An improved, ‘‘phase-relaxed’’ F -statistic for gravitational-wave data analysis

Rapidly rotating, slightly nonaxisymmetric 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 maximum likelihood 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 grid points is many orders of magnitude too large for that. Therefore, in practice some nonoptimal detection statistic is used for all-sky searches. 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 ‘‘semicoherent’’ F -statistic that is currently used. Moreover, as a by-product of computing F pr, one obtains a rough determination of the time-evolving phase offset between one’s template and the true signal imbedded in the detector noise. Almost all the ingredients that go into calculating F pr are already implemented in the LIGO Algorithm Library, so we expect that relatively little additional effort would be required to develop a search code that uses F pr.