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

Aims. Galaxy clusters are key targets in the search for ultra high energy particle accelerators. The Coma cluster represents one of the best candidates for such a search owing to its high mass, proximity, and the established non-thermal radio emission centred on the cluster core. Methods. The HESS (High Energy Stereoscopic System) telescopes observed Coma for similar to 8 h in a search for gamma-ray emission at energies > 1 TeV. The large 3.5 degrees FWHM field of view of HESS is ideal for viewing a range of targets at various sizes including the Coma cluster core, the radio-relic (1253+275) and merger/infall (NGC 4839) regions to the southwest, and features greater than 1 degrees away. Results. No evidence for point-like nor extended TeV gamma-ray emission was found and upper limits to the TeV flux F(E) for E > 1, > 5, and > 10 TeV were set for the Coma core and other regions. Converting these limits to an energy flux (EF)-F-2(E) the lowest or most constraining is the E > 5 TeV upper limit for the Coma core (0.2 degrees radius) at similar to 8% Crab flux units or similar to 10(-13) ph cm(-2) s(-1). Conclusions. The upper limits for the Coma core were compared with a prediction for the gamma-ray emission 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 alpha E-2.1 and spatial distribution following the thermal gas in the cluster, is found to be similar to 0.2 times the thermal energy, or similar to 10(62) erg. The E > 5 TeV gamma-ray threshold in this case corresponds to cosmic-ray proton energies greater than or similar to 50 TeV. Our upper limits rule out the most optimistic theoretical models for gamma ray emission 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.