Detection of gravitational waves using a network of detectors

TL;DR

This paper develops a maximum likelihood-based method for detecting gravitational waves from coalescing binaries using a network of laser interferometers, optimizing detection and sensitivity.

Contribution

It introduces a formalism for combining signals from multiple detectors, showing the network's sensitivity scales with the square root of the number of detectors, applicable to various detector types.

Findings

Optimal detection statistic is the network correlation vector magnitude.

Network sensitivity improves as the square root of the number of detectors.

Results hold for both full and restricted post-Newtonian filters.

Abstract

We formulate the data analysis problem for the detection of the Newtonian coalescing-binary signal by a network of laser interferometric gravitational wave detectors that have arbitrary orientations, but are located at the same site. We use the maximum likelihood method for optimizing the detection problem. We show that for networks comprising of up to three detectors, the optimal statistic is essentially the magnitude of the network correlation vector constructed from the matched network-filter. Alternatively, it is simply a linear combination of the signal-to-noise ratios of the individual detectors. This statistic, therefore, can be interpreted as the signal-to-noise ratio of the network. The overall sensitivity of the network is shown to increase roughly as the square-root of the number of detectors in the network. We further show that these results continue to hold even for the restricted post-Newtonian filters. Finally, our formalism is general enough to be extended to address the problem of detection of such waves from other sources by some other types of detectors, e.g., bars or spheres, or even by networks of spatially well-separated detectors.