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Evidence of a fraction of LIGO/Virgo/KAGRA events coming from active galactic nuclei

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper reports that 29-39 percent of 94 LIGO/Virgo/KAGRA gravitational-wave events are spatially correlated with lower-luminosity or lower-Eddington-ratio AGNs, with the signal dominated by four well-localized O4 events.

desk verdict A useful method paper with a headline result that does not survive contact with its own robustness checks: the claimed AGN excess is 1.3–1.6σ, uncorrected for trials, and driven by three well-localized O4 events. read the letter →

arxiv 2505.02924 v2 pith:JN2YG4ED submitted 2025-05-05 astro-ph.HE astro-ph.GAastro-ph.IMgr-qc

Liang-Gui Zhu , Xian Chen This is my paper · ORCID
classification astro-ph.HEastro-ph.GAastro-ph.IMgr-qc
keywords GravitationalwavesourcesBlackholesActivegalacticnucleiSkysurveysBinaryholemergersEddingtonratioSpatialcorrelationAGNformationchannel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that a sizable minority of the black-hole mergers detected by LIGO/Virgo/KAGRA formed inside active galactic nuclei (AGNs), specifically the dimmer and less actively accreting ones. Using 94 gravitational-wave events from the O1 through early O4 runs and roughly $3\times10^5$ SDSS AGNs, the authors look for a statistical excess of AGNs inside the three-dimensional localization volume of each merger. They find that a fraction $f_{\rm agn} = 0.39^{+0.41}_{-0.32}$ (lower-luminosity AGNs) or $0.29^{+0.40}_{-0.25}$ (lower-Eddington-ratio AGNs) is needed to explain the overlap, at 90\% confidence. Monte Carlo mock catalogs with no AGN-merger link produce smaller overlaps, which the authors take as evidence that the correlation is not random coincidence. If correct, the result identifies a specific astrophysical birth environment for black-hole binaries and predicts that electromagnetic counterparts should be hunted around faint, low-accretion AGNs.

What carries the argument

The statistical engine is the event-wise likelihood $\mathcal{L}(f_{\rm agn}) = \prod_i \left[0.9 c_i f_{\rm agn} S_i + (1 - 0.9 c_i f_{\rm agn}) B_i\right]$, whose maximum over $f_{\rm agn}$ is the inferred AGN-origin fraction. The signal probability is $S_i = \sum_j p_i(\mathbf{x}_j)/n_{\rm agn}(\mathbf{x}_j)$, summing over cataloged AGNs inside the 90\% localization volume, with each AGN weighted by the GW sky-map probability density at its position and downweighted by the local AGN density. A 3D first-order Voronoi tessellation of the SDSS AGN sample supplies $n_{\rm agn}(\mathbf{x})$, letting the AGN number density vary over the sky and with redshift instead of assuming it constant as earlier work did. The background probability is $B_i = 0.9 f_{{\rm cover},i}$, where $f_{{\rm cover},i}$ is the fraction of the error volume covered by the AGN catalog. This machine converts a stack of imperfect 3D localizations into one number, $f_{\rm agn}$, plus its uncertainty.

What would settle it

The reported excess disappears when the four best-localized O4 events are removed, so the decisive check is external: re-run the same likelihood on the next several hundred well-localized events from ongoing and future runs. If the peak in $f_{\rm agn}$ does not reappear once localization volumes shrink well below the typical AGN spacing, the correlation is a small-sample artifact. A reader could also build null catalogs that preserve the galaxy density field but randomize which galaxies host AGNs; a persistent excess there would invalidate the independence assumption.

Watch

Extended reading notes

Core claim

The paper's central claim is that the spatial distribution of lower-luminosity and lower-Eddington-ratio AGNs is not independent of the localization volumes of the LVK events. Dividing the SDSS DR16 AGN catalog into sub-catalogs by bolometric luminosity and Eddington ratio, the lower-$L_{\rm bol}$ ($10^{44.5} \lesssim L_{\rm bol} \le 10^{45}$ erg s$^{-1}$) and lower-$\lambda_{\rm Edd}$ ($0.01 \lesssim \lambda_{\rm Edd} \le 0.05$) populations show an excess around GW sources, while the moderate-, higher-, and full-catalog samples peak at $f_{\rm agn}=0$. The likelihood fit gives $f_{\rm agn} = 0.39^{+0.41}_{-0.32}$ and $0.29^{+0.40}_{-0.25}$ at 90\% confidence. The authors argue the excess is unlikely to be random coincidence because mock realizations with injected $f_{\rm agn}=0$ rarely produce as small a $\Delta P_{0.05}$ as the real data, and because the inferred distribution narrows rather than broadens when the sample is reduced from the full catalog to O1-O3 alone for the two sub-catalogs in question. The paper also reports that the signal is dominated by the four best-localized O4 events; removing them returns the best-fit $f_{\rm agn}$ to zero, which the authors interpret as the expected sensitivity of the test to high-quality localizations rather than as evidence against the correlation.

Load-bearing premise

When no merger actually occurs in an AGN, the analysis assumes that AGNs and gravitational-wave sources are placed independently, so overlaps are pure chance; if both merely trace the same large-scale cosmic structure, the null expectation is too small and the inferred positive $f_{\rm agn}$ would be inflated.

Editorial extensions

If this is right

  • If the correlation is real, roughly 30-40 percent of the 94 analyzed events formed in low-luminosity or low-Eddington-ratio AGNs, making the AGN channel a major rather than negligible formation route at these redshifts.
  • The absence of a signal for luminous AGNs (best-fit zero, with 90% upper limits of 0.16-0.37 depending on the sample) sharpens earlier upper limits and redirects electromagnetic counterpart searches toward fainter nuclei.
  • The spatial-correlation estimate agrees with an independent hierarchical-Bayesian analysis that finds $f_{\rm agn} \approx 0.34$ for O1-O3 events, so two different statistical approaches bracket the same channel.
  • As the ongoing run completes toward roughly 300 candidates and new AGN catalogs cover more than 70 percent of the sky, the same machinery should shrink the $f_{\rm agn}$ errors by about half and roughly double the significance of a nonzero fraction if the true value is near 0.2.
  • The method's sensitivity comes disproportionately from well-localized events, so future runs with improved localization will provide the decisive test of whether the excess persists.

Reading between the lines

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

  • The authors do not push the obvious follow-up: a targeted look inside the error volumes of the four best-localized O4 events (S240413p, S250114ax, S250119cv, S230627c) for faint AGNs or AGN flaring would directly test whether these few events really host the claimed population.
  • Because the null mock catalogs draw hosts from the SDSS galaxy catalog, one natural extension is to scramble AGN positions within that same galaxy density field; if the excess survives such scrambling, the independence assumption in the null, not a physical AGN association, would be the explanation.
  • If low-Eddington-ratio AGNs are the preferred birthplaces, the controlling variable may be disk gas density rather than total luminosity, which suggests a cross-correlation split by galaxy environment or emission-line properties as a sharper test.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper constrains the fraction f_agn of LIGO/Virgo/KAGRA events that originate from active galactic nuclei by comparing GW localization volumes (O1-O4a) with SDSS DR16 AGN sub-catalogs split by bolometric luminosity and Eddington ratio. The method extends the Bartos et al. approach by using a 3D Voronoi estimate of the AGN density field, a coverage factor f_cover,i for partial sky coverage, and a modified background probability B_i=0.9 f_cover,i. The authors report non-zero best-fit values f_agn=0.39^{+0.41}_{-0.32} for the lower-Lbol sub-catalog and f_agn=0.29^{+0.40}_{-0.25} for the lower-Eddington-ratio sub-catalog, with zero best fits for the other sub-catalogs and for the full catalog. Mock-injection tests are quoted as rejecting f_agn=0 at 1.3 sigma and 1.6 sigma credibility, and Section 4.2 investigates the origin of the signal by removing the four best-localized O4 events. The paper concludes that a fraction of LVK events come from lower-luminosity or lower-accretion-rate AGNs.

Significance. If the claimed excess is real, the paper would provide the first quantification of the AGN-origin fraction for specific AGN sub-populations, with a clear environmental prediction that lower-luminosity and lower-Eddington-ratio AGNs dominate the AGN channel. The methodological contribution is genuine: the Voronoi-based density estimate, the explicit coverage factor, the mock-injection tests, and the Appendix B unbiasedness argument are useful extensions of earlier work. The authors also make the data publicly available on Zenodo, which supports reproducibility, and their upper limits for the higher-luminosity sub-catalogs are consistent with previous constraints from Veronesi et al. My assessment is that the central evidence claim is not yet supported by the statistics presented; the paper is more defensible as a method demonstration with upper limits and a tentative hint, rather than as evidence of a non-zero AGN fraction.

major comments (3)
  1. [Section 4.1, Fig. 4] The quantitative support for the abstract's claim that the correlation is 'unlikely to arise from random coincidence' is a 1.3 sigma (lower-Lbol) and 1.6 sigma (lower-Eddington) rejection based on DeltaP0.05 in the f_agn=0 mocks. These significances are not corrected for the number of AGN sub-catalogs searched, and the two positive sub-catalogs overlap by about 40%, so the effective number of trials is smaller than six but definitely larger than one. A nominal 1.3-1.6 sigma excess, before any trials penalty, is too weak to support the language of evidence; the authors should report trials-corrected p-values or explicitly downgrade the conclusion to a tentative hint.
  2. [Section 4.2, Fig. 5] Removing the four best-localized O4 candidates makes the best-fit f_agn drop to zero in all six sub-catalogs. The non-zero signal is therefore dominated by a very small number of well-localized events, three of which contain AGNs in their error volumes. The subsequent argument that the signal persists because the 90% upper limit narrows when going from the 29-event O1-O3 sample to the 90-event sample is not a calibrated significance test: the comparison is post hoc, and no null distribution for this upper-limit ratio is provided. This does not corroborate the statement in Section 5 that the signal 'remains consistent across different samples.'
  3. [Section 3, Eqs. (4)-(5)] The null background B_i=0.9 f_cover,i assumes that under f_agn=0 the expected number of AGNs in a GW error volume is proportional only to the survey-covered fraction of that volume. If the non-AGN BBH population and the AGN population trace the same large-scale structure, the likelihood in Eq. (1) will systematically pull f_agn away from zero. The f_agn=0 mocks that draw hosts from SDSS galaxies may partly capture this correlation, but the paper does not demonstrate that the recovered f_agn is unbiased under the null; a concrete test would be to compare mocks with galaxy-drawn hosts against mocks with uniformly random hosts. Without such a demonstration, the positive best-fit values in Section 4.1 have an unmodeled systematic component in addition to the weak statistical significance.
minor comments (5)
  1. [Abstract and Section 4.1] The text uses '90% confidence level' for what are Bayesian posterior intervals from the likelihood in Eq. (1); the authors should say 'credible interval' or explicitly state the prior and posterior interpretation.
  2. [Section 4.1, DeltaP0.05 discussion] The 1.3 sigma and 1.6 sigma statements should specify whether these are one-sided or two-sided Gaussian-equivalent significances; DeltaP0.05 is a lower-tail probability, and the conversion to sigma depends on this choice.
  3. [Section 5] The forecast that f_agn errors scale as 1/sqrt(SNR) is unclear; presumably the intended scaling is with the number of events or the combined signal-to-noise ratio, and the text should be corrected.
  4. [Appendix A] The statement that the AGN catalog has not been corrected for Malmquist bias is important because it bears directly on the completeness assumption ci=fcover,i; this limitation should be mentioned in the main-text discussion, not only in the appendix.
  5. [Figure 4 caption] The caption contains a grammatical error ('the cyan solid line correspond') and should define what is meant by 'Mock expectation' in the legend or caption text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: f_agn is a fitted mixture-model parameter with an explicit null background, and the central estimate does not reduce by construction to its inputs.

full rationale

The central claim is a maximum-likelihood estimate of f_agn from a mixture likelihood whose signal term sums the GW localization density at catalog AGN positions weighted by the reciprocal Voronoi density (Eq. 2), and whose background term is the null expectation of that sum, B_i = 0.9 f_cover,i (Eqs. 4-5). This construction is not circular: under the null of no spatial correlation between GW localizations and AGN positions, the expectation of S_i equals B_i, so the fit is measuring an actual excess rather than renaming its input. The f_agn values are fitted parameters, and the mock injections (f_agn = 0, 0.4, 0.3) are calibration and null-hypothesis checks, not predictions derived from the fit itself. The only self-citation, Zhu et al. (2024), is used to support mock validation of the likelihood, but the paper independently proves unbiasedness in Appendix B, so that citation is not load-bearing. The weaknesses raised by the skeptic — 1.3-1.6 sigma mock significance, no trials correction, and the disappearance of the best-fit when four localized O4 events are removed — are statistical robustness concerns, not circularity; they do not show that the estimate is equivalent to its inputs. I therefore find no circular step requiring a nonzero circularity score.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The analysis has one central fitted parameter (f_agn) and several hand-chosen thresholds (sub-catalog boundaries, GW selection cuts, the 1e6 Mpc^3 robustness cut). The core assumptions are the statistical independence of the null background, the validity of the Voronoi density estimate, and the representativeness of the SDSS galaxy-based mock null. No new physical entities are introduced.

free parameters (4)
  • f_agn (AGN-origin fraction) = 0.39^{+0.41}_{-0.32} (lower Lbol); 0.29^{+0.40}_{-0.25} (lower Eddington ratio)
    The central parameter constrained by likelihood maximization.
  • Sub-catalog boundaries in Lbol and Eddington ratio = lgLbol thresholds: 45, 45.5; lgEddington thresholds: -1.3, -0.9
    Chosen a priori based on sample size and theory, but the boundaries define the populations that produce the signal; the result is sensitive to these choices.
  • GW selection thresholds = DeltaVc < 1e11 Mpc^3, sky coverage > 20%, z < 1.5
    Applied uniformly to all events; chosen to balance localization quality and catalog overlap, but they determine the 94-event sample.
  • Robustness cut in Section 4.2 = 1e6 Mpc^3
    Post-hoc threshold to test robustness by excluding four best-localized events.
assumptions (4)
  • domain assumption GW sources are either AGN-associated with weight 0.9 c_i f_agn or background with weight 1 - 0.9 c_i f_agn (Eq. 1).
    This two-component mixture is the statistical model; any mis-specification of the mixture changes the meaning of f_agn.
  • domain assumption Under the null, the expectation of the signal statistic S_i equals B_i = 0.9 f_cover,i (Eq. 5).
    Assumes AGN density and GW source positions are independent under the null; if BBHs trace the same large-scale structure as AGNs even without AGN formation, B_i is biased and f_agn is overestimated.
  • domain assumption The Voronoi cell volume gives an unbiased estimate of the local AGN number density n_agn(x) used in Eq. (2).
    Requires the AGN catalog to be a Poisson sample of the density field; incompleteness and boundary effects are handled ad hoc with alphashape and density cuts.
  • domain assumption SDSS galaxies are a valid random-host distribution for the f_agn = 0 mock.
    The mock null pastes skymaps onto random SDSS galaxies; if BBH hosts are environmentally biased relative to SDSS galaxies, the null distribution is wrong.

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Cite this review

Pith. "Pith review of Evidence of a fraction of LIGO/Virgo/KAGRA events coming from active galactic nuclei." pith.science (2026). https://pith.science/paper/JN2YG4ED

@misc{pith2026250502924,
  author       = {Pith},
  title        = {Pith review of: Evidence of a fraction of LIGO/Virgo/KAGRA events coming from active galactic nuclei},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JN2YG4ED}},
  note         = {Machine review of arXiv:2505.02924}
}
abstract

The formation channels of the gravitational-wave (GW) sources detected by LIGO/Virgo/KAGRA (LVK) remain poorly constrained. Active galactic nucleus (AGN) has been proposed as one of the potential hosts, but the fraction of GW events originating from AGNs has not been quantified. Here, we constrain the AGN-origin fraction $f_{\rm agn}$ by analyzing the spatial correlation between GW source localizations ($O1\!-\!O4$a) and AGNs (SDSS DR16). We report preliminary evidence of an excess of lower-luminosity ($10^{44.5} \lesssim L_{\rm bol} \le 10^{45}~\!\mathrm{erg~s}^{-1}$) as well as lower-Eddington ratio ($0.01 \lesssim \lambda_{\rm Edd} \le 0.05$) AGNs around the LVK events, the explanation of which requires $f_{\rm agn} = 0.39^{+0.41}_{-0.32}$ and $0.29^{+0.40}_{-0.25}$ (90\% confidence level) of the LVK events originating from these respective AGN populations. Monte Carlo simulations confirm that this correlation is unlikely to arise from random coincidence, further supported by anomalous variation of the error of $f_{\rm agn}$ with GW event counts. These results support the theoretical speculation that some LVK events come from lower-luminosity or lower-accretion-rate AGNs, offering critical insights into the environmental dependencies of the formation of GW sources.

Figures

Figures reproduced from arXiv: 2505.02924 by the authors.

Figure 1
Figure 1. Distributions of AGNs in the Lbol − λEdd plane. The two white contours represent the 50% and 90% CLs of the AGN distribution. The cyan, blue, and red regions (dots) correspond to the lower, moderate and higher Lbol (λEdd) AGN sub-catalogs, respectively. The division is partly based on a comparable number of AGNs in different sub-catalogs and partly motivated by the predictions from previous theoretical works (Bartos… view at source ↗
Figure 2
Figure 2. Skymaps of three precisely localized O4 GW candidates and scatter plots of their neighboring AGNs. The two white contours in each panel represent the 50% and 90% CLs of the skymap. The blue/gray stars represent the AGNs inside/outside the localization error volume of 90% CL. 0.1 0.3 0.5 0.7 0.9 fagn 0 2 4 6 8 10 12 p ( fagn ) lg Lbol 45 lg Lbol (45, 45.5] lg Lbol > 45.5 All AGNs 0.1 0.3 0.5 0.7 0.9 fagn 0 2 4 6 8 10… view at source ↗
Figure 3
Figure 3. Probability distributions of fagn derived for all O1−O4a GW events. Different curves correspond to lower (cyan), moderate (blue), and higher (red) Lbol (left panel) or λEdd (right) sub-catalogs. Results for the full catalog are shown with black curves. Vertical dotted lines mark the 90% CL upper limits. However, when using the lower-Lbol (44.5 ≲ lg Lbol ≤ 45) and lower-λEdd (−2 ≲ lg λEdd ≤ −1.3) sub-catalogs (cyan c… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Comparison between real and mock constraints on fagn based on all O1−O4a GW events. Top panels: con￾straints using the lower Lbol sub-catalog with injected values f inj agn = 0 and f inj agn = 0.4, respectively. Bottom panels: con￾straints using the lower λEdd sub-cata…
Figure 5
Figure 5. Figure 5: Probability distributions of fagn derived from O1−O4a (top) and O1−O3 (bottom) after excluding the four best localized LVK events. The line styles are the same as in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: AGN density distributions and completeness analysis. Top left: On-sky surface density distribution of SDSS AGNs, showing cumulative area versus density. The sky area element for statistics is ∆Ω ≈ 1.56 deg2 . Bottom left: Redshift-dependent spatial density of AGNs in l…

Discussion (0). Continue with ORCID to comment.

Forward citations

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Pith tools

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