Strategy to detect the gravitational radiation counterpart of gamma-ray bursts

Both observational and theoretical rates of binary neutron star coalescence give low prospects for detection of a single event by the initial LIGO/VIRGO interferometers. However, by utilizing at the best all the a priori information on the expected signal, a positive detection can be achieved. This relies on the hypothesis that $\gamma$-ray bursts are the electromagnetic signature of neutron star coalescences. The information about the direction of the source can then be used to add in phase the signals from different detectors in order (i) to increase the signal-to-noise ratio and (ii) to make the noise more Gaussian. Besides, the information about the time of arrival can be used to drastically decrease the observation time and thereby the false alarm rate. Moreover the fluence of the $\gamma$-ray emission gives some information about the amplitude of the gravitational signal. One can then add the signals from $\sim 10^4$ observation boxes ($\sim$ number of $\gamma$-ray bursts during 10 years) to yield a positive detection. Such a detection, based on the Maximum a Posteriori Probability Criterium, is a minimal one, in the sense that no information on the position and time of the events, nor on any parameter of the model, is collected. The advantage is that this detection requires an improvement of the detector sensitivity by a factor of only $\sim 1.5$ with respect to the initial LIGO/VIRGO interferometers, and that, if positive, it will confirm the $\gamma$-ray burst model.