Study of Flat-spectrum Radio Quasars and BL Lacertae Objects as Sources of Diffusive Ultrahigh-energy Cosmic Rays

Abstract We examine whether flat-spectrum radio quasars (FSRQs) and BL Lac objects can act as plausible astrophysical sources of diffuse ultrahigh-energy cosmic rays (UHECRs). Using realistic luminosity-dependent density evolution functions derived from observed γ -ray luminosity functions for FSRQs and BL Lac objects, we calculate the redshift evolution of the cosmic-ray source population through integrated luminosity functions. The diffuse UHECR flux from these sources is modelled by propagating nuclei through extragalactic space, including energy losses from interactions with cosmic photon backgrounds. The resulting UHECR spectra are compared with observational data from the Pierre Auger Observatory and the Telescope Array, with fluxes normalized at reference energies. We also construct illustrative full sky maps of the integral UHECR flux from 10 to 100 EeV using the HEALPix framework, assuming a uniform distribution of synthetic sources and including energy-dependent magnetic diffusion. Our results show that although both FSRQs and BL Lac objects can reproduce the observed UHECR flux, the FSRQ scenario is disfavoured by anisotropy and an inconsistent source density, while BL Lac objects remain consistent with observations.