Modeling the merger-ringdown of an eccentric test-mass inspiral into a Kerr black hole using the effective-one-body framework

We characterize and phenomenologically model the merger-ringdown of gravitational waves emitted by a small compact object that plunges and merges into a Kerr black hole from equatorial-eccentric inspirals. The waveforms are generated employing a time-domain Teukolsky code sourced with trajectories computed using the effective-one-body framework. We span values of the Kerr spin $a\in[-0.9, 0.9]$, eccentricity at the last stable orbit (LSO) $e_{\rm LSO} \in [0,0.9]$, and relativistic anomaly $\xi_{\rm LSO} \in [0 , 2 \pi]$. We characterize the last peak of the waveform and ringdown features across the parameter space, finding that the eccentricity mainly affects the last peak features, while it has a smaller impact on the ringdown signal. In contrast, the relativistic anomaly measured at the LSO influences the morphology of the last peak in a restricted portion of the parameter space and has no impact on the ringdown part. We perform the analysis for all the spin-weighted spherical harmonic modes normally included in the $\texttt{SEOBNR}$ family of models, $(\ell,m)\in\{ (2,2), (3,3), (4,4), (5,5), (2,1), (3,2), (4,3)\}$. Finally, we introduce a merger-ringdown model for $\texttt{SEOB-TMLE}$, a forthcoming inspiral-merger-ringdown waveform model for eccentric spin-aligned binary black holes in the test-mass limit, whose features can be extended to comparable-mass regimes. The model also accounts for quasinormal mode mixing during the ringdown. It provides a first step toward incorporating the impact of residual eccentricity close to merger into spin-aligned effective-one-body merger-ringdown models for binary black holes.