2009A&A...508..599B

Giant radio halos are the most relevant examples of diffuse synchrotron emission from galaxy clusters. A number of these sources have very steep spectra, of spectral index α≥1.5-1.6 (F(ν)∝ν^–α), and are ideal targets for testing current models of the origin of the relativistic particles. A2256 hosts the nearest radio halo with a very steep spectrum, of α=1.61, and a very large population of relativistic protons in the cluster would be necessary if the halo were produced by synchrotron emission from secondary particles. In this case, the 0.1-1GeV γ-ray luminosity is expected to be 10-20 times higher than that of clusters hosting radio halos of similar radio power at GHz frequencies but with spectra more typical of the presently observed halo population, α∼1.2. Based on these assumptions, future FERMI/GLAST observations are expected to detect A2256, provided that the magnetic field in the central cluster region is ≤10-15µG. We show that this will provide a prompt test of hadronic models for the origin of radio halos, and complementary constraints on both the cluster magnetic field and the physics of particle acceleration mechanisms.