Constraints on the multi-TeV particle population in the Coma galaxy cluster with HESS observations

The H.E.S.S. ( High Energy Stereoscopic System) telescopes observed Comafor ~8hr in a search for gamma-rayemission at energies >1TeV. The large 3.5deg FWHM field of view of H.E.S.S. is ideal for viewing a range of targets at various sizes including the Coma clustercore, the radio-relic(1253+275) and merger/ infall(NGC 4839) regions to the southwest, and features greater than deg away. No evidence for point-like nor extended TeV gamma-rayemission was found and upper limits to the TeV flux F(E) for E>1, >5, and >10TeV were set for the Comacore and other regions. Converting these limits to an energy flux E^2F(E) the lowest or most constraining is the E>5TeV upper limit for the Comacore (0.2deg radius) at ~8Crab flux units or ~10^{-13}ph cm^{-2} s^{-1}. The upper limits for the Comacore were compared with a prediction for the gamma-rayemission from proton--proton interactions, the level of which ultimately scales with the mass of the Coma cluster. A direct constraint using our most stringent limit for E>5 TeV, on the total energy content in non-thermal protons with injection energy spectrum proportional to E^{-2.1} and spatial distribution following the thermal gas in the cluster, is found to be ~0.2 times the thermal energy, or ~10^{62}erg. The E>5 TeV gamma-raythreshold in this case corresponds to cosmic-ray proton energies >50TeV. Our upper limits rule out the most optimistic theoretical models for gamma rayemission from clusters and complement radio observations which constrain the cosmic ray content in clusters at significantly lower proton energies, subject to assumptions on the magnetic field strength.