The underlying physics of giant and mini radio halos in galaxy clusters is still an open question. We find that mini halos (such as in Perseus and Ophiuchus) can be explained by radio-emitting electrons that are generated in hadronic cosmic ray (CR) interactions with protons of the intracluster medium. By contrast, the hadronic model either fails to explain the extended emission of giant radio halos (as in Coma at low frequencies) or would require a flat CR profile, which can be realized through outward streaming and diffusion of CRs (in Coma and A2163 at 1.4 GHz). We suggest that a second, leptonic component could be responsible for the missing flux in the outer parts of giant halos within a new hybrid scenario and we describe its possible observational consequences. To study the hadronic emission component of the radio halo population statistically, we use a cosmological mock galaxy cluster catalog built from the MultiDark simulation. Because of the properties of CR streaming and the different scalings of the X-ray luminosity (L_X) and the Sunyaev-Zeldovich flux (Y) with gas density, our model can simultaneously reproduce the observed bimodality of radio-loud and radio-quiet clusters at the same L_X as well as the unimodal distribution of radio-halo luminosity versus Y; thereby suggesting a physical solution to this apparent contradiction. We predict radio halo emission down to the mass scale of galaxy groups, which highlights the unique prospects for low-frequency radio surveys (such as the LOFAR Tier 1 survey) to increase the number of detected radio halos by at least an order of magnitude.
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