Optimal Reconstruction of the Hellings and Downs Correlation

verfasst von: Bruce Allen, Joseph D. Romano
Abstract: Pulsar timing arrays (PTAs) detect gravitational waves (GWs) via the correlations they create in the arrival times of pulses from different pulsars. The mean correlation, a function of the angle between the directions to two pulsars, was predicted in 1983 by Hellings and Downs (HD). Observation of this angular pattern is crucial evidence that GWs are present, so PTAs "reconstruct the HD curve"by estimating the correlation using pulsar pairs separated by similar angles. Several studies have examined the amount by which this curve is expected to differ from the HD mean. The variance arises because (a) a finite set of pulsars at specific sky locations is used, (b) the GW sources interfere, and (c) the data are contaminated by noise. Here, for a Gaussian ensemble of sources, we predict that variance by constructing an optimal estimator of the HD correlation, taking into account the pulsar sky locations and the frequency distribution of the GWs and the pulsar noise. The variance is a ratio: the numerator depends upon the pulsar sky locations, and the denominator is the (effective) number of frequency bins for which the GW signal dominates the noise. In effect, after suitable combination, each such frequency bin gives an independent estimate of the HD correlation.
Organisationseinheit(en): Institut für Gravitationsphysik
Externe Organisation(en): Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)
University of Texas Rio Grande Valley
Typ: Artikel
Journal: Physical review letters
Band: 134
Anzahl der Seiten: 8
ISSN: 0031-9007
Publikationsdatum: 22.01.2025
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Allgemeine Physik und Astronomie
Elektronische Version(en): https://doi.org/10.1103/PhysRevLett.134.031401 (Zugang: Offen)
https://doi.org/10.48550/arXiv.2407.10968 (Zugang: Offen)

BibTeX

@article{422c8cd41832466d9206cbc640bfc968,
title = "Optimal Reconstruction of the Hellings and Downs Correlation",
abstract = "Pulsar timing arrays (PTAs) detect gravitational waves (GWs) via the correlations they create in the arrival times of pulses from different pulsars. The mean correlation, a function of the angle between the directions to two pulsars, was predicted in 1983 by Hellings and Downs (HD). Observation of this angular pattern is crucial evidence that GWs are present, so PTAs {"}reconstruct the HD curve{"}by estimating the correlation using pulsar pairs separated by similar angles. Several studies have examined the amount by which this curve is expected to differ from the HD mean. The variance arises because (a) a finite set of pulsars at specific sky locations is used, (b) the GW sources interfere, and (c) the data are contaminated by noise. Here, for a Gaussian ensemble of sources, we predict that variance by constructing an optimal estimator of the HD correlation, taking into account the pulsar sky locations and the frequency distribution of the GWs and the pulsar noise. The variance is a ratio: the numerator depends upon the pulsar sky locations, and the denominator is the (effective) number of frequency bins for which the GW signal dominates the noise. In effect, after suitable combination, each such frequency bin gives an independent estimate of the HD correlation.",
author = "Bruce Allen and Romano, {Joseph D.}",
note = "Publisher Copyright: {\textcopyright} 2025 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the {"}https://creativecommons.org/licenses/by/4.0/{"}Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.",
year = "2025",
month = jan,
day = "22",
doi = "10.1103/PhysRevLett.134.031401",
language = "English",
volume = "134",
journal = "Physical review letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "3",
}