Gravitational Wave Phase shifts of black hole mergers in AGN Disks

TL;DR

This work investigates acceleration-induced GW phase shifts in BBH mergers within AGN disks as a tool to identify merger environments. By combining a semi-analytic AGN-disk model with a 1D N-body-like population synthesis, it characterizes the phase-shift distributions for non-GWC, GWC-SS, and GWC-BS merger channels, including gas-drag effects that shrink triple systems and boost GW frequencies. The results show that GWC mergers, especially during binary-single interactions, yield substantial phase shifts often exceeding 0.1 rad near or above the LVK band, and that gas effects can further elevate detectability to higher frequencies; a non-negligible minority may already be observable with current detectors. Overall, the study proposes GW phase shifts as a promising discriminator for AGN-disk merger origins, with implications for future GW observatories such as TianQin, DECIGO, Taiji, Einstein Telescope, and Cosmic Explorer.

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 (SMBH) 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 semi-analytical model combined with a one-dimensional 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 ($\gtrsim~{\rm 1\ rad}$) at frequencies above $10~{\rm Hz}$, 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 $\gtrsim 10~{\rm Hz}$, potentially further aiding in the detection of the phase shift.

Figures (8)

• Figure 1: A schematic picture of BH mergers within an AGN disk and their GW phase shifts caused by acceleration from nearby compact objects. Non-GWC binaries and GWC binaries formed through single-single interactions experience strong gravitational acceleration due to the central SMBH. A GWC binary formed during binary-single interactions undergoes gravitational acceleration from its triple companion. In this case, gas drag may significantly harden the triple system, thereby boosting the GW frequency.
• Figure 2: The evolution of the orbital eccentricity and the cumulative phase shift until mergers for model M1. Points represent values at binary formation, and lines represent their evolution. Blue, orange and brown, and red lines display the results for mergers due to non-GWC processes, mergers due to the GWC mechanism during binary-single interactions, and those during single-single interactions, respectively. For GWC binaries during binary-single interactions, the solid lines correspond to cases where the acceleration from the bound third BH is dominant, while the dashed lines correspond to cases where the acceleration from the SMBH is dominant. In the lower panel, the dashed gray lines depict the evolution for phases in which the binary moves more than $1/4$ of the orbit around its companion (third BH or SMBH) before merging. The lines are shown for the final $5~{\rm yr}$ to merger, and are not connected to the points in the upper panel for cases with long merger time. The gray vertical dashed line in the lower panel represents the typical value for the LVK sensitivity band.
• Figure 3: The distribution of cumulative phase shifts above $10~{\rm Hz}$. Solid, dashed, and dotted lines represent the results for mergers due to non-GWC processes, mergers due to the GWC mechanism during binary-single interactions, and those during single-single interactions, respectively. The upper panel shows the result for model M1, and orange, blue, and red lines in the lower panel shows those for models M2, M4, and M12, respectively.
• Figure 4: Same as in Fig. \ref{['fig:phi_dist']}, but for cumulative phase shifts above $0.1~{\rm Hz}$.
• Figure 5: The distribution of acceleration from the third body at binary formation. In the upper panel, solid, dotted, and dashed lines represent the results for model M1 for mergers occurring due to non-GWC processes, mergers resulting from the GWC mechanism during binary-single interactions, and those occurring during single-single interactions, respectively. In the lower panel, blue, orange, and red lines represent the results for all the mergers for models M2, M4, and M12, respectively. In upper and bottom panels, thick lines indicate cases where the acceleration from the SMBH is dominant, while thin dashed lines indicate cases where the acceleration from the third bound BH is dominant. The purple vertical box and line represent 90$\%$ confidence intervals and median for acceleration in GW190814 suggested by Yang2025.