# Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies. IV. Analytic Fitting Formula for the Numerical Results

@article{Nozawa2000RelativisticCT, title={Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies. IV. Analytic Fitting Formula for the Numerical Results}, author={Satoshi Nozawa and Naoki Itoh and Youhei Kawana and Yasuharu Kohyama}, journal={The Astrophysical Journal}, year={2000}, volume={536}, pages={31-35} }

We present an accurate analytic fitting formula for the numerical results 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 fitting is carried out for the ranges 0.02 ≤ θe ≤ 0.05 and 0 ≤ X ≤ 20, where θe ≡ kBTe/mec2, X ≡ ω/kBT0, Te is the electron temperature, ω is the angular frequency of the…

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