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

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

2009-04-24

arxiv.org/abs/0904.3811v2

Phys.Rev.D79:123007,2009

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

13 pages, 5 figures, accepted by PRD for publication

Scientific paper

10.1103/PhysRevD.79.123007

Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the formal solutions in three different representation forms for the Sunyaev-Zeldovich effect. By expanding the formal solution in the operator representation in powers of both the derivative operator and electron velocity, we derive a formal solution that is equivalent to the Fokker-Planck expansion approximation. We extend the present formalism to the kinematical Sunyaev-Zeldovich effect. The properties of the frequency redistribution functions are studied. We find that the kinematical Sunyaev-Zeldovich effect is described by the redistribution function related to the electron pressure. We also solve the rate equations numerically. We obtain the exact numerical solutions, which include the full-order terms in powers of the optical depth.

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