The origin of the metallicity difference between star-forming and passive galaxies: Insights from {\nu}2GC semi-analytic model

Masahiro Nagashima; Qiansheng Liu; Taira Oogi; Takashi Okamoto

REVIEW 4 major objections 5 minor 53 references

The origin of the metallicity difference between star-forming and passive galaxies: Insights from {\nu}2GC semi-analytic model

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that the observed stellar metallicity excess of passive galaxies at fixed mass is produced by slow strangulation, with the size of the gap set by the star formation timescale.

desk verdict A transparent model study that pins the passive/star-forming metallicity offset on long star formation timescales in dwarfs—convincing as a diagnostic, conditional on its tau* law. read the letter →

arxiv 2506.00378 v1 pith:TUNPT3FH submitted 2025-05-31 astro-ph.GA

Qiansheng Liu , Takashi Okamoto , Taira Oogi , Masahiro Nagashima This is my paper

classification astro-ph.GA

keywords galaxies:abundancesevolutionformationstrangulationstartimescalestellarmetallicityquenchingsemi-analyticmodel

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 argues that the observed excess of stellar metallicity in passive galaxies over star-forming galaxies of the same stellar mass is produced by strangulation, a quenching process that cuts off the supply of fresh low-metallicity gas while letting the galaxy keep forming stars from its existing cold gas. Using the ν2GC semi-analytic model, the paper reproduces the local mass–metallicity and potential–metallicity relations for both populations and shows that the size of the metallicity gap is controlled by the star formation timescale: longer timescales give larger gaps, and shorter timescales erase them. If correct, the measured offset is direct evidence that much of the quenching in low-mass galaxies is slow, acting on a star-formation timescale, rather than instantaneous gas removal, and it turns the metallicity gap into a clean diagnostic for star-formation prescriptions in galaxy models.

What carries the argument

The load-bearing mechanism is the combination of strangulation with the velocity-dependent star formation timescale law $\tau_* = \epsilon_*^{-1} \tau_d [1 + (V_d/V_*)^{-\alpha_*}]$, with fiducial values $\epsilon_*=0.46$, $V_*=197\,\mathrm{km\,s^{-1}}$, and $\alpha_*=2.14$. Cold gas is consumed at the rate $\Psi = M_{\rm cold}/\tau_*$, and the metal content of that gas evolves as $d(M_{\rm cold}Z_{\rm cold})/dt = [p - (\alpha + \beta)Z_{\rm cold}]\Psi$ with yield $p = 1.68\,Z_\odot$; once accretion is cut off, the absence of dilution makes the remaining cold gas and the stars formed from it progressively more metal-rich. The velocity-dependent term makes low-mass galaxies build stars several times more slowly than a dynamical-time Schmidt law, which is exactly what gives strangulation time to create a pronounced metallicity gap.

What would settle it

Measure the molecular gas depletion times of low-mass galaxies with $M_* \sim 10^9$–$10^{10}\,M_\odot$ at $z \approx 0$: if the typical depletion time is significantly shorter than the value implied by $\tau_* = \epsilon_*^{-1}\tau_d[1+(V_d/V_*)^{-\alpha_*}]$ with $\epsilon_*=0.46$, $V_*=197\,\mathrm{km\,s^{-1}}$, and $\alpha_*=2.14$, the long timescales on which the gap depends do not exist. A cheaper check already in the paper is replacing that law with $\tau_*=\epsilon_*^{-1}\tau_d$, which makes the predicted gap vanish.

Watch

Extended reading notes

Core claim

The central claim is that the stellar metallicity gap between passive and star-forming galaxies at fixed stellar mass, which past cosmological simulations and several semi-analytic models failed to reproduce, arises naturally when passive galaxies are quenched by strangulation and when low-mass galaxies form stars on timescales longer than their dynamical times. In the fiducial model, halting cold-gas accretion prevents dilution of the already enriched cold gas; the quenched galaxy keeps forming stars and enriching until the gas is exhausted, so its final stellar population ends up more metal-rich than a comparable star-forming galaxy that continues to accrete low-metallicity gas. The model matches the observed mass–metallicity and potential–metallicity relations simultaneously. The paper further shows that adopting a Schmidt law with $\tau_* \propto \tau_d$ removes the gap, that varying the star formation efficiency $\epsilon_*$ changes the gap in the expected direction, and that instantaneous cold-gas stripping does not produce the observed offset.

Load-bearing premise

Everything rests on low-mass galaxies forming stars slowly, taking several times longer than their free-fall or orbital time to consume their gas; if real low-mass galaxies consume their cold gas quickly, strangulation cannot build the observed metallicity gap.

Editorial extensions

If this is right

If the claim is right, the size of the metallicity gap at fixed stellar mass is a direct indicator of the star formation timescale, so it can be used to test the star-formation and feedback prescriptions adopted in galaxy simulations.
Cosmological simulations that currently predict nearly identical metallicities for passive and star-forming dwarfs need an additional physical process that preferentially extends star formation timescales in low-mass galaxies to match both the gap and the stellar ages of dwarfs.
Instantaneous cold-gas stripping and quasar-mode feedback that removes gas quickly should not, on their own, generate the observed offset; models that invoke them need an extra ingredient such as a size-dependent quenching probability to match the data.
Gradual hot-gas stripping from satellites with timescales of 1–3 Gyr leaves the metallicity gap nearly unchanged, because the enhancement only begins once the hot gas is mostly depleted.
The model predicts metal-enhanced passive galaxies among isolated central dwarfs that live in slowly growing halos; these objects are a direct test of the discrete gas-accretion prescription.

Reading between the lines

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

One editorial extension: if the velocity-dependent timescale law is correct, the amplitude of the metallicity gap should scale with circular velocity, so resolved surveys of low-mass galaxies could measure $\alpha_*$ directly from the mass dependence of the gap.
Another editorial inference: the same argument predicts that recently quenched galaxies should show a stronger metallicity offset at higher redshift, when the time since strangulation is closer to one star-formation timescale; this could be searched for in deep spectroscopic samples.
One more: if a future model replaces the discrete 'gas only accretes when the halo mass doubles' prescription with continuous accretion, the enhanced metallicities of isolated central dwarfs should disappear while the satellite gap survives, cleanly separating accretion physics from quenching physics.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's my read on 2506.00378.

The headline: this is a clean, honest model-experiment paper that identifies long star formation timescales in low-mass galaxies as the missing ingredient for reproducing the observed stellar metallicity offset between passive and star-forming galaxies. Strangulation itself is Peng et al. (2015); the failure of simulations to reproduce the offset is Okamoto et al. (2017). The new piece is the demonstration inside nu2GC, backed by control experiments that actually target the mechanism: varying the SFE changes the gap in the expected direction, instantaneous removal of cold gas erases it, and swapping Eq. (4) for a Schmidt law (Eq. 11) eliminates the offset entirely. That last experiment is the most useful one—it shows the offset in this model is a monotonic consequence of the assumed tau* law for dwarfs, which is exactly the law Makiya et al. built when calibrating Eq. (4) to cold gas fractions in dwarfs.

Credit where due: the internal logic is transparent, the control set is clean, and the authors flag the low-mass passive central prediction as probably artificial (the discrete halo-mass-doubling gas accretion treatment) instead of burying it. They even repurpose it into a testable proposal: measure metallicities of isolated low-mass passive galaxies to constrain hot-halo growth models. That's honest. Their treatment of the Vaughan et al. alternative is fair too—they don't claim to rule out compactness-driven quenching.

The soft spots, in proportion: the central conclusion is only as strong as Eq. (4), and the paper offers no direct, independent evidence that real dwarfs have such long star formation timescales. The cold-gas-fraction calibration is suggestive but not independent—it's the same law that produces the gap. The comparison with Gallazzi et al. is visual, with no uncertainty treatment. And the cleanest test, satellites, still lives inside the same tau* assumption. The stress-test note has this right: the diagnostic claim is conditional, not proof. But the paper's own wording—"can be explained," "serves as a valuable constraint"—stays in the right register, so I don't read this as overclaiming. No code or data release is a minor loss for reproducibility, though the model is documented in earlier papers.

Bottom line: for anyone working on quenching physics or star-formation recipes in galaxy formation models, this is a genuine and useful result. It deserves a serious referee. I'd send it to review, and I'd push the referee to probe the external support for long tau* in dwarfs, but I expect it to survive with a tightened quantitative comparison. Yes, take it to reading group.

Referee Report

4 major / 5 minor

Summary. The paper uses the ν2GC semi-analytic galaxy formation model to study the origin of the observed stellar metallicity difference between passive and star-forming galaxies at fixed stellar mass. In the fiducial model, passive galaxies have higher metallicities than star-forming galaxies, in qualitative agreement with Gallazzi et al. (2021). The authors vary the star formation efficiency, split the population into centrals and satellites, and test alternative star formation and quenching prescriptions. They find that the metallicity gap appears only when the star formation timescale is long for low-mass galaxies (Eq. 4), and that instantaneous cold-gas removal erases the gap. They interpret this as evidence that strangulation is the primary quenching mechanism producing the observed offset. They also identify an artifact in low-mass central passive galaxies caused by discrete gas accretion onto halos and propose observations of such galaxies as a probe of hot-gas growth models.

Significance. If the interpretation is correct, the paper offers a natural explanation for why previous cosmological simulations and semi-analytic models failed to reproduce the passive/star-forming metallicity offset, and establishes the offset as a useful diagnostic of star formation timescales. The controlled model variations (ε* changes, Schmidt law, instantaneous quenching, gradual stripping) are well designed and clearly show that the gap is governed by the assumed τ*–Vd relation. The authors are also commendably transparent about the artificial nature of low-mass central passive galaxies. However, the significance is moderated by the fact that the central result rests on an unvalidated τ* law and that a previously published alternative model (Vaughan et al. 2022) is not quantitatively tested. The paper is therefore a conditional success: it demonstrates a mechanism in the model, not an unambiguous measurement of the actual quenching timescale in galaxies.

major comments (4)

[§4.1, Eq. (11)] The Schmidt-law experiment shows that the metallicity gap disappears when Eq. (4) is replaced by τ* = ε*^{-1} τ_d, but this only demonstrates that the gap in the model is a direct consequence of the adopted star formation timescale law. The parameters ε*=0.46, V*=197 km/s, and α*=2.14 in Eq. (4) were calibrated in earlier work to cold gas mass fractions and other scaling relations (Makiya et al. 2016; Shirakata et al. 2019b), not to the metallicity offset, and the paper provides no independent validation that real low-mass galaxies have such long τ*. The appeal to hydrodynamical simulations producing old stellar ages in dwarfs is suggestive but not a direct measurement of τ*. To support the central claim, the paper should either provide external constraints on τ* in low-mass galaxies (e.g., gas depletion times from resolved star formation relations) or explicitly frame the result as a conditional prediction: if the observed offset is due to strangulation, then low-mass galaxies must have long star formation timescales.
[§4.4] The paper claims that strangulation is the 'primary driver' of the metallicity difference, but it does not confront the alternative model of Vaughan et al. (2022), which reproduces the observed offset with instantaneous quenching and a size-dependent quenching probability at fixed stellar mass. The authors acknowledge this alternative and state that exploring it is beyond the present scope, but that admission directly undermines the strength of the conclusion. Without a quantitative test of a Vaughan-type model (or a clear statement that the data cannot distinguish between the two mechanisms), the conclusion should be softened to 'consistent with strangulation' rather than 'primary driver.'
[§3, Figs. 1–2] The claimed success in reproducing the Gallazzi et al. (2021) data is based on visual comparison of median relations; no uncertainties are shown for the model predictions or the observational compilation, and no goodness-of-fit statistic is given. Because the size of the metallicity gap is strongly sensitive to the star formation efficiency (Fig. 2), a quantitative comparison (e.g., model scatter/error bars and a formal likelihood or distance measure) is needed to support the abstract's statement that the fiducial model 'successfully reproduces' the observed metallicity differences.
[§3, Figs. 4–5] The cleanest evidence for strangulation, the satellite/central comparison, is not independent of the star formation timescale assumption: satellites in the model are quenched by strangulation, but the duration over which they continue forming stars is exactly the τ* from Eq. (4), so the satellite test is a restatement of the assumed timescale law rather than an independent confirmation. In addition, the low-mass central passive galaxies that show the largest metallicity enhancement are produced by the discrete gas-accretion treatment that the paper itself describes as 'likely artificial' (Sec. 3). The paper should state this circularity explicitly and present the satellite comparison as a consistency check, not as independent evidence for strangulation.

minor comments (5)

[§3] The passive galaxy classification threshold is printed as '1011 yr−1'; it should read '10^{-11} yr^{-1}' (the minus sign is missing from the exponent).
[§4.1] The author name 'Vogelsberger' appears as 'V ogelsberger' (a spurious space in the LaTeX/type-setting); please correct it.
[§4.2] The sentence 'observed in passive galaxies star-forming galaxies of the same stellar mass' is missing a linking phrase; it should read 'observed in passive galaxies relative to star-forming galaxies of the same stellar mass.'
[General typesetting] Several powers of ten appear as inline text rather than superscripts (e.g., '1010 M⊙', '1011 M⊙'); ensure all such exponents are typeset as superscripts for readability.
[§2.1.2] The phrase 'The increase rate in stellar mass' should be 'The rate of increase of stellar mass' for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the metallicity offset is a forward-model prediction from a star-formation law calibrated to independent observables, not a fit to the offset itself.

full rationale

The paper's central claim is a forward-model prediction: the nu2GC semi-analytic model is run with the star-formation timescale law of Eq. (4), whose parameters (eps_star=0.46, V*=197 km/s, alpha_star=2.14) were calibrated in earlier work to cold gas mass fractions and other scaling relations, not to the stellar metallicity offset. The observed offset between passive and star-forming galaxies at fixed stellar mass is then compared with the model output, and the model's metallicity gap emerges from the chemical-enrichment equations (Eqs. 7-9) together with the strangulation prescription, rather than being imposed by a fitted parameter. The paper's own sensitivity tests—varying SFE (Fig. 2) and replacing Eq. (4) with the Schmidt-law form Eq. (11) (Fig. 6)—show that the gap depends on the assumed star-formation timescale, but this is assumption-dependence, not circularity: a prediction that depends on a free parameter is not equivalent to its input by construction. The self-citations (Makiya et al. 2016; Shirakata et al. 2019b; Oogi et al. 2023) provide the model calibration, but those calibrations target independent observables such as stellar mass functions, AGN luminosity functions, and cold gas fractions, so they are real external evidence rather than a self-referential chain. The acknowledgments that low-mass passive centrals are produced by an artificial discrete gas-accretion treatment (Secs. 3 and 5, Fig. 5) are explicit limitations and do not make the satellite-based strangulation conclusion circular. No step in the derivation reduces by construction to its own inputs, so the correct circularity score is 0.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a set of calibrated baryonic parameters from previous papers, especially the star formation timescale parameters in Eq. (4), and on the discrete halo gas accretion rule that the authors admit is artificial. No new physical entities are introduced. Because code and data are not provided, the model itself is an upstream black box for the reader.

free parameters (7)

epsilon_* (star formation efficiency) = 0.46 (fiducial); 0.1 and 1.0 in low/high SFE variants; 0.23 in Schmidt-law variant
Normalizes the star formation timescale in Eq. (4); calibrated to observed galaxy properties in previous nu2GC papers. Directly controls the metallicity gap in Fig. 2.
V_* = 197 km/s
Velocity scale in Eq. (4); determines below which rotation velocity the star formation timescale becomes long. Chosen in Makiya et al. (2016) to match dwarf galaxy cold gas fractions.
alpha_* = 2.14
Power-law index in Eq. (4); sets the strength of the timescale extension in low-mass galaxies.
V_hot and alpha_hot = 121.64 km/s and 3.92
Parameters of SN feedback efficiency in Eq. (6); calibrated to stellar mass functions and affect metallicities through outflows.
p (chemical yield) = 1.68 Z_sun
Metal yield per unit star formation in Eq. (8); sets the absolute metallicity scale, assumed from stellar evolution models.
f_BH = 0.02
Fraction of cold gas accreted onto the SMBH during starbursts; fixed to match AGN observations (Shirakata et al. 2019b).
tau_strip = 1 Gyr and 3 Gyr in gradual stripping variants
Chosen stripping timescales in Eq. (12) to test sensitivity; not fitted.

assumptions (5)

domain assumption Baryon fraction fb = Omega_b/Omega_m before reionization, reduced in small halos after z=9 following Okamoto et al. (2008).
Sets the gas reservoir available for cooling and star formation; affects metallicities through gas supply.
domain assumption Hot gas follows a cored isolated isothermal profile with cooling radius computed from Eq. (1).
Determines when and how much gas cools onto galaxies; a simplified density profile without hydrodynamic calibration.
ad hoc to paper Gas accretion onto halos occurs only when the halo mass doubles since its last formation epoch.
The paper itself calls the resulting quenching 'likely an artificial effect' and states there is 'no physical justification' for this discretization. It drives the central dwarf passive galaxy prediction.
domain assumption Instantaneous recycling approximation and neglect of Type Ia SNe for metal enrichment.
Acknowledged to 'slightly overestimate' metallicities; affects absolute values but likely not the mass-dependent offset.
domain assumption Star formation timescale formula Eq. (4) with calibrated parameters.
Phenomenological law chosen for the model; the central mechanism result depends on its long timescales in low-mass galaxies.

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Cite this review

Pith. "Pith review of The origin of the metallicity difference between star-forming and passive galaxies: Insights from {\nu}2GC semi-analytic model." pith.science (2026). https://pith.science/paper/TUNPT3FH

@misc{pith2026250600378,
  author       = {Pith},
  title        = {Pith review of: The origin of the metallicity difference between star-forming and passive galaxies: Insights from \nu2GC semi-analytic model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TUNPT3FH}},
  note         = {Machine review of arXiv:2506.00378}
}

read the original abstract

We investigate the origin of the observed metallicity difference between star-forming and passive galaxies using the semi-analytic galaxy formation model nu2GC. Our fiducial model successfully reproduces the observed metallicity differences in local galaxies while simultaneously matching the potential-metallicity relations of both star-forming and passive galaxies. By varying the star formation efficiency, we identify strangulation as the primary driver of the metallicity difference. This finding highlights the critical role of star formation timescales in explaining the observed metallicity difference. Our results suggest that metallicity differences serve as a valuable diagnostic for evaluating star formation models in both semi-analytic models and cosmological simulations. Furthermore, galaxies quenched by processes resembling strangulation -- where the supply of cold gas is halted in a slowly growing halo -- exhibit higher metallicities than star-forming galaxies of the same stellar mass. In our model, this occurs in isolated, low-mass galaxies where rapid cooling leads to an effect resembling strangulation due to the discrete treatment of gas accretion onto dark matter halos. We propose that the metallicities of isolated, low-mass passive galaxies could provide key insights into refining models of hot gas halo growth.

Figures

Figures reproduced from arXiv: 2506.00378 by the authors.

**Figure 1.** Left: Stellar MZRs for passive and star-forming galaxies in the fiducial model. The red solid and blue dashed lines represent the medians of the model predictions for passive and star-forming galaxies, respectively. The red filled circle and blue filled squares represent the MZRs of the SDSS galaxies (Gallazzi et al. 2021) compiled by Fontanot et al. (2020). for quiescent and star-forming galaxies, respectively. R… view at source ↗

**Figure 2.** The left and right panels show the stellar MZRs for passive and star-forming galaxies in the low SFE and high SFE models, respectively. The predictions by the fiducial model is also shown by the thin lines. 8.5 9.0 9.5 10.0 10.5 11.0 = log (M* M ) log ( Re kpc) 1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 lo g(Z [Z ]) passive (low SFE) star-forming (low SFE) passive (fiducial) star-forming (fiducial) 8.5 9.0 9.5 10.0 10.5 11.0 =… view at source ↗

**Figure 3.** The left and right panels show the stellar metallicities for passive and star-forming galaxies against Φ in the low SFE and high SFE models, respectively. The predictions by the fiducial model are also shown by the thin lines. 9.0 9.5 10.0 10.5 11.0 11.5 log(M [M ]) 1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 lo g(Z [Z ]) passive (centrals) star-forming (centrals) 9.0 9.5 10.0 10.5 11.0 11.5 log(M [M ]) passive (satellites) sta… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: The left and right panels show the stellar MZRs for passive and star-forming galaxies for the central and satellite galaxies in the fiducial model, respectively. To investigate whether strangulation explains the metallicity difference more directly, we analyze the stel…

**Figure 5.** Figure 5: Normalized halo mass evolution as a function of redshift for both star-forming and passive galaxies whose stellar mass at z = 0 is ∼ 109.7M⊙. The vertical axis represents the normalized halo mass Mhalo(z)/Mhalo(z = 0), and the horizontal axis denotes redshift. The blue…

**Figure 8.** Figure 8: Stellar MZRs for passive and star-forming galaxies in models with gradual hot gas stripping. We assume τstrip = 1 Gyr and 3 Gyr in the left and right panels, respectively. Line styles follow the same convention as in previous figures. In [PITH_FULL_IMAGE:figures/full_…

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