Faithful effective-one-body waveform of small-mass-ratio coalescing black hole binaries: the eccentric, nonspinning, case

TL;DR

This paper introduces a new effective-one-body waveform model for eccentric, nonspinning black hole binaries in the extreme mass ratio limit, achieving high accuracy through detailed modeling of plunge, merger, and ringdown phases.

Contribution

The work develops a novel EOB waveform incorporating noncircular corrections and phenomenological ringdown modeling, including QNM beating, with systematic analysis of waveform completion prescriptions.

Findings

Phase differences less than 0.01 radians for quasi-circular cases.

Phase differences less than 0.05 radians for eccentric cases.

Modeled higher multipoles up to 5.

Abstract

We present a new effective-one-body (EOB) waveform for eccentric, nonspinning, binaries in the extreme mass ratio limit, with initial eccentricities up to $0.95$. The EOB analytical waveform, that includes noncircular corrections up to second post-Newtonian order, is completed by a phenomenological ringdown model that is informed by Regge-Wheeler-Zerilli (RWZ) type waveforms generated by a point-particle source. This model notably includes the beating between positive and negative frequency quasi-normal-modes (QNMs). We analyze various prescriptions to faithfully complete the analytical EOB waveform in the transition from plunge to merger. In particular, we systematically explore the effect of: (i) the generic Newtonian prefactor; (ii) next-to-quasi-circular (NQC) corrections to amplitude and phase; (iii) the point were NQC corrections are determined; (iv) the ringdown attachment point. This yields EOB/RWZ quadrupolar phase differences through merger and ringdown $\lesssim 0.01$~rad for the quasi-circular case and $\lesssim 0.05$~rad for the eccentric case. Higher modes are also modeled up to the $\ell=m=5$ multipole. We finally discuss the excitation of the QNMs and present a heuristic model to motivate it in correlation with the presence of a point-particle source.