Constraining Binary Mergers in Active Galactic Nuclei Disks Using the Nonobservation of Lensed Gravitational Waves

Abstract The dense and dynamic environments within active galactic nuclei (AGN) accretion disks may serve as prolific birthplaces for binary black holes (BBHs) and one possible origin for some of the BBHs detected by gravitational-wave (GW) observatories. We show that a considerable fraction of the BBH in AGN disks will be strongly lensed by the central supermassive black hole (SMBH). Thus, the nonobservation of lensed GW signals can be used to constrain the fraction of BBH binaries residing in AGN disks. The nondetection of lensing with current <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>100</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> detections will be sufficient to start placing constraints on the fraction of BBHs living within accretion disks near the SMBH. In the next-generation detectors era, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> BBH observations and no lensed events, we will be able to rule out most migration traps as dominant birthplaces of BBH mergers; moreover, we will be able to constrain the minimum size of the accretion disk. On the other hand, should AGNs constitute a major formation channel, lensed events from AGNs will become prominent in the future.