Eccentric features in the gravitational wave phase of dynamically formed black hole binaries

TL;DR

This paper investigates the gravitational wave phase shifts caused by center-of-mass accelerations in dynamically formed eccentric black hole binaries within three-body systems, providing models to identify their formation channels.

Contribution

It introduces a semi-analytical model for GW phase shifts in eccentric, dynamically formed black hole binaries, enabling rapid evaluation and channel identification.

Findings

Maximum phase shifts occur near the outer orbit pericentre.

High outer orbit eccentricity causes distinct phase shift imprints.

Model accurately matches phase shifts from numerical 3-body scatterings.

Abstract

We study the gravitational wave (GW) phase shift arising from center-of-mass accelerations of binary black hole mergers formed dynamically in three-body systems, where both the inner orbit of the merging binary and the outer orbit are eccentric. We provide a semi-analytical model and several analytical approximations that allow for fast evaluation of both the temporal evolution and the maximum value of the phase shift. The highest phase shifts occur when the binary merges close to the pericentre of the outer orbit, and can in this case be orders-of-magnitude larger compared to the circular limit. At high outer orbit eccentricities, the orbital curvature leaves distinct imprints onto the phase shift if the binary passes the outer pericentre during its inspiral. By comparing with phase shifts measured in numerical chaotic 3-body scatterings, we show that our model accurately describes the observed phase of dynamically assembled binary systems in realistic astrophysical scenarios, providing a way to directly determine their formation channel via single GW observations.