The origin and formation of stellar-mass binary black holes remains an open question that can be addressed by precise measurements of the binary and orbital parameters from their gravitational wave signal. Such binaries are expected to circularize due to the emission of gravitational waves as they approach merger. However, depending on their formation channel, some binaries could retain a non-negligible eccentricity when entering the frequency band of current gravitational wave detectors, which will decay as the binary inspirals. In order to meaningfully measure the eccentricity in an observed gravitational wave signal, two main ingredients are then necessary; an accurate waveform model that describes binaries on eccentric orbits, and an estimator to measure the noncircularity of the orbit as a function of frequency. In this work we first demonstrate the efficacy of the improved TEOBResumS waveform model for eccentric coalescing binaries with aligned spins. We validate the model against mock signals of aligned-spin binary black hole mergers and quantify the impact of eccentricity on the estimation of other intrinsic binary parameters. We then perform a fully Bayesian reanalysis of GW150914 with the eccentric waveform model. We find (i) that the model is reliable for aligned-spin binary black holes and (ii) that GW150914 is consistent with a noneccentric merger although we cannot rule out small values of initial eccentricity at a reference frequency of 20 Hz. Secondly, we present a systematic, model-agnostic method to measure the orbital eccentricity and its evolution directly from the gravitational-wave posterior samples. This method mitigates against the contamination of eccentricity measurements through the use of gauge-dependent quantities and has the advantage of allowing for the direct comparison between different analyses, as the definition of eccentricity may differ between models. Our scheme can be applied even in the case of small eccentricities and can be adopted straightforwardly in postprocessing to allow for direct comparison between analyses.

• Received 27 July 2022
• Accepted 26 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.064024