A complete model of the signal in surface detector arrays and its application for the reconstruction of mass-sensitive observables

The principle of air-shower universality yields a method of understanding extensive air showers of UHECRs as a superposition of different particle components whose spatial and temporal distributions follow individual analytical profile functions. We present a model of the expected densities of particles in time and space that uses the depth of the shower maximum, X$_{max}$, and the relative muonic content of the shower, R$_{µ}$ , as input parameters besides the shower geometry and energy. The model is parametrized using simulated showers using different hadronic interaction models. Furthermore, we present results for the reconstruction of X$_{max}$ and R$_{µ}$ that allow for an event-by-event estimation of the mass of the primary particle, based on the responses of the water-Cherenkov and scintillator surface detectors of the Pierre Auger Observatory