Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. V. Multiple Scattering

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 k_{B}T_{e} = 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.

15 pages + 2 figures, LaTeX with AASMS macro. Submitted to ApJ

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