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Skewness in the Hellings-Downs curve

Ryosuke Fujimoto* and Keitaro Takahashi

  • *Contact author: MTryou369@gmail.com
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Phys. Rev. D 113, 124066 – Published 22 June, 2026

DOI: https://doi.org/10.1103/ghgl-vjv7

Abstract

Recent pulsar timing array datasets provide compelling evidence for a nanohertz gravitational-wave background, but robust detection requires characterizing statistical fluctuations of the Hellings-Downs (HD) correlation expected from a finite population of discrete sources. Building on the variance calculation of Allen [Variance of the Hellings-Downs correlation, Phys. Rev. D 107, 043018 (2023)], we derive the third central moment (skewness) of the HD correlation for a single unpolarized point source and an ensemble of many interfering point sources in the confusion-noise regime. To isolate the intrinsic non-Gaussianity of the background, we extend the pulsar-averaging formalism to third order by introducing a three-point-averaged correlation function, which allows us to define the cosmic skewness. We find that the skewness remains nonzero in the large-source-number limit and is controlled by a new geometric three-point function. These results suggest that incorporating higher-order moments could provide additional information on source discreteness beyond standard Gaussian analyses.

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Phys. Rev. D 113, 124066– Published 22 June, 2026
  • Received 30 January 2026
  • Accepted 15 May 2026
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