2 Data analysis and results

The INCA experiment is running since December 1996 at Mount Chacaltaya in Bolivia, at 5200 m above the sea level. It consists of 12 scintillator modules of 2 $\times$ 2 m² area, distributed over a $\sim$ 20 $\times$ 20 m² area. Its geographic location is suitable for the observation of a large part of the southern sky.

The data analysis consists in the search for significant excesses in the scintillators counting rates during the GRBs observed by BATSE [(Castellina 1997)]. In 20 months of data taking, 70 BATSE events have occurred in the INCA field of view (zenith angle $\theta <$ 60$^{\circ}$) [(Brainerd 1998)]. For each BATSE event the INCA data recorded during 10000 s around the burst time were selected. In this time interval the counting rates of each detector were carefully studied in order to identify possible electronic noises or anomalous behaviours. Finally the detector counts were summed and the time distribution of the total counting rate was studied to single out statistically significant fluctuations.

  

Figure 1: Mean number of ${\rm e}^{\pm}$ reaching the ground generated by a gamma-ray of different energy and zenith angle $\theta=30^{\circ}$,as a function of the altitude above the sea level

We looked for excesses of different durations $\Delta t=1$, 2, 6, 10, 20, 50, 100, 200 s, setting the excess start time in time coincidence with the BATSE trigger time. The counts C recorded in $\Delta t$ were compared with the expected background B calculated using the counts measured in 30 minutes around $\Delta t$. The distribution of the C-B difference in unit of standard deviations obtained in the 560 trials (70 events $\times$ 8 time durations), is well fitted by a Gauss distribution with rms = 1.17. We found no statistically significant excess for any burst and time duration. Looking for possible delayed or anticipated excesses with respect to the BATSE burst, the same search was performed in a 2 hours time interval centered around the BATSE time. Also in this case non excess was found.

  

Figure 2: Upper limits on the energy fluence in the energy range $1~{\rm GeV}\div 1~{\rm TeV}$ for the 70 GRBs analyzed, in a time window of 10 s starting from the BATSE trigger time, as a function of the zenith angle of the events

Figure 2 shows the obtained upper limits on the energy fluence in the photon energy range $1~{\rm GeV}\div 1~{\rm TeV}$ for the 70 bursts analyzed, in a time window of 10 s starting from the BATSE trigger time, as a function of the zenith angles of the events. The fluences have been calculated at 5 standard deviations level, assuming a GRB spectrum dN/d$E~\propto~E^{\alpha}$ with $\alpha = -2$, extending up to 1 TeV.

Among the GRBs whose afterglow was observed by Beppo-Sax only GRB 980326 was in the INCA field of view, but with the very unfavorable zenith angle $\theta=55^{\circ}$.The obtained upper limit on the fluence in the $1~{\rm GeV}\div 1~{\rm TeV}$ energy range during the time duration of the gamma event (5 s) is $4.9 \ 10^{-3}~{\rm erg}~{\rm cm}^{-2}$.

If GRBs sources are located at cosmological distances, the high energy gamma-ray flux is absorbed in the intergalactic space through the interaction $\gamma + \gamma \rightarrow {\rm e}^+{\rm e}^-$on low energy starlight photons. Assuming the GRB sources located at the distance z=0.5(1.0), according to the opacity calculated by [Salomon & Stecker (1998)], the fluence upper limits have to be increased by a factor $\sim 7(10)$.