On the ability of various circular inspiral templates to capture inspiral gravitational waves from compact binaries having tiny orbital eccentricities

We probe the ability of various types of post-Newtonian(PN)-accurate circular templates to capture inspiral gravitational-wave (GW) signals from compact binaries having tiny orbital eccentricities. The GW signals are constructed by adapting the phasing formalism, available in T. Damour, A. Gopakumar, and B. R. Iyer, [Phys. Rev. D 70, 064028 (2004)], employing the orbital energy and the time-eccentricity to describe the orbital evolution. Using the fitting factor estimates, relevant for the initial LIGO, we show that circular templates, based on the adiabatic TaylorT1, complete adiabatic TaylorT1 and TaylorT4 approximants are unable to capture our GW signals from compact binaries having tiny residual orbital eccentricities. However, the 2PN-order circular inspiral templates based on the recently introduced TaylorEt approximant are found to be both effectual and faithful in capturing GWs from inspiralling compact binaries having moderate eccentricities and we provide physical explanations for our observations.