Optimal reconstruction of the Hellings and Downs correlation

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.

Final published version, 8 pages, 2 figures

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Cited by in corpus (9)

• Regularizing the Pulsar Timing Array likelihood: A path towards Fourier Space
• Mitigating cosmic variance in the Hellings-Downs curve: a Cosmic Microwave Background analogy
• The impact of large-scale galaxy clustering on the variance of the Hellings-Downs correlation: numerical results
• Accurate pulsar timing array residual variances and correlation of the stochastic gravitational wave background
• Finite Populations & Finite Time: The Non-Gaussianity of a Gravitational Wave Background
• Rapid inference for individual binaries and a stochastic background with pulsar timing array data
• Timing Gamma-ray Pulsars using Gibbs Sampling
• Spatial Correlation between Pulsars from Interfering Gravitational-Wave Sources in Massive Gravity
• Pulsar timing array analysis in a Legendre polynomial basis