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We present a new method for probing the hadronic interaction models atultra-high energy and extracting details about mass composition. This is doneusing the time profiles of the signals recorded with the water-Cherenkovdetectors of the Pierre Auger Observatory. The profiles arise from a mix of themuon and electromagnetic components of air-showers. Using the risetimes of therecorded signals we define a new parameter, which we use to compare ourobservations with predictions from simulations. We find, firstly,inconsistencies between our data and predictions over a greater energy rangeand with substantially more events than in previous studies. Secondly, bycalibrating the new parameter with fluorescence measurements from observationsmade at the Auger Observatory, we can infer the depth of shower maximum for asample of over 81,000 events extending from 0.3 EeV to over 100 EeV. Above 30EeV, the sample is nearly fourteen times larger than currently available fromfluorescence measurements and extending the covered energy range by half adecade. The energy dependence of the average depth of shower maximum iscompared to simulations and interpreted in terms of the mean of the logarithmicmass. We find good agreement with previous work and extend the measurement ofthe mean depth of shower maximum to greater energies than before, reducingsignificantly the statistical uncertainty associated with the inferences aboutmass composition.

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