Understanding the gravitational-wave Hellings and Downs curve for pulsar timing arrays in terms of sound and electromagnetic waves

TL;DR

This paper provides a pedagogical explanation of the Hellings and Downs curve for pulsar timing arrays by exploring analogous scenarios with sound and electromagnetic waves, and develops a framework for general correlation calculations.

Contribution

It introduces simplified models with sound and electromagnetic waves to elucidate the Hellings and Downs curve and proposes a general framework for correlation analysis in pulsar timing arrays.

Findings

Derived Hellings-and-Downs-type functions for sound and electromagnetic waves.

Developed a versatile framework for correlation calculations in pulsar timing arrays.

Enhanced understanding of gravitational-wave background signatures.

Abstract

Searches for stochastic gravitational-wave backgrounds using pulsar timing arrays look for correlations in the timing residuals induced by the background across the pulsars in the array. The correlation signature of an isotropic, unpolarized gravitational-wave background predicted by general relativity follows the so-called Hellings and Downs curve, which is a relatively simple function of the angle between a pair of Earth-pulsar baselines. In this paper, we give a pedagogical discussion of the Hellings and Downs curve for pulsar timing arrays, considering simpler analogous scenarios involving sound and electromagnetic waves. We calculate Hellings-and-Downs-type functions for these two scenarios and develop a framework suitable for doing more general correlation calculations.