What can be learnt from UHECR anisotropies observations

Context. Various signals of anisotropy of the ultra-high-energy cosmic rays (UHECRs) have recently been reported, whether at large angular scales, with a dipole modulation in right ascension observed in the data of the Pierre Auger observatory ( Auger ), as discussed in the first paper accompanying the present one, or at intermediate angular scales, with flux excesses identified in specific directions by Auger and the Telescope Array (TA) Collaborations. Aims. We investigated the implications of the current data regarding these intermediate scale anisotropies, and examined to what extent they can be used to shed light on the origin of UHECRs, and constrain the astrophysical and/or physical parameters of the viable source scenarios. We also investigated what could be learnt from the study of the evolution of the various UHECR anisotropy signals, and discussed the expected benefit of an increased exposure of the UHECR sky using future observatories. Methods. We simulated realistic UHECR sky maps for a wide range of astrophysical scenarios satisfying the current observational constraints, with the assumption that the UHECR source distribution follows that of the galaxies in the Universe, also implementing possible biases towards specific classes of sources. In each case, several scenarios were explored with different UHECR source compositions and spectra, a range of source densities and different models of the Galactic magnetic field. We also implemented the Auger sky coverage, and explored various levels of statistics. For each scenario, we produced 300 independent datasets on which we applied similar analyses as those recently used by the Auger Collaboration, searching for flux excesses through either blind or targeted searches and quantifying correlations with predefined source catalogues through a likelihood analysis. Results. We find the following. First, with reasonable choices of the parameters, the investigated astrophysical scenarios can easily account for the significance of the anisotropies reported by Auger , even with large source densities. Second, the direction in which the maximum flux excess is found in the Auger data differs from the region where it is found in most of our simulated datasets, although an angular distance as large as that between the Auger direction and the direction expected from the simulated models at infinite statistics, of the order of ∼20°, occurs in ∼25% of the cases. Third, for datasets simulated with the same underlying astrophysical scenario, and thus the same actual UHECR sources, the significance with which the isotropy hypothesis is rejected through the Auger likelihood analysis can be largest either when ‘all galaxies’ or when only ‘starburst’ galaxies are used to model the signal, depending on which model is used to model the Galactic magnetic field and the resulting deflections. Fourth, the study of the energy evolution of the anisotropy patterns can be very instructive and provide new astrophysical insight about the origin of the UHECRs. Fifth, the direction in which the most significant flux excess is found in the Auger dataset above 8 EeV appears to essentially disappear in the dataset above 32 EeV, and, conversely, the maximum excess at high energy has a much reduced significance in the lower energy dataset. Sixth, both of these appear to be very uncommon in the simulated datasets, which could point to a failure of some generic assumption in the investigated astrophysical scenarios, such as the dominance of one type of source with essentially the same composition and spectrum in the observed UHECR flux above the ankle. Seventh, given the currently observed level of anisotropy signals, a meaningful measurement of their energy evolution, say from 10 EeV to the highest energies, will require a significant increase in statistics and a new generation of UHECR observatories.