Searching for gravitational waves from known pulsars using the $\mathcal{F}$ and $\mathcal{G}$ statistics

TL;DR

This paper develops and evaluates statistical methods for detecting gravitational waves from known pulsars, focusing on the $\

Contribution

It introduces the $\\mathcal{F}$ and $\\mathcal{G}$ statistics for targeted gravitational wave searches and assesses their theoretical and empirical accuracy.

Findings

The $\\mathcal{G}$-statistic effectively detects signals with two unknown parameters.

The $\\mathcal{F}$-statistic is suitable for signals with four unknown parameters.

Monte Carlo simulations confirm the estimators' accuracy.

Abstract

In searches for gravitational waves emitted by known isolated pulsars in data collected by a detector one can assume that the frequency of the wave, its spindown parameters, and the position of the source in the sky are known, so the almost monochromatic gravitational-wave signal we are looking for depends on at most four parameters: overall amplitude, initial phase, polarization angle, and inclination angle of the pulsar's rotation axis with respect to the line of sight. We derive two statistics by means of which one can test whether data contains such gravitational-wave signal: the $\mathcal{G}$-statistic for signals which depend on only two unknown parameters (overall amplitude and initial phase), and the $\mathcal{F}$-statistic for signals depending on all four parameters. We study, by means of the Fisher matrix, the theoretical accuracy of the maximum-likelihood estimators of the signal's parameters and we present the results of the Monte Carlo simulations we performed to test the accuracy of these estimators.