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.

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.

Ultrahigh energy cosmic ray air showers probe particle physics at energies beyond the reach of accelerators. Here we introduce a new method to test hadronic interaction models without relying on the absolute energy calibration, and apply it to events with primary energy 6–16 EeV ($E_{\mathrm{CM}}=110–170\mathrm{TeV}$), whose longitudinal development and lateral distribution were simultaneously measured by the Pierre Auger Observatory. The average hadronic shower is $1.33\pm 0.16$ ($1.61\pm 0.21$) times larger than predicted using the leading LHC-tuned models EPOS-LHC (QGSJetII-04), with a corresponding excess of muons.

We present the first hybrid measurement of the average muon number in air showers at ultrahigh energies, initiated by cosmic rays with zenith angles between 62° and 80°. The measurement is based on 174 hybrid events recorded simultaneously with the surface detector array and the fluorescence detector of the Pierre Auger Observatory. The muon number for each shower is derived by scaling a simulated reference profile of the lateral muon density distribution at the ground until it fits the data. A ${10}^{19}\mathrm{eV}$ shower with a zenith angle of 67°, which arrives at the surface detector array at an altitude of 1450 m above sea level, contains on average $(2.68\pm 0.04\pm 0.48(\text{sys}))\times {10}^7$ muons with energies larger than 0.3 GeV. The logarithmic gain $\mathrm{d}\ln N_{\mu }/\mathrm{d}\ln E$ of muons with increasing energy between $4\times {10}^{18}\mathrm{eV}$ and $5\times {10}^{19}\mathrm{eV}$ is measured to be $(1.029\pm 0.024\pm 0.030(\text{sys}))$.

Neutrinos in the cosmic ray flux with energies near 1 EeV and above are detectable with the Surface Detector array (SD) of the Pierre Auger Observatory. We report here on searches through Auger data from 1 January 2004 until 20 June 2013. No neutrino candidates were found, yielding a limit to the diffuse flux of ultrahigh energy neutrinos that challenges the Waxman-Bahcall bound predictions. Neutrino identification is attempted using the broad time structure of the signals expected in the SD stations, and is efficiently done for neutrinos of all flavors interacting in the atmosphere at large zenith angles, as well as for “Earth-skimming” neutrino interactions in the case of tau neutrinos. In this paper the searches for downward-going neutrinos in the zenith angle bins 60°–75° and 75°–90° as well as for upward-going neutrinos, are combined to give a single limit. The 90% C.L. single-flavor limit to the diffuse flux of ultrahigh energy neutrinos with an $E^{-2}$ spectrum in the energy range $1.0\times 10^{17}\mathrm{eV}–2.5\times 10^{19}\mathrm{eV}$ is $E_{\nu }^{2}d{N}_{\nu }/d{E}_{\nu }<6.4\times {10}^{-9}\mathrm{GeV}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$.