Full analytic expression of overlap reduction function for gravitational wave background with pulsar timing arrays

Abstract

Pulsar timing array (PTA) is expected to detect gravitational wave background (GWB) in the nanohertz band within the next decade. This provides an opportunity to test the gravity theory and cosmology. A typical data analysis method to detect GWB is cross-correlation analysis. The overlap reduction function (ORF) plays an important role in the correlation data analysis of GWB. The present approach to dealing with the intricate integration in ORF is to use short-wave approximation to drop out the tricky terms. In this paper, we provide the full analytic expression of the ORF for PTA without any approximation for all possible polarizations allowed by modifications of general relativity. Compared with the numerical simulation and short-wave approximation, our results are more efficient and widely applicable. Especially for the scalar-longitudinal mode where the short-wave approximation is not available, our analytical expression is particularly significant.

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Cited by in corpus (7)

• Stochastic gravitational wave background phenomenology in a pulsar timing array
• Beyond the Hellings-Downs curve: Non-Einsteinian gravitational waves in pulsar timing array correlations
• Non-linear corrections of overlap reduction functions for pulsar timing arrays
• Unveiling the existence of nontensorial gravitational-wave polarizations from individual supermassive black hole binaries with pulsar timing arrays
• Full analytic expressions of overlap reduction functions for anisotropies of the stochastic gravitational-wave background with pulsar timing arrays
• Ultralight scalar dark matter versus nonadiabatic perfect fluid dark matter in pulsar timing
• Constraints on typical relic gravitational waves based on data of LIGO