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Assembling GW231123 in star clusters through the combination of stellar binary evolution and hierarchical mergers

T0 review · 3 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read The paper argues that GW231123, the most massive and highly spinning binary black hole merger detected, can be assembled in metal-poor star clusters through a combination of stellar-binary evolution that produces black holes in the upper ma

desk verdict A competent B-POP application to GW231123, but the abstract's high-spin claim overstates what is really a sensitivity test with the high spins put in by hand. read the letter →

arxiv 2509.10609 v1 pith:L5DYS4D7 submitted 2025-09-12 astro-ph.GA astro-ph.HE

Lavinia Paiella , Cristiano Ugolini , Mario Spera , Marica Branchesi , Manuel Arca Sedda This is my paper
classification astro-ph.GAastro-ph.HE
keywords gravitationalwavesbinaryblackholesGW231123starclustershierarchicalmergersuppermassgapnatalspinspopulationsynthesis
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

GW231123 is the heaviest binary black hole merger LIGO-Virgo-KAGRA has seen, with both components in the upper mass gap and spins above 0.8, properties that standard isolated binary evolution cannot easily produce. This paper proposes that the event was assembled dynamically in star clusters: in young and globular clusters, black holes born in primordial stellar binaries and boosted into the gap by stellar mergers and collisions provide the mass, while in nuclear clusters repeated hierarchical mergers also contribute. Using the B-POP population synthesis code, they show that only low-metallicity clusters (Z ≤ 0.002) can form such systems, and that matching the high spins requires the natal spins of gap black holes to be large. If true, GW231123-like events should be found in metal-poor dwarf galaxies or globular clusters at low redshift, at rates consistent with current gravitational-wave observations.

What carries the argument

The B-POP semi-analytic population synthesis code, which couples black hole natal masses from stellar evolution catalogs (SEVN) with a model of cluster dynamics: three-body and binary–single scatterings harden binaries until they merge or are ejected, and relativistic kicks decide whether merger remnants are retained for further hierarchical mergers. The central mechanism is the splitting of the simulated mergers into BSE (stellar-binary products with a gap black hole), H (hybrid, combining gap black holes with hierarchical growth), and MC (merger chains of only sub-gap black holes) categories, which lets the authors attribute GW231123-like events to environment-dependent channels.

What would settle it

If stellar evolution simulations of binary stellar mergers and collapse show that the resulting black holes typically have low spin (χ < 0.5), the BSE channel proposed for young and globular clusters would be ruled out for GW231123-like events. Alternatively, a future LIGO-Virgo-KAGRA detection of a GW231123-mass binary with both component spins below ~0.3 would contradict the high-spin requirement of the BSE channel and point instead to low-spin hierarchical chains or an unknown formation path.

Watch

Extended reading notes

Core claim

The paper's central claim is that the extreme properties of GW231123 – two black holes of roughly 137 and 103 solar masses with spins around 0.8–0.9 – can be produced in star clusters, rather than by isolated binary evolution. In their simulations, the mass is supplied either by black holes that form in the upper mass gap through stellar mergers and collisions inside primordial binaries (the BSE channel) or, in nuclear clusters with high escape velocities, by chains of repeated mergers (hierarchical mergers). The crucial ingredient is the natal spin of the gap black holes: adopting a low-spin Maxwellian yields almost no spin-compatible analogs, whereas resampling those spins from a Gaussian

Load-bearing premise

The load-bearing assumption is that black holes formed in the upper mass gap through stellar mergers in binaries are born with high spins (resampled to medians of 0.5–0.9); if their true natal spins are low (as in the Maxwellian with σ=0.2), the stellar-binary channel in young and globular clusters can no longer match GW231123's spin, and only nuclear-cluster hierarchical chains remain.

Editorial extensions

If this is right

  • GW231123-like mergers should be confined to metal-poor environments (Z ≤ 0.002); solar-metallicity clusters produce none, so searches for similar events can be targeted at metal-poor dwarf galaxies and globular clusters.
  • If gap black holes from stellar binaries are born with high spins, the number of GW231123-like mergers increases by two to three orders of magnitude, making the BSE channel viable in young and globular clusters.
  • In nuclear clusters, hierarchical merger chains can provide an alternative route to GW231123-like masses even without high-spin stellar-binary products, with some primaries undergoing 10–12 mergers.
  • Simulated GW231123-like systems have short delay times (0.1–1 Gyr), so their progenitor clusters likely formed near the inferred merger redshift, z ≈ 0.39, in dwarf galaxies or Milky-Way-like hosts.
  • The estimated local merger rates for globular clusters in Milky-Way-like galaxies (up to ~0.72 yr^-1 Gpc^-3) are broadly consistent with the LIGO-Virgo-KAGRA-inferred rate for all binary black holes.

Reading between the lines

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

  • The paper's inference that gap black holes are 'likely high-spin' is partly an input assumption: the high-spin model is a resampling of natal spins, not a prediction from stellar evolution physics. If future models show that stellar merger products collapse with low spins, the young/globular-cluster BSE channel would essentially vanish, leaving only nuclear-cluster merger chains.
  • A testable discriminator is the spin distribution of future events: if GW231123-like masses are accompanied by low measured spins, that would favour the MC/hierarchical channel in nuclear clusters over the BSE channel.
  • The rate estimates are upper limits; the true rates depend on the unknown fraction of metal-poor clusters and on the possibility of a top-heavy IMF, which would increase the number of binary stars contributing.
  • The paper notes that eccentric waveforms could change the inferred spins of GW231123, so the spin-based conclusions are tied to the quasi-circular assumption in the event's parameter estimation.
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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 uses the B-POP semi-analytic cluster population synthesis code to investigate the formation of BBH mergers similar to GW231123 in young, globular, and nuclear star clusters at metallicities Z = 0.02, 0.002, and 0.0002. With a primordial binary fraction f_bin = 0.6, the authors simulate 5e7 BBHs per environment/metallicity combination and classify GW231123-like events according to their masses and, in a second step, their spins. They find that mass-compatible events only occur at Z <= 0.002, that stellar-binary products dominate in young and globular clusters while hierarchical merger chains contribute in nuclear clusters, and that high natal spins of upper-mass-gap BHs formed in stellar binaries boost the number of spin-compatible analogs. They also estimate short delay times and derive upper-limit local merger rates for dwarf and Milky Way-like host scenarios, concluding that a dynamical origin for GW231123 is plausible.

Significance. If the central claim holds, the paper provides a concrete, computationally extensive pathway to explain the most massive detected BBH merger within the cluster dynamics framework, combining stellar binary evolution and hierarchical mergers. The mass and metallicity findings—especially the absence of GW231123-like masses at solar metallicity and the dominant role of stellar binaries in producing upper-mass-gap BHs—are internally consistent and valuable. The delay-time analysis and rate estimates are also useful as proof-of-concept upper limits. However, the spin part of the abstract and conclusions is not derived from the simulations: high natal spins are injected as an input in §3.2 and then counted as an output. This weakens the paper's main qualitative claim, although the sensitivity of the results to the natal spin prescription is a legitimate and clearly presented exercise.

major comments (3)
  1. [§3.2, Table 1, Abstract, §4] The claim that 'BHs from stellar binaries are likely characterized by high-spins' is circular as presented. In §3.2, the spins of upper-mass-gap BHs from BSE events are resampled from Gaussians centered at chi_med = 0.5 or 0.9 with sigma = 0.2, and Table 1 then shows that the number of GW231123-like events increases from 10 to 435 to 2250 for YCs at Z = 0.002. This demonstrates sensitivity to an input assumption, not that high natal spins are a prediction of the model. The low-spin Maxwellian model yields f_mer,chi = 3e-6 for the same case, i.e., essentially no analogs; the paper itself admits that 'natal BH spins are still poorly constrained' and that 'a solid theoretical framework to model this quantity is still missing.' The abstract and conclusion should be rephrased as a conditional statement: if upper-mass-gap BHs from stellar binaries have high natal spins, the BSE channel can exp
  2. [§2 (Methods), §3.2, Fig. 2] The hierarchical merger channel cannot independently supply the high secondary spin inferred for GW231123. The paper states that B-POP 'follows only primary BHs along the chain, assuming that any secondary BH is a first generation BH' (Methods). Thus the secondary in an MC or H event retains a low natal spin drawn from the Maxwellian with sigma = 0.2, while the ~0.7 spin from merger remnants applies only to the primary. The claim that nuclear clusters have 'a significant contribution from BHs built-up via hierarchical mergers' to GW231123-like events is therefore only valid for the primary component; the secondary high spin (chi_2 ~ 0.8 median) is not produced by the chain but must already be present among first-generation BHs, which is precisely the unconstrained low-spin/high-spin dichotomy. The authors should quantify how many of the spin-compatible MC events actually have a secondary
  3. [§3.3, Eq. (2), Eqs. (3)-(4), Table 1] The merger-rate estimates use the mass-only fraction f_mer, not the spin-compatible fraction f_mer,chi. For example, for YCs at Z = 0.002, f_mer = 1e-3 but f_mer,chi = 3e-6 in the low-spin model—a factor of ~300. The subsequent statement that the rates are 'broadly consistent with the LVK-inferred rate' therefore holds only if one adopts the high-spin resampling or if the quoted rates are understood strictly as upper limits with spins ignored. Since the abstract reports these rates without this caveat, the comparison to R_LVK is misleading. The authors should either recompute the rates using the spin-compatible fractions (possibly for each spin prescription) or explicitly state that the rates are mass-only upper limits and refrain from comparing them to the LVK event rate without that qualification.
minor comments (5)
  1. [§3.3] Typo: 'consensous' should be 'consensus'.
  2. [Title page] The author listing and affiliations formatting contains a typo: 'La viniaPaiella' should be 'Lavinia Paiella'.
  3. [References] Some references are listed with incomplete journal names or duplicated entries (e.g., Miller & Hamilton 2002 appears twice, and 'T. L. S. Collaboration et al. 2022' should be formatted consistently with the journal style).
  4. [§2, Software] The code B-POP is described as 'available under reasonable request' and catalogs are promised on Zenodo only upon publication. For reproducibility, consider releasing the catalogs and a minimal code version at submission or at least stating a clear embargo date.
  5. [Eq. (3)] The notation 'N* = 10^6 - 5x10^5 - 10^4' is ambiguous: it should clearly indicate which values correspond to NCs, GCs, and YCs, and whether these are point estimates or ranges.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the spin analysis is a parameter sensitivity study, not a circular prediction.

full rationale

The paper's central spin claim arises from testing two ad hoc natal-spin prescriptions against the observed GW231123 spin posteriors. The low-spin Maxwellian (σ=0.2) yields essentially no spin-compatible analogs, while the mid- and high-spin Gaussians produce many more. This is a standard inference that the data favor high natal spins under the model, not a derivation of high spins from the model itself. The conclusion 'BHs from stellar binaries are likely characterized by high-spins' is a constraint from the data, not a prediction that is equivalent to the input; the input is an assumed distribution, and the output is a compatibility fraction. The mass and metallicity results (Z≤0.002, BSE vs. hierarchical channels) are independent of the spin resampling and are based on stellar evolution catalogs and dynamical modeling. No load-bearing self-citation chain was found; the B-POP and SEVN citations are normal methodology references, not uniqueness theorems. While the abstract's phrasing overstates the strength of the spin conclusion, this is a modeling limitation rather than a circular step. Therefore, no circularity is present.

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

No new physical entities are introduced. The paper relies on established scenarios: stellar binary merger products, hierarchical BBH merger chains, and BH retention in cluster potentials. The main free parameters are the binary fraction, the natal spin prescriptions, and the cluster population assumptions used for rate normalization.

free parameters (6)
  • f_bin = 0.6
    Fraction of BHs formed in primordial stellar binaries, fixed for all runs based on observed massive-star binary fraction (Moe and Stefano 2017). It determines the BSE channel contribution.
  • low-spin Maxwellian dispersion = 0.2
    Natal spin dispersion for first-generation BHs in the fiducial model, taken from LVK O1-O3 population inference. This sets the baseline spin distribution.
  • mid-spin Gaussian median = 0.5
    Resampled spins of gap BHs in the mid-spin model, chosen ad hoc to test sensitivity rather than derived from stellar evolution theory.
  • high-spin Gaussian median = 0.9
    Resampled spins of gap BHs in the high-spin model. This value is close to the observed GW231123 spins, so matching the observed spin credible interval is partly by construction.
  • cluster stellar populations for rate estimate = N_* = 1e6 (NC), 5e5 (GC), 1e4 (YC)
    Assumed representative cluster stellar masses in dwarf and Milky Way-like galaxies, used to normalize the merger rate in Eq. (2).
  • cluster counts per galaxy for rate estimate = dwarf: N_clu = 1 NC, 10 GC/YC; MW-like: 200 GC, 1e3 YC
    Adopted cluster abundances from the literature to estimate local merger rates. Different choices would change the derived upper limits.
assumptions (6)
  • domain assumption PISN and PPISN suppress BH formation in the upper-mass gap, so gap BHs require stellar mergers, accretion, or hierarchical mergers.
    Used in Section 1 and Appendix A to argue that GW231123-like masses cannot come from single stellar evolution.
  • domain assumption A fraction f_bin = 0.6 of BHs form in primordial stellar binaries.
    Section 2; based on Moe and Stefano 2017 and central to the BSE channel.
  • ad hoc to paper B-POP follows only primary BHs along hierarchical merger chains; all secondaries are first-generation BHs.
    Section 2; explicitly stated and acknowledged as potentially failing in the densest clusters (Kritos et al. 2024).
  • ad hoc to paper Natal spins of BHs from stellar mergers are poorly constrained and can be resampled from Gaussians centered at 0.5 or 0.9.
    Section 3.2; the high-spin conclusion depends entirely on this assumption.
  • domain assumption Merger remnants have spins near 0.7, and higher spins produce larger relativistic kicks.
    Section 3.2; used to explain why higher spins suppress hierarchical mergers involving gap BHs.
  • domain assumption The rate estimate assumes all considered clusters are metal-poor (Z <= 0.002).
    Before Eqs. (3)-(4); acknowledged as an upper limit for young clusters, which are often metal-rich.

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Pith. "Pith review of Assembling GW231123 in star clusters through the combination of stellar binary evolution and hierarchical mergers." pith.science (2026). https://pith.science/paper/L5DYS4D7

@misc{pith2026250910609,
  author       = {Pith},
  title        = {Pith review of: Assembling GW231123 in star clusters through the combination of stellar binary evolution and hierarchical mergers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L5DYS4D7}},
  note         = {Machine review of arXiv:2509.10609}
}
abstract

GW231123 is the most massive binary black hole (BBH) merger detected to date by the LIGO-Virgo-KAGRA collaboration. With at least one black hole (BH) in the upper-mass gap and both BHs exhibiting high spins ($\chi_{1,2} \gtrsim 0.8$), this event challenges standard isolated binary evolution models. A compelling alternative is a dynamical origin in star clusters, where stellar binaries and hierarchical mergers may both contribute to the formation of similar BBHs. In this work, we investigate the formation of GW231123-like events in different cluster environments using the B-POP semi-analytic population synthesis code. We find that low-metallicity environments ($Z \lesssim 0.002$) are ideal for producing BBH mergers similar to GW231123. In young and globular clusters, these BBHs have components formed in stellar binaries, whilst in nuclear clusters there is also a significant contribution from BHs built-up via hierarchical mergers. Natal spins of BHs formed in stellar binaries are crucial to find GW231123 analogs. In particular, our models suggest that BHs from stellar binaries are likely characterized by high-spins. Simulated GW231123-like systems exhibit short delay times, $t_\mathrm{del} \sim 0.1 - 1$ Gyr, which suggests their progenitors formed close to the inferred merger redshift ($z = 0.39^{+0.27}_{-0.24}$). We argue that star clusters in metal-poor dwarf galaxies or Milky Way-like galaxies are ideal nurseries, inferring an upper limit to the local merger rate of $\mathcal{R} \sim 1.6\times10^{-3} - 0.16$ yr$^{-1}$ Gpc$^{-3}$ for nuclear clusters, $\sim 0.036 - 0.72$ yr$^{-1}$ Gpc$^{-3}$ for globular clusters, and $4\times10^{-4}-0.041$ yr$^{-1}$ Gpc$^{-3}$ for young clusters.

Figures

Figures reproduced from arXiv: 2509.10609 by the authors.

Figure 1
Figure 1. BBH populations for different metallicities(Z = 0.02 on the left column, Z = 0.002 on the central column, and Z = 0.0002 on the right column) and cluster environments, namely YCs (upper row), GCs (central row), and NCs (bottom row). The bins are normalized over the number of BBHs with brighter (darker) colors corresponding to more (less) BBHs. GW231123 primary and secondary masses are indicated with a red cross. The… view at source ↗
Figure 2
Figure 2. Distribution of primary BHs generations for simulated BBH mergers with component masses in 90 % C.I. of GW231123. We distinguish between models with a metallicity Z = 0.002 (filled steps) or Z = 0.0002 (open steps), and among YCs (blue steps), GCs (purple steps), and NCs (orange steps). 3.2. The fundamental impact of spins In the previous section, we restricted the analysis to BBH mergers with component masses compa… view at source ↗
Figure 3
Figure 3. Masses and effective spin distributions for YCs, GCs and NCs in our fiducial simulation. The metallicity is set to Z = 0.002. The contour lines refer to the 68%, 95%, 99 % (solid lines) and 99.99 % (dotted-dashed line) contours. The 1-D distributions are normalized to 1 and displayed in log-scale. It is worth mentioning that the inference of GW231123 pa￾rameters assumes the binary orbit to be quasi-circular. How- [… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Masses and effective spin distributions for stellar BBHs in YCs in our fiducial simulation. The metallicity is set to Z = 0.002. The contour lines refer to the 68%, 95%, 99 % (solid lines) and 99.99 % (dotted-dashed line) contours. The 1-D distributions are normalized …
Figure 5
Figure 5. Figure 5: Delay times of mergers in the GW231123 masses C.I. for different cluster environments in our simulations. The filled his￾tograms refer to Z = 0.002 runs, while the empty histograms refers to Z = 0.0002 runs. In the latter case, the solid lines refer to primary BHs unde…
Figure 6
Figure 6. Figure 6: Mass spectrum of BHs produced in primordial stellar binaries for Z = 0.002 and Z = 0.0002. The black line denotes the primary mass of GW231123 while the gray band indicates the 90 % C.I.. The dashed lines show the maximum mass that a BH can attain as a product of singl…

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Forward citations

Cited by 8 Pith papers

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