Pulsar timing array observations of gravitational wave source timing parallax

TL;DR

This paper investigates how pulsar timing arrays can detect gravitational wave sources by accounting for wavefront curvature, enabling measurement of source distance and position for nearby sources within 100 Mpc.

Contribution

It introduces a method to include wavefront curvature effects in PTA response analysis, improving localization and distance estimation of gravitational wave sources.

Findings

Wavefront curvature significantly affects PTA signals for sources within 100 Mpc.

Including curvature allows simultaneous measurement of source distance and sky position.

The approach enhances the capability of PTAs to localize nearby gravitational wave sources.

Abstract

Pulsar timing arrays act to detect gravitational waves by observing the small, correlated effect the waves have on pulse arrival times at Earth. This effect has conventionally been evaluated assuming the gravitational wave phasefronts are planar across the array, an assumption that is valid only for sources at distances $R\gg2\pi{}L^2/\lambda$, where $L$ is physical extent of the array and $\lambda$ the radiation wavelength. In the case of pulsar timing arrays (PTAs) the array size is of order the pulsar-Earth distance (kpc) and $\lambda$ is of order pc. Correspondingly, for point gravitational wave sources closer than $\sim100$~Mpc the PTA response is sensitive to the source parallax across the pulsar-Earth baseline. Here we evaluate the PTA response to gravitational wave point sources including the important wavefront curvature effects. Taking the wavefront curvature into account the relative amplitude and phase of the timing residuals associated with a collection of pulsars allows us to measure the distance to, and sky position of, the source.