Comptonization of CMB in galaxy clusters. Monte Carlo computations
  The problem under consideration is to determine the change of the Cosmic
Microwave Background (CMB) spectral shape due to the thermal Sunyaev-Zeldovich
effect. We numerically model the spectral intensity of the CMB radiation
Comptonized by the hot intergalactic Maxwellian plasma. To this aim, a
relativistic Monte Carlo code with photon weights is developed. The code
enables us to construct the Comptonized CMB spectrum in a wide energy range.
The results are compared with known analytical solutions and previous numerical
simulations. We also calculate the angular distributions of the intensity of
radiation emerging from the cloud, which show that the spectral shape of the
tSZ effect is not universal for different directions of escaping photons. The
numerical method can be applied to simulate the processes of Comptonization for
different optical depths, temperatures, initial spectra of photon sources and
their spatial distributions, the obtained results may have implications on
investigating the profiles of galaxy clusters.
