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Description
The Pierre Auger Observatory has reported a dipolar anisotropy in the distribution of arrival directions of ultra-high-energy cosmic rays (UHECRs), with an amplitude that shows a linear dependence on energy. A further investigation of the dipole amplitude can provide important information about the origin of these particles, as it is particularly sensitive to variations in the number density of UHECR sources. In this work, we use these measurements to constrain the source number density in astrophysical models where nearby galaxies within $27\:\rm{Mpc}$, along with sources randomly distributed beyond this distance, are responsible for the particle emission. In particular, we consider three sets of local sources – active galactic nuclei (AGN) and/or starburst galaxies (SBG) – and three variations in source luminosity: uniform, proportional to the radio luminosity of these galaxies, and proportional to the gamma-ray luminosity. For our developed models, we determine the number density of background sources to lie between $2.20 \times 10^{-4}$ and $57.44 \times 10^{-4} \:\rm{Mpc^{-3}}$ within a $3\sigma$ confidence level. We also show how the case with AGN plus SBG as local sources and radio luminosity most strongly increases the upper limit of our findings, as well as the behavior of the dipole amplitude when varying the set of local sources, the luminosity, and the background source density.