Comptonization of the cosmic microwave background by relativistic plasma

We investigate the spectral distortion of the cosmic microwave background ( CMB) caused by relativistic plasma. Within the Thomson regime, an exact ana lytic expression for the photon scattering kernel of a momentum power-law e lectron distribution is given, which is valid from the non- to the ultra-re lativistic regime. The decrement in the photon spectrum saturates for elect ron momenta above 3 m(e) c to that of an optically thick absorber with the optical depth of the relativistic electrons given by the Thomson limit. Thu s, the ultra-relativistic Sunyaev-Zeldovich (SZ) decrement measures the ele ctron number and not the energy content. On the other hand, the relativisti c SZ increment at higher frequencies depends strongly on the spectral shape of the electrons, allowing for investigation of relativistic electron popu lations with future instruments. We calculate the expected Comptonization due to the energy release of radio galaxies, which we estimate to be approximate to 3 . 10(66) erg Gpc(-3). W e investigate Comptonization from (a) the part of the released energy which is thermalized and (b) the relativistic, remnant radio plasma, which may f orm a second, relativistic phase in the intergalactic medium, nearly unobse rvable for present day instruments (presence of so called 'radio ghosts'). We find a thermal Comptonization parameter due to (a) of y approximate to 1 0(-6) and (b) an optical depth of relativistic electrons in old radio plasm a of tau(rel) less than or equal to 10(-7). If a substantial fraction of th e volume of clusters of galaxies is filled with such old radio plasma the S Z effect based determination of the Hubble constant is biased to lower valu es, if this is not accounted for. Finally, it is shown that a supra-thermal population of electrons in the Coma cluster would produce a signature in t he Wien-tail of the CMB, which is marginally detectable with a multifrequen cy measurement by the Planck satellite. Such an electron population is expe cted to exist, since its bremsstrahlung would explain Coma's recently repor ted high energy X-ray excess.