Effect of Internal Flows on Sunyaev-Zeldovich Measurements of Cluster Peculiar Velocities

Galaxy clusters are potentially powerful probes of the large-scale velocity field in the Universe because their peculiar velocity can be estimated directly via the kinematic Sunyaev-Zeldovich effect. This distortion of the microwave background is given by a density-weighted average over the peculiar velocity field of the cluster gas and only weakly depends on distance. Using high-resolution cosmological simulations of an evolving cluster of galaxies, we evaluate how well the averaged gas velocity on different scales reflects the actual cluster peculiar velocity, and how well Sunyaev-Zeldovich measurements can determine the peculiar velocity. The internal bulk velocities in the cluster gas are comparable to the overall cluster peculiar velocity, so sizable systematic velocity errors are expected. In an ideal situation with a noiseless map, the velocity averaged over the pixels of the kinematic Sunyaev-Zeldovich map inside a circular aperture matched to the cluster virial region provides an unbiased estimate of a cluster's radial peculiar velocity with a dispersion of 50 to 100 km/s. We discuss the extent to which these systematic errors might be modelled or averaged, and the resulting limitations on using galaxy clusters as cosmological velocity tracers.