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arxiv: 2603.19883 · v1 · submitted 2026-03-20 · 🌌 astro-ph.SR · astro-ph.HE

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· Lean Theorem

Constraints on the ¹²C(α, γ)¹⁶O and ¹⁶O+¹⁶O Reaction Rates from Binary Black Holes Detected via Gravitational Wave Signals

Wenyu Xin , Xiaokun Hou , Xianfei Zhang , Shaolan Bi , Gang Zhao
Authors on Pith no claims yet

Pith reviewed 2026-05-15 07:27 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.HE
keywords black hole mass gapgravitational wavesnuclear astrophysicspair-instability supernovae12C(alpha,gamma)16O reactionhelium star evolutionMESA stellar modelsbinary black hole mergers
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The pith

Gravitational wave data from binary black holes constrains the 12C(α,γ)16O reaction rate at 300 keV to 137.6-263.4 keV barn.

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

This paper explores how uncertainties in key nuclear reaction rates during the evolution of massive helium stars influence the masses of the black holes they leave behind. By running a grid of models with the MESA code at very low metallicity, the authors show that the carbon-alpha reaction rate has a strong effect on where the pair-instability mass gap appears in the black hole spectrum. The oxygen fusion rate, in comparison, mainly affects the upper boundary of that gap. Matching the lower edge of the gap to values inferred from gravitational-wave catalogs then produces a new, observationally derived range for the strength of the carbon-alpha reaction.

Core claim

The central claim is that the astrophysical S-factor S300 for the 12C(α, γ)16O reaction is constrained to the interval 137.6–263.4 keV barn. This follows from computing the final black-hole mass distributions for helium stars with initial masses 40–150 solar masses, finding that a ±3σ variation in the carbon-alpha rate moves the lower edge of the predicted pair-instability gap from ~104 M⊙ down to ~45 M⊙, while the observed gap edge of 44–68 M⊙ selects only the portion of rate space that reproduces this location.

What carries the argument

The pair-instability supernova mechanism, whose mass threshold is set by the carbon-oxygen core mass reached at the end of helium burning, which in turn depends sensitively on the 12C(α,γ)16O reaction rate.

Load-bearing premise

The lower edge of the observed black hole mass gap arises exclusively from the pair-instability supernova process operating in single-star evolution.

What would settle it

A future gravitational-wave catalog that places the lower edge of the mass gap below 45 solar masses or above 135 solar masses, or that finds a substantial population of black holes inside the gap, would falsify the constrained range for the reaction rate.

Figures

Figures reproduced from arXiv: 2603.19883 by Gang Zhao, Shaolan Bi, Wenyu Xin, Xianfei Zhang, Xiaokun Hou.

Figure 1
Figure 1. Figure 1: The σ12Cα and f16O computed in the stellar mod￾els. The red points show the parameter grid computed in R. Farmer et al. (2020) and the black crosses show those com￾puted in this work. recent experimental measurements (R. J. deBoer et al. 2017; Y. P. Shen et al. 2020). In this work, we investigate the effects of the 12C(α, γ) 16O and the 16O+16O reaction rates on the PPISN/PISN with finer grids sampling, as… view at source ↗
Figure 2
Figure 2. Figure 2: The BH masses as a function of initial He core mass. Green points, blue stars, and red diamonds denote the results from R. Farmer et al. (2020); E. Farag et al. (2022) and W. Xin et al. (2023b). It should be noted that W. Xin et al. (2023b) adopted Z = 10−3 while other studies employ Z = 10−5 . These studies also adopt different reaction rate tables. R. Farmer et al. (2020) used STARLIB tables for both 3α … view at source ↗
Figure 3
Figure 3. Figure 3: The PISN BH mass gap as a function of σ12Cα. The orange region indicates that the BHs are formed from CCSNe below the mass gap or PPISNe, while the light blue region represents that the BHs are formed by the CCSNe above the mass gap. The white region indicates the mass gap formed due to the PISNe explosion. Left: The red, blue, and green lines represent PPISN/PISN and PISN/CC boundaries from this work, R. … view at source ↗
Figure 4
Figure 4. Figure 4: Performance of the RBF model as a computational substitute for the discrete MESA calculations in determining the lower edge of the mass gap. Left panel: Color map of the RBF-predicted m over the σ12Cα − σ16O space. Black contour lines denote iso-m levels. Right panel: One-dimensional slices of the RBF surface at fixed values of σ16O = −1, 0, and 1. Solid curves represent the RBF predictions, while symbols … view at source ↗
Figure 5
Figure 5. Figure 5: Posterior distribution of the 12C(α, γ) 16O and 16O+16O reaction rates, inferred using the lower edge of mass gap from F. Antonini et al. (2025a) (m0 = 45.3 +6.5 −6.8 ). The top and right panels show the marginalized posterior distributions of σ12Cα and σ16O, respectively, while the low￾er-left panel displays their joint posterior distribution. The blue dashed lines indicate the posterior medians, and the … view at source ↗
read the original abstract

Gravitational-wave observations of binary black hole (BH) mergers provide a novel avenue for testing massive-star evolution and the resulting BH mass spectrum. Recent population analyses under the hierarchical-merger hypothesis have offered evidence for the BH mass gap and inferred its lower edge to $\sim 44 - 68$ M$_\odot$. Motivated by these findings, we compute low-metallicity ($Z=10^{-5}$) helium star models with MESA and systematically explore the effect of uncertainties in the $^{12}$C$(\alpha, \gamma)^{16}$O and $^{16}$O+$^{16}$O reaction rates on the final fate. Varying the $^{12}$C$(\alpha, \gamma)^{16}$O reaction rate by $-3 \sigma$ to $+3\sigma$, we find that the predicted BH mass gap shifts from $\sim104 - 184$ M$_\odot$ to $\sim45 - 135$ M$_\odot$. In contrast, scaling the $^{16}$O+$^{16}$O reaction rate by global factors of 0.1, 1, and 10 has only a modest effect on the lower edge of the BH mass gap (less than 5 M$_\odot$), and shifts the upper edge by more than 10 M$_\odot$. Using the predictions of our models together with the literature estimates for the lower edge of the BH mass gap, we constrain the astrophysical S factor of $^{12}$C$(\alpha, \gamma)^{16}$O reaction at 300 keV of $S_{300} \simeq$ 137.6 - 263.4 keV barn.

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 paper computes low-metallicity (Z=10^{-5}) helium-star models with MESA, systematically varying the ^{12}C(α,γ)^{16}O rate by ±3σ and the ^{16}O+^{16}O rate by factors of 0.1–10. It reports that the predicted lower edge of the black-hole mass gap shifts from ~104–184 M⊙ to ~45–135 M⊙ with the carbon-alpha rate variation, while the oxygen-oxygen rate produces only modest shifts. Combining these model predictions with literature values for the observed mass-gap lower edge (~44–68 M⊙) under the hierarchical-merger hypothesis, the authors constrain the astrophysical S-factor S_{300} of ^{12}C(α,γ)^{16}O to 137.6–263.4 keV barn.

Significance. If the central mapping and assumptions hold, the work supplies an independent astrophysical constraint on a key nuclear reaction rate that directly influences the pair-instability supernova threshold and the black-hole mass spectrum, complementing laboratory measurements. The explicit demonstration that the ^{16}O+^{16}O rate has limited impact on the lower gap edge is a useful negative result.

major comments (2)
  1. [Abstract and results section] The derivation of the numerical bounds S_{300} ≃ 137.6–263.4 keV barn from the reported model shifts (104–184 M⊙ to 45–135 M⊙) is not shown; no interpolation, fitting procedure, or explicit mapping between rate multiplier and gap edge is provided in the abstract or main text, yet this step is load-bearing for the central claim.
  2. [Introduction and discussion] The constraint assumes the observed 44–68 M⊙ lower edge arises exclusively from the pair-instability threshold in single-star He-core evolution under the hierarchical-merger hypothesis, with negligible contribution from other channels (dynamical capture, primordial BHs, or altered mass loss). No population-synthesis robustness test against these alternatives is presented, rendering the inferred window sensitive to this untested premise.
minor comments (2)
  1. [Methods] Define the precise criterion used to identify the lower and upper edges of the mass gap in the MESA models (e.g., the mass range with zero BH formation probability).
  2. [Methods] Specify the exact reaction-rate libraries and the functional form of the ±3σ variations applied to the ^{12}C(α,γ)^{16}O rate.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful review and constructive comments. We address each major point below, indicating where revisions will be made to improve clarity and transparency while remaining within the scope of the present study.

read point-by-point responses

  1. Referee: [Abstract and results section] The derivation of the numerical bounds S_{300} ≃ 137.6–263.4 keV barn from the reported model shifts (104–184 M⊙ to 45–135 M⊙) is not shown; no interpolation, fitting procedure, or explicit mapping between rate multiplier and gap edge is provided in the abstract or main text, yet this step is load-bearing for the central claim.

    Authors: We agree that the explicit mapping from model gap edges to the S_{300} bounds was not detailed. In the revised manuscript we will add a short subsection in the Results section that describes the linear interpolation between the lower gap edges obtained at the −3σ and +3σ rate multipliers and the literature range 44–68 M⊙, thereby making the derivation of 137.6–263.4 keV barn fully transparent. revision: yes

  2. Referee: [Introduction and discussion] The constraint assumes the observed 44–68 M⊙ lower edge arises exclusively from the pair-instability threshold in single-star He-core evolution under the hierarchical-merger hypothesis, with negligible contribution from other channels (dynamical capture, primordial BHs, or altered mass loss). No population-synthesis robustness test against these alternatives is presented, rendering the inferred window sensitive to this untested premise.

    Authors: The work is explicitly framed under the hierarchical-merger hypothesis supported by existing population analyses. A comprehensive robustness test against all alternative channels would require a separate population-synthesis study that lies outside the scope of this paper, which focuses on nuclear-rate sensitivities within detailed stellar models. We will expand the discussion to state this assumption more clearly and to note the associated caveat with appropriate references. revision: partial

standing simulated objections not resolved
  • Absence of population-synthesis robustness tests against alternative black-hole formation channels

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper varies the 12C(α,γ)16O rate by ±3σ as an explicit input to MESA He-star models at fixed Z=10^{-5}, computes the resulting shift in the predicted BH mass-gap lower edge (from ~104-184 M⊙ to ~45-135 M⊙), and intersects that model output with independent literature values for the observed gap edge (~44-68 M⊙) to obtain the S300 bound. This is forward modeling: nuclear-rate variation is the free parameter, gap location is the computed output, and the final constraint uses external observational data. No equation reduces to its own input by construction, no parameter is fitted to the target data and relabeled a prediction, and no load-bearing step relies on self-citation or an ansatz imported from prior work by the same authors. The chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on two domain assumptions about the origin of the black hole mass gap and the interpretation of gravitational-wave data; no new free parameters are fitted inside the paper itself, and no new physical entities are postulated.

free parameters (2)
  • 12C(α,γ)16O rate multiplier
    Scanned from -3σ to +3σ around the nominal value to map uncertainty onto the mass gap.
  • 16O+16O rate scaling factor
    Tested at global factors 0.1, 1, and 10.
axioms (2)
  • domain assumption The black hole mass gap arises exclusively from pair-instability supernovae in massive stars.
    Invoked to link nuclear reaction rates directly to the location of the gap edges.
  • domain assumption The lower edge of the observed mass gap (44-68 M⊙) is correctly inferred under the hierarchical-merger hypothesis from gravitational-wave population analyses.
    Used as the external benchmark to derive the S300 constraint.

pith-pipeline@v0.9.0 · 5642 in / 1765 out tokens · 73240 ms · 2026-05-15T07:27:08.017336+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. The Black Hole Mass Gap as a New Probe of Millicharged Particles

    hep-ph 2026-04 unverdicted novelty 7.0

    Millicharged particles weaken pulsational pair-instability in massive stars, shifting the lower edge of the black hole mass gap upward and turning gravitational wave observations into a probe for particles with masses...

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