Unveiling radio halos in galaxy clusters in the LOFAR era

Aims. Giant radio halos are mega-parsec scale synchrotron sources detected in a 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. Statistics of their properties can be used to discriminate among various models for their origin. Therefore, theoretical predictions of the occurrence of radio halos are important as several new radio telescopes are about to begin to survey the sky at low frequencies with unprecedented sensitivity. Methods. We carry out Monte Carlo simulations to model the formation and evolution of radio halos in a cosmological framework. In the context of the turbulent re-acceleration model, we extend previous work on the statistical properties of radio halos. Results. We first compute the fraction of galaxy clusters that show radio halos and derive the luminosity function of the radio halos. We then derive differential and integrated number count distributions of radio halos at low radio frequencies to explore the potential of the upcoming LOFAR surveys. By restricting ourselves to clusters at redshifts < 0.6, we find that the planned LOFAR all-sky survey at 120 MHz is expected to detect about 350 giant radio halos. About half of these halos have spectral indices greater than 1.9 and brighten substantially at lower frequencies. If detected they will enable us to confirm that turbulence accelerates the emitting particles. We also propose that commissioning surveys, such as MS(3), have the potential to detect about 60 radio halos in clusters of the ROSAT brightest cluster sample and its extension (eBCS). These surveys will allow us to constrain how the rate of formation of radio halos in these clusters depends on cluster mass.