Galaxy clusters are being assembled today in the most energetic phase of hierarchical structure formation which manifests itself in powerful shocks that contribute to a substantial energy density of cosmic rays ( CRs ) .
Hence , clusters are expected to be luminous gamma-ray emitters since they also act as energy reservoirs for additional CR sources , such as active galactic nuclei and supernova-driven galactic winds .
To detect the gamma-ray emission from CR interactions with the ambient cluster gas , we conducted the deepest to date observational campaign targeting a galaxy cluster at very high-energy gamma-rays and observed the Perseus cluster with the MAGIC Cherenkov telescopes for a total of \sim 85 h of effective observing time .
This campaign resulted in the detection of the central radio galaxy NGC 1275 at energies E > 100 GeV with a very steep energy spectrum .
Here , we restrict our analysis to energies E > 630 GeV and detect no significant gamma-ray excess .
This constrains the average CR-to-thermal pressure ratio to be \lesssim 1 –2 % , depending on assumptions and the model for CR emission .
Comparing these gamma-ray upper limits to models inferred from cosmological cluster simulations that include CRs constrains the maximum CR acceleration efficiency at structure formation shocks to be < 50 \% .
Alternatively , this may argue for non-negligible CR transport processes such as CR streaming and diffusion into the outer cluster regions .
Finally , we derive lower limits on the magnetic field distribution assuming that the Perseus radio mini-halo is generated by secondary electrons/positrons that are created in hadronic CR interactions : assuming a spectrum of E ^ { -2.2 } around TeV energies as implied by cluster simulations , we limit the central magnetic field to be > 4–9 \mu G , depending on the rate of decline of the magnetic field strength toward larger radii .
This range is well below field strengths inferred from Faraday rotation measurements in cool cores .
Hence , the hadronic model remains a plausible explanation of the Perseus radio mini-halo .