ИСТИНА

While the precise origins of high-energy cosmic rays remain elusive, various constraints can be placed on their possible sources. One such approach involves the Hillas diagram, a graphical representation that delineates the range of geometric sizes and magnetic fields of plausible astrophysical accelerators. Previous iterations of this diagram considered geometric criteria and radiation losses to establish these boundaries. In this study, we expand on the Hillas diagram for protons, incorporating the energy losses associated with photohadronic and photopair interactions. This updated diagram links the allowable regions to the source’s electromagnetic luminosity, resulting in the most stringent constraints for compact, bright sources like the central regions of active galactic nuclei.