Eccentricity evolution consistency test to distinguish eccentric gravitational-wave signals from eccentricity mimickers

Eccentric compact binary coalescences (CBCs) are expected to be observed in current and future gravitational-wave (GW) detector networks. However, it has been recently pointed out that a number of other physical and beyond-GR effects, could imitate, or be mimicked by, eccentric CBCs. In this work, we propose a conceptually simple but powerful method to directly confirm or reject the eccentric hypothesis, without needing to compare the hypothesis with the plethora of other possible hypotheses. The key idea is that while spurious non-zero values of eccentricity, at some reference frequency, could be acquired when a non-eccentric CBC with additional physical/beyond-GR effects is recovered with an eccentric CBC waveform model, the {\itshape evolution} of eccentricity with frequency will in general not be mimicked. We accordingly formulate an eccentricity evolution consistency test (EECT). The method compares the eccentricity recovered at some low frequency value (e.g, $10$ Hz), evolved to higher frequencies assuming GR, with eccentricities recovered at those same higher frequencies. Discrepancy between the two eccentricities at any reference frequency would violate EECT and indicate the presence of a mimicker. As a proof of concept, assuming a few eccentric CBC systems, quasi-circular CBCs with additional physics mimicking eccentricity, and an O4-like three-detector-network configuration, we demonstrate that our proposed method is indeed able to reject mimickers at $\geq 68\%$ confidence, while ensuring that truly eccentric CBCs satisfy EECT.