Some galaxy clusters show diffuse radio emission in the form of giant halos ( GHs ) on Mpc scales or minihalos ( MHs ) on smaller scales .
Comparing Very Large Array and XMM-Newton radial profiles of several such clusters , we find a universal linear correlation between radio and X-ray surface brightness , valid in both types of halos .
It implies a halo central emissivity \nu j _ { \nu } = 10 ^ { -31.4 \pm 0.2 } ( n / 10 ^ { -2 } \mbox { cm } ^ { -3 } ) ^ { 2 } ( T / T _ { 0 } ) ^ { 0.2 \pm 0 % .5 } \mbox { erg } \mbox { s } ^ { -1 } \mbox { cm } ^ { -3 } , where T and T _ { 0 } are the local and central temperatures , and n is the electron number density .
We argue that the tight correlation and the scaling of j _ { \nu } , combined with morphological and spectral evidence , indicate that both GHs and MHs arise from secondary electrons and positrons , produced in cosmic-ray ion ( CRI ) collisions with a strongly magnetized , B \gtrsim 3 \mbox { $ \mu$G } intracluster gas .
When the magnetic energy density drops below that of the microwave background , the radio emission weakens considerably , producing halos with a clumpy morphology ( e.g. , RXC J2003.5–-2323 and A2255 ) or a distinct radial break .
We thus measure a magnetic field B = 3 \mbox { $ \mu$G } at a radius r \simeq 110 \mbox { kpc } in A2029 and r \simeq 50 \mbox { kpc } in Perseus .
The spectrum of secondaries , produced from hadronic collisions of \sim 20 \mbox { GeV } CRIs , reflects the energy dependence of the collision cross section .
We use the observed spectra of halos , in particular where they steepen with increasing radius or frequency , to ( i ) measure B \simeq 10 ( \nu / 700 \mbox { MHz } ) \mbox { $ \mu$G } , with \nu the spectral break frequency ; ( ii ) identify a correlation between the average spectrum and the central magnetic field ; and ( iii ) infer a CRI spectral index s \lesssim - 2.7 and energy fraction \xi _ { p } \sim 10 ^ { -3.6 \pm 0.2 } at particle energies above 10 GeV .
Our results favor a model where CRIs diffuse away from their sources ( which are probably supernovae , according to a preliminary correlation with star formation ) , whereas the magnetic fields are generated by mergers in GHs and by core sloshing in MHs .