Final Stages of Small-Mass-Ratio Binaries: Eccentric Transition to Plunge*

Black hole binaries with small mass ratios will be critical targets for the forthcoming Laser Interferometer Space Antenna (LISA) mission, and serve as useful tools for understanding the properties of binaries at general mass ratios. In its early stages, such a binary's gravitational-wave-induced inspiral can be modeled as the small body flowing through a sequence of geodesic orbits of the larger black hole's spacetime. Its motion through this sequence is determined by the rate at which gravitational-wave backreaction changes an orbit's integrals of motion $E$, $L$, and $Q$. Key to the motion being close to a geodesic at any moment is the idea that the effect of backreaction is small compared to a "restoring force'' arising from the potential which governs geodesic motion. This restoring force holds the small body on a geodesic trajectory as the backreaction causes that geodesic to slowly evolve. As the inspiraling body approaches the last stable orbit (LSO), the restoring force becomes weaker and the backreaction becomes stronger. Once the small body evolves past the LSO, its trajectory converges to a plunging geodesic into the larger black hole. This work aims to smoothly connect these two disparate regimes: the slowly evolving adiabatic inspiral and the final plunge. Past work has focused on this "transition to plunge" for circular orbits. Here, we study the transition for orbits with eccentricity. A well-defined transition will help generate waveforms for LISA, and could also shed light on the physics of late-stage inspiral for less extreme mass ratio binaries observed by ground-based detectors