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

T0 review · 3 major / 7 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read Galactic chemical evolution can constrain which massive stars explode, and a metallicity-dependent rule can ease the red-supergiant problem without breaking abundance trends.

desk verdict Solid GCE constraints on metallicity-dependent explodability; the RSG-compatible window is real but only opens under low net outflow (or near-solar Z_th), which the paper states clearly rather than hides. read the letter →

arxiv 2605.15462 v2 pith:QSJXS7ON submitted 2026-05-14 astro-ph.HE astro-ph.GAastro-ph.SR

Sojun Ono , Keiichi Maeda , Akihiro Suzuki This is my paper · ORCID
classification astro-ph.HEastro-ph.GAastro-ph.SR
keywords galacticchemicalevolutioncore-collapsesupernovaeexplodabilityredsupergiantproblemmetallicityblackholeformationoxygenabundanceinitialmassfunction
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

Whether a massive star ends as a core-collapse supernova or a black hole decides how much oxygen and other metals it returns to the galaxy. That fate, called explodability, is still uncertain and may change with the star’s mass and metallicity. This paper folds recent metallicity-dependent explodability maps into a one-zone galactic chemical evolution model and shows that the physics-motivated maps already match the main observed abundance patterns, especially [O/Fe] versus [Fe/H]. Maximizing black-hole formation, however, under-produces oxygen and fails. Building on that, the authors construct a simple rule that lets stars up to about 40 solar masses explode at low metallicity but only up to about 18 solar masses near solar metallicity—the cut that would ease the missing high-mass red-supergiant progenitors. That rule works only if net metal outflows are small or absent and the transition occurs at sub-solar metallicity. The same framework also shows that a top-heavy low-metallicity initial mass function improves the fit once it is paired with metallicity-dependent explodability. The result is a concrete demonstration that chemical evolution supplies useful limits on stellar death, and that a solution to the red-supergiant problem need not violate those limits.

What carries the argument

Metallicity-dependent explodability (whether a star of given zero-age mass and metallicity produces a core-collapse supernova or a black hole) implemented inside a one-zone galactic chemical evolution model, diagnosed primarily by the [O/Fe]–[Fe/H] track.

What would settle it

If multi-zone or outflow-inclusive models that still match the metallicity distribution function and solar [O/Fe] still require explosions above ~18 solar masses at solar metallicity, or if the transition metallicity must sit at or above solar, the RSG-compatible solution fails.

Watch

Extended reading notes

Core claim

Physics-motivated metallicity-dependent explodability prescriptions reproduce observed galactic abundance trends, while galactic chemical evolution itself bounds the black-hole-forming region in mass–metallicity space. A simplified explodability that restricts successful explosions above ~18 solar masses near solar metallicity—thereby addressing the red-supergiant problem—remains compatible with those trends only when net outflows are negligible and the transition lies at sub-solar metallicity.

Load-bearing premise

The solar-neighborhood metal budget can be treated as a one-zone system with little or no net outflow of metals.

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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

3 major / 7 minor

Summary. The paper implements recently proposed metallicity-dependent massive-star explodability maps (Maltsev et al. 2025; Ebinger et al. 2019, 2020) in a one-zone GCE code and shows that the physics-motivated maps (group Ex) reproduce the observed MDF, present-day SFR, [Fe/H](t_⊙), and the [O/Fe]–[Fe/H] trend, while extreme BH-maximizing variants (group Ex-BH) underproduce oxygen. Guided by those failures, the authors introduce a simplified explodability boundary M_th(Z) (Eq. 4) that forces M_th→18 M_⊙ at Z≥Z_⊙ (motivated by the RSG problem) while allowing explosions up to 40 M_⊙ below a transition metallicity Z_th. They find that this RSG-friendly map can still match solar composition and [O/Fe] only if net outflows are negligible (ε_out≈0) and Z_th is sub-solar (≳0.5 Z_⊙), or if Z_th is forced near Z_⊙ when outflows are retained. They further show that a top-heavy low-Z IMF (Chon et al. 2024) improves the metal-poor [O/Fe] plateau once coupled to metallicity-dependent explodability, and that explodability changes alone do not resolve the missing-SN rate discrepancy.

Significance. If the GCE constraints hold, the work supplies a practical, observationally falsifiable filter on the mass–metallicity domain of black-hole formation: successful explosions of oxygen-rich progenitors up to ∼30–40 M_⊙ at low Z are required, while strong suppression of high-mass explosions at solar Z is tightly limited. That is a useful bridge between stellar-explosion theory and Galactic abundances, and the systematic Z_th–ε_out exploration plus the yield-contribution appendices make the oxygen diagnostic more transparent than in many GCE studies. The RSG-compatible construction is more provisional—it is explicitly conditional on net metal retention—but it correctly reframes the RSG problem as a joint stellar-physics and chemical-evolution question rather than a pure progenitor-mass cut. Credit is due for validating models against MDF/SFR/[Fe/H] before interpreting [O/Fe], for documenting that Fe is far less sensitive than O to the high-mass window, and for showing that metallicity-dependent IMF and explodability should be treated together.

major comments (3)
  1. §3.2.2–3.2.3 and abstract: The central claim that an RSG-compatible explodability (M_th=18 M_⊙ at Z≥Z_⊙) can be constructed without violating GCE observables is demonstrated only for ε_out=0 (with Z_th≳0.5 Z_⊙) or for ε_out=0.75 with Z_th forced near Z_⊙ (which the text itself calls fine-tuned). The multi-zone radial-migration analogy offered as a physical justification for zero net outflow is qualitative only—no multi-zone run is shown, and Table 1 already retunes ε_out, τ_in, and τ_s whenever the IMF or explodability changes. Please either (i) add a multi-zone or effective metal-retention calculation that recovers the ε_out=0 tracks, or (ii) rephrase the abstract/conclusions so that the RSG solution is clearly a necessary condition on net metal retention rather than a demonstrated MW solution.
  2. §2.2 and Appendix A: Explodability and nucleosynthetic yields are treated as separable, with a piecewise M_56Ni cut (0.02/0.07 M_⊙) imposed on Chieffi & Limongi (2004) rather than taken from the same neutrino-driven models that supply the explodability maps. Appendix A shows that oxygen is relatively robust across yield sets, which supports the main diagnostic, but the solar [O/Fe] and the Ex-BH failures also depend on the Fe yield and the mass-cut choice (Appendix B). A short sensitivity test—varying the M_56Ni prescription or swapping one self-consistent yield+explodability set (e.g., PUSH yields with Ex-PUSH)—would make the claimed GCE constraints on the BH region more robust.
  3. §2.2.2–2.2.3: The metallicity interpolation of the Maltsev and PUSH maps (log(Z) slope, freeze of M_CO,bound below Z_⊙/20, linear connection at Z≤10^{-4} Z_⊙, and the artificial discontinuity at Z=Z_⊙/10 for Case B) is load-bearing for the group-Ex success and for the location of the allowed BH region. Please quantify how [O/Fe]–[Fe/H] and the solar point shift under alternate interpolations (e.g., linear in Z, or holding the Z_⊙/10 map to lower Z), or state explicitly that the GCE constraints apply only within the adopted interpolation scheme.
minor comments (7)
  1. Abstract: “this effect becomes importance” → “becomes important”.
  2. §2.2.3: “model Ex-PHSH” is a typo for Ex-PUSH.
  3. Title line and several places: “T oward”, “matallicity”, “metallicty-dependent” — residual spacing/typo issues.
  4. Figure 1 / §2.2.2: The 85%/15% mixed-region probability is stated but not motivated; a one-sentence reference to Maltsev et al. would help.
  5. §4.4 / Figure 8: With the Chon IMF the MDF peak shifts to [Fe/H]∼−0.2; this is noted but not shown. A small MDF panel would make the residual tension clearer.
  6. Table 1: Base-40 is used in §3 but listed only under “Base models” without the same parameter block clarity as the simplified models; a one-line note would avoid confusion.
  7. §1: “A small description added in the above sentence.” appears to be an editorial leftover and should be removed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; external explodability maps are tested against independent [O/Fe] diagnostics after ordinary GCE parameter calibration, and the RSG-compatible window is a conditional scan result, not a forced prediction.

full rationale

The load-bearing inputs are external: metallicity-dependent explodability maps from Maltsev et al. (2025) and Ebinger et al. (2019/2020), CCSN yields from Chieffi & Limongi (2004), and observational [O/Fe]–[Fe/H] compilations. These are inserted into a one-zone GCE framework (Suzuki & Maeda 2018 code, reused as a tool). Free parameters (ε_out, τ_in, τ_s, Ṁ_in,0) are calibrated once to MDF, SFR and [Fe/H](t_⊙); the resulting [O/Fe] tracks (and the full evolutionary shape, not merely the solar point) are then compared to independent data. Group Ex-BH and low-Z_th simplified models fail this test, while group Ex succeeds—showing the diagnostic has discriminating power. The simplified RSG-motivated form (Eq. 4) is an explicit ansatz scanned over Z_th and ε_out; the paper reports success only conditionally (“if net outflows negligible and transition at sub-solar Z”) and does not claim the solution is derived or forced. The acknowledged near-tautology that solar Z + [Fe/H]=0 implies [O/Fe]≈0 is used only as a consistency remark; the low-metallicity plateau and track shape remain independent. No self-definitional identity, fitted-input-as-prediction, uniqueness theorem, or ansatz smuggling appears. Ordinary self-citation of the prior code does not close any logical loop on the new metallicity-dependent claims.

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The central claims rest on a calibrated one-zone GCE integrator, literature yields, and two free-parameter families (GCE timescales/outflow and the simplified Z_th transition). No new physical entities are postulated beyond the phenomenological explodability map itself.

free parameters (4)
  • ε_out (outflow efficiency) = 0.75 or 0.00
    Calibrated to 0.75 (fiducial) or 0.00 (RSG-compatible case) to match MDF and solar abundances; the RSG solution exists only for the low-outflow choice.
  • τ_in, τ_s, Ṁ_in,0 = 5 Gyr / 3 Gyr / 20 M⊙ yr⁻¹ (fiducial); 3.5/2.5/71 for Chon IMF
    Inflow and star-formation timescales plus initial inflow rate retuned for each model family (Table 1) to satisfy MDF, SFR and [Fe/H](t_⊙).
  • Z_th (transition metallicity in simplified model) = scanned 0.01–0.99 Z_⊙
    Free parameter in Eq. (4) scanned from 0.01 Z_⊙ to 0.99 Z_⊙; only Z_th ≳ 0.5 Z_⊙ with ε_out=0 yields both solar [O/Fe] and M_th≈18 M_⊙.
  • M_56Ni piecewise cut = 0.02 / 0.07 M_⊙
    Ad-hoc 0.02 M_⊙ (≤14 M_⊙) / 0.07 M_⊙ (>14 M_⊙) chosen to match average observed nickel and neutrino-driven models.
assumptions (4)
  • domain assumption One-zone instantaneous mixing adequately captures solar-neighborhood chemical evolution for the purpose of constraining explodability.
    Stated in §2.1; multi-zone effects are acknowledged only as a possible rescue for the zero-outflow case.
  • domain assumption Explodability and nucleosynthetic yields may be treated as separable; Chieffi & Limongi (2004) yields with adjusted mass cut remain valid across the adopted explodability maps.
    Explicitly adopted in §2.2; oxygen is argued to be relatively insensitive to yield-set differences (Appendix A).
  • domain assumption Failed explosions (BH formation) eject negligible metal-rich material.
    Used throughout for mixed and pure-BH regions; fallback is assumed to lock all newly synthesized metals.
  • domain assumption Kroupa (or Chon) IMF and W7 SN Ia yields with fixed DTD are adequate.
    Standard choices listed in §2.1 and Table 1.
invented entities (1)
  • Simplified metallicity-dependent explodability M_th(Z) of Eq. (4)
    purpose: Minimal functional form that enforces M_th=40 M_⊙ at low Z and M_th=18 M_⊙ at Z≥Z_⊙, allowing a controlled test of RSG-compatible solutions.
    Constructed ad hoc in §3.1; not derived from stellar models but guided by the GCE constraints of §2.

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Pith. "Pith review of Constraints on the Metallicity-dependent Explodability of Massive Stars from Galactic Chemical Evolution: Toward Alleviating the Red Supergiant Problem." pith.science (2026). https://pith.science/paper/QSJXS7ON

@misc{pith2026260515462,
  author       = {Pith},
  title        = {Pith review of: Constraints on the Metallicity-dependent Explodability of Massive Stars from Galactic Chemical Evolution: Toward Alleviating the Red Supergiant Problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QSJXS7ON}},
  note         = {Machine review of arXiv:2605.15462}
}
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 important 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 important once coupled with the metallicity-dependent explodability.

Figures

Figures reproduced from arXiv: 2605.15462 by the authors.

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 patterns repre… view at source ↗
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 present t… view at source ↗
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 downward triangl… view at source ↗
Figures from the paper (7 more)
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 t…
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]
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 mai…
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]
Figure 8
Figure 8. Figure 8: GCE with metallicity-dependent IMF. Same as [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
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 differe…
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 …

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. VENUS: an ultra-faint galaxy hosting the metal-poor type II supernova at $z=5.13$ Witnessing the initial metal enrichment with extremely frequent core-collapse supernovae?

    astro-ph.GA 2026-07 conditional novelty 7.0 of 10

    The z=5.13 supernova SN Eos exploded in an ultra-faint, very metal-poor dwarf galaxy, suggesting core-collapse supernovae were much more frequent in early low-metallicity environments.

  2. JWST observations of a planetary nebula support jet-driven explosion of core-collapse supernova remnant RCW 103

    astro-ph.HE 2026-05 unverdicted novelty 4.0 of 10

    Morphological similarity between JWST images of planetary nebula PMR 1 and X-ray images of CCSN remnant RCW 103 indicates that two pairs of jets shaped RCW 103, supporting the jittering-jets explosion mechanism.

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