On the Physics of Radio Halos in Galaxy Clusters: Scaling Relations and Luminosity Functions
The underlying physics of giant radio halos and mini halos in galaxy clusters is still an open question, which becomes more pressing with the growing number of detections. In this paper, we explore the possibility that radio-emitting electrons are generated in hadronic cosmic ray (CR) proton interactions with ambient thermal protons of the intra-cluster medium. Our CR model derives from cosmological hydrodynamical simulations of cluster formation and additionally accounts for CR transport in the form of CR streaming and diffusion. This opens the possibility of changing the radio halo luminosity by more than an order of magnitude on a dynamical time scale. We build a mock galaxy cluster catalog from the large MultiDark N-body LCDM simulation by adopting a phenomenological gas density model for each cluster based on X-ray measurements that matches Sunyaev-Zel'dovich (SZ) and X-ray scaling relations and luminosity function. Using magnetic field strength estimates from Faraday rotation measure studies, our model successfully reproduces the observed surface brightness profiles of giant radio halos (Coma, A2163) as well as radio mini-halos (Perseus, Ophiuchus), while obeying upper limits on the gamma-ray emission in these clusters. Our model is also able to 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 the SZ flux Y; thereby suggesting a physical solution to this apparent contradiction. For a plausible fraction of 10% radio-loud clusters, our model matches the NVSS radio-halo luminosity function. Constructing an analytical radio-halo luminosity function, we demonstrate the unique prospects for low-frequency radio surveys (such as the LOFAR Tier 1 survey) to detect ~3500 radio halos back to redshift two and to probe the underlying physics of radio halos. [abridged]