How accurately can the SZ effect measure peculiar cluster velocities and bulk flows?

The Sunyaev-Zel'dovich effect is a powerful tool for cosmology that can be used to measure the radial peculiar velocities of galaxy clusters, and thus to test, and constrain theories of structure formation and evolution. This requires, in principle, an accurate measurement of the effect, a good separation between the Sunyaev-Zel'dovich components, and a good understanding of the sources contributing to the signal and their effect on the measured velocity. In this study, we evaluate the error in the individual radial peculiar velocities determined with Sunyaev-Zel'dovich measurements. We estimate, for three cosmological models, the errors induced by the major contributing signals (primary Cosmic Microwave Background anisotropies, Sunyaev-Zel'dovich effect due to the background cluster population, residuals from component separation and instrumental noise). We generalise our results to estimate the error in the bulk velocity on large scales. In this context, we investigate the limitation due to the Sunyaev-Zel'dovich source (or spatial) confusion in a Planck-like instrumental configuration. Finally, we propose a strategy based on the future all-sky Sunyaev-Zel'dovich survey, that will be provided by the Planck mission, to measure accurately the bulk velocities on large scales up to redshift 1, or more.