3 Sensitivity to high energy GRBs

A high energy GRB is detectable if the number of air showers from the gamma-rays is significant larger than the fluctuations of the background, due to showers from cosmic rays with arrival directions compatible with the burst position. A good angular resolution is of major importance in order to reduce the background and increase the detection sensitivity. The angular resolution and the effective area of ARGO-YBJ to detect gamma-rays as a function of the energy have been obtained by means of simulations. For gamma-rays with energy as low as $E \sim 10-20$ GeV, the opening angle around the source direction in which 70$\%$ of the signal showers are contained is $\sim$ 5$^{\circ}$.

To evaluate the sensitivity of ARGO-YBJ to detect GRBs, we considered a burst with a power law energy spectrum ${\rm d}N/{\rm d}E \propto E^{-\alpha}$ extending in the range 1 GeV $\div \,E_{\rm max}$,a duration $\Delta t=1$ s, and a zenith angle $\theta=20^{\circ}$.The burst will give a signal with a significance larger than 4 standard deviations if the energy fluence in the range 1 GeV $\div \,E_{\rm max}$ is larger than a minimum value $F_{\rm min}$. Figure 1 shows $F_{\rm min}$ as a function of $E_{\rm max}$for 3 spectral slopes. For a generic duration $\Delta t$the minimum fluences detectable are given by $F_{\rm min} \sqrt{\Delta t}$.

  

Figure 1: The minimum energy fluence in the range $1~{\rm GeV}\div E_{\rm max}$ of a GRB detectable by ARGO-YBJ as a function of the maximum energy of the spectrum $E_{\rm max}$ for 3 spectral slopes

In the energy range considered the sensitivity is strongly dependent on the maximum energy of the spectrum $E_{\rm max}$.ARGO-YBJ can observe GRBs with energy fluences of a few 10^-6 erg cm^-2 if the energy spectrum extends at least up to $\sim$ 200 GeV with a slope $\alpha\leq 2$;the minimum detectable fluence is $\sim$ 10^-5 if $E_{\rm max}~\sim$ 30 GeV.

This is of particular importance, since if GRB sources are located at cosmological distances, the high energy tail of the spectrum is affected by the $\gamma \gamma \rightarrow {\rm e}^+{\rm e}^-$ interaction of gamma-rays with low energy starlight photons in the intergalactic space. According to [Salomon & Stecker (1998)], at a distance corresponding to a redshift z=0.1 the absorption is almost negligible, while at $z=0.5\,(1.0)$ the absorption becomes important for photons of energy E>100 (50) GeV. These values give an idea of the possible maximum energy of the GRBs spectra as a function of their distance, and from Fig. 1 one can infer the maximum sensitivity of ARGO-YBJ to detect cosmological GRBs. The minimum observable fluences can be compared with the fluences measured by EGRET in the $1~{\rm MeV}-1$ GeV energy range: $F \sim 10^{-5} \div 10^{-4}$ erg cm^-2 [(Catelli et al. 1997)]. Since EGRET spectral slopes $\alpha$are mostly $\sim$ 2, one could expect fluences of the same order of magnitude at energies above 1 GeV. From Fig. 1 one can conclude that ARGO-YBJ could detect GRBs with the same intensity of those observed by EGRET provided that the energy spectrum extends up to few tens of GeVs; the sensitivity increases by a factor $\sim$10 for spectra extending up to $E_{\rm max} \sim$ 200 GeV.