Skewness in the Hellings-Downs curve

TL;DR

This paper derives the skewness of the Hellings-Downs correlation in pulsar timing arrays, revealing non-Gaussian features that could enhance understanding of the gravitational-wave background's source discreteness.

Contribution

It introduces a third-order formalism to quantify the skewness of the HD correlation, extending previous variance calculations to include non-Gaussianity in the gravitational-wave background.

Findings

Skewness remains non-zero even with many sources.

Skewness is governed by a new geometric three-point function.

Higher-order moments can provide additional information beyond Gaussian assumptions.

Abstract

Recent Pulsar Timing Array datasets provide compelling evidence for a nano-Hertz 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 (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 non-zero 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.