Characterizing the merger of equatorial-eccentric-geodesic plunges in rotating black holes

We study the gravitational waveforms generated by critical, equatorial plunging geodesics of the Kerr metric that start from an unstable-circular-orbit, which describe the test-mass limit of spin-aligned eccentric black hole mergers. The waveforms are generated employing a time-domain eukolsky code. We span different values of the Kerr spin −0.99≤a≤0.99 and of the critical eccentricity ec, for bound (0≤ec1) and unbound plunges (ec≥1). We find that, contrary to expectations, the waveform modes hℓm do not always manifest a peak for high eccentricities or spins. In case of the dominant h22 mode, we determine the precise region of the parameter space in which its peak exists. In this region, we provide a characterization of the merger quantities of the h22 mode and of the higher-order modes, providing the merger structure of the equatorial-eccentric plunges of the Kerr spacetime in the test-mass limit.