Residual eccentricity of inspiralling orbits at the gravitational-wave detection threshold: Accurate estimates using post-Newtonian theory

To date, gravitational wave detections have been predominantly from quasi-circular binary mergers. However, a significant percentage of mergers could have measurable residual eccentricities, resulting from external perturbations or short timescales between formation and merger. Understanding how the orbits of such binaries evolve could aid in creating eccentric gravitational waveform templates and provide astrophysical information about the environment and formation channels of these systems. We have used equations of motion containing gravitational radiation-reaction terms through 4.5 post-Newtonian and lowest order tail terms to calculate the late-time eccentricities of inspiralling binary systems of non-spinning compact bodies as they cross the detection threshold of ground-based gravitational-wave interferometers. We found that the final eccentricities are systematically smaller than those predicted by the leading quadrupole approximation and are independent of the ratio of the masses of the compact bodies. Additionally, we developed an analytic formula for the late-time eccentricity that accurately accounts for the higher-order post-Newtonian effects, generalizing a formula derived by Peters and Mathews. We will discuss these results.