Analytical studies on the Sunyaev Zeldovich effect in the cluster of galaxies for three Lorentz frames

Understand

We study the Sunyaev-Zeldovich effect for clusters of galaxies.

• The Boltzmann equations for the CMB photon distribution function are studied in three Lorentz frames.
• We clarify the relations of the SZ effects among the different Lorentz frames.
• We derive analytic expressions for the photon redistribution functions.