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 sepa ration 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 pec uliar velocities determined with Sunyaev-Zel'dovich measurements. We estima te, for three cosmological models, the errors induced by the major contribu ting signals (primary Cosmic Microwave Background anisotropies, Sunyaev-Zel 'dovich effect due to the background cluster population, residuals from com ponent separation and instrumental noise). We generalise our results to est imate the error in the bulk velocity on large scales. In this context, we i nvestigate 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 wil l be provided by the Planck mission, to measure accurately the bulk velocit ies on large scales up to redshift 1, or more.