Effective-one-body model for black-hole binaries with generic mass ratios and spins (1311.2544v1)

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.

• The paper presents a calibrated effective-one-body model that accurately simulates black-hole binaries with mass ratios from 1 to 8 and spin magnitudes up to 98% of extremality.
• The methodology achieves over 99% overlap with nonprecessing and above 97% with precessing numerical waveforms, ensuring robust and efficient template generation.
• The work enhances gravitational wave detection capabilities and paves the way for future improvements in radiation-reaction theories and multimode waveform modeling.

Effective-One-Body Model for Black-Hole Binaries with Generic Mass Ratios and Spins

The paper presents an advanced approach for modeling gravitational waveforms emitted by black-hole binary systems, focusing on generic mass ratios and spins. Utilizing the effective-one-body (EOB) framework, the researchers have extended previous models—crucial for gravitational wave detection by LIGO and Virgo detectors—by encompassing a broader range of mass ratios and spin configurations. The calibration of this model involves aligning it with 38 nonprecessing waveforms produced via numerical relativity (NR) simulations supplied by the SXS Collaboration.

Key Contributions

1. Calibration Across Extensive Parameter Space:
   • The model ensures compatibility with black-hole binaries spanning mass ratios from 1 to 8 and spin magnitudes up to 98% of extremality.
   • The resulting EOB waveforms display overlaps exceeding 99% with all 38 calibrated nonprecessing numerical waveforms, reflecting negligible event rate loss in potential detections.
2. Model Fidelity and Computational Efficiency:
   • A key feature of the extended EOB model is its ability to generate accurate waveform templates for matched-filtering techniques used by gravitational-wave detectors with enhanced computational efficiency.
3. Precessing Binary Systems:
   • While primarily focusing on nonprecessing waveforms, the model was able to achieve overlaps above 97% with strongly precessing waveforms without additional calibration, indicating robustness in handling precessional dynamics.

Implications and Future Developments

The implications of this research are significant for both the theoretical and practical domains of astrophysics. The refined EOB model can facilitate more precise gravitational wave detection from binary systems with diverse characteristics, thereby improving our understanding of black hole dynamics.

1. Enhanced Detector Sensitivity:
   • By extending to high-spin magnitudes and accounting for a wider range of mass ratios, the EOB model increases the astrophysical reach of detectors like advanced LIGO, pushing the boundaries of observable events.
2. Computational Advancements:
   • Despite being computationally intensive, the EOB model is still far more efficient than direct NR simulations, with ongoing efforts aimed at further optimization.
3. Theoretical Extensions:
   • Future research will focus on refining radiation-reaction theories within the model, extending it to higher-order modes, and enhancing stability testing with longer NR simulations.

Conclusion

By successfully extending the EOB framework to include extreme mass ratios and spin configurations, this research provides an invaluable tool for the computational astrophysics community. The predictive accuracy and efficiency of these waveforms strengthen the observational capabilities of gravitational wave detectors, thereby advancing our ability to probe the complex dynamics of black-hole binaries. The implementation of this model within the LIGO Algorithm Library is expected to significantly enhance the capture and analysis of gravitational-wave events.