A substantial number of processes have been suggested as possible contributors to the extragalactic ɤ-ray background (EGRB). Yet another contribution to this background will be emission produced in hadronic interactions of cosmic-ray protons with the cluster thermal gas; this class of cosmic rays (CRs) has been shown to be responsible for the EUV emission in the Coma Cluster of galaxies. In this paper we assume the CRs in the Coma Cluster is prototypic of all clusters and derive the contribution to the EGRB from all clusters over time. We examine two different possibilities for the scaling of the CR flux with cluster size: the number density of the CRs scale with the number density of the thermal plasma, and alternatively, the energy density of the CRs scale with the energy density of the plasma. We find that in all scenarios the EGRB produced by this process is sufficiently low that it will not be observable in comparison with other mechanisms that are likely to produce an EGRB.

We investigate the role of secondary electrons in galaxy clusters and in ultra-luminous infrared galaxies (ULIGs). The radio emission in galaxy clusters and ULIGs is believed to be produced by the synchrotron radiation of relativistic electrons. Nonetheless, the sources of these relativistic electrons are still unclear. Relativistic secondary electrons can be produced from the hadronic interactions of cosmic-ray nuclei with the intra-cluster media (ICM) of galaxy clusters and the dense molecular clouds of ULIGs. We estimate the contribution of the secondary electrons in galaxy clusters and ULIGs by comparing observational results with theoretical calculations for the radio emission in these sources. We find that the radio halos of galaxy clusters can not be produced from the secondary electrons; on the other hand, at least for some ULIGs, the radio emission can be dominated by the synchrotron emission of the secondary electrons.