Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order

Abstract

We obtain an efficient description for the dynamics of nonspinning compact binaries moving in inspiralling eccentric orbits to implement the phasing of gravitational waves from such binaries at the 3.5 post-Newtonian (PN) order. Our computation heavily depends on the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D 70, 064028 (2004)], and the 3PN accurate generalized quasi-Keplerian parametric solution to the conservative dynamics of nonspinning compact binaries moving in eccentric orbits, available in [R.-M. Memmesheimer, A. Gopakumar, and G. Sch\"afer, Phys. Rev. D 70, 104011 (2004)]. The gravitational-wave (GW) polarizations ${h}_{+}$ and ${h}_{\ifmmode\times\else\texttimes\fi{}}$ with 3.5PN accurate phasing should be useful for the earth-based GW interferometers, current and advanced, if they plan to search for gravitational waves from inspiralling eccentric binaries. Our results will be required to do astrophysics with the proposed space-based GW interferometers like LISA, BBO, and DECIGO.