The radio-X-ray luminosity correlation of radio halos at low radio frequency. Application of the turbulent re-acceleration model

Aims: We show expectations on the radio-X-ray luminosity correlation of radio halos at 120 MHz. According to the turbulent re-acceleration scenario, we expect that low-frequency observations can 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 are also supposed to be less luminous than presently observed halos hosted in clusters with the same X-ray luminosity. Methods: With Monte Carlo procedures we show that these ultra-steep spectrum halos at 120 MHz cause 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. Results: We investigate the role of future low-frequency radio surveys and find that the upcoming LOFAR surveys will be able to test these expectations.