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 } \simeq 10 ^ { - { [ 12.4 , 13.3 ] } } \mbox { erg } \mbox { cm } ^ { -3 } , with a spectral index s _ { p } = -2.20 \pm 0.05 , and identify an \epsilon _ { B } \sim 0.1 magnetic fraction in some halos and behind relics , as far as 2 \mbox { Mpc } from the cluster ’ s centre .
The CRI homogeneity suggests strong CR diffusion , D ( 100 \mbox { GeV } ) \gtrsim 10 ^ { 32 } \mbox { cm } ^ { 2 } \mbox { s } ^ { -1 } .
The strong magnetisation imposes strict upper limits on > 10 \mbox { GeV } CRE ( re ) acceleration in weak shocks ( efficiency \epsilon _ { e } < 10 ^ { -4 } ) and turbulence ; indeed , each weak shock slightly lowers the energy fraction of flat CRs .