Rise and fall of radio haloes in simulated merging galaxy clusters

We present the first high-resolution magnetohydrodynamic simulation of cosmic-ray electron re-acceleration by turbulence in cluster mergers. We use an idealized model for cluster mergers, combined with a numerical model for the injection, cooling and re-acceleration of cosmic-ray electrons, to investigate the evolution of cluster-scale radio emission in these objects. In line with theoretical expectations, we for the first time show in a simulation that re-acceleration of cosmic-ray electrons has the potential to reproduce key observables of radio haloes. In particular, we show that clusters evolve being radio loud or radio quiet, depending on their evolutionary stage during the merger. We thus recover the observed transient nature of radio haloes. In the simulation, the diffuse emission traces the complex interplay between the spatial distribution of turbulence injected by the halo infall and the spatial distribution of the seed electrons to re-accelerate. During the formation and evolution of the halo, the synchrotron emission spectra show the observed variety: from power laws with spectral index of 1-1.3 to curved and ultra-steep spectra with index >1.5.