Timing-residual power spectrum of a polarized stochastic gravitational-wave background in pulsar-timing-array observation

TL;DR

This paper develops a harmonic-space analysis method for pulsar-timing-array data to study the anisotropies in the stochastic gravitational-wave background, enabling efficient computation and testing of isotropy.

Contribution

It introduces a harmonic-space framework for analyzing pulsar-timing data, including a fast algorithm for overlap reduction functions and the first calculation of polarization anisotropy coefficients.

Findings

Developed a harmonic-space method for SGWB analysis.

Created a fast algorithm for overlap reduction functions.

First calculation of polarization anisotropy coefficients.

Abstract

We study the observation of stochastic gravitational-wave background (SGWB) made by pulsar-timing arrays in the spherical harmonic space. Instead of using the Shapiro time delay, we keep the Sachs-Wolfe line-of-sight integral for the timing residual of an observed pulsar. We derive the power spectrum of the timing residual, from which the overlap reduction functions and the bipolar spherical harmonics coefficients are constructed for the SGWB intensity and polarization anisotropies. We have reproduced the previous results, noting that we have developed a fast algorithm for computing accurate overlap reduction functions and the bipolar spherical harmonics coefficients for the linear-polarization anisotropy are worked out for the first time. Our harmonic-space method is useful for future pulsar-timing-array observation on a few thousand pulsars and provides optimal estimators for testing the statistical isotropy of the SGWB.