Simulating cosmic rays in clusters of galaxies – II. A unified scheme for radio haloes and relics with predictions of the γ-ray emission

The thermal plasma of galaxy clusters lost most of its information on how structure formation proceeded as a result of dissipative processes. In contrast, non-equilibrium distributions of cosmic rays (CRs) preserve the information about their injection and transport processes and provide thus a unique window of current and past structure formation processes. This information can be unveiled by observations of non-thermal radiative processes, including radio synchrotron, hard X-ray and -ray emission. To explore this, we use high-resolution simulations of a sample of galaxy clusters spanning a mass range of about two orders of magnitudes, and follow self-consistent CR 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 CRs with ambient gas protons. We find that the CR proton pressure traces the time integrated non-equilibrium activities of clusters and is modulated by the recent dynamical activities. In contrast, the pressure of primary shock-accelerated CR electrons resembles current accretion and merging shock waves that break at the shallow cluster potential in the virial regions. The resulting synchrotron emission is predicted to be polarized and has an inhomogeneous and aspherical spatial distribution which matches the properties of observed radio relics. We propose a unified scheme for the generation of giant radio haloes as well as radio minihaloes that naturally arises from our simulated synchrotron surface brightness maps and emission profiles. Giant radio haloes are dominated in the centre by secondary synchrotron emission with a transition to the radio synchrotron radiation emitted from primary, shock-accelerated electrons in the cluster periphery. This model is able to explain the regular structure of radio haloes by the dominant contribution of hadronically produced electrons. At the same time, it is able to account for the observed correlation of mergers with radio haloes, the larger peripheral variation of the spectral index, and the large scatter in the scaling relation between cluster mass and synchrotron emission. Future low-frequency radio telescopes (LOFAR, GMRT, MWA, LWA) are expected to probe the accretion shock regions of clusters and the warm-hot intergalactic medium, depending on the adopted model for the magnetic fields. The hadronic origin of radio haloes can be scrutinized by the detection of pion-decay-induced -rays following hadronic CR interactions. The high-energy -ray emission depends only weakly on whether radiative or non-radiative gas physics is simulated due to the self-regulated nature of the CR cooling processes. Our models predict a -ray emission level that should be observable with the GLAST satellite.