The thermal and kinematic Sunyaev-Zel'dovich effects revisited
arXiv:astro-ph/0310465 · doi:10.1007/s10714-005-0068-1
Abstract
This paper shows that a simple convolution integral expression based on the mean value of the isotropic frequency distribution corresponding to photon scattering off electrons leads to useful analytical expressions describing the thermal Sunyaev-Zel'dovich effect. The approach, to first order in the Compton parameter is able to reproduce the Kompaneets equation describing the effect. Second order effects in the parameter induce a slight increase in the crossover frequency.
7 pages, 2 figures