Detecting a stochastic background of gravitational waves by correlating n detectors

TL;DR

This paper develops an optimal detection strategy for a stochastic gravitational wave background using multiple detectors, showing that combining 2-point correlators maximizes the signal-to-noise ratio and enhances sensitivity.

Contribution

It generalizes previous two- and n-point correlator analyses to m-point correlators, demonstrating the optimality of 2-point correlators for n detectors and quantifying the sensitivity improvement.

Findings

Combining 2-point correlators maximizes detection sensitivity.

The signal-to-noise ratio improves by the fourth root of n(n-1)/2.

Sensitivity for multi-mode spherical antennas can be significantly enhanced.

Abstract

We discuss the optimal detection strategy for a stochastic background of gravitational waves in the case n detectors are available. In literature so far, only two cases have been considered: 2- and n-point correlators. We generalize these analysises to m-point correlators (with m<n) built out of the n detector signals, obtaining the result that the optimal choice is to combine 2-point correlators. Correlating n detectors in this optimal way will improve the (suitably defined) signal-to-noise ratio with respect to the n=2 case by a factor equal to the fourth root of n(n-1)/2. Finally we give an estimation of how this could improve the sensitivity for a network of multi-mode spherical antennas.