Radio haloes from simulations and hadronic models – I. The Coma cluster

We use the results from a constrained, cosmological magnetohydrodynamic simulation of the Local Universe to predict the radio halo and the γ-ray flux from the Coma cluster and compare it to current observations. The simulated magnetic field within the Coma cluster is the result of turbulent amplification of the magnetic field during the build-up of the cluster. The magnetic seed field originates from starburst driven, galactic outflows. The synchrotron emission is calculated assuming a hadronic model. We follow four approaches with different distributions for the cosmic ray proton population within galaxy clusters. The radial profile of the radio halo can only be reproduced with a radially increasing energy fraction within the cosmic ray proton population, reaching >100 per cent of the thermal-energy content at ≈1 Mpc, for example the edge of the radio-emitting region. Additionally, the spectral steepening of the observed radio halo in Coma cannot be reproduced, even when accounting for the negative flux from the thermal Sunyaev–Zeldovich effect at high frequencies. Therefore, the hadronic models are disfavoured from the present analysis. The emission of γ-rays expected from our simulated Coma is still below the current observational limits (by a factor of ～6) but would be detectable by FERMI observations in the near future.