Detecting gravitational waves from inspiraling binaries with a network of geographically separated detectors: coherent versus coincident strategies

Abstract

We compare two strategies of multidetector detection of compact binary inspiral signals, namely, the coincidence and the coherent for the realistic case of geographically separated detectors. The naive coincident strategy treats the detectors as if they are isolated— compares individual detector statistics with their respective thresholds while the coherent strategy combines the detector network data coherently to obtain a single detection statistic which is then compared with a single threshold. We also consider an enhanced coincidence strategy which is intermediate in the sense that though the individual statistics are added in quadrature and the sum compared with a single threshold, the estimated parameters are also checked for consistency. For simplicity, we consider detector pairs having the same power spectral density of noise, as that of initial LIGO and also assume the noise to be stationary and Gaussian. Further, since we consider the detectors to be widely separated on Earth, we take the instrumental noises to be uncorrelated; the wide separation implicitly means that since the detector arms must lie parallel to the Earth's surface, the detectors necessarily have different orientations. We compare the performances of the methods by plotting the receiver operating characteristics for the strategies. Several results are derived analytically in order to gain insight. Simulations are performed in order to plot the receiver operating characteristic (ROC) curves. A single astrophysical source as well as a distribution of sources is considered. We assume a 1 yr data train and a mass range of 1-40M_⊙ for the case of astrophysically distributed sources. We find that the coherent strategy is superior to the two coincident strategies that we consider. Remarkably, the detection probability of the coherent strategy is 50% better than the naive coincident strategy. One the other hand, the difference in performance between the coherent strategy and enhanced coincident strategy is not very large. Even in this situation, it is not difficult to perform the real data analysis with the coherent strategy. The bottom line is that the coherent strategy is a good detection strategy.