The search for continuous gravitational waves: metric of the multi-detector F-statistic

TL;DR

This paper develops a formalism for the parameter-space metric of the multi-detector F-statistic used in continuous gravitational wave searches, showing how detector combination affects computational efficiency and search sensitivity.

Contribution

It introduces a family of F-statistic metrics parametrized by unknown amplitudes, and demonstrates that combining similar sensitivity detectors is computationally advantageous for wide-parameter searches.

Findings

The multi-detector metric can be expressed via noise-weighted averages of single-detector metrics.

Combining detectors of similar sensitivity is more cost-effective than longer observation times.

The metric predictions align with measured mismatches, with identified regimes where local metrics fail.

Abstract

We develop a general formalism for the parameter-space metric of the multi-detector F-statistic, which is a matched-filtering detection statistic for continuous gravitational waves. We find that there exists a whole family of F-statistic metrics, parametrized by the (unknown) amplitude parameters of the gravitational wave. The multi-detector metric is shown to be expressible in terms of noise-weighted averages of single-detector contributions, which implies that the number of templates required to cover the parameter space does not scale with the number of detectors. Contrary to using a longer observation time, combining detectors of similar sensitivity is therefore the computationally cheapest way to improve the sensitivity of coherent wide-parameter searches for continuous gravitational waves. We explicitly compute the F-statistic metric family for signals from isolated spinning neutron stars, and we numerically evaluate the quality of different metric approximations in a Monte-Carlo study. The metric predictions are tested against the measured mismatches and we identify regimes in which the local metric is no longer a good description of the parameter-space structure.