Harmonic space analysis of pulsar timing array redshift maps

TL;DR

This paper introduces a harmonic space framework for analyzing pulsar timing array data, using angular power spectra to characterize gravitational wave backgrounds and their anisotropies.

Contribution

It applies cosmic microwave background analysis techniques to pulsar timing data, providing a new method to study gravitational wave anisotropies and their angular power spectra.

Findings

The angular power spectrum is the harmonic transform of the Hellings & Downs curve.

Pulsar timing arrays are most sensitive to quadrupole anisotropies.

The variance in the Hellings & Downs curve can be examined using the power spectrum.

Abstract

In this paper, we propose a new framework for treating the angular information in the pulsar timing array response to a gravitational wave background based on standard cosmic microwave background techniques. We calculate the angular power spectrum of the all-sky gravitational redshift pattern induced at the earth for both a single bright source of gravitational radiation and a statistically isotropic, unpolarized Gaussian random gravitational wave background. The angular power spectrum is the harmonic transform of the Hellings & Downs curve. We use the power spectrum to examine the expected variance in the Hellings & Downs curve in both cases. Finally, we discuss the extent to which pulsar timing arrays are sensitive to the angular power spectrum and find that the power spectrum sensitivity is dominated by the quadrupole anisotropy of the gravitational redshift map.