Physics
Scientific paper
May 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999aipc..476..332i&link_type=abstract
Conference on 3K cosmology. AIP Conference Proceedings, Volume 476, pp. 332-342 (1999).
Physics
Background Radiations, Relativity And Gravitation
Scientific paper
We review on the recent developments in the calculation of the relativistic corrections to the thermal and kinematic Sunyaev-Zel'dovich effects. In order to study the kinematic Sunyaev-Zel'dovich effect, we extend the formalism of the relativistic thermal Sunyaev-Zel'dovich effect to the system moving with a velocity βvec ≡vvec /c with respect to the cosmic microwave background radiation. In the present formalism, the kinematic Sunyaev-Zel'dovich effect for the cluster of galaxies with a peculiar velocity βvec is derived in a straightforward manner by the Lorentz boost of the generalized Kompaneets equation. We give an analytic expression for the kinematic Sunyaev-Zel'dovich effect which is valid up to O(β2) with the power series expansion approximation in terms of θe≡kBTe/mc2, where Te and m are the electron temperature and the electron mass, respectively. It is found that the relativistic corrections to the kinematic Sunyaev-Zel'dovich effect are significant. For a typical electron temperature kBTe=10 keV, one obtains -8.2% and +1.3% corrections from the O(βθe) and O(βθe2) contributions, respectively. The O(β2) correction is extremely small, +0.2% for β=1/300 at kBTe=10 keV. Therefore it can be safely neglected. These relativistic corrections are directly reflected on the determination of the peculiar velocity β of the cluster of galaxies with the observation of the kinematic Sunyaev-Zel'dovich effect.
Itoh Naoki
Kohyama Yasuharu
Nozawa Satoshi
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