Gravitational Waveforms for Precessing, Quasi-circular Binaries via Multiple Scale Analysis and Uniform Asymptotics: The Near Spin Alignment Case

TL;DR

This paper develops an analytical method to generate gravitational waveforms for precessing, quasi-circular binary systems with nearly aligned spins, improving waveform modeling for gravitational wave detection.

Contribution

It introduces a novel analytical approach combining multiple scale analysis and uniform asymptotics to model precession effects in gravitational waveforms.

Findings

High overlap with numerical waveforms

Extends stationary-phase approximation for precession

Provides foundation for accurate spin precession modeling

Abstract

We calculate analytical gravitational waveforms in the time- and frequency-domain for precessing quasi-circular binaries with spins of arbitrary magnitude, but nearly aligned with the orbital angular momentum. We first derive an analytical solution to the precession equations by expanding in the misalignment angle and using multiple scale analysis to separate timescales. We then use uniform asymptotic expansions to analytically Fourier transform the time-domain waveform, thus extending the stationary-phase approximation, which fails when precession is present. The resulting frequency-domain waveform family has a high overlap with numerical waveforms obtained by direct integration of the post-Newtonian equations of motion and discrete Fourier transformations. Such a waveform family lays the foundations for the accurate inclusion of spin precession effects in analytical gravitational waveforms, and thus, it can aid in the detection and parameter estimation of gravitational wave signals from the inspiral phase of precessing binary systems.