Parametrized-4.5PN TaylorF2 approximants and tail effects to quartic nonlinear order from the effective one body formalism

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. [Classical Quantum Gravity 33, 244003 (2016)] is actually contained in the resummed expression; this is also the case of the next-to-leading-order tail-induced spin-orbit term of Marsat et al. [Classical Quantum Gravity 31, 025023 (2014)]; (ii) in performing this expansion, we also obtain, for the first time, the explicit 3.5PN leading-order tail-induced spin-spin flux term; and (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 Taylor F2 approximant. Focusing for simplicity on the nonspinning case and using the numerical-relativity calibrated IMRPhenomD waveform model as a 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 these types 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.