Gravitational-wave signatures of highly eccentric stellar-mass binary black holes in galactic nuclei

ABSTRACT A significant fraction of compact-object mergers in galactic nuclei are expected to be eccentric in the Laser Interferometer Space Antenna (LISA) frequency sensitivity range, $10^{-4}\!-\! 10^{-1}\ \rm Hz$. Several compact binaries detected by the LIGO-Virgo-KAGRA Collaboration may retain hints of residual eccentricity at $\sim 10$ Hz, suggesting dynamical or triple origins for a significant fraction of the gravitational-wave-observable population. In triple systems, von-Zeipel-Lidov-Kozai oscillations perturb both the eccentricity and the argument of pericentre, $\omega$, of the inner black hole binary. The latter could be fully circulating, where $\omega$ cycles through $2\pi$, or may librate, with $\omega$ ranges about a fixed value with small or large variation. We use TSUNAMI, a regularized N-body code with up to 3.5 post-Newtonian (PN) term corrections, to identify four different families of orbits: (i) circulating, (ii) small and (iii) large amplitude librating, and (iv) merging orbits. We develop and demonstrate a new method to construct gravitational waveforms using the quadrupole formula utilizing the instantaneous total acceleration of each binary component in TSUNAMI. We show that the four orbital families have distinct waveform phenomenologies, enabling them to be distinguished if observed in LISA. The orbits are also distinguishable from an isolated binary or from a binary perturbed by a different tertiary orbit, even if the secular time-scale is the same. Future burst timing models will be able to distinguish the different orbital configurations. For efficient binary formation, about $\sim 1000$ binaries can have highly eccentric, librating orbits in the Galactic Centre.