The energy spectrum of cosmic rays above $2.5\times {10}^{18}\mathrm{eV}$, derived from 20 000 events recorded at the Pierre Auger Observatory, is described. The spectral index $\gamma$ of the particle flux, $J\propto E^{-\gamma }$, at energies between $4\times {10}^{18}\mathrm{eV}$ and $4\times {10}^{19}\mathrm{eV}$ is $2.69\pm 0.02(\mathrm{stat})\pm 0.06(\mathrm{syst})$, steepening to $4.2\pm 0.4(\mathrm{stat})\pm 0.06(\mathrm{syst})$ at higher energies. The hypothesis of a single power law is rejected with a significance greater than 6 standard deviations. The data are consistent with the prediction by Greisen and by Zatsepin and Kuz’min.

We report a study of the distributions of the depth of maximum, $X_{\max }$, of extensive air-shower profiles with energies above $10^{17.8}\mathrm{eV}$ as observed with the fluorescence telescopes of the Pierre Auger Observatory. The analysis method for selecting a data sample with minimal sampling bias is described in detail as well as the experimental cross-checks and systematic uncertainties. Furthermore, we discuss the detector acceptance and the resolution of the $X_{\max }$ measurement and provide parametrizations thereof as a function of energy. The energy dependence of the mean and standard deviation of the $X_{\max }$ distributions are compared to air-shower simulations for different nuclear primaries and interpreted in terms of the mean and variance of the logarithmic mass distribution at the top of the atmosphere.

Using the data taken at the Pierre Auger Observatory between December 2004 and December 2012, we have examined the implications of the distributions of depths of atmospheric shower maximum ($X_{\max }$), using a hybrid technique, for composition and hadronic interaction models. We do this by fitting the distributions with predictions from a variety of hadronic interaction models for variations in the composition of the primary cosmic rays and examining the quality of the fit. Regardless of what interaction model is assumed, we find that our data are not well described by a mix of protons and iron nuclei over most of the energy range. Acceptable fits can be obtained when intermediate masses are included, and when this is done consistent results for the proton and iron-nuclei contributions can be found using the available models. We observe a strong energy dependence of the resulting proton fractions, and find no support from any of the models for a significant contribution from iron nuclei. However, we also observe a significant disagreement between the models with respect to the relative contributions of the intermediate components.

53 pages. Submitted to Nuclear Instruments and Methods in Physics Research Section AInternational audienceThe Pierre Auger Observatory is a hybrid detector for ultra-high energy cosmic rays. It combines a surface array to measure secondary particles at ground level together with a fluorescence detector to measure the development of air showers in the atmosphere above the array. The fluorescence detector comprises 24 large telescopes specialized for measuring the nitrogen fluorescence caused by charged particles of cosmic ray air showers. In this paper we describe the components of the fluorescence detector including its optical system, the design of the camera, the electronics, and the systems for relative and absolute calibration. We also discuss the operation and the monitoring of the detector. Finally, we evaluate the detector performance and precision of shower reconstructions

We report a measurement of the proton-air cross section for particle production at the center-of-mass energy per nucleon of 57 TeV. This is derived from the distribution of the depths of shower maxima observed with the Pierre Auger Observatory: systematic uncertainties are studied in detail. Analyzing the tail of the distribution of the shower maxima, a proton-air cross section of $[505\pm 22(\mathrm{stat}{)}_{-36}^{+28}(\mathrm{syst})]\mathrm{mb}$ is found.