The Energy Spectrum of Primary Cosmic Ray Electrons in Clusters of Galaxies and Inverse Compton Emission

Models for the evolution of the integrated energy spectrum of primary cosmic ray electrons in clusters of galaxies have been calculated, including the effects of losses due to inverse Compton (IC), synchrotron, and bremsstrahlung emission, and Coulomb losses to the intracluster medium (ICM). The combined time scale for these losses reaches a maximum of ~3e9 yr for electrons with a Lorentz factor ~300. Only clusters in which there has been a substantial injection of relativistic electrons since z <~ 1 will have any significant population of primary cosmic ray electrons at present. In typical models, there is a broad peak in the electron energy distribution extending to gamma~300, and a steep drop in the electron population beyond this. In clusters with current particle injection, there is a power-law tail of higher energy electrons with an abundance determined by the current rate of injection. A significant population of electrons with gamma~300, associated with the peak in the particle loss time, is a generic feature of the models. The IC and synchrotron emission from these models was calculated. In the models, EUV and soft X-ray emission are nearly ubiquitous. This emission is produced by electrons with gamma~300. The spectra are predicted to drop rapidly in going from the EUV to the X-ray band. The IC emission also extends down the UV, optical, and IR bands with a fairly flat spectrum. Hard X-ray (HXR) and diffuse radio emission due to high energy electrons (gamma~10e4) is present only in clusters which have current particle acceleration. Assuming that the electrons are accelerated in ICM shocks, one would only expect diffuse HXR/radio emission in clusters which are currently undergoing a large merger.