The F-statistic, derived by Jaranowski, Krolak & Schutz (1998), is the optimal (frequentist) statistic for the detection of nearly periodic gravitational waves from known neutron stars, in the presence of stationary, Gaussian detector noise. The F-statistic was originally derived for the case of a single detector, whose noise spectral density was assumed constant in time, and for a single known neutron star. Here we show how the F-statistic can be straightforwardly generalized to the cases of 1) a network of detectors with time-varying noise curves, and 2) a population of known sources. Fortunately, all the important ingredients that go into our generalized F-statistics are already calculated in the single-source/single-detector searches that are currently implemented, e.g., in the LIGO Software Library, so implementation of optimal multi-detector, multi-source searches should require negligible additional cost in computational power or software development.
@article{arxiv.gr-qc/0504011,
title = {The generalized F-statistic: multiple detectors and multiple GW pulsars},
author = {Curt Cutler and Bernard F. Schutz},
journal= {arXiv preprint arXiv:gr-qc/0504011},
year = {2015}
}
Comments
6 pages, 0 figures, submitted to PRD; section IV substantially enlarged and revised, and a few typos corrected