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Pulsar timing arrays (PTAs) hunt for gravitational waves (GWs) by searching for the correlations that GWs induce in the time-of-arrival residuals from different pulsars. If the GW sources are of astrophysical origin, then they are located at discrete points on the sky. However, PTA data are often modeled, and subsequently analyzed, via a “standard Gaussian ensemble.” That ensemble is obtained in the limit of an infinite density of vanishingly weak, Poisson-distributed sources. In this paper, we move away from that ensemble, to study the effects of two types of “source anisotropy.” The first (a), which is often called “shot noise,” arises because there are discrete GW sources at specific sky locations. The second (b) arises because the GW source positions are not a Poisson process, for example, because galaxy locations are clustered. Here, we quantify the impact of (a) and (b) on the mean and variance of the pulsar-averaged Hellings and Downs correlation. For conventional PTA sources, we show that the effects of shot noise (a) are much larger than the effects of clustering (b). Published by the American Physical Society2024
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This content will become publicly available on January 1, 2026
Optimal Reconstruction of the Hellings and Downs Correlation
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. Published by the American Physical Society2025
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- Award ID(s):
- 2020265
- PAR ID:
- 10579487
- Publisher / Repository:
- Physical Review Letters
- Date Published:
- Journal Name:
- Physical Review Letters
- Volume:
- 134
- Issue:
- 3
- ISSN:
- 0031-9007
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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