The combined fit of the measured energy spectrum and distribution of depths of shower maximum of ultra-high-energy cosmic rays is known to constrain the parameters of astrophysical scenarios with homogeneous source distributions. Further measurements show that the cosmic-ray arrival directions agree better with the directions and fluxes of catalogs of starburst galaxies and active galactic nuclei than with isotropy.

Here, we present a novel combination of both analyses. For that, a three-dimensional universe model containing a nearby source population and a homogeneous background source distribution is built, and its parameters are adapted using a combined fit of the energy spectrum, depth of shower maximum distribution and energy-dependent arrival directions. The model takes into account a symmetric magnetic field blurring, source evolution and interactions during propagation.

We use simulated data, which resemble measurements of the Pierre Auger Observatory, to evaluate the method’s sensitivity. With this, we are able to verify that the source parameters as well as the fraction of events from the nearby source population and the size of the magnetic field blurring are determined correctly, and that the data is described by the fitted model including the catalog sources with their respective fluxes and three-dimensional positions. We demonstrate that by combining all three measurements we reach the sensitivity necessary to discriminate between the catalogs of starburst galaxies and active galactic nuclei.