Common origin for radio relics and halos: galaxy cluster-wide, homogeneous cosmic-ray distribution, and evolving magnetic fields

Some galaxy clusters show diffuse radio emission in the form of peripheral relics (so far attributed to primary, shock-(re)accelerated electrons) or central halos. Analysing radio and X-ray data from the literature, we find new connections between halos and relics, such as a universal linear relation between their peak radio brightness and the gas column density. Our results indicate that halos, relics, and halo-relic bridges in a cluster, all arise from the same, homogeneous cosmic ray (CR) ion (CRI) distribution. We analytically derive the signature of synchrotron emission from secondary electrons and positrons (CREs) produced in hadronic CRI collisions, for an arbitrary magnetic field evolution. In our model, flat spectrum halos (both giant and minihalos) arise from steady-state magnetic fields, whereas relics and steep halos reflect recent or irregular magnetic growth. This naturally explains the properties of halos, relics, and the connections between them, without invoking particle (re)acceleration in weak shocks or turbulence. We find CRI energy densities in the range u_p~10^-[12.4,13.3]erg cm^-3, with a spectral index s_p=-2.20+-0.05, and identify a ~0.1 magnetic energy fraction in some halos and behind relics, as far as 2Mpc from the cluster's centre. The CRI homogeneity suggests strong CR diffusion, D(100GeV)>~10^32cm^2s^-1. The strong magnetisation imposes strict upper limits on >10GeV CRE (re)acceleration in weak shocks (efficiency <10^-4) and turbulence; indeed, each weak shock slightly lowers the energy fraction of flat CRs.