The impact of large-scale galaxy clustering on the variance of the Hellings-Downs correlation: numerical results

TL;DR

This paper numerically evaluates how large-scale galaxy clustering affects the variance of the Hellings-Downs correlation in pulsar timing arrays, finding the effect to be minimal and not a significant contamination.

Contribution

It provides the first numerical analysis of galaxy clustering anisotropies on the HD correlation variance, extending previous theoretical work.

Findings

Anisotropies cause at most a 1% increase in HD variance.

Galaxy clustering effects are negligible compared to standard variance contributions.

Results support the robustness of PTA correlations against galaxy clustering anisotropies.

Abstract

Pulsar timing array experiments have recently found evidence for a stochastic gravitational wave (GW) background, which induces correlations among pulsar timing residuals described by the Hellings and Downs (HD) curve. Standard calculations of the HD correlation and its variance assume an isotropic background. However, for a background of astrophysical origin, we expect a higher GW spectral density in directions with higher galaxy number densities. In a companion paper, we have developed a theoretical formalism to account for the anisotropies arising from large-scale galaxy clustering, leading to a new contribution to the variance of the HD correlation. In this subsequent work, we provide numerical results for this novel effect. We consider a GW background resulting from mergers of supermassive black hole binaries, and relate the merger number density to the overdensity of galaxies. We find that anisotropies due to large-scale galaxy clustering lead to a standard deviation of the HD correlation at most at percent level, remaining well below the standard contributions to the HD variance. Hence, this kind of anisotropies in the GW source distribution does not represent a substantial contamination to the correlations of timing residuals in present and future PTA surveys. Suitable statistical methods to extract the galaxy clustering signal from PTA data will be investigated in the future.