Cherenkov light shape of gamma and hadronic VHE air showers: Fit to analytical formulae

A detailed Monte Carlo simulation of Cherenkov light (300–480 nm) from electromagnetic and hadronic cascades in the atmosphere has been performed in the energy range 1012–1014 eV of γ, proton, oxygen, and iron primary cosmic rays for vertically incident showers. In the calculations of both cascade development and Cherenkov light production, the CORSIKA (COsmic Ray SImulator for KAscade) code [J.N. Capdevielle et al., Kerforschungszentrum Karlsruhe GmbH, Repr. KfK 4998 (1992)] has been used to allow for all, electromagnetic and hadronic, interactions. The main aim of our simulation is to obtain possibly accurate information on the lateral spread, longitudinal development, and temporal profile of Cherenkov light, from both pure electromagnetic and hadronic cascades, in order to obtain information to separate both. Time profile Cherenkov light pulse and primary cosmic ray dependence have been obtained. Parametrization of Cherenkov light pulses has been performed making use of gamma distributions. Apart from their value as new results, they may be used for the design, of current studies at mountain altitude. We also seek to provide relations to interpret the experimental data, for those who do not have detailed simulation calculations available.