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

TL;DR

The paper introduces a phase-relaxed F-statistic (F_pr) that enhances the sensitivity of gravitational-wave pulsar searches by combining short-interval coherent results, offering a computationally feasible and more sensitive alternative to existing semi-coherent methods.

Contribution

It presents a novel phase-relaxed F-statistic (F_pr) for gravitational-wave data analysis, improving sensitivity and computational efficiency in all-sky pulsar searches.

Findings

F_pr is approximately 10-15% more sensitive than current semi-coherent methods.

F_pr allows rough estimation of the phase offset between template and true signal.

Most components for calculating F_pr are already implemented in LAL.

Abstract

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 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 LAL, so we expect that relatively little additional effort would be required to develop a search code that uses F_pr.