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arxiv: 2606.31757 · v1 · pith:BGLWB3RSnew · submitted 2026-06-30 · 🌌 astro-ph.HE · astro-ph.CO· astro-ph.IM· astro-ph.SR· gr-qc

The location of the upper edge of the pair-instability supernovae black hole mass gap

Jeremy Sakstein , Djuna Croon This is my paper

Pith reviewed 2026-07-01 04:21 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.COastro-ph.IMastro-ph.SRgr-qc
keywords pair-instability supernovaeblack hole mass gapnuclear reaction ratesstellar evolutiongravitational waves12C(alpha,gamma)16Otriple-alpha processoxygen fusion
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The pith

The 12C(α,γ)16O reaction rate dominates uncertainty in the upper edge of the pair-instability black hole mass gap, shifting it by about 30 solar masses.

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

This paper runs suites of stellar evolution simulations to measure how different inputs move the upper boundary of the mass gap where pair-instability supernovae prevent black hole formation. The dominant effect comes from the carbon-12 alpha capture reaction on oxygen-16, which changes the edge location by roughly 30 solar masses. The triple-alpha reaction produces a comparable shift of 25 solar masses, and oxygen-oxygen fusion shifts the upper edge by 15 solar masses while leaving the lower edge fixed. Mixing, winds, and other processes produce smaller changes of 10 solar masses or less. The upper edge stays stable when the simulations change spatial or temporal resolution.

Core claim

The upper edge of the pair-instability supernova black hole mass gap is most sensitive to the 12C(α,γ)16O reaction rate, which shifts the edge by approximately 30 solar masses. The triple-α rate produces a shift of about 25 solar masses, while 16O+16O reactions shift the upper edge by 15 solar masses without affecting the lower edge. Other processes contribute shifts at the level of 10 solar masses or less. The upper edge is robust to variations in spatial and temporal resolution.

What carries the argument

A suite of stellar evolution simulations that independently vary nuclear reaction rates (12C(α,γ)16O, triple-α, 16O+16O), mixing processes, and stellar winds to locate the upper edge of the PISN black hole mass gap.

If this is right

  • The upper edge can serve as a direct probe of the nuclear processes that govern pair instability.
  • 16O+16O reactions can widen or narrow the mass gap by shifting only the upper edge.
  • The upper edge is reliably resolved in current simulations because it is insensitive to resolution changes.
  • High-mass black hole detections in gravitational wave data can be compared against models that incorporate these nuclear uncertainties.

Where Pith is reading between the lines

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

  • Tighter experimental constraints on the 12C(α,γ)16O rate would reduce the theoretical spread in the predicted upper edge location.
  • Because some reactions affect only the upper edge, the observed width of the mass gap could encode information about specific nuclear rates.
  • Catalogs of high-mass black holes from gravitational wave detectors could test which nuclear rate assumptions best match the data.

Load-bearing premise

Varying the listed nuclear reaction rates, mixing, and wind inputs independently in the simulations captures the dominant uncertainties in the upper edge location.

What would settle it

A laboratory measurement of the 12C(α,γ)16O reaction rate lying outside the range used in the simulations that would place the predicted upper edge at a mass inconsistent with observed black holes in gravitational wave catalogs.

Figures

Figures reproduced from arXiv: 2606.31757 by Djuna Croon, Jeremy Sakstein.

Figure 1
Figure 1. Figure 1: Largest shifts in the upper-edge BH mass under vari￾ations of individual physical inputs and modeling assumptions around a fiducial configuration with Z = 10−5 (Z = 5 × 10−4 for winds). Further details in text. the location of the upper edge, focusing on its sensitivity to nuclear and stellar physics and numerical resolution. Our findings are summarized in [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Variation of the upper edge of the BHMG with nuclear rates, as described in text. uncertainty, but rather reflects environmental variation across stellar populations. It can therefore be considered a source of astrophysical scatter in the location of the upper BHMG edge. We note that this is a larger scatter than found for the lower edge in similar simulations e.g., Croon & Sakstein (2025) find 3 M⊙. (iv) … view at source ↗
read the original abstract

Gravitational wave observations are beginning to probe the upper edge of the pair-instability supernova (PISN) black hole mass gap, a key prediction of stellar evolution. In this work, we quantify the sensitivity of this boundary to uncertainties in stellar evolution using a suite of simulations that vary inputs including nuclear reaction rates, mixing processes, and stellar winds. We find that the $^{12}{\rm C}(\alpha,\gamma)^{16}{\rm O}$ reaction rate is the dominant source of uncertainty, shifting the upper edge by $\Delta M\sim30\,{\rm M}_\odot$, with the triple-$\alpha$ rate producing a comparable shift of $\sim25\,{\rm M}_\odot$. Notably, $^{16}{\rm O}+^{16}{\rm O}$ reactions shift the upper edge by $\sim15\,{\rm M}_\odot$ while leaving the lower edge unchanged, implying they can widen or narrow the mass gap. Other processes affect the location at the $\lesssim10\,{\rm M}_\odot$ level. In contrast to the lower edge, we find that the upper edge is robust to variations in spatial and temporal resolution, indicating that it is reliably resolved in current simulations. Our results demonstrate that the upper edge carries substantial theoretical uncertainty and, while comparatively less affected by astrophysical contamination than the lower edge, provides a direct probe of the nuclear processes governing pair instability. We discuss the implications for interpreting high-mass black hole detections in gravitational wave data.

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 uses a suite of stellar evolution simulations to quantify how uncertainties in nuclear reaction rates (including 12C(α,γ)16O, triple-α, and 16O+16O), mixing processes, and stellar winds affect the location of the upper edge of the pair-instability supernova black hole mass gap. It reports that the 12C(α,γ)16O rate dominates with a ~30 M⊙ shift, triple-α produces a comparable ~25 M⊙ shift, 16O+16O shifts the upper edge by ~15 M⊙ without affecting the lower edge, and other processes contribute ≲10 M⊙; the upper edge is robust to resolution changes.

Significance. If the results hold, the work provides a systematic quantification of theoretical uncertainties in the upper PISN edge, positioning it as a cleaner probe of nuclear physics than the lower edge for gravitational-wave interpretations of high-mass black holes. The simulation suite approach to varying inputs is a strength for mapping sensitivities.

major comments (2)
  1. [simulation suite description] The central ranking of uncertainties (12C(α,γ)16O as dominant) rests on one-at-a-time parameter variations in the simulation suite. No joint variations or sensitivity matrix is reported, leaving open whether non-additive interactions (e.g., between the 12C(α,γ)16O rate and convective overshoot) could reorder the quoted ΔM shifts of ~30 M⊙ versus ~25 M⊙.
  2. [results on nuclear rate variations] The reported shifts (e.g., ΔM∼30 M⊙ for 12C(α,γ)16O) lack accompanying uncertainty estimates or convergence tests across the varied inputs, making it difficult to assess whether the differences between rates are statistically distinguishable.
minor comments (2)
  1. [abstract] The abstract states that the upper edge is 'reliably resolved' due to robustness to resolution, but the specific resolution parameters and convergence criteria used are not detailed.
  2. [results] Notation for the mass shifts (ΔM∼30 M⊙) would benefit from explicit definition of the reference fiducial model mass in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: The central ranking of uncertainties (12C(α,γ)16O as dominant) rests on one-at-a-time parameter variations in the simulation suite. No joint variations or sensitivity matrix is reported, leaving open whether non-additive interactions (e.g., between the 12C(α,γ)16O rate and convective overshoot) could reorder the quoted ΔM shifts of ~30 M⊙ versus ~25 M⊙.

    Authors: Our suite isolates individual parameter effects via one-at-a-time variations, a standard method for ranking sensitivities in stellar evolution studies. While non-additive interactions between inputs such as the 12C(α,γ)16O rate and convective overshoot cannot be excluded without a full sensitivity matrix, the large individual shifts indicate that the dominant rates would likely retain their ordering even under combined variations. A complete joint analysis exceeds the computational scope of the present work. In revision we will add an explicit discussion of this methodological limitation and its implications for the reported ranking. revision: partial

  2. Referee: The reported shifts (e.g., ΔM∼30 M⊙ for 12C(α,γ)16O) lack accompanying uncertainty estimates or convergence tests across the varied inputs, making it difficult to assess whether the differences between rates are statistically distinguishable.

    Authors: The quoted shifts represent direct differences in upper-edge location between simulations that differ only in the specified nuclear rate. These differences substantially exceed the variations found in our spatial and temporal resolution tests, which serve as a measure of numerical uncertainty. We agree that explicit comparison to these tests would improve clarity. In the revised manuscript we will incorporate the resolution variations as uncertainty estimates on the reported shifts and demonstrate that the rate-induced changes remain distinguishable. revision: yes

Circularity Check

0 steps flagged

No circularity: upper-edge shifts obtained by direct one-at-a-time input variation in stellar-evolution simulations.

full rationale

The paper reports results from a suite of simulations in which nuclear rates, mixing, and winds are varied independently around a fiducial model; the quoted ΔM values are direct numerical outputs of those runs. No equation is defined in terms of its own output, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on a self-citation chain. The derivation chain is therefore self-contained against external benchmarks (the stellar codes and nuclear libraries).

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, preventing a complete audit. The study rests on the domain assumption that the chosen simulation inputs represent the main uncertainties in stellar evolution models for pair instability.

axioms (1)
  • domain assumption Stellar evolution simulations with varied nuclear rates, mixing, and winds accurately capture the location of the upper PISN mass gap edge.
    This underpins the sensitivity analysis and reported shifts described in the abstract.

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