Final Stages of Extreme Mass Ratio Inspirals: 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 $Q$. Once the small body evolves past its last stable orbit, 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 rapidly evolving 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 binaries at less extreme mass ratios which are being observed by ground-based detectors.