Cross-correlation between gravitational wave detectors for detecting association with gamma ray bursts

Abstract

Cross-correlation of the outputs of two gravitational wave (GW) detectors has recently been proposed as a method for detecting statistical association between GWs and gamma ray bursts (GRBs). Unfortunately, the method can be effectively used only in the case of stationary noise. In this work a different cross-correlation algorithm is presented, which may effectively be applied also in nonstationary conditions for the cumulative analysis of a large number of GRBs. The value of the cross-correlation at zero delay, which is the only one expected to be correlated to any astrophysical signal, is compared with the distribution of cross-correlation of the same data for all nonzero delays within the integration time interval. This background distribution is Gaussian, so the statistical significance of an experimentally observed excess is well defined. Computer simulations using real noise data of the cryogenic GW detectors Explorer and Nautilus with superimposed deltalike signals were performed to test the effectiveness of the method, and theoretical estimates of its sensitivity were compared to the results of the simulation. The effectiveness of the proposed algorithm is compared to that of other cumulative techniques, showing that the algorithm is particularly effective in the case of non-Gaussian noise and of a large (100\char21{}1000 s) and unpredictable delay between GWs and GRBs.