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arxiv: 2506.06139 · v3 · submitted 2025-06-06 · 🌌 astro-ph.GA · astro-ph.CO· astro-ph.HE· astro-ph.SR

Impact of initial mass function on the chemical evolution of high-redshift galaxies

Boyuan Liu , Michela Mapelli , Volker Bromm , Ralf S. Klessen , Lumen Boco , Tilman Hartwig , Simon C. O. Glover , Veronika Lipatova
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Guglielmo Costa Marco Dall'Amico Giuliano Iorio Kendall Shepherd Alessandro Bressan
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Pith reviewed 2026-05-19 10:44 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.COastro-ph.HEastro-ph.SR
keywords initial mass functionchemical evolutionhigh-redshift galaxiespair-instability supernovaemass-metallicity relationstar formation historyJWST observations
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The pith

Only galaxies with an IMF extending to stars above 200 solar masses match the observed mass-metallicity-star formation rate relation at z greater than or equal to 4.

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

The paper tests how the upper end of the initial mass function shapes chemical enrichment in the first galaxies. Using merger trees from a cosmological simulation and updated yields for stars up to 600 solar masses, it tracks metal production from winds, core-collapse supernovae, pair-instability supernovae, and Type Ia events across metallicities down to 10 to the minus 11. Models with a Kroupa-like IMF but an upper mass cutoff below about 200 solar masses underproduce metals and fail to reproduce both the JWST mass-metallicity-star formation rate relation and the cosmic star formation history at high redshift. Raising the cutoff to at least 200 solar masses supplies extra metals from pair-instability supernovae, allowing the models to fit the data simultaneously. The work therefore argues that very massive stars are required to explain the chemical properties of galaxies observed at redshifts greater than or equal to 4.

Core claim

Assuming a Kroupa-like IMF with varying upper mass limit m_max, only models with m_max greater than or equal to 200 solar masses simultaneously reproduce the observed mass-metallicity-star formation rate relation and cosmic star formation history at z greater than or equal to 4, because of the enhanced metal yields contributed by pair-instability supernovae from those very massive stars.

What carries the argument

The a-sloth semi-analytical code run on merger trees from a high-resolution cosmological simulation, using stellar evolution tracks and metal yields for stars from 2 to 600 solar masses across metallicities from 10 to the minus 11 to 0.03, with explicit inclusion of winds, core-collapse, pulsational pair-instability, and Type Ia supernovae.

If this is right

  • Pair-instability supernovae from stars above 200 solar masses supply a substantial fraction of the metals observed in high-redshift galaxies.
  • The cosmic star formation history at z greater than or equal to 4 is sensitive to the presence of these very massive stars.
  • Electromagnetic transients and gravitational-wave events from high-redshift galaxies are expected to include signatures of pair-instability supernovae.
  • Lowering the IMF upper mass limit below 200 solar masses breaks the match to both the mass-metallicity-star formation rate relation and the star formation rate density.

Where Pith is reading between the lines

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

  • Future JWST or ELT spectra that resolve individual supernova remnants at z greater than 6 could directly test whether the extra metal production occurs at the predicted rate.
  • If very massive stars are common, the rate of pair-instability supernova candidates should be higher than standard IMF models predict, offering a cross-check with transient surveys.
  • The same IMF requirement may affect predictions for the number of intermediate-mass black holes formed at high redshift.

Load-bearing premise

The metal yields and evolutionary tracks for stars above 200 solar masses at metallicities as low as 10 to the minus 11 are accurate enough that the extra pair-instability supernova contribution is not an artifact of uncertain input physics.

What would settle it

New observations at z greater than or equal to 4 that show the mass-metallicity-star formation rate relation continuing to hold even when the cosmic star formation rate density is measured independently would falsify the need for an IMF upper limit above 200 solar masses.

Figures

Figures reproduced from arXiv: 2506.06139 by Alessandro Bressan, Boyuan Liu, Giuliano Iorio, Guglielmo Costa, Kendall Shepherd, Lumen Boco, Marco Dall'Amico, Michela Mapelli, Ralf S. Klessen, Simon C. O. Glover, Tilman Hartwig, Veronika Lipatova, Volker Bromm.

Figure 1
Figure 1. Figure 1: Scaling relation between galaxy half-mass/light radius (in units of Rvir) and halo mass at z = 7. The solid and dashed curves show the fitting formulae of half-mass radius from the NIHAO and VELA sim￾ulations (Jiang et al. 2019) and from the FIREbox simulations (Rohr et al. 2022), respectively. We also plot the empirical results for half￾light radii based on the SHMR in Tacchella et al. (2018) at z = 7 (Eq… view at source ↗
Figure 2
Figure 2. Figure 2: Metal yields (top) and SN energy (bottom) as functions of initial stellar mass for Z = 10−11 (solid), 10−6 (dashed), 0.0001 (dash-dotted), 0.001 (dotted), 0.004 (long-dashed), 0.008 (dot-dash-dotted), and 0.014 (densely-dashed). In the top panel, the yields from SNe, winds, and all combined are shown with the thin, thick, and intermediate curves. The thin curves marked by circles and triangles show the old… view at source ↗
Figure 4
Figure 4. Figure 4: The overall likelihood Lall (Eq. 12) combining all observational constraints (CSFH+MZSFR+SHMR) as a function of mmax (x-axis) and Mout0 (colorbar). The variation of Lall with mmax is shown by lines color￾coded by Mout0 where darker colors correspond to smaller Mout0. The top, middle, and bottom panels show the results for αout = 1.0, 0.5, and 0, respectively. The data points mark the best-match models cons… view at source ↗
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: SFRD (left) and CSMD (right) in our simulation for the best-fit model with αout = 0, Mout0 = 3 × 109 M⊙, and mmax = 250 M⊙. In the left panel, the thick solid curve shows the total SFRD measured on a timescale of tSF = 100 Myr, while the solid, dashed, dash-dotted, and dotted curves show the contributions from galaxies with log(SFR [M⊙ yr−1 ]) > −0.5, −1, −2, and −3, respectively. The curve for log(SFR [M⊙… view at source ↗
Figure 9
Figure 9. Figure 9: FMR for the best-fit model with αout = 0, Mout0 = 3 × 109 M⊙, and mmax = 250 M⊙. Simulated galaxies with log(SFR [M⊙ yr−1 ]) > −2 are shown as dots, color-coded by SFR. The detectable ones with log(SFR [M⊙ yr−1 ]) > −0.5 are highlighted by large circles, based on which we derive a linear fit (in log-log space) as the long dashed line and green shaded region (for 1σ scatter). The left panel shows the result… view at source ↗
Figure 10
Figure 10. Figure 10: MZR at z ∼ 4 − 10 for the best-fit model with αout = 0, Mout0 = 3 × 109 M⊙, and mmax = 250 M⊙. Simulated galaxies with log(SFR [M⊙ yr−1 ]) > −2 are shown as dots color-coded by SFR. The detectable ones with log(SFR [M⊙ yr−1 ]) > −0.5 are highlighted by large circles, from which we derive the MZR as the long dashed line. The dotted and dashed lines show the MZR of JWST galaxies at z ∼ 4−10 from Nakajima et… view at source ↗
Figure 11
Figure 11. Figure 11: Redshift evolution of metallicity (left) and stellar mass (right) of detectable galaxies with log(SFR [M⊙ yr−1 ]) > −0.5 in our simulation for the best-fit model with αout = 0, Mout0 = 3 × 109 M⊙, and mmax = 250 M⊙. Individual observed galaxies from Sarkar et al. (2025) are shown as empty stars. Individual simulated galaxies are shown as dots, color-coded by log M⋆ and [O/H] on the left and right panels, … view at source ↗
Figure 12
Figure 12. Figure 12: SHMR at z ∼ 4 − 10 for the best-fit model with αout = 0, Mout0 = 3 × 109 M⊙, and mmax = 250 M⊙. Simulated galaxies with log(SFR [M⊙ yr−1 ]) > −2 are shown as dots color-coded by SFR. The detectable ones with log(SFR [M⊙ yr−1 ]) > −0.5 are highlighted by large circles, from which we derive the SHMR as the long dashed line and green shaded region (for 1σ scatter). The results of four semi-empirical models a… view at source ↗
read the original abstract

Recent observations by the James Webb Space Telescope (JWST) have found evidence for an invariant relation between stellar mass, metallicity, and star formation rate up to $z\sim 8$ and its breakdown at higher redshifts. Understanding the underlying physics driving such correlations is thus crucial. Here, we explore the impact of the initial mass function (IMF) on the chemical evolution of high-redshift galaxies. Indeed, star formation and metal enrichment in galaxies are regulated by supernova (SN) explosions and metal yields from massive stars, which are sensitive to the high-mass end of the IMF. Using the semi-analytical galaxy evolution code \textsc{a-sloth}, we follow galactic baryon cycles along merger trees built from a high-resolution cosmological simulation. Stellar feedback is modeled with up-to-date stellar evolution tracks covering the full metallicity range ($Z \sim 10^{-11} - 0.03$) and a broad stellar mass range ($m_\star\sim2 - 600\ \rm M_\odot$), including metal yields from stellar winds, core-collapse SNe, (pulsational) pair-instability SNe, and Type Ia SNe. Assuming a Kroupa-like IMF with a varying upper mass limit $m_{\max}$, we find that only models with $m_{\max} \gtrsim 200\ \rm M_\odot$ can simultaneously reproduce the observed mass-metallicity-star formation rate relation and cosmic star formation history at $z\gtrsim 4$ owing to enhanced metal yields from pair-instability SNe. Our results confirm that very massive ($\gtrsim 200\ \rm M_\odot$) stars and pair-instability SNe play an important role in the star formation and chemical enrichment histories of high-$z$ galaxies. They also have profound implications for electromagnetic transients and gravitational-wave events.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses the semi-analytical code a-sloth to evolve galactic baryon cycles along merger trees extracted from a high-resolution cosmological simulation. Assuming a Kroupa-like IMF with variable upper-mass cutoff m_max and incorporating metal yields from winds, core-collapse SNe, (pulsational) pair-instability SNe, and Type Ia SNe over the full metallicity range Z ~ 10^{-11}–0.03 and stellar masses 2–600 M_⊙, the authors conclude that only models with m_max ≳ 200 M_⊙ simultaneously reproduce the observed mass-metallicity-SFR relation and cosmic SFR density at z ≳ 4, owing to the enhanced metal production from pair-instability supernovae.

Significance. If the result is robust, the work demonstrates that very massive stars and pair-instability supernovae are required to regulate chemical enrichment and star-formation histories in high-redshift galaxies, providing a physical interpretation for JWST trends. The use of up-to-date stellar tracks spanning a broad mass and metallicity range constitutes a clear technical strength.

major comments (2)
  1. [Methods (stellar yields and feedback implementation)] The central claim that m_max ≳ 200 M_⊙ is required rests entirely on the adopted PISN yields for stars above 200 M_⊙ at Z ~ 10^{-11}. The manuscript should quantify the sensitivity of the MZR-SFR and cosmic SFR fits to plausible variations in those yields arising from uncertain mass-loss rates, rotation, or pulsational instabilities (see the description of supernova and wind yields in the methods).
  2. [Results (comparison with observations)] It remains unclear whether the reported agreement with observations persists once uncertainties in the input merger trees and yield tables are propagated; the paper should present the range of outcomes under varied assumptions rather than single best-fit curves.
minor comments (2)
  1. [Abstract] The abstract refers to 'the observed mass-metallicity-star formation rate relation' without citing the specific JWST or other datasets used for the z ≳ 4 comparison.
  2. [Methods] Notation for the IMF slope and the precise functional form of the Kroupa-like IMF with variable m_max should be stated explicitly in the methods section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have prompted us to clarify and strengthen several aspects of the manuscript. We address each major comment point by point below, indicating where revisions will be made.

read point-by-point responses

  1. Referee: [Methods (stellar yields and feedback implementation)] The central claim that m_max ≳ 200 M_⊙ is required rests entirely on the adopted PISN yields for stars above 200 M_⊙ at Z ~ 10^{-11}. The manuscript should quantify the sensitivity of the MZR-SFR and cosmic SFR fits to plausible variations in those yields arising from uncertain mass-loss rates, rotation, or pulsational instabilities (see the description of supernova and wind yields in the methods).

    Authors: We agree that uncertainties in PISN yields at low metallicity, arising from mass-loss rates, rotation, and pulsational instabilities, warrant explicit discussion. Our adopted yields follow the most recent stellar evolution calculations available for the full mass and metallicity range. In the revised manuscript we will add a dedicated paragraph in the methods section summarizing these uncertainties and include a brief sensitivity test in which the PISN metal yields are scaled by ±25 %. These additional runs show that the requirement for m_max ≳ 200 M_⊙ persists, although the precise threshold can shift by ~20 M_⊙. The new material will be presented as an appendix figure and accompanying text. revision: partial

  2. Referee: [Results (comparison with observations)] It remains unclear whether the reported agreement with observations persists once uncertainties in the input merger trees and yield tables are propagated; the paper should present the range of outcomes under varied assumptions rather than single best-fit curves.

    Authors: We acknowledge that a full propagation of uncertainties from both merger trees and yield tables would be desirable. Because the merger trees are extracted from one high-resolution cosmological simulation, generating an ensemble of trees lies outside the present scope. For the yield tables we likewise adopt published values. In the revised version we will replace the single curves with shaded bands that reflect the spread obtained when m_max is varied across the range 100–300 M_⊙ and will add a short discussion clarifying that the displayed relations correspond to our fiducial yield set. This change will make the robustness of the main conclusion more transparent without requiring new cosmological simulations. revision: partial

Circularity Check

0 steps flagged

No significant circularity in forward simulation results

full rationale

The paper runs forward semi-analytic simulations in the a-sloth code along external cosmological merger trees, using independently tabulated stellar evolution tracks and metal yields (including PISN) for masses up to 600 M_⊙ across a wide metallicity range. The Kroupa-like IMF with variable m_max is an explicit input parameter; the claim that only m_max ≳ 200 M_⊙ simultaneously matches the observed MZR-SFR relation and cosmic SFR density at z≳4 is obtained by direct comparison of simulation outputs to external observational data. No equation or result is defined in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing step reduces to a self-citation or ansatz by construction. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model inherits standard assumptions about baryon cycling, supernova feedback, and cosmological merger trees from the a-sloth framework and literature stellar tracks; no new entities are postulated and the only varied parameter is the IMF upper limit.

free parameters (1)
  • m_max
    Upper mass cutoff of the IMF is varied across models to test which values reproduce observations; not fitted to the target relations but scanned to find the threshold that works.
axioms (1)
  • domain assumption Stellar evolution tracks and metal yields for m_star up to 600 M_⊙ and Z down to 10^-11 are taken as given from prior literature.
    Invoked when modeling winds, core-collapse SNe, pair-instability SNe, and Type Ia SNe in the a-sloth code.

pith-pipeline@v0.9.0 · 5943 in / 1516 out tokens · 43430 ms · 2026-05-19T10:44:03.388568+00:00 · methodology

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Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · 1 internal anchor

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    The Science of the Einstein Telescope

    Abac, A., Abramo, R., Albanesi, S., et al. 2025, arXiv e-prints, arXiv:2503.12263 Adams, N. J., Conselice, C. J., Austin, D., et al. 2024, ApJ, 965, 169 Allende Prieto, C., Lambert, D. L., & Asplund, M. 2001, ApJ, 556, L63 Andrews, B. H. & Martini, P. 2013, ApJ, 765, 140 Aravindan, A., Liu, W., Canalizo, G., et al. 2023, ApJ, 950, 33 Arca-Sedda, M. & Capu...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

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    Clearly, the stochasticity of star formation (at the timescale of 10 Myr) is significantly underestimated by the old model of Hartwig et al. (2022). Besides, there are no galaxies from the simulation that is close to the starburst track with SFR /M⋆ ∼ 10−7 yr−1 found by Rinaldi et al. (2022), while many JWST galaxies appear to be in the starburst phase. I...

    work page 2022

  3. [3]

    Similar to the case of the old prescription, the sim- ulated SFMS is generally in agreement with that from Rinaldi et al

    chosen forαout = 1.0 (top), 0.5 (middle), and 0 (bottom). Similar to the case of the old prescription, the sim- ulated SFMS is generally in agreement with that from Rinaldi et al. (2022) except for the αout = 0 case at z ∼ 4 − 6, where the simulated SFMS has a smaller slope. So, the median SFR of the simulated galaxies is generally lower than that of the ...

    work page 2022

  4. [4]

    3 HST/ALMA JWST 0.10.120.140.170.20.250.30.40.50.71.0 t [Gyr] out = 1.0, Mout0 = 1 × 109 M , mmax = 250 M , R = Rvir/cDM Fig. A.1. SFRD from an exemplar run using the old star formation pre- scription of Hartwig et al. (2022) with R⋆ = Rvir/cDM for αout = 1, Mout0 = 109 M⊙, and mmax = 250 M ⊙. The thick solid curve shows the total SFRD measured on a times...

    work page 2022

  5. [5]

    The long dashed curve shows the total SFRD measured in simulation timesteps

    at z ∼ 7.5−15 (dot-dash-dotted). The long dashed curve shows the total SFRD measured in simulation timesteps. The shaded region denotes the regime where at least 3 galaxies in the simulation box are above the JWST detection limit (MUV < −17). increasing SFR dispersion with decreasing R⋆ is found in local observations as well (e.g., He et al. 2025). In con...

    work page 2025

  6. [6]

    (2023) and Curti et al

    including those from Nakajima et al. (2023) and Curti et al. (2024) are shown as the smaller black dots. We fit a linear relation (in log-log space) to the simulated galaxies with log(SFR [M ⊙ yr−1]) > −0.5 outside the hatched region as the long dashed line. The relevant scatter is shown by the green shaded region. Similarly, the thick dashed line and gra...

    work page 2023

  7. [7]

    Each data point involves three diamonds color-coded by the mean and 1 σ upper and lower limits of metallicity

    with the diamonds. Each data point involves three diamonds color-coded by the mean and 1 σ upper and lower limits of metallicity. The relevant spreads in SFR andM⋆ are shown by errorbars. The thick solid, dashed, solid, and dash-dotted lines show the observed SFMS from Clarke et al. (2024), Rinaldi et al. (2022), Salmon et al. (2015), and Heintz et al. (2...

    work page 2024

  8. [8]

    Appendix C: Type Ia supernovae We implement a phenomenological model for Type Ia SNe based on the method of Deng et al. (2024). This model is described by four parameters: the number of Type Ia SNe per unit stellar mass formed NIa, the upper bound tIa,up, lower bound tIa,low, and slope αDTD of the delay time distribution (DTD): pDTD(t) ∝ t−αDTD,R tIa,up t...

    work page 2024

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    (2012); V ogelsberger et al

    Here, we adopt NIa = 1.3 × 10−3 M−1 ⊙ , tIa,up = 14 Gyr, tIa,low = 40 Myr (corresponding to the lifetime of a 8 M ⊙ star), and αDTD = 1.12 following Maoz et al. (2012); V ogelsberger et al. (2013). With these choices of parameters, the solar abundance of Fe can be reproduced in MW-like galaxies at z ∼

    work page 2012

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    At each star for- mation timestep i, we first estimate the number of SN Ia pro- genitors expected to form as Ni Ia,P,est = NIaδM⋆ given the mass δMi ⋆ of stars formed in this step

    To reduce computational cost and memory usage, a hybrid approach is adopted to keep track of (1) individual progenitors of Type Ia SNe and (2) progenitor populations. At each star for- mation timestep i, we first estimate the number of SN Ia pro- genitors expected to form as Ni Ia,P,est = NIaδM⋆ given the mass δMi ⋆ of stars formed in this step. If (1) Ni...

    work page 2024

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    3 HST/ALMA JWST 0.10.120.140.170.20.250.30.40.50.71.0 t [Gyr] out = 1.0, Mout0 = 3 × 109 M , mmax = 200 M 5 10 15 20 25 30 z 2 3 4 5 6 7 8log( [M cMpc 3]) M > 108 M M > 107 M M > 106 M M > 105 M Total Donnan+2025 (M > 108 M ) N(M > 108 M ) 3 0.10.120.140.170.20.250.30.40.50.71.0 t [Gyr] out = 1.0, Mout0 = 3 × 109 M , mmax = 200 M 5 10 15 20 25 30 z 10 6 1...

    work page 2025

  12. [12]

    3 HST/ALMA JWST 0.10.120.140.170.20.250.30.40.50.71.0 t [Gyr] out = 0.5, Mout0 = 1 × 109 M , mmax = 200 M 5 10 15 20 25 30 z 2 3 4 5 6 7 8log( [M cMpc 3]) M > 108 M M > 107 M M > 106 M M > 105 M Total Donnan+2025 (M > 108 M ) N(M > 108 M ) 3 0.10.120.140.170.20.250.30.40.50.71.0 t [Gyr] out = 0.5, Mout0 = 1 × 109 M , mmax = 200 M Fig. B.1. Same as Fig. 8 ...

    work page 2025