Nonthermal Bremsstrahlung and Hard X-ray Emission from Clusters of Galaxies

We have calculated nonthermal bremsstrahlung (NTB) models for the hard X-ray (HXR) tails recently observed by BeppoSAX in clusters of galaxies. In these models, the HXR emission is due to suprathermal electrons with energies of about 10-200 keV. Under the assumption that the suprathermal electrons form part of a continuous spectrum of electrons including highly relativistic particles, we have calculated the inverse Compton (IC) extreme ultraviolet (EUV), HXR, and radio synchrotron emission by the extensions of the same populations. For accelerating electron models with power-law momentum spectra (N[p] propto p^{- mu}) with mu <~ 2.7, which are those expected from strong shock acceleration, the IC HXR emission exceeds that due to NTB. Thus, these models are only of interest if the electron population is cut-off at some upper energy <~1 GeV. Similarly, flat spectrum accelerating electron models produce more radio synchrotron emission than is observed from clusters if the ICM magnetic field is B >~ 1 muG. The cooling electron model produces vastly too much EUV emission as compared to the observations of clusters. We have compared these NTB models to the observed HXR tails in Coma and Abell 2199. The NTB models require a nonthermal electron population which contains about 3% of the number of electrons in the thermal ICM. If the suprathermal electron population is cut-off at some energy above 100 keV, then the models can easily fit the observed HXR fluxes and spectral indices in both clusters. For accelerating electron models without a cutoff, the electron spectrum must be rather steep >~ 2.9.