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arxiv: 2604.18709 · v1 · submitted 2026-04-20 · 🌌 astro-ph.GA · astro-ph.CO· gr-qc

Recognition: unknown

Investigating the formation channel of GW231123: Population III stars or hierarchical mergers?

Federico Angeloni , Konstantinos Kritos , Raffaella Schneider , Emanuele Berti , Luca Graziani , Stefano Torniamenti , Michela Mapelli , Ataru Tanikawa
Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:50 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.COgr-qc
keywords gravitational wavesblack hole mergershierarchical mergersglobular clusterspair-instability gapGW231123binary population synthesis
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The pith

GW231123 formed through repeated mergers of black holes inside a dense globular cluster rather than from an isolated binary or Population III stars.

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

The paper tests whether the massive black holes in GW231123, which fall inside or above the pair-instability gap, arose from single-star collapse at extremely low metallicity or from multiple mergers. Coupling a cosmological galaxy formation simulation to cluster and binary population synthesis codes shows that isolated binaries either form with orbits too wide to merge in time or require metallicities so low they contribute almost nothing to the star formation rate. In contrast, successive mergers inside globular clusters readily produce the observed masses and high spins while matching the event's redshift distribution. This result implies that similar high-mass events trace the formation history of early, dense star clusters rather than exotic single-star pathways.

Core claim

Although both binary population synthesis codes can generate black holes with masses compatible with GW231123, isolated evolution fails to reproduce the inferred merger redshift: SEVN produces binaries with semi-major axes larger than 1000 solar radii, and BSEEMP requires metallicities of 10 to the minus 10 that are negligible in the simulated volume. The observed properties instead arise naturally from dynamical, hierarchical mergers in dense globular clusters, yielding a local merger rate density of 0.78 Gpc^{-3} yr^{-1} that peaks at redshifts 4 to 6, coinciding with the maximum formation rate of metal-poor clusters.

What carries the argument

The coupled framework of the GAMESH cosmological simulation with the RAPSTER cluster synthesis code and the SEVN and BSEEMP binary evolution codes, which tracks the full life cycle of candidate events from formation through merger within the same simulated volume.

If this is right

  • Isolated binary channels are excluded for this event because the required orbital separations or metallicities are incompatible with the observed merger time and rate density.
  • Hierarchical mergers inside globular clusters simultaneously explain the component masses, the high dimensionless spins, and the peak formation epoch at z equals 4 to 6.
  • The predicted local rate of 0.78 Gpc^{-3} yr^{-1} provides a benchmark for the contribution of early-universe cluster mergers to the overall black-hole merger population.
  • GW231123 can serve as a template for identifying further members of a hierarchical population whose redshift distribution follows the formation history of metal-poor globular clusters.

Where Pith is reading between the lines

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

  • If cluster mergers dominate the high-mass end, the redshift distribution of future events should show a clear peak between z=4 and 6 that can be tested with next-generation detectors.
  • The same modeling framework could be used to predict the fraction of events that retain measurable spin signatures from prior mergers, offering a direct observational test of the hierarchical channel.

Load-bearing premise

The specific prescriptions for binary evolution, common-envelope efficiency, and cluster dynamics in the chosen codes accurately capture the relevant physics at the metallicities and densities of the early universe.

What would settle it

Detection of a GW231123-like event at a redshift well below 4 or well above 6, or discovery that isolated binaries at moderate metallicities routinely merge within a Hubble time, would undermine the hierarchical cluster channel.

Figures

Figures reproduced from arXiv: 2604.18709 by Ataru Tanikawa, Emanuele Berti, Federico Angeloni, Konstantinos Kritos, Luca Graziani, Michela Mapelli, Raffaella Schneider, Stefano Torniamenti.

Figure 1
Figure 1. Figure 1: (a) Cosmological evolution of the total star formation rate density (black line), the Pop III star formation rate density (green [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) BBH number density as a function of hierarchical merger generation for the primary (red) and secondary (blue) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

The gravitational wave event GW231123, with component black hole masses lying within or above the pair-instability mass gap, poses a significant challenge to current stellar evolution models. In this Letter, we investigate its origin by coupling the galaxy formation model GAMESH with the cluster population synthesis code RAPSTER, and with two distinct binary population synthesis codes (SEVN and BSEEMP). This framework allows us, for the first time, to reconstruct the life cycle of GW231123-like candidates within the same cosmological simulation, enabling a self-consistent comparison between different formation channels. We find that, although both population synthesis codes can in principle produce black holes compatible with GW231123, isolated binary evolution fails to reproduce the inferred merger redshift. In SEVN, massive black hole binaries form with semi-major axes > 10^3 Rsun , preventing coalescences within a Hubble time. In BSEEMP, candidates arise only at extremely low metallicities (Z = 10^{-10}), which contribute negligibly to the star formation rate density in our overdense simulated volume. Our results instead strongly support a dynamical, hierarchical origin. The observed black hole masses are naturally reproduced through successive mergers in dense globular clusters. The high dimensionless spins reported by the LIGO-Virgo-KAGRA Collaboration are consistent with this hierarchical population. We find a local merger rate density of 0.78 Gpc^{-3} yr^{-1}, with a peak at z = 4 - 6, tracing the maximum formation rate of globular clusters in metal-poor environments (Z = 0.006). Overall, GW231123 may represent a benchmark event for a robust population of hierarchical black holes formed in the early Universe.

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 couples the GAMESH galaxy formation model with RAPSTER cluster synthesis and two binary population synthesis codes (SEVN and BSEEMP) to compare formation channels for GW231123. It reports that isolated binary evolution cannot reproduce the inferred merger redshift—SEVN yields semi-major axes >10^3 R_sun while BSEEMP requires Z=10^{-10} with negligible contribution—whereas hierarchical mergers in dense globular clusters naturally produce the observed masses and high spins. The work predicts a local merger rate density of 0.78 Gpc^{-3} yr^{-1} peaking at z=4-6, tracing metal-poor globular cluster formation.

Significance. If the central claims hold, the self-consistent cosmological embedding of multiple channels within one simulation volume is a clear strength, enabling direct apples-to-apples comparison of isolated versus dynamical pathways without ad-hoc normalization. The redshift peak and rate offer falsifiable predictions for the high-mass end of the GW population. The framework also highlights how cluster dynamics can populate the pair-instability gap via successive mergers.

major comments (2)
  1. [Section 3 (binary population synthesis setup) and Section 4 (channel comparison)] The exclusion of the isolated channel rests on fixed prescriptions in SEVN (a > 10^3 R_sun) and BSEEMP (Z = 10^{-10} only). No systematic variation of common-envelope efficiency, supernova kicks, or wind mass loss is reported, even though these parameters directly control final separations and merger timescales. Because this is the load-bearing step for ruling out isolated binaries, the conclusion is not shown to be robust.
  2. [Section 5 (rate and redshift results)] The local rate 0.78 Gpc^{-3} yr^{-1} and z = 4-6 peak are direct outputs of the simulated overdense volume and GAMESH star-formation history. It is unclear whether the normalization accounts for the full cosmic variance or selection effects when comparing to the single observed event GW231123; a broader population-level consistency check would strengthen the claim.
minor comments (2)
  1. [Abstract and Introduction] The title references Population III stars, yet the text emphasizes Z = 10^{-10} without explicitly labeling these as Pop III or showing their distinct IMF/formation physics; a short clarification would avoid confusion.
  2. [Throughout] Notation for semi-major axis (a) and metallicity (Z) is used without a dedicated table of symbols; adding one would improve readability for readers outside the subfield.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments on our manuscript. We address each major comment point by point below, providing our responses and indicating where revisions will be made to strengthen the paper.

read point-by-point responses

  1. Referee: [Section 3 (binary population synthesis setup) and Section 4 (channel comparison)] The exclusion of the isolated channel rests on fixed prescriptions in SEVN (a > 10^3 R_sun) and BSEEMP (Z = 10^{-10} only). No systematic variation of common-envelope efficiency, supernova kicks, or wind mass loss is reported, even though these parameters directly control final separations and merger timescales. Because this is the load-bearing step for ruling out isolated binaries, the conclusion is not shown to be robust.

    Authors: We acknowledge that our conclusions regarding the isolated binary channel rely on the default parameter sets of SEVN and BSEEMP without a comprehensive parameter study. These settings are standard in the literature, and the qualitative failure of isolated evolution to produce mergers at the observed redshift is reproduced independently by both codes despite their differing treatments of binary physics. To address the concern directly, we will revise Section 4 to include a targeted discussion of parameter sensitivity, referencing ranges for common-envelope efficiency, supernova kicks, and wind mass loss from prior studies. We will show that even under optimistic assumptions, the semi-major axes in SEVN remain too large for Hubble-time mergers and the metallicity threshold in BSEEMP stays extreme relative to our simulated star-formation history. A full grid of new simulations is beyond the scope of this Letter, but the added discussion will clarify the robustness limits. revision: partial

  2. Referee: [Section 5 (rate and redshift results)] The local rate 0.78 Gpc^{-3} yr^{-1} and z = 4-6 peak are direct outputs of the simulated overdense volume and GAMESH star-formation history. It is unclear whether the normalization accounts for the full cosmic variance or selection effects when comparing to the single observed event GW231123; a broader population-level consistency check would strengthen the claim.

    Authors: The reported local rate and redshift peak are self-consistently derived from the GAMESH simulation volume and its embedded star-formation and globular-cluster formation history, without external normalization between channels. The volume represents an overdense region where metal-poor cluster formation is enhanced, and the z = 4-6 peak directly follows the simulated cluster formation rate at Z = 0.006. For the single event GW231123, the comparison is intended to demonstrate channel viability rather than statistical population inference. We will revise Section 5 to add a brief comparison of our predicted rate to existing LIGO-Virgo-KAGRA constraints on the high-mass merger rate, along with a short discussion of cosmic variance and selection effects for individual events. This provides the broader consistency check requested while remaining within the Letter format. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper's central results follow from running the coupled GAMESH+RAPSTER framework with the standard SEVN and BSEEMP binary evolution prescriptions to generate populations of black hole mergers and compare channels against the observed properties of GW231123. The reported local rate density of 0.78 Gpc^{-3} yr^{-1} and redshift peak at z=4-6 are direct numerical outputs of the simulated volume and globular cluster formation history at Z=0.006, not parameters fitted to the single event or redefined by construction. No load-bearing step reduces to a self-citation chain, an ansatz smuggled via prior work, or a uniqueness theorem imported from the same authors; the comparison between isolated and hierarchical channels is performed within one self-consistent cosmological setup using externally developed codes whose internal prescriptions are treated as fixed inputs rather than derived outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the accuracy of the stellar evolution and cluster dynamics prescriptions inside the named codes; these are treated as black boxes whose outputs are compared to the single observed event.

free parameters (2)
  • local merger rate density
    Value 0.78 Gpc^{-3} yr^{-1} is reported as an output but depends on the normalization of the simulated overdense volume and the assumed globular cluster formation efficiency.
  • metallicity thresholds
    Z = 10^{-10} for BSEEMP candidates and Z = 0.006 for the rate peak are chosen thresholds that determine which environments contribute.
axioms (2)
  • domain assumption The pair-instability mass gap prevents single-star formation of black holes in the observed mass range
    Invoked in the first sentence of the abstract as the reason the event challenges stellar models.
  • domain assumption The simulated overdense volume is representative for estimating cosmic rates
    Used to convert the simulated count into the quoted 0.78 Gpc^{-3} yr^{-1} rate.

pith-pipeline@v0.9.0 · 5645 in / 1350 out tokens · 37107 ms · 2026-05-10T03:50:46.712755+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.

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Reference graph

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