Astronomy and Astrophysics – Astrophysics
Scientific paper
1997-12-22
Astrophys.J.502:7-15,1998
Astronomy and Astrophysics
Astrophysics
18 pages, 7 figures, LaTeX with AASMS macros, accepted for publication in the Astrophysical Journal
Scientific paper
10.1086/305876
We study the generalized Kompaneets equation (kinetic equation for the photon distribution function taking into account the Compton scattering by electrons) using a relativistically covariant formalism. Using the generalized Kompaneets equation, we derive an analytic expression for the Sunyaev-Zel'dovich effect, which takes into account up to O(theta**5) terms, where theta=kT/mc**2 is the relativistic expansion parameter and T is the electron temperature. We carefully study the applicable region of the obtained analytic expression by comparing with the result of the direct numerical integration. We conclude that the present analytic expression can be reliably applied to the calculation of the Sunyaev-Zel'dovich effect for kT < 15keV, which is the highest electron temperature in the presently known clusters of galaxies. Therefore, the present analytic expression can be applied to all known clusters of galaxies.
Itoh Naoki
Kohyama Yasuharu
Nozawa Satoshi
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