{"id":"4eaf7db5-2be8-4963-af2e-e9996498f3ba","arxiv_id":"2509.10609","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Metal-poor star clusters can form GW231123-like black hole mergers, but matching its high spins requires assuming high natal spins for stellar-binary black holes.","lead":"This paper simulates star cluster populations to show that GW231123, the most massive black hole merger ever detected, could have formed in metal-poor clusters through stellar binary evolution and repeated black hole mergers. A general reader might care because it offers a plausible origin for an extreme gravitational-wave event that standard isolated binary evolution struggles to explain.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"High-spin conclusion for gap BHs is imposed by resampling in §3.2, not derived; low-spin fiducial yields negligible GW231123-like events, so the spin explanation is circular.","rationale":"The reader's weakest assumption correctly identifies the most load-bearing vulnerability: the high-spin result is constructed by resampling gap-BH spins, so the conclusion that such BHs are 'likely' high-spin is an input, not an independent prediction. I agree with this assessment. The mass-metallicity finding (Z≤0.002 producing GW231123-like masses) is supported by large simulations and is not undermined by the spin issue; the authors are also transparent in §3.2 that natal spin models for stellar-merger products are poorly constrained. However, the abstract and conclusions elevate the high-spin scenario from a sensitivity test to a model prediction ('our models suggest... likely'), which overstates what the simulations establish. The proposed test—running the same models without the Gaussian resampling and applying the LVK selection function—would quantitatively show whether the event's high spins can be explained without assuming them. Since this concern directly corroborates the reader's condition, no verdict change is needed.","tokens_in":18178,"tokens_out":7980,"duration_ms":86059,"concrete_test":"Re-run the B-POP fiducial models with the spin resampling removed entirely: draw natal spins for all BHs, including those above the upper-mass gap, from the same Maxwellian with σ=0.2. Then apply the LVK detection selection function and compute the expected rate of GW231123-like events (both masses and spins within the 90% C.I.). If the rate is below ~10^-6 yr^-1 Gpc^-3, the paper's explanation of the event's high spins is entirely driven by the ad hoc high-spin injection, and the 'likely high-spin' conclusion should be reframed as an assumption rather than a prediction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central spin claim—that BHs formed in stellar binaries are 'likely characterized by high-spins'—is not derived from the simulations but is imposed in §3.2. There, natal spins of gap BHs are resampled from Gaussians centered at χ_med=0.5 or 0.9 (σ=0.2) for BSE events, and the resulting increase in GW231123-like counts (Table 1: from 10→435→2250 for YCs at Z=0.002) is presented as evidence that high natal spins are necessary. This is circular: the observation that high spins are required to match the event merely restates the input. The fiducial low-spin Maxwellian (σ=0.2) yields f_mer,χ≈3×10^-6–2×10^-4, i.e., essentially no spin-compatible analogs. Moreover, the hierarchical channel in NCs—offered as an alternative explanation—cannot independently supply the observed high spins: B-pop tracks only the primary BH through chains, while secondaries are assumed to be first-generation low-spin BHs, so the secondary component of an MC event retains a low natal spin; the ~0.7 spin from merger remnants applies only to the primary. Thus both proposed channels rely on the same unconstrained high-spin assumption to satisfy the χ_2 constraint. If the true natal spin distribution of upper-mass-gap BHs is closer to the low-spin Maxwellian, the stellar-binary channel fails and the hierarchical channel provides, at best, a marginal explanation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":18650,"tokens_out":5457,"duration_ms":63783,"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":[{"comment":"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","section":"§3.2, Table 1, Abstract, §4"},{"comment":"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","section":"§2 (Methods), §3.2, Fig. 2"},{"comment":"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.","section":"§3.3, Eq. (2), Eqs. (3)-(4), Table 1"}],"minor_comments":[{"comment":"Typo: 'consensous' should be 'consensus'.","section":"§3.3"},{"comment":"The author listing and affiliations formatting contains a typo: 'La viniaPaiella' should be 'Lavinia Paiella'.","section":"Title page"},{"comment":"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).","section":"References"},{"comment":"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.","section":"§2, Software"},{"comment":"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.","section":"Eq. (3)"}],"recommendation":"major_revision","confidential_remarks":"The mass and metallicity results are solid and the paper is well suited to ApJL in principle. My main concern is that the abstract and conclusions present the high-spin requirement as a model output when it is actually an input assumption. The rate estimate also omits the spin selection, which materially affects the claimed consistency with LVK. Both issues are fixable with rewriting and additional analysis, so I do not recommend rejection, but the paper needs a substantial revision before the central claims can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a serious, competent application of the established B-POP framework to GW231123. The genuinely new part is the event-specific grid: three metallicities, three cluster types, 5e7 BBHs each, with the mass and spin credible intervals of the event applied, plus delay-time distributions and made-to-measure rate estimates. The metallicity result—Z <= 0.002 required, Z = 0.002 optimal—is plausible and supported by the simulations. The appendix's check that the result is sensitive to the PISN gap edge and to shifts in the mass interval is honest and useful.\n\nThe soft spot is the spin part, and it is central to the abstract. In Sec. 3.2 the authors resample natal spins of gap BHs from Gaussians centered at chi_med = 0.5 or 0.9, then count how many events fall into the GW231123 spin interval. Unsurprisingly, high spins boost the count by two to three orders of magnitude. The paper is candid that this is a sampling procedure and that natal spins are poorly constrained, so on a careful reading it is a sensitivity test. But the abstract and one of the bullet conclusions go further: 'our models suggest that BHs from stellar binaries are likely characterized by high-spins.' That is not something the model can say. The high-spin input is doing the work, not the stellar binary physics. The stress-test gets this right: if the true natal spins of gap BHs are well described by the low-spin Maxwellian, essentially no spin-compatible analogs are produced. So the spin-matching result is partly circular, and the claim should be reframed as a condition for the model to match the event, not a prediction about natal spins.\n\nThe other limitation is also noted in the paper: B-pop follows only the primary along hierarchical chains, and secondaries are assumed to be first-generation low-spin BHs. That means the hierarchical channel cannot explain the secondary's high spin without the same unconstrained natal-spin assumption. The paper deserves credit for stating this caveat, but it weakens the claimed alternative for nuclear clusters.\n\nRates are back-of-envelope with many free parameters and are presented as upper limits; that is fine for a proof-of-concept. Code and catalogs are not yet public, though the authors say they will release them on acceptance. Citation pattern looks fine.\n\nVerdict: this deserves peer review. A referee should ask for the spin language to be softened and predictions separated from input assumptions, but the mass-based scenario is worth airing. I'd bring it to a reading group for the discussion of how easy it is to talk yourself into a spin result, and I'd cite it at least for the metallicity and delay-time parts.","headline":"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.","tokens_in":19058,"tokens_out":2456,"would_cite":true,"duration_ms":26018,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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","keywords":["gravitational waves","binary black holes","GW231123","star clusters","hierarchical mergers","upper mass gap","natal spins","population synthesis"],"falsifier":"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.","tokens_in":18093,"feed_emoji":"🕳️","tokens_out":4572,"duration_ms":48368,"temperature":0.7,"pith_summary":"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.","feed_headline":"Star clusters can assemble the heaviest black hole merger","feed_subtitle":"Simulations match GW231123's huge masses and high spins, placing its birth in metal-poor clusters at rates LIGO-Virgo-KAGRA can see.","key_machinery":"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.","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["GW231123's heavy black holes born in star clusters","Metal-poor star clusters explain extreme BBH spins","Two cluster channels assemble the heaviest BBH","Hierarchical mergers and binary evolution spawn GW231123"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["GW231123's heavy black holes born in star clusters","Metal-poor star clusters explain extreme BBH spins","Two cluster channels assemble the heaviest BBH","Hierarchical mergers and binary evolution spawn GW231123"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000213,"raw_usage":{"total_tokens":1360,"prompt_tokens":945,"completion_tokens":415,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":689,"completion_tokens_details":{"reasoning_tokens":352}},"tokens_in":689,"tokens_out":415,"duration_ms":5427,"temperature":1.0,"reasoning_tokens":352,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T17:44:54.162560+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}