Rapidly rotating, slightly non-axisymmetric neutron stars emit nearly periodic gravitational waves (GWs), quite possibly at levels detectable by ground-based GW interferometers. We refer to these sources as GW pulsars. For any given sky position and frequency evolution, the F-statistic is the optimal (frequentist) statistic for the detection of GW pulsars. However, in all-sky searches for previously unknown GW pulsars, it would be computationally intractable to calculate the (fully coherent) F-statistic at every point of a (suitably fine) grid covering the parameter space: the number of gridpoints is many orders of magnitude too large for that. Here we introduce a phase-relaxed F-statistic, which we denote F_pr, for incoherently combining the results of fully coherent searches over short time intervals. We estimate (very roughly) that for realistic searches, our F_pr is ~10-15% more sensitive than the semi-coherent F-statistic that is currently used. Moreover, as a byproduct of computing F_pr, one obtains a rough determination of the time-evolving phase offset between ones template and the true signal imbedded in the detector noise. Almost all the ingredients that go into calculating F_pr are already implemented in LAL, so we expect that relatively little additional effort would be required to develop a search code that uses F_pr.
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