Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. V. Multiple Scattering
Naoki Itoh, Youhei Kawana, Satoshi Nozawa, Yasuharu Kohyama
Abstract
We extend the formalism for the calculation of the relativistic corrections to the Sunyaev-Zel'dovich effect for clusters of galaxies and include the multiple scattering effects. We present a systematic method for the inclusion of the multiple scattering effects. The multiple scattering contribution is found to be very small compared with the single scattering contribution. For high-temperature galaxy clusters of kBTe = 15keV, the ratio of the both contributions is -0.3% in the Wien region. In the Rayleigh--Jeans region the ratio is -0.03%. Therefore the multiple scattering contribution is safely neglected for the observed galaxy clusters.
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