Reconstruction of longitudinal profiles of ultra-high energy cosmic ray showers from fluorescence and Cherenkov light measurements

We present a new method for the reconstruction of the longitudinal profile of extensive air showers induced by ultra-high energy cosmic rays. In contrast to the typically considered shower size profile, this method employs directly the ionization energy deposit of the shower particles in the atmosphere. Due to universality of the energy spectra of electrons and positrons, both fluorescence and Cherenkov light can be used simultaneously as signal to infer the shower profile from the detected light. The method is based on an analytic least-square solution for the estimation of the shower profile from the observed light signal. Furthermore, the extrapolation of the observed part of the profile with a Gaisser–Hillas function is discussed and the total statistical uncertainty of shower parameters like total energy and shower maximum is calculated.