Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. III. Polarization Effect

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  • 21 December 1998
Abstract
We extend the formalism of the relativistic thermal and kinematic Sunyaev-Zel'dovich effects and include the polarization of the cosmic microwave background photons. We consider the situation that a cluster of galaxies is moving with a velocity v with respect to the cosmic microwave background radiation. In the present formalism, polarization of the scattered cosmic microwave background radiation caused by the proper motion of a cluster of the galaxies is naturally derived as a special case of the kinematic Sunyaev-Zel'dovich effect. The relativisitic corrections are included also in a natural way. It is found that the polarization is positive and small in the long wavelength region. In the short wavelength region, however, the polarization becomes large with a negative sign, and the relativistic correction is significant.

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