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Inverse Compton Scattering in Mildly Relativistic Plasma

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and we calculated the Sunyaev-Zeldovich effect in the cosmic background radiation. Our semianalytic method is based on a separation of photon diffusion in frequency and real space. We use a Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zeldovich effect (not possible with the extended Kompaneets equation), and we discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high-temperature clusters (kBTe ≳ 15 keV) relativistic corrections based on a fifth-order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zeldovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the crossover frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections and should be taken into account for high-precision work, but they are smaller than the typical kinematic effect from cluster radial velocities.