  We suggest that the luminous extreme ultraviolet (EUV) emission which has
been detected recently from clusters of galaxies is Inverse Compton (IC)
scattering of Cosmic Microwave Background (CMB) radiation by low energy cosmic
ray electrons in the intracluster medium. The cosmic ray electrons would have
Lorentz factors of gamma ~ 300, and would lose energy primarily by emitting EUV
radiation. These particles have lifetimes comparable to the Hubble time; thus,
the electrons might represent a relic population of cosmic rays produced by
nonthermal activity over the history of the cluster. The IC model naturally
explains the observed increase in the ratio of EUV to X-ray emission with
radius in clusters. The required energy in cosmic ray electrons is typically
1--10% of the thermal energy content of the intracluster gas. We suggest that
the cosmic ray electrons might have been produced by supernovae in galaxies, by
radio galaxies, or by particle acceleration in intracluster shocks.
