Relativistic Corrections to the Sunyaev‐Zeldovich Effect for Clusters of Galaxies. IV. Analytic Fitting Formula for the Numerical Results | Zendy

Satoshi Nozawa | Zendy; Naoki Itoh | Zendy; Youhei Kawana | Zendy; Yasuharu Kohyama | Zendy

Open Access

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

Author(s) -

Satoshi Nozawa,

Naoki Itoh,

Youhei Kawana,

Yasuharu Kohyama

Publication year - 2000

Publication title -

the astrophysical journal

Language(s) - English

Resource type - Journals

eISSN - 1538-4357

pISSN - 0004-637X

DOI - 10.1086/308938

Subject(s) - cosmic microwave background , physics , boltzmann equation , galaxy , sunyaev–zel'dovich effect , computational physics , astrophysics , galaxy cluster , boltzmann constant , numerical integration , thermal , cosmic background radiation , quantum mechanics , thermodynamics , mathematical analysis , anisotropy , mathematics

We present an accurate analytic fitting formula for the numerical results forthe relativistic corrections to the thermal Sunyaev-Zel'dovich effect forclusters of galaxies. The numerical results for the relativistic correctionshave been obtained by numerical integration of the collision term of theBoltzmann equation. The fitting is carried out for the ranges 0.02 < theta_{e}< 0.05 and 0 < X < 20, where theta_{e} = k_{B}T_{e}/m_{e}c^{2}, X =omega/k_{B}T_{0}, T_{e} is the electron temperature, omega is the angularfrequency of the photon, and T_{0} is the temperature of the cosmic microwavebackground radiation. The accuracy of the fitting is generally better than0.1%. The present analytic fitting formula will be useful for the analyses ofthe thermal Sunyaev-Zel'dovich effect for high-temperature galaxy clusters.Comment: 11 pages + 1 table + 2 figures, LaTeX with AASMS macro. Accepted by Astrophysical Journal for publicatio

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