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arxiv: 2607.00565 · v1 · pith:5D7HMUWPnew · submitted 2026-07-01 · 🌌 astro-ph.HE

Distinct spin properties and astrophysical origin of low mass binary black holes in gravitational wave data

Elizabeth Flanagan , Jakob Stegmann , Isobel Romero-Shaw , Thomas Callister , Aleksandra Olejak , Fabio Antonini This is my paper

Pith reviewed 2026-07-02 07:53 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords binary black holesgravitational waveseffective spinformation channelsnatal kicksstellar multipleshierarchical inference
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The pith

Binary black hole mergers change spin behavior at a transition mass of about 15 solar masses, marking two distinct formation channels.

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

The analysis fits a two-component mixture model to the effective spins of binary black hole mergers in the GWTC-5.0 catalog, with the dividing mass scale left free to be determined by the data itself. A clear transition appears near 15 solar masses: the lower-mass group, which dominates the observed mergers near 10 solar masses, shows a narrow spin distribution peaked at a small positive value yet still allowing negative values, while the higher-mass group shows a broader distribution centered near zero. Mock tests confirm this split is not produced by sampling noise or selection effects under a single mass-independent spin population. The low-mass properties match formation through massive stellar multiples in the field, either via isolated binaries that impart large natal kicks or via dynamical evolution in hierarchical triples, but rule out standard isolated binary evolution that assumes smaller fallback kicks.

Core claim

Hierarchical Bayesian inference on GWTC-5.0 data infers a transition mass of 15.2 solar masses separating two effective-spin populations. Below the transition the distribution is narrow, peaks at small positive values, and retains significant support for negative values; above the transition it is broader with its peak shifted to values consistent with zero. The dominant low-mass population near 10 solar masses is therefore statistically distinct and arises from a different channel, broadly consistent with massive stellar multiples in the field but incompatible with isolated binary evolution under standard fallback-kick prescriptions.

What carries the argument

A data-driven transition mass that partitions the binary black hole population into two components, each with its own effective-spin distribution, recovered through hierarchical Bayesian inference.

If this is right

  • The low-mass population requires either natal kicks exceeding roughly 100 km/s or dynamical processing inside hierarchical triples.
  • Isolated binary evolution with standard fallback kicks cannot account for the observed negative effective spins below the transition.
  • The spin properties of the two populations remain distinguishable even after accounting for measurement uncertainty and selection.
  • The concentration of mergers near 10 solar masses traces to a formation route separate from that producing higher-mass events.

Where Pith is reading between the lines

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

  • Mass-dependent spin evolution must be built into population-synthesis codes if they are to reproduce the observed split.
  • The relative rates of the two channels could be tracked by counting events on either side of the transition in future data releases.
  • If the low-mass channel is dominated by triples, the fraction of mergers with measurable eccentricity or higher-order effects may also rise at low mass.

Load-bearing premise

The observed mergers are produced by exactly two spin populations whose dividing mass can be read directly from the catalog, and mock catalogs fully represent the null case of no mass dependence together with all selection effects.

What would settle it

A future catalog in which the effective-spin distributions inferred below and above 15 solar masses become statistically indistinguishable, or in which the recovered transition mass lies well outside the present uncertainty interval.

Figures

Figures reproduced from arXiv: 2607.00565 by Aleksandra Olejak, Elizabeth Flanagan, Fabio Antonini, Isobel Romero-Shaw, Jakob Stegmann, Thomas Callister.

Figure 2
Figure 2. Figure 2: The effective spin posteriors for both the non– parametric GP + GP (left) and parametric N + N U (right) models. For the effective spin posteriors, the shaded area represents the 90% confidence interval and the solid lines are the recovered median of the distribution. population models. Below ˜m, the effective-spin distribu￾tion is narrow and peaks at positive values of χeff. The distribution exhibits sign… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between the χeff distribution inferred for the low-mass subpopulation (m1 < m˜ ) using the non– parametric GP +GP model and predictions from isolated bi￾nary evolution models. The blue curve shows model M30.B from K. Belczynski et al. (2020), in which BBH mergers form through common-envelope evolution, and BHs receive fall￾back-modulated natal kicks. The orange curve corresponds to the standard … view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between the χeff distribution inferred for the low-mass subpopulation (m1 < m˜ ) in the non-para￾metric GP +GP analysis and the expected distribution from BBH mergers that form in hierarchical triples. For the lat￾ter, we show the simulation outcomes of a triple population synthesis study that assumes the standard fallback model for natal kicks at BH formation. The BH component spin mag￾nitudes … view at source ↗
Figure 5
Figure 5. Figure 5: Posterior distributions for hyper-parameters described in [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Simulated dataset including 256 mock events (blue line histogram), their simulated posterior samples (filled blue histogram), and found injections (black line histogram). The simulated dataset shown is mock population 7 (see text). This parameterization allows the data to determine both the shape and support of the effective-spin distribution on either side of the transition mass, without imposing a Gaussi… view at source ↗
Figure 7
Figure 7. Figure 7: Top row: Inferred χeff distribution on two mock populations using the N U + U model. Bottom row: Inferred ˜m distribution for the same two mock populations. On the left we show a typical case where the posterior of ˜m rails against the lower boundary of the prior, and on the right we show a case with a recovered transition-like feature [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

We analyze the effective-spin distribution of binary black hole mergers in GWTC-5.0 as a function of primary black hole mass using hierarchical Bayesian inference. We model the population as a mixture of two spin components separated by a transition mass scale inferred directly from the data. We find strong evidence for a transition at $\tilde{m} = 15.2^{+4.3}_{-3.6}\, M_\odot$. Mock-catalog analyses show that such a transition is unlikely to arise from finite-sample fluctuations of a mass-independent $\chi_{\rm eff}$ population and the posterior predictive distributions of $\chi_{\rm eff}$ inferred below and above the transition are clearly distinct. Below the transition mass, the effective-spin distribution is narrow, peaks at a small positive value $\chi_{\rm eff}>0$, but also shows significant support for negative $\chi_{\rm eff}$. Above the transition, the distribution is broader and its peak shifts to values consistent with $\chi_{\rm eff}\simeq0$, making its support at both positive and negative $\chi_{\rm eff}$ roughly similar. These findings suggest that the dominant merger population concentrated around $10\,M_{\odot}$ is statistically distinct from the rest and that it arises from a different formation channel. We show that this low-mass population is broadly consistent with formation from massive stellar multiples in the field: it may either arise from isolated binary star evolution but only if black hole natal kicks below $\tilde{m}$ are generally very large ($\gtrsim100\,\rm km/s$) or be caused by the dynamical evolution of hierarchical triples. In contrast, isolated binary evolution with standard fallback kick models cannot reproduce the support for negative $\chi_{\rm eff}$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper applies hierarchical Bayesian inference to the effective-spin (χ_eff) distribution of binary black hole mergers in GWTC-5.0, modeling the population as a two-component mixture whose transition mass ilde{m} is inferred from the data. It reports a transition at ilde{m} = 15.2^{+4.3}_{-3.6} M_⊙, with the low-mass component showing a narrow χ_eff distribution peaked at small positive values (yet with negative support) and the high-mass component showing a broader distribution centered near zero. Mock-catalog tests are presented to argue that the transition is unlikely under a mass-independent χ_eff population, and the low-mass population is interpreted as arising from a distinct channel (isolated evolution with large kicks or dynamical triples) inconsistent with standard fallback-kick isolated binaries.

Significance. If the central inference holds after addressing selection modeling, the result would provide direct evidence for multiple formation channels in the observed BBH population and would constrain natal-kick magnitudes and the relative contributions of isolated versus dynamical channels at low masses. The use of data-driven transition inference and mock validation under a null hypothesis are positive features that strengthen falsifiability.

major comments (2)
  1. [Abstract] Abstract and methods section on mock catalogs: the statement that the mocks 'fully capture' selection effects does not include explicit verification that the null (mass-independent χ_eff) catalogs reproduce the observed joint mass-χ_eff distribution after forward-modeling the full GW detection probability (SNR and waveform morphology dependence on both mass and spin) and the parameter-estimation covariances present in GWTC-5.0; without this check an apparent transition could be induced by unmodeled selection rather than intrinsic population structure.
  2. [Results] Results section on posterior predictive distributions: the reported distinction between the χ_eff posteriors below and above ilde{m} relies on the two-component mixture model; no quantitative model-comparison metric (e.g., Bayes factor against a single mass-dependent spin distribution or against a three-component model) is provided to demonstrate that the two-component transition is preferred over smoother alternatives.
minor comments (2)
  1. Notation for the transition mass alternates between ilde{m} and m_tilde without a single defining equation; a dedicated equation block would improve clarity.
  2. The interpretation paragraph comparing to isolated binary evolution with fallback kicks would benefit from a brief quantitative reference to the kick-velocity distributions used in the cited population-synthesis studies.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment point by point below, with plans to revise where appropriate to strengthen the analysis.

read point-by-point responses

  1. Referee: [Abstract] Abstract and methods section on mock catalogs: the statement that the mocks 'fully capture' selection effects does not include explicit verification that the null (mass-independent χ_eff) catalogs reproduce the observed joint mass-χ_eff distribution after forward-modeling the full GW detection probability (SNR and waveform morphology dependence on both mass and spin) and the parameter-estimation covariances present in GWTC-5.0; without this check an apparent transition could be induced by unmodeled selection rather than intrinsic population structure.

    Authors: We acknowledge that while our mock catalogs were constructed by drawing from the observed mass distribution and applying the selection effects incorporated in the hierarchical inference (including detection probability), we did not include an explicit end-to-end forward simulation verifying reproduction of the full joint mass-χ_eff distribution under the null hypothesis after accounting for SNR and waveform morphology dependence on mass and spin, nor the parameter-estimation covariances from GWTC-5.0. We will add this verification step in the revised manuscript to rule out selection-induced artifacts. revision: yes

  2. Referee: [Results] Results section on posterior predictive distributions: the reported distinction between the χ_eff posteriors below and above ilde{m} relies on the two-component mixture model; no quantitative model-comparison metric (e.g., Bayes factor against a single mass-dependent spin distribution or against a three-component model) is provided to demonstrate that the two-component transition is preferred over smoother alternatives.

    Authors: We agree that a quantitative metric such as a Bayes factor would provide stronger evidence for the two-component model over alternatives. Our current emphasis is on the data-driven inference of the transition mass and the resulting distinct posterior predictive distributions for χ_eff. We will compute and report Bayes factors comparing the two-component model to a single mass-dependent spin distribution (and note results for a three-component variant) in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central result is direct hierarchical inference from GWTC-5.0

full rationale

The paper models the BBH population as a two-component mixture with a transition mass ilde{m} treated as a free parameter inferred via hierarchical Bayesian inference on the observed events. The transition value, the component spin distributions, and the claim of statistical distinction are outputs of that fit, not inputs redefined as predictions. Mock-catalog tests compare against an explicit null (mass-independent \chi_eff) and are described as capturing selection effects; this is an external falsification step rather than a self-referential loop. No self-citation, ansatz smuggling, or uniqueness theorem from prior author work is invoked as load-bearing in the derivation chain. The result remains a data-driven posterior statement whose validity hinges on modeling assumptions that are stated and tested rather than tautological.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on fitting a transition mass and two spin-component distributions to the observed events. The two-component mixture is introduced as the population model for this analysis.

free parameters (2)
  • transition mass scale \tilde{m} = 15.2 M_\odot
    Inferred directly from the data as the dividing scale between the two spin components in the mixture model.
  • parameters of the narrow and broad chi_eff distributions
    Fitted as part of the hierarchical Bayesian model for each mass regime.
axioms (1)
  • domain assumption The binary black hole population can be modeled as a mixture of two distinct spin components separated by a transition mass scale.
    Core modeling choice invoked to perform the hierarchical Bayesian inference and to interpret the posterior predictive distributions.

pith-pipeline@v0.9.1-grok · 5861 in / 1385 out tokens · 60211 ms · 2026-07-02T07:53:14.896908+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

111 extracted references · 108 canonical work pages · 22 internal anchors

  1. [1]

    G., Abouelfettouh , I., Acernese , F., et al

    Abac , A. G., Abouelfettouh , I., Acernese , F., et al. 2025, title GW241011 and GW241110: Exploring Binary Formation and Fundamental Physics with Asymmetric, High-spin Black Hole Coalescences , , 993, L21, 10.3847/2041-8213/ae0d54

    work page doi:10.3847/2041-8213/ae0d54 2025

  2. [2]

    D., Abraham , S., et al

    Abbott , R., Abbott , T. D., Abraham , S., et al. 2021, title Population Properties of Compact Objects from the Second LIGO-Virgo Gravitational-Wave Transient Catalog , , 913, L7, 10.3847/2041-8213/abe949

    work page doi:10.3847/2041-8213/abe949 2021

  3. [3]

    D., Acernese , F., et al

    Abbott , R., Abbott , T. D., Acernese , F., et al. 2023, title Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3 , Physical Review X, 13, 011048, 10.1103/PhysRevX.13.011048

    work page doi:10.1103/physrevx.13.011048 2023

  4. [4]

    Abbott, R. e. a. 2020a, title GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run , . 2010.14527

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  5. [5]

    Abbott, R. e. a. 2021, title GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo during the First Half of the Third Observing Run, Physical Review X, 11, 10.1103/physrevx.11.021053

    work page doi:10.1103/physrevx.11.021053 2021

  6. [6]

    Abbott, R. e. a. 2023, title GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run, Phys. Rev. X, 13, 041039, 10.1103/PhysRevX.13.041039

    work page doi:10.1103/physrevx.13.041039 2023

  7. [7]

    Abbott et al. 2019, title GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs , Physical Review X, 9, 031040, 10.1103/PhysRevX.9.031040

    work page doi:10.1103/physrevx.9.031040 2019

  8. [8]

    2025 a , Phase Space of Binary Black Holes from Gravitational Wave Observations to Unveil its Formation History, 2411.07304

    Afroz, S., & Mukherjee, S. 2025 a , Phase Space of Binary Black Holes from Gravitational Wave Observations to Unveil its Formation History, 2411.07304

    work page arXiv 2025

  9. [9]

    2025 b , Binary Black Hole Phase Space Discovers the Signature of Pair Instability Supernovae Mass Gap, 2509.09123

    Afroz, S., & Mukherjee, S. 2025 b , Binary Black Hole Phase Space Discovers the Signature of Pair Instability Supernovae Mass Gap, 2509.09123

    work page arXiv 2025

  10. [10]

    2011, title Inspiral-Merger-Ringdown Waveforms for Black-Hole Binaries with Nonprecessing Spins , Physical Review Letters, 106, 241101, 10.1103/PhysRevLett.106.241101

    Ajith, P., Hannam, M., Husa, S., et al. 2011, title Inspiral-Merger-Ringdown Waveforms for Black-Hole Binaries with Nonprecessing Spins , Physical Review Letters, 106, 241101, 10.1103/PhysRevLett.106.241101

    work page doi:10.1103/physrevlett.106.241101 2011

  11. [11]

    Alvarez-Lopez , S., Heinzel , J., & Vitale , S. 2026, title Evidence for additional structure in the effective spin distribution hints at multiple formation pathways in GWTC-5.0 , arXiv e-prints, arXiv:2606.12205, 10.48550/arXiv.2606.12205

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2606.12205 2026

  12. [12]

    2022, title Numerical simulations of the random angular momentum in convection: Implications for supergiant collapse to form black holes , , 511, 176, 10.1093/mnras/stab3776

    Antoni , A., & Quataert , E. 2022, title Numerical simulations of the random angular momentum in convection: Implications for supergiant collapse to form black holes , , 511, 176, 10.1093/mnras/stab3776

    work page doi:10.1093/mnras/stab3776 2022

  13. [13]

    M., & Chattopadhyay, D

    Antonini, F., Callister, T., Dosopoulou, F., Romero-Shaw, I. M., & Chattopadhyay, D. 2025, title Inferring the pair-instability mass gap from gravitational wave data, Phys. Rev. D, 112, 063040, 10.1103/nxnr-pdyx

    work page doi:10.1103/nxnr-pdyx 2025

  14. [14]

    2023, title Coalescing black hole binaries from globular clusters: mass distributions and comparison to gravitational wave data from GWTC-3 , , 522, 466, 10.1093/mnras/stad972

    Antonini , F., Gieles , M., Dosopoulou , F., & Chattopadhyay , D. 2023, title Coalescing black hole binaries from globular clusters: mass distributions and comparison to gravitational wave data from GWTC-3 , , 522, 466, 10.1093/mnras/stad972

    work page doi:10.1093/mnras/stad972 2023

  15. [15]

    Antonini , F., & Rasio , F. A. 2016, title Merging Black Hole Binaries in Galactic Nuclei: Implications for Advanced-LIGO Detections , , 831, 187, 10.3847/0004-637X/831/2/187

    work page doi:10.3847/0004-637x/831/2/187 2016

  16. [16]

    L., Petrovich , C., & Fischer , C

    Antonini , F., Rodriguez , C. L., Petrovich , C., & Fischer , C. L. 2018, title Precessional dynamics of black hole triples: binary mergers with near-zero effective spin , Mon. Not. R. Astron. Soc., 480, L58, 10.1093/mnrasl/sly126

    work page doi:10.1093/mnrasl/sly126 2018

  17. [17]

    2026, title Gravitational-wave constraints on the pair-instability mass gap and nuclear burning in massive stars, Nat Astron, 10.1038/s41550-026-02847-0

    Antonini, F., Romero-Shaw, I., & Callister, T. 2026, title Gravitational-wave constraints on the pair-instability mass gap and nuclear burning in massive stars, Nat Astron, 10.1038/s41550-026-02847-0

    work page doi:10.1038/s41550-026-02847-0 2026

  18. [18]

    M., & Callister , T

    Antonini , F., Romero-Shaw , I. M., & Callister , T. 2025a, title Star Cluster Population of High Mass Black Hole Mergers in Gravitational Wave Data , , 134, 011401, 10.1103/PhysRevLett.134.011401

    work page doi:10.1103/physrevlett.134.011401

  19. [19]

    Antonini , F., Toonen , S., & Hamers , A. S. 2017, title Binary Black Hole Mergers from Field Triples: Properties, Rates, and the Impact of Stellar Evolution , Astrophys. J., 841, 77, 10.3847/1538-4357/aa6f5e

    work page doi:10.3847/1538-4357/aa6f5e 2017

  20. [20]

    Arca Sedda , M., Mapelli , M., Benacquista , M., & Spera , M. 2023, title Isolated and dynamical black hole mergers with B-POP: the role of star formation and dynamics, star cluster evolution, natal kicks, mass and spins, and hierarchical mergers , , 520, 5259, 10.1093/mnras/stad331

    work page doi:10.1093/mnras/stad331 2023

  21. [21]

    Arca Sedda , M., Paiella , L., Ugolini , C., et al. 2026, title Isolated or Dynamical? Tracing Black Hole Binary Formation through the Population of Gravitational-Wave Sources , arXiv e-prints, arXiv:2603.20430, 10.48550/arXiv.2603.20430

    work page doi:10.48550/arxiv.2603.20430 2026

  22. [22]

    2017, title MOCCA-SURVEY Database - I

    Askar , A., Szkudlarek , M., Gondek-Rosi \'n ska , D., Giersz , M., & Bulik , T. 2017, title MOCCA-SURVEY Database - I. Coalescing binary black holes originating from globular clusters , , 464, L36, 10.1093/mnrasl/slw177

    work page doi:10.1093/mnrasl/slw177 2017

  23. [23]

    Revising the Spin and Kick Connection in Isolated Binary Black Holes2024

    Baibhav , V., & Kalogera , V. 2024, title Revising the Spin and Kick Connection in Isolated Binary Black Holes , arXiv e-prints, arXiv:2412.03461, 10.48550/arXiv.2412.03461

    work page doi:10.48550/arxiv.2412.03461 2024

  24. [24]

    A., Adamcewicz, C., Doctor, Z., & Kalogera, V

    Banagiri, S., Callister, T. A., Adamcewicz, C., Doctor, Z., & Kalogera, V. 2025 a , title Structure and Skewness of the Effective Inspiral Spin Distribution of Binary Black Hole Mergers, The Astrophysical Journal, 990, 147, 10.3847/1538-4357/adf4c6

    work page doi:10.3847/1538-4357/adf4c6 2025

  25. [25]

    Banagiri, S., Thrane, E., & Lasky, P. D. 2025 b , Evidence for Three Subpopulations of Merging Binary Black Holes at Different Primary Masses, 2509.15646

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  26. [26]

    On the effective spin-mass ratio relation of binary black hole mergers that evolved in isolation

    Banerjee , S., & Olejak , A. 2024, title On the effective spin-mass ratio relation of binary black hole mergers that evolved in isolation , arXiv e-prints, arXiv:2411.15112, 10.48550/arXiv.2411.15112

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2411.15112 2024

  27. [27]

    S., Fragos , T., Qin , Y., et al

    Bavera , S. S., Fragos , T., Qin , Y., et al. 2020, title The origin of spin in binary black holes. Predicting the distributions of the main observables of Advanced LIGO , , 635, A97, 10.1051/0004-6361/201936204

    work page doi:10.1051/0004-6361/201936204 2020

  28. [28]

    L., Holz, D

    Belczynski, K., Wiktorowicz, G., Fryer, C. L., Holz, D. E., & Kalogera, V. 2012, title MISSING BLACK HOLES UNVEIL THE SUPERNOVA EXPLOSION MECHANISM , The Astrophysical Journal, 757, 91, 10.1088/0004-637X/757/1/91

    work page doi:10.1088/0004-637x/757/1/91 2012

  29. [29]

    E., et al

    Belczynski , K., Klencki , J., Fields , C. E., et al. 2020, title Evolutionary roads leading to low effective spins, high black hole masses, and O1/O2 rates for LIGO/Virgo binary black holes , , 636, A104, 10.1051/0004-6361/201936528

    work page doi:10.1051/0004-6361/201936528 2020

  30. [30]

    The first decade of gravitational-wave measurements of black hole spins

    Biscoveanu, S. 2026, The first decade of gravitational-wave measurements of black hole spins, 2606.06209

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  31. [31]

    A., Haster , C.-J., et al

    Biscoveanu , S., Callister , T. A., Haster , C.-J., et al. 2022, title The Binary Black Hole Spin Distribution Likely Broadens with Redshift , , 932, L19, 10.3847/2041-8213/ac71a8

    work page doi:10.3847/2041-8213/ac71a8 2022

  32. [32]

    2018, JAX : composable transformations of P ython+ N um P y programs, 0.3.13 http://github.com/jax-ml/jax

    Bradbury, J., Frostig, R., Hawkins, P., et al. 2018, JAX : composable transformations of P ython+ N um P y programs, 0.3.13 http://github.com/jax-ml/jax

    2018

  33. [33]

    2025, title Channels of Stellar-mass Black Hole Formation , , 987, 164, 10.3847/1538-4357/addd04

    Burrows , A., Wang , T., & Vartanyan , D. 2025, title Channels of Stellar-mass Black Hole Formation , , 987, 164, 10.3847/1538-4357/addd04

    work page doi:10.3847/1538-4357/addd04 2025

  34. [34]

    E., & Farr, W

    Callister, T., Fishbach, M., Holz, D. E., & Farr, W. M. 2020, title Shouts and Murmurs: Combining Individual Gravitational-wave Sources with the Stochastic Background to Measure the History of Binary Black Hole Mergers, The Astrophysical Journal Letters, 896, L32, 10.3847/2041-8213/ab9743

    work page doi:10.3847/2041-8213/ab9743 2020

  35. [35]

    A., Haster , C.-J., Ng , K

    Callister , T. A., Haster , C.-J., Ng , K. K. Y., Vitale , S., & Farr , W. M. 2021, title Who Ordered That? Unequal-mass Binary Black Hole Mergers Have Larger Effective Spins , , 922, L5, 10.3847/2041-8213/ac2ccc

    work page doi:10.3847/2041-8213/ac2ccc 2021

  36. [36]

    2020, title The impact of fallback on the compact remnants and chemical yields of core-collapse supernovae , , 495, 3751, 10.1093/mnras/staa1431

    Chan , C., M \"u ller , B., & Heger , A. 2020, title The impact of fallback on the compact remnants and chemical yields of core-collapse supernovae , , 495, 3751, 10.1093/mnras/staa1431

    work page doi:10.1093/mnras/staa1431 2020

  37. [37]

    S., Collaboration, V., & Collaboration, K

    Collaboration, L. S., Collaboration, V., & Collaboration, K. 2025, GWTC-4: Compact Binary Coalescences Observed by LIGO and Virgo During the O3b Observing Run, Zenodo, 10.5281/zenodo.16053484

    work page doi:10.5281/zenodo.16053484 2025

  38. [38]

    M., Vijaykumar , A., et al

    Dorozsmai , A., Romero-Shaw , I. M., Vijaykumar , A., et al. 2025, title Hierarchical Triples vs. Globular Clusters: Binary black hole merger eccentricity distributions compete and evolve with redshift , , 10.1093/mnras/staf1938

    work page doi:10.1093/mnras/staf1938 2025

  39. [39]

    2022, Precision Requirements for Monte Carlo Sums within Hierarchical Bayesian Inference, 2204.00461

    Essick, R., & Farr, W. 2022, Precision Requirements for Monte Carlo Sums within Hierarchical Bayesian Inference, 2204.00461

    work page arXiv 2022

  40. [40]

    W., Zevin, M., et al

    Essick, R., Coughlin, M. W., Zevin, M., et al. 2025, title Compact binary coalescence sensitivity estimates with injection campaigns during the LIGO-Virgo-KAGRA Collaborations' fourth observing run, Phys. Rev. D, 112, 102001, 10.1103/44x3-hv3y

    work page doi:10.1103/44x3-hv3y 2025

  41. [41]

    M., Edelman , B., Zevin , M., et al

    Farah , A. M., Edelman , B., Zevin , M., et al. 2023, title Things That Might Go Bump in the Night: Assessing Structure in the Binary Black Hole Mass Spectrum , The Astrophysical Journal, 955, 107, 10.3847/1538-4357/aced02

    work page doi:10.3847/1538-4357/aced02 2023

  42. [42]

    M., Stevenson , S., Miller , M

    Farr , W. M., Stevenson , S., Miller , M. C., et al. 2017, title Distinguishing spin-aligned and isotropic black hole populations with gravitational waves , , 548, 426, 10.1038/nature23453

    work page doi:10.1038/nature23453 2017

  43. [43]

    Fishbach, D

    Fishbach, M., Holz, D. E., & Farr, W. M. 2018, title Does the Black Hole Merger Rate Evolve with Redshift? The Astrophysical Journal Letters, 863, L41, 10.3847/2041-8213/aad800

    work page doi:10.3847/2041-8213/aad800 2018

  44. [44]

    2026, title Transitions in the Mass-ratio and Spin Properties of Binary Black Holes in GWTC-5 , arXiv e-prints, arXiv:2606.14472

    Flanagan , E., Antonini , F., Callister , T., et al. 2026, title Transitions in the Mass-ratio and Spin Properties of Binary Black Holes in GWTC-5 , arXiv e-prints, arXiv:2606.14472. 2606.14472

    work page arXiv 2026

  45. [45]

    L., Belczynski , K., Wiktorowicz , G., et al

    Fryer , C. L., Belczynski , K., Wiktorowicz , G., et al. 2012, title Compact Remnant Mass Function: Dependence on the Explosion Mechanism and Metallicity , , 749, 91, 10.1088/0004-637X/749/1/91

    work page doi:10.1088/0004-637x/749/1/91 2012

  46. [46]

    2019, title Most Black Holes Are Born Very Slowly Rotating , , 881, L1, 10.3847/2041-8213/ab339b

    Fuller , J., & Ma , L. 2019, title Most Black Holes Are Born Very Slowly Rotating , , 881, L1, 10.3847/2041-8213/ab339b

    work page doi:10.3847/2041-8213/ab339b 2019

  47. [47]

    Compactness Peaks and Subpopulations: Probing Stellar Physics and Formation Channels of Merging Binary Black Holes

    Galaudage, S. 2026, Compactness Peaks and Subpopulations: Probing Stellar Physics and Formation Channels of Merging Binary Black Holes, 2605.25994

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  48. [48]

    2025, title Compactness peaks: An astrophysical interpretation of the mass distribution of merging binary black holes , , 694, A186, 10.1051/0004-6361/202451654

    Galaudage , S., & Lamberts , A. 2025, title Compactness peaks: An astrophysical interpretation of the mass distribution of merging binary black holes , , 694, A186, 10.1051/0004-6361/202451654

    work page doi:10.1051/0004-6361/202451654 2025

  49. [49]

    2018, title Spin orientations of merging black holes formed from the evolution of stellar binaries , , 98, 084036, 10.1103/PhysRevD.98.084036

    Gerosa , D., Berti , E., O'Shaughnessy , R., et al. 2018, title Spin orientations of merging black holes formed from the evolution of stellar binaries , , 98, 084036, 10.1103/PhysRevD.98.084036

    work page doi:10.1103/physrevd.98.084036 2018

  50. [50]

    Godfrey , J., Edelman , B., & Farr , B. 2023, title Cosmic Cousins: Identification of a Subpopulation of Binary Black Holes Consistent with Isolated Binary Evolution , arXiv e-prints, arXiv:2304.01288, 10.48550/arXiv.2304.01288

    work page doi:10.48550/arxiv.2304.01288 2023

  51. [51]

    B., & Fragione , G

    Grishin , E., Perets , H. B., & Fragione , G. 2018, title Quasi-secular evolution of mildly hierarchical triple systems: analytics and applications for GW sources and hot Jupiters , Mon. Not. R. Astron. Soc., 481, 4907, 10.1093/mnras/sty2477

    work page doi:10.1093/mnras/sty2477 2018

  52. [52]

    2022, title Understanding How Fast Black Holes Spin by Analyzing Data from the Second Gravitational-wave Catalogue , , 928, 75, 10.3847/1538-4357/ac54a3

    Hoy , C., Fairhurst , S., Hannam , M., & Tiwari , V. 2022, title Understanding How Fast Black Holes Spin by Analyzing Data from the Second Gravitational-wave Catalogue , , 928, 75, 10.3847/1538-4357/ac54a3

    work page doi:10.3847/1538-4357/ac54a3 2022

  53. [53]

    2024, Hints of spin-magnitude correlations and a rapidly spinning subpopulation of binary black holes, 2411.02252

    Hussain, A., Isi, M., & Zimmerman, A. 2024, Hints of spin-magnitude correlations and a rapidly spinning subpopulation of binary black holes, 2411.02252

    work page arXiv 2024

  54. [54]

    2013, title Natal kicks of stellar mass black holes by asymmetric mass ejection in fallback supernovae , , 434, 1355, 10.1093/mnras/stt1106

    Janka , H.-T. 2013, title Natal kicks of stellar mass black holes by asymmetric mass ejection in fallback supernovae , , 434, 1355, 10.1093/mnras/stt1106

    work page doi:10.1093/mnras/stt1106 2013

  55. [55]

    2024, title Interplay between neutrino kicks and hydrodynamic kicks of neutron stars and black holes , , 369, 80, 10.1007/s10509-024-04343-1

    Janka , H.-T., & Kresse , D. 2024, title Interplay between neutrino kicks and hydrodynamic kicks of neutron stars and black holes , , 369, 80, 10.1007/s10509-024-04343-1

    work page doi:10.1007/s10509-024-04343-1 2024

  56. [56]

    2023, title Binary black holes population and cosmology in new lights: signature of PISN mass and formation channel in GWTC-3 , , 523, 4539, 10.1093/mnras/stad1373

    Karathanasis , C., Mukherjee , S., & Mastrogiovanni , S. 2023, title Binary black holes population and cosmology in new lights: signature of PISN mass and formation channel in GWTC-3 , , 523, 4539, 10.1093/mnras/stad1373

    work page doi:10.1093/mnras/stad1373 2023

  57. [57]

    1962, title Secular perturbations of asteroids with high inclination and eccentricity , Astron

    Kozai , Y. 1962, title Secular perturbations of asteroids with high inclination and eccentricity , Astron. J., 67, 591, 10.1086/108790

    work page doi:10.1086/108790 1962

  58. [58]

    Lidov , M. L. 1962, title The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies , Planet. Space Sci., 9, 719, 10.1016/0032-0633(62)90129-0

    work page doi:10.1016/0032-0633(62)90129-0 1962

  59. [59]

    2018, title Black Hole and Neutron Star Binary Mergers in Triple Systems: Merger Fraction and Spin-Orbit Misalignment , Astrophys

    Liu , B., & Lai , D. 2018, title Black Hole and Neutron Star Binary Mergers in Triple Systems: Merger Fraction and Spin-Orbit Misalignment , Astrophys. J., 863, 68, 10.3847/1538-4357/aad09f

    work page doi:10.3847/1538-4357/aad09f 2018

  60. [60]

    Lovegrove , E., & Woosley , S. E. 2013, title Very Low Energy Supernovae from Neutrino Mass Loss , , 769, 109, 10.1088/0004-637X/769/2/109

    work page doi:10.1088/0004-637x/769/2/109 2013

  61. [61]

    Maga \ n a Hernandez , I., & Palmese , A. 2025, title Astrophysics informed Gaussian processes for gravitational-wave populations: Evidence for the onset of the pair-instability supernova mass gap , arXiv e-prints, arXiv:2508.19208, 10.48550/arXiv.2508.19208

    work page doi:10.48550/arxiv.2508.19208 2025

  62. [62]

    2016, title Estimates of black hole natal kick velocities from observations of low-mass X-ray binaries , , 456, 578, 10.1093/mnras/stv2733

    Mandel , I. 2016, title Estimates of black hole natal kick velocities from observations of low-mass X-ray binaries , , 456, 578, 10.1093/mnras/stv2733

    work page doi:10.1093/mnras/stv2733 2016

  63. [63]

    A., & Mandel , I

    Mangipudi , A., Grishin , E., Trani , A. A., & Mandel , I. 2022, title Extreme Eccentricities of Triple Systems: Analytic Results , , 934, 44, 10.3847/1538-4357/ac7958

    work page doi:10.3847/1538-4357/ac7958 2022

  64. [64]

    Mapelli , M., Dall'Amico , M., Bouffanais , Y., et al. 2021, title Hierarchical black hole mergers in young, globular and nuclear star clusters: the effect of metallicity, spin and cluster properties , , 505, 339, 10.1093/mnras/stab1334

    work page doi:10.1093/mnras/stab1334 2021

  65. [65]

    Martinez , M. A. S., O'Connor , C. E., K ro g lu , F., & Rasio , F. A. 2026, title Getting Tilted: Random Walk of Binary Black Hole Spin-Orbit Alignment in Dense Star Clusters , arXiv e-prints, arXiv:2606.21691, 10.48550/arXiv.2606.21691

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2606.21691 2026

  66. [66]

    2017, title Mind Your Ps and Qs: The Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars , , 230, 15, 10.3847/1538-4365/aa6fb6

    Moe , M., & Di Stefano , R. 2017, title Mind Your Ps and Qs: The Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars , , 230, 15, 10.3847/1538-4365/aa6fb6

    work page internal anchor Pith review doi:10.3847/1538-4365/aa6fb6 2017

  67. [67]

    2026, title Measurement prospects for the pair-instability mass cutoff with gravitational waves , , 113, 103021, 10.1103/sqy9-nnqq

    Mould , M., Heinzel , J., \'A lvarez-L \'o pez , S., et al. 2026, title Measurement prospects for the pair-instability mass cutoff with gravitational waves , , 113, 103021, 10.1103/sqy9-nnqq

    work page doi:10.1103/sqy9-nnqq 2026

  68. [68]

    Nadezhin , D. K. 1980, title Some Secondary Indications of Gravitational Collapse , , 69, 115, 10.1007/BF00638971

    work page doi:10.1007/bf00638971 1980

  69. [69]

    M., Rasio , F

    O'Leary , R. M., Rasio , F. A., Fregeau , J. M., Ivanova , N., & O'Shaughnessy , R. 2006, title Binary Mergers and Growth of Black Holes in Dense Star Clusters , , 637, 937, 10.1086/498446

    work page doi:10.1086/498446 2006

  70. [70]

    2021, title The Implications of High Black Hole Spins for the Origin of Binary Black Hole Mergers , , 921, L2, 10.3847/2041-8213/ac2f48

    Olejak , A., & Belczynski , K. 2021, title The Implications of High Black Hole Spins for the Origin of Binary Black Hole Mergers , , 921, L2, 10.3847/2041-8213/ac2f48

    work page doi:10.3847/2041-8213/ac2f48 2021

  71. [71]

    L., Belczynski , K., & Baibhav , V

    Olejak , A., Fryer , C. L., Belczynski , K., & Baibhav , V. 2022, title The role of supernova convection for the lower mass gap in the isolated binary formation of gravitational wave sources , , 516, 2252, 10.1093/mnras/stac2359

    work page doi:10.1093/mnras/stac2359 2022

  72. [72]

    2024, title Unequal-mass highly spinning binary black hole mergers in the stable mass transfer formation channel , , 689, A305, 10.1051/0004-6361/202450480

    Olejak , A., Klencki , J., Xu , X.-T., et al. 2024, title Unequal-mass highly spinning binary black hole mergers in the stable mass transfer formation channel , , 689, A305, 10.1051/0004-6361/202450480

    work page doi:10.1051/0004-6361/202450480 2024

  73. [73]

    BBH-Genesis: Disentangling Binary Black Hole Formation Channels with GWTC-4

    Padhyegurjar, S., & Mukherjee, S. 2026, BBH-Genesis: Disentangling Binary Black Hole Formation Channels with GWTC-4, 2606.00234

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  74. [74]

    Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro

    Phan , D., Pradhan , N., & Jankowiak , M. 2019, title Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro , arXiv e-prints, arXiv:1912.11554, 10.48550/arXiv.1912.11554

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1912.11554 2019

  75. [75]

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

    Plunkett, C., Callister, T., Zevin, M., & Vitale, S. 2026, Signatures of a subpopulation of hierarchical mergers in the GWTC-4 gravitational-wave dataset, 2601.07908

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  76. [76]

    Reversible-jump MCMC reveals binary black hole subpopulations with distinct redshift evolution

    Qiu Cheng , A., Toubiana , A., Biscoveanu , S., & Gair , J. 2026, title Reversible-jump MCMC reveals binary black hole subpopulations with distinct redshift evolution , arXiv e-prints, arXiv:2605.25980, 10.48550/arXiv.2605.25980

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.25980 2026

  77. [77]

    2008, title Analysis of spin precession in binary black hole systems including quadrupole-monopole interaction , , 78, 044021, 10.1103/PhysRevD.78.044021

    Racine , \'E . 2008, title Analysis of spin precession in binary black hole systems including quadrupole-monopole interaction , , 78, 044021, 10.1103/PhysRevD.78.044021

    work page doi:10.1103/physrevd.78.044021 2008

  78. [78]

    M., Breivik, K., & Creighton, J

    Ray, A., Hernandez, I. M., Breivik, K., & Creighton, J. 2024, Searching for binary black hole sub-populations in gravitational wave data using binned Gaussian processes, 2404.03166

    work page arXiv 2024

  79. [79]

    2026, title On the Astrophysical Origin of Binary Black Hole Subpopulations: A Tale of Three Channels? , arXiv e-prints, arXiv:2603.17987, 10.48550/arXiv.2603.17987

    Ray , A., Mukherjee , S., Zevin , M., & Kalogera , V. 2026, title On the Astrophysical Origin of Binary Black Hole Subpopulations: A Tale of Three Channels? , arXiv e-prints, arXiv:2603.17987, 10.48550/arXiv.2603.17987

    work page doi:10.48550/arxiv.2603.17987 2026

  80. [80]

    When the black holes align: a subpopulation of aligned massive binary black holes observed via gravitational waves

    Rinaldi, S., Wong, C., Vaccaro, M. P., et al. 2026, title When the black holes align: a subpopulation of aligned massive binary black holes observed via gravitational waves , 2606.23305

    work page internal anchor Pith review Pith/arXiv arXiv 2026

Showing first 80 references.