Quasi-5.5PN TaylorF2 approximant for compact binaries: point-mass phasing and impact on the tidal polarizability inference
Résumé
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 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 Qω=ω^2/ω^˙, where ω^ 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 ΔΨEOBPN∼10-3 rad (0.13 rad) up to frequency ω^≃0.06, 6 orbits to merger, (ω^≃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 Λ˜ 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 Λ˜ that are instead found when the standard 3.5PN point-mass baseline is used. Methodologically, we demonstrate that the combined use of Qω analysis and of the Bayesian parameter estimation offers a new tool to investigate the impact of systematics on gravitational-wave inference.