Constraints on diffuse gamma-ray emission from structure formation processes in the Coma cluster

We analyze 5-year (63 months) data of the Large Area Telescope on board Fermi satellite from the Coma galaxy cluster in the energy range between 100 MeV and 100 GeV. The likelihood analyses are performed with several templates motivated by models predicting gamma-ray emission due to structure formation processes. We find no excess emission and derive the most stringent constraints to date on the Coma cluster above 100 MeV, and on the tested scenarios in general. The upper limits on the integral flux range from 10^-10 to 10^-9 cm^-2s^-1, and are stringent enough to challenge different scenarios. We find that the acceleration efficiency of cosmic ray protons and electrons at shocks must be below approximately 15% and 1%, respectively. Additionally, we argue that the proton acceleration efficiency should be lower than 5% in order to be consistent with radio data. This, however, relays on magnetic field estimates in the cluster. In particular, this implies that the contribution to the diffuse extragalactic gamma-ray background due to gamma-rays from structure formation processes in clusters of galaxies is negligible, below 1%. Finally, we discuss future detectability prospects for Astro-H, Fermi after 10-yr of operation, and the Cherenkov Telescope Array.