Direction-of-arrival estimation of a gravitational wave by correlations between quadrupole moments of pulsar timings

TL;DR

This paper proposes a novel method to estimate the direction of arrival of gravitational waves using correlations between quadrupole moments of pulsar timings, which could enhance GW source localization with future telescopes.

Contribution

It introduces a new approach leveraging quadrupole moment correlations to determine GW source directions, addressing an inverse problem in pulsar timing array analysis.

Findings

Correlation matrices are rank 2 and relate to GW projection tensors

The method enables DOA estimation of GWs from pulsar timing data

Angular resolution and error estimates are provided for future observations

Abstract

Can we estimate the direction of arrival (DOA) of a gravitational wave (GW) signal from pulsar timing array observations? The present paper addresses the inverse problem, for which we consider quadrupole moments of pulsar timings due to GWs from a dominant isolated source such as a binary of supermassive black holes over an isotropic stochastic background. Correlations between the quadrupole moments are discussed, where the correlations between pulsar pairs over the full sky are taken into account. The correlations turn out to be in the form of a three-dimensional traceless matrix with rank 2 that can be closely related with a projection tensor for the GW. Thereby, we demonstrate that the rank-2 matrix allows to estimate the DOA of the GW. In expectation of the forthcoming Square Kilometer Array, angular resolutions as well as DOA estimation errors are also examined.