Numerical and analytical predictions for the large-scale Sunyaev-Zel’dovich effect

The hot gas embedded in the large-scale structures in the Universe produces secondary fluctuations in the cosmic microwave background (CMB). Because it is proportional to the gas pressure integrated along the line of sight, this effect, the thermal Sunyaev-Zel’dovich (SZ) effect, provides a direct measure of large-scale structure and of cosmological parameters. We study the statistical properties of this effect using both hydrodynamical simulations and analytical predictions from an extended halo model. The adaptive mesh refinement scheme, used in the newly developed code RAMSES, provides a dynamic range of almost 4 order of magnitudes, and thus allows us to significantly improve upon earlier grid-based calculations and match the resolution reached by the latest particle-based simulations. After accounting for the finite mass resolution and box size of the simulation, we find that the halo model agrees well with the simulations. We discuss and quantify the uncertainty in both methods, and thus derive an accurate prediction for the SZ power spectrum in the ${10}^2\lesssim l\lesssim {10}^5$ range of multipole. We show how this combined analytical and numerical approach is essential for accuracy, and useful for the understanding of the physical processes and scales which contribute to large-scale SZ anisotropies.