations across three redshift bins up to z = 2.5, the authors find that both simulations reproduce the trend at all redshifts, whereas the observations only show it clearly below z ≈ 1.5. The two simulations disagree on its strength: EAGLE makes the size drop with SFMS offset too steeply relative to observations, and TNG100 too shallowly. If the paper is right, this relative-size measure becomes a sharp new constraint on how feedback and gas accretion shape galaxies, and the trend's physical origin lies in time-variable star formation — compact galaxies at fixed mass scatter more in SFR over time while having similar average rates.

Core claim

In the paper's own terms, the central discovery is that the mass–SFR–size relation is a genuine, persistent feature of galaxy formation physics, not a calibration artifact: both EAGLE and TNG100, which were not tuned to reproduce it, yield the observed decrease of relative galaxy size ΔlogR_e with increasing offset ΔlogSFR from the star-forming main sequence, from z = 0 to z = 2.5. The observed samples show the same 'ridge-largest' pattern at z < 1.5 but not at 1.5 < z < 2.5, which the authors attribute to larger measurement uncertainties at high redshift. Quantitatively, EAGLE predicts a stronger size dependence on SFMS offset than observed at all redshifts, while TNG100 predicts a weaker o

What carries the argument

The analysis is carried by a relative-size metric, ΔlogR_e: each galaxy's logarithmic size is compared with the average size expected at its stellar mass from a power-law mass–size relation fitted to galaxies on the SFMS ridge. This removes the dominant mass dependence and, the authors argue, mostly cancels the systematic differences between simulated 3D stellar half-mass radii and observed projected half-light radii. The partner quantity is the SFMS offset ΔlogSFR, the logarithmic distance of a galaxy above or below the best-fit star-forming main sequence, computed separately for each sample and redshift bin. The paper then compares the median ΔlogR_e versus ΔlogSFR curves for observations,

Load-bearing premise

The argument leans on treating the 3D stellar half-mass radius stored in the simulations as a stand-in for the observed projected half-light radius, assuming that any systematic mismatch mostly cancels in the relative-size metric; if the ratio between these radii depends on how far a galaxy sits from the star-forming main sequence or on redshift, the simulated-versus-observed strength of the trend could be biased.

What would settle it

Measure the projected half-light radii of the simulated galaxies themselves (or compute the half-mass-to-half-light ratio as a function of ΔlogSFR): if that ratio varies systematically with SFMS offset or redshift, the direct adoption of 3D half-mass radii as a proxy for observed sizes is invalidated and the claimed strength comparison between EAGLE, TNG100, and observations no longer follows. Alternatively, a high-precision observational measurement of the size–offset relation at 1.5 < z < 2.5 that still shows no size decrease away from the SFMS would falsify the claim that the trend persists

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

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If this is right

  • The joint mass–SFR–size relation is an emergent property of cosmological simulations: neither EAGLE nor TNG100 was calibrated to match it, so its presence in both indicates it follows from the standard physics they share.
  • The observed non-detection at 1.5 < z < 2.5 is likely a measurement-uncertainty effect rather than a physical absence of the trend, since both simulations keep producing it there; higher-precision size measurements at those redshifts should recover it.
  • The EAGLE–TNG100 difference in trend strength supplies a new observational constraint: any model that wishes to match both the SFMS and the mass–size relation must also reproduce the intermediate slope of the ΔlogR_e–ΔlogSFR relation.
  • Interpreting the relation through SFR time variability implies that compact and extended galaxies of the same mass and time-averaged SFR can nevertheless be distinguished by their SFR scatter, linking galaxy size to the burstiness of star formation.
  • The near-flat relation for galaxies above log(M*/M⊙) ≈ 10.8 localizes the mechanism to lower-mass galaxies, where gas cycling and feedback-driven fluctuations are strongest.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the half-mass-to-half-light ratio of simulated galaxies varies with SFMS offset or redshift, the paper's strength comparison could be biased; a direct check — measuring projected half-light radii of simulated galaxies or computing that ratio as a function of ΔlogSFR — would settle how much of the EAGLE–observation gap is physical rather than definitional.
  • The compactness–burstiness link suggests a common driver with the fundamental metallicity relation and the scatter of the SFMS: size may serve as a cheap observational proxy for SFR stochasticity in galaxies where direct variability measures are unavailable.
  • A testable extension is to track individual galaxies in the simulations through the ΔlogR_e–ΔlogSFR plane over time to verify that compact systems actually oscillate between the upper and lower SFMS envelopes; if they instead sit at one offset, the time-variability explanation would need revision.
  • The z > 1.5 observational null could be tested with rest-optical sizes at high redshift and matched SFR indicators; if the trend still fails to appear, the interpretation would shift from measurement error to a genuine redshift evolution in the coupling.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper compares the joint stellar mass–SFR–size relation in two cosmological hydrodynamical simulations (EAGLE and TNG100) with observations from SDSS (z<0.2) and CANDELS (0.5<z<2.5). Using a relative size metric ΔlogRe defined from the mass–size relation of star-forming main-sequence (SFMS) galaxies, the authors report that both simulations reproduce the observed trend that galaxy sizes decrease with increasing offset from the SFMS ridge, that this trend weakens and is not detected in the observed sample at 1.5<z<2.5, and that EAGLE predicts a stronger size dependence while TNG100 predicts a weaker one. The paper interprets the trend as an emergent property of the simulations and relates it to time variability in star formation.

Significance. If the qualitative and differential claims are robust, the result is significant: the joint mass–SFR–size relation would provide a new, non-trivially emergent constraint on galaxy formation models, with different simulation implementations making different predictions. The paper's use of two independent simulation suites and its choice of a relative size metric to remove mass dependence are sensible, and the qualitative comparison is clearly presented. However, the central quantitative claims—especially the EAGLE-vs-observed and TNG-vs-observed differences in trend strength—rest on two unquantified assumptions: the equivalence of 3D half-mass radius to observed half-light radius in a relative sense, and the absence of significant measurement/scatter uncertainties. Because these are not tested, the paper is better viewed as presenting a promising qualitative result that needs strengthening before the quantitative conclusions can be accepted.

major comments (3)
  1. [Section 4 and Section 6 (R_hsm vs R_e proxy)] The analysis directly adopts the 3D stellar half-mass radius R_hsm as a proxy for the observed projected half-light radius R_e, and the paper acknowledges in Section 6 that forward-modeling is needed. The relative metric ΔlogRe removes only constant offsets between the two size definitions; it does not remove a dependence of R_hsm/R_e on ΔlogSFR or on redshift. For galaxies far above the SFMS, young stars, dust, and varying Sérsic index can shift the light-weighted radius relative to the mass-weighted radius by amounts comparable to the trend strength shown in Fig. 4 (≈0.1–0.2 dex per dex in ΔlogSFR). If this ratio varies with ΔlogSFR, the claimed EAGLE-vs-observed and TNG-vs-observed slope differences in Section 5.2 could be biased or even inverted. The limitation is acknowledged, but no quantitative test is provided. I request at least a check using the TNG100 2D half-light radii (whic
  2. [Section 5.2 and Fig. 4 (error bars and significance)] The central claims—that the trend is 'not detected' at 1.5<z<2.5 in observations, and that EAGLE predicts a stronger and TNG100 a weaker dependence—are stated without any uncertainty quantification. Fig. 4 shows median lines and 16th–84th percentile shaded regions, but no confidence intervals on the medians, no significance tests for the slope of ΔlogRe versus ΔlogSFR, and no assessment of whether the EAGLE/observed difference is statistically meaningful. The high-z CANDELS sample has only 5,111 galaxies above the mass cut (Table 1), and the measurement uncertainties are plausibly large, but this is asserted rather than demonstrated. Please provide bootstrap/jackknife confidence intervals on the median trends and, ideally, fitted slopes with uncertainties, so the reader can judge whether the differential claims are supported.
  3. [Section 4 (SFMS and mass–size fitting procedure)] The iterative SFMS fitting is described briefly, and the mass–size relation is fitted only to the SFMS-selected galaxies. The choice of a 1 dex lower threshold and the exclusion of zero-SFR galaxies could affect the resulting ΔlogSFR distribution and thus the ΔlogRe–ΔlogSFR relation. No convergence criterion, error on the fitted parameters, or test of the sensitivity to the threshold is given. This is not fatal, but since the offsets ΔlogSFR are defined relative to the fitted SFMS, a more detailed description or a robustness test would help support the quantitative comparison.
minor comments (4)
  1. [Figure 3 caption] The caption labels the color axis as 'Δ log SFR' but the text and figure description indicate the color scale should be ΔlogRe. Please correct the caption.
  2. [General typography] There are typographical issues, e.g., 'Fig.,1' in the Figure 3 caption, 'amnd' in the Fortuné et al. reference, and inconsistent use of 'Sersic' vs 'Sérsic'. These should be cleaned up.
  3. [Section 5.1] The discussion of the low-mass feature ('the largest galaxies from each of the stellar mass bins collectively follow a somewhat steeper log M*–log SFR relation') is interesting but not quantified; a short explanation of what is meant by 'steeper' would improve clarity.
  4. [Section 2.2] The photometric-redshift uncertainties for CANDELS are not discussed; given that the SFRs and masses come from SED fitting, some statement about redshift-dependent completeness or uncertainties (beyond the qualitative sentence in Section 5.1) would be useful.

Circularity Check

0 steps flagged

No significant circularity: the joint mass–SFR–size relation is measured independently from simulation and observational catalogs; self-citations are interpretive only.

full rationale

The central claim is a comparison of measured scaling relations, not a fitted prediction. The relative-size metric ΔlogRe is obtained by fitting the mass–size relation to SFMS galaxies and then examining how ΔlogRe varies with ΔlogSFR; no trend slope is fitted, and the off-ridge compactness is not imposed by construction. Both EAGLE and TNG100 are external simulations that were not calibrated to the joint relation, as the paper itself states: 'neither EAGLE nor TNG100 simulation were designed or calibrated to reproduce this joint mass–SFR–size relation.' Using each sample's own fitted SFMS to define offsets is standard and does not force the size trend. Self-citations to Wang et al. (2019), Gui et al. (2025), and Wang et al. (2022) appear only in the interpretive discussion of time-variable star formation and are not used to derive the scaling relation, so they are not load-bearing. The paper does acknowledge an important caveat in Section 4: 'we do not generate synthetic images... directly adopt the cataloged half–stellar–mass radius, R_hsm, as a proxy for the observed effective radius R_e.' This could bias the amplitude of the slope comparison if R_hsm/R_e varies with ΔlogSFR, but that is a measurement-systematics concern, not a circular reduction of the result to its inputs.

Axiom & Free-Parameter Ledger

5 free parameters · 3 axioms · 0 invented entities

The central claim rests mainly on the comparability of simulated half-mass radii with observed half-light radii via a relative-size metric, and on the fitted SFMS and mass–size relations used to define offsets. No new physical entities are introduced.

free parameters (5)
  • SFMS power-law slope and intercept per dataset and redshift bin
    Used to define the star-forming main sequence and hence the offset ΔlogSFR; fitted to each sample.
  • Mass–size relation power-law slope and intercept for SFMS galaxies per dataset and redshift bin
    Defines the expected size at fixed mass used to compute relative size ΔlogRe; fitted to each sample.
  • Iterative SFMS fitting threshold = 1 dex below the relation
    Chosen by hand to exclude outliers while defining the main-sequence ridge.
  • Stellar mass cut log(M*/M_sun) > 9.7 = 9.7
    To ensure resolved stellar particles in simulations and completeness in observations.
  • SFR selection range and zero-SFR exclusion = -2 < log SFR < 3
    Applied to both simulations and observations to focus on star-forming and nearby population.
axioms (3)
  • domain assumption Simulations reproduce the real galaxy population faithfully enough for the comparison
    The central claim assumes EAGLE and TNG100 outputs (masses, SFRs, half-mass radii) can be compared directly with observed half-light radii.
  • domain assumption Relative sizes remove systematic differences between half-mass and half-light radii
    Section 4 states that using ΔlogRe 'minimizes the impact and uncertainty rising from the adopted assumptions and corrections'; this is asserted, not verified.
  • domain assumption The SFMS and mass-size relation fits are unbiased references for defining offsets
    The entire analysis depends on the fitted power laws being a good representation of the mass–SFR and mass–size relations; outliers and non-linearities could bias the offsets.

pith-pipeline@v1.3.0-alltime-deepseek · 20593 in / 10565 out tokens · 91710 ms · 2026-08-02T19:31:14.354301+00:00 · methodology

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Cite this review

Pith. "Pith review of The Galaxy Stellar Mass-SFR-Size Relation in EAGLE, TNG100, and Observations." pith.science (2026). https://pith.science/paper/LMV6K4UJ

@misc{pith2026260301726,
  author       = {Pith},
  title        = {Pith review of: The Galaxy Stellar Mass-SFR-Size Relation in EAGLE, TNG100, and Observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LMV6K4UJ}},
  note         = {Machine review of arXiv:2603.01726}
}
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read the original abstract

Stellar mass, size, and star formation rate (SFR) are fundamental properties that encode the structural and evolutionary states of galaxies. Observations reveal a mass-SFR-size relation whereby galaxies become more compact both above and below the ridge of the star-forming main sequence (SFMS), linking galaxy structure to star formation activity. We investigate this relation by comparing galaxies from two cosmological hydrodynamical simulations, EAGLE and TNG100, with observational samples from SDSS and CANDELS over three redshift intervals (0 < z < 0.2, 0.5 < z < 1.5, and 1.5 < z < 2.5). Both simulations reproduce the observed trend that galaxy sizes decrease with increasing offset away from the SFMS. This trend, however, weakens and is not detected in the observational sample at 1.5 < z < 2.5, likely due to increased measurement uncertainties. In contrast, the trend persists in both simulations up to z = 2.5. Across all redshifts, EAGLE predicts a stronger size dependence on SFMS offset than observed, whereas TNG100 exhibits a weaker dependence. We discuss how this mass-SFR-size relation can be understood in terms of different time variability in star formation rate across the SFMS.

Figures

Figures reproduced from arXiv: 2603.01726 by Dandan Xu, Enci Wang, Jiani Chu, Stijn Wuyts.

Figure 1
Figure 1. Figure 1: Mass–size–SFR relation of SDSS galaxies. The left panel shows central galaxies (296,557), and the right panel shows the full sample (416,550). Contours correspond to the 10th, 30th, 50th, 70th, and 90th percentiles of the joint distribution of stellar mass and star formation rate (SFR). The black line denotes the star-forming main sequence. The color scale represents the median galaxy size of galaxies with… view at source ↗
Figure 2
Figure 2. Figure 2: Mass–size–SFR relation of CANDELS galaxies at 0.5 < z < 1.5 (left, 40,209 galaxies) and 1.5 < z < 2.5 (right, 37,842 galaxies), following the same plotting style as [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Relative galaxy size, ∆ log SFR, as a function of galaxy SFR and stellar mass: panels are arranged from top to bottom in order of increasing redshift, and from left to right for observations, EAGLE, and TNG100, as indicated in the legend, same plotting style as in Fig.,1. In the simulation panels, the corresponding observational SFMS relation is overlaid as a white dashed line. Note that only galaxies with… view at source ↗
Figure 4
Figure 4. Figure 4: Relative galaxy size, ∆ log Re, as a function of star formation rate offset, ∆ log SFR (i.e., deviation from the ridge of SFMS). Panels are arranged from top to bottom in order of increasing redshift, and from left to right for the observational sample, EAGLE, and TNG100, as indicated in the legend. In each panel, the black solid line shows the median ∆ log Re as a function of ∆ log SFR, while the gray sha… view at source ↗

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