Pulsar timing array harmonic analysis and source angular correlations

authored by: Bruce Allen
Abstract: Gravitational waves (GWs) influence the arrival times of radio signals coming from pulsars. Here, we investigate the harmonic space approach to describing a pulsar's response to GWs. We derive and discuss the "diagonalized form"of the response, which is a sum of spin-2-weighted spherical harmonics of the GW direction multiplied by normal (spin-weight 0) spherical harmonics of the pulsar direction. We show how this allows many useful objects, for example, the Hellings and Downs two-point function, to be easily calculated. The approach also provides a clear description of the gauge dependence. We then employ this harmonic approach to model the effects of angular correlations in the sky locations of GW sources (sometimes called "statistical isotropy"). To do this, we construct ensembles made up of many Gaussian subensembles. While each of the individual subsensembles breaks rotational invariance, the full ensemble is rotationally invariant. Using harmonic techniques, we compute the cosmic covariance and the total covariance of the Hellings and Downs correlation in these models. The results may be used to assess the impact of angular source correlations on the Hellings and Downs correlation, and for optimal reconstruction of the Hellings and Downs curve in models where GW sources have correlated sky locations.
Organisation(s): Institute of Gravitation Physics
Type: Article
Journal: Physical Review D
Volume: 110
ISSN: 2470-0010
Publication date: 28.08.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Nuclear and High Energy Physics
Electronic version(s): https://doi.org/10.48550/arXiv.2404.05677 (Access: Open)
https://doi.org/10.1103/PhysRevD.110.043043 (Access: Open)

BibTeX

@article{eadb776e12374ff8a3f894043b6a1813,
title = "Pulsar timing array harmonic analysis and source angular correlations",
abstract = "Gravitational waves (GWs) influence the arrival times of radio signals coming from pulsars. Here, we investigate the harmonic space approach to describing a pulsar's response to GWs. We derive and discuss the {"}diagonalized form{"}of the response, which is a sum of spin-2-weighted spherical harmonics of the GW direction multiplied by normal (spin-weight 0) spherical harmonics of the pulsar direction. We show how this allows many useful objects, for example, the Hellings and Downs two-point function, to be easily calculated. The approach also provides a clear description of the gauge dependence. We then employ this harmonic approach to model the effects of angular correlations in the sky locations of GW sources (sometimes called {"}statistical isotropy{"}). To do this, we construct ensembles made up of many Gaussian subensembles. While each of the individual subsensembles breaks rotational invariance, the full ensemble is rotationally invariant. Using harmonic techniques, we compute the cosmic covariance and the total covariance of the Hellings and Downs correlation in these models. The results may be used to assess the impact of angular source correlations on the Hellings and Downs correlation, and for optimal reconstruction of the Hellings and Downs curve in models where GW sources have correlated sky locations.",
author = "Bruce Allen",
note = "Publisher Copyright: {\textcopyright} 2024 authors. Published by the American Physical Society.",
year = "2024",
month = aug,
day = "28",
doi = "10.48550/arXiv.2404.05677",
language = "English",
volume = "110",
journal = "Physical Review D",
issn = "2470-0010",
publisher = "American Institute of Physics",
number = "4",
}