On the fluctuations of Cerenkov photon densities in very high-energy gamma ray showers

The number distributions of Cerenkov photons seen by a mirror from pure electromagnetic cascades in the atmosphere initiated by very high-energy gamma rays are calculated. It is shown that the fluctuations of the number of these photons are not Poissonian, in general. It is also shown that the characteristics of the distribution depend on the distance of the mirror from the shower core. Significant correlations are observed between spatially separated mirrors. Also significant correlation is observed between the number distribution and the distribution of the shower maximum position. Differences in the nature of the number distributions and their correlations for different primary energies are discussed.