Study on the Solutions of the Sunyaev-Zeldovich Effect for Clusters of Galaxies
Abstract
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.
Keywords
Cite
@article{arxiv.0904.3811,
title = {Study on the Solutions of the Sunyaev-Zeldovich Effect for Clusters of Galaxies},
author = {Satoshi Nozawa and Yasuharu Kohyama and Naoki Itoh},
journal= {arXiv preprint arXiv:0904.3811},
year = {2009}
}
Comments
13 pages, 5 figures, accepted by PRD for publication