Radio halos in future surveys in the radio continuum

Aims. Giant radio halos are mega-parsec scale synchrotron source sd etected in as ignif icant fraction of massive and merging galaxy clusters. Radio halos provide one of the most important pieces of evidence of non-thermal components in large-scale structure. Their statistical properties can be used to discriminate among various models for their origin. Therefore, theoretical predictions of the occurrence of radio halos are important as new radio telescopes are about to begin to survey the sky at low and high frequencies with unprecedented sensitivity. Methods. We carry out Monte Carlo simulations to model the formation and evolution of radio halos in a cosmological framework and extend previous calculations based on the hypothesis of turbulent-acceleration origin of radio halos. We adopt a phenomenological approach to model the population of radio halos by assuming that halos are either generated in turbulent merging clusters, or are purely hadronic halos generated in more relaxed clusters, “o! -state” halos. Results. The models predict that the luminosity function of radio halos at high radio luminosities is dominated by the contribution of radio halos generated in turbulent clusters. The generation of these halos becomes less e" cient in less massive systems causing afl attening of the luminosity function at lower radio luminosities, as also pointed out in previous studies. However, we find that potentially this can be more than compensated for by the intervening contribution of “o! -state” radio halos that dominate at lower radio luminosities. We derive the expected number of halos t oe xplore the potential of the EMU+WODAN surveys that will be carried out with ASKAP and Aperitif, respectively, in the near future. By restricting to clusters at redshifts " 0.6, we show that the planned EMU+WODAN surveys at 1.4 GHz have the potential to detect up to about 200 giant radio halos, increasing by one order of magnitude the number of currently known halos. A fraction of these halos will be “o! -state” halos that should be found at flux level f1.4 " 10 mJy, presently accessible only to deep pointed observations. We also explore the synergy between surveys at di! erent radio frequencies, the Tier 1 LOFAR survey at 150 MHz and the EMU+WODAN surveys at 1.4 GHz. We predict a larger number of radio halos in the LOFAR survey due to the high LOFAR sensitivity, but also due to the existence of halos with very steep spectrum that glow up preferentially at lower frequencies. These halos ar eo nly predicted in the framework of turbulent re-acceleration models and should not have counterparts in the EMU+WODAN surveys, thus the combination of the two surveys will test models for the origin of giant radio halos.