Fast Frequency-domain Waveforms for Spin-Precessing Binary Inspirals

TL;DR

This paper introduces the Shifted Uniform Asymptotics (SUA) method to efficiently generate accurate frequency-domain waveforms for spin-precessing binary inspirals, overcoming limitations of the stationary phase approximation.

Contribution

The paper develops the SUA method to produce fast, accurate frequency-domain waveforms for precessing binaries, addressing the divergence issues of SPA and enabling computationally efficient template generation.

Findings

SUA significantly reduces computational cost compared to time-domain Fourier transforms.

The mismatch between SUA and discrete Fourier transform waveforms is approximately 10^{-5}.

SUA effectively cures SPA divergences for precessing systems.

Abstract

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 non-precessing, quasi-circular binary inspirals. However, until now, no fast frequency-domain waveforms have existed for generic, spin-precessing quasi-circular 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. Presently there is no general solution to the first problem, so we must resort to numerical integration of the spin precession equations. This is not a significant obstacle, as numerical integration on the slow precession timescale 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, or 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 $10^{-5}$.