Gravitational Wave Phase Shifts in Eccentric Black Hole Mergers as a Probe of Dynamical Formation Environments

Understand

We quantify for the first time the gravitational wave (GW) phase shift appearing in the waveform of eccentric binary black hole (BBH) mergers formed dynamically in three-body systems.

• For this, we have developed a novel numerical method where we construct a reference binary, by evolving the post-Newtonian (PN) evolution equations backwards from a point near merger without the inclusion of the third object, that can be compared to the real binary that evolves under the influence from the third BH.
• From this we quantify how the interplay between dynamical tides, PN-effects, and the time-dependent Doppler shift of the eccentric GW source results in unique observable GW phase shifts that can be mapped to the gravitational dynamics taking place at formation.
• We further find a new analytical expression for the GW phase shift, which surprisingly has a universal functional form that only depends on the time-evolving BBH eccentricity.