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Giant radio halos are the most relevant examples of diffuse synchrotronemission from galaxy clusters. A number of these sources have very steepspectrum, with spectral index $\alpha \geq 1.5-1.6$ ($F(\nu) \propto\nu^{-\alpha}$), and are ideal targets to test current models for the origin ofthe relativistic particles. A2256 hosts the nearest radio halo with very steepspectrum, with $\alpha =1.61$, and a very large population of relativisticprotons in the cluster would be necessary to explain the halo as due tosynchrotron emission from secondary particles. In this case the 0.1-1 GeV$\gamma$--ray luminosity is expected 10-20 times larger than that of clustershosting radio halos with similar radio power at GHz frequencies but withspectra more typical of the presently observed halo population, $\alpha \sim1.2$. Under these assumptions incoming FERMI/GLAST observations are expected todetect A2256, provided that the magnetic field in the central cluster region is$\leq$10-15 $\mu$G. We show that this will allow for a prompt test of hadronicmodels for the origin of radio halos, and for complementary constraints on boththe cluster magnetic field and the physics of particle acceleration mechanisms.

Constraining relativistic protons and magnetic fields in galaxy clusters through radio and gamma-ray observations : the case of A2256