  (Abridged) High-E electrons produce Hard X-Ray (HXR) emission in galaxy
clusters by via Inverse Compton Scattering (ICS) of CMB photons. We derive the
ICS HXR emission of Ophiuchus under various scenarios: primary cosmic ray
model, secondary cosmic rays model and neutralino DM annihilation scenario. We
further discuss the predictions of the Warming Ray model for the cluster
atmosphere. Under the assumption to fit the observed HXR emission, we find that
the high-E electrons induce various consequences on the cluster atmosphere: i)
primary electrons can be marginally consistent with the data provided that
their spectrum is cutoff at E~30(90) MeV for spectral index of 3.5 (4.4); ii)
secondary electron models from pp collisions are inconsistent with gamma-ray
limits, cosmic ray protons produce too much heating of the IC gas and their
pressure at the cluster center largely exceeds the thermal one; iii) secondary
electron models from DM annihilation are inconsistent with gamma-ray and radio
limits and electrons produce too much heating of the IC gas at the cluster
center, unless the neutralino annihilation cross section is much lower than the
proposed value. We conclude that ICS by secondary electrons from both
neutralino DM annihilation and pp collisions cannot be the mechanism
responsible for the HXR excess emission; primary electrons are still a
marginally viable solution provided that their spectrum has a low-energy cutoff
at E~30-90 MeV. The WR model offers, so far, the best description of the
cluster in terms of temperature distribution, heating, pressure and spectral
energy distribution. Fermi observations of Ophiuchus will set further
constraints to this model.
