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.

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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 review open questions and prospects for progress in ultrahigh-energy cosmic ray (UHECR) research, based on a series of discussions that took place during the “The High-Energy Universe: Gamma-Ray, Neutrino, and Cosmic-ray Astronomy” MIAPP workshop in 2018. Specifically, we overview open questions on the origin of the bulk of UHECRs, the UHECR mass composition, the origin of the end of the cosmic-ray spectrum, the transition from Galactic to extragalactic cosmic rays, the effect of magnetic fields on the trajectories of UHECRs, anisotropy expectations for specific astrophysical scenarios, hadronic interactions, and prospects for discovering neutral particles as well as new physics at ultrahigh energies. We also briefly overview upcoming and proposed UHECR experiments and discuss their projected science reach.

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 $(1.029\pm 0.024\pm 0.030(\text{sys}))$.