Constraints on direct acceleration of UHECRs in astrophysical sources

A toy model of the population of numerous non-identical extragalactic sources of ultra-high-energy cosmic rays is presented. In the model, the acceleration of cosmic-ray particles is direct (not diffusive) and takes place in magnetospheres of supermassive black holes in galactic nuclei, the key parameter of acceleration being the black-hole mass. We use astrophysical data to describe the population of these cosmic-ray accelerators and confront the model with cosmic-ray and gamma-ray data