Peaking into the abyss: Characterizing the merger of equatorial-eccentric-geodesic plunges in rotating black holes

TL;DR

This paper analyzes gravitational waveforms from equatorial plunges into rotating black holes, revealing complex dependencies on spin and eccentricity, and characterizing the merger features across parameter space.

Contribution

It provides a detailed characterization of gravitational wave modes during equatorial eccentric plunges in Kerr spacetime, including the conditions for waveform peaks.

Findings

Waveform modes do not always peak at high eccentricities or spins.

Identified parameter regions where the dominant mode $h_{22}$ peaks.

Characterized the merger structure of various modes in Kerr plunges.

Abstract

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 Teukolsky code. We span different values of the Kerr spin $-0.99 \le a \le 0.99 $ and of the critical eccentricity $e_c$, for bound ($0 \le e_c<1$) and unbound plunges ($e_c \ge 1$). We find that, contrary to expectations, the waveform modes $h_{\ell m}$ do not always manifest a peak for high eccentricities or spins. In case of the dominant $h_{22}$ 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 $h_{22}$ 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.