We aim at an unbiased census of the radio halo population in galaxy clusters and test whether current low number counts of radio halos have arisen from selection biases. We construct near-complete samples based on X-ray and Sunyaev-Zeldovich (SZ) effect cluster catalogues and search for diffuse, extended (Mpc-scale) emission near the cluster centers by analyzing data from the National Radio Astronomy Observatory Very Large Array Sky Survey. We remove compact sources using a matched filtering algorithm and model the diffuse emission using two independent methods. The relation between radio halo power at 1.4 GHz and mass observables is modelled using a power law, allowing for a dropout population of clusters hosting no radio halo emission. An extensive suite of simulations is used to check for biases in our methods. Our findings suggest that the fraction of targets hosting radio halos may have to be revised upwards for clusters selected using the SZ effect: while approximately 60 per cent of the X-ray selected targets are found to contain no extended radio emission, in agreement with previous findings, the corresponding fraction in the SZ selected samples is roughly 20 per cent. We propose a simple explanation for this selection difference based on the distinct time evolution of the SZ and X-ray observables during cluster mergers, and a bias towards relaxed, cool-core clusters in the X-ray selection.
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