Spectral analysis of the gravitational radiation emitted by binary systems in moderately eccentric orbits: application to coalescing binaries

Moreno-Garrido, C.; Buitrago, J.; Mediavilla, E.

doi:10.1093/mnras/266.1.16

Cited by 23 publications

(35 citation statements)

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“…[39]. These relations allow us to express the gravitational waveforms for eccentric inspirals as explicit functions of the orbital frequency.…”

Section: The Basics Of the Kepler Problemmentioning

confidence: 99%

“…We shall employ the quadrupole formalism, similar to that presented by Moreno-Garrido, Buitrago and Mediavilla [39,40], but improved through the techniques introduced by Pierro and Pinto [41,42].…”

Section: Post-circular Expansion Of Time-domain Eccentric Inspirmentioning

confidence: 99%

“…The eccentricity is itself a function of the orbital frequency, which we invert in the limit e ≪ 1 and insert into the time-domain waveforms to obtain explicit expressions whose only independent variables are the orbital frequency and the mean anomaly. The prescription described above to compute time-domain waveforms is a completion of the analytic work of Moreno-Garrido, Buitrago and Mediavilla [39,40], improved through the resummation methods of Pierro and Pinto [41,42] and the more general waveform expressions of Martel and Poisson [32].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2009

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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 smalleccentricity approximation. The time-dependent, "plus" and "cross" polarizations are expanded in Bessel functions, which are then self-consistently re-expanded 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 amplitude corrections both to the amplitude and the phase 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.

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“…[39]. These relations allow us to express the gravitational waveforms for eccentric inspirals as explicit functions of the orbital frequency.…”

Section: The Basics Of the Kepler Problemmentioning

confidence: 99%

Section: Post-circular Expansion Of Time-domain Eccentric Inspirmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2009

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“…Using Newtonian accurate orbital motion, Refs. [18,19] studied the effect on gravitational wave polarizations of introducing by hand some secular effects either in the longitude of the periastron [18] or in the semi-major axis and eccentricity [19]. Using such waveforms, the influence of eccentricity on the signal to noise ratio in gravitational wave data analysis, was examined in [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…[18,19] studied the effect on gravitational wave polarizations of introducing by hand some secular effects either in the longitude of the periastron [18] or in the semi-major axis and eccentricity [19]. Using such waveforms, the influence of eccentricity on the signal to noise ratio in gravitational wave data analysis, was examined in [19][20][21]. These waveforms were also used to show that LISA will be sensitive to eccentric Galactic binary neutron stars [22] and that by measuring their periastron advance, accurate estimates for the total mass of these binaries may be obtained [23].…”

Section: Introductionmentioning

confidence: 99%

Phasing of gravitational waves from inspiralling eccentric binaries

Damour¹,

Gopakumar²,

Iyer³

2005

Class. Quantum Grav.

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We provide a method for analytically constructing high-accuracy templates for the gravitational wave signals emitted by compact binaries moving in inspiralling eccentric orbits. By contrast to the simpler problem of modeling the gravitational wave signals emitted by inspiralling circular orbits, which contain only two different time scales, namely those associated with the orbital motion and the radiation reaction, the case of inspiralling eccentric orbits involves three different time scales: orbital period, periastron precession and radiation-reaction time scales. By using an improved 'method of variation of constants', we show how to combine these three time scales, without making the usual approximation of treating the radiative time scale as an adiabatic process. We explicitly implement our method at the 2.5PN post-Newtonian accuracy. Our final results can be viewed as computing new 'post-adiabatic' short period contributions to the orbital phasing, or equivalently, new short-period contributions to the gravitational wave polarizations, h +,× , that should be explicitly added to the 'post-Newtonian' expansion for h +,× , if one treats radiative effects on the orbital phasing of the latter in the usual adiabatic approximation. Our results should be of importance both for the LIGO/VIRGO/GEO network of ground based interferometric gravitational wave detectors (especially if Kozai oscillations turn out to be significant in globular cluster triplets), and for the future space-based interferometer LISA.

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Full-analytic frequency-domain gravitational wave forms from eccentric compact binaries to 2PN accuracy

Tessmer

Schäfer

2011

Ann. Phys.

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The article provides full-analytic gravitational wave (GW) forms for eccentric nonspinning compact binaries of arbitrary mass ratio in the time Fourier domain. The semi-analytical property of recent descriptions, i.e. the demand of inverting the higher-order Kepler equation numerically but keeping all other computations analytic, is avoided for the first time.The article is a completion of a previous one (M. Tessmer and G. Schäfer, Phys. Rev. D 82, 124064 (2010)) to second post-Newtonian (2PN) order in the harmonic GW amplitude and conservative orbital dynamics. A fully analytical inversion formula of the Kepler equation in harmonic coordinates is provided, as well as the analytic time Fourier expansion of trigonometric functions of the eccentric anomaly in terms of sines and cosines of the mean anomaly. Tail terms are not considered.

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Spectral analysis of the gravitational radiation emitted by binary systems in moderately eccentric orbits: application to coalescing binaries

Cited by 23 publications

References 0 publications

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

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

Phasing of gravitational waves from inspiralling eccentric binaries

Full-analytic frequency-domain gravitational wave forms from eccentric compact binaries to 2PN accuracy

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