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Optimal reconstruction of the Hellings and Downs correlation
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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.
Forward citations
Cited by 7 Pith papers
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Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Fundamental Resolution Limits
A PTA's sky-map resolution is capped at multipoles l~ωL, and the pulsar-term information becomes usable for full-sky mapping only with ~10^11 pulsars, far beyond any realistic array.
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Modeling non-stationary noise: applications in gravitational wave astronomy
A positive dynamic spectrum S(f,t) generalizes the stationary power spectrum by defining Gramian closed-form noise covariances in Fourier and Wilson-Daubechies wavelet bases for gravitational wave data.
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Finite Populations & Finite Time: The Non-Gaussianity of a Gravitational Wave Background
Finite source number and finite observation time make PTA gravitational-wave-background Fourier coefficients non-Gaussian, with an analytically computed excess kurtosis and a Cauchy-distributed argument probe.
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Mapping the Gravitational-wave Background Across the Spectrum with a Next-Generation Anisotropic Per-frequency Optimal Statistic
A new pulsar-timing-array pipeline maps the gravitational-wave sky per frequency, folds cosmic variance into significance estimates, and detects a simulated loud source at p=0.01 versus 0.2 broadband.
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Optimal robust detection statistics for pulsar timing arrays
In simulations, a new cross-correlation-only statistic NPMV detects a gravitational-wave background more often than the standard PTA statistic, improving detection probability by about 47% at the 5-sigma threshold.
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Harmonic spectrum of pulsar timing array angular correlations
Optimal estimators and variance formulas are derived for the Legendre harmonic coefficients of the pulsar timing array Hellings-Downs correlation, with effective degrees of freedom computed for real arrays.
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Mitigating cosmic variance in the Hellings-Downs curve: a Cosmic Microwave Background analogy
An optimal multipole-space frequency weighting shows that PTA cosmic variance can be reduced with longer observations and better cadence, and the CMB would show a Hellings-Downs curve only if n_T>4.
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