Cumulative analysis of the association between the data of the gravitational wave detectors NAUTILUS and EXPLORER and the gamma ray bursts detected by BATSE and BeppoSAX

The statistical association between the output of the Gravitational Wave (GW) detectors EXPLORER and NAUTILUS and a list of Gamma Ray Bursts (GRBs) detected by the satellite experiments BATSE and BeppoSAX has been analyzed using cumulative algorithms. GW detector data collected between 1991 and 1999 have been searched for an energy excess in a 10 s interval around the GRB flux peak times. The cumulative analysis of the data relative to a large number of GRBs (387) allows to push the upper bound for the corresponding GW burst amplitude down to $h=2.5\times {10}^{-19}$.

Figure 1

Histograms of the effective temperature of the minimum mode of the Wiener filtered data computed in the 1150 time intervals of 30 min around each GRB time.

Figure 2

Experimental histogram of ${sin}^4\theta$ for the 387 GRB in the selected time intervals of 30 min around each GRB time (net area). The distribution is compared to theoretical isotropic distribution (solid line). The four regions of increasing ${sin}^4\theta$, separated by vertical lines, correspond to the data subsets separately analyzed to look for a correlation with ${sin}^4\theta$.

Figure 3

Cumulative average ($E_a$) and cumulative median ($E_m$) of the GW detector energy as a function of the GW-GRB delay.

Figure 4

Distributions of the median and of the average of the GW detector energy value (see Fig. 3) and gaussian fits.

Figure 5

SNR of the excess at zero-delay of the GW-median, as a function of ${sin}^4\theta$.

Figure 6

Relative belief updating ratio as a function of $h$, using the average (solid line) and median (dashed line) algorithms.