Detecting a stochastic background of gravitational waves by correlating n detectors

We discuss the optimal detection strategy for a stochastic background of gravitational waves in the case n detectors are available. In the literature so far, only two cases have been considered: 2- and n-point correlators. We generalize these analyses 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. © 2006 IOP Publishing Ltd.