Quasi-5.5PN TaylorF2 approximant for compact binaries: point-mass phasing and impact on the tidal polarizability inference

Abstract

We derive a point-mass (nonspinning) frequency-domain TaylorF2 phasing approximant at quasi-5.5 post-Newtonian (PN) accuracy for the gravitational wave from coalescing compact binaries. The new approximant is obtained by Taylor-expanding the effective-one-body (EOB) resummed energy and and angular momentum flux along circular orbits with all the known test-particle information up to 5.5PN. The -- yet uncalculated -- terms at 4PN order and beyond entering both the energy flux and the energy are taken into account as free parameters and then set to zero. We compare the quasi-5.5PN and 3.5PN approximants against full EOB waveforms using gauge-invariant phasing diagnostics $Q_{\omega }={\hat{\omega }}^2/\dot{\hat{\omega }}$, where $\hat{\omega }$ is the dimensionless gravitational-wave frequency. The quasi-5.5PN phasing is found to be systematically closer to the EOB one than the 3.5PN one. Notably, the quasi-5.5PN (3.5PN) approximant accumulates a EOB$-$PN dephasing of $\Delta {\Psi }^{\mathrm{EOBPN}}\sim 10^{-3}$rad ($0.13$rad) up to frequency $\hat{\omega }\simeq 0.06$, 6 orbits to merger, ($\hat{\omega }\simeq 0.086$, 2 orbits to merger) for a fiducial binary neutron star system. We explore the performance of the quasi-5.5PN approximant on the measurement of the tidal polarizability parameter $\tilde{\Lambda }$ using injections of EOB waveforms hybridized with numerical relativity merger waveforms. We prove that the quasi-5.5PN point-mass approximant augmented with 6PN-accurate tidal terms allows one to reduce (and in many cases even eliminate) the biases in the measurement of $\tilde{\Lambda }$ that are instead found when the standard 3.5PN point-mass baseline is used. Methodologically, we demonstrate that the combined use of $Q_{\omega }$ analysis and of the Bayesian parameter estimation offers a new tool to investigate the impact of systematics on gravitational-wave inference.

arXiv comment13 pages, 7 figures, submitted to Phys. Rev. D

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