2002ApJ...577..658O

We develop a magnetoturbulent model for the cosmic-ray (CR) electrons seen in the radio halo clusters of galaxies. Steady-state momentum distribution functions of the CR electrons are calculated for given spectra of the turbulent Alfvén waves. The radio spectrum produced by the obtained CR electron distribution is compared to the observed radio spectrum of the Coma radio halo. We find that the observed radio spectrum of the Coma Cluster is well reproduced when the spectral index of the turbulent Alfvén waves is ∼2.8. The obtained energy spectrum of the turbulent Alfvén waves is steeper than that expected from the turbulence theory, suggesting back-reaction of the particle acceleration. The fitting procedure constraints the amplitude of the turbulent Alfvén waves as well as the spectral index. Then we estimate the dissipation of the turbulent Alfvén waves, which is found to be less than the cooling rate by X-ray radiation. We suggest that the turbulence that is sufficient for particle acceleration is developed in the clusters containing the radio halo. It is most likely that cluster mergers create the turbulence and seed relativistic electrons.