Unveiling radio halos in galaxy clusters in the LOFAR era
  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 for 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. In this paper we carry out Monte Carlo simulations to model the
formation and evolution of radio halos in a cosmological framework. We extend
previous works on the statistical properties of radio halos in the context of
the turbulent re-acceleration model. First we compute the fraction of galaxy
clusters that show radio halos and derive the luminosity function of radio
halos. Then, we derive differential and integrated number count distributions
of radio halos at low radio frequencies with the main goal to explore the
potential of the upcoming LOFAR surveys. By restricting to the case of 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 larger than 1.9 and substantially brighten at lower
frequencies. If detected they will allow for a confirmation that turbulence
accelerates the emitting particles. We expect that also commissioning surveys,
such as MSSS, 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.
