Investigating the quasinormal mode content of eccentric black hole coalescences: signatures of eccentricity in late-time merger waveforms

Black hole binaries with small mass ratios will be critical targets for the forthcoming Laser Interferometer Space Antenna (LISA) mission. They also serve as useful tools for studying the dynamics of compact binary systems and the gravitational waves they emit. Using an eccentric Ori-Thorne procedure, we build trajectories that describe the full inspiral and plunge of a small body on an initially eccentric orbit of a Kerr black hole. We then calculate the gravitational waves associated with these trajectories with a code that solves the Teukolsky equation in the time domain. The final cycles of these waveforms are a superposition of Kerr quasinormal modes. In this work, we examine the impact of orbital eccentricity and its associated phase parameters on quasinormal mode excitation. We find that a binary's eccentricity during its last orbital revolutions has notable signatures on the relative mode excitation. If these signatures from the small-mass-ratio regime are present at less extreme mass ratios, then measuring gravitational ringdown modes from binary black hole mergers may provide key insight into a binary's geometry. A diagnostic of eccentricity in the late waveform could be a valuable tool for understanding the systems that create these signals for next-generation detectors like LISA, as well as the ground-based detectors operating today.