Limits to the energy resolution of a single Air Cherenkov Telescope at low energies

The photon density on the ground is a fundamental quantity in all experiments based on Cherenkov light measurements, e.g. in the Imaging Air Cherenkov Telescopes (IACT). IACT’s are commonly and successfully used in order to search and study Very High Energy (VHE) γ-ray sources. Difficulties with separating primary photons from primary hadrons (mostly protons) in Cherenkov experiments become larger at lower energies. I have calculated longitudinal and lateral density distributions and their fluctuations at low energies basing on Monte Carlo simulations (for vertical γ cascades and protonic showers) to check the influence of the detector parameters on the possible measurement. Relative density fluctuations are significantly higher in proton than in photon induced showers. Taking into account the limited detector field of view (FOV) implies the changes of these calculated distributions for both types of primary particles and causes an enlargement in relative fluctuations. Absorption due to Rayleigh and Mie scattering has an impact on mean values but does not change relative fluctuations. The total number of Cherenkov photons is more sensitive to the observation height in γ cascades than in proton showers at low primary energies. The relative fluctuations of the density do not depend on the reflector size in the investigated size range (from 240 m up to 960 m). This implies that a single telescope with a mirror area larger than that of the MAGIC telescope cannot achieve better energy resolution than estimated and presented in this paper. The correlations between longitudinal and lateral distributions are much more pronounced for primary γ-ray than for primary proton showers. PACS numbers: 95.55.Ka;95.55.Vj;95.75-z;95.85.Pw;95.85.Ry