Constraining the Baryon Loading Factor of AGN Jets: Implication from the ?-Ray Emission of the Coma Cluster

High-energy cosmic rays (CRs) can be accelerated in the relativistic jets of Active Galactic Nuclei (AGNs) powered by supermassive black holes. The baryon loading efficiency onto CR baryons from accreting holes is poorly constrained observations so far. In this paper, we suggest that $\gamma$-ray emission galaxy clusters used to study factor AGN jets, since CRs injected are completely confined and sufficiently interact with intra-cluster medium via hadronic process, producing diffuse $\gamma$-rays. We propagation calculate radial distribution gamma-rays cluster different injection rates AGNs. By comparison flux upper limits Coma measured $Fermi$-LAT VERITAS, find limit average {(defined as which gravitational energy converted into particles)} $\eta_{p, \mathrm{grav}} < 0.1$. much lower than required account for neutrino conventional blazar models.