Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries

TL;DR

The paper addresses the challenge of producing accurate analytical gravitational-wave waveforms for coalescing binary black holes by refining the Effective-One-Body (EOB) formalism with flexible parameters that encode uncalculated higher-order effects.It introduces a joint fitting strategy that uses both published inspiral NR data (Caltech-Cornell) and newly generated coalescence NR data (Jena) to constrain the EOB parameters a5, v_pole, and a_bar_RR, yielding an approximately unique best-fit waveform that matches NR across equal- and unequal-mass binaries.Quantitative comparisons show extremely small dephasing, on the order of 0.001–0.02 radians across relevant time intervals and mass ratios, with a5 around 25 providing robust agreement through inspiral, plunge, merger, and ringdown, while amplitude differences near merger remain within NR uncertainties.The results validate the EOB approach as a highly accurate, detector-ready analytic model for BBH waveforms and clarify the limitations of TaylorT4, illustrating the value of NR-calibrated EOB templates for current gravitational-wave detectors.

Abstract

The Effective-One-Body (EOB) formalism contains several flexibility parameters, notably $a_5$, $\vp$ and $\a$. We show here how to jointly constrain the values of these parameters by simultaneously best-fitting the EOB waveform to two, independent, numerical relativity (NR) simulations of inspiralling and/or coalescing binary black hole systems: published Caltech-Cornell {\it inspiral} data (considered for gravitational wave frequencies $Mω\leq 0.1$) on one side, and newly computed {\it coalescence} data on the other side. The resulting, approximately unique, "best-fit" EOB waveform is then shown to exhibit excellent agreement with NR coalescence data for several mass ratios. The dephasing between this best-fit EOB waveform and published Caltech-Cornell inspiral data is found to vary between -0.0014 and +0.0008 radians over a time span of $\sim 2464M$ up to gravitational wave frequency $Mω= 0.1$, and between +0.0013 and -0.0185 over a time span of 96M after $Mω=0.1$ up to $Mω=0.1565$. The dephasings between EOB and the new coalescence data are found to be smaller than: (i) $\pm 0.025$ radians over a time span of 730M (11 cycles) up to merger, in the equal mass case, and (ii) $\pm 0.05$ radians over a time span of about 950M (17 cycles) up to merger in the 2:1 mass-ratio case. These new results corroborate the aptitude of the EOB formalism to provide accurate representations of general relativistic waveforms, which are needed by currently operating gravitational wave detectors.

Figures (14)

• Figure 1: Differences between the phase extracted at $R_{ex} = 90M$, and the phase extrapolated to infinity based on two choices of the retarded time and on two choices of the extrapolating polynomial, as described in the text. The choice of retarded time makes little difference to the result.
• Figure 2: Comparison between Caltech-Cornell and Jena actual numerical data: the phase difference $\Delta\phi_{22}^{\rm CCJena}={\phi^{\rm CC}-\phi_{90M}^{\rm Jena} }$ is shown versus Caltech-Cornell GW frequency $\omega_{\rm CC}$.
• Figure 3: Functional relationships linking $v_{\rm pole}$ and ${\bar{a}_{\rm RR}}$ to $a_5$ obtained by imposing the two constraints \ref{['constraints']}-\ref{['constraints2']} based on published Caltech-Cornell inspiral waveform data.
• Figure 4: Top panel: near-perfect agreement between T4-EOB and T4-NR phase differences when $a_5=25$, ${\bar{a}_{\rm RR}}=27.9197$ and $v_{\rm pole}=0.51563$. Here NR refers to the published results of the Caltech-Cornell inspiral simulation. The corresponding EOB-NR phase difference (bottom panel) is of the order of $10^{-3}$ radians over the 30 GW cycles of the Caltech-Cornell inspiral simulation.
• Figure 5: $L_{\infty}$ norm of the EOB-NR late-inspiral ($[t_{\rm L},t_{\rm R}]$) phase difference, as a function of $a_5$ for $\nu=0.25$ (1:1 mass ratio) and $\nu\simeq 0.2222$ (2:1 mass ratio). NR refers to results of Jena coalescence simulations reported here.