ausblenden:
Schlagwörter:
General Relativity and Quantum Cosmology, gr-qc
Zusammenfassung:
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.
