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Effective-one-body model for black-hole binaries with generic mass ratios and spins

Andrea Taracchini, Alessandra Buonanno, Yi Pan, Tanja Hinderer, Michael Boyle, Daniel A. Hemberger, Lawrence E. Kidder, Geoffrey Lovelace, Abdul H. Mroue, Harald P. Pfeiffer, Mark A. Scheel, Bela Szilagyi, Nicholas W. Taylor, Anil Zenginoglu

Abstract

Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio in LIGO and Virgo detectors when black-hole spins are aligned with the orbital angular momentum and extremal. For such systems, we extend the effective-one-body inspiral-merger-ringdown waveforms to generic mass ratios and spins calibrating them to 38 numerical-relativity nonprecessing waveforms produced by the SXS Collaboration. The numerical-relativity simulations span mass ratios from 1 to 8, spin magnitudes up to 98% of extremality, and last for 40 to 60 gravitational-wave cycles. When the total mass of the binary is between 20Msun and 200Msun, the effective-one-body nonprecessing (dominant mode) waveforms have overlaps above 99% (using the advanced-LIGO design noise spectral density) with all of the 38 nonprecessing numerical waveforms, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling. Moreover, without further calibration, we show that the precessing effective-one-body (dominant mode) waveforms have overlaps above 97% with two very long, strongly precessing numerical-relativity waveforms, when maximizing only on the initial phase and time.

Effective-one-body model for black-hole binaries with generic mass ratios and spins

Abstract

Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio in LIGO and Virgo detectors when black-hole spins are aligned with the orbital angular momentum and extremal. For such systems, we extend the effective-one-body inspiral-merger-ringdown waveforms to generic mass ratios and spins calibrating them to 38 numerical-relativity nonprecessing waveforms produced by the SXS Collaboration. The numerical-relativity simulations span mass ratios from 1 to 8, spin magnitudes up to 98% of extremality, and last for 40 to 60 gravitational-wave cycles. When the total mass of the binary is between 20Msun and 200Msun, the effective-one-body nonprecessing (dominant mode) waveforms have overlaps above 99% (using the advanced-LIGO design noise spectral density) with all of the 38 nonprecessing numerical waveforms, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling. Moreover, without further calibration, we show that the precessing effective-one-body (dominant mode) waveforms have overlaps above 97% with two very long, strongly precessing numerical-relativity waveforms, when maximizing only on the initial phase and time.

Paper Structure

This paper contains 6 equations, 4 figures.

Figures (4)

  • Figure 1: Unfaithfulness of (2,2) EOB waveforms for all the 38 nonprecessing BH binaries in the SXS catalog. Only a few selected cases are labeled in the legend.
  • Figure 2: NR and EOB (2,2) waveforms of the BH binary with $q=1$ and $\chi_{1}=\chi_{2}=0.98$. The two waveforms are aligned at their amplitude peak (marked by a vertical dashed line). $R$ is the distance to the source.
  • Figure 3: The specific binding energy $\hat{E}=E/\mu$ as a function of the dimensionless total angular momentum $\hat{J}=J/(\mu M)$ of the BH binaries with $q=1$ and $\chi_{1}=\chi_{2}=-0.95,\,0.98$ computed in NR, conservative uncalibrated EOB model and the calibrated EOB model of this paper.
  • Figure 4: NR and EOB (2,2) precessing waveforms of the BH binary with $q=5$ and initial spins $|\hbox{$\bm{S}$}_1|/m_{1}^{2}=0.5$ in the orbital plane and $|\hbox{$\bm{S}$}_2|/m_{2}^{2}=0$. The two waveforms are aligned at low frequency. $R$ is the distance to the source.