The generalized F-statistic: multiple detectors and multiple GW pulsars

TL;DR

This paper extends the F-statistic for gravitational wave detection to multiple detectors with varying noise and multiple sources, enabling more efficient searches with minimal additional computational cost.

Contribution

It introduces a straightforward generalization of the F-statistic for multi-detector and multi-source gravitational wave searches, building on existing single-source, single-detector calculations.

Findings

Generalized F-statistic for multiple detectors and sources

Implementation requires negligible additional computational resources

Facilitates more comprehensive gravitational wave searches

Abstract

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.