Gravitationally Lensed Gravitational Waves from Black Holes Around Black Holes

Gravitational-wave detectors have captured the chirps of dozens of merging black holes. Could any of these mergers have happened in the disk around a supermassive black hole?

Black Holes Around Black Holes

At the centers of galaxies across the universe, the disks surrounding accreting supermassive black holes — known as active galactic nuclei — provide an extreme ecosystem for stars and stellar-mass black holes. When a pair of black holes within an active galactic nucleus disk merges, the collision produces gravitational waves that can be picked up by detectors on Earth. If, from our perspective, that merger takes place behind the supermassive black hole, the gravitational-wave signal will be gravitationally lensed: split into two “images” of the same wave with slightly different properties.

Detecting a gravitationally lensed gravitational-wave signal from merging black holes would provide valuable information about the population of black holes that reside in active galactic nucleus disks, as well as the properties of the disks themselves.

Lensing Likelihood

So far, no gravitationally lensed gravitational waves have been detected — but luckily, even this non-detection contains valuable information. To explore the implications of this non-detection, Samson Leong (The Chinese University of Hong Kong) and collaborators developed an analytical model that describes a binary black hole pair orbiting and merging within the disk of an active galactic nucleus. The team calculated the probability that gravitational waves from the merger of these black holes would be gravitationally lensed from the perspective of a distant observer. This probability is dependent upon the orientation of the disk relative to the viewer, as well as the distance from the binary system to the central supermassive black hole.

Then, given the fact that none of the dozens of mergers detected so far have had gravitationally lensed signals, Leong’s team constrained the fraction of observed mergers happening in active galactic nucleus disks. With only about 100 binary black hole merger observed to date, the constraining power of the non-detection is limited. For now, all that can be said is that no more than 47% of the observed mergers took place in the disks around active galactic nuclei. As the number of detected black hole mergers grows, the constraint will grow more stringent; if no lensed events have been observed after roughly 1,000 mergers have been detected, that would mean that no more than 5% of the mergers took place within an active galactic nucleus disk.

To Be Constrained

This estimate is based on the assumption that all black holes in active galactic nucleus disks merge within the migration trap nearest the central supermassive black hole. Several migration traps — particular orbital radii within the disk where black holes are expected to collect — are predicted to exist. If the black holes instead merge within a migration trap at a much larger radius, many more observations will be needed to narrowly constrain the number of mergers happening within accretion disks.

Future observations may yield new information about active galactic nucleus accretion disks. In particular, it may be possible to discern the minimum size of an accretion disk, as well as where within the disk binary black holes are most likely to merge.

Citation

“Constraining Binary Mergers in Active Galactic Nuclei Disks Using the Nonobservation of Lensed Gravitational Waves,” Samson H. W. Leong et al 2025 ApJL 979 L27. doi:10.3847/2041-8213/ad9ead