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Complementary views of galaxy clusters in the radio synchrotron, hard X‐ray inverse Compton and high‐energy γ‐ray regimes are critical in calibrating them as high‐precision cosmological probes. We present predictions for scaling relations between cluster mass and these non‐thermal observables. To this end, we use high‐resolution simulations of a sample of galaxy clusters spanning a mass range of almost two orders of magnitudes, and follow self‐consistent cosmic ray physics on top of the radiative hydrodynamics. We model relativistic electrons that are accelerated at cosmological structure formation shocks and those that are produced in hadronic interactions of cosmic rays with ambient gas protons. Calibrating the magnetic fields of our model with Faraday rotation measurements, the synchrotron emission of our relativistic electron populations matches the radio synchrotron luminosities and morphologies of observed giant radio haloes and minihaloes surprisingly well. Using the complete sample of the brightest X‐ray clusters observed by  ROSAT  in combination with our γ‐ray scaling relation, we predict  GLAST  to detect about ten clusters allowing for Eddington bias due to the scatter in the scaling relation. The expected brightest γ‐ray clusters are Ophiuchus, Fornax, Coma, A3627, Perseus and Centaurus. The high‐energy γ‐ray emission above 100 MeV is dominated by pion decays resulting from hadronic cosmic ray interactions. We provide an absolute lower flux limit for the γ‐ray emission of Coma in the hadronic model which can be made tighter for magnetic field values derived from rotation measurements to match the  GLAST  sensitivity, providing thus a unique test for the possible hadronic origin of radio haloes. Our predicted hard X‐ray emission, due to inverse Compton emission of shock accelerated and hadronically produced relativistic electrons, falls short of the detections in Coma and Perseus by a factor of 50. This casts doubts on inverse Compton interpretation and reinforces the known discrepancy of magnetic field estimates from Faraday rotation measurements and those obtained by combining synchrotron and inverse Compton emission.

Simulating cosmic rays in clusters of galaxies – III. Non‐thermal scaling relations and comparison to observations