An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors (1611.03703v3)

Abstract: We improve the accuracy of the effective-one-body (EOB) waveforms that were employed during the first observing run of Advanced LIGO for binaries of spinning, nonprecessing black holes by calibrating them to a set of 141 numerical-relativity (NR) waveforms. The NR simulations expand the domain of calibration towards larger mass ratios and spins, as compared to the previous EOBNR model. Merger-ringdown waveforms computed in black-hole perturbation theory for Kerr spins close to extremal provide additional inputs to the calibration. For the inspiral-plunge phase, we use a Markov-chain Monte Carlo algorithm to efficiently explore the calibration space. For the merger-ringdown phase, we fit the NR signals with phenomenological formulae. After extrapolation of the calibrated model to arbitrary mass ratios and spins, the (dominant-mode) EOBNR waveforms have faithfulness --- at design Advanced-LIGO sensitivity --- above $99\%$ against all the NR waveforms, including 16 additional waveforms used for validation, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling for these binary configurations. We find that future NR simulations at mass ratios $\gtrsim 4$ and double spin $\gtrsim 0.8$ will be crucial to resolve discrepancies between different ways of extrapolating waveform models. We also find that some of the NR simulations that already exist in such region of parameter space are too short to constrain the low-frequency portion of the models. Finally, we build a reduced-order version of the EOBNR model to speed up waveform generation by orders of magnitude, thus enabling intensive data-analysis applications during the upcoming observation runs of Advanced LIGO.

• The paper improves EOB modeling by calibrating 141 numerical-relativity waveforms, achieving over 99% accuracy in waveform matches.
• The paper employs black-hole perturbation theory and a Markov-chain Monte Carlo method to optimize the inspiral-plunge phase across diverse parameter ranges.
• The paper constructs a reduced-order model that accelerates waveform generation, enhancing gravitational-wave detection and parameter estimation with advanced detectors.

Improved Effective-One-Body Model of Spinning, Nonprecessing Binary Black Holes

The paper "An Improved Effective-One-Body Model of Spinning, Nonprecessing Binary Black Holes" presents advances in modeling gravitational waveforms from binary black hole (BBH) mergers. This research is crucial for analyzing data from the Advanced LIGO and similar detectors, which require accurate waveform models to extract astrophysical information from gravitational wave signals.

Key Contributions and Methodology

The authors introduce enhancements to the effective-one-body (EOB) formalism, which synthesizes information from perturbative and numerical relativity (NR) to model BBH mergers. The improvements focus on:

1. Calibration to Numerical-Relativity Waveforms: The model is calibrated against 141 NR waveforms, expanding the calibration domain to include larger mass ratios and spin values compared to previous EOB models. This step is essential to capture diverse physical scenarios across the parameter space.
2. Incorporation of Black-Hole Perturbation Theory: For near-extremal spins, perturbation theory waveforms inform the calibration, enhancing accuracy in regions where NR data is sparse or challenging to compute.
3. Markov-Chain Monte Carlo Calibration: A Markov-chain Monte Carlo (MCMC) algorithm is employed to explore the calibration space, particularly for the inspiral-plunge phase of the waveform. This technique allows efficient exploration in high-dimensional spaces, ensuring the optimized parameter choices accurately represent physical dynamics.
4. Reduced-Order Model Construction: By building a reduced-order model (ROM), the waveform generation process is accelerated significantly, enabling comprehensive data analysis applications without prohibitive computational costs.

Numerical Results and Model Validation

The paper reports that the EOB model, after calibration, achieves a match above 99% against NR waveforms within the calibration set when optimized over initial phase and time. This level of accuracy implies minimal event rate loss due to modeling errors with the current Advanced-LIGO sensitivity. The model shows exceptional performance even against additional waveforms set aside for validation, demonstrating robustness.

However, the authors identify regions, notably at mass ratios $q \gtrsim 4$ and spins $\chi \gtrsim 0.8$, where future NR simulations are essential to resolve discrepancies from extrapolation limitations. Cases with short NR simulations are particularly challenging for constraining models at low frequencies.

Theoretical and Practical Implications

The improved EOB model significantly enhances our ability to simulate gravitational wave signals from spinning, nonprecessing BBH systems. Theoretical implications involve deeper insights into BBH dynamics and the validation of general relativity in strong-field regimes. Practically, this model aids in the effective detection and parameter estimation of BBH mergers, facilitating better understanding and classification of gravitational wave events.

Future Directions

This research underscores the importance of integrating high-fidelity NR data with semi-analytical models like EOB. Future developments may involve extending these methods to precessing systems and incorporating higher-mode and eccentric corrections, further refining waveform accuracy. As NR simulations become more feasible for extreme mass ratios and spins, incorporating such data will bolster the model's reliability across an ever-broader range of astrophysical scenarios, enhancing the scientific yield from gravitational wave observatories.