Unified model for cosmic rays above $10^{17}$ eV and the diffuse gamma-ray and neutrino backgrounds

We investigate how the extragalactic proton component derived within the "escape model" can be explained by astrophysical sources. We consider as possible cosmic ray (CR) sources normal/starburst galaxies and radio-loud active galactic nuclei (AGN). We find that the contribution to the total extragalactic proton flux from normal and starburst galaxies is only subdominant and does not fit the spectral shape deduced in the escape model. In the case of radio-loud AGN, we show that the complete extragalactic proton spectrum can be explained by a single source population, BL Lac/FR I, for any of the potential acceleration sites in these sources. We calculate the diffuse neutrino and $\gamma$-ray fluxes produced by these CR protons interacting with gas inside their sources. For a spectral slope of CRs close to $\alpha=2.1-2.2$ as suggested by shock acceleration, we find that these UHECR sources contribute the dominant fraction of both the isotropic $\gamma$-ray background and of the extragalactic part of the astrophysical neutrino signal observed by IceCube.