The IceCube Collaboration has previously discovered a high-energy astrophysical neutrino flux using neutrino events with interaction vertices contained within the instrumented volume of the IceCube detector. We present a complementary measurement using charged current muon neutrino events where the interaction vertex can be outside this volume. As a consequence of the large muon range the effective area is significantly larger but the field of view is restricted to the Northern Hemisphere. IceCube data from 2009 through 2015 have been analyzed using a likelihood approach based on the reconstructed muon energy and zenith angle. At the highest neutrino energies between and a significant astrophysical contribution is observed, excluding a purely atmospheric origin of these events at significance. The data are well described by an isotropic, unbroken power-law flux with a normalization at neutrino energy of and a hard spectral index of . The observed spectrum is harder in comparison to previous IceCube analyses with lower energy thresholds which may indicate a break in the astrophysical neutrino spectrum of unknown origin. The highest-energy event observed has a reconstructed muon energy of which implies a probability of less than for this event to be of atmospheric origin. Analyzing the arrival directions of all events with reconstructed muon energies above no correlation with known γ-ray sources was found. Using the high statistics of atmospheric neutrinos we report the current best constraints on a prompt atmospheric muon neutrino flux originating from charmed meson decays which is below 1.06 in units of the flux normalization of the model in Enberg et al.

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.