Study of the composition of ultra-high energy cosmic rays detected by the Pierre Auger Observatory and analysis of the associated hadronic mechanisms

Ultra high energy cosmic rays (UHECR), i.e. E ≥ 1 EeV, raise many questions about their origin and constitute a challenge to modern physics. These cosmic rays entering the atmosphere dissipate their huge energy by generating a shower of secondary particles whose development is significantly different depending on the nature of the primaries. The study of the composition of UHECR is therefore a major interest both in understanding the hadronic processes which govern the evolution of showers and in identifying the sources of this radiation. Given its hybrid structure and the size of its unmatched network of ground detectors, the Pierre Auger Observatory can provide clear answers to the issues raised by UHECR. In this thesis, we are particularly interested in the muon component of air showers. First, we show how the hadronic parameters define the production of muons. Then we present an original method to extract this muon component and deduce the implications on the composition of UHECR. The results of this approach suggest a transition from a heavy composition to a light one when the energy increases. Finally, we address the measurement of cosmic-air cross section and present the first results derived from the Pierre Auger Observatory data. (author)