2014/08/31 by Antoine Klein, Neil J. Cornish, Neil Cornish +1 · 3 citations
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Binary number #Computer science #Computer vision #Domain (mathematical analysis) #Frequency domain #Geophysics and Sensor Technology #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Seismic Waves and Analysis #Spin (aerodynamics) #Waveform #astro-ph.HE #gr-qc
paper · pdf · doi:10.1103/physrevd.90.124029
published as Phys. Rev. D 90, 124029 (2014) · 14 pages, 2 figures, 4 tables
openalex publication_date 2014/12/08 · arxiv created 2014/12/09 · arxiv updated 2014/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The detection and characterization of gravitational wave signals from compact binary coalescence events relies on accurate waveform templates in the frequency domain. The stationary phase approximation (SPA) can be used to compute closed-form frequency-domain waveforms for nonprecessing, quasicircular binary inspirals. However, until now, no fast frequency-domain waveforms have existed for generic, spin-precessing quasicircular compact binary inspirals. Templates for these systems have had to be computed via a discrete Fourier transform of finely sampled time-domain waveforms, which is far more computationally expensive than those constructed directly in the frequency domain, especially for those systems that are dominated by the inspiral part. There are two obstacles to deriving frequency-domain waveforms for precessing systems: (i) the spin-precession equations do not admit closed-form solutions for generic systems; (ii) the SPA fails catastrophically, i.e. in some situations, the second derivative of the signal phase vanishes, so that the direct application of the SPA predicts a divergent amplitude. Presently there is no general solution to the first problem, so we must resort to numerical integration of the spin-orbit precession equations. This is not a significant obstacle, as numerical integration on the slow precession time scale adds very little to the computational cost of generating the waveforms. Our main result is to solve the second problem, by providing an alternative to the SPA that we call the method of shifted uniform asymptotics (SUA) that cures the divergences in the SPA. The construction of frequency-domain templates using the SUA can be orders of magnitude more efficient than the time-domain ones obtained through a discrete Fourier transform. Moreover, this method is very faithful to the discrete Fourier transform, with mismatches on the order of 10^\ensuremath-5.