Pith. sign in

REVIEW 3 major objections 6 minor 170 references

A four-dimensional data-driven map of binary black hole masses and spins reveals four mass-based subpopulations with new spin correlations that constrain which formation channels dominate where.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-31 01:52 UTC pith:CE7G5T4K

load-bearing objection First real 4D data-driven BBH map on GWTC-5; the density work holds, the channel story is still qualitative. the 3 major comments →

arxiv 2607.28622 v1 pith:CE7G5T4K submitted 2026-07-30 astro-ph.HE gr-qc

A Four-dimensional Model-agnostic Probe into the Astrophysical Origins of Binary Black Hole Subpopulations

Anarya Ray , Vicky Kalogera This is my paper
classification astro-ph.HE gr-qc
keywords binary black holesgravitational wavesstellar mass black holescompact binary starsstellar populationshierarchical mergerspopulation inferenceeffective spin
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Gravitational-wave catalogs show multiple groups of merging black-hole pairs, but theorists disagree on how much each formation route contributes because models of stellar evolution and dense environments are uncertain. Strongly parametric population fits often bake those uncertainties into the answer, while flexible methods have struggled to handle more than three parameters at once and therefore miss correlations. This Letter reconstructs, without strong population priors, the joint four-dimensional distribution of primary mass, mass ratio, effective aligned spin, and effective precessing spin for the latest LIGO-Virgo-KAGRA catalog. The reconstruction isolates four subpopulations that live in different primary-mass windows and carry distinct mass-ratio and spin fingerprints, including previously unseen correlations that appear only inside specific mass slices. Those fingerprints are then read as relative abundances of isolated binary evolution, first-generation dynamical assembly, and hierarchical mergers, giving a model-agnostic census of how the channels share the observed population across mass.

Core claim

The first fully data-driven reconstruction of the joint four-dimensional BBH distribution in primary mass, mass ratio, effective inspiral spin, and effective precessing spin shows four distinct mass-spanning subpopulations, each with its own mass-ratio and spin structure, plus new mass-restricted correlations (most notably a broadening of effective inspiral spin with effective precessing spin above roughly 44 solar masses that is not produced by marginalizing over mass or mass ratio). These features supply model-agnostic constraints on the relative contributions of isolated evolution, dynamical first-generation assembly, and hierarchical mergers in each mass window.

What carries the argument

GPU-accelerated binned Gaussian processes: the merger-rate density is a piecewise-constant function on a four-dimensional grid whose logarithmic values are drawn from a Gaussian-process prior with an exponential-quadratic kernel; Hamiltonian Monte Carlo on GPUs samples the high-dimensional hyperposterior while the Kronecker structure of the kernel keeps the covariance factorization tractable.

Load-bearing premise

The mapping from observed shapes in effective spins and mass ratio onto named formation channels is qualitative and can be degenerate; if those fingerprints are incomplete, the abundance claims fail even when the four-dimensional density is correctly recovered.

What would settle it

A larger catalog or a targeted mixture model that recovers a clean elliptical feature in the high-mass effective-spin plane, or that erases the reported chi-eff broadening with chi-p inside every high-mass and mass-ratio slice, would directly contradict the channel assignments drawn from the four-dimensional map.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The ~10 solar-mass peak is dominated by slowly spinning, preferentially aligned systems consistent with isolated evolution, with only a modest anti-aligned or in-plane fraction that may admit some dynamical or hierarchical contribution.
  • The 15–25 solar-mass window favors unequal masses and positively skewed aligned spins, requiring a mixture of hierarchical (likely AGN-disk) mergers and isolated sub-channels rather than either alone.
  • The 30–40 solar-mass window is consistent with isotropic, slowly spinning, equal-mass first-generation dynamical assembly, with possible triple-system contributions indicated by elevated precessing spin.
  • Above ~44 solar masses the population is not exclusively hierarchical: isotropic high- and moderate-spin components coexist, with hierarchical mergers growing in relative abundance toward higher mass but never monopolizing the slice.
  • No statistically significant pair-instability mass gap or exclusive hierarchical onset near 45 solar masses is required by the present four-dimensional reconstruction.

Where Pith is reading between the lines

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

  • Because the high-mass chi-eff–chi-p broadening survives every mass and mass-ratio cut, future parametric mixture models should treat it as an intrinsic two-component isotropic feature rather than a marginalization artifact.
  • The absence of a recovered pair-instability cut-off implies that claims of a sharp ~45 solar-mass edge in strongly modeled analyses are prior-sensitive and should be re-tested against the same four-dimensional nonparametric density.
  • Scaling the same binned-GP machinery to five dimensions that include redshift would directly measure how the relative channel abundances evolve with cosmic time, a measurement the present Letter flags as already computationally feasible.

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

3 major / 6 minor

Summary. This Letter presents the first fully data-driven reconstruction of the joint four-dimensional BBH distribution in (m1, q, χeff, χp) from GWTC-5, using GPU-accelerated binned Gaussian processes with a Kronecker-separable exponential-quadratic kernel, injection-based selection correction, and a Monte Carlo variance penalty on the hierarchical likelihood (Eq. 1; App. D–E). From the inferred rate densities the authors identify four mass-spanning subpopulations (m1 windows in §3.2), quantify differences via Jensen–Shannon divergences (Fig. 2), and report mass-restricted correlations—most notably χeff broadening with χp for m1 ≳ 44 M⊙ that persists after slicing in m1 (Fig. 4) and q (Fig. 5). Section 4 maps these features onto relative contributions of isolated binary evolution, 1G+1G dynamical assembly, and hierarchical mergers across mass, arguing against exclusively hierarchical high-mass origins and against a clear pair-instability onset near ∼45 M⊙ in the current data.

Significance. If the 4D reconstruction and the reported conditional correlations hold, the work is a genuine methodological and empirical step beyond existing 3D non-parametric and strongly modeled mixture analyses. Scaling flexible population inference to four BBH parameters with publicly released code (gppop), Kronecker GP structure (App. E), variance-penalized likelihood (Eq. D8), and documented robustness to κ and binning (App. C) is a concrete technical contribution. The mass-conditional χeff–χp structure at high mass, checked against marginalization artifacts in m1 and q, is a falsifiable empirical result that can guide subsequent parametric mixture models. The channel-abundance narrative in §4 is more interpretive than quantitative, but the density reconstruction itself is of clear interest to the GW population community.

major comments (3)
  1. [§4, Abstract] §4 and the Abstract claim “novel insights into the abundances of specific subchannels” and several exclusionary statements (e.g., §4.2: hierarchical AGN mergers “cannot be the only channel”; §4.4: high-mass subpopulation “inconsistent with… exclusively hierarchical” origin; no concrete PI cut-off). These rest on qualitative spin/q fingerprints and visual reading of posterior-median heatmaps, not a quantitative mixture likelihood or comparison to theory grids. The 4D density results can stand without those abundance claims; please either (i) reframe §4/Abstract as hypothesis-generating consistency arguments with explicit degeneracy caveats (super-Eddington/tidal isolated channels vs AGN hierarchical; triples vs clusters), or (ii) add a minimal quantitative comparison (e.g., posterior predictive checks or mixture weights against published channel predictions) so that “abundance” language i
  2. [§3.2] §3.2 defines four subpopulation windows—(8,15), (15,25), (30,41), (44,200) M⊙—by eye around clusters in the m1–χeff plane, with a gap between 25–30 M⊙ and 41–44 M⊙ left unassigned. JS divergences (Fig. 2) show the conditional distributions differ, but do not justify the precise edges or the number of components. Because every subsequent correlation and channel assignment is conditioned on these windows, please either demonstrate stability under reasonable edge shifts / an extra intermediate bin, or replace fixed windows with a data-driven change-point or clustering criterion and show that the key claims (especially high-mass χeff–χp broadening and the SP2 unequal-q / positive-χeff features) survive.
  3. [Appendix A; Figs. 3–5] Appendix A notes that unphysical regions of the χeff–χp plane are not zeroed a priori, contrary to the physical support of those parameters. The authors argue sparse neighboring data make the bias negligible, but this is untested. Because the headline high-mass result is precisely a χeff–χp correlation (Figs. 3–5), please either impose the physical support constraint (set nγ=0 on unphysical bins) and rerun, or provide a controlled test showing that posterior medians and credible regions in the physical high-mass region are unchanged when unphysical bins are removed or heavily down-weighted.
minor comments (6)
  1. [Table 1; Appendix C] Table 1 and the default binning use highly irregular χeff/χp edges; App. C shows Model Z with uniform spin bins yields consistent 1D conditionals and key 2D features, which is good—please state the default vs Z comparison more prominently in the main text (one sentence near Table 1) so readers need not dig into the appendix for reassurance.
  2. [§3.1–3.2; Appendix B] Fig. 1 caption and main text refer to “four distinct clusters” in m1–χeff; the heatmaps are posterior medians only. Pointing readers explicitly to the fractional-uncertainty panels in App. B (Figs. 6–9) when each new correlation is introduced would strengthen the significance claims.
  3. [§2; §5] κ is fixed to the GWTC-5 median (2.7) with robustness at 1.9 and 3.9 (Models X,Y). A brief statement that redshift evolution is not jointly inferred, and that (m1,q,χeff,χp,z) is left to future work (§5), would clarify scope in §2.
  4. [Throughout] Typographical/formatting issues: “F our-dimensional” in the title block; “L VK” spacing; “bear 0.2” → “near 0.2” (§3.1); “sunject” → “subject” (App. A); “two-dimenstional” (§3.3); inconsistent “χ ef f” spacing throughout. Clean these before acceptance.
  5. [§4.1; §4.4] §4.1 quotes a 22.4+11.5−9.7% anti-aligned fraction and §4.4 a 30.6+21.2−15.4% q>0.7 fraction; please define exactly how these percentages are computed from the binned posterior (which bins, which mass slice, prior volume) in the text or appendix.
  6. [§1; §3] The parallel strongly modeled analysis by Guttman et al. (2026) is cited; a short explicit comparison of which mass-conditional features agree or disagree would help place the model-agnostic results.

Circularity Check

0 steps flagged

No significant circularity: 4D BGP reconstruction is a standard hierarchical inference from GWTC-5; channel claims are post-hoc interpretation, not inputs renamed as predictions.

full rationale

The load-bearing empirical chain is Eq. (1) piecewise rate densities under a GP prior, sampled from the variance-penalized hierarchical likelihood (D6–D8) on public GWTC-5 PE and injection sets. Conditional densities, JS divergences, and the χeff–χp checks in Figs. 4–5 are functionals of that posterior, not quantities fitted then re-labeled as predictions. Mass-slice edges in §3.2 are analyst-chosen around visual clusters—a methodological choice that can bias interpretation, but not a definitional reduction of output to input. §4 channel-abundance statements are qualitative mappings from spin/q shapes to formation scenarios; they do not claim a first-principles derivation that algebraically equals those fingerprints. Self-citations (Sridhar et al. 2025; Ray et al. 2026) supply prior 3D motivation and comparison baselines; they are not uniqueness theorems or ansatze that force the 4D density. Appendix C robustness to binning/κ further shows the reported features are not forced by a single prior choice. No step reduces by construction to its own inputs.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 1 invented entities

The empirical core assumes standard hierarchical GW population inference plus a flexible GP-smoothed piecewise rate. Channel conclusions add domain lore mapping spin/q morphology to formation physics. Free choices that affect claimed subpopulations include binning, fixed κ, GP kernel/hyperpriors, variance-cut exponent, and analyst-defined mass windows.

free parameters (6)
  • GP length scales λ_θ for (m1, q, χeff, χp) = Inferred (not numerically tabulated in text)
    Inferred under LogNormal hyperpriors tied to bin-center separations; they set the minimum recoverable feature scale and thus which correlations can appear.
  • GP covariance amplitude σ_GP and mean μ_GP = Inferred
    Control overall rate contrast and baseline log-density; HalfNormal/TruncatedNormal hyperpriors in App. D.
  • Redshift evolution index κ = 2.7 (default)
    Fixed to median 2.7 from GWTC-5 population papers; varied only in robustness tests (1.9, 3.9).
  • Four subpopulation mass window edges = 8,15,25,30,41,44,200 M⊙
    Chosen by hand in §3.2 as (8–15), (15–25), (30–41), (44–200) M⊙ around visual clusters rather than jointly inferred.
  • Spin and mass-ratio bin edges = Table 1 default grid
    Irregular χeff/χp grids and 10 q bins (Table 1) set resolution; alternate Model Z bins tested in App. C.
  • MC variance penalty exponent n = 30
    Asymptotic cut on log-likelihood variance uses n=30 (tested 30–75) in App. D; affects which hypersamples are down-weighted.
axioms (5)
  • domain assumption Detected BBHs are an inhomogeneous Poisson process with selection effects correctable by found injections above a FAR threshold.
    Standard Loredo/Mandel hierarchical setup stated in §2; underpins the entire likelihood.
  • ad hoc to paper Log rate densities across bins are drawn from a Gaussian process with exponential-quadratic kernel (Kronecker-separable across parameters).
    Core nonparametric prior (§2, App. D–E); alternative kernels are not explored beyond discussion in App. A.
  • domain assumption Redshift factors as (1+z)^{κ-1} with κ independent of m1,q,χeff,χp in the default model.
    §2 fixes separable redshift evolution; authors argue shape bias is small and test κ variations in App. C.
  • domain assumption Effective-spin and mass-ratio morphologies map qualitatively onto isolated vs dynamical 1G+1G vs hierarchical (and AGN vs cluster) channels.
    Load-bearing for §4 abundance claims; standard in the field but not re-derived here against simulations.
  • ad hoc to paper Nonzero model support in unphysical χeff–χp regions does not materially bias physical-region posteriors given sparse neighboring data.
    App. A acknowledges the issue and argues it away without a hard physicality constraint run.
invented entities (1)
  • Four mass-based BBH subpopulations (SP1–SP4) no independent evidence
    purpose: Organize distinct conditional (q, χeff, χp) structures and host channel interpretations.
    Operationally defined by chosen m1 windows plus JS divergence comparisons; useful taxonomy but not a new physical object with an external conserved charge or predicted microphysical scale.

pith-pipeline@v1.2.0-daily-grok45 · 32516 in / 3958 out tokens · 87790 ms · 2026-07-31T01:52:12.934925+00:00 · methodology

0 comments
read the original abstract

There is strong evidence of multiple binary black hole~(BBH) subpopulations in the cumulative gravitational wave catalog by the LIGO-Virgo-KAGRA collaboration that likely originate through distinct evolutionary channels. The astrophysical interpretation of this complex underlying population is subject to theoretical uncertainties in treatments of binary stellar evolution, core collapse, and host environments. Due to a lack of robust predictions and the sheer diversity of plausible features, strongly modelled population analyses often lead to prior-driven conclusions. On the other hand, flexible alternatives are often difficult to scale in higher dimensions, which can lead to a loss of critical information on astrophysically meaningful correlations. In this \textit{Letter}, we present the first data-driven reconstruction of the joint four-dimensional distribution of BBH primary masses, mass ratios, effective inspiral and effective precessing spin parameters, which yields novel model-agnostic constraints on the astrophysical origins of BBH subpopulations. We characterize four distinct subpopulations spanning different ranges of BBH masses and report new correlations in these specific mass ranges that are beyond the reach of strongly modeled parametrizations and lower-dimensional data-driven frameworks. Our results unveil novel insights into the abundances of specific subchannels of isolated binary evolution, dynamical assembly, and hierarchical mergers across various mass ranges in the astrophysical BBH population.

Figures

Figures reproduced from arXiv: 2607.28622 by Anarya Ray, Vicky Kalogera.

Figure 1
Figure 1. Figure 1: Marginal distributions in 1 and 2 dimensions. In the diagonal panels, the shaded regions represent 90% posterior credible intervals on the marginal 1-dimensional population distributions and the solid lines represent the medians. In the off-diagonal panels, the heat map represents the posterior median on the two-dimensional population density marginalized over the remaining BBH parameters and the orange li… view at source ↗
Figure 2
Figure 2. Figure 2: One dimensional distributions conditioned on primary mass and the JS divergences between the distributions corresponding to the different mass-ranges, -1 0 1 Âeff 0.00 0.25 0.50 0.75 1.00 Â p m1 2 (8; 15) M¯ 10 −5 10 −3 10 −1 10 1 -1 0 1 Âeff 0.00 0.25 0.50 0.75 1.00 Â p m1 2 (15; 25) M¯ 10 −5 10 −3 10 −1 10 1 -1 0 1 Âeff 0.00 0.25 0.50 0.75 1.00 Â p m1 2 (30; 41) M¯ 10 −5 10 −3 10 −1 10 1 -1 0 1 Âeff 0.00… view at source ↗
Figure 3
Figure 3. Figure 3: Posterior median of the two-dimensional distributions (density heatmap and the corresponding 95%, 90%, and 50% contours) in different mass-ranges. mass ratio and a broadening of the χef f dis￾tribution with increasing mass ratios, unlike subpopulations 1 and 2. 4. Subpopulation 4, which comprises of high mass (m1 > 44M⊙), prefers unequal mass ratios but has higher support at q > 0.7 than subpopu- [PITH_FU… view at source ↗
Figure 4
Figure 4. Figure 4: Posterior median of the χeff −χp distributions (density heatmap and the corresponding 95%, 90%, and 50% contours) in specific mass ranges above 44M⊙, -1 0 1 Âeff 0.00 0.25 0.50 0.75 1.00 Â p m1 2 (8; 15) M¯ , q < 0:7 10 −5 10 −3 10 −1 10 1 -1 0 1 Âeff 0.00 0.25 0.50 0.75 1.00 Â p m1 2 (15; 25) M¯ , q < 0:7 10 −5 10 −3 10 −1 10 1 -1 0 1 Âeff 0.00 0.25 0.50 0.75 1.00 Â p m1 2 (30; 41) M¯ , q < 0:7 10 −5 10 −… view at source ↗
Figure 5
Figure 5. Figure 5: Posterior median of the χeff −χp distributions (density heatmap and the corresponding 95%, 90%, and 50% contours) in different mass and mass ratio ranges. lation 2, has a broad χef f distribution symmetric about zero and prefers higher χp values than all other subpopulations. There is evidence of a broadening of the χef f distribution with in￾creasing χp in this mass range alone and no significant correlat… view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Posterior median (first, third, and fifth row) and fractional uncertainties (second, fourth, and sixth row) of the two-dimensional distributions in different mass and mass ratio ranges [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Posterior median (top) and fractional uncertainty (bottom)of the χeff −χp distribution in specific mass ranges above 44M⊙, To avoid clutter, we do not reproduce every single plot presented in the main text for all three models. We instead show in Figures 10, and 11, the key results, namely the conditional one-dimensional distributions in various mass ranges, the joint χef f − χp broadening at high masses, … view at source ↗
Figure 9
Figure 9. Figure 9: Posterior median (first and third row) and fractional uncertainties (second and fourth row) of the χeff − χp distributions in different mass and mass ratio ranges. (σ γ V T ) 2 = − (µ γ V T ) 2 Ndraw + 1 N2 draw X j∼p(θ⃗|det, draw) " 1 pdraw(m1,j , qj , χeff,j , χp,j , zj ) 1 m1,j dV dz [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: One dimensional distributions conditioned on primary mass for the default binning choice (row 1 ), and models X,Y,Z (rows 2,3,4 ) σ 2 log p(d⃗|⃗n) = X γ n 2 γ (σ γ V T ) 2 + X i P γ n 2 γ (σ γ w(di))2 P γ nγµ γ w(di) 2 . (D7) Here, the variance in the log-likelihood estimator (σ 2 log p(d⃗|⃗n) ) due to the finite number of Monte Carlo samples can become large for certain values of hyperparameters which … view at source ↗
Figure 11
Figure 11. Figure 11: Robustness of the χeff − χp (row 1 ) broadening at high masses, the χeff − q broadening in the 15 − 25M⊙ (row 2 ) and 30 − 40 (row 3) mass ranges, and the χp − q broadening in the 30 − 40M⊙ range (row 4 ) against variations in binning and κ values (from left to right models default, X, Y, and Z). required by HMC) we impose this variance-cut asymptotically and modify the log-likelihood function as follows:… view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

170 extracted references · 1 canonical work pages

  1. [1]

    An introduction to Bayesian inference in gravitational-wave astronomy: parameter estimation, model selection, and hierarchical models

    Thrane, Eric and Talbot, Colm. An introduction to Bayesian inference in gravitational-wave astronomy: parameter estimation, model selection, and hierarchical models. Publ. Astron. Soc. Austral. 2019. doi:10.1017/pasa.2019.2. arXiv:1809.02293

    Pith/arXiv arXiv 2019

  2. [2]

    Loredo , title =

    Thomas J. Loredo , title =. 2004 , publisher =. doi:10.1063/1.1835214 , url =

    doi:10.1063/1.1835214 2004

  3. [3]

    and Taylor, Stephen R

    Vitale, Salvatore and Gerosa, Davide and Farr, Will M. and Taylor, Stephen R. Inferring the properties of a population of compact binaries in presence of selection effects. 2020. doi:10.1007/978-981-15-4702-7\_45-1. arXiv:2007.05579

    Pith/arXiv arXiv 2020

  4. [4]

    Reconstructing phenomenological distributions of compact binaries via gravitational wave observations , author =. Phys. Rev. D , volume =. 2019 , month =. doi:10.1103/PhysRevD.100.043012 , url =

    doi:10.1103/physrevd.100.043012 2019

  5. [5]

    and Gair, Jonathan R

    Mandel, Ilya and Farr, Will M. and Gair, Jonathan R. Extracting distribution parameters from multiple uncertain observations with selection biases. Mon. Not. Roy. Astron. Soc. 2019. doi:10.1093/mnras/stz896. arXiv:1809.02063

    Pith/arXiv arXiv 2019

  6. [6]

    Farr , title =

    Will M. Farr , title =. Research Notes of the AAS , abstract =. 2019 , month =. doi:10.3847/2515-5172/ab1d5f , url =

    doi:10.3847/2515-5172/ab1d5f 2019

  7. [7]

    2022 , eprint=

    Precision Requirements for Monte Carlo Sums within Hierarchical Bayesian Inference , author=. 2022 , eprint=

    2022

  8. [8]

    Journal of Open Source Software , doi =

    Colm Talbot and Amanda Farah and Shanika Galaudage and Jacob Golomb and Hui Tong , title =. Journal of Open Source Software , doi =. 2025 , publisher =

    2025

  9. [9]

    Nonparametric Inference of the Population of Compact Binaries from Gravitational-wave Observations Using Binned Gaussian Processes

    Ray, Anarya and Maga \ n a Hernandez, Ignacio and Mohite, Siddharth and Creighton, Jolien and Kapadia, Shasvath. Nonparametric Inference of the Population of Compact Binaries from Gravitational-wave Observations Using Binned Gaussian Processes. Astrophys. J. 2023. doi:10.3847/1538-4357/acf452. arXiv:2304.08046

    Pith/arXiv arXiv 2023

  10. [10]

    Searching for Binary Black Hole Subpopulations in Gravitational-wave Data Using Binned Gaussian Processes

    Ray, Anarya and Maga \ n a Hernandez, Ignacio and Breivik, Katelyn and Creighton, Jolien. Searching for Binary Black Hole Subpopulations in Gravitational-wave Data Using Binned Gaussian Processes. Astrophys. J. 2025. doi:10.3847/1538-4357/adf22a. arXiv:2404.03166

    Pith/arXiv arXiv 2025

  11. [11]

    Characterizing Binary Black Hole Subpopulations in GWTC-4 with Binned Gaussian Processes: On the Origins of the 35M_ Peak

    Sridhar, Omkar and Ray, Anarya and Kalogera, Vicky. Characterizing Binary Black Hole Subpopulations in GWTC-4 with Binned Gaussian Processes: On the Origins of the 35M_ Peak. 2025. arXiv:2511.22093

    Pith/arXiv arXiv 2025

  12. [12]

    2022 , url =

    Mohite, Siddharth , title =. 2022 , url =

    2022

  13. [13]

    Farr and Andrea Colonna and Simon Stevenson and Peter Ti

    Ilya Mandel and Will M. Farr and Andrea Colonna and Simon Stevenson and Peter Ti. Model-independent inference on compact-binary observations , journal =. 2017 , doi =

    2017

  14. [14]

    and Morton, Timothy D

    Foreman-Mackey, Daniel and Hogg, David W. and Morton, Timothy D. , title =. The Astrophysical Journal , volume =. 2014 , doi =

    2014

  15. [15]

    Abac, A. G. and others. GWTC-5.0: Observations from the Second Part of the Fourth LIGO-Virgo-KAGRA Observing Run and Updates to the Gravitational-Wave Transient Catalog. 2026. arXiv:2605.27225

    Pith/arXiv arXiv 2026

  16. [16]

    GWTC-5.0 : Parameter estimation data release (Part 2 of 2)

    LIGO Scientific Collaboration and Virgo Collaboration and KAGRA Collaboration. GWTC-5.0 : Parameter estimation data release (Part 2 of 2)

  17. [17]

    GWTC-5.0 : Cumulative search sensitivity estimates

    LIGO Scientific Collaboration and Virgo Collaboration and KAGRA Collaboration. GWTC-5.0 : Cumulative search sensitivity estimates

  18. [18]

    Abac, A. G. and others. GWTC-5.0: Population Properties of Merging Compact Binaries. 2026. arXiv:2605.27226

    Pith/arXiv arXiv 2026

  19. [19]

    PyTorch: An Imperative Style, High-Performance Deep Learning Library

    Paszke, Adam and others. PyTorch: An Imperative Style, High-Performance Deep Learning Library. 2019. arXiv:1912.01703

    Pith/arXiv arXiv 2019

  20. [20]

    arXiv e-prints , keywords =

    Pyro: Deep Universal Probabilistic Programming. arXiv e-prints , keywords =. doi:10.48550/arXiv.1810.09538 , archivePrefix =. 1810.09538 , primaryClass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1810.09538

  21. [21]

    Handbook of Markov Chain Monte Carlo , ISBN=

    Brooks, Steve and Gelman, Andrew and Jones, Galin and Meng, Xiao-Li , year=. Handbook of Markov Chain Monte Carlo , ISBN=. doi:10.1201/b10905 , publisher=

    doi:10.1201/b10905

  22. [22]

    Journal of Machine Learning Research , volume =

    The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo , author =. Journal of Machine Learning Research , volume =. 2014 , url =

    2014

  23. [23]

    On the Astrophysical Origin of Binary Black Hole Subpopulations: A Tale of Three Channels?

    Ray, Anarya and Mukherjee, Shirsha and Zevin, Michael and Kalogera, Vicky. On the Astrophysical Origin of Binary Black Hole Subpopulations: A Tale of Three Channels?. Astrophys. J. Lett. 2026. doi:10.3847/2041-8213/ae80cb. arXiv:2603.17987

    Pith/arXiv arXiv 2026

  24. [24]

    Evidence for additional structure in the effective spin distribution hints at multiple formation pathways in GWTC-5.0

    Alvarez-Lopez, Sofia and Heinzel, Jack and Vitale, Salvatore. Evidence for additional structure in the effective spin distribution hints at multiple formation pathways in GWTC-5.0. 2026. arXiv:2606.12205

    Pith/arXiv arXiv 2026

  25. [25]

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

    Cheng, April Qiu and Toubiana, Alexandre and Biscoveanu, Sylvia and Gair, Jonathan. Reversible-jump MCMC reveals binary black hole subpopulations with distinct redshift evolution. 2026. arXiv:2605.25980

    Pith/arXiv arXiv 2026

  26. [26]

    and Farr, Will M

    Fishbach, Maya and Holz, Daniel E. and Farr, Will M. Does the Black Hole Merger Rate Evolve with Redshift?. Astrophys. J. Lett. 2018. doi:10.3847/2041-8213/aad800. arXiv:1805.10270

    Pith/arXiv arXiv 2018

  27. [27]

    Evidence for Three Subpopulations of Merging Binary Black Holes at Different Primary Masses

    Banagiri, Sharan and Thrane, Eric and Lasky, Paul D. Evidence for Three Subpopulations of Merging Binary Black Holes at Different Primary Masses. 2025. arXiv:2509.15646

    Pith/arXiv arXiv 2025

  28. [28]

    and Callister, Thomas

    Antonini, Fabio and Romero-Shaw, Isobel M. and Callister, Thomas. Star Cluster Population of High Mass Black Hole Mergers in Gravitational Wave Data. Phys. Rev. Lett. 2025. doi:10.1103/PhysRevLett.134.011401. arXiv:2406.19044

    Pith/arXiv arXiv 2025

  29. [29]

    and Colonna, Andrea and Stevenson, Simon and Ti n o, Peter and Veitch, John

    Mandel, Ilya and Farr, Will M. and Colonna, Andrea and Stevenson, Simon and Ti n o, Peter and Veitch, John. Model-independent inference on compact-binary observations. Mon. Not. Roy. Astron. Soc. 2017. doi:10.1093/mnras/stw2883. arXiv:1608.08223

    Pith/arXiv arXiv 2017

  30. [30]

    and Holz, Daniel E

    Fishbach, Maya and Farr, Will M. and Holz, Daniel E. The Most Massive Binary Black Hole Detections and the Identification of Population Outliers. Astrophys. J. Lett. 2020. doi:10.3847/2041-8213/ab77c9. arXiv:1911.05882

    Pith/arXiv arXiv 2020

  31. [31]

    Flexible and fast estimation of binary merger population distributions with an adaptive kernel density estimator

    Sadiq, Jam and Dent, Thomas and Wysocki, Daniel. Flexible and fast estimation of binary merger population distributions with an adaptive kernel density estimator. Phys. Rev. D. 2022. doi:10.1103/PhysRevD.105.123014. arXiv:2112.12659

    Pith/arXiv arXiv 2022

  32. [32]

    and Vijaykumar, Aditya and Fishbach, Maya

    Farah, Amanda M. and Vijaykumar, Aditya and Fishbach, Maya. The steep redshift evolution of the hierarchical merger rate may cause the z - _ eff correlation. 2026. arXiv:2601.03456

    Pith/arXiv arXiv 2026

  33. [33]

    and Thrane, Eric

    Guttman, Nir and Lasky, Paul D. and Thrane, Eric. Revealing Four Subpopulations of Binary Black-Hole Mergers with the Fifth Gravitational-Wave Transient Catalog. 2026. arXiv:2607.22011

    Pith/arXiv arXiv 2026

  34. [34]

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

    Padhyegurjar, Shaunak and Mukherjee, Suvodip. BBH-Genesis: Disentangling Binary Black Hole Formation Channels with GWTC-4. 2026. arXiv:2606.00234

    Pith/arXiv arXiv 2026

  35. [35]

    Spin Doctors: How to Diagnose a Hierarchical Merger Origin

    Payne, Ethan and Kremer, Kyle and Zevin, Michael. Spin Doctors: How to Diagnose a Hierarchical Merger Origin. Astrophys. J. Lett. 2024. doi:10.3847/2041-8213/ad3e82. arXiv:2402.15066

    Pith/arXiv arXiv 2024

  36. [36]

    The First Detection of Sub-Populations in the Delay-Time Distribution of Binary Black Holes in GWTC-4 of LIGO-Virgo-KAGRA

    Padhyegurjar, Shaunak and Mukherjee, Suvodip. The First Detection of Sub-Populations in the Delay-Time Distribution of Binary Black Holes in GWTC-4 of LIGO-Virgo-KAGRA. 2026. arXiv:2606.02318

    Pith/arXiv arXiv 2026

  37. [37]

    Reexamining Evidence of a Pair-instability Mass Gap in the Binary Black Hole Population

    Ray, Anarya and Kalogera, Vicky. Reexamining Evidence of a Pair-instability Mass Gap in the Binary Black Hole Population. Astrophys. J. Lett. 2026. doi:10.3847/2041-8213/ae374d. arXiv:2510.18867

    arXiv 2026

  38. [38]

    Gravitational waves reveal the pair-instability mass gap and constrain nuclear burning in massive stars

    Antonini, Fabio and Romero-Shaw, Isobel and Callister, Thomas and Dosopoulou, Fani and Chattopadhyay, Debatri and Gieles, Mark and Mapelli, Michela. Gravitational waves reveal the pair-instability mass gap and constrain nuclear burning in massive stars. 2025. arXiv:2509.04637

    Pith/arXiv arXiv 2025

  39. [39]

    Evidence of the pair instability gap in the distribution of black hole masses

    Tong, Hui and others. Evidence of the pair instability gap in the distribution of black hole masses. 2025. arXiv:2509.04151

    Pith/arXiv arXiv 2025

  40. [40]

    Phase space of binary black holes from gravitational wave observations to unveil its formation history

    Afroz, Samsuzzaman and Mukherjee, Suvodip. Phase space of binary black holes from gravitational wave observations to unveil its formation history. Phys. Rev. D. 2025. doi:10.1103/7zc2-g9vq. arXiv:2411.07304

    Pith/arXiv arXiv 2025

  41. [41]

    Binary Black Hole Phase Space Discovers the Signature of Pair Instability Supernovae Mass Gap

    Afroz, Samsuzzaman and Mukherjee, Suvodip. Binary Black Hole Phase Space Discovers the Signature of Pair Instability Supernovae Mass Gap. 2025. arXiv:2509.09123

    Pith/arXiv arXiv 2025

  42. [42]

    and Fishbach, Maya

    Vijaykumar, Aditya and Farah, Amanda M. and Fishbach, Maya. The maximum mass ratio of hierarchical mergers may cause the q - _ eff correlation. 2026. arXiv:2601.03457

    arXiv 2026

  43. [43]

    In-plane Black-hole Spin Measurements Suggest Most Gravitational-wave Mergers Form in Triples

    Stegmann, Jakob and Antonini, Fabio and Olejak, Aleksandra and Biscoveanu, Sylvia and Raymond, Vivien and Rinaldi, Stefano and Flanagan, Beth. In-plane Black-hole Spin Measurements Suggest Most Gravitational-wave Mergers Form in Triples. 2025. arXiv:2512.15873

    arXiv 2025

  44. [44]

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

    Plunkett, Cailin and Callister, Thomas and Zevin, Michael and Vitale, Salvatore. Signatures of a subpopulation of hierarchical mergers in the GWTC-4 gravitational-wave dataset. 2026. arXiv:2601.07908

    Pith/arXiv arXiv 2026

  45. [45]

    and Fishbach, Maya and Thrane, Eric and Antonini, Fabio and Stevenson, Simon and Romero-Shaw, Isobel M

    Tong, Hui and Callister, Thomas A. and Fishbach, Maya and Thrane, Eric and Antonini, Fabio and Stevenson, Simon and Romero-Shaw, Isobel M. and Dosopoulou, Fani. A subpopulation of low-mass, spinning black holes: signatures of dynamical assembly. 2025. arXiv:2511.05316

    arXiv 2025

  46. [46]

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

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

    Pith/arXiv arXiv 2026

  47. [47]

    Paola and Mislimi, Elvir and Hannuksela, Otto A

    Rinaldi, Stefano and Wong, Charmaine and Vaccaro, M. Paola and Mislimi, Elvir and Hannuksela, Otto A. and Leong, Samson H. W. and Mapelli, Michela. When the black holes align: a subpopulation of aligned massive binary black holes observed via gravitational waves. 2026. arXiv:2606.23305

    Pith/arXiv arXiv 2026

  48. [48]

    Aligned Hierarchical Black Hole Mergers in Active-Galactic-Nuclei Disks Revealed by GWTC-4

    Li, Yin-Jie and Wang, Yuan-Zhu and Tang, Shao-Peng and Fan, Yi-Zhong. Aligned Hierarchical Black Hole Mergers in Active-Galactic-Nuclei Disks Revealed by GWTC-4. Phys. Rev. Lett. 2026. doi:10.1103/qyfv-wkv1. arXiv:2509.23897

    Pith/arXiv arXiv 2026

  49. [49]

    and others

    Aasi, J. and others. Advanced LIGO. Class. Quant. Grav. 2015. doi:10.1088/0264-9381/32/7/074001. arXiv:1411.4547

    Pith/arXiv arXiv 2015

  50. [50]

    and others

    Acernese, F. and others. Advanced Virgo: a second-generation interferometric gravitational wave detector. Class. Quant. Grav. 2015. doi:10.1088/0264-9381/32/2/024001. arXiv:1408.3978

    Pith/arXiv arXiv 2015

  51. [51]

    and others

    Akutsu, T. and others. Overview of KAGRA: Calibration, detector characterization, physical environmental monitors, and the geophysics interferometer. PTEP. 2021. doi:10.1093/ptep/ptab018. arXiv:2009.09305

    arXiv 2021

  52. [52]

    A new group of low-spin 50-70M_ Black Holes and the high pair-instability mass cutoff

    Wang, Yuan-Zhu and Li, Yin-Jie and Gao, Shi-Jie and Tang, Shao-Peng and Fan, Yi-Zhong. A new group of low-spin 50-70M_ Black Holes and the high pair-instability mass cutoff. 2025. arXiv:2510.22698

    Pith/arXiv arXiv 2025

  53. [53]

    Rates of compact object coalescences

    Mandel, Ilya and Broekgaarden, Floor S. Rates of compact object coalescences. Living Rev. Rel. 2022. doi:10.1007/s41114-021-00034-3. arXiv:2107.14239

    Pith/arXiv arXiv 2022

  54. [54]

    Population Synthesis of Gravitational Wave Sources

    Breivik, Katelyn. Population Synthesis of Gravitational Wave Sources. 2025. doi:10.1016/B978-0-443-21439-4.00115-2. arXiv:2502.03523

    Pith/arXiv arXiv 2025

  55. [55]

    Merging stellar-mass binary black holes

    Mandel, Ilya and Farmer, Alison. Merging stellar-mass binary black holes. Phys. Rept. 2022. doi:10.1016/j.physrep.2022.01.003. arXiv:1806.05820

    Pith/arXiv arXiv 2022

  56. [56]

    Formation Channels of Single and Binary Stellar-Mass Black Holes

    Mapelli, Michela. Formation Channels of Single and Binary Stellar-Mass Black Holes. 2021. doi:10.1007/978-981-15-4702-7_16-1. arXiv:2106.00699

    Pith/arXiv arXiv 2021

  57. [57]

    and Berry, Christopher P

    Zevin, Michael and Bavera, Simone S. and Berry, Christopher P. L. and Kalogera, Vicky and Fragos, Tassos and Marchant, Pablo and Rodriguez, Carl L. and Antonini, Fabio and Holz, Daniel E. and Pankow, Chris. One Channel to Rule Them All? Constraining the Origins of Binary Black Holes Using Multiple Formation Pathways. Astrophys. J. 2021. doi:10.3847/1538-4...

    Pith/arXiv arXiv 2021

  58. [58]

    Colloms, Storm and Berry, Christopher P. L. and Veitch, John and Zevin, Michael. Exploring the Evolution of Gravitational-wave Emitters with Efficient Emulation: Constraining the Origins of Binary Black Holes Using Normalizing Flows. Astrophys. J. 2025. doi:10.3847/1538-4357/ade546. arXiv:2503.03819

    Pith/arXiv arXiv 2025

  59. [59]

    What You Don t Know Can Hurt You: Use and Abuse of Astrophysical Models in Gravitational-wave Population Analyses

    Cheng, April Qiu and Zevin, Michael and Vitale, Salvatore. What You Don t Know Can Hurt You: Use and Abuse of Astrophysical Models in Gravitational-wave Population Analyses. Astrophys. J. 2023. doi:10.3847/1538-4357/aced98. arXiv:2307.03129

    Pith/arXiv arXiv 2023

  60. [60]

    Black-hole kicks from numerical-relativity surrogate models

    Gerosa, Davide and H \'e bert, Fran c ois and Stein, Leo C. Black-hole kicks from numerical-relativity surrogate models. Phys. Rev. D. 2018. doi:10.1103/PhysRevD.97.104049. arXiv:1802.04276

    Pith/arXiv arXiv 2018

  61. [61]

    Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures

    Gerosa, Davide and Fishbach, Maya. Hierarchical mergers of stellar-mass black holes and their gravitational-wave signatures. Nature Astron. 2021. doi:10.1038/s41550-021-01398-w. arXiv:2105.03439

    Pith/arXiv arXiv 2021

  62. [62]

    and Jermyn, Adam S

    Fuller, Jim and Piro, Anthony L. and Jermyn, Adam S. Slowing the spins of stellar cores. Mon. Not. Roy. Astron. Soc. 2019. doi:10.1093/mnras/stz514. arXiv:1902.08227

    Pith/arXiv arXiv 2019

  63. [63]

    Angular momentum transport in massive stars and natal neutron star rotation rates

    Ma, Linhao and Fuller, Jim. Angular momentum transport in massive stars and natal neutron star rotation rates. Mon. Not. Roy. Astron. Soc. 2019. doi:10.1093/mnras/stz2009. arXiv:1907.03713

    Pith/arXiv arXiv 2019

  64. [64]

    Most Black Holes are Born Very Slowly Rotating

    Fuller, Jim and Ma, Linhao. Most Black Holes are Born Very Slowly Rotating. Astrophys. J. Lett. 2019. doi:10.3847/2041-8213/ab339b. arXiv:1907.03714

    Pith/arXiv arXiv 2019

  65. [65]

    and Heger, Alexander

    Woosley, Stanford Earl and Blinnikov, S. and Heger, Alexander. Pulsational pair instability as an explanation for the most luminous supernovae. Nature. 2007. doi:10.1038/nature06333. arXiv:0710.3314

    Pith/arXiv arXiv 2007

  66. [66]

    and Woosley, S

    Heger, A. and Woosley, S. E. The nucleosynthetic signature of population III. Astrophys. J. 2002. doi:10.1086/338487. arXiv:astro-ph/0107037

    Pith/arXiv arXiv 2002

  67. [67]

    and others

    Belczynski, K. and others. The Effect of Pair-Instability Mass Loss on Black Hole Mergers. Astron. Astrophys. 2016. doi:10.1051/0004-6361/201628980. arXiv:1607.03116

    Pith/arXiv arXiv 2016

  68. [68]

    Constraints from gravitational wave detections of binary black hole mergers on the ^ 12 C ( , )^ 16 \! O rate

    Farmer, Robert and Renzo, Mathieu and de Mink, Selma and Fishbach, Maya and Justham, Stephen. Constraints from gravitational wave detections of binary black hole mergers on the ^ 12 C ( , )^ 16 \! O rate. Astrophys. J. Lett. 2020. doi:10.3847/2041-8213/abbadd. arXiv:2006.06678

    Pith/arXiv arXiv 2020

  69. [69]

    van Son, L. A. C. and de Mink, S. E. and Broekgaarden, F. S. and Renzo, M. and Justham, S. and Laplace, E. and Moran-Fraile, J. and Hendriks, D. D. and Farmer, R. Polluting the pair-instability mass gap for binary black holes through super-Eddington accretion in isolated binaries. Astrophys. J. 2020. doi:10.3847/1538-4357/ab9809. arXiv:2004.05187

    Pith/arXiv arXiv 2020

  70. [70]

    Filling the black hole mass gap: Avoiding pair instability in massive stars through addition of nonnuclear energy

    Ziegler, Joshua and Freese, Katherine. Filling the black hole mass gap: Avoiding pair instability in massive stars through addition of nonnuclear energy. Phys. Rev. D. 2021. doi:10.1103/PhysRevD.104.043015. arXiv:2010.00254

    Pith/arXiv arXiv 2021

  71. [71]

    Very massive stars, pair-instability supernovae and intermediate-mass black holes with the SEVN code

    Spera, Mario and Mapelli, Michela. Very massive stars, pair-instability supernovae and intermediate-mass black holes with the SEVN code. Mon. Not. Roy. Astron. Soc. 2017. doi:10.1093/mnras/stx1576. arXiv:1706.06109

    Pith/arXiv arXiv 2017

  72. [72]

    Hendriks, D. D. and van Son, L. A. C. and Renzo, M. and Izzard, R. G. and Farmer, R. Pulsational pair-instability supernovae in gravitational-wave and electromagnetic transients. Mon. Not. Roy. Astron. Soc. 2023. doi:10.1093/mnras/stad2857. arXiv:2309.09339

    Pith/arXiv arXiv 2023

  73. [73]

    and Renzo, M

    Farmer, R. and Renzo, M. and de Mink, S. E. and Marchant, P. and Justham, S. Mind the gap: The location of the lower edge of the pair instability supernovae black hole mass gap. 2019. doi:10.3847/1538-4357/ab518b. arXiv:1910.12874

    Pith/arXiv arXiv 2019

  74. [74]

    Cosmological black hole spin evolution by mergers and accretion

    Berti, Emanuele and Volonteri, Marta. Cosmological black hole spin evolution by mergers and accretion. Astrophys. J. 2008. doi:10.1086/590379. arXiv:0802.0025

    Pith/arXiv arXiv 2008

  75. [75]

    The final spin from binary black holes in quasi-circular orbits

    Hofmann, Fabian and Barausse, Enrico and Rezzolla, Luciano. The final spin from binary black holes in quasi-circular orbits. Astrophys. J. Lett. 2016. doi:10.3847/2041-8205/825/2/L19. arXiv:1605.01938

    Pith/arXiv arXiv 2016

  76. [76]

    and Zevin, Michael and Amaro-Seoane, Pau and Chatterjee, Sourav and Kremer, Kyle and Rasio, Frederic A

    Rodriguez, Carl L. and Zevin, Michael and Amaro-Seoane, Pau and Chatterjee, Sourav and Kremer, Kyle and Rasio, Frederic A. and Ye, Claire S. Black holes: The next generation repeated mergers in dense star clusters and their gravitational-wave properties. Phys. Rev. D. 2019. doi:10.1103/PhysRevD.100.043027. arXiv:1906.10260

    Pith/arXiv arXiv 2019

  77. [77]

    and Fishbach, Maya

    Borchers, Angela and Ye, Claire S. and Fishbach, Maya. Gravitational-wave Kicks Impact the Spins of Black Holes from Hierarchical Mergers. Astrophys. J. 2025. doi:10.3847/1538-4357/addec6. arXiv:2503.21278

    Pith/arXiv arXiv 2025

  78. [78]

    and McMillan, Stephen

    Portegies Zwart, Simon F. and McMillan, Stephen. Black hole mergers in the universe. Astrophys. J. Lett. 2000. doi:10.1086/312422. arXiv:astro-ph/9910061

    Pith/arXiv arXiv 2000

  79. [79]

    Fitchett, M. J. The influence of gravitational wave momentum losses on the centre of mass motion of a Newtonian binary system. Mon. Not. Roy. Astron. Soc. 1983. doi:10.1093/mnras/203.4.1049

    work page doi:10.1093/mnras/203.4.1049 1983

  80. [80]

    and Holz, Daniel E

    Favata, Marc and Hughes, Scott A. and Holz, Daniel E. How black holes get their kicks: Gravitational radiation recoil revisited. Astrophys. J. Lett. 2004. doi:10.1086/421552. arXiv:astro-ph/0402056

    Pith/arXiv arXiv 2004

Showing first 80 references.