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ABSTRACT  Large‐scale diffuse radio emission is observed in some clusters of galaxies. There is ample of evidence that the emission has its origin in synchrotron losses of relativistic electrons that have been accelerated in cluster mergers. In a cosmological simulation, we estimate the radio emission of structure formation shocks as follows: introducing a novel approach to identify strong shock fronts in an smoothed particle hydrodynamics (SPH) simulation, we determine the Mach number as well as the downstream density and temperature in the MareNostrum Universe simulation which has  2 × 1024 3   particles in a  500  h  −1  Mpc  box. Then, we estimate the radio emission using the formalism derived in Hoeft &amp; Brüggen to produce artificial radio maps of massive clusters and to derive a luminosity function of diffuse radio sources. Several of our clusters show radio objects with similar morphology to observed large‐scale radio relics, whereas about half of the clusters show only very little radio emission. In agreement with observational findings, the maximum diffuse radio emission of our clusters depends strongly on their X‐ray temperature. We find that the so‐called accretion shocks cause only very little radio emission. We conclude that a moderate efficiency of shock acceleration, namely  ξ e = 0.005 , and moderate magnetic fields in the region of the relics, namely  0.07–0.8 μG  are sufficient to reproduce the number density and luminosity of radio relics.

Diffuse radio emission from clusters in the MareNostrum Universe simulation