Data analysis of gravitational-wave signals from spinning neutron stars. V. A narrow-band all-sky search

TL;DR

This paper develops efficient algorithms for an all-sky coherent search of gravitational waves from spinning neutron stars using the $ ext{F}$-statistic, leveraging FFT techniques for improved computational speed.

Contribution

It introduces novel algorithms and interpolation methods that enable fast computation of the $ ext{F}$-statistic for narrow-band gravitational wave data analysis.

Findings

Algorithms efficiently compute the $ ext{F}$-statistic using FFT.

Interpolation methods approximate integrals as Fourier transforms.

Monte Carlo simulations validate the effectiveness of the algorithms.

Abstract

We present theory and algorithms to perform an all-sky coherent search for periodic signals of gravitational waves in narrow-band data of a detector. Our search is based on a statistic, commonly called the $\mathcal{F}$-statistic, derived from the maximum-likelihood principle in Paper I of this series. We briefly review the response of a ground-based detector to the gravitational-wave signal from a rotating neuron star and the derivation of the $\mathcal{F}$-statistic. We present several algorithms to calculate efficiently this statistic. In particular our algorithms are such that one can take advantage of the speed of fast Fourier transform (FFT) in calculation of the $\mathcal{F}$-statistic. We construct a grid in the parameter space such that the nodes of the grid coincide with the Fourier frequencies. We present interpolation methods that approximately convert the two integrals in the $\mathcal{F}$-statistic into Fourier transforms so that the FFT algorithm can be applied in their evaluation. We have implemented our methods and algorithms into computer codes and we present results of the Monte Carlo simulations performed to test these codes.