Optimal reconstruction of the Hellings and Downs correlation

TL;DR

This paper develops an optimal estimator for the Hellings and Downs correlation in pulsar timing arrays, accounting for pulsar locations, GW frequency distribution, and noise, to improve GW detection accuracy.

Contribution

It introduces a method to optimally reconstruct the HD correlation by considering pulsar sky positions and GW frequency distribution, reducing variance in the estimate.

Findings

Predicts variance of the HD correlation estimator based on pulsar locations and GW frequency bins.

Shows each frequency bin can provide an independent estimate of the HD correlation after optimal combination.

Provides a framework for improving GW detection confidence in pulsar timing arrays.

Abstract

Pulsar timing arrays (PTAs) detect gravitational waves (GWs) via the correlations they create in the arrival times of pulses from different pulsars. The mean correlation, a function of the angle between the directions to two pulsars, was predicted in 1983 by Hellings and Downs (HD). Observation of this angular pattern is crucial evidence that GWs are present, so PTAs "reconstruct the HD curve'' by estimating the correlation using pulsar pairs separated by similar angles. Several studies have examined the amount by which this curve is expected to differ from the HD mean. The variance arises because (a) a finite set of pulsars at specific sky locations is used, (b) the GW sources interfere, and (c) the data are contaminated by noise. Here, for a Gaussian ensemble of sources, we predict that variance by constructing an optimal estimator of the HD correlation, taking into account the pulsar sky locations and the frequency distribution of the GWs and the pulsar noise. The variance is a ratio: the numerator depends upon the pulsar sky locations, and the denominator is the (effective) number of frequency bins for which the GW signal dominates the noise. In effect, after suitable combination, each such frequency bin gives an independent estimate of the HD correlation.