Relativistic corrections to the Sunyaev-Zeldovich effect for clusters of galaxies: effect of the motion of the observer

¹ Josai Junior College for Women, 1-1 Keyakidai, Sakado-shi, Saitama 350-0290, Japan e-mail: snozawa@josai.ac.jp
² Department of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan e-mail: n_itoh@sophia.ac.jp
³ Mizuho Information and Research Institute, 2-3 Kanda-Nishiki-cho, Chiyoda-ku, Tokyo 101-8443, Japan e-mail: yasuharu.kohyama@gene.mizuho-ir.co.jp

Received: 23 February 2005
Accepted: 26 April 2005

Abstract

We extend the formalism of the relativistic thermal and kinematical Sunyaev-Zeldovich effects to the observer's system (the Solar System) moving with a velocity with respect to the cosmic microwave background radiation. The present formulation makes full use of the Lorentz covariance properties of the problem and gives solutions with high precision. We confirm the results recently obtained by Chluba, Huetsi, and Sunyaev in the lowest order of the observer's velocity . We give a more general analytic expression for the thermal and kinematical Sunyaev-Zeldovich effects corresponding to the observer's system (the Solar System) with the power series expansion approximation in terms of , where T_e and m are the electron temperature and the electron mass, respectively.