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

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

2005-07-20

arxiv.org/abs/astro-ph/0507466v4

Nuovo Cim.B121:487-500,2006

Astronomy and Astrophysics

Astrophysics

14 pages, 4 figures, accepted version, Nuovo Cimento B (a subroutine is added)

Scientific paper

10.1393/ncb/i2005-10223-0

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_ec^2, 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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