Update on testing of air-shower modelling using combined data of the Pierre Auger Observatory and phenomenological consequences

Abstract: The combined data of Fluorescence and Surface Detectors of the Pierre Auger Observatory has recently provided the strongest constraints on the validity of predictions from current models of hadronic interactions. The unmodified predictions of these models on the depth of shower maximum ($X_\text{max}$) and the hadronic part of the ground signal are unable to accurately describe the measured data at a level of more than 5$\sigma$ in the energy range 3-10 EeV. This inconsistency has been shown to originate not only from the predicted amount of muons at the ground level, but also from the predicted scale of $X_\text{max}$, which must be adjusted to better match the observed data. The resulting deeper $X_\text{max}$ scales of the models imply a heavier mass composition to be interpreted from the $X_\text{max}$ measurements. We show the results of the test with an updated data set of the Pierre Auger Observatory, studying also the energy evolution of the fitted modification parameters and new versions of the models of hadronic interactions. Additionally, we discuss the phenomenological consequences of the deeper $X_\text{max}$ scale of models on the interpretation of the features of the energy spectrum and the muon problem in air-shower modelling.