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Evolution of the star formation rate surface density main sequence. Insights from a semi-analytic simulation since $z = 12$

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A semi-analytic simulation traces the star formation rate surface density of galaxies from z=12 to z=0, finding a ~3.5 dex decline and a main-sequence slope that peaks at 0.709±0.005 near z≈2.9 before falling to 0.085±0.003 at z=0.

desk verdict A useful and novel SAM-based Sigma_SFRMS fitting formula, but the size assumption needs an explicit caveat before the agreement claims can be fully trusted. read the letter →

arxiv 2412.00188 v2 pith:F44IFVAI submitted 2024-11-29 astro-ph.GA

Jakub Nadolny , Micha{l} J. Micha{l}owski , Massimiliano Parente , Martín Solar , Przemys{l}aw Nowaczyk , Oleh Ryzhov , Aleksandra Leśniewska This is my paper · ORCID
classification astro-ph.GA
keywords starformationratesurfacedensitymainsequencesemi-analyticmodelL-Galaxies2020galaxyevolutionhigh-redshiftgalaxiesJWSTcosmic
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper uses the L-Galaxies2020 semi-analytic galaxy formation model to trace how the star formation rate per unit area of galaxies, $\Sigma_{\rm SFR}$, evolves from $z=12$ to today. It finds that $\Sigma_{\rm SFR}$ declines by about 3.5 orders of magnitude over that time, and that the slope of the $\Sigma_{\rm SFR}$–stellar mass main sequence rises to a maximum of about 0.71 near $z\approx3$ before falling to about 0.09 at $z=0$. The paper attributes this slope evolution mainly to a dramatic drop in star formation rate in the most massive galaxies, with a smaller contribution from galaxy size growth. If right, the result explains why JWST sees a steeper and higher $\Sigma_{\rm SFR}$ main sequence at high redshift and provides a redshift-dependent fitting formula for the sequence.

What carries the argument

The central object is the L-Galaxies2020 semi-analytic model, specifically its predicted effective radius (StellarHalfLightRadius) and SFR, combined through the definition $\Sigma_{\rm SFR} = {\rm SFR}/(2\pi R_e^2)$. The argument is carried by fitting the slope and normalization of the $\Sigma_{\rm SFR}$–$M_*$ main sequence as polynomial functions of redshift (Equations 1 and 2) and combining them into Equation 3, which predicts the sequence at any redshift up to $z\sim10.8$. The physical mechanism identified is that the most massive galaxies dominate the cosmic star formation rate density below $z\sim4.5$ and undergo a much larger fractional SFR drop than lower-mass galaxies, which steepens and then flattens the main-sequence slope.

What would settle it

A mass-complete sample of galaxies with measured half-light radii and SFRs at $z\approx3$ and $z\approx0$ would settle the central claim: the model predicts a $\Sigma_{\rm SFR}{\rm MS}$ slope of $0.71\pm0.02$ at $z\approx3$ and $0.085\pm0.02$ at $z=0$, along with a ~5000% drop in SFR for $10^{11}\,M_\odot$ galaxies. Observing a significantly flatter high-redshift slope or a smaller SFR drop would falsify the explanation.

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Extended reading notes

Core claim

The central claim is that the star formation rate surface density main sequence ($\Sigma_{\rm SFR}{\rm MS}$) in the L-Galaxies2020 model evolves with a slope that peaks at $0.709\pm0.005$ at $z\approx2.9$ and declines to $0.085\pm0.003$ at $z=0$, while the overall $\Sigma_{\rm SFR}$ drops by roughly 3.5 dex from $z=12$ to $z=0$. The decline in slope is driven primarily by a rapid decrease in SFR in the most massive galaxies (about 5000% from $z\approx4$ to $0$), with a smaller contribution from their size growth; bulge build-up alone is insufficient to explain the evolution. The simulated $\Sigma_{\rm SFR}{\rm MS}$ agrees with observed relations at $z=0,1,2,5,7.5$ and with individual galaxies at $z>10$. The paper also derives a redshift-dependent fitting formula, $\log(\Sigma_{\rm SFR})=y_{\rm slope}(z)[\log(M_*/M_\odot)-9]+y_{\rm norm}(z)$, with polynomial coefficients given in Equations 1 and 2.

Load-bearing premise

The model's simulated half-light radii match real galaxy sizes at every redshift, even though $\Sigma_{\rm SFR}$ depends on the square of size and those sizes are not independently validated against the JWST samples used here.

Editorial extensions

If this is right

  • The fitting formula (Equation 3) predicts the $\Sigma_{\rm SFR}{\rm MS}$ at any redshift up to $z\sim11$, giving future JWST surveys a direct model-based expectation to test.
  • The slope peak near $z\approx3$ coincides with the peak of the cosmic star formation rate density, implying that the high-mass end of the main sequence was evolving fastest at cosmic noon.
  • The model implies that the decline of the $\Sigma_{\rm SFR}{\rm MS}$ slope toward low redshift is a signature of massive-galaxy quenching, visible even without invoking bulge feedback as the dominant driver.
  • Individual $z>10$ galaxies should fall within roughly $0.4$ dex of the simulated $\Sigma_{\rm SFR}{\rm MS}$, a testable prediction for the growing sample of spectroscopically confirmed high-redshift galaxies.
  • The dominance of massive galaxies in the cosmic star formation rate density below $z\sim4.5$ connects the main-sequence slope evolution to the overall history of star formation in the Universe.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the simulated half-light radii carry even a moderate systematic error, the inferred $\Sigma_{\rm SFR}$ normalization changes by about twice that error because $R_e$ enters squared; the agreement with observations is therefore as sensitive to size calibration as to SFR accuracy.
  • The redshift-dependent fitting formula could be repurposed as an empirical prior for correcting selection effects in surveys that under-detect low-surface-brightness galaxies, an application the paper does not explore.
  • A direct test of the model's mechanism would be to measure half-light radii and SFRs for a mass-complete sample of massive galaxies at $z\approx3$ and $z\approx0$; if the SFR drop of $10^{11}\,M_\odot$ galaxies relative to lower-mass galaxies is smaller than the simulated ~5000%, the predicted slope decline would be too steep.
  • The slope-peak redshift of about 2.9 could serve as a diagnostic for when massive galaxies transition from gas-rich star formation to quiescence in any galaxy formation model, not just in this SAM.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The manuscript uses the L-Galaxies2020 semi-analytic model to predict the evolution of the star-formation-rate surface density Sigma_SFR and its main sequence (Sigma_SFRMS) from z=12 to z=0. The authors define Sigma_SFR = SFR/(2*pi*R_e^2), compare the SAM predictions with literature observations at z=0, 1, 2, 5, and 7.5 and with individual galaxies at z>10, fit the evolution of the slope and normalization of the Sigma_SFRMS, and attribute the slope decline from 0.709 at z~2.9 to 0.085 at z=0 to a faster SFR decline in the most massive galaxies, with a smaller contribution from size growth. They also provide a redshift-dependent fitting formula, Eq. (3).

Significance. If the assumed size proxy is accurate, this is a useful first SAM-based prediction of the Sigma_SFRMS evolution and it provides a compact, easy-to-use fitting formula. The analysis is transparent in important ways: the mass-bin definitions, sample sizes, and fit coefficients are tabulated, and the comparisons with observed data are clearly described. The CSFRD comparison in Appendix A is also a valuable consistency check. However, the quantitative agreement with observations is weaker than the abstract suggests, and the central slope evolution depends on an unvalidated half-light-radius proxy, so the significance of the specific quantitative claims is currently conditional.

major comments (4)
  1. [§2.1, §2.3, Fig. 2, Table 2] The central quantitative results use the SAM's StellarHalfLightRadius as the effective radius R_e entering Sigma_SFR = SFR/(2*pi*R_e^2), but the manuscript does not validate the simulated size-mass relation against the observed half-light radii of the comparison samples. Since R_e enters squared, a mass-dependent systematic offset of delta dex in log R_e shifts log Sigma_SFR by -2*delta and changes the fitted slope by -2*d(delta)/dlogM*. The claimed slope peak of 0.709 at z~2.9, the decline to 0.085 at z=0, and the agreement at z=0, 1, 2, 5, and 7.5 are therefore not secure. The sentence in §2.3 that "we consistently used the same size estimates in the simulated data and observational results" describes an operational definition, not an accuracy validation. Please add a quantitative comparison of the SAM size-mass relation with observed R_e at the relevant redshifts, such as the JWST samples in Calabrò et al. (2024), and re-derive the slope evolution after applying any measured size correction, or explicitly state the magnitude of the residual size systematic and its effect on the slopes.
  2. [Abstract and §3.2] The abstract's claim that the simulated Sigma_SFRMS "agrees with the observed one at z=0, 1, 2, 5, and 7.5" is overstated relative to the body of the paper. In §3.2 the z=2 simulated normalization is about 0.5 dex higher than the Salim et al. (2023) relation, and at z=5 the simulated low-mass end is about 0.5 dex below the Calabrò et al. (2024) relation. The abstract should be rephrased to say agreement within about 0.5 dex with these offsets acknowledged, or the analysis must show that these offsets are within the combined systematic uncertainties.
  3. [Table 2 and §3.2] The claim that the Sigma_SFRMS is already present at z~11 is weakly supported. The z=11.5 fit is based on 42 galaxies with slope 0.95 ± 0.655, and the z=12.5 fit on 7 galaxies with slope 0.637 ± 1.593; the combined z=10.8 fit uses 220 galaxies and yields slope 0.65 ± 0.26. These uncertainties are large enough that a well-defined main-sequence slope at z>10 is not established. Please either restrict the claim to z ≲ 10.8 or present a robustness test, such as a bootstrap or a fixed-slope comparison, demonstrating that the high-z slope is meaningful.
  4. [§3.3] The causal attribution of the slope evolution would benefit from an explicit decomposition. Since log Sigma_SFR = log SFR - 2*log R_e - const, the per-mass-bin change between z~4 and z=0 should be expressed as Δlog Sigma_SFR = Δlog SFR - 2*Δlog R_e. Using the quoted values, the SFR drop dominates, with Δlog SFR ranging from about -1.9 to -1.2 dex while 2*Δlog R_e ranges from about 0.95 to 0.83 dex, but this calculation is not presented. In addition, the sentence "the change in Re also increases ΣSFR" is directionally ambiguous: an increase in R_e decreases Sigma_SFR. Please correct the wording and add the numerical decomposition.
minor comments (4)
  1. [Abstract] There is a typo in the abstract: "Telesescope" should be "Telescope".
  2. [§2.3] The text contains formatting artifacts such as "di fferences" and "di ffuse" that should be corrected to "differences" and "diffuse".
  3. [Table 2] The last row of Table 2, labeled z=10.8, appears after the z=12.5 row; the ordering should be chronological or the combined-fit row should be clearly separated with a note.
  4. [Eq. (3)] Equation (3) has a spacing typo in the term "ΣS FR"; it should be "Σ_SFR".

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central Sigma_SFR tracks, main-sequence slopes, and their evolution are direct outputs of the L-Galaxies2020 SAM compared with external observations, with no fitted parameter renamed as a prediction.

full rationale

The paper's derivation chain is self-contained rather than circular. The simulated galaxy population is produced by the L-Galaxies2020 SAM with fixed physical prescriptions, and Sigma_SFR is computed from the model's SFR and StellarHalfLightRadius. None of the observed Sigma_SFR measurements used for comparison (Calabro et al. 2024, Salim et al. 2023, etc.) are used to calibrate the SAM, so the agreement between simulated and observed Sigma_SFRMS is a genuine external comparison, not a fit recycled as a prediction. The redshift-dependent formula in Eq. 3 is a polynomial parameterization of the simulated slope and normalization evolution (Eqs. 1-2); it is an interpolation of the model output rather than an independent physical prediction, but the paper does not use Eq. 3 as evidence of model validity, so this is not load-bearing circularity. The causal interpretation in Section 3.3 (SFR drop dominates over size growth) is a decomposition of Sigma_SFR = SFR/(2*pi*R_e^2) applied to the same simulated quantities that produced the slope evolution; it is internally self-consistent but is an explanation of model behavior, not an independent test. The use of StellarHalfLightRadius as the observed half-light radius is an assumption about model fidelity and could affect the quantitative results, but it is a correctness/robustness concern, not a circularity, because the model sizes are not tuned to the target observed Sigma_SFRMS values. Overall, no step reduces by construction to its own input, and no load-bearing claim depends on a self-citation chain.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central results rest on the fidelity of the L-Galaxies2020 SAM and on the choice to treat its simulated stellar half-light radii as the physical R_e. The paper introduces no new entities, but its fitting formula (Eq 3) adds 11 polynomial coefficients fitted to the simulated slopes and normalizations, and several sample-selection choices (mass bins, fit ranges) shape the results.

free parameters (4)
  • Sixth-degree polynomial coefficients for Sigma_SFRMS slope (Eq 1) = [3.8972e-5, -0.001401, 0.01848, -0.1024, 0.1688, 0.2272, 0.0877]
    Fitted to the 12 snapshot slope values in Table 2; used to build Eq 3.
  • Third-degree polynomial coefficients for Sigma_SFRMS normalization (Eq 2) = [0.002315, -0.04812, 0.5879, -1.8406]
    Fitted to the snapshot normalizations at log(M*/M_sun)=9; used in Eq 3.
  • Stellar mass bin boundaries = 8 < log(M*/M_sun) < 9, 9 to 10, > 10; full sample > 8
    Chosen by hand for the mass-resolved evolution analysis (Section 2.2); the different evolutionary paths in Fig 1 depend on these bins.
  • Stellar mass range used for each Sigma_SFRMS fit = 8.0 to 11.0 at low z, narrowing to 8.0 to 9.2 at z=10.6 and 8.2 to 8.8 at z=12.5
    Set per snapshot in Table 2 because massive galaxies are absent at high z; this affects the fitted slopes, especially at z > 8.
assumptions (5)
  • domain assumption The L-Galaxies2020 SAM prescriptions produce realistic galaxy populations.
    Section 2.1 adopts the model of Parente et al. (2023); all Sigma_SFR predictions are model outputs and inherit any inadequacies in star formation, feedback, and size recipes.
  • domain assumption StellarHalfLightRadius from the SAM equals the physical effective radius used in observations.
    Section 2.1: 'We used StellarHalfLightRadius as the effective radius Re'. Because Sigma_SFR = SFR/(2*pi*Re^2), systematic size errors shift the predicted relation.
  • domain assumption Half-light radii from different observational surveys are mutually comparable.
    Section 2.3 combines literature sizes without a full homogenization; the paper argues only slopes, not normalizations, are robust across size definitions.
  • domain assumption A single power law in stellar mass describes the Sigma_SFRMS at each redshift.
    Table 2 fits log Sigma_SFR = a(log M* - 9) + b; if the true relation is curved, the quoted slopes and Eq 3 misrepresent the population.
  • ad hoc to paper High-redshift snapshots with very few galaxies are sufficient to define a main sequence.
    Table 2 gives N=42 at z=11.5 and N=7 at z=12.5 with slope errors of +/- 0.655 and +/- 1.593; the text still claims the MS is 'already observed' at z~11.

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Cite this review

Pith. "Pith review of Evolution of the star formation rate surface density main sequence. Insights from a semi-analytic simulation since $z = 12$." pith.science (2026). https://pith.science/paper/F44IFVAI

@misc{pith2026241200188,
  author       = {Pith},
  title        = {Pith review of: Evolution of the star formation rate surface density main sequence. Insights from a semi-analytic simulation since $z = 12$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F44IFVAI}},
  note         = {Machine review of arXiv:2412.00188}
}
abstract

Recent high-redshift ($z>4$) spatially resolved observations with the James Webb Space Telesescope have shown the evolution of the star formation rate (SFR) surface density ($\Sigma_{\rm SFR}$) and its main sequence in the $\Sigma_{\rm SFR}$-$M_*$ diagram ($\Sigma_{\rm SFR}{\rm MS}$). The $\Sigma_{\rm SFR}{\rm MS}$\ is already observed at cosmic morning ($z\sim7.5$). The use of $\Sigma_{\rm SFR}$\ is physically motivated because it is normalized by the area in which the star formation occurs, and this indirectly considers the gas density. The $\Sigma_{\rm SFR}$-$M_*$ diagram has been shown to complement the widely used (specific) SFR-$M_*$, particularly when selecting passive galaxies. We establish the $\Sigma_{\rm SFR}$\ evolution since $z=12$ in the framework of the L-Galaxies2020 semi-analytical model (SAM), and we interpret recent observations. We estimated $\Sigma_{\rm SFR}$(-$M_*$) and the cosmic star formation rate density (CSFRD) for the simulated galaxy population and for the subsamples, which were divided into stellar mass bins in the given redshift. The simulated $\Sigma_{\rm SFR}$\ decreases by $\sim3.5$ dex from $z=12$ to $z=0$. We show that galaxies with different stellar masses have different paths of $\Sigma_{\rm SFR}$\ evolution. We find that $\Sigma_{\rm SFR}{\rm MS}$\ is already observed at $z\sim11$. The simulated $\Sigma_{\rm SFR}{\rm MS}$\ agrees with the observed one at $z=0, 1, 2, 5$, and $7.5$ and with individual galaxies at $z>10$. We show that the highest $\Sigma_{\rm SFR}{\rm MS}$\ slope of $0.709\pm0.005$ is at $z\sim3$ and decreases to $\sim0.085\pm0.003$ at $z=0$. This is mostly driven by a rapid decrease in SFR with an additional size increase for the most massive galaxies in this redshift range. This coincides with the dominance of the most massive galaxies in the CSFRD from the SAM.

Figures

Figures reproduced from arXiv: 2412.00188 by the authors.

Figure 1
Figure 1. Star formation rate surface density ΣSFR as a function of redshift. The empty black squares show the median values for all the galaxies from L-Galaxies2020 with M∗> 108M⊙. The empty green, blue and redsquares show the median values for the L-Galaxies2020 sample divided into stellar mass bins with log(M∗/M⊙) between 8 and 9, 9 and 10, and above 10. The lines of the same colors are the second-degree polynomial, and th… view at source ↗
Figure 2
Figure 2. Star formation surface density ΣSFR main sequence (ΣSFRMS). The dotted lines show ΣSFRMS estimated using simulated galaxies from L-Galaxies2020 at a given reshift from z = 0 up to z ∼ 10.8 (the last dot-dashed fit includes three snapshots to increase the sample size; see Tab. 2). The colors indicate the (mean) redshift of the points corresponding to the ΣSFRMS with the same color. Salim et al. (2023) ΣSFRMS at z = 0… view at source ↗
Figure 3
Figure 3. Bulge-to-total mass ratio, effective radius, and SFR as a function of redshift, and SFR as a function of effective radius for simulated galaxies in three stellar mass bins as indicated in the legend. The redshifts in the right panel are shown for reference. These follow (roughly) the evolution of ΣSFR considering their stellar mass, and they are close to the predicted simulated ΣSFRMS at a similar redshift. This sho… view at source ↗

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  1. Mass--size evolution and the emerging passive--density relation revealed by JWST/NIRCam in the Spiderweb protocluster

    astro-ph.GA 2026-07 conditional novelty 6.0 of 10

    In the Spiderweb protocluster, passive fraction rises with local density to ~60% while passive mass–size intercepts sit between field and cluster values, indicating advanced quenching but ongoing size growth.

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.