期刊
PHYSICAL REVIEW D
卷 80, 期 8, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.80.084001
关键词
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资金
- Division Of Physics
- Direct For Mathematical & Physical Scien [745779] Funding Source: National Science Foundation
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.
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