Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies

Details Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies

2009-02-16

arxiv.org/abs/0902.2595v2

Phys.Rev.D79:083005,2009

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

published in Physical Review D79, 083005 (2009)

Scientific paper

10.1103/PhysRevD.79.083005

Starting from a covariant formalism of the Sunyaev-Zeldovich effect for the thermal and non-thermal distributions, we derive the frequency redistribution function identical to Wright's method assuming the smallness of the photon energy (in the Thomson limit). We also derive the redistribution function in the covariant formalism in the Thomson limit. We show that two redistribution functions are mathematically equivalent in the Thomson limit which is fully valid for the cosmic microwave background photon energies. We will also extend the formalism to the kinematical Sunyaev-Zeldovich effect. With the present formalism we will clarify the situation for the discrepancy existed in the higher order terms of the kinematical Sunyaev-Zeldovich effect.

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