Radio haloes from simulations and hadronic models - II. The scaling relations of radio haloes

We use results from a constrained, cosmological magnetohydrodynamic (MHD) simulation of the Local Universe to predict radio haloes and their evolution for a volume-limited set of galaxy clusters and compare to current observations. The simulated magnetic field inside the clusters is a result of turbulent amplification within them, with the magnetic seed originating from starburst-driven, galactic outflows. We evaluate three models, where we choose different normalizations for the cosmic ray proton population within clusters. Similar to our previous analysis of the Coma cluster, the radial profile and the morphological properties of observed radio haloes cannot be reproduced, even with a radially increasing energy fraction within the cosmic ray proton population. Scaling relations between X-ray luminosity and radio power can be reproduced by all models; however all models fail in the prediction of clusters with no radio emission. Also the evolutionary tracks of our largest clusters in all models fail to reproduce the observed bi-modality in radio luminosity. This provides additional evidence that the framework of hadronic, secondary models is disfavoured to reproduce the large-scale diffuse radio emission of galaxy clusters. We also provide predictions for the unavoidable emission of γ-rays from the hadronic models for the full cluster set. None of such secondary models is yet excluded by the observed limits in γ-ray emission, emphasizing that large-scale diffuse radio emission is a powerful tool to constrain the amount of cosmic ray protons in galaxy clusters.