On the radio -- X-ray luminosity correlation of radio halos at low radio
  frequency - Application of the turbulent re-acceleration model
  In this paper we show expectations on the radio--X-ray luminosity correlation
of radio halos at 120 MHz. According to the "turbulent re-acceleration
scenario", low frequency observations are expected to detect a new population
of radio halos that, due to their ultra-steep spectra, are missed by present
observations at ~ GHz frequencies. These radio halos should also be less
luminous than presently observed halos hosted in clusters with the same X-ray
luminosity. Making use of Monte Carlo procedures, we show that the presence of
these ultra-steep spectrum halos at 120 MHz causes a steepening and a
broadening of the correlation between the synchrotron power and the cluster
X-ray luminosity with respect to that observed at 1.4 GHz. We investigate the
role of future low frequency radio surveys, and find that the upcoming LOFAR
surveys will be able to test these expectations.
