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arxiv: 2606.04428 · v1 · pith:NFGV33MInew · submitted 2026-06-03 · 🌌 astro-ph.SR

Fast-spinning massive black holes from slowly rotating low-metallicity stars: implications for GW231123

N. H. Ismail , N. Yusof , R. Hirschi , A. Griffiths , M. \'A. Aloy , S. Ekstr\"om , G. Meynet This is my paper

Pith reviewed 2026-06-28 04:42 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords population III starsblack hole formationpair instabilitygravitational wavesstellar rotationangular momentum transportdirect collapseGW231123
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The pith

Slowly rotating massive Pop III stars can collapse directly into 80-85 solar mass black holes with spins up to 0.7.

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

The paper computes stellar evolution models for 80, 85, and 90 solar mass Population III stars that begin with zero or slow rotation. These models incorporate rotationally induced mixing and magnetic torques to track how angular momentum is redistributed inside the star. The resulting carbon-oxygen cores stay stable against pair creation, allowing the stars to retain nearly all their mass and angular momentum until they collapse. A sympathetic reader would care because the outcome supplies a single-star route to the very massive, rapidly spinning black holes seen in some gravitational-wave events, without requiring binary interactions or exotic initial conditions.

Core claim

Our non-rotating and slowly rotating 80 and 85 M⊙ models develop carbon-oxygen core masses between 31 and 36 M⊙ and have an adiabatic index that remains above 4/3. Our models thus predict that Pop III stars can keep most of their mass and collapse directly to form black holes of 80 to 85 M⊙ with dimensionless spins up to a_BH ≲ 0.7. Initially slowly rotating, massive Pop III stars can form very massive, rapidly spinning black holes just below the pair-instability regime.

What carries the argument

Direct-collapse assumption applied to the final angular-momentum profiles of GENEC models that include magnetic-torque transport, used to convert core mass and specific angular momentum into black-hole mass and dimensionless spin.

If this is right

  • Black holes of 80-85 solar masses with spins up to 0.7 form from single, slowly rotating Pop III stars.
  • The lower edge of the pair-instability mass gap acts as a smooth, structure-dependent transition rather than an abrupt cutoff.
  • Single-star Pop III evolution supplies one channel for the massive, fast-spinning black holes detected by gravitational-wave observatories.
  • The 90 solar mass models are more likely to encounter pair-instability effects, narrowing the viable mass window for this channel.

Where Pith is reading between the lines

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

  • If the channel operates, the observed spin distribution of high-mass black holes should show a tail toward moderate spins even in low-metallicity environments without binary spin-up.
  • Rates of such events at high redshift could be estimated from the initial mass function of Pop III stars once the uncertain mass-loss and torque efficiencies are bracketed by observations.
  • The same modeling framework could be reapplied to slightly higher metallicities to test how quickly the channel shuts off as metallicity rises.

Load-bearing premise

The stars lose negligible mass and the magnetic torques transport angular momentum at exactly the efficiency assumed in the GENEC code.

What would settle it

A direct measurement or simulation showing that an 80-85 solar mass Pop III star loses more than a few solar masses before core collapse or that its CO core adiabatic index drops below 4/3.

Figures

Figures reproduced from arXiv: 2606.04428 by A. Griffiths, G. Meynet, M. \'A. Aloy, N. H. Ismail, N. Yusof, R. Hirschi, S. Ekstr\"om.

Figure 1
Figure 1. Figure 1: Kippenhahn diagram of the 80 M⊙ model with an initial rotation set to 5% of the critical velocity. The black lines denote radius contours at 0.1, 0.3, 1, 10, and 50 R⊙; the orange line marks the total mass of the star, constant for this model. Light-blue shaded regions correspond to convective zones. The coloured lines show the locations of the peak (solid lines) and of 10% of the peak (dotted lines) in th… view at source ↗
read the original abstract

The origin of massive black holes in the early universe remains uncertain and still unexplored. Pop III stars are among the first stellar sources capable of producing such remnants, but their evolution is very sensitive to rotation. We explore how slow initial rotation influences the evolution and black hole formation of very massive Pop III stars, and assess their potential to become massive, fast-spinning black holes consistent with GW events such as GW231123. We compute a grid of non-rotating and slowly rotating Pop III stellar models with initial masses of 80, 85, and 90 $M_\odot$ using the GENEC code. Our models include rotationally induced mixing and angular-momentum transport by magnetic torques. We analyse the CO core masses and their volume-averaged adiabatic index to assess stability against electron-positron pair creation. From the angular-momentum profiles at the end of He burning, we estimate the resulting black hole masses and dimensionless spins under the assumption of direct collapse. Our non-rotating and slowly rotating 80 and 85 $M_\odot$ models develop carbon-oxygen core masses between 31 and 36 $M_\odot$ and have an adiabatic index that remains above 4/3. Our models thus predict that Pop III stars can keep most of their mass and collapse directly to form black holes of 80 to 85 $M_\odot$ with dimensionless spins up to $a_{\rm BH} \lesssim 0.7$. Initially slowly rotating, massive Pop III stars can form very massive, rapidly spinning black holes just below the pair-instability regime. This supports interpreting the lower boundary of the PISN mass gap as a smooth, structure-dependent transition and identifies single-star Pop III evolution as a possible channel for massive fast-spinning black holes observed by gravitational-wave detectors, subject to the uncertain efficiency of internal angular-momentum transport and mass-loss prescriptions.

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 computes a grid of non-rotating and slowly rotating Pop III stellar models (initial masses 80, 85, 90 M⊙) with the GENEC code, including rotationally induced mixing and magnetic-torque angular-momentum transport. It reports that the 80 and 85 M⊙ models develop CO cores of 31–36 M⊙ with volume-averaged adiabatic index >4/3, avoid pair instability, and, under the assumption of direct collapse with no mass loss, produce black holes of 80–85 M⊙ with dimensionless spins a_BH ≲ 0.7. The work argues that this single-star channel can explain massive, rapidly spinning black holes such as those inferred for GW231123 and implies a smooth lower edge to the pair-instability mass gap.

Significance. If the numerical results are robust, the paper supplies a concrete, single-star pathway for high-mass, moderate-spin black holes from the first stellar generation, directly relevant to LIGO/Virgo events and to the interpretation of the pair-instability gap. The explicit use of GENEC models with magnetic torques and the adiabatic-index stability check are positive technical features; the conclusions remain conditional on the adopted transport efficiency and collapse assumption.

major comments (2)
  1. [Abstract] Abstract and § on angular-momentum transport: the reported upper bound a_BH ≲ 0.7 is obtained from the CO-core angular-momentum profile at the end of core helium burning under the default GENEC magnetic-torque prescription. The abstract itself states that this efficiency is uncertain, yet no additional models with stronger or weaker torques are presented; altering the torque strength would change the retained core angular momentum and therefore the derived spin, making the quoted limit dependent on an unvaried parameter.
  2. [Black-hole formation] Section on black-hole formation and direct collapse: the mapping from final stellar mass to black-hole mass assumes negligible mass loss and direct collapse for the 80–85 M⊙ models. While the reported CO-core masses (31–36 M⊙) lie below the nominal pair-instability regime, the paper does not quantify the sensitivity of the final black-hole mass or spin to even modest wind or eruptive mass loss near the pair-instability boundary.
minor comments (2)
  1. [Methods] The manuscript states that spins are estimated from angular-momentum profiles but does not provide the explicit formula or the assumed moment-of-inertia factor used to convert specific angular momentum to dimensionless spin a_BH.
  2. [Results] No error bars or ranges are attached to the quoted CO-core masses, adiabatic indices, or spin values, even though the models are described as a grid.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below, indicating planned revisions where appropriate. Our responses focus on clarifying the scope of the presented models while acknowledging the limitations noted.

read point-by-point responses

  1. Referee: [Abstract] Abstract and § on angular-momentum transport: the reported upper bound a_BH ≲ 0.7 is obtained from the CO-core angular-momentum profile at the end of core helium burning under the default GENEC magnetic-torque prescription. The abstract itself states that this efficiency is uncertain, yet no additional models with stronger or weaker torques are presented; altering the torque strength would change the retained core angular momentum and therefore the derived spin, making the quoted limit dependent on an unvaried parameter.

    Authors: We agree that the quoted a_BH ≲ 0.7 bound is specific to the default GENEC magnetic-torque implementation and that varying the torque efficiency would alter the retained angular momentum. The abstract already flags this uncertainty, but we accept that the dependence should be made more explicit. Running a full grid with modified torque strengths is beyond the computational scope of the current study. In revision we will expand the angular-momentum transport section with a brief analytic estimate, drawing on published scalings for magnetic braking efficiency, to illustrate how stronger or weaker torques would shift the final core angular momentum and thus a_BH. This will clarify the parameter dependence without new simulations. revision: partial

  2. Referee: [Black-hole formation] Section on black-hole formation and direct collapse: the mapping from final stellar mass to black-hole mass assumes negligible mass loss and direct collapse for the 80–85 M⊙ models. While the reported CO-core masses (31–36 M⊙) lie below the nominal pair-instability regime, the paper does not quantify the sensitivity of the final black-hole mass or spin to even modest wind or eruptive mass loss near the pair-instability boundary.

    Authors: The direct-collapse assumption with negligible mass loss follows from the CO-core masses lying below the pair-instability threshold and the volume-averaged adiabatic index remaining above 4/3 throughout the models. We nevertheless recognize that even modest mass loss near the boundary could reduce the final black-hole mass. In the revised manuscript we will add a short quantitative discussion in the black-hole formation section, considering illustrative cases of 5–10 % mass loss (consistent with the upper limits from our stability analysis) and noting the consequent shift in black-hole mass while preserving the spin estimate under the assumption that any lost material carries negligible specific angular momentum. This will address the requested sensitivity analysis for the fiducial models. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward stellar models under stated assumptions

full rationale

The paper computes a grid of Pop III stellar models in GENEC with explicit initial masses, slow rotation, and magnetic-torque angular-momentum transport, then extracts CO-core properties and angular-momentum profiles at the end of He burning to estimate BH mass and spin under the direct-collapse assumption. These outputs are produced by numerical integration of the stellar-structure equations; they are not obtained by fitting parameters to GW231123 data, nor do any equations reduce the final a_BH ≲ 0.7 result to a tautological re-expression of the inputs. The abstract itself flags the torque efficiency as uncertain, confirming the result is conditional on model physics rather than self-defined. No self-citation chains, ansatzes smuggled via prior work, or renaming of known results appear as load-bearing steps.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The claim rests on standard stellar-evolution assumptions plus two domain-specific modeling choices whose uncertainties are explicitly flagged by the authors.

free parameters (2)
  • initial rotation velocity
    Slow rotation is adopted but the precise value is not quantified in the abstract.
  • mass-loss efficiency
    Uncertain mass-loss prescriptions are invoked and noted as uncertain.
axioms (2)
  • domain assumption Direct collapse to black hole with no significant mass ejection after helium burning
    Used to convert final angular-momentum profiles into black-hole mass and spin estimates.
  • domain assumption Angular-momentum transport dominated by magnetic torques
    Implemented inside the GENEC code and required for the final spin distribution.

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discussion (0)

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Reference graph

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