Eccentric Features in the Gravitational-wave Phase of Dynamically Formed Black Hole Binaries - Kai Hendriks; Lorenz Zwick; Johan Samsing (The Astrophysical Journal)
We study the gravitational-wave (GW) phase shift arising from center-of-mass accelerations of binary black hole (BBH) 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 pericenter 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 on the phase shift if the binary passes the outer pericenter during its inspiral. By comparing with phase shifts measured in numerical chaotic three-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. Phase shifts produced in such environments may receive additional amplifications due to the tidal pull from the perturber on the BBH.