# Parametrized-4.5PN TaylorF2 approximant(s) and tail effects to quartic nonlinear order from the effective one body formalism

## TL;DR

This paper derives a 4.5PN TaylorF2 approximant from the effective one-body formalism, incorporating tail effects and higher-order contributions, and demonstrates its potential for improved gravitational wave modeling and data analysis.

## Contribution

It introduces a parametrized 4.5PN TaylorF2 approximant derived from EOB formalism, including tail effects and higher-order PN terms, enhancing gravitational wave template accuracy.

## Key findings

- The 4.5PN tail-of-tails-of-tails contribution is contained in the resummed EOB flux.
- First explicit 3.5PN tail-induced spin-spin flux term obtained.
- The approximant can reproduce the phase derivative of IMRPhenomD with only one effective parameter.

## Abstract

By post-Newtonian (PN) expanding the well-known, factorized and resummed, effective-one-body energy flux for circularized binaries we show that: (i) because of the presence of the resummed tail factor, the 4.5PN-accurate tails-of-tails-of-tails contribution to the energy flux recently computed by Marchand et al. [Class. Q. Grav. 33 (2016) 244003] is actually contained in the resummed expression; this is also the case of the the next-to-leading-order tail-induced spin-orbit term of Marsat et al. [Class. Q. Grav. 31 (2014) 025023]; (ii) in performing this expansion, we also obtain, for the first time, the explicit 3.5PN leading-order tail-induced spin-spin flux term; (iii) pushing the PN expansion of the (nonspinning) EOB flux up to 5.5PN order, we compute 4PN, 5PN and 5.5PN contributions to the energy flux, though in a form that explicitly depends on, currently unknown, 4PN and 5PN non-test-mass corrections to the factorized waveform amplitudes. Within this (parametrized) 4.5PN accuracy, we calculate the TaylorF2 approximant. Focusing for simplicity on the nonspinning case and using the numerical-relativity calibrated IMRPhenomD waveform model as benchmark, we demonstrate that it is possible to reproduce the derivative of the IMRPhenomD phase (say up to the frequency of the Schwarzschild last-stable-orbit) by flexing only a 4PN "effective" waveform amplitude parameter. A preliminary analysis also illustrates that similar results can be obtained for the spin-aligned case provided only the leading-order spin-orbit and spin-spin terms are kept. Our findings suggest that this kind of, EOB-derived, (parametrized), higher-order, PN approximants may serve as promising tools to construct Inspiral-Merger-Ringdown phenomenological models or even to replace the standardly used 3.5PN-accurate TaylorF2 approximant in searches of small-mass binaries.