On the inverse Compton scattering interpretation of the hard X-ray excesses in galaxy clusters: the case of Ophiuchus

Context. Populations of high energy electrons can produce hard X-ray (HXR) emission in galaxy clusters by up-scattering CMB photons via the inverse Compton scattering (ICS) mechanism. However, this scenario has various astrophysical consequences. Aims. We discuss here the consequences of the presence of a population of high energy particles for the multi-frequency emissivity of the same clusters and the structure of their atmospheres. Methods. We derive predictions for the ICS HXR emission in the specific case of the Ophiuchus cluster (for which an interesting combination of observational limits and theoretical scenarios have been presented) for three main scenarios producing high-E electrons: 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 HXR emission observed in Ophiuchus, we explore the consequences that these electron populations induce on the cluster atmosphere. Results. We find that: i) primary electrons can be marginally consistent with the available data provided that the electron spectrum is cutoff at E ≲ 30 and E ≲ 90 MeV for electron spectral index values of 3.5 and 4.4, respectively; ii) secondary electron models from pp collisions are strongly inconsistent with the viable gamma-ray limits, cosmic ray protons produce too much heating of the intracluster (IC) gas and their pressure at the cluster center largely exceeds the thermal one; iii) secondary electron models from DM annihilation are also strongly inconsistent with the viable 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. In that case, however, these models no longer reproduce the HXR excess in Ophiuchus. Conclusions. 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. We also find that diffuse radio emission localized at the cluster center is expected in all these models and requires quite low values of the average magnetic field (B ~ 0.1-0.2 μG in primary and secondary-pp models; B ~ 0.055-0.39 μG in secondary-DM models) to agree with the available observations. Finally, the WR model (with B ~ 0.4-2.0 μG) offers, so far, the most accurate description of the cluster in terms of the temperature distribution, heating and pressure and multi-frequency spectral energy distribution. Fermi observations of Ophiuchus will provide further constraints to this model