Ringdown modeling for effective-one-body waveforms in the test-mass limit for eccentric equatorial orbits around a Kerr black hole

TL;DR

This paper develops a detailed model for the plunge and merger phases of eccentric, equatorial orbits around Kerr black holes, improving waveform accuracy for gravitational wave detection.

Contribution

It introduces a novel ringdown modeling approach starting near the light-ring crossing, extending to high spins and eccentricities, and includes multiple multipoles and mode-mixing effects.

Findings

Model accurately captures plunge and merger phases.

Extends to high spins and eccentricities.

Provides a complete effective-one-body waveform.

Abstract

We study the plunge and merger of a non-spinning particle falling into a Kerr black hole following an eccentric planar inspiral. The dynamics is driven by an effective-one-body radiation reaction, and the corresponding numerical inspiral-merger-ringdown waveforms are obtained by solving the Teukolsky equation with the 2+1 time-domain code Teukode. We then analyze in detail the plunge and merger phases, modeling the merger-ringdown waveform using closed-form ans\"atze. Crucially, our modeling starts from a point closely related to the light-ring crossing, rather than from the amplitude peaks. This choice allows us to neglect the impact of the relativistic anomaly at the separatrix-crossing, and to extend the modeling to high spins and high eccentricities. We model all the multipoles with $m\geq 1$ up to $\ell=4$, as well as the $(2,0)$, $(5,5)$, $(5,4)$, and $(5,3)$ modes, including spherical-spheroidal mode-mixing and the beating between co-rotating and counter-rotating quasi-normal modes. The post-merger waveform model is then employed to complete an effective-one-body inspiral-plunge waveform, thus providing a complete description. Our model, built using elliptic-like configurations for the merger-ringdown phase, naturally extends to dynamical capture scenarios without any further modification. Finally, we provide insights into the extension of this framework to generic mass ratios, arguing that a time closely related to the inflection point of the (2,2) waveform frequency could be used as anchoring point for the ringdown modeling.