On the Physics of Radio Halos in Galaxy Clusters: Scaling Relations and
  Luminosity Functions
  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-Zel'dovich 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.
