Finite distance effects on the Hellings–Downs curve in modified gravity

authored by: Guillem Domènech, Apostolos Tsabodimos
Abstract: There is growing interest in the overlap reduction function in pulsar timing array observations as a probe of modified gravity. However, current approximations to the Hellings–Downs curve for subluminal gravitational wave propagation, say v<1, diverge at small angular pulsar separation. In this paper, we find that the overlap reduction function for the v<1 case is sensitive to finite distance effects. First, we show that finite distance effects introduce an effective cut-off in the spherical harmonics decomposition at ℓ∼1-v²kL, where ℓ is the multipole number, k the wavenumber of the gravitational wave and L the distance to the pulsars. Then, we find that the overlap reduction function in the small angle limit approaches a value given by πkLv²(1-v2)² times a normalization factor, exactly matching the value for the autocorrelation recently derived. Although we focus on the v<1 case, our formulation is valid for any value of v.
Organisation(s): Institute of Theoretical Physics
External Organisation(s): Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Type: Article
Journal: European Physical Journal C
Volume: 84
ISSN: 1434-6044
Publication date: 07.10.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Engineering (miscellaneous), Physics and Astronomy (miscellaneous)
Electronic version(s): https://doi.org/10.1140/epjc/s10052-024-13418-w (Access: Open)
https://doi.org/10.1140/epjc/s10052-024-13492-0 (Access: Open)

BibTeX

@article{31e90932ec5541d6997782470b27a76a,
title = "Finite distance effects on the Hellings–Downs curve in modified gravity",
abstract = "There is growing interest in the overlap reduction function in pulsar timing array observations as a probe of modified gravity. However, current approximations to the Hellings–Downs curve for subluminal gravitational wave propagation, say v<1, diverge at small angular pulsar separation. In this paper, we find that the overlap reduction function for the v<1 case is sensitive to finite distance effects. First, we show that finite distance effects introduce an effective cut-off in the spherical harmonics decomposition at ℓ∼1-v2kL, where ℓ is the multipole number, k the wavenumber of the gravitational wave and L the distance to the pulsars. Then, we find that the overlap reduction function in the small angle limit approaches a value given by πkLv2(1-v2)2 times a normalization factor, exactly matching the value for the autocorrelation recently derived. Although we focus on the v<1 case, our formulation is valid for any value of v.",
author = "Guillem Dom{\`e}nech and Apostolos Tsabodimos",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",
year = "2024",
month = oct,
day = "7",
doi = "10.1140/epjc/s10052-024-13418-w",
language = "English",
volume = "84",
journal = "European Physical Journal C",
issn = "1434-6044",
publisher = "Springer New York",
number = "10",
}