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

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 signal. 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 gravitational-wave background. In this paper, we provide a "back-of-the-envelope"illustration of the NANOGrav 12.5-yr results for the nonexpert reader, using a very simple signal+noise model and frequentist statistics. We show 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 arrays are 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 common-spectrum and cross-correlation estimators.