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arxiv: 2605.15462 · v1 · pith:QSJXS7ONnew · submitted 2026-05-14 · 🌌 astro-ph.HE · astro-ph.GA· astro-ph.SR

Constraints on the Metallicity-dependent Explodability of Massive Stars from Galactic Chemical Evolution: Toward Alleviating the Red Supergiant Problem

Sojun Ono , Keiichi Maeda , Akihiro Suzuki This is my paper

Pith reviewed 2026-05-19 14:42 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.GAastro-ph.SR
keywords galactic chemical evolutionmassive star explodabilityblack hole formationred supergiant problemcore-collapse supernovaemetallicity dependencestellar abundances
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The pith

Galactic chemical evolution constrains where massive stars form black holes and permits a simplified explodability rule that can ease the red supergiant problem.

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

The paper incorporates recently proposed metallicity-dependent explodability prescriptions into a galactic chemical evolution framework and shows that they reproduce observed abundance trends. The models yield strong limits on the combinations of initial mass and metallicity that lead to black hole formation instead of core-collapse supernovae. A simplified explodability prescription is then constructed to reduce the number of red supergiants while remaining consistent with chemical evolution data, provided net galactic outflows are absent and the behavioral transition occurs below solar metallicity. A metallicity-dependent initial mass function is also shown to improve the fit once coupled with the explodability changes.

Core claim

The galactic chemical evolution model provides strong constraints on the region of black hole formation in the mass-metallicity space. A simplified form of the metallicity-dependent explodability can be constructed to alleviate the red supergiant problem without violating chemical-evolution observables if net outflows are negligible or absent and the transition takes place at sub-solar metallicity.

What carries the argument

Metallicity-dependent explodability prescriptions that determine whether a massive star explodes as a core-collapse supernova or collapses directly to a black hole, implemented inside the galactic chemical evolution calculation to track resulting abundance patterns.

If this is right

  • Physics-motivated explodability prescriptions reproduce the key observed abundance trends in the Milky Way.
  • The galactic chemical evolution framework places strong limits on the black hole formation region across mass and metallicity.
  • A simplified metallicity-dependent explodability model alleviates the red supergiant problem while staying compatible with chemical evolution constraints under the stated conditions.
  • Coupling the explodability model with a metallicity-dependent initial mass function further improves agreement with observations.

Where Pith is reading between the lines

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

  • Galactic chemical evolution can serve as an independent test of stellar explosion models beyond direct supernova observations.
  • The requirement of negligible outflows highlights the need for accurate galactic wind prescriptions in future chemical evolution studies.
  • The sub-solar transition metallicity implies testable predictions for abundance patterns in low-metallicity dwarf galaxies.

Load-bearing premise

Net outflows from the galactic system are negligible or absent.

What would settle it

Abundance ratio measurements at sub-solar metallicities that deviate systematically from the predictions of the simplified explodability model and cannot be reconciled by reasonable adjustments to other parameters.

Figures

Figures reproduced from arXiv: 2605.15462 by Akihiro Suzuki, Keiichi Maeda, Sojun Ono.

Figure 1
Figure 1. Figure 1: Schematic representation of the metallicity-dependent explodability adopted in group Ex. The left, center, and right panels show the explodability as functions of ZAMS mass and metallicity for models Ex-M25-S, Ex-M25-B, and Ex-PUSH, respectively. Red regions indicate successful CCSNe leaving neutron stars (NSs), while black regions denote direct black hole (BH) formation. The orange region with dotted patt… view at source ↗
Figure 2
Figure 2. Figure 2: Metallicity distribution function (MDF) and the evolution of the star formation rate (SFR) and [Fe/H] are shown as indicators of model validation. The left panel displays the MDF as a function of [Fe/H], together with observational estimates from L. Casagrande et al. (2011) (blue dashed line), S. Buder et al. (2019) (green dotted line), and T. Bensby et al. (2014) (brown dash-dotted line). The right panels… view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of [O/Fe] as a function of [Fe/H] for group Ex. The top-left, top-right, and bottom-left panels show the results for models Ex-M25-S, Ex-M25-B, and Ex-PUSH, respectively. All panels also display the reference models Base-100 and Base-18. The colored symbols represent observational data; red squares from R. Cayrel et al. (2004), green-yellow circles from B. Edvardsson et al. (1993), magenta downwa… view at source ↗
Figure 4
Figure 4. Figure 4: Evolution of metallicity and supernova (SN) rate. The top panel shows the evolution of CCSN rate (solid lines) and SN Ia rate (dashed lines). The bottom panel shows the evolution of metallicity Z. The blue dotted horizontal line in the bottom line denotes Z = Z⊙, and the blue dotted vertical lines mark t = t⊙ = 9.2 Gyr. The error bar in the top right panel indicates the observational present-day CCSN rate … view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of [O/Fe] for group Ex-BH. The solid lines correspond to the same models shown in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Evolution and explodability in the simplified models. The top-right sub-panel presents the explodability as a function of ZAMS mass (vertical axis) and metallicity (horizontal axis), where Zth is the threshold metallicity treated as a free parameter in Eq. (4). The main top panels show the [Fe/H]–metallicity planes, and the bottom panels display the [O/Fe]–[Fe/H] planes. The left and right columns correspo… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the evolutionary trends of oxygen and other α-elements (C, Mg, Si, S, Ca, Ti, and Cr) as a function of [Fe/H]. The colors and line styles for models Base-100, Base-18, and Ex-M25-S are the same as in [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: GCE with metallicity-dependent IMF. Same as [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the elemental yield contributions as a function of ZAMS mass. The horizontal axis denotes the ZAMS mass, and the vertical axis represents the contribution to galactic chemical enrichment per unit ZAMS mass, Xi Mej dN/dM. Each line corresponds to a different published yield set (including both supernova and hypernova models): A. Chieffi & M. Limongi (2004) adjusted using the 56Ni yields in thi… view at source ↗
Figure 10
Figure 10. Figure 10: Metallicity-dependent CCSN yields and [O/Fe] in our models. The left panel shows the IMF-averaged CCSN yields of oxygen (solid) and iron (dashed) obtained when 1 M⊙ of gas is fully converted into stars for each explodability model. The right panel shows [O/Fe] of the IMF-averaged CCSN yields. The horizontal axis denotes the metallicity in both panels. The colors for the base models and group Ex models are… view at source ↗
read the original abstract

The explodability of massive stars, namely whether they undergo core-collapse supernovae (CCSNe) or form black holes (BHs), strongly influences galactic chemical evolution (GCE). Details of the explodability are still controversial, but realistic predictions including metallicity-dependence are becoming available through stellar-evolution and explosion calculations. In the present work, we implement recently-proposed metallicity-dependent explodability prescriptions into a GCE framework. We show that the physics-motivated explodability prescriptions reproduce the key observed abundance trends. Further, within uncertainties of the explodability models, the GCE model provides strong constraints on the region of the BH formation in the mass-metallicity space. Guided by these findings, we further construct a simplified form of the metallicity-dependent explodability designed to alleviate the red supergiant (RSG) problem and explore its compatibility with GCE constraints. We find that such a solution exists, if (1) the net outflows from the system are negligible/absent, and (2) the transition of the explodability takes place at sub-solar metallicity. These results demonstrate that GCE can provide meaningful constraints on massive-star explodability and that explodability prescriptions capable of addressing the RSG problem can be constructed without violating chemical-evolution observables. We also show that a metallicity-dependent initial mass function can improve agreement with observations; this effect becomes importance once coupled with the metallicity-dependent explodability.

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 implements recently proposed metallicity-dependent explodability prescriptions for massive stars into a one-zone galactic chemical evolution (GCE) framework. It reports that these prescriptions reproduce key observed abundance trends, that the GCE model supplies strong constraints on the black-hole formation region in mass-metallicity space, and that a simplified explodability form can be constructed to alleviate the red-supergiant problem while remaining compatible with GCE observables provided net outflows are negligible and the transition occurs at sub-solar metallicity. A metallicity-dependent initial mass function is additionally shown to improve agreement with observations.

Significance. If the central claims hold, the work supplies a concrete link between stellar-explosion calculations and GCE observables, offering a pathway to resolve the red-supergiant problem without violating chemical-evolution constraints. The explicit identification of the outflow and transition-metallicity conditions under which compatibility is achieved, together with the exploration of a metallicity-dependent IMF, provides falsifiable guidance for both stellar-evolution and GCE modeling communities.

major comments (2)
  1. [Abstract] Abstract: the claim that a simplified explodability form alleviates the RSG problem without violating GCE observables only if net outflows are negligible/absent is load-bearing for the central result, yet the manuscript does not quantify how the allowed transition metallicity or the BH-formation region in mass-metallicity space shifts when standard mass-loading factors (0.5–2) are included, as required by most one-zone Milky Way models to match gas fractions and the metallicity distribution function.
  2. [Abstract and results section] Abstract and results section: the statement that the physics-motivated prescriptions 'reproduce the key observed abundance trends' within model uncertainties is presented without an explicit error budget, data-exclusion criteria, or step-by-step comparison of predicted versus observed [X/Fe] ratios, making it difficult to assess whether the GCE constraints on the BH-formation region are tighter than the input explodability uncertainties.
minor comments (2)
  1. The coupling between the metallicity-dependent explodability and the metallicity-dependent IMF is mentioned only briefly; a short dedicated paragraph or figure panel showing the joint effect on the integrated yields would improve clarity.
  2. Notation for the transition metallicity and the boundaries of the BH-formation region should be defined once in the methods and used consistently in all subsequent figures and text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive report. We address the major comments point by point below, indicating where revisions to the manuscript will be made to strengthen the presentation and analysis.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that a simplified explodability form alleviates the RSG problem without violating GCE observables only if net outflows are negligible/absent is load-bearing for the central result, yet the manuscript does not quantify how the allowed transition metallicity or the BH-formation region in mass-metallicity space shifts when standard mass-loading factors (0.5–2) are included, as required by most one-zone Milky Way models to match gas fractions and the metallicity distribution function.

    Authors: We agree that quantifying the effects of including mass-loading factors would provide valuable additional context. Our central claim is explicitly conditional on negligible net outflows, which is the regime in which the simplified explodability prescription remains compatible with observed abundance trends while addressing the RSG problem. In the revised manuscript we will add a new set of calculations that incorporate mass-loading factors in the range 0.5–2. These will show how the allowed transition metallicity and the permitted BH-formation region in mass-metallicity space are modified, thereby clarifying the robustness of the proposed solution under more standard one-zone model assumptions. revision: yes

  2. Referee: [Abstract and results section] Abstract and results section: the statement that the physics-motivated prescriptions 'reproduce the key observed abundance trends' within model uncertainties is presented without an explicit error budget, data-exclusion criteria, or step-by-step comparison of predicted versus observed [X/Fe] ratios, making it difficult to assess whether the GCE constraints on the BH-formation region are tighter than the input explodability uncertainties.

    Authors: We acknowledge that a more transparent presentation of the comparison would help readers evaluate the strength of the GCE constraints. In the revised version we will add an explicit error budget that combines uncertainties from the explodability prescriptions, yield tables, and observational data. We will also specify the data-exclusion criteria applied and include a detailed, element-by-element comparison of predicted versus observed [X/Fe] ratios, with quantitative measures of agreement. This will allow a clearer assessment of whether the GCE-derived limits on the BH-formation region are indeed tighter than the input model uncertainties. revision: yes

Circularity Check

0 steps flagged

No significant circularity; GCE constraints and simplified explodability construction remain independent of self-definition or fitted renaming

full rationale

The paper implements external metallicity-dependent explodability prescriptions (from stellar-evolution calculations) into a GCE framework, reproduces key abundance trends, and derives constraints on the BH-formation region in mass-metallicity space. It then explicitly constructs a simplified explodability form guided by those constraints to address the RSG problem and verifies compatibility under openly stated assumptions (negligible net outflows and sub-solar transition metallicity). No step equates a claimed prediction or first-principles result to its own inputs by construction, nor relies on self-citation for a uniqueness theorem. The derivation is self-contained against external benchmarks (observed abundances) and the construction is presented as an existence demonstration rather than a forced output. Standard one-zone GCE assumptions are flagged as conditions, not hidden in the chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Conclusions rest on the accuracy of input stellar-evolution explodability prescriptions and on domain assumptions about galactic gas flows and the location of the explodability transition; the simplified model introduces additional tuned parameters to achieve dual compatibility.

free parameters (1)
  • transition metallicity
    Location of the change in explodability behavior, set to sub-solar values to satisfy both RSG and GCE requirements simultaneously.
axioms (1)
  • domain assumption Net outflows from the galactic system are negligible or absent
    Explicitly required for the simplified explodability solution to exist while matching chemical evolution observables.

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