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Very Massive, Rapidly Spinning Binary Black Hole Progenitors through Chemically Homogeneous Evolution -- The Case of GW231123

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Chemically homogeneous twin stars can forge GW231123's black holes.

desk verdict A useful new CHE grid that can match GW231123's masses and spins, but the direct-collapse assumption is load-bearing and the a∝M^-0.9 relation is in-sample; worth refereeing, not yet a confirmed channel. read the letter →

arxiv 2509.00154 v1 pith:ZBVG3YDH submitted 2025-08-29 astro-ph.HE astro-ph.SRgr-qc

Silvia A. Popa , Selma E. de Mink This is my paper
classification astro-ph.HEastro-ph.SRgr-qc
keywords gravitationalwavesblackholemergerschemicallyhomogeneousevolutionstellarrotationpair-instabilitymassgapGW231123massivebinarystarsMESAmodels
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

The paper asks how the two black holes in GW231123, the most massive and most rapidly spinning merger detected so far, could have formed in an isolated binary. It argues that chemically homogeneous evolution (CHE) in very massive, tight binaries at low metallicity naturally produces the right progenitors: helium stars with masses near 120–130 solar masses and dimensionless spins 0.8–0.9, matching the event's inferred properties. The same models produce a tight mass-spin relation a ∝ M^-0.9 for hydrogen-free stars, set by the critical rotation limit. If correct, this makes CHE a viable, non-exotic origin for the most extreme gravitational-wave event; the main uncertainty is whether such rotating cores actually collapse into black holes above the pair-instability gap.

What carries the argument

Chemically homogeneous evolution (CHE): in very tight, tidally locked binaries, rotationally induced mixing keeps the stars nearly uniform in composition, so they stay compact and become close helium stars that later collapse into black holes. The argument is carried by the critical rotation rate, which falls as the luminosity approaches the Eddington limit; stars are spun up by contraction and then shed mass and angular momentum as they hit this limit, producing the tight a ∝ M^-0.9 spin-mass correlation.

What would settle it

Run a three-dimensional collapse simulation of a ~160 solar-mass helium star rotating at the critical rate, with magnetic angular-momentum transport included: if it ends in a pair-instability supernova with no remnant, this channel cannot produce GW231123. Alternatively, a future gravitational-wave event with total mass above 200 solar masses and component spins far above the a ∝ M^-0.9 relation would contradict the spin-capping mechanism.

Watch

Extended reading notes

Core claim

Using a grid of MESA binary models with initial masses 120–180 solar masses, periods 0.7–1.8 days and metallicity Z=10^-5, the paper evolves chemically homogeneous binaries to core helium depletion. Initial masses above about 140 solar masses naturally yield rapidly rotating, near-equal-mass progenitors with final masses 120–130 solar masses and dimensionless spins 0.8–0.9, matching GW231123's inferred total mass and spins. Hydrogen-free models converge on a tight spin-mass correlation a ∝ M^-0.9, traced to the critical rotation limit: contraction and the rising Eddington factor lower the critical rotation rate, so winds shed angular momentum and cap the spin. The paper concludes CHE is a vi

Load-bearing premise

The argument collapses if helium cores above about 120 solar masses that are rotating near the critical limit do not collapse directly into black holes—for example, if pair-instability supernovae disrupt them instead, or if rotation shifts the upper mass gap enough to leave no remnant.

Editorial extensions

If this is right

  • GW231123's black holes can be explained by standard isolated binary evolution at low metallicity, without dynamical mergers, Population III stars, or exotic relics.
  • The predicted a ∝ M^-0.9 spin-mass correlation gives a testable signature: future very massive, high-spin merger detections should track this relation.
  • All matched models merge within a Hubble time, with prompt delays of tens of Myr, so this channel yields observable events in the nearby universe.
  • The extreme event would be tied to metal-poor star formation, giving an astrophysical route to the pair-instability mass-gap region.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If future detections of very massive binary black holes also follow the a ∝ M^-0.9 track, that would distinguish the CHE channel from dynamical assembly, which predicts lower and more isotropic spins.
  • A decisive next test is a rotating-collapse calculation that includes magnetic angular-momentum transport: the paper's direct-collapse assumption may fail if pair-instability disrupts critically rotating helium cores near 160 solar masses.
  • Extending the grid to non-equal mass ratios and slightly higher metallicities could map how often this channel operates and whether it produces events like GW190521 as well.
  • Because the quoted masses and spins are upper limits from the pre-collapse models, coupling CHE binary evolution to full collapse simulations would show how much the final black holes deviate from these values.
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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 / 5 minor

Summary. The paper investigates whether chemically homogeneous evolution (CHE) in very massive, tight binaries at Z=10^-5 can produce the progenitor black holes of GW231123. The authors compute a MESA grid of binary models with initial masses 120-180 Msun and periods 0.7-1.8 d, evolve them to central helium depletion, and map helium-core mass and angular momentum to black-hole mass and spin under a direct-collapse assumption. They find several models with total masses 240-266 Msun and dimensionless spins 0.8-0.9, overlapping the GW231123 credible regions. They also identify a tight a ∝ M^-0.9 relation for fully CHE, hydrogen-free models, which they attribute to the critical rotation limit. The paper explicitly discusses the large uncertainties in the final collapse and in tidal shutdown.

Significance. If the progenitor models are accepted, this is a valuable demonstration that an isolated-binary channel can in principle produce the most massive, highest-spin merger observed to date, adding to the dynamical/AGN/Pop III explanations. The main strengths are the modern MESA input physics, the explicit mapping to GW event properties, and the honest caveats. The result is, however, contingent on two assumptions that the paper itself flags as uncertain: direct collapse of >120 Msun helium cores with rotation, and negligible tides after core hydrogen depletion. The a ∝ M^-0.9 relation is a useful empirical scaling but is derived from fits to the same grid (in-sample), so it should be presented as such. The paper's value is in narrowing the range of plausible CHE progenitors and setting up a target for collapse simulations, not in providing a definitive formation rate or final remnant prediction.

major comments (3)
  1. [Sec. 2, 'Assumptions for the Final Mass and Spin'; Sec. 4 'Fate and Properties of the Remnants'] The central claim that the models match GW231123's black holes rests on the assumption that helium cores >120 Msun with near-critical rotation collapse directly into black holes, conserving mass and angular momentum. The paper acknowledges that Croon et al. (2025) find a 160 Msun helium star rotating above 0.4 Ωcrit is completely disrupted by pair instability, while the models here reach Ω/Ωcrit near unity (Fig. 3f). The rebuttal that Croon et al. omit magnetic angular-momentum transport is plausible but does not establish the fate of these specific cores. This is load-bearing: if rotation shifts the upper mass gap, the matched progenitors leave no remnant and the claimed match evaporates. Please add a quantitative sensitivity test (e.g., applying Croon et al.'s fate criterion to the grid) or substantially weaken the concluding 'viable' claim to 'viable only if direct collapse holds.'
  2. [Sec. 2, 'Tidal Interactions'; Sec. 4 'The Role of Tides'] The high spins (a≈0.8-0.9) depend directly on the assumption that tides become inefficient once Xc<0.005. The paper's justification is the strong R^9 dependence of the synchronization timescale, and it cites Ma & Fuller (2023) for potential overestimates. However, no sensitivity test is provided, and earlier CHE models that keep tides active produce much lower spins. Since the paper's main new result is the high spins, the assumption needs quantitative backing: e.g., compute the tidal synchronization timescale for the actual helium-star models at late stages, or run a test with tides maintained through helium burning. Without this, the spin predictions are not robust.
  3. [Appendix A; Sec. 3.1] The a ∝ M^-0.9 relation is presented as a 'derivation', but the exponents α, β, γ in Eq. (6) are obtained by fitting to the same grid models (Fig. 4). This makes the relation an in-sample fit, not an independent prediction. It is a useful phenomenological description of the models, but the paper should explicitly say so and avoid implying it is a universal law. This does not undermine the main viability claim, but it affects how the result is interpreted.
minor comments (5)
  1. [Tables 1-2] The columns 'Final mass' and 'Kerr' are progenitor properties at helium depletion and are only upper limits on the BH mass and spin. Please state this in the table captions, not only in the text.
  2. [Fig. 2] The x-axis labels 'Progenitor Mass' and 'Total System Mass' are confusing; clarify that component masses on the lower axis assume q=1.
  3. [Abstract] Typo: 'hold the record' should be 'holds the record'.
  4. [Sec. 3.1] The statement that stellar winds widen the CHE window at higher masses may be misleading at Z=10^-5; clarify that this refers to rotationally enhanced winds or the interplay with critical rotation.
  5. [Sec. 2, Grid Setup] Only q=1 initial ratios are used in the main grid. The paper states test simulations show similar behavior, but a brief quantitative statement or figure would strengthen the claim that q=1 is sufficient for the GW231123 match.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's modeling and comparisons are self-contained, and the a–M relation is presented as an in-sample explanation, not a fitted prediction.

full rationale

The paper's central claims are that very massive CHE binaries at low metallicity produce high-mass, high-spin progenitors consistent with GW231123 and that the critical rotation limit yields a tight a ∝ M^-0.9 correlation. The stellar evolution is computed with MESA from explicitly stated physical assumptions (mixing, tides, winds, critical-rotation cap), and the final masses/spins are compared against external LIGO/Virgo/KAGRA data. The a–M correlation is not presented as an independent first-principles prediction; Appendix A transparently fits structural scaling exponents (α, β, γ) from the same helium-star models and then combines them in Eq. 6 to reproduce the slope. This is a post-hoc consistency explanation, not a circular derivation, and the paper explicitly credits Marchant et al. (2024) for the identical explanatory framework. The direct-collapse remnant map (helium cores >120 Msun collapse to BHs) is an acknowledged external assumption supported by Farmer et al. (2019, 2020) and Mehta et al. (2022); although Farmer et al. includes an overlapping author, it is a separate calculation with stated assumptions that do not include the target result, and the paper explicitly flags the countervailing Croon et al. (2025) result and discusses the uncertainty. No step reduces by definition to its own inputs, and no load-bearing claim rests solely on a self-citation chain.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard stellar physics packages and several adopted modeling choices (mixing efficiencies, tidal and wind prescriptions), plus two load-bearing assumptions: tides switch off after core H depletion, and very massive rapidly rotating helium stars directly collapse to black holes. The scaling-law derivation in Appendix A adds three exponents explicitly fitted to the same grid, which is the main in-sample component.

free parameters (8)
  • Scaling exponents alpha, beta, gamma for k, R, 1-Gamma vs M = alpha = -0.5, beta = 0.77, gamma = -0.60
    Linear fits to the critically rotating helium star models in the grid (Fig. 4); they determine the derived slope a proportional to M^-0.9 in Eq. 7, so the correlation is partly an interpolation of the same models.
  • Rotational mixing efficiency f_c = 1/30
    Adopted from Pinsonneault et al. 1989, Chaboyer & Zahn 1992, Heger et al. 2000, Brott et al. 2011; sets the strength of rotationally induced mixing that enables CHE.
  • Tidal circulation enhancement D_ES = 2.1
    Enhancement of Eddington-Sweet circulation due to tides, adopted from Hastings et al. 2020 as in Sharpe et al. 2024; boosts chemical mixing in close binaries.
  • Convective overshoot alpha_OV = 0.345
    Step-function overshoot during core hydrogen burning, taken from Brott et al. 2011.
  • Semiconvection efficiency alpha_sc = 1.0
    From Langer et al. 1983; affects structure during H and He burning.
  • Mixing-length parameter alpha = 1.5
    Standard mixing-length theory (Bohm-Vitense 1958).
  • Wind mass-loss reduction for hydrogen-poor stars = factor 10 reduction of Hamann et al. 1995 rates
    Adopted reduction that strongly affects final masses and spins at low metallicity; the paper notes mass loss drives the spin-down and critical rotation behavior.
  • Initial mass ratio q = 1
    Grid uses equal masses; the observed GW231123 has unequal components, and the paper only qualitatively states that other mass ratios give similar behavior.
assumptions (6)
  • domain assumption CHE occurs: tidally locked, rapidly rotating massive stars remain chemically homogeneous during central H burning because rotational mixing and large convective cores mix the interior.
    Central assumption of the channel, taken from de Mink et al. 2008, 2009, Marchant et al. 2016, Hastings et al. 2020. The efficiency of rotational mixing is debated (Section 2).
  • domain assumption Spruit-Tayler dynamo describes internal angular momentum transport, keeping models near rigid rotation until the end of helium burning.
    Adopted from Spruit 2002; the paper notes the precise implementation is debated but needed to match observed AM transport (Section 2).
  • domain assumption Tides synchronize the stars only during the main sequence; after central H depletion they become inefficient, so stars spin up during contraction.
    Implemented once Xc < 0.005; motivated by tsync proportional to R^9 and a radius drop factor 2.5. This assumption is the main reason final spins reach about 1; earlier CHE studies that kept tides on found low spins (Sections 2 and 4).
  • domain assumption Helium cores more massive than about 120 Msun collapse directly to black holes above the pair-instability gap, and rotation does not substantially move the gap edges.
    Adopted from Farmer et al. 2019, 2020 and Mehta et al. 2022 for enhanced 12C(alpha,gamma)16O, plus Marchant & Moriya 2020 for rotation. Croon et al. 2025 find rotating 160 Msun helium stars may instead be disrupted by pair instability, a possibility the paper flags in Section 4.
  • domain assumption The final pre-collapse mass and angular momentum at central He depletion provide upper limits to the black hole mass and Kerr parameter via direct collapse.
    The paper explicitly states this is an upper limit, with large uncertainties from collapse and accretion (Sections 2 and 4).
  • domain assumption The chosen grid (Mi = 120 to 180 Msun, Z = 1e-5, P = 0.7 to 1.8 d, q = 1) samples the relevant parameter space for GW231123-like progenitors; such very massive low-metallicity stars exist.
    Supported by observations of very massive stars and high close-binary fractions, but the IMF and binary fraction at Z = 1e-5 are highly uncertain, and no rate estimates are given (Section 4).

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Pith. "Pith review of Very Massive, Rapidly Spinning Binary Black Hole Progenitors through Chemically Homogeneous Evolution -- The Case of GW231123." pith.science (2026). https://pith.science/paper/ZBVG3YDH

@misc{pith2026250900154,
  author       = {Pith},
  title        = {Pith review of: Very Massive, Rapidly Spinning Binary Black Hole Progenitors through Chemically Homogeneous Evolution -- The Case of GW231123},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZBVG3YDH}},
  note         = {Machine review of arXiv:2509.00154}
}
abstract

Among the over 200 gravitational wave detections reported so far, GW231123 is a remarkable event that not only holds the record for the most massive black hole merger, but also exhibits extreme spins. Its origin is actively debated. Proposed scenarios include dynamical formation involving a sequence of mergers, Population III stars, accretion in an AGN disk and also more exotic explanations including primordial black holes and cosmic strings, each facing different challenges. Recent work showed that the incoming black holes of GW231123 can be formed out of massive rapidly rotating collapsing helium stars. Here, we address the question how such very massive rapidly rotating helium stars can be formed in very close binary systems. For this we explore chemically homogeneous evolution (CHE) involving progenitors with masses above the pair-instability mass gap. We compute a grid of detailed massive binary models with the stellar evolution code MESA to follow the early evolution of binary progenitors and show that: (i) very massive ($M_i > 140\, M_\odot$) CHE binaries at low metallicity ($Z=10^{-5}$) naturally produce rapidly rotating progenitors with high masses and high spins matching the properties of the black holes in GW231123 and (ii) the maximum spin of the progenitors is bound by their critical rotation rate leading to a tight correlation between the dimensionless spin and mass, $a \propto M^{-0.9}$, in models that have no hydrogen left. We conclude that the CHE channel appears to be a viable and natural scenario to produce progenitors. We compare and discuss the differences with earlier studies and comment on the large uncertainties in the final fate and collapse.

Figures

Figures reproduced from arXiv: 2509.00154 by the authors.

Figure 1
Figure 1. Grid of binary systems showing the different evolutionary outcomes: chemically homogeneously evolving (CHE) systems (color-coded by the resulting black hole (BH) mass assuming direct collapse), non-CHE systems (gray) and systems that overflow their L2 point on the main sequence (black). We mark overcontact systems at the onset of hydro￾gen burning by white dots and systems that leave no remnant behind due to pair in… view at source ↗
Figure 2
Figure 2. Dimensionless spin and final masses of our CHE progenitors, colorcoded by their final total hydrogen mass. The x-axis shows both the total mass of the binary system and the component masses assuming a mass ratio of q = 1. The background contours indicate 90 % credible intervals of the total BH masses and individual spins inferred for GW231123 from The LIGO Scientific Collaboration et al. (2025), for three waveform m… view at source ↗
Figure 3
Figure 3. Evolution of CHE systems with model properties shown in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Scaling relations for our critically rotating he￾lium star models, showing the dependence of the gyration constant (top), stellar radius (middle) and one minus the Eddington factor (bottom) on mass. The linear fits are used to determined the exponents α, β and γ from E…
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Surface vs center helium evolution for the models shown in [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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Forward citations

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