Data Analysis Implications of Moderately Eccentric Gravitational Waves

TL;DR

This paper introduces a new gravitational wave model for moderate eccentricity binaries and explores its implications for data analysis, showing improved measurement accuracy and early detection potential for eccentric signals.

Contribution

The paper presents a 3rd post-Newtonian order waveform model for moderate eccentricity gravitational waves and analyzes its impact on parameter estimation and systematic errors.

Findings

Eccentricity and mass can be measured with 2 orders of magnitude better accuracy as eccentricity increases.

Eccentric signals with eccentricity > 0.008 (low mass) and > 0.05 (high mass) can be confidently identified.

Systematic errors are below statistical errors for signals with SNR 15 and moderate eccentricities.

Abstract

While the expectation is that the majority of gravitational wave events observable by ground-based detectors will be emitted by compact binaries in quasi-circular orbits, the growing number of detections suggests the possibility of detecting waves from binaries with non-negligible orbital eccentricity in the near future. Several gravitational wave models incorporate the effects of small orbital eccentricities ($e \lesssim 0.2$), but these models may not be sufficient to analyze waves from systems with moderate eccentricity. We recently developed a gravitational wave model that faithfully accounts for eccentric corrections in the moderate eccentricity regime ($e \lesssim 0.8$ for certain source masses) at 3rd post-Newtonian order. Here we consider the data analysis implications of this particular waveform model by producing and analyzing posteriors via Markov Chain Monte Carlo methods. We find that the accuracy to which eccentricity and source masses can be measured can increase by 2 orders of magnitude with increasing eccentricity of the signal. We also find that signals with low eccentricity can be confidently identified as eccentric as soon as their eccentricity exceeds 0.008 (0.05) for low (high) mass systems, suggesting eccentric detections are likely to come first from low-mass systems. We complete our analysis by investigating the systematic (mismodeling) error inherent in our post-Newtonian model, finding that for signals with a signal-to-noise ratio of 15, the systematic error is below the statistical error for eccentricities as high as 0.8 (0.5) for low (high) mass systems. We also investigate the systematic error that arises from using a model that neglects eccentricity when the signal is truly eccentric, finding that the systematic error exceeds the statistical error in mass for eccentricities as small as 0.02.