Abstract
In gamma-ray astronomy through Imaging Atmospheric Cherenkov Telescopes (IACT), the atmosphere is used as a calorimeter. Incident gamma-rays in the GeV-TeV energy range are observed through the electromagnetic showers they produce in the atmosphere and the Cherenkov light emitted by them. We aim to obtain a parameterisation of the longitudinal profiles of electromagnetic showers in the atmosphere. The longitudinal Cherenkov emission profiles of these showers can be used for the reconstruction of the parameters of the gamma-photon as well gamma-hadron discrimination. Obtaining an accurate parameterisation of these profiles can therefore be used in the analysis of IACT images as well as fast simulation of the Cherenkov emission from gamma-induced showers in the atmosphere. Such parameterisations are not known to have been systematically carried out prior to this. We carry out Monte Carlo simulations of gamma-induced showers in the atmosphere. The parameterisation of their Cherenkov emission longitudinal profiles is based on the well-known gamma-function used in particle detector physics. We evaluate the dependence of the depth of the maximum and the average depth of the longitudinal Cherenkov emission profile, as well as the parameter $1/\beta$ on the energy of the initial shower. We also study the distributions of various parameters associated with the gamma-function and find that $\beta/\alpha$ and $1/\alpha$ have Gaussian distributions and are not correlated with each other which makes them appropriate variables for evaluating the fluctuations of the Cherenkov emission profiles. We finally present parameterisations of the fluctuations of these two variables.