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

Abstract

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.

Waveform model for an eccentric binary black hole based on the effective-one-body-numerical-relativity formalism

“…For space-based detectors such as eLISA [24], LISA [25,26], Taiji [27] and Tianqin [28], the orbit of the involved binary black hole systems may be highly eccentric due to recent perturbations by other orbiting objects [29,30]. Recently there are many authors care about the binary black hole systems with eccentric orbit regarding to gravitational wave detection [31][32][33][34].…”

Gravitational wave tests of general relativity with the parameterized post-Einsteinian framework

“…The amplitude A(f ) and phase Ψ(f ) are developed as a series in u = πMf = η 3/5 v 3 , where v is the relative velocity between the two bodies [30] : The coefficients γ k (η), ψ k (η) and ψ kl (η) are currently known up to k = 7 in the post-Newtonian expansion of GR.…”

Rosetta stone for parametrized tests of gravity

“…In the future, the restriction to circular, non spinning systems can be relaxed, building on work done in Ref. [33] for eccentric systems in GR and Ref. [34] for spinning systems in GR.…”