Inferences on Mass Composition and Tests of Hadronic Interactions from 0.3 to 100 EeV using the water-Cherenkov Detectors of the Pierre Auger Observatory

We present a new method for probing the hadronic interaction models at ultra-high energy and extracting details about mass composition. This is done using the time profiles of the signals recorded with the water-Cherenkov detectors of the Pierre Auger Observatory. The profiles arise from a mix of the muon and electromagnetic components of air-showers. Using the risetimes of the recorded signals we define a new parameter, which we use to compare our observations with predictions from simulations. We find, firstly, inconsistencies between our data and predictions over a greater energy range and with substantially more events than in previous studies. Secondly, by calibrating the new parameter with fluorescence measurements from observations made at the Auger Observatory, we can infer the depth of shower maximum for a sample of over 81,000 events extending from 0.3 EeV to over 100 EeV. Above 30 EeV, the sample is nearly fourteen times larger than currently available from fluorescence measurements and extending the covered energy range by half a decade. The energy dependence of the average depth of shower maximum is compared to simulations and interpreted in terms of the mean of the logarithmic mass. We find good agreement with previous work and extend the measurement of the mean depth of shower maximum to greater energies than before, reducing significantly the statistical uncertainty associated with the inferences about mass composition.