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  1. Abstract A promising energy range to look for angular correlations between cosmic rays of extragalactic origin and their sources is at the highest energies, above a few tens of EeV (1 EeV ≡ 10 18 eV). Despite the flux of these particles being extremely low, the area of ∼3000 km 2 covered at the Pierre Auger Observatory, and the 17 yr data-taking period of the Phase 1 of its operations, have enabled us to measure the arrival directions of more than 2600 ultra-high-energy cosmic rays above 32 EeV. We publish this data set, the largest available at such energies from an integrated exposure of 122,000 km 2 sr yr, and search it for anisotropies over the 3.4 π steradians covered with the Observatory. Evidence for a deviation in excess of isotropy at intermediate angular scales, with ∼15° Gaussian spread or ∼25° top-hat radius, is obtained at the 4 σ significance level for cosmic-ray energies above ∼40 EeV. 
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  2. Abstract Ultra-high-energy photons with energies exceeding 10 17 eV offer a wealth of connections to different aspects of cosmic-ray astrophysics as well as to gamma-ray and neutrino astronomy. The recent observations of photons with energies in the 10 15 eV range further motivate searches for even higher-energy photons. In this paper, we present a search for photons with energies exceeding 2 × 10 17 eV using about 5.5 yr of hybrid data from the low-energy extensions of the Pierre Auger Observatory. The upper limits on the integral photon flux derived here are the most stringent ones to date in the energy region between 10 17 and 10 18 eV. 
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  3. Abstract Lorentz invariance violation (LIV) is often described by dispersion relations of the form E i 2  =  m i 2 + p i 2 +δ i,n E 2+n with delta different based on particle type i , with energy E , momentum p and rest mass m . Kinematics and energy thresholds of interactions are modified once the LIV terms become comparable to the squared masses of the particles involved. Thus, the strongest constraints on the LIV coefficients δ i,n tend to come from the highest energies. At sufficiently high energies, photons produced by cosmic ray interactions as they propagate through the Universe could be subluminal and unattenuated over cosmological distances. Cosmic ray interactions can also be modified and lead to detectable fingerprints in the energy spectrum and mass composition observed on Earth. The data collected at the Pierre Auger Observatory are therefore possibly sensitive to both the electromagnetic and hadronic sectors of LIV. In this article, we explore these two sectors by comparing the energy spectrum and the composition of cosmic rays and the upper limits on the photon flux from the Pierre Auger Observatory with simulations including LIV. Constraints on LIV parameters depend strongly on the mass composition of cosmic rays at the highest energies. For the electromagnetic sector, while no constraints can be obtained in the absence of protons beyond 10 19 eV, we obtain δ γ,0  > -10 -21 , δ γ,1  > -10 -40 eV -1 and δ γ,2  > -10 -58 eV -2 in the case of a subdominant proton component up to 10 20 eV. For the hadronic sector, we study the best description of the data as a function of LIV coefficients and we derive constraints in the hadronic sector such as δ had,0  < 10 -19 , δ had,1  < 10 -38 eV -1 and δ had,2  < 10 -57 eV -2 at 5σ CL. 
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  4. Abstract We present a measurement of the cosmic-ray spectrum above 100 PeV using the part of the surface detector of the Pierre Auger Observatory that has a spacing of 750 m. An inflection of the spectrum is observed, confirming the presence of the so-called second-knee feature. The spectrum is then combined with that of the 1500 m array to produce a single measurement of the flux, linking this spectral feature with the three additional breaks at the highest energies. The combined spectrum, with an energy scale set calorimetrically via fluorescence telescopes and using a single detector type, results in the most statistically and systematically precise measurement of spectral breaks yet obtained. These measurements are critical for furthering our understanding of the highest energy cosmic rays. 
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