We present correlation results for the radio halo power in galaxy clusters with the integrated thermal Sunyaev-Zeldovich (SZ) effect signal, including new results obtained at sub-GHz frequencies. The radio data is compiled from several published works, and the SZ measurements are taken from the Planck ESZ cluster catalog. The tight correlation between the radio halo power and the SZ effect demonstrates a clear correspondence between the thermal and non-thermal electron populations in the intra-cluster medium, as already has been shown in X-ray based studies. The radio power varies roughly as the square of the global SZ signal, but when the SZ signal is scaled to within the radio halo radius the correlation becomes approximately linear, with reduced intrinsic scatter. We do not find any strong indication of a bi-modal division in the radio halo cluster population, as has been reported in the literature, which suggests that such duality could be an artifact of X-ray selection. We compare the SZ signal dependence of radio halos with simplified predictions from theoretical models, and discuss some implications and shortcomings of the present work.
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