pith. sign in

arxiv: 2509.04151 · v2 · submitted 2025-09-04 · 🌌 astro-ph.HE

Evidence of the pair instability gap from black hole masses

Hui Tong , Maya Fishbach , Eric Thrane , Matthew Mould , Thomas A. Callister , Amanda Farah , Nir Guttman , Sharan Banagiri
show 8 more authors
Daniel Beltran-Martinez Ben Farr Shanika Galaudage Jaxen Godfrey Jack Heinzel Marios Kalomenopoulos Simona J. Miller Aditya Vijaykumar
This is my paper

Pith reviewed 2026-05-18 19:13 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords pair-instability supernovaeblack hole mass gapgravitational waveshierarchical mergersGWTC-4nuclear reaction rate
0
0 comments X

The pith

Gravitational-wave data reveals the pair-instability gap only in the smaller black hole of each merging pair, at a lower edge of 44 solar masses.

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

Stellar theory predicts that stars cannot leave behind black holes in the mass range of roughly 50 to 130 solar masses because pair-instability supernovae blow the entire star apart. This paper analyzes the fourth LIGO-Virgo-KAGRA catalog and finds statistical evidence for a gap whose lower boundary sits at 44 solar masses with 90 percent credibility. The gap is absent from the distribution of the larger primary black holes but stands out clearly among the smaller secondary black holes. The authors interpret the pattern, together with a matching shift toward higher spins, as the signature of a subpopulation in which the larger black hole is itself the remnant of an earlier merger. The measured location of the gap supplies a new constraint on the rate of the carbon-alpha nuclear reaction inside massive stars.

Core claim

Stellar theory predicts a forbidden range of black-hole masses between ~50--130 M_⊙ due to pair-instability supernovae. We report evidence of the pair-instability gap in GWTC-4, with a lower boundary of 44_{-4}^{+5} M_⊙ (90% credibility). While the gap is not present in the distribution of primary masses m1, it appears unambiguously in the distribution of secondary masses m2, where m2 ≤ m1. The location of the gap lines up well with a previously identified transition in the binary black-hole spin distribution; binaries with primary components in the gap tend to spin more rapidly than those below the gap. We interpret these findings as evidence for a subpopulation of hierarchical mergers. Our

What carries the argument

The separate mass distributions of primary (larger) and secondary (smaller) black holes in each binary, together with their spin properties, used to isolate the pair-instability cutoff and link it to prior mergers.

Load-bearing premise

The observed cutoff and spin transition in secondary masses mark a true hierarchical-merger subpopulation rather than selection effects or choices in the population model.

What would settle it

A future catalog showing many secondary black holes with masses above 50 solar masses, or the disappearance of the aligned spin transition when the sample size increases.

read the original abstract

Stellar theory predicts a forbidden range of black-hole masses between ${\sim}50$--$130\,M_\odot$ due to pair-instability supernovae, but evidence for such a gap in the mass distribution from gravitational-wave astronomy has proved elusive. Early hints of a cutoff in black-hole masses at ${\sim} 45\,M_\odot$ disappeared with the subsequent discovery of more massive binary black holes. Here, we report evidence of the pair-instability gap in LIGO--Virgo--KAGRA's fourth gravitational wave transient catalog (GWTC-4), with a lower boundary of $44_{-4}^{+5} M_\odot$ (90\% credibility). While the gap is not present in the distribution of \textit{primary} masses $m_1$ (the bigger of the two black holes in a binary system), it appears unambiguously in the distribution of \textit{secondary} masses $m_2$, where $m_2 \leq m_1$. The location of the gap lines up well with a previously identified transition in the binary black-hole spin distribution; binaries with primary components in the gap tend to spin more rapidly than those below the gap. We interpret these findings as evidence for a subpopulation of hierarchical mergers: binaries where the primary component is the product of a previous black-hole merger and thus populates the gap. Our measurement of the location of the pair-instability gap constrains the $S$-factor for $^{12}\rm{C}(\alpha,\gamma)^{16}\rm{O}$ at 300keV to $260_{-108}^{+190}$ keV barns.

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 / 0 minor

Summary. The manuscript analyzes black-hole masses in the LIGO-Virgo-KAGRA GWTC-4 catalog and reports evidence for the lower edge of the pair-instability gap at 44_{-4}^{+5} M_⊙ (90% credibility). The gap is absent from the primary-mass (m1) distribution but appears in the secondary-mass (m2) distribution subject to m2 ≤ m1; the authors link this feature, together with a spin transition, to a subpopulation of hierarchical mergers in which the primary is a second-generation black hole. The measured gap location is mapped to a constraint on the S-factor for ^{12}C(α,γ)^{16}O at 300 keV of 260_{-108}^{+190} keV barns.

Significance. If the statistical inference of a sharp cutoff in the marginal m2 distribution is robust, the result would constitute the first clear observational signature of the pair-instability gap in gravitational-wave data. It would simultaneously provide a new, independent constraint on a key nuclear reaction rate and support the existence of a hierarchical-merger channel in the observed population. The m1–m2 distinction and the alignment with the reported spin transition would have direct implications for binary-formation models.

major comments (2)
  1. [Abstract] Abstract: the claim that a gap 'appears unambiguously' in the m2 distribution (while absent from m1) is load-bearing for the hierarchical-merger interpretation. The enforced ordering m2 ≤ m1 together with any mass-ratio or selection function p(det|m1,m2,z) can shift probability mass and produce an apparent hard edge in the marginal p(m2) even if the underlying first-generation mass function has no gap. The manuscript must demonstrate, via explicit model-comparison or injection studies, that this artifact is ruled out at the reported credibility level.
  2. [Abstract] The spin transition is invoked to break the degeneracy between a true gap and selection-induced features, yet the abstract supplies no quantitative model-comparison statistic (Bayes factor, posterior odds, or information criterion) between a single-population model with mass-dependent spins and the two-population hierarchical model. Without this comparison the interpretation remains suggestive rather than demonstrated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which identify key points that merit clarification and strengthening. We address each major comment below and are prepared to revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that a gap 'appears unambiguously' in the m2 distribution (while absent from m1) is load-bearing for the hierarchical-merger interpretation. The enforced ordering m2 ≤ m1 together with any mass-ratio or selection function p(det|m1,m2,z) can shift probability mass and produce an apparent hard edge in the marginal p(m2) even if the underlying first-generation mass function has no gap. The manuscript must demonstrate, via explicit model-comparison or injection studies, that this artifact is ruled out at the reported credibility level.

    Authors: We acknowledge that the ordering m2 ≤ m1 and selection effects could in principle induce apparent features in the marginal m2 distribution. Our hierarchical Bayesian model infers the joint (m1, m2) population while explicitly including the detection probability p(det|m1, m2, z) and the ordering constraint. The gap is recovered only in the m2 marginal and is absent from m1, which is not the expected signature of a pure selection artifact. To address the referee's request directly, we will add explicit injection-recovery studies in the revised manuscript that inject populations without a gap and quantify the posterior probability of recovering a spurious 44 M_⊙ edge at the reported credibility level. revision: yes

  2. Referee: [Abstract] The spin transition is invoked to break the degeneracy between a true gap and selection-induced features, yet the abstract supplies no quantitative model-comparison statistic (Bayes factor, posterior odds, or information criterion) between a single-population model with mass-dependent spins and the two-population hierarchical model. Without this comparison the interpretation remains suggestive rather than demonstrated.

    Authors: We agree that a quantitative model-comparison statistic would make the hierarchical-merger interpretation more definitive. The manuscript currently presents the alignment between the mass gap and the spin transition as supporting qualitative evidence. In the revision we will compute and report the Bayes factor (or equivalent information criterion) between a single-population model that allows mass-dependent spins and the two-population model that includes a hierarchical-merger subpopulation, thereby providing the requested quantitative measure. revision: yes

Circularity Check

0 steps flagged

No significant circularity: gap location inferred directly from GWTC-4 data

full rationale

The paper's central result is a hierarchical Bayesian population inference on the joint (m1, m2) distribution from GWTC-4 events, with the reported lower gap edge at 44 M⊙ emerging as a feature in the marginal p(m2) but not p(m1). This is a direct fit to the catalog data under the m2 ≤ m1 constraint and selection effects; it does not reduce by construction to any input parameter or prior. The subsequent S-factor constraint is a downstream mapping that takes the measured gap location as an external input to nuclear astrophysics and does not feed back into the mass inference. No self-definitional loops, fitted inputs relabeled as predictions, or load-bearing self-citations that render the gap location tautological appear in the derivation chain. The hierarchical-merger interpretation is presented as one consistent reading of the data plus spin trends, but remains an open claim subject to model comparison rather than a definitional necessity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The analysis relies on standard stellar theory for the existence and location of the pair-instability gap and introduces a hierarchical merger subpopulation to explain the data; the gap boundary itself is inferred from the observations.

free parameters (1)
  • gap lower boundary = 44 M_⊙
    Inferred from the secondary mass distribution in GWTC-4; reported with 90% credibility interval.
axioms (1)
  • domain assumption Pair-instability supernovae create a mass gap between approximately 50 and 130 solar masses
    Invoked to interpret the observed cutoff at 44 M_⊙ as the lower edge of the pair-instability gap.
invented entities (1)
  • hierarchical merger subpopulation no independent evidence
    purpose: Accounts for black holes populating the pair-instability gap and the observed spin-mass correlation
    Postulated to explain why the gap appears in secondary masses and why systems with primaries in the gap spin more rapidly.

pith-pipeline@v0.9.0 · 5891 in / 1567 out tokens · 74829 ms · 2026-05-18T19:13:35.660918+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Secondary-Mass Features improve Spectral-Siren $H_0$ Constraints

    astro-ph.CO 2026-05 unverdicted novelty 7.0

    A new model emphasizing secondary mass features and pairing transitions improves spectral siren H0 constraints by ~30% using 142 GW events from GWTC-4.0.

  2. The Black Hole Mass Gap as a New Probe of Millicharged Particles

    hep-ph 2026-04 unverdicted novelty 7.0

    Millicharged particles weaken pulsational pair-instability in massive stars, shifting the lower edge of the black hole mass gap upward and turning gravitational wave observations into a probe for particles with masses...

  3. Second-Generation Mass Peak in the Gravitational-Wave Population as a Probe of Globular Clusters

    astro-ph.HE 2026-04 unverdicted novelty 6.0

    Dynamical formation in globular clusters produces a robust second black-hole mass peak at ~70 solar masses from second-generation mergers when the first-generation spectrum is truncated by pair-instability supernovae.

  4. Measurement prospects for the pair-instability mass cutoff with gravitational waves

    astro-ph.HE 2026-02 conditional novelty 6.0

    Simulations show a 40-50 solar-mass black-hole cutoff is not guaranteed to be confidently recovered from GWTC-4-like catalogs, spurious detections are unlikely, and O4 data would reduce cutoff-mass uncertainty by at l...

  5. Signatures of a subpopulation of hierarchical mergers in the GWTC-4 gravitational-wave dataset

    gr-qc 2026-01 unverdicted novelty 6.0

    GWTC-4 data show a transition to nearly all hierarchical mergers above 46 solar masses, with the hierarchical rate peaking at 15.7 solar masses, indicating mass-dependent substructure in black hole spins.

  6. A new group of low-spin $50-70M_\odot$ Black Holes and the high pair-instability mass cutoff

    astro-ph.HE 2025-10 conditional novelty 6.0

    GWTC-4.0 data shows low-spin black holes up to 70 solar masses, moving the low-spin cutoff to 68.5 solar masses and favoring a high pair-instability mass gap.

  7. Is the Binary Black Hole Population Inference from Gravitational-Wave Data Robust?

    astro-ph.HE 2026-05 unverdicted novelty 5.0

    Waveform modeling uncertainties can distort features in the binary black hole mass distribution inferred from gravitational-wave data more than statistical uncertainties.

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

    astro-ph.HE 2026-05 unverdicted novelty 5.0

    No evidence for core-collapse IMBHs in GWTC-4; heavy BHs from hierarchical mergers, with low-spin mass distribution truncating at ~65 solar masses and PIMG upper edge estimated at 150 solar masses.

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

    astro-ph.HE 2026-05 unverdicted novelty 5.0

    No evidence for core-collapse formed low-spin IMBHs in GWTC-4, with 90% upper limit on merger rate of 0.077 Gpc^{-3} yr^{-1}, low-spin BH mass truncation at 65 solar masses consistent with pair-instability gap lower e...

  10. Constraints on the $^{12}$C$(\alpha, \gamma)^{16}$O and $^{16}$O+$^{16}$O Reaction Rates from Binary Black Holes Detected via Gravitational Wave Signals

    astro-ph.SR 2026-03 unverdicted novelty 5.0

    Stellar models show that the 12C(alpha,gamma)16O rate uncertainty moves the black hole mass gap, constraining its S300 to 137.6-263.4 keV barn when matched to the observed gap from gravitational waves.

  11. Biased parameter inference of eccentric, spin-precessing binary black holes

    gr-qc 2025-10 unverdicted novelty 5.0

    Eccentric BBH signals recovered with quasi-circular precessing models show biases in chirp mass and χ_p; Bayes factors favor eccentric aligned-spin models when both eccentricity and precession are present.

Reference graph

Works this paper leans on

116 extracted references · 116 canonical work pages · cited by 10 Pith papers · 5 internal anchors

  1. [1]

    Astrophys

    Fowler, W.A., Hoyle, F.: Neutrino Processes and Pair Formation in Massive Stars and Supernovae. Astrophys. J. Suppl. 9, 201–319 (1964)

    work page 1964

  2. [2]

    Astro- phys

    Rakavy, G., Shaviv, G.: Instabilities in Highly Evolved Stellar Models. Astro- phys. J. 148, 803 (1967)

    work page 1967

  3. [3]

    Barkat, Z., Rakavy, G., Sack, N.: Dynamics of supernova explosion resulting from pair formation. Phys. Rev. Lett. 18, 379–381 (1967) 21

    work page 1967

  4. [4]

    Ap&SS 2(1), 96–114 (1968)

    Fraley, G.S.: Supernovae Explosions Induced by Pair-Production Instability. Ap&SS 2(1), 96–114 (1968)

    work page 1968

  5. [5]

    Astrophys

    Heger, A., Woosley, S.E.: The nucleosynthetic signature of population III. Astrophys. J. 567, 532–543 (2002)

    work page 2002

  6. [6]

    Nature 450, 390 (2007)

    Woosley, S.E., Blinnikov, S., Heger, A.: Pulsational pair instability as an explanation for the most luminous supernovae. Nature 450, 390 (2007)

    work page 2007

  7. [7]

    Astrophys

    Woosley, S.E.: Pulsational Pair-Instability Supernovae. Astrophys. J. 836(2), 244 (2017)

    work page 2017

  8. [8]

    : The Effect of Pair-Instability Mass Loss on Black Hole Mergers

    Belczynski, K., et al. : The Effect of Pair-Instability Mass Loss on Black Hole Mergers. Astron. Astrophys. 594, 97 (2016)

    work page 2016

  9. [9]

    The Astrophysical Journal 878(1), 49 (2019)

    Woosley, S.E.: The evolution of massive helium stars, including mass loss. The Astrophysical Journal 878(1), 49 (2019)

    work page 2019

  10. [10]

    Astrophys

    Woosley, S.E., Heger, A.: The Pair-Instability Mass Gap for Black Holes. Astrophys. J. Lett. 912(2), 31 (2021)

    work page 2021

  11. [11]

    Astrophys

    Farmer, R., Renzo, M., de Mink, S.E., Marchant, P., Justham, S.: Mind the Gap: The Location of the Lower Edge of the Pair-instability Supernova Black Hole Mass Gap. Astrophys. J. 887(1), 53 (2019)

    work page 2019

  12. [12]

    Renzo, M., Smith, N.: Pair-instability evolution and explosions in massive stars (2024) arXiv:2407.16113 [astro-ph.HE]

    work page arXiv 2024

  13. [13]

    Schulze, S., et al.: 1100 days in the life of the supernova 2018ibb - The best pair- instability supernova candidate, to date. Astron. Astrophys. 683, 223 (2024)

    work page 2024

  14. [14]

    : Double acct: a distinct double-peaked supernova matching pulsational pair-instability models

    Angus, C.R., et al. : Double acct: a distinct double-peaked supernova matching pulsational pair-instability models. Astrophys. J. Lett. 977, 41 (2024)

    work page 2024

  15. [15]

    : Advanced LIGO

    Aasi, J., et al. : Advanced LIGO. Class. Quant. Grav. 32, 074001 (2015)

    work page 2015

  16. [16]

    : Advanced Virgo: a second-generation interferometric gravitational wave detector

    Acernese, F., et al. : Advanced Virgo: a second-generation interferometric gravitational wave detector. Class. Quant. Grav. 32, 024001 (2015)

    work page 2015

  17. [17]

    : Overview of KAGRA: Detector design and construction history

    Akutsu, T., et al. : Overview of KAGRA: Detector design and construction history. PTEP 2021(5), 05–101 (2021)

    work page 2021

  18. [18]

    Fishbach, M., Holz, D.E.: Where Are LIGO’s Big Black Holes? Astrophys. J. Lett. 851(2), 25 (2017)

    work page 2017

  19. [19]

    Astrophys

    Talbot, C., Thrane, E.: Measuring the binary black hole mass spectrum with an astrophysically motivated parameterization. Astrophys. J. 856, 173 (2018) 22

    work page 2018

  20. [20]

    Ray, A., Maga˜ na Hernandez, I., Breivik, K., Creighton, J.: Searching for binary black hole sub-populations in gravitational wave data using binned Gaussian processes (2024) arXiv:2404.03166 [astro-ph.HE]

    work page arXiv 2024

  21. [21]

    Astrophys

    Farmer, R., Renzo, M., Mink, S., Fishbach, M., Justham, S.: Constraints from gravitational wave detections of binary black hole mergers on the 12C (α, γ)16O rate. Astrophys. J. Lett. 902(2), 36 (2020)

    work page 2020

  22. [22]

    The Astrophysical Journal Letters 913, 7 (2021)

    Abbott, R., Abbott, T.D., Abraham, S., Acernese, F., al.: Population properties of compact objects from the second LIGO–virgo gravitational-wave transient catalog. The Astrophysical Journal Letters 913, 7 (2021)

    work page 2021

  23. [23]

    : GW190521: A Binary Black Hole Merger with a Total Mass of 150M⊙

    Abbott, R., et al. : GW190521: A Binary Black Hole Merger with a Total Mass of 150M⊙. Phys. Rev. Lett. 125, 101102 (2020)

    work page 2020

  24. [24]

    : The population of merging compact binaries inferred using gravitational waves through GWTC-3

    Abbott, R., et al. : The population of merging compact binaries inferred using gravitational waves through GWTC-3. Phys. Rev. X 13, 011048 (2023)

    work page 2023

  25. [25]

    Astrophys

    Edelman, B., Doctor, Z., Farr, B.: Poking Holes: Looking for Gaps in LIGO/Virgo’s Black Hole Population. Astrophys. J. Lett. 913(2), 23 (2021)

    work page 2021

  26. [26]

    Mould, M., Gerosa, D., Taylor, S.R.: Deep learning and Bayesian inference of gravitational-wave populations: Hierarchical black-hole mergers. Phys. Rev. D 106(10), 103013 (2022)

    work page 2022

  27. [27]

    Astrophys

    Wang, Y.-Z., Li, Y.-J., Vink, J.S., Fan, Y.-Z., Tang, S.-P., Qin, Y., Wei, D.-M.: Potential Subpopulations and Assembling Tendency of the Merging Black Holes. Astrophys. J. Lett. 941(2), 39 (2022)

    work page 2022

  28. [28]

    Karathanasis, C., Mukherjee, S., Mastrogiovanni, S.: Binary black holes popula- tion and cosmology in new lights: signature of PISN mass and formation channel in GWTC-3. Mon. Not. Roy. Astron. Soc. 523(3), 4539–4555 (2023)

    work page 2023

  29. [29]

    Li, Y.-J., Wang, Y.-Z., Tang, S.-P., Fan, Y.-Z.: Resolving the Stellar-Collapse and Hierarchical-Merger Origins of the Coalescing Black Holes. Phys. Rev. Lett. 133(5), 051401 (2024)

    work page 2024

  30. [30]

    Antonini, F., Romero-Shaw, I.M., Callister, T.: Star cluster population of high mass black hole mergers in gravitational wave data. Phys. Rev. Lett.134, 011401 (2025)

    work page 2025

  31. [31]

    Antonini, F., Callister, T., Dosopoulou, F., Romero-Shaw, I., Chattopadhyay, D.: Inferring the pair-instability mass gap from gravitational wave data using flexible models (2025) arXiv:2506.09154 [astro-ph.HE]

    work page arXiv 2025

  32. [32]

    Astrophys

    Abbott, B.P., Abbott, R., Abbott, T.D., Abraham, S., Acernese, F., Ackley, K., Adams, C., Adhikari, R.X., Adya, V.B., Affeldt, C., al.: Binary Black Hole 23 Population Properties Inferred from the First and Second Observing Runs of Advanced LIGO and Advanced Virgo. Astrophys. J. Lett. 882(2), 24 (2019)

    work page 2019

  33. [33]

    : Properties and Astrophysical Implications of the 150 M⊙ Binary Black Hole Merger GW190521

    Abbott, R., et al. : Properties and Astrophysical Implications of the 150 M⊙ Binary Black Hole Merger GW190521. Astrophys. J. Lett. 900, 13 (2020)

    work page 2020

  34. [34]

    Astrophys

    Ruiz-Rocha, K., Yelikar, A.B., Lange, J., Gabella, W., Weller, R.A., O’Shaughnessy, R., Holley-Bockelmann, K., Jani, K.: Properties of “Lite” Intermediate-mass Black Hole Candidates in LIGO-Virgo’s Third Observing Run. Astrophys. J. Lett. 985(2), 37 (2025)

    work page 2025

  35. [35]

    Hendriks, D.D., Son, L.A.C., Renzo, M., Izzard, R.G., Farmer, R.: Pulsational pair-instability supernovae in gravitational-wave and electromagnetic transients. Mon. Not. Roy. Astron. Soc. 526(3), 4130–4147 (2023)

    work page 2023

  36. [36]

    Astrophys

    Golomb, J., Isi, M., Farr, W.M.: Physical Models for the Astrophysical Pop- ulation of Black Holes: Application to the Bump in the Mass Distribution of Gravitational-wave Sources. Astrophys. J. 976(1), 121 (2024)

    work page 2024

  37. [37]

    Stevenson, S., Sampson, M., Powell, J., Vigna-G´ omez, A., Neijssel, C.J., Sz´ ecsi, D., Mandel, I.: The impact of pair-instability mass loss on the binary black hole mass distribution (2019)

    work page 2019

  38. [38]

    Croon, D., Sakstein, J.: Prediction of Multiple Features in the Black Hole Mass Function due to Pulsational Pair-Instability Supernovae (2023) arXiv:2312.13459

    work page arXiv 2023

  39. [39]

    Winch, E.R.J., Sabhahit, G.N., Vink, J.S., Higgins, E.R.: The black hole - pair instability boundary for high stellar rotation. Mon. Not. R. Ast. Soc. 540(1), 90–105 (2025)

    work page 2025

  40. [40]

    Nature 5 (2021)

    Gerosa, D., Fishbach, M.: Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures. Nature 5 (2021)

    work page 2021

  41. [41]

    Di Carlo, U.N., Giacobbo, N., Mapelli, M., Pasquato, M., Spera, M., Wang, L., Haardt, F.: Merging black holes in young star clusters. Mon. Not. Roy. Astron. Soc. 487(2), 2947–2960 (2019)

    work page 2019

  42. [42]

    Astrophys

    Renzo, M., Cantiello, M., Metzger, B.D., Jiang, Y.-F.: The Stellar Merger Sce- nario for Black Holes in the Pair-instability Gap. Astrophys. J. Lett. 904(2), 13 (2020)

    work page 2020

  43. [43]

    Astrophys

    Kremer, K., Spera, M., Becker, D., Chatterjee, S., Di Carlo, U.N., Fragione, G., Rodriguez, C.L., Ye, C.S., Rasio, F.A.: Populating the upper black hole mass gap through stellar collisions in young star clusters. Astrophys. J. 903(1), 45 (2020) 24

    work page 2020

  44. [44]

    Super-kilonovae

    Siegel, D.M., Agarwal, A., Barnes, J., Metzger, B.D., Renzo, M., Villar, V.A.: “Super-kilonovae” from Massive Collapsars as Signatures of Black Hole Birth in the Pair-instability Mass Gap. Astrophys. J. 941(1), 100 (2022)

    work page 2022

  45. [45]

    Production and growth

    McKernan, B., Ford, K.E.S., Lyra, W., Perets, H.B.: Intermediate mass black holes in AGN discs - I. Production and growth. Mon. Not. R. Ast. Soc. 425(1), 460–469 (2012)

    work page 2012

  46. [46]

    Astrophys

    Safarzadeh, M., Haiman, Z.: Formation of GW190521 via gas accretion onto Population III stellar black hole remnants born in high-redshift minihalos. Astrophys. J. Lett. 903(1), 21 (2020)

    work page 2020

  47. [47]

    Astrophys

    Son, L.A.C., Mink, S.E., Broekgaarden, F.S., Renzo, M., Justham, S., Laplace, E., Moran-Fraile, J., Hendriks, D.D., Farmer, R.: Polluting the pair-instability mass gap for binary black holes through super-Eddington accretion in isolated binaries. Astrophys. J. 897(1), 100 (2020)

    work page 2020

  48. [48]

    Astrophys

    Kıro˘ glu, F., Kremer, K., Biscoveanu, S., Prieto, E.G., Rasio, F.A.: Black Hole Accretion and Spin-up through Stellar Collisions in Dense Star Clusters. Astrophys. J. 979(2), 237 (2025)

    work page 2025

  49. [49]

    Abac, A.G., et al.: GWTC-4.0: Updating the Gravitational-Wave Transient Cat- alog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run (2025) arXiv:2508.18082 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  50. [50]

    Abac, A.G., et al.: GWTC-4.0: Population Properties of Merging Compact Binaries (2025) arXiv:2508.18083 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  51. [51]

    Spera, M., Mapelli, M.: Very massive stars, pair-instability supernovae and intermediate-mass black holes with the SEVN code. Mon. Not. Roy. Astron. Soc. 470(4), 4739–4749 (2017)

    work page 2017

  52. [52]

    Marchant, P., Renzo, M., Farmer, R., Pappas, K.M.W., Taam, R.E., Mink, S., Kalogera, V.: Pulsational pair-instability supernovae in very close binaries (2018)

    work page 2018

  53. [53]

    Abac, A.G., et al.: GW231123: a Binary Black Hole Merger with Total Mass 190-265 M⊙ (2025) arXiv:2507.08219 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  54. [54]

    Croon, D., Sakstein, J., Gerosa, D.: Can stellar physics explain GW231123? (2025) arXiv:2508.10088 [astro-ph.HE]

    work page arXiv 2025

  55. [55]

    Gottlieb, O., Metzger, B.D., Issa, D., Li, S.E., Renzo, M., Isi, M.: Spinning into the Gap: Direct-Horizon Collapse as the Origin of GW231123 from End-to-End GRMHD Simulations (2025) arXiv:2508.15887 [astro-ph.HE]

    work page arXiv 2025

  56. [56]

    Payne, E., Thrane, E.: Model exploration in gravitational-wave astronomy with 25 the maximum population likelihood. Phys. Rev. Res. 5, 023013 (2023)

    work page 2023

  57. [57]

    : GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run

    Abbott, R., et al. : GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run. Phys. Rev. X 13, 041039 (2023)

    work page 2023

  58. [58]

    Monthly Notices of the Royal Astronomical Society 203(4), 1049–1062 (1983)

    Fitchett, M.J.: The influence of gravitational wave momentum losses on the centre of mass motion of a newtonian binary system. Monthly Notices of the Royal Astronomical Society 203(4), 1049–1062 (1983)

    work page 1983

  59. [59]

    Astrophys

    Favata, M., Hughes, S.A., Holz, D.E.: How black holes get their kicks: Gravita- tional radiation recoil revisited. Astrophys. J. Lett. 607, 5–8 (2004)

    work page 2004

  60. [60]

    Gonzalez, J.A., Sperhake, U., Bruegmann, B., Hannam, M., Husa, S.: Total recoil: The Maximum kick from nonspinning black-hole binary inspiral. Phys. Rev. Lett. 98, 091101 (2007)

    work page 2007

  61. [61]

    Gerosa, D., H´ ebert, F., Stein, L.C.: Black-hole kicks from numerical-relativity surrogate models. Phys. Rev. D 97(10), 104049 (2018)

    work page 2018

  62. [62]

    Astrophys

    Mahapatra, P., Gupta, A., Favata, M., Arun, K.G., Sathyaprakash, B.S.: Rem- nant Black Hole Kicks and Implications for Hierarchical Mergers. Astrophys. J. Lett. 918(2), 31 (2021)

    work page 2021

  63. [63]

    Astrophys

    Antonini, F., Rasio, F.A.: Merging black hole binaries in galactic nuclei: implications for advanced-LIGO detections. Astrophys. J. 831(2), 187 (2016)

    work page 2016

  64. [64]

    Rodriguez, C.L., Zevin, M., Amaro-Seoane, P., Chatterjee, S., Kremer, K., Rasio, F.A., Ye, C.S.: Black holes: The next generation—repeated mergers in dense star clusters and their gravitational-wave properties. Phys. Rev. D 100(4), 043027 (2019)

    work page 2019

  65. [65]

    Astrophys

    Doctor, Z., Farr, B., Holz, D.E.: Black Hole Leftovers: The Remnant Population from Binary Black Hole Mergers. Astrophys. J. Lett. 914(1), 18 (2021)

    work page 2021

  66. [66]

    Mahapatra, P., Chattopadhyay, D., Gupta, A., Favata, M., Sathyaprakash, B.S., Arun, K.G.: Predictions of a simple parametric model of hierarchical black hole mergers. Phys. Rev. D 111(2), 023013 (2025)

    work page 2025

  67. [67]

    Astrophys

    Mahapatra, P., Chattopadhyay, D., Gupta, A., Antonini, F., Favata, M., Sathyaprakash, B.S., Arun, K.G.: Reconstructing the Genealogy of LIGO-Virgo Black Holes. Astrophys. J. 975(1), 117 (2024)

    work page 2024

  68. [68]

    Pretorius, F.: Evolution of binary black hole spacetimes. Phys. Rev. Lett. 95, 121101 (2005)

    work page 2005

  69. [69]

    Buonanno, A., Kidder, L.E., Lehner, L.: Estimating the final spin of a binary black hole coalescence. Phys. Rev. D 77, 026004 (2008) 26

    work page 2008

  70. [70]

    Fishbach, M., Holz, D.E., Farr, B.: Are LIGO’s Black Holes Made from Smaller Black Holes? Astrophys. J. Lett. 840(2), 24 (2017)

    work page 2017

  71. [71]

    : Evidence for Hierarchical Black Hole Mergers in the Second LIGO–Virgo Gravitational Wave Catalog

    Kimball, C., et al. : Evidence for Hierarchical Black Hole Mergers in the Second LIGO–Virgo Gravitational Wave Catalog. Astrophys. J. Lett.915(2), 35 (2021)

    work page 2021

  72. [72]

    Astrophys

    Fishbach, M., Kimball, C., Kalogera, V.: Limits on Hierarchical Black Hole Mergers from the Most Negative χ ef f Systems. Astrophys. J. Lett. 935(2), 26 (2022)

    work page 2022

  73. [73]

    Astrophys

    Tiwari, V., Fairhurst, S.: The Emergence of Structure in the Binary Black Hole Mass Distribution. Astrophys. J. Lett. 913(2), 19 (2021)

    work page 2021

  74. [74]

    Astrophys

    Tiwari, V.: Exploring Features in the Binary Black Hole Population. Astrophys. J. 928(2), 155 (2022)

    work page 2022

  75. [75]

    Pierra, G., Mastrogiovanni, S., Perri` es, S.: The spin magnitude of stellar-mass black holes evolves with the mass. Astron. Astrophys. 692, 80 (2024)

    work page 2024

  76. [76]

    Sadiq, J., Dent, T., Lorenzo-Medina, A.: Seeking Spinning Subpopulations of Black Hole Binaries via Iterative Density Estimation (2025) arXiv:2506.02250 [astro-ph.HE]

    work page arXiv 2025

  77. [77]

    Damour, T.: Coalescence of two spinning black holes: An effective one-body approach. Phys. Rev. D 64, 124013 (2001)

    work page 2001

  78. [78]

    Astrophys

    Fishbach, M., Farr, W.M., Holz, D.E.: The Most Massive Binary Black Hole Detections and the Identification of Population Outliers. Astrophys. J. Lett. 891(2), 31 (2020)

    work page 2020

  79. [79]

    Galaudage, S., Talbot, C., Thrane, E.: Gravitational-wave inference in the cat- alog era: Evolving priors and marginal events. Phys. Rev. D 102(8), 083026 (2020)

    work page 2020

  80. [80]

    The Astrophysical Journal Letters 904(2), 26 (2020)

    Fishbach, M., Holz, D.E.: Minding the gap: Gw190521 as a straddling binary. The Astrophysical Journal Letters 904(2), 26 (2020)

    work page 2020

Showing first 80 references.