Study on the Solutions of the Sunyaev-Zeldovich Effect for Clusters of Galaxies

Understand

Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the formal solutions in three different representation forms for the Sunyaev-Zeldovich effect.

• By expanding the formal solution in the operator representation in powers of both the derivative operator and electron velocity, we derive a formal solution that is equivalent to the Fokker-Planck expansion approximation.
• We extend the present formalism to the kinematical Sunyaev-Zeldovich effect.
• The properties of the frequency redistribution functions are studied.