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

TL;DR

This paper derives a comprehensive analytical formula for the overlap reduction function in pulsar timing arrays, enabling more accurate gravitational wave background detection across all polarization modes without approximations.

Contribution

It provides the first exact analytic expression for the ORF for all polarizations, improving over previous approximations and numerical methods, especially for scalar-longitudinal modes.

Findings

Exact analytical ORF expression for all polarizations.

Enhanced efficiency over numerical simulations.

Applicable to scalar-longitudinal polarization modes.

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.