Post-circular expansion of eccentric binary inspirals: Fourier-domain waveforms in the stationary phase approximation

Nicolas Yunes, K. G. Arun, Emanuele Berti, Clifford M. Will

Research output: Contribution to journalArticlepeer-review


We lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waveforms produced by eccentric, inspiraling compact binaries in a post-circular or small-eccentricity approximation. The time-dependent, "plus" and "cross" polarizations are expanded in Bessel functions, which are then self-consistently reexpanded in a power series about zero initial eccentricity to eighth order. The stationary-phase approximation is then employed to obtain explicit analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify this framework by considering Newtonian-accurate waveforms, which in the post-circular scheme give rise to higher harmonics of the orbital phase and to amplitude corrections of the Fourier-domain waveform. Such higher harmonics lead to an effective increase in the inspiral mass reach of a detector as a function of the binary's eccentricity e0 at the time when the binary enters the detector sensitivity band. Using the largest initial eccentricity allowed by our approximations (e0<0.4), the mass reach is found to be enhanced up to factors of approximately 5 relative to that of circular binaries for Advanced LIGO, LISA, and the proposed Einstein Telescope at a signal-to-noise ratio of ten. A post-Newtonian generalization of the post-circular scheme is also discussed, which holds the promise to provide "ready-to-use" Fourier-domain waveforms for data analysis of eccentric inspirals.

Original languageEnglish (US)
Article number084001
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number8
StatePublished - Oct 1 2009
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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