Diffuse $\gamma$-ray emission from misaligned active galactic nuclei

We calculate the diffuse $\gamma$-ray emission due to the population of misaligned AGN (MAGN) unresolved by the Large Area Telescope (LAT) on the {\it Fermi} Gamma-ray Space Telescope ({\it Fermi}). A correlation between the $\gamma$-ray luminosity and the radio-core luminosity is established and demonstrated to be physical by statistical tests, as well as compatible with upper limits based on {\it Fermi}-LAT data for a large sample of radio-loud MAGN. We constrain the derived $\gamma$-ray luminosity function by means of the source count distribution of the MAGN detected by the {\it Fermi}-LAT. We finally estimate the diffuse $\gamma$-ray flux due to the whole MAGN population which ranges from 10% up to nearly the entire measured Isotropic Gamma-Ray Background (IGRB). We evaluate also the room left to galactic DM at high latitudes ($>10^\circ$), by taking into account the results on the MAGN together with the other significant galactic and extragalactic $\gamma$-rays emitting sources.