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How do the LIGO-Virgo-KAGRA's Heavy Black Holes Form? No evidence for core-collapse Intermediate-mass black holes in GWTC-4

T0 review · 1 major / 2 minor · reviewed 2026-05-12 · grok-4.3

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Pith's one-line read Analysis of the latest LIGO-Virgo-KAGRA catalog finds no evidence for intermediate-mass black holes formed by core collapse, instead attributing heavy black holes to hierarchical mergers.

desk verdict GWTC-4 rules out a detectable low-spin core-collapse IMBH population and gives a clean 90% rate upper limit of 0.077 Gpc^{-3} yr^{-1}, with the low-spin mass cutoff at 65 solar masses. read the letter →

arxiv 2605.05563 v2 submitted 2026-05-07 astro-ph.HE astro-ph.COastro-ph.GAastro-ph.SR

Fan-Xiao-Yu Xia , Yuan-Zhu Wang , Ying Qin This is my paper · ORCID
classification astro-ph.HEastro-ph.COastro-ph.GAastro-ph.SR
keywords intermediate-massblackholesgravitationalwavespair-instabilitymassgaphierarchicalmergersholeformationLIGO-Virgo-KAGRAGWTC-4stellarevolution
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 examines the population of binary black holes in the GWTC-4 catalog to clarify how the heaviest ones formed. It searches for a distinct group of low-spin intermediate-mass black holes that would mark direct formation through stellar core collapse. No such group appears in the data, which yields a tight upper bound on the merger rate for these objects. Low-spin black holes instead show a mass cutoff near 65 solar masses, matching the expected lower edge of the pair-instability mass gap. The heavy black holes that are seen carry high spins, which aligns with repeated mergers of smaller black holes rather than single-star collapse.

What carries the argument

Separation of black-hole populations by spin to isolate a possible low-spin core-collapse channel from a high-spin hierarchical-merger channel in the GWTC-4 mass-spin distribution.

What would settle it

Detection of one or more low-spin black holes with masses well above 65 solar masses, or an inferred merger rate for such objects exceeding 0.077 Gpc^{-3} yr^{-1}, in future expanded catalogs.

Watch

Extended reading notes

Core claim

We investigate the population properties of binary black holes from the LIGO-Virgo-KAGRA collaboration, focusing especially on those in the high-mass range, using the newly released GWTC-4 catalog. For the first time, we search for a subpopulation of low-spin intermediate-mass black holes that would indicate formation via stellar core collapse. With the currently available catalog, we find no evidence for such a subpopulation, and set a 90% upper limit on the merger rate of collapse-formed IMBHs at 0.077 Gpc^{-3} yr^{-1}. The mass distribution of low-spin stellar-origin black holes truncates at 65 solar masses, consistent with the lower edge of the pair-instability mass gap, although we do 1

Load-bearing premise

Any core-collapse intermediate-mass black holes would appear as a distinct low-spin subpopulation that can be cleanly separated from high-spin merger products without major detection biases or model degeneracies.

Editorial extensions

If this is right

  • The lower edge of the pair-instability mass gap sits near 65 solar masses, as shown by the truncation of the low-spin black-hole mass distribution.
  • Stellar-evolution models combined with the data place the upper edge of the pair-instability mass gap near 150 solar masses.
  • All currently observed intermediate-mass black holes belong to a high-spin subpopulation produced by successive mergers.
  • The merger rate of core-collapse intermediate-mass black holes is limited to less than 0.077 events per cubic gigaparsec per year.

Reading between the lines

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

  • Hierarchical mergers must operate efficiently enough to populate the observed high-mass end without a large direct-collapse contribution.
  • Future catalogs with improved spin precision or additional high-mass events could directly test whether the high-spin channel continues to dominate.
  • If the low-spin cutoff remains fixed, it would tighten constraints on the supernova physics that sets the lower boundary of the pair-instability gap.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 2 minor

Summary. The manuscript analyzes the GWTC-4 catalog to search for a low-spin subpopulation of intermediate-mass black holes (IMBHs) formed via stellar core collapse. It reports no evidence for such a subpopulation and sets a 90% upper limit on the merger rate at 0.077 Gpc^{-3} yr^{-1}. The low-spin black hole mass distribution truncates at 65^{+23}_{-22} M_odot (consistent with the lower edge of the pair-instability mass gap), while the upper edge is estimated at 150±24 M_odot from stellar evolution theory. Observed IMBHs are attributed to a high-spin subpopulation formed via hierarchical mergers.

Significance. If robust, the result supplies useful constraints on high-mass black hole formation channels by showing consistency with stellar-origin black holes below the pair-instability gap and hierarchical assembly for the observed high-mass systems. Strengths include the data-driven (rather than prior-dominated) rate upper limit, explicit spin and mass parametrizations in a standard mixture-model hierarchical inference, selection-function corrections, and posterior sampling; these elements make the no-evidence conclusion and truncation measurement falsifiable with future catalogs.

major comments (1)
  1. [Population model and inference section] The separability assumption—that any core-collapse IMBHs would appear as a distinct low-spin component cleanly separable from high-spin hierarchical products—is load-bearing for the no-evidence claim and rate limit. The manuscript uses a standard mixture model, but explicit checks for model degeneracies, selection biases, or spin-mass correlations that could mask a low-spin subpopulation (e.g., via injection-recovery tests or alternative parametrizations) would strengthen the result.
minor comments (2)
  1. [Abstract] The abstract reports the mass truncation with uncertainties but does not state the confidence level for those uncertainties (in contrast to the explicit 90% for the rate limit); this should be clarified for consistency.
  2. [Introduction and results sections] Notation for the pair-instability mass gap (PIMG) edges and the distinction between data-driven truncation and theory-informed upper edge should be defined once in the main text before repeated use.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for the constructive recommendation of minor revision. We address the single major comment below and will incorporate the suggested strengthening of the analysis in the revised version.

read point-by-point responses

  1. Referee: [Population model and inference section] The separability assumption—that any core-collapse IMBHs would appear as a distinct low-spin component cleanly separable from high-spin hierarchical products—is load-bearing for the no-evidence claim and rate limit. The manuscript uses a standard mixture model, but explicit checks for model degeneracies, selection biases, or spin-mass correlations that could mask a low-spin subpopulation (e.g., via injection-recovery tests or alternative parametrizations) would strengthen the result.

    Authors: We agree that the separability assumption is central to the no-evidence conclusion and the derived rate upper limit. Our hierarchical mixture model explicitly parametrizes two subpopulations with independent mass and spin distributions (low-spin component for potential core-collapse IMBHs and high-spin component for hierarchical products), which by construction allows the data to assign negligible weight to the low-spin IMBH subpopulation. We have examined the joint posteriors for parameter correlations and performed basic model-consistency checks. However, we did not include targeted injection-recovery tests that inject low-spin IMBH populations under the GWTC-4 selection function or explore alternative parametrizations to quantify possible masking from spin-mass correlations. We will add these explicit validation tests to the revised manuscript, reporting recovery fractions and any biases in the inferred rate and truncation mass. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity detected

full rationale

The paper performs standard hierarchical Bayesian population inference on GWTC-4 to derive a data-driven 90% upper limit on the merger rate of a hypothesized low-spin IMBH subpopulation and a mass truncation for the low-spin component. The upper edge of the pair-instability mass gap is taken from external stellar-evolution theory rather than any internal fit or self-definition. No derivation step reduces by construction to its own inputs, renames a fitted parameter as a prediction, or relies on a load-bearing self-citation chain; the modeling uses explicit parametrizations, selection corrections, and posterior sampling that remain independent of the reported conclusions.

Assumptions & free parameters 2 free parameters · 2 assumptions · 0 invented entities

The paper relies on standard domain assumptions about spin signatures for formation channels and external stellar theory for mass gap boundaries; no new entities postulated.

free parameters (2)
  • PIMG upper edge estimate = 150±24 M_sun
    Value of 150±24 M_sun derived from stellar evolution theory informed by data.
  • Merger rate upper limit = 0.077 Gpc^{-3} yr^{-1}
    90% confidence upper bound of 0.077 Gpc^{-3} yr^{-1} from statistical analysis of catalog.
assumptions (2)
  • domain assumption Low-spin IMBHs indicate core-collapse formation while high-spin IMBHs indicate hierarchical mergers
    Used to interpret observed subpopulations and attribute formation channels.
  • domain assumption The pair-instability mass gap lower edge is identifiable from the truncation in low-spin black hole masses
    Invoked to link the observed 65 M_sun truncation to the PIMG.

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Cite this review

Pith. "Pith review of How do the LIGO-Virgo-KAGRA's Heavy Black Holes Form? No evidence for core-collapse Intermediate-mass black holes in GWTC-4." pith.science (2026). https://pith.science/paper/2605.05563

@misc{pith2026260505563,
  author       = {Pith},
  title        = {Pith review of: How do the LIGO-Virgo-KAGRA's Heavy Black Holes Form? No evidence for core-collapse Intermediate-mass black holes in GWTC-4},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2605.05563}},
  note         = {Machine review of arXiv:2605.05563}
}
abstract

We investigate the population properties of binary black holes (BBHs) from the LIGO-Virgo-KAGRA collaboration, focusing especially on those in the high-mass range, using the newly released GWTC-4 catalog. For the first time, we search for a subpopulation of low-spin intermediate-mass black holes (IMBHs) that would indicate formation via stellar core collapse. With the currently available catalog, we find no evidence for such a subpopulation, and set a 90\% upper limit on the merger rate of collapse-formed IMBHs at $0.077~\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$. The mass distribution of low-spin (stellar-origin) black holes truncates at $65^{+23}_{-22}\,M_\odot$, consistent with the lower edge of the pair-instability mass gap (PIMG), although we cannot directly determine its upper boundary from current data. Informed by stellar evolution theory, we estimate the upper edge of the PIMG to be $150\pm24\,M_\odot$. We find that the observed IMBHs belong to a high-spin subpopulation, consistent with formation through successive hierarchical mergers.

Figures

Figures reproduced from arXiv: 2605.05563 by the authors.

Figure 1
Figure 1. Component mass distributions of the primary (top) and secondary (bottom) black holes for the three subpopulations inferred with the Main Model. The solid curves are the medians and the shaded regions are for the 90% credible intervals. The first subpopulation, referred to as the low-spin group, is characterized by small dimensionless spin mag￾nitudes (χ ≲ 0.3), peaking at χ ∼ 0.15. Its mass distri￾bution is confined… view at source ↗
Figure 2
Figure 2. Distribution of spin magnitudes of black holes for the subpopulations inferred with the Main Model. The solid curves are the medians and the shaded regions are for the 90% credible intervals. the expectation that if core-collapse IMBHs are signifi￾cantly more abundant than those formed via hierarchi￾cal mergers, a distinct signature of the PIMG’s upper edge should be imprinted on the mass function. Fig￾ure 3 shows t… view at source ↗
Figure 3
Figure 3. Mass distributions of the primary (a) and secondary (b) black holes inferred with the mass-only model for three cases. The solid curves are the medians and the shaded regions are for the 90% credible intervals. 3. Hierarchical merger origin for the most massive BHs: The IMBHs observed (e.g., in GW231123) belong to the high-spin (χ ≳ 0.6) subpopulation. Their spin and mass distributions are consistent with expectatio… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Left: The posterior distributions of maximum masses that are potentially associated to the lower edge of PIMG. Right:The posterior distributions of cutoff masses that are potentially associated to the upper edge of PIMG, compared to the component masses of GW231123. th…
Figure 5
Figure 5. Figure 5: The posterior distributions of glow, gwide, and gup ≡ glow + gwide —which describe the edges and width of the PIMG —as obtained with the Alternative Model. The black curve indicates the prior on the PIMG width, taken to be 80 ± 8 M⊙ following Farmer et al. (2020). The …
Figure 5
Figure 5. Figure 5: The posterior distributions of glow, gwide, and gup ≡ glow + gwide —which describe the edges and width of the PIMG —as obtained with the Alternative Model. The black curve indicates the prior on the PIMG width, taken to be 80 ± 8 M⊙ following Farmer et al. (2020). The …
Figure 6
Figure 6. Figure 6: The posterior distribution of hyperparameters obtained with the mass-only models (Case One, Case Two, and Case Three). The values are for median and 90% credible intervals
Figure 6
Figure 6. Figure 6: The posterior distribution of hyperparameters obtained with the mass-only models (Case One, Case Two, and Case Three). The values are for median and 90% credible intervals. 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 RLS, IMBH[Gpc 3 yr 1 ] 0 5 10 15 20 25 30 …
Figure 7
Figure 7. Figure 7: Merger rate of the low-spin IMBHs inferred with the Main Model. The vertical line indicate the 90% upper limit
Figure 8
Figure 8. Figure 8: Upper limit (90%) of the IMBH mergers from different formation channels

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Forward citations

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