Gravitational Waveforms for Precessing, Quasicircular Compact Binaries with Multiple Scale Analysis: Small Spin Expansion

TL;DR

This paper derives analytical frequency-domain gravitational waveforms for precessing, quasi-circular compact binaries with small spins, using multiple-scale analysis and stationary phase approximation, suitable for binary neutron star detection.

Contribution

It introduces a novel analytical method for modeling precessing binary waveforms with small spins, improving computational efficiency and accuracy.

Findings

High overlap with numerical waveforms

Applicable to binary neutron star inspirals

Valid for small spin systems

Abstract

We obtain analytical gravitational waveforms in the frequency-domain for precessing, quasi-circular compact binaries with small spins, applicable, for example, to binary neutron star inspirals. We begin by calculating an analytic solution to the precession equations, obtained by expanding in the dimensionless spin parameters and using multiple-scale analysis to separate timescales. We proceed by analytically computing the Fourier transform of time-domain waveform through the stationary phase approximation. We show that the latter is valid for systems with small spins. Finally, we show that these waveforms have a high overlap with numerical waveforms obtained through direct integration of the precession equations and discrete Fourier transformations. The resulting, analytic waveform family is ideal for detection and parameter estimation of gravitational waves emitted by inspiraling binary neutron stars with ground-based detectors.