Forecasting pulsar timing array sensitivity to anisotropy in the stochastic gravitational wave background

TL;DR

This paper develops a statistical framework to predict the sensitivity of pulsar timing arrays to anisotropy in the gravitational wave background, providing scaling relations and simulations for near-future detection prospects.

Contribution

It introduces a positive-restricted frequentist method for GWB anisotropy detection and derives scaling relations for decision thresholds based on PTA properties.

Findings

Larger pulsar numbers improve detection sensitivity.

Lower measurement uncertainty enhances anisotropy detection.

Simulations suggest anisotropic signals may be detectable with current PTA data.

Abstract

Statistical anisotropy in the nanohertz-frequency gravitational-wave background (GWB) is expected to be detected by pulsar timing arrays (PTAs) in the near future. By developing a frequentist statistical framework that intrinsically restricts the GWB power to be positive, we establish scaling relations for multipole-dependent anisotropy decision thresholds that are a function of the noise properties, timing baselines, and cadences of the pulsars in a PTA. We verify that $(i)$ a larger number of pulsars, and $(ii)$ factors that lead to lower uncertainty on the cross-correlation measurements between pulsars, lead to a higher overall GWB signal-to-noise ratio, and lower anisotropy decision thresholds with which to reject the null hypothesis of isotropy. Using conservative simulations of realistic NANOGrav datasets, we predict that an anisotropic GWB with angular power $C_{l=1} > 0.3\,C_{l=0}$ may be sufficient to produce tension with isotropy at the $p = 3\times10^{-3}$ ($\sim3\sigma$) level in near-future NANOGrav data with a $20$~yr baseline. We present ready-to-use scaling relationships that can map these thresholds to any number of pulsars, configuration of pulsar noise properties, and sky coverage. We discuss how PTAs can improve the detection prospects for anisotropy, as well as how our methods can be adapted for more versatile searches.