EDP Sciences
Free Access
Volume 417, Number 3, April III 2004
Page(s) 827 - 832
Section Cosmology (including clusters of galaxies)
DOI https://doi.org/10.1051/0004-6361:20034236

A&A 417, 827-832 (2004)
DOI: 10.1051/0004-6361:20034236

Relativistic corrections to the Sunyaev-Zeldovich effect for extremely hot clusters of galaxies

N. Itoh1 and S. Nozawa2

1  Department of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
2  Josai Junior College for Women, 1-1 Keyakidai, Sakado-shi, Saitama 350-0290, Japan
    e-mail: snozawa@josai.ac.jp

(Received 28 August 2003 / Accepted 17 November 2003 )

We present an accurate numerical table for the relativistic corrections to the thermal Sunyaev-Zeldovich effect for clusters of galaxies. The numerical results for the relativistic corrections have been obtained by numerical integration of the collision term of the Boltzmann equation. The numerical table is provided for the ranges $0.002 \leq \theta_{\rm e} \leq 0.100$ and $0 \leq X \leq 20$, where $\theta_{\rm e} \equiv k_{\rm B}T_{\rm e}/m_{\rm e}c^{2}$, $X \equiv \hbar \omega/k_{\rm B}T_{0}$, $T_{\rm e}$ is the electron temperature, $\omega$ is the angular frequency of the photon and T0 is the temperature of the cosmic microwave background radiation. We also present an accurate analytic fitting formula that reproduces the numerical results with high precision.

Key words: cosmology: cosmic microwave background -- cosmology: theory -- galaxies: clusters: general -- radiation mechanisms: thermal -- relativity

Offprint request: N. Itoh, n_itoh@sophia.ac.jp

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