Eccentricity signatures in LIGO-Virgo-KAGRA’s binary neutron star and neutron-star black holes

Measurement of the eccentricity of low-mass binary systems through gravitational waves is crucial to distinguish between various formation channels. However, detecting eccentricity in these systems has been challenging due to the lack of accurate eccentric waveform models and the high computational cost associated with Bayesian inferences for systems with low-mass objects. In this work, we assess the eccentricities of seven previously observed low-mass gravitational wave events using publicly available data from the O1-O4a observing runs of the LIGO and Virgo observatories. We analyze the events using a new eccentric waveform model, seobnrv5ehm, and compare our results with the existing model, teobresums-dali. We also present the first eccentricity constraints for GW190814. To improve the accuracy of our parameter estimation, we include higher-order modes in both waveform models. We optimize inference by employing efficient marginalization techniques to alleviate the computational costs associated with low-mass systems and parallelization techniques for sampling large parameter spaces. We find that one of the sources, GW200105, exhibits a non-negligible eccentricity, with a measured eccentricity of $e=0.12{5}_{\ensuremath{-}0.082}^{+0.029}$ at 20 Hz (90% credible level) for seobnrv5ehm and $e=0.13{5}_{\ensuremath{-}0.088}^{+0.019}$ for teobresums-dali for a uniform eccentricity prior ranging from 0 to 0.2 at a reference frequency of 20 Hz. We find moderate support for the eccentric waveform hypothesis with a Bayes factor of $\ensuremath{\sim}6--7$ times more preference for the eccentric model over the noneccentric one. When using a uniform log prior on eccentricity with a minimum bound of ${10}^{\ensuremath{-}4}$, the support for the eccentric model decreases, with the Bayes factor reduced to 2.35. For the remaining five sources, the results are consistent with low eccentricity, with 90% upper limits ranging from $e\ensuremath{\le}0.011$ to $e\ensuremath{\le}0.066$. We do not find any support for non-negligible eccentricity in GW190814. Finally, we discuss the challenges of performing Bayesian inference in eccentric, multimodal parameter spaces, including issues related to sampling efficiency and waveform systematics.