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Star Formation Rates, Metallicities, and Stellar Masses on kpc-scales in TNG50

T0 review · 5 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper argues that TNG50's resolved star-forming main sequence is a by-product of the Schmidt-Kennicutt law and a local gas-to-stellar mass relation, with its shallow slope coming from AGN feedback in massive hosts.

desk verdict Useful TNG50 measurements with an honest but unclosed 33% gap in the origin-of-rSFMS derivation. read the letter →

arxiv 2501.18687 v2 pith:62HI3IBR submitted 2025-01-30 astro-ph.GA

Jia Qi , Alex M. Garcia , Davis Robinson , Paul Torrey , Jorge Moreno , Kara N. Green , Aaron S. Evans , Z. S. Hemler
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Lars Hernquist Sara L. Ellison
This is my paper · ORCID
classification astro-ph.GA
keywords resolvedstar-formingmainsequencemass-metallicityrelationIllustrisTNGSchmidt-Kennicuttlawleaky-boxmodelAGNfeedbackintegralfieldspectroscopygalaxyevolution
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 asks whether a cosmological galaxy-formation simulation reproduces the kpc-scale relations that integral-field surveys now measure, and what the answer says about the physics. It shows that TNG50's resolved star-forming main sequence (the power-law relation between star-formation rate surface density and stellar mass surface density on 1-kpc patches) is too shallow compared with observed galaxies, and it argues the shortfall is not missing star-formation physics but AGN feedback acting too strongly in massive hosts. The same spaxel-by-spaxel analysis finds that the resolved mass-metallicity relation matches the observed shape and that the local star-formation rate does not drive its scatter; host stellar mass does. The paper then derives the rSFMS as a composition of the resolved Schmidt-Kennicutt law and a local gas-to-stellar mass relation, and shows that a generalized leaky-box model reproduces the simulated gas and metallicity relations best when the net outflow rate is low. This matters because it turns resolved scaling relations into concrete tests of feedback implementations rather than just descriptions of the interstellar medium.

What carries the argument

The central machinery is a sample of 1-kpc $\times$ 1-kpc spaxel maps built from TNG50 galaxies with $M_\star>10^9\,M_\odot$, treated as individual parcels that can gain and lose gas. Three elements carry the argument: the Springel & Hernquist (2003) volumetric star-formation prescription, which makes the resolved Schmidt-Kennicutt relation a written-in rule rather than an emergent result; the composition identity $\Sigma_{\rm SFR}\propto\Sigma_{\rm gas}^k\propto\Sigma_\star^{nk}$, which converts the two host-independent gas relations into the rSFMS; and the generalized leaky-box equations (8), (13), and (22), which evolve stellar, gas, and metal surface densities with explicit inflow and outflow mass-loading factors $\eta_{\rm in}$ and $\eta_{\rm out}$.

What would settle it

Measure the resolved star-forming main sequence in galaxies with $M_\star<10^{10}\,M_\odot$ using an integral-field survey; if the slope is near $0.3$ rather than the $\sim0.66$ that TNG50 produces for such hosts, the claim that AGN feedback causes the shallow stacked slope fails.

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Extended reading notes

Core claim

On 1-kpc spaxels at $z=0$, TNG50 produces a resolved star-forming main sequence $\Sigma_{\rm SFR}\propto\Sigma_\star^\alpha$ with a stacked slope $\alpha=0.30$, shallower than the $0.7$ to $1.1$ slopes reported by integral-field surveys. The paper's central claim is that this relation is not independently fundamental: it is the composition of the resolved Schmidt-Kennicutt law $\Sigma_{\rm SFR}\propto\Sigma_{\rm gas}^k$ (best-fit $k=1.52$) and the local gas-stellar mass relation $\Sigma_{\rm gas}\propto\Sigma_\star^n$ (best-fit $n=0.137$), which together predict $\alpha=nk\simeq0.20$. The remaining difference from the measured slope, and the flattening of the rSFMS with host mass, is attributed to AGN feedback: per-galaxy slopes fall from $0.66$ in the lowest-mass hosts to $0.30$ or inverted in the highest-mass hosts, and the high-mass systems dominate the stacked sample. The resolved mass-metallicity relation, by contrast, matches the observed shape, with its scatter governed by host stellar mass; and a generalized leaky-box model with explicit inflow and outflow terms describes the simulated gas and metallicity relations, preferring a near-zero net outflow rate.

Load-bearing premise

The whole leaky-box argument rests on the assumption that the gas inflow rate into a 1-kpc patch is proportional to that patch's star formation rate, an assumption the paper itself calls crude and untested at sub-galactic scales.

Editorial extensions

If this is right

  • The rSFMS slope in TNG50 is not set by the star-formation law alone; it is the product of the Schmidt-Kennicutt index and the local gas-to-stellar mass index, so matching observed slopes means getting both gas relations right.
  • Because low-mass TNG50 hosts already produce per-galaxy slopes near the observed range, the simulation's overall mismatch is concentrated above roughly $10^{10.5}\,M_\odot$, identifying AGN feedback as the physics to adjust.
  • The good resolved mass-metallicity agreement indicates that metal production, return, and redistribution in TNG50 are consistent with integral-field observations even where star-formation feedback appears too aggressive.
  • In the leaky-box model, the gas-stellar mass relation is controlled by the net outflow rate while the metallicity relation is controlled mainly by inflow dilution, so TNG50's resolved relations imply a low net outflow rate.
  • Resolved scaling relations therefore provide a comparative test of feedback implementations: a simulation tuned to reproduce global galaxy properties can still fail or succeed on 1-kpc scales, and these relations show where to look.

Reading between the lines

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

  • If the mass dependence is real, integral-field surveys that deliberately include low-mass star-forming galaxies should measure a steeper rSFMS than surveys dominated by $M_\star>10^{10.5}\,M_\odot$ systems; the mass-slope trend itself could become a calibrator for AGN feedback strength.
  • The compositional derivation is quantitatively incomplete (predicted $\alpha=0.20$ versus measured $0.30$); redoing the same derivation with a molecular-gas version of the local gas-stellar relation could close the gap in TNG50, just as molecular gas does for the observed rSFMS.
  • The paper's leaky-box conclusions rest on the proportionality between inflow and SFR at kpc scales; measuring the actual gas flux across spaxel boundaries in TNG50 would test Equation 11 directly and would either validate or revise the low-net-outflow preference.
  • The absence of a resolved fundamental metallicity relation in TNG50, in tension with some observational analyses, may reflect AGN-driven central enrichment; forward-modeling synthetic integral-field observations from the simulation could determine whether the discrepancy is physical or diagnostic.
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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

5 major / 5 minor

Summary. This manuscript uses TNG50-1 to construct 1 kpc spaxel maps for 2,734 galaxies with Mstar > 1e9 Msun at z=0, and measures the resolved star-forming main sequence (rSFMS), the resolved mass-metallicity relation (rMZR), their host-mass dependence, and the resolved Schmidt-Kennicutt (SK) and gas-mass relations. It reports an rSFMS slope alpha=0.302, compares it with CALIFA, MaNGA, ALMaQUEST, PHANGS, and EAGLE, and argues that the rSFMS is an indirect consequence of the SK law combined with the local gas-stellar mass relation (predicted alpha=nk=0.20). The paper also extends the Zhu et al. (2017) resolved leaky-box model with explicit inflow and outflow terms, and interprets the TNG scaling relations as preferring a low net outflow rate.

Significance. The paper provides a useful TNG50 benchmark for kpc-scale scaling relations, with careful spaxel construction and explicit robustness tests in Appendices A and B, and it makes the code and data products publicly available. Its transparency about the prescribed nature of the SK law in TNG is a strength. The rMZR comparison and the host-mass decomposition of the rSFMS are valuable. If the quantitative gap in the origin argument and the ad hoc sub-kpc inflow assumption were addressed, the proposed interpretive framework would be a meaningful step toward connecting resolved observations with simulation subgrid physics.

major comments (5)
  1. [Section 4.1, Eq. (7)] The claimed origin of the rSFMS is only qualitative: combining the fitted SK law (epsilon=5.89e-14, k=1.52) with the gas-mass relation n=0.137 gives alpha=nk=0.20, while the rSFMS slope measured in Section 3.1 is alpha=0.302. The 33% shortfall is acknowledged but not closed, and the suggested molecular-gas explanation is not tested. Because this is the quantitative basis for conclusion (iii), the central claim should either be reframed as a qualitative tendency or be supported by a molecular-gas or radial-inclusive calculation.
  2. [Section 4.1.1, Figure 10] Equation (7) assumes a single-power-law SK normalization, but Figure 10 shows that the SK normalization depends on galactocentric radius, and Section 4.1.1 invokes exactly this radial dependence to explain the host-mass dependence of the rSFMS. Omitting the radial term from the derivation while making it central to the mass-dependence argument is internally inconsistent: the same mechanism cannot be negligible in the origin claim and dominant in the mass-dependence explanation. A derivation that includes the radial dependence of epsilon, or an explicit justification for averaging it out, is needed.
  3. [Section 3.1.1, Table 1] The host-mass-resolved slopes in Table 1 range from alpha=0.671 in the lowest-mass bin to alpha=0.25-0.33 at high mass. The low-mass slope is more than three times the predicted 0.20 from Section 4.1, and this is the regime where AGN feedback in TNG is weakest. The attribution of the simulated-versus-observed slope difference to over-strong AGN feedback in massive hosts (Section 3.1.1) therefore does not address the failure of the origin model at low host masses.
  4. [Section 4.2, Eq. (11)] The leaky-box model's conclusions about net outflow rates depend on the assumption dSigma_gas,in/dt = eta_in Sigma_SFR at 1 kpc scales, which the paper itself labels as '(crude)'. Equations (12)-(14) and the Section 4.2.2 preference for a low net outflow rate all follow from this proportionality. The assumption should be checked directly in TNG, for example by measuring gas fluxes across spaxel boundaries; without such a check, the outflow/inflow conclusion is not established.
  5. [Section 4.2, Eqs. (20)-(22)] The conclusion that the rMZR is insensitive to eta_out (Section 4.2.2) follows from the assumption in Equation (20) that outflowing gas has exactly the spaxel's current metallicity. This assumption is not checked against TNG, where wind metal loading can differ from the local ISM value. If outflows are preferentially metal-enriched or metal-poor, the rMZR would depend on eta_out and the contrast with 'net outflow' models would weaken.
minor comments (5)
  1. [Section 3, introductory paragraph] The text refers to the 'Kennicut-Schmidt relation'; this should be 'Kennicutt-Schmidt relation'.
  2. [Figure 2 caption] The PHANGS comparison is described as a 'solid purple line' in the text and as a 'solid black line' in the caption; please make the line descriptors consistent.
  3. [Section 4.2.2] The text says Figures 14 and 15 show predictions for the rSFMS and rMZR, but Figure 14 shows the gas-mass main sequence; please correct the figure reference.
  4. [Section 5, item (ii)] The word 'IllutrisTNG' is a typo and should read 'IllustrisTNG'.
  5. [Section 4.2.1, Figures 12-13] The 'five representative spaxels' are mentioned repeatedly but their initial Sigma_gas values are not defined in the text or figures; please identify these tracks explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the rSFMS derivation combines a prescribed (but explicitly acknowledged) SK law with an emergent gas–stellar mass relation and is not forced; the leaky-box model is a calibrated toy rather than a prediction.

full rationale

The paper's central derivation (Section 4.1) combines Eq. 5 (SK: ΣSFR=εΣgas^k) with Eq. 6 (Σgas∝Σ⋆^n) to obtain Eq. 7 (ΣSFR∝Σ⋆^{nk}) and compares α=nk=0.20 with the directly measured rSFMS slope 0.302. This is an algebraic combination of two independently measured relations, not a restatement of the rSFMS: the predicted slope is not imposed and in fact differs by about 33%, which the authors explicitly concede. The SK relation is indeed a prescribed subgrid input in TNG (Section 2.1: "The existence of the (resolved) Schmidt-Kennicutt relation in these models is therefore not emergent, it is prescribed"), but the paper says so and does not claim otherwise; the Σgas–Σ⋆ relation is emergent, so the derivation contains independent content. The leaky-box model (Section 4.2) is calibrated using TNG's SK parameters (ε,k), return fraction R, and yield y, and the inflow/outflow loading factors are varied to match the same TNG relations; the resulting "preference for a low net outflow rate" is a parameter constraint from fitting, not a prediction dressed as a first-principles result. No load-bearing self-citation or imported uniqueness theorem is used: self-citations (Hemler et al. 2021; Garcia et al. 2023/2024/2025) support peripheral statements about TNG metallicity gradients and are not the basis of the main argument. External benchmarks (CALIFA, MaNGA, PHANGS, EAGLE) are used for comparison, and the rMZR agreement is an independent check. Therefore no circular step meets the bar of Eq. X = Eq. Y by construction or a fitted parameter renamed as a prediction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claims rest on TNG subgrid prescriptions (especially the prescribed SK law), on several untested assumptions in the leaky-box model, and on parameters that are either fitted to the same TNG data or adopted from earlier TNG papers. No genuinely new physical entities are introduced.

free parameters (6)
  • initial gas surface density (Sigma_gas,0) range = 10^7.5 to 10^10.0 M_sun/kpc^2 in steps of 0.25 dex
    Initial condition for leaky-box integrations; chosen to cover the observed spaxel range, not fitted to TNG.
  • inflow mass loading factor eta_in = 0.0, 0.25, 0.5
    Grid of values in the leaky-box model; comparison with TNG suggests low values are preferred, but no formal fit is performed.
  • outflow mass loading factor eta_out = 0.0, 0.25, 0.5
    Grid of values in the leaky-box model; the net outflow rate is effectively tuned to match the TNG Sigma_gas-Sigma_star relation.
  • return fraction R = 0.5
    Estimated from the Chabrier IMF; treated as a fixed input, not fitted.
  • metal yield y = 0.05
    Taken from Torrey et al. (2019) for TNG; treated as a fixed input.
  • SK slope k and normalization epsilon = k=1.52, epsilon=5.89e-14
    Fitted to TNG spaxels in Section 4.1, then used as fixed inputs to the leaky-box model; these are measurements from the same data that the model is later compared to.
assumptions (5)
  • domain assumption Star formation follows the volumetric Schmidt-Kennicutt relation with free-fall time proportionality (Equation 2).
    This is the TNG subgrid prescription; the existence of the resolved SK relation is therefore not emergent, as the authors themselves note.
  • ad hoc to paper Inflow rate is proportional to SFR at sub-galactic scales (Equation 11).
    The authors call this a crude assumption; it is needed for the leaky-box model to have a closed form.
  • ad hoc to paper Outflowing gas has the same metallicity as the current spaxel (Equation 20).
    This assumption makes the rMZR insensitive to eta_out, a key qualitative result; it is not independently validated.
  • domain assumption Inflowing gas is pristine, with Z_in = 0.
    Assumed for simplicity; the paper argues non-zero Z_in would not change the qualitative behavior.
  • domain assumption Average stellar mass migration into and out of spaxels is negligible.
    Stated before Equation 8; needed for the simple stellar mass evolution equation.

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Cite this review

Pith. "Pith review of Star Formation Rates, Metallicities, and Stellar Masses on kpc-scales in TNG50." pith.science (2026). https://pith.science/paper/62HI3IBR

@misc{pith2026250118687,
  author       = {Pith},
  title        = {Pith review of: Star Formation Rates, Metallicities, and Stellar Masses on kpc-scales in TNG50},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/62HI3IBR}},
  note         = {Machine review of arXiv:2501.18687}
}
abstract

Integral field units (IFU) have extended our knowledge of galactic properties to kpc (or, sometimes, even smaller) patches of galaxies. These scales are where the physics driving galaxy evolution (feedback, chemical enrichment, etc.) take place. Quantifying the spatially-resolved properties of galaxies, both observationally and theoretically, is therefore critical to our understanding of galaxy evolution. To this end, we investigate spatially-resolved scaling relations within galaxies of $M_\star>10^{9.0}$ at $z=0$ in IllustrisTNG. We examine both the resolved star-forming main sequence (rSFMS) and the resolved mass-metallicity relation (rMZR) using $1~{\rm kpc}\times1~{\rm kpc}$ maps. We find that the rSFMS in IllustrisTNG is well-described by a power-law, but is significantly shallower than the observed rSFMS. However, the disagreement between the rSFMS of IllustrisTNG and observations is likely driven by an overestimation of AGN feedback in IllustrisTNG for the higher mass hosts. Conversely, the rMZR for IllustrisTNG has very good agreement with observations. Furthermore, we argue that the rSFMS is an indirect result of the Schmidt-Kennicutt (SK) law and local gas relation, which are both independent of host galaxy properties. Finally, we expand upon a localized leaky-box model to study the evolution of idealized spaxels and find that it provides a good description of these resolved relations. The degree of agreement, however, between idealized spaxels and simulated spaxels depends on the `net' outflow rate for the spaxel, and the IllustrisTNG scaling relations indicate a preference for a low net outflow rate.

Figures

Figures reproduced from arXiv: 2501.18687 by the authors.

Figure 1
Figure 1. Example of Our Spaxel Construction in IllustrisTNG. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. The Resolved Star Formation Main Se￾quence (rSFMS) in IllustrisTNG The rSFMS in TNG at z = 0 with 1 kpc spaxel resolution. The solid orange line shows the median value of ΣSFR in each Σ⋆ bin, whilst the two dashed orange lines indicate the 16th-84th percentiles. The background 2D distribution displays our selected spax￾els, color-coded by the number in each bin. For comparison, we show the rSFMS from the EAGLE simul… view at source ↗
Figure 3
Figure 3. Best-fitting parameters for the rSFMS of individual galaxies. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: The rSFMS for galaxies binned by total mass. The rSFMS for galaxies within different mass bins as indicated by the title. The black solid line plots the median rSFMS relation and the black dashed line indicates the 1σ scatter. The colored background shows the distribut…
Figure 6
Figure 6. Figure 6: The rMZR for galaxies binned by total mass. The rMZR split into different global stellar-mass bins (colored lines). The black solid line represents the median rMZR and the gray shaded region is the 1σ scatter (same as [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: The Resolved Fundamental Metallicity Re [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Resolved Schmidt-Kennicutt (SK) rela￾tionship in TNG. The SK relation for spaxels in TNG at z = 0 with 1 kpc spaxel resolution. The colored lines rep￾resent the median SK relation in different mass bins, while the black line represents the median relation including all…
Figure 10
Figure 10. Figure 10: Radial dependence of the SK relation. The SK (same as [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: The radial dependence of the rSFMS. Same as [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: The gas mass main sequence in a resolved [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 14
Figure 14. Figure 14: The gas mass main sequence in a re￾solved leaky-box model. The fgas-Σ⋆ formed with differ￾ent choices of ηin and ηout. The colored background shows the distribution of actual IllustrisTNG spaxels included in this study. The colored-solid lines are the relations formed…
Figure 15
Figure 15. Figure 15: The rMZR in a resolved leaky-box model. The rMZR formed with different choices of ηin and ηout. The colored background shows the distribution of actual Illus￾trisTNG spaxels included in this study, the same as [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: Modified Smoothing Kernel A. MODIFIED SMOOTHING KERNEL In Section 2.3, we discuss our method for construct￾ing resolved maps of the TNG galaxies. Throughout the main text, we utilize the cubic-spline kernel smoothing function to “reconstruct” the density by distributi…
Figure 17
Figure 17. Figure 17: Dependence on Definition of “Resolved” Pixel solid line, and the scatter is represented by the shaded region (the upper and lower bounds representing the 84th and 16th percentile of the log ΣSFR at each log Σ⋆ bin, respectively). We find that the choice of kernel has …

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.