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

作者：Yunes Nicolas^*; Arun K G; Berti Emanuele; Will Clifford M

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2009, 80(8): 084001.

DOI：10.1103/PhysRevD.80.084001

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 e(0) at the time when the binary enters the detector sensitivity band. Using the largest initial eccentricity allowed by our approximations (e(0) < 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.

• 出版日期2009-10