A study of the elongation rate and air shower properties of ultra high energy cosmic rays from the Southern Pierre Auger Observatory

The Southern Pierre Auger Observatory is the largest hybrid cosmic ray detector in operation, consisting of a 3000km2 array of surface detectors as well as air fluorescence detectors. It is designed to measure the properties such as mass, energy, and arrival direction of the incident ultra high energy cosmic rays with an outstanding statistical precision in order to improve our understanding of their cosmological origins. Here I demonstrate the use of statistical analysis in determining the optimal parameters for Auger event reconstruction, selection of air shower modeling tools, and identification of the mass composition of cosmic rays. I use Monte Carlo simulations of air shower events to investigate the dependence of the mean particle density at 1000m from the air shower core, S(1000), on several different variables associated with air shower parameters. Using the same simulations, I investigate how calculating this mean particle density at distances other than 1000m from the core affects the uncertainties in the reconstructed parameters. Furthermore, I explore the differences between hadronic interaction models used in air shower simulations, and I demonstrate crucial deviations between simulated showers and real Auger data. Finally, I present a preliminary analysis of the primary mass composition of ultra high energy cosmic rays. After introducing novel anti-bias cuts, I find that, based on two years' worth of Auger data, the mass composition changes from heavy primaries to light primaries at energy of about $10^{18.45}$eV.