Formation of Merging Stellar-Mass Black Hole Binaries by Gravitational Wave Emission in Active Galactic Nucleus Disks

TL;DR

This paper investigates how stellar-mass black hole binaries form and evolve via gravitational wave emission in active galactic nucleus disks, predicting their eccentricity distribution and detectability with current and future gravitational wave observatories.

Contribution

It provides an analytical study of the dynamics and eccentricity distribution of black hole binaries formed in AGN disks, highlighting their potential high eccentricity at detection.

Findings

Most merging binaries are highly eccentric at detection.

Some binaries circularize before entering the LVK band.

Higher eccentricities are expected for certain conditions and future detectors.

Abstract

Many stellar-mass Black Holes (sBHs) are expected to orbit supermassive black holes at galactic centers. For galaxies with Active Galactic Nuclei (AGN), it is likely that the sBHs reside in a disk. We study the formation of sBH binaries via gravitational wave emission in such disks. We examine analytically the dynamics of two sBHs orbiting a supermassive black hole, estimate the capture cross section, and derive the eccentricity distribution of bound binaries at different frequency bands. We find that the majority of the merging sBH binaries, assembled in this manner, can be measured as highly eccentric, detectable in the LIGO-Virgo-KAGRA (LVK) band from their formation, with $(1-e)\ll1$, through their circularization and up to their merger; the remaining binaries circularize to small eccentricities ($e\lesssim0.3$) before entering the LVK band. More eccentric mergers would be observed for sBHs with higher random velocities, closer to the supermassive black hole, or at lower observing frequency bands, as planned in future gravitational wave detectors such as the Einstein Telescope and LISA.