Inverse Compton Scattering in Mildly Relativistic Plasma

Abstract

We investigated the effect of inverse Compton scattering in mildlyrelativistic static and moving plasmas with low optical depth usingMonte Carlo simulations, and we calculated the Sunyaev-Zeldovicheffect in the cosmic background radiation. Our semianalytic methodis based on a separation of photon diffusion in frequency and realspace. We use a Monte Carlo simulation to derive the intensity andfrequency of the scattered photons for a monochromatic incoming radiation.The outgoing spectrum is determined by integrating over the spectrumof the incoming radiation using the intensity to determine the correctweight. This method makes it possible to study the emerging radiationas a function of frequency and direction. As a first applicationwe have studied the effects of finite optical depth and gas infallon the Sunyaev-Zeldovich effect (not possible with the extended Kompaneetsequation), and we discuss the parameter range in which the Boltzmannequation and its expansions can be used. For high-temperature clusters( k B T e ##IMG## [http://ej.iop.org/icons/Entities/gtrsim.gif] {gtrsim}15 keV) relativistic corrections based on a fifth-order expansionof the extended Kompaneets equation seriously underestimate the Sunyaev-Zeldovicheffect at high frequencies. The contribution from plasma infall isless important for reasonable velocities. We give a convenient analyticalexpression for the dependence of the crossover frequency on temperature,optical depth, and gas infall speed. Optical depth effects are oftenmore important than relativistic corrections and should be takeninto account for high-precision work, but they are smaller than thetypical kinematic effect from cluster radial velocities.