Radio haloes and relics from extended cosmic-ray ion distributions with strong diffusion in galaxy clusters

A joint hadronic model is shown to quantitatively explain the observations of diffuse radio emission from galaxy clusters in the form of minihaloes, giant haloes, relics, and their hybrid, transitional stages. Cosmic-ray diffusion of order D ~ 10^31-32 cm² s^-1, inferred independently from relic energies, the spatial variability of giant-halo spectra, and the spectral evolution of relics, reproduces the observed spatio-spectral distributions, explains the recently discovered mega-haloes as enhanced peripheral magnetization, and quenches electron (re)acceleration by weak shocks or turbulence. For instance, the hard-to-soft evolution along secondary-electron diffusion explains both the soft spectra in most halo peripheries and relic downstreams, and the hard spectra in most halo centres and relic edges, where the photon index can reach α ≃ -0.5 regardless of the Mach number $\mathcal {M}$ of the coincident shock. Such spatio-spectral modelling, recent γ-ray observations, and additional accumulated evidence are thus shown to support a 2010 claim that the seamless transitions among minihaloes, giant haloes, and relics, their similar energetics, integrated spectra, and delineating discontinuities, the inconsistent $\mathcal {M}$ inferred from radio versus X-rays in leptonic models, and additional observations, all indicate that these diffuse radio phenomena are manifestations of the same cosmic-ray ion population, with no need to invoke less natural alternatives.