Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes

TL;DR

The paper presents the first calibration of the spin-augmented effective-one-body (EOB) framework to accurate numerical-relativity simulations of spinning, non-precessing, equal-mass black-hole binaries. By aligning NR and EOB waveforms at low frequency over a long interval and calibrating a small set of parameters—two dynamics terms, four non-quasi-circular/waveform terms, and a merger-time offset—the authors achieve near NR accuracy for the leading $h_{22}$ mode, with overlaps exceeding 0.999 for total masses in the LIGO band. They also demonstrate strong agreement for several subleading modes, with the main exception being $h_{32}$ in the anti-aligned case, attributed to incomplete PN spin effects in higher modes. The results indicate that the spin EOB model can provide highly faithful, computationally efficient templates for spinning BBHs, enabling robust detection and parameter estimation with current and future gravitational-wave detectors, while highlighting areas for further improvement in the spin-sector Hamiltonian and broader NR coverage.

Abstract

We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can be reduced to 0.01 radians and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin anti-aligned case, these differences can be reduced to 0.13 radians and 1% during inspiral and plunge, and to 0.4 radians and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin anti-aligned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical (2,2) mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30-200Ms. In addition to the leading (2,2) mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the (3,2) mode in the spin anti-aligned case. We believe that the larger difference in the (3,2) mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.

Figures (8)

• Figure 1: (color online). Numerical error estimates for the UU configuration. We show the phase difference between several numerical $\Psi_4^{22}$ waveforms aligned using the procedure defined by Eq. \ref{['waveshifts']}.
• Figure 2: (color online). Numerical error estimates for the DD configuration. We show the phase difference between several numerical $\Psi_4^{22}$ waveforms aligned using the procedure defined by Eq. (\ref{['waveshifts']}).
• Figure 3: Phase and relative amplitude difference between the $(l,m)\!=\!(2,2)$ modes of the RWZ waveform $h_{\rm RWZ}$ and NP scalar $\Psi_4$ for the UU case.
• Figure 4: Phase and relative amplitude difference between the $(l,m)\!=\!(2,2)$ modes of the RWZ waveform $h_{\rm RWZ}$ and NP scalar $\Psi_4$ for the DD case. The right panel shows an enlargement of merger and ringdown, with the dotted vertical lines indicating time of maximum of $|\Psi_4|$, and where $|\Psi_4|$ has decayed to 10% and 1% of the maximal value. (The blue lines are smoothed; the grey data in the background represents the unsmoothed data.)
• Figure 5: (color online). Comparison between the numerical and EOB waveform for the UU configuration using $b(\nu)=-1.65$ and $a^{\rm 3PN}_{\rm SS}=1.5$. The top panels show the real part of the numerical and EOB $h_{22}$, the bottom panels show amplitude and phase differences between them. The left panels show times $t=0$ to $2950M$, whereas the right panels present an enlargement of the later portion of the waveform.