  Some clusters of galaxies in addition to thermal bremsstrahlung (TB), emit
diffuse radiation from the intercluster medium (ICM) at radio, EUV and hard
x-ray (HXR) ranges. The radio radiation is due to synchrotron by relativistic
electrons, and the inverse Compton (IC) scattering by the cosmic microwave
background radiation of the same electrons is the most natural source for the
HXR and perhaps the EUV emissions. However, simple estimates give a weaker
magnetic field than that suggested by Faraday rotation measurements.
Consequently, non-thermal bremsstrahlung (NTB) and TB have also been suggested
as sources of these emissions. We show that NTB cannot be the source of the
HXRs and that the difficulty with the low magnetic field in the IC model is
alleviated if we take into account the effects of observational bias,
nonisotropic pitch angle distribution and spectral breaks. We derive a spectrum
for the radiating electrons and discuss acceleration scenarios. We show that
continuous and in situ acceleration in the ICM of the background thermal
electrons requires unreasonably high energy input and acceleration of injected
relativistic electrons gives rise to a much flatter spectrum than desired,
unless a large fraction of electrons escape the ICM, in which case one obtains
EUV and HXR emissions extending well beyond the boundaries of the cluster. A
continuous emission by a cooling spectrum resulting from interaction with ICM
of electrons accelerated elsewhere also suffers from similar shortcomings. The
most likely scenario appears to be an episodic injection-acceleration model,
whereby one obtains a time dependent spectrum that for certain phases of its
evolution satisfies all the requirements.
