Effects of waveform model systematics on the interpretation of GW150914

Abstract: Parameter estimates of GW150914 were obtained using Bayesian inference, based on three semi-analytic waveform models for binary black hole coalescences. These waveform models differ from each other in their treatment of black hole spins, and all three models make some simplifying assumptions, notably to neglect sub-dominant waveform harmonic modes and orbital eccentricity. Furthermore, while the models are calibrated to agree with waveforms obtained by full numerical solutions of Einstein's equations, any such calibration is accurate only to some non-zero tolerance and is limited by the accuracy of the underlying phenomenology, availability, quality, and parameter-space coverage of numerical simulations. This paper complements the original analyses of GW150914 with an investigation of the effects of possible systematic errors in the waveform models on estimates of its source parameters. To test for systematic errors we repeat the original Bayesian analyses on mock signals from numerical simulations of a series of binary configurations with parameters similar to those found for GW150914. Overall, we find no evidence for a systematic bias relative to the statistical error of the original parameter recovery of GW150914 due to modeling approximations or modeling inaccuracies. However, parameter biases are found to occur for some configurations disfavored by the data of GW150914: for binaries inclined edge-on to the detector over a small range of choices of polarization angles, and also for eccentricities greater than $\sim$0.05. For signals with higher signal-to-noise ratio than GW150914, or in other regions of the binary parameter space (lower masses, larger mass ratios, or higher spins), we expect that systematic errors in current waveform models may impact gravitational-wave measurements, making more accurate models desirable for future observations.

• The paper quantifies systematic errors in gravitational wave parameter recovery using Bayesian analyses with NR-derived mock signals.
• It reveals that while GW150914 shows no bias compared to statistical errors, unfavorable configurations may induce significant deviations.
• The study emphasizes the necessity for more accurate waveform models to enhance parameter estimation for future high signal-to-noise events.

Overview of Waveform Model Systematics and Implications for Gravitational Wave Event GW150914

The paper "Effects of waveform model systematics on the interpretation of GW150914" presents an in-depth analysis of systematic errors arising from the application of various waveform models to gravitational wave (GW) data, specifically focusing on the seminal detection of the binary black hole merger event, GW150914. The study employs Bayesian inference to analyze parameter estimates using three semi-analytic waveform models designed for binary black hole coalescences. The models under consideration differ mainly in their treatment of black hole spins, and they make simplifying assumptions to neglect sub-dominant waveform harmonic modes and orbital eccentricity.

Key Findings and Numerical Results

The investigation reveals that, while no systematic bias was detected relative to the statistical error of the original parameter recovery for GW150914, potential biases could occur in certain unfavorable configurations. Such configurations include binaries inclined edge-on relative to the detector with specific polarization angles and those with eccentricities exceeding approximately 0.05. Notably, for binary systems yielding higher signal-to-noise ratios (SNRs) than GW150914, or those situated in parameter regions characterized by lower masses, larger mass ratios, or higher spins, systematic errors present in current waveform models might impact GW measurements significantly. This indicates a desideratum for more precise models in the sphere of gravitational wave astronomy.

Methodological Approach

The study utilizes NR simulations to create mock signals, mimicking environments akin to GW150914, and applies them to Bayesian analyses designed to detect systematic errors. The authors present a rigorous testing framework, involving varying inclinations and polarization angles, to comprehensively assess potential systematic biases introduced by the waveform models.

Implications and Future Directions

The implications of this research are multifaceted. Practically, it underscores the necessity of developing more accurate and comprehensive waveform models to minimize systematic errors in GW parameter estimation—especially for future events with higher SNR or diverse parameter spaces. Theoretically, it calls attention to the limitations of current models in capturing complex dynamics such as precession or eccentricity, which might become increasingly important as detectors enhance their sensitivity and more nuanced GW observations become feasible.

The study also suggests avenues for future development in both analytical and numerical waveform modeling, aiming to encompass broader regions of the parameter space, including non-negligible eccentricities and spin-induced precessions. As LIGO, Virgo, and future observatories broaden their observational bandwidth and sensitivity, these advancements will be crucial in unraveling the complexities of binary black hole dynamics and their emissions.

Overall, this paper provides a critical analysis of the current state of waveform modeling in gravitational wave astronomy, highlighting areas for improvement that could significantly enhance the precision of GW source parameter estimation. Through its rigorous approach and findings, it contributes to refining the methodologies employed in this rapidly advancing field.