Exploiting Newton-factorized, 2PN-accurate, waveform multipoles in effective-one-body models for spin-aligned noncircularized binaries

• Published in: arXiv.org 2022-03
• Main Authors: Placidi, Andrea, Albanesi, Simone, Nagar, Alessandro, Orselli, Marta, Bernuzzi, Sebastiano, Grignani, Gianluca
• Format: Article
• Language: English
• Subjects: Eccentricity; Factorization; Mathematical models; Multipoles; Numerical relativity; Outliers (statistics); Relativity; Waveforms
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2112.05448

We present a new approach to factorize and resum the post-Newtonian (PN) waveform for generic equatorial motion to be used within effective-one-body (EOB) based waveform models. The new multipolar waveform factorization improves previous prescriptions in that: (i) the generic Newtonian contribution is factored out from each multipole; (ii) the circular part is factored out and resummed using standard EOB methods and (iii) the residual, 2PN-accurate, noncircular part, and in particular the tail contribution, is additionally resummed using Padé approximants. The resulting waveform is validated in the extreme-mass-ratio limit by comparisons with nine (mostly nonspinning) numerical waveforms either from eccentric inspirals, with eccentricities up to \(e=0.9\), or dynamical captures . The resummation of the noncircular tail contribution is found essential to obtain excellent (\({\lesssim}0.05\)~rad at periastron for \(e=0.9\)) analytical/numerical agreement and to considerably improve the prescription with just the Newtonian prefactor. In the comparable mass case, the new 2PN waveform shows only a marginal improvement over the previous Newtonian factorization, though yielding maximal unfaithfulness \(\simeq 10^{-3}\) with the 28 publicly available numerical relativity simulations with eccentricity up to \(\sim 0.3\) (except for a single outlier that grazes \(10^{-2}\)). We finally use test-particle data to validate the waveform factorization proposed by Khalil et al.~[Phys.~Rev.~104 (2021) 2, 024046] and conclude that its amplitude can be considered reliable (though less accurate, \(\sim 6\%\) fractional difference versus \(1.5\%\) of our method) only up to eccentricities \(\sim 0.3\).