Cosmic-ray measurements with an array of Cherenkov telescopes using reconstruction of longitudinal profiles of air showers

We present a method to reconstruct the longitudinal profile of electrons in showers using Cherenkov telescopes. We show how the Cherenkov light collected by an array of telescopes can be transformed into the number of electrons as a function of atmospheric depth. This method is validated using air shower and simplified telescope simulations. The reconstruction of the depth in which the shower has the maximum number of electrons (${\mathrm{X}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$) opens the possibility of cosmic ray composition studies with Cherenkov telescopes in the energy range from 10 to 100 TeV. A resolution of less than 16 $\mathrm{g}\mathrm{/}\mathrm{c}{\mathrm{m}}^2$ in the ${\mathrm{X}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ reconstruction is obtained.