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

Yunes, Nicolas and Arun, K. G. and Berti, Emanuele and Will, Clifford M. (2009) Post-circular expansion of eccentric binary inspirals: Fourier-domain waveforms in the stationary phase. Physical Review D, 80 (8). Art. no. 084001. ISSN 2470-0010.

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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 (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.

Item Type:Article
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URLURL TypeDescription
Yunes, Nicolas0000-0001-6147-1736
Berti, Emanuele0000-0003-0751-5130
Additional Information:We thank Eric Poisson, Sai Iyer, David Spergel and Frans Pretorius for very useful discussions. K. G. A. and C. M.W. were supported in part by the National Science Foundation, Grant No. PHY 06-52448, the National Aeronautics and Space Administration, Grant No. NNG- 06GI60G, and the Centre National de la Recherche Scientifique, Programme Internationale de la Coope´ration Scientifique (CNRS-PICS), Grant No. 4396. N.Y. acknowledges support from NSF Grant No. PHY-0745779. E. B. acknowledges support from NSF Grant No. PHY- 0900735.
Funding AgencyGrant Number
NSFPHY 06-52448
Centre National de la Recherche ScientifiqueUNSPECIFIED
Programme Internationale de la Coopération Scientifique4396
Issue or Number:8
Classification Code:PACS numbers: 04.30.w, 04.25.Nx, 04.30.Db, 04.30.Tv
Record Number:CaltechAUTHORS:20091119-112558364
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Official Citation:Post-circular expansion of eccentric binary inspirals: Fourier-domain waveforms in the stationary phase approximation Nicolas Yunes, K. G. Arun, Emanuele Berti, and Clifford M. Will, Phys. Rev. D 80, 084001 (2009), DOI:10.1103/PhysRevD.80.084001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16762
Deposited By: Jason Perez
Deposited On:25 Nov 2009 18:42
Last Modified:09 Mar 2020 13:19

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