Comptonization of the Cosmic Microwave Background by Relativistic Plasma

(Abridged) We investigate the spectral distortion of the cosmic microwave background (CMB) caused by relativistic plasma. Within the Thomson regime, an exact analytic expression for the photon scattering kernel of a momentum power-law electron distribution is given. The ultra-relativistic Sunyaev-Zeldovich (SZ) decrement measures the electron number and not the energy content. On the other hand, the relativistic SZ increment at higher frequencies depends strongly on the spectral shape of the electrons. We calculate the expected Comptonization due to the energy release of radio galaxies, which we estimate to be 3 10^66 erg Gpc^-3. We investigate Comptonization from (a) the part of the released energy which is thermalized and (b) the relativistic, remnant radio plasma, which may form a second, relativistic phase in the inter galactic medium, nearly unobservable for present day instruments (presence of so called 'radio ghosts'). We find a thermal Comptonization parameter due to (a) of y = 10^-6 and (b) an optical depth of relativistic electrons in old radio plasma of tau_rel < 10^-7. If a substantial fraction of the volume of clusters of galaxies is filled with such old radio plasma the SZ effect based determination of the Hubble constant is biased to lower values. Finally, it is shown that a supra-thermal population of electrons in the Coma cluster would produce a signature in the Wien-tail of the CMB, which is marginally detectable with a multifrequency measurement by the Planck satellite. Such a population is expected to exist, since its bremsstrahlung would explain Coma's recently reported high energy X-ray excess.