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Using Radio Halos and Minihalos to Measure the Distributions of Magnetic Fields and Cosmic-Rays in Galaxy Clusters

Some galaxy clusters show diffuse radio emission in the form of giant halos (GHs) on Mpc scales or minihalos (MHs) on smaller scales. Comparing VLA and XMM 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+-0.2}*(n/10^-2cm^-3)^2*(T/T_0)^{0.2+-0.5} erg/s/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 >3 muG 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. RXCJ2003.5-2323 and A2255) or a distinct radial break. We thus measure a magnetic field B=3 muG at a radius r~110 kpc in A2029 and r~50 kpc in Perseus. The spectrum of secondaries, produced from hadronic collisions of ~20 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~10(nu/700 MHz) muG, 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 <-2.7 and energy fraction xi_p~10^{-3.6+-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.