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3 Searching for coincidences

In order to find a time correlation between the two different phenomena we have chosen as reference time ($t_{\rm R}$) the GRB trigger time. Then we searched how many EXPLORER events occured in a time window of $\pm 1$ s around the $t_{\rm R}$. In this way we found 4 GRBs, over the 557 analysed, that have a GW event in this time window.

The Table 1 reports the occurrence date and the peak flux counts in photons cm-2 s-1 of the GRBs. As the EXPLORER detector has $\sin ^4 \theta $ dependent GW cross section, where $\theta$ is the angle between the direction of the source and the principle axis of the antenna, we also report this value in the table. These coincidence events are then analysed to search particular deviations from the ${\rm Log}N-{\rm Log}C$ BATSE distribution and from the $\sin ^4 \theta $ distribution of all 557 GRBs, because we would expect an excess of events in coincidence with GRBs located closer to us and in better direction respect to the antenna.

The Kolmogorov-Smirnov test between the two distribution with the $\sin ^4 \theta $ and the peak flux of these 4 bursts, and those obtained with the all 557 GRBs, gives respectively a value of 75% and 53% that they are compatible.


  
Table 1: GRBs with an event in $\pm 1$ s near their trigger time

\begin{tabular}
{lll}
\hline
GRB & peak flux & $\sin ^4 \theta$\space \\  
\hlin...
 ....43 & 0.13 \\ 960522 & - & 0.95 \\ 960623c & 0.29 & 0.98 \\  \hline\end{tabular}


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