Astronomy and Astrophysics – Astrophysics
Scientific paper
2003-05-08
Astronomy and Astrophysics
Astrophysics
3 pages. Typos corrected
Scientific paper
In a previous publication we have derived an expression for the full distorted spectrum arising when the photons of the cosmic background radiation are absorbed and emitted by an optically thin gas. The expression simply adds up the effects of the joint probability that an electron absorbs an incoming photon of frequency}$\bar{\nu}${\small and emits it with a frequency}$\nu ${\small . We here show that such an expression is identical to the Kompaneets equation describing the thermal Sunyaev-Zel'dovich effect. This clearly shows that the two pictures, diffusion and absorption-emission are mathematically equivalent to first order in the Compton parameter. Other consequences of this result are also discussed.
Garcia-Colin Leopoldo S.
Sandoval-Villalbazo Alfredo
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