Gravitational-Wave Signatures of Highly Eccentric Stellar-Mass Binary Black Holes in Galactic Nuclei

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 Hz. Several compact binaries detected by the LIGO-Virgo-KAGRA Collaboration may retain hints of residual eccentricity at 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, ω, of the inner black hole binary. The latter could be fully circulating, where ω cycles through 2π, or may librate, with ω ranges about a fixed value with small or large variation. We use TSUNAMI, a regularised 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 utilising 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 timescale is the same. Future burst timing models will be able to distinguish the different orbital configurations. For efficient binary formation, about ~50 binaries can have librating orbits in the Galactic Centre.