LAUSR

Eccentricity of binary systems is not a gauge invariant quantity, but has an important impact on the observed gravitational wave signal of such systems, generating power in all possible harmonics of the orbital period. We here clarify the possible discrepancies between different eccentricity parameters used to describe the orbital dynamics of binary systems across different approximations, specifically the post-Newtonian approximation, the self-force approximation, and numerical relativity. To this end, we highlight disparities between the typically used orbit averaged method of evolving binary systems under radiation reaction, and more direct techniques of solving the two-body problem in post-Newtonian theory. We show, both numerically and analytically, that the orbit averaged method breaks down in the late inspiral, failing to capture a strong secular growth in the Keplerian eccentricity parameter and producing a orbital de-phasing relative to direct integration of the two-body equations of motion. We show that the secular growth and de-phasing affect the observed gravitational wave signal, which could bias how accurately we may recover parameters for systems with signal-to-noise ratios $\gtrsim 100$. We further develop a frequency domain post-adiabatic waveform model to capture these effects, and study the precision to which we may estimate parameters with this model through a Fisher information matrix analysis.