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Faithful Effective-One-Body waveforms of equal-mass coalescing black-hole binaries

Thibault Damour, Alessandro Nagar, Ernst Nils Dorband, Denis Pollney, Luciano Rezzolla

TL;DR

The paper addresses the need for accurate analytical gravitational-wave templates for equal-mass, non-spinning binary black hole coalescences by testing a resummed $3^{+2}$ PN EOB quadrupolar waveform against a high-precision NR simulation. The authors employ an enhanced EOB model featuring a resummed radial potential, Padé-resummed radiation reaction, a refined insplunge waveform with NQC corrections, and a five-tooth comb matching to a ringdown formed from five QNMs, with initial data incorporating post-post-circular corrections. Across two representative values of the effective 4 PN parameter $a_5$ and corresponding $v_{pole}$, they achieve remarkable phase agreement (phase dephasing $ ext{<} ext{±}0.01$ cycles over ~13 GW cycles) and sub-1% amplitude agreement up to late inspiral, with larger but quantified deviations near merger and ringdown. These results, together with a comparison to a restricted EOB implementation, demonstrate the fidelity of the EOB formalism in capturing the general-relativistic waveforms and underscore its potential for generating accurate GW templates for detectors.

Abstract

We continue the program of constructing, within the Effective-One-Body (EOB) approach, high-accuracy analytic waveforms describing the signal emitted by inspiralling and coalescing black hole binaries. Here, we compare a recently derived, resummed 3 PN-accurate EOB quadrupolar waveform to the results of a numerical simulation of the inspiral and merger of an equal-mass black hole binary. We find a remarkable agreement, both in phase and in amplitude, with a maximal dephasing which can be reduced below $\pm 0.005$ gravitational-wave (GW) cycles over 12 GW cycles corresponding to the end of the inspiral, the plunge, the merger and the beginning of the ringdown. This level of agreement is shown for two different values of the effective 4 PN parameter a_5, and for corresponding, appropriately "flexed" values of the radiation-reaction resummation parameter v_pole. In addition, our resummed EOB amplitude agrees to better than the 1% level with the numerical-relativity one up to the late inspiral. These results, together with other recent work on the EOB-numerical-relativity comparison, confirm the ability of the EOB formalism to faithfully capture the general relativistic waveforms.

Faithful Effective-One-Body waveforms of equal-mass coalescing black-hole binaries

TL;DR

The paper addresses the need for accurate analytical gravitational-wave templates for equal-mass, non-spinning binary black hole coalescences by testing a resummed PN EOB quadrupolar waveform against a high-precision NR simulation. The authors employ an enhanced EOB model featuring a resummed radial potential, Padé-resummed radiation reaction, a refined insplunge waveform with NQC corrections, and a five-tooth comb matching to a ringdown formed from five QNMs, with initial data incorporating post-post-circular corrections. Across two representative values of the effective 4 PN parameter and corresponding , they achieve remarkable phase agreement (phase dephasing cycles over ~13 GW cycles) and sub-1% amplitude agreement up to late inspiral, with larger but quantified deviations near merger and ringdown. These results, together with a comparison to a restricted EOB implementation, demonstrate the fidelity of the EOB formalism in capturing the general-relativistic waveforms and underscore its potential for generating accurate GW templates for detectors.

Abstract

We continue the program of constructing, within the Effective-One-Body (EOB) approach, high-accuracy analytic waveforms describing the signal emitted by inspiralling and coalescing black hole binaries. Here, we compare a recently derived, resummed 3 PN-accurate EOB quadrupolar waveform to the results of a numerical simulation of the inspiral and merger of an equal-mass black hole binary. We find a remarkable agreement, both in phase and in amplitude, with a maximal dephasing which can be reduced below gravitational-wave (GW) cycles over 12 GW cycles corresponding to the end of the inspiral, the plunge, the merger and the beginning of the ringdown. This level of agreement is shown for two different values of the effective 4 PN parameter a_5, and for corresponding, appropriately "flexed" values of the radiation-reaction resummation parameter v_pole. In addition, our resummed EOB amplitude agrees to better than the 1% level with the numerical-relativity one up to the late inspiral. These results, together with other recent work on the EOB-numerical-relativity comparison, confirm the ability of the EOB formalism to faithfully capture the general relativistic waveforms.

Paper Structure

This paper contains 8 sections, 5 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Brief description of the numerical simulation
  3. Effective-One-Body (EOB) method and waveform
  4. Comparing the NR waveform to EOB ones
  5. Comparing NR to resummed EOB for $a_5 = 25$
  6. Comparing NR to resummed EOB for $a_5 = 60$
  7. Contrasting resummed EOB with restricted EOB, for $a_5 = 60$, by comparing NR to a standard restricted EOB waveform
  8. Conclusions

Figures (3)

  • Figure 1: Comparison between EOB and NR waveforms for $a_5=25$ and $v_{\rm pole}=0.6241$: frequencies (top--left), phase difference (top--right), amplitudes (bottom--left) and real parts (bottom--right) of the two gravitational waveforms. The vertical line at $t_{\rm NR}=1509$ locates the maximum of (twice) the orbital frequency $\Omega$ (alias the "EOB-light-ring") and indicates the center of our matching comb (whose total width is indicated by the two neighboring vertical lines in the top--left panel). The vertical dashed line at $t^{\rm NR}=1482$ indicates the crossing time of the adiabatic LSO orbital frequency ($\Omega_{\rm LSO}= 0.1003$).
  • Figure 2: Comparison between EOB and NR waveforms for $a_5=60$, $v_{\rm pole}=0.5356$: frequencies (top--left), phase difference (top--right), amplitudes (bottom--left) and real parts (bottom--right) of the two gravitational waveforms. The vertical line at $t_{\rm NR}=1510$ locates the maximum of (twice) the orbital frequency $\Omega$ (alias the "EOB-light-ring") and indicates the center of our matching comb (whose total width is indicated by the two neighboring vertical lines in the top--left panel). The vertical dashed line at $t^{\rm NR}=1487$ indicates the crossing time of the adiabatic LSO orbital frequency ($\Omega_{\rm LSO}= 0.1081$).
  • Figure 3: Comparison between the EOB restricted waveform approximation, Eq. (\ref{['psiEOB_BD']}), and NR for $a_5=60$ and $v_{\rm pole}=v_{\rm pole}^{\rm DIS}(\nu=1/4)=0.6907$: frequencies (top--left), phase difference (top--right), amplitudes (bottom--left) and real parts (bottom--right) of the two gravitational waveforms. The vertical line at $t_{\rm NR}=1510$ locates the maximum of (twice) the orbital frequency $\Omega$ (alias the "EOB-light-ring") and indicates the matching time. The vertical dashed line at $t^{\rm NR}=1490$ indicates the crossing time of the adiabatic LSO orbital frequency ($\Omega_{\rm LSO}= 0.1081$).