The contribution to the extragalactic gamma-ray background by hadronic interactions of cosmic rays producing extreme-ultraviolet emission in clusters of galaxies

A substantial number of processes have been suggested as possible contributors to the extragalactic gamma-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 estimate this contribution. We first derive an improved estimate of the gamma-ray emission produced by this population of CRs in the Coma Cluster. We consider the impact of different strength shocks in the production of this flux. We then assume the that CRs in the Coma Cluster are prototypical 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 scales with the number density of the thermal plasma, and alternatively, the energy density of the CRs scales 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. Nonetheless, it is quite likely that future missions will be able to detect emission produced by this process in large clusters of galaxies. In particular, a signature of this process should be observable in the Coma Cluster with instruments on the GLAST satellite. We show that the spectral shape of this emission in the Coma Cluster may well allow a determination as to whether strong or mild shocks are primarily responsible for the production of CRs in this cluster.