Common-spectrum process versus cross-correlation for gravitational-wave searches using pulsar timing arrays
Joseph D. Romano, Jeffrey S. Hazboun, Xavier Siemens, Anne M. Archibald
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 $\mathrm{signal}+\mathrm{noise}$ 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.