Common-spectrum process versus cross-correlation for gravitational-wave searches using pulsar timing arrays

TL;DR

This paper analyzes the distinction between common-spectrum noise and spatial correlations in pulsar timing arrays, showing current data is consistent with intermediate-signal regimes and providing analytic tools for comparison.

Contribution

It introduces a frequentist analysis framework and analytic expressions to compare common-spectrum and cross-correlation estimators in pulsar timing array data.

Findings

Current lack of spatial correlation evidence is consistent with intermediate-signal regime

Analytic expressions enable comparison of expected SNR for different estimators

The analysis supports the interpretation of a common-spectrum process without confirmed quadrupolar correlations

Abstract

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong statistical evidence for a common-spectrum red-noise process for all pulsars, as seen in their 12.5-yr analysis for an isotropic stochastic gravitational-wave background. However, there is currently very little evidence for quadrupolar spatial correlations across the pulsars in the array, which is needed to make a confident claim of detection of a stochastic background. Here we give a frequentist analysis of a very simple signal+noise model showing that the current lack of evidence for spatial correlations is consistent with the magnitude of the correlation coefficients for pairs of Earth-pulsar baselines in the array, and the fact that pulsar timing arraysbare most-likely operating in the intermediate-signal regime. We derive analytic expressions that allow one to compare the expected values of the signal-to-noise ratios for both the common-spectrum and cross-correlation estimators.