Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion

TL;DR

The paper advances the analytic EOB description of nonspinning black-hole binaries by incorporating 4PN/5PN logarithmic corrections to the conservative dynamics, resummed horizon-absorption contributions to angular-momentum loss, and a radial radiation-reaction term, then completes the model by calibrating to high-accuracy NR simulations. It introduces a NR-derived $Q_\omega(\omega)$ diagnostic to quantify intrinsic phase evolution and uses NR data to fix the main radial potential $A(u;ν)$ with precision near $10^{-4}$, while matching the inspiral–plunge waveform to NR and attaching 5 QNMs for merger–ringdown. The resulting NR-completed EOB model achieves excellent phase and amplitude agreement with NR across mass ratios $q=(1,2,3,4,6)$ and several subdominant multipoles, without ad hoc tuning, and provides a detailed ν-dependent parameterization of the EOB potentials for extension to arbitrary mass ratios. These advances yield highly faithful GW templates suitable for detection and parameter estimation, and establish a framework for extending EOB to spinning and tidally interacting systems.

Abstract

We improve the effective-one-body (EOB) description of nonspinning coalescing black hole binaries by incorporating several recent analytical advances, notably: (i) logarithmic contributions to the conservative dynamics; (ii) resummed horizon-absorption contribution to the orbital angular momentum loss; and (iii) a specific radial component of the radiation reaction force implied by consistency with the azimuthal one. We then complete this analytically improved EOB model by comparing it to accurate numerical relativity (NR) simulations performed by the Caltech-Cornell-CITA group for mass ratios $q=(1,2,3,4,6)$. In particular, the comparison to NR data allows us to determine with high-accuracy ($\sim 10^{-4}$) the value of the main EOB radial potential: $A(u;\,ν)$, where $u=GM/(R c^2)$ is the inter-body gravitational potential and $ν=q/(q+1)^2$ is the symmetric mass ratio. We introduce a new technique for extracting from NR data an intrinsic measure of the phase evolution, ($Q_ω(ω)$ diagnostics). Aligning the NR-completed EOB quadrupolar waveform and the NR one at low frequencies, we find that they keep agreeing (in phase and amplitude) within the NR uncertainties throughout the evolution for all mass ratios considered. We also find good agreement for several subdominant multipoles without having to introduce and tune any extra parameters.

Figures (22)

• Figure 1: (color online) Comparing the Taylor-expanded $\hat{\delta}_{22}$ with its (2,2) Padé approximant for two mass ratios.
• Figure 2: (color online) Top panel: Raw NR, curvature waveform, data; smoothed data and fit. Bottom panel: difference between smoothed data and the fit.
• Figure 3: (color online) Fitting the Newton-rescaled $\hat{Q}_\omega$, curvature waveform, function. The top panel contrasts the smoothed data with the outcome of the fit. The bottom panel shows their difference.
• Figure 4: (color online) Hierarchy of important points of the test-mass (Zerilli-normalized) quadrupolar metric waveform (divided by $\nu$), $\Psi_{2 2}/\nu \equiv (R/M) h_{2 2} /( \nu \sqrt{24})$ around the merger point. The orbital frequency $\Omega$ peaks at approximately 2/3 of the time interval between the peak of the metric amplitude and the inflection point of the GW frequency, i.e. the first peak of $\dot{\omega}_{22}$.
• Figure 5: (color online) Test-mass waveform: comparison between RWZ waveform extracted at ${\mathrsfs{I}}^+$ and EOB waveform completed by the 6-parameter NQC correction factor to the waveform, Eq. \ref{['eq:hNQC']}. Top panels: $\ell=m=2$ multipole, modulus and frequency (left) and phasing (right). Bottom panels: $\ell=2$ and $m=1$ and $\ell=m=3$ frequency and modulus. The ringdown is modeled using 5 (positive-frequency only) QNMs.