Source anisotropies and pulsar timing arrays

TL;DR

This paper investigates how source anisotropies, such as discrete source locations and galaxy clustering, affect gravitational wave detection via pulsar timing arrays, revealing shot noise impacts are more significant than clustering effects.

Contribution

It introduces a framework to analyze the effects of source anisotropies on PTA correlation statistics, moving beyond the standard Gaussian ensemble assumption.

Findings

Shot noise has a larger impact than clustering on PTA correlations.

Source anisotropies alter the mean and variance of the Hellings and Downs correlation.

Clustering effects are comparatively minor for conventional PTA sources.

Abstract

Pulsar timing arrays (PTA) hunt for gravitational waves (GW) by searching for the correlations that GWs induce in the time-of-arrival residuals from different pulsars. If the GW sources are of astrophysical origin, then they are located at discrete points on the sky. However, PTA data are often modeled, and subsequently analyzed, via a "standard Gaussian ensemble". That ensemble is obtained in the limit of an infinite density of vanishingly weak, Poisson-distributed sources. In this paper, we move away from that ensemble, to study the effects of two types of "source anisotropy". The first (a), which is often called "shot noise", arises because there are $N$ discrete GW sources at specific sky locations. The second (b) arises because the GW source positions are not a Poisson process, for example, because galaxy locations are clustered. Here, we quantify the impact of (a) and (b) on the mean and variance of the pulsar-averaged Hellings and Downs correlation. For conventional PTA sources, we show that the effects of shot noise (a) are much larger than the effects of clustering (b).