  We show that the hard X-ray (HXR) emission observed from several galaxy
clusters is naturally explained by a simple model, in which the nonthermal
emission is produced by inverse Compton scattering of cosmic microwave
background photons by electrons accelerated in cluster accretion shocks: The
dependence of HXR surface brightness on cluster temperature is consistent with
that predicted by the model, and the observed HXR luminosity is consistent with
the fraction of shock thermal energy deposited in relativistic electrons being
\lesssim 0.1. Alternative models, where the HXR emission is predicted to be
correlated with the cluster thermal emission, are disfavored by the data. The
implications of our predictions to future HXR observations (e.g. by NuStar,
Simbol-X) and to (space/ground based) gamma-ray observations (e.g. by Fermi,
HESS, MAGIC, VERITAS) are discussed.
