Abstract Ground-based gravitational wave (GW) detectors have discovered about 200 compact object mergers. The astrophysical origins of these events are highly debated, and it is possible that at least a fraction of them originate from dynamical environments. Among these, the disks of active galactic nuclei (AGN) are particularly interesting as promising environments, as some observed properties may be more readily produced there. When compact objects merge in these environments, acceleration from the central supermassive black hole or nearby companions is inevitable. Such acceleration induces a phase shift in the observed GW waveforms, which can serve as a useful tool to distinguish the underlying merging environments for each GW event. In this paper, we investigate the expected distribution of such acceleration-induced GW phase shifts, using a semianalytical model combined with a 1D AGN population synthesis code. We find significant contributions from three-body interactions involving a nearby third object. Our results indicate that the GW phase shift is likely to be larger compared to other channels, making it distinguishable by future GW facilities such as TianQin, DECIGO, Taiji, Einstein Telescope, and Cosmic Explorer. Interestingly, a notable fraction of mergers in fact exhibit a significant GW phase shift (≳1 rad) at frequencies above 10 Hz, which could even be detectable by current GW detectors such as LIGO/Virgo/KAGRA. Additionally, if gas-hardening during three-body interactions is taken into account, the GW frequency can be boosted to ≳10 Hz, potentially further aiding in the detection of the phase shift.
Tagawa et al. (2026) studied this question.