An improved formula for the relativistic corrections to the kinematical Sunyaev-Zeldovich effect for clusters of galaxies

2005/07/31 by Satoshi Nozawa, Naoki Itoh, Yasuhiko Suda +1 · 1 citation
Physics and Astronomy · #astro-ph

paper · pdf · doi:10.1393/ncb/i2005-10223-0

published as Nuovo Cim.B121:487-500,2006 · 14 pages, 4 figures, accepted version, Nuovo Cimento B (a subroutine is added)

arxiv created 2007/07/30 · arxiv updated 2009/12/01

Abstract

We improve the calculation of Nozawa, Itoh, and Kohyama (1998) to provide a formula for relativistic corrections to the thermal and kinematical Sunyaev-Zeldovich effects that is accurate to fourth order in theta_e = kT_e/m_ec², T_e and m_e being the electron temperature and electron mass, respectively. We also carry out a direct numerical integration of the Boltzmann collision term and confirm the excellent accuracy of the analytic formula. This formula will be useful for the analysis of the observational data of the forthcoming experiments of the kinematical Sunyaev-Zeldovich effect for clusters of galaxies.

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