COSMIC MICROWAVE BACKGROUND COMPTONIZATION BY HOT INTRACLUSTER GAS

The commonly used expressions for the cosmic microwave background inte nsity and temperature changes due to Compton scattering by hot gas in clusters of galaxies (the Sunyaev-Zel'dovich effect) are based on a so lution to the Kompaneets nonrelativistic diffusion equation. These exp ressions are insufficiently accurate because of the high electron velo cities and low scattering probability in the hot intracluster gas. The results of an improved relativistic treatment show significant deviat ions, at frequencies on the Wien side, from what is predicted from the Kompaneets-based calculation. Useful expressions are given which can be readily integrated to determine the exact magnitude of the effect a t any frequency and gas temperature. An important feature of the relat ivistic spectral distribution of the intensity change is the dependenc e of the critical frequency-where the effect vanishes-on the gas tempe rature. This dependence must be taken into account in determinations o f peculiar velocities of clusters from measurements of the kinematic S unyaev-Zel'dovich effect.