Relativistic Corrections to the Sunyaev-zeldovich Effect for Clusters of Galaxies. v. Effect of the Motion of the Observer

We extend the formalism of the relativistic thermal and kinematical SunyaevZeldovich effects to the observer’s system (the Solar System) moving with a velocity ~ βS ≡ ~vS/c with respect to the cosmic microwave background radiation. We confirm the results recently obtained by Chluba, Huetsi, and Sunyaev in the lowest order of the observer’s velocity βS. 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 θe ≡ kBTe/mc , where Te and m are the electron temperature and the electron mass, respectively. It is found that the effect of the motion of the observer (the Solar System) on the Sunyaev-Zeldovich effect will become important in the future high precision observation projects of the Sunyaev-Zeldovich effect.