Modeling Integrated Properties and the Polarization of the   Sunyaev-Zeldovich Effect
  Two little explored aspects of Compton scattering of the CMB in clusters are discussed: The statistical properties of the Sunyaev-Zeldovich (S-Z) effect in the context of a non-Gaussian density fluctuation field, and the polarization patterns in a hydrodynamcially-simulated cluster. We have calculated and compared the power spectrum and cluster number counts predicted within the framework of two density fields that yield different cluster mass functions at high redshifts. This is done for the usual Press & Schechter mass function, which is based on a Gaussian density fluctuation field, and for a mass function based on a chi^2-distributed density field. We quantify the significant differences in the respective integrated S-Z observables in these two models.   S-Z polarization levels and patterns strongly depend on the non-uniform distributions of intracluster gas and on peculiar and internal velocities. We have therefore calculated the patterns of two polarization components that are produced when the CMB is doubly scattered in a simulated cluster. These are found to be very different than the patterns calculated based on spherical clusters with uniform structure and simplified gas distribution. 
Y. Rephaeli, S. Sadeh, M. Shimon