Calculation of the Kinetic Sunyaev-Zeldovich Effect from the Boltzmann Equation

Abstract

We calculate the kinetic Sunyaev-Zeldovich effect in a simple model in which the electrons in the ionized gas trapped within a galactic cluster are replaced by massive scattering centers which all have the same radial drift velocity relative to the cosmic microwave background radiation. In this approximation, the electron temperature is zero and recoil can be neglected. The resulting Boltzmann equation can be solved for any value of the drift velocity.