Spherical harmonic moments are well-suited for capturing anisotropy at any scale in the flux of cosmic rays. An unambiguous measurement of the full set of spherical harmonic coefficients requires full-sky coverage. This can be achieved by combining data from observatories located in both the northern and southern hemispheres. To this end, a joint analysis using data recorded at the Telescope Array and the Pierre Auger Observatory above 10 19 eV is presented in this work. The resulting multipolar expansion of the flux of cosmic rays allows us to perform a series of anisotropy searches, and in particular to report on the angular power spectrum of cosmic rays above 10 19 eV. No significant deviation from isotropic expectations is found throughout the analyses performed. Upper limits on the amplitudes of the dipole and quadrupole moments are derived as a function of the direction in the sky, varying between 7% and 13% for the dipole and between 7% and 10% for a symmetric quadrupole.

A search for ultra-high energy photons with energies above 1 EeV is performed using nine years of data collected by the Pierre Auger Observatory in hybrid operation mode. An unprecedented separation power between photon and hadron primaries is achieved by combining measurements of the longitudinal air-shower development with the particle content at ground measured by the fluorescence and surface detectors, respectively. Only three photon candidates at energies 1 − 2 EeV are found, which is compatible with the expected hadroninduced background. Upper limits on the integral flux of ultra-high energy photons of 0.027, 0.009, 0.008, 0.008 and 0.007 km −2 sr −1 yr −1 are derived at 95% C.L. for energy thresholds of 1, 2, 3, 5 and 10 EeV. These limits bound the fractions of photons in the all-particle integral flux below 0.1%, 0.15%, 0.33%, 0.85% and 2.7%. For the first time the photon fraction at EeV energies is constrained at the sub-percent level. The improved limits are below the flux of diffuse photons predicted by some astrophysical scenarios for cosmogenic photon production. The new results rule-out the early top-down models − in which ultra-high energy cosmic rays are produced by, e.g., the decay of super-massive particles − and challenge the most recent super-heavy dark matter models.

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 ≡ 1018 eV). Despite the flux of these particles being extremely low, the area of ∼3000 km2 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 km2 sr yr, and search it for anisotropies over the 3.4π 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 4σ significance level for cosmic-ray energies above ∼40 EeV.

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