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Unifying spatial correlation with hierarchical population inference to constrain the AGN channel for binary black hole mergers

This paper introduces a hierarchical Bayesian framework that unifies spatial correlation and intrinsic property modeling to constrain the fraction of binary black hole mergers originating from active galactic nuclei, finding that while an AGN contribution cannot be excluded, specific luminosity thresholds allow for the exclusion of high AGN fractions at the 95% credible level.

Original authors: Lucas Pouw, Lorenzo Speri, Niccolò Veronesi, Elena Maria Rossi

Published 2026-09-17

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CC0 1.0

Original authors: Lucas Pouw, Lorenzo Speri, Niccolò Veronesi, Elena Maria Rossi

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep in the vast, silent dark between galaxies, invisible collisions are reshaping the universe. When two black holes spiral into one another, they send out ripples in the fabric of space and time called gravitational waves. These waves carry a unique signature of the crash, telling us the mass and spin of the objects involved. For years, scientists have been catching these signals, but a major mystery remains: how do these black holes find each other in the first place? Some form from stars that were born as a pair, while others are likely thrown together by the chaotic gravity of crowded star clusters. One particularly exciting theory suggests that some of these mergers happen inside the swirling, super-hot disks of gas that feed the supermassive black holes at the centers of active galaxies. If true, these "active galactic nucleus" mergers would be a distinct family of cosmic events, potentially creating black holes with spins and masses that are impossible to form elsewhere.

A team of researchers has now developed a new way to test this idea by combining two different types of cosmic data. They took the catalog of gravitational wave events detected by the LIGO, Virgo, and KAGRA observatories and cross-referenced them with a massive map of active galaxies. Instead of just looking for a direct match where a gravitational wave signal lines up perfectly with a visible galaxy, they built a statistical framework to ask a broader question: do the locations and properties of the gravitational waves look more like they came from active galaxies or from the rest of the universe? By treating the entire population of detected black hole mergers as a single group to be analyzed, they could determine what fraction of these events might be hosted by active galaxies, even if they couldn't point to a specific one.

The researchers applied this method to the latest catalog of 256 gravitational wave events from binary black hole mergers. They paired this data with a comprehensive list of active galaxies, specifically focusing on those that are not hidden by dust and shine brightly in optical and infrared light. The team was careful to account for the fact that our telescopes are not perfect; they adjusted their calculations to reflect that we are more likely to see the brightest, closest galaxies and that our measurements of distance and speed have inherent uncertainties. They also considered that the rate of these mergers changes over cosmic time, meaning the universe looked different billions of years ago than it does today. By weaving all these factors into a single mathematical model, they could estimate the maximum possible contribution of the active galaxy channel to the total number of mergers we see.

The results show that while active galaxies could be hosting a significant portion of these cosmic crashes, we cannot yet prove they are. The analysis places an upper limit on how many of these events could come from active galaxies. For the brightest, most luminous active galaxies, the team found that they could account for up to about 41 percent of the observed mergers. For slightly less luminous ones, the limit rises to about 52 percent, and for the most energetic group, it reaches 61 percent. Crucially, the data does not rule out the possibility that zero percent of the mergers come from this channel, nor does it confirm that any specific event definitely did. However, the study does find that there is a 98 percent probability that at least one of the 256 events in their sample originated in an active galaxy. This suggests that the active galaxy channel is likely a real player in the cosmic drama, even if it is not the main star.

One of the most important findings of this work is how the precision of our galaxy maps affects the answer. The researchers discovered that if we ignore the uncertainty in the distance measurements of the galaxies, we get a misleadingly low estimate of how many mergers come from active galaxies. By properly accounting for the fact that we don't know the exact distance to every galaxy, the constraints become looser but much more reliable. They also found that the ability to distinguish these events depends heavily on how well we can measure the distances to the galaxies. To get the best possible answer, the distance measurements for the galaxies need to be roughly ten times more precise than the distance measurements for the gravitational waves themselves. Currently, our galaxy catalogs are not quite there yet, which limits how tightly we can pin down the fraction of active galaxy mergers.

Looking ahead, the team suggests that the next generation of gravitational wave detectors will change the game. As these instruments become more sensitive, they will detect thousands of new events, many of which will be much farther away and closer to the active galaxies in the universe. The researchers estimate that with just a few years of observations from the upcoming O5 run of the detectors, they will have enough data to determine if active galaxies are the dominant source of the most massive, rapidly spinning black hole mergers. Until then, this new method stands as a powerful tool, unifying the study of where these events happen with what they look like, offering a clearer path to understanding the hidden lives of black holes in the centers of galaxies.

Technical Summary: Unifying Spatial Correlation with Hierarchical Population Inference to Constrain the AGN Channel for Binary Black Hole Mergers

Problem Statement
The formation channels of stellar-mass binary black holes (BBHs) observed by the LIGO-Virgo-KAGRA (LVK) detectors remain uncertain. While isolated binary evolution and dynamical formation are the broad categories, the specific contribution of the Active Galactic Nucleus (AGN) channel—where BBHs merge within AGN accretion discs—has not been robustly quantified. Previous attempts to constrain the fraction of AGN-hosted events ( $f_{\text{agn}}$ ) have relied on either spatial correlations between gravitational wave (GW) localizations and AGN catalogues or on modeling the intrinsic properties of GW sources (e.g., spins, masses). However, these approaches have been treated separately, often ignoring the full GW posterior information or failing to account for selection effects and redshift uncertainties in electromagnetic (EM) catalogues.

Methodology
The authors develop a hierarchical Bayesian framework that unifies spatial correlation and population inference into a single likelihood function for $f_{\text{agn}}$ . The methodology extends "dark siren" cosmological inference techniques to distinguish between two populations: GWs originating from the AGN channel and those from alternative formation channels.

Key methodological components include:

Likelihood Construction: The framework constructs a population prior that is a mixture model of AGN-origin and alternative-origin GWs. The AGN-origin prior is derived from an EM catalogue (Quaia), accounting for the probability of detecting a host ( $P_{\text{det}}^{\text{EM}}$ ) and the full redshift posteriors of AGN sources. The alternative-origin prior follows a Madau-Dickinson cosmic star-formation rate evolution.
Data Integration: The analysis utilizes 256 BBH merger events from the GWTC-5.0 catalogue and the Quaia AGN catalogue (a cross-section of Gaia DR3 and unWISE).
Refinements over Previous Work: Unlike prior spatial-correlation studies (e.g., Veronesi et al. 2023, 2025), this framework explicitly includes:
- GW selection effects (detection efficiency).
- Redshift-dependent merger rates.
- Full AGN redshift posteriors (rather than point-source approximations).
- A spatially varying EM selection function.
- Consistent modeling of the AGN distribution, including sources without host detections.
Mock Data Validation: The authors validate the likelihood using 200 mock data realizations, demonstrating that the framework consistently recovers injected values of $f_{\text{agn}}$ and quantifying the biases introduced by neglecting AGN redshift errors.

Key Results
Applying the framework to real data yields the following constraints and findings:

Constraints on $f_{\text{agn}}$ : For unobscured AGN with bolometric luminosities $L_{\text{bol}} \geq \{10^{44.5}, 10^{45.5}, 10^{46.5}\} \text{ erg s}^{-1}$ , the authors place 95% credible upper limits of $f_{\text{agn}} \leq \{0.52, 0.41, 0.61\}$ , respectively. The inclusion of the Quaia catalogue tightens these limits compared to GW-only analyses, though the authors cannot exclude $f_{\text{agn}} = 0$ at this significance level.
Comparison to Previous Studies: The constraints are looser than those reported by Veronesi et al. (2025) ( $f_{\text{agn}} \leq \{0.21, 0.13, 0.11\}$ ). The authors attribute this relaxation to the removal of downward biases caused by neglecting AGN redshift uncertainties and differences in GW detection efficiency between populations.
Event Probabilities: No individual GW event is more likely to have an AGN origin than an alternative origin. The event GW230704_212616 has the highest probability of AGN origin ( $p(\text{AGN}) \approx 0.250$ ). However, combining probabilities across the dataset yields a 98.1% chance that at least one event in the sample originated in an AGN.
Redshift Evolution: The inferred AGN-channel merger rate evolution is consistent with the hierarchically merging subpopulation identified by Farah et al. (2026) for $f_{\text{agn}} \approx 0.07$ up to $z \approx 1$ .
Catalogue Requirements: Mock data analysis indicates that to achieve near-optimal constraints, AGN catalogues must have redshift uncertainties roughly an order of magnitude smaller than those of the GW sample ( $\sigma_{z, \text{agn}} \lesssim 0.01$ compared to $\sigma_{z, \text{GW}} \approx 0.1$ ). Neglecting AGN redshift errors biases $f_{\text{agn}}$ downwards.

Significance and Claims
The paper claims to lay the pathway for combining full GW posteriors with EM observations to infer GW population properties and AGN disc characteristics. The authors emphasize that their method unifies spatial-correlation analyses with population studies, providing a more robust statistical foundation for $f_{\text{agn}}$ inference.

The authors modestly note that their results are moderately model-dependent, particularly regarding the redshift evolution of the alternative-origin population. They state that future GW observations at higher redshifts (e.g., from LVK O5) and improved EM catalogues (e.g., from Euclid) are required to lift degeneracies and test the AGN channel as the dominant source of hierarchical mergers. The framework is presented as a tool to directly probe GW populations and the properties of AGN accretion discs and nuclear star clusters, regardless of the final value of $f_{\text{agn}}$ .

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