The radio luminosity function of cluster radio halos

A significant fraction of galaxy clusters exhibits cluster-wide radio halos. We give a simple prediction of the local and higher redshift radio halo luminosity function (RHLF) on the basis of (i) an observed and a theoretical X-ray cluster luminosity function (XCLF) (ii) the observed radio-X-ray luminosity correlation (RXLC) of galaxy clusters with radio halos (iii) an assumed fraction of f(rh) approximate to 1/3 galaxy clusters to have radio halos as supported by observations. We then find 300-700 radio halos with S (1.4) (GHz) > 1 mJy, and 10(5) - 10(6) radio halos with S (1.4) (GHz) > 1 muJy should be visible on the sky. 14% of the S (1.4) (GHz) > 1 mJy and 56% of the S (1.4) (GHz) > 1 muJy halos are located at z > 0.3. Subsequently, we give more realistic predictions taking into account (iv) a refined estimate of the radio halo fraction as a function of redshift and cluster mass, and (v) a decrease in intrinsic radio halo luminosity with redshift due to increased inverse Compton electron energy losses on the Cosmic Microwave Background (CMB). We find that this reduces the radio halo counts from the simple prediction by only 30% totally, but the high redshift (z > 0.3) counts are more strongly reduced by 50-70%. These calculations show that the new generation of sensitive radio telescopes, including LOFAR, ATA, EVLA, SKA and the already-operating GMRT should be able to detect large numbers of radio halos and will provide unique information for studies of galaxy cluster merger rates and associated non-thermal processes.