Measuring cluster peculiar velocities with the Sunyaev- Zel'dovich effect: scaling relations and systematics

The fluctuations in the cosmic microwave background (CMB) intensity due to the Sunyaev-Zel'dovich (SZ) effect are the sum of a thermal and a kinetic contribution. Separating the two components to measure the peculiar velocity of galaxy clusters requires radio and microwave observations at three or more frequencies, and knowledge of the temperature Te of the intracluster medium (ICM) weighted by the electron number density. To quantify the systematics of this procedure, we extract a sample of 117 massive clusters at redshift z= 0 from an N-body hydrodynamical simulation, with 2 7 4803 particles, of a cosmological volume 192h-1 Mpc on a side of a flat cold dark matter model with \u3a90= 0.3 and \u3a9\u39b= 0.7. Our simulation includes radiative cooling, star formation and the effect of feedback and galactic winds from supernovae. We find that: (i) our simulated clusters reproduce the observed scaling relations between X-ray and SZ properties; (ii) bulk flows internal to the ICM affect the velocity estimate by less than 200 km s-1 in 93 per cent of the cases; (iii) using the X-ray emission weighted temperature, as an estimate of Te, can overestimate the peculiar velocity by 20-50 per cent, if the microwave observations do not spatially resolve the cluster. For spatially resolved clusters, the assumptions on the spatial distribution of the ICM, required to separate the two SZ components, still produce a velocity overestimate of 10-20 per cent, even with an unbiased measure of Te. Thanks to the large size of our cluster samples, these results set a robust lower limit of ~200 km s-1 to the systematic errors that will affect upcoming measures of cluster peculiar velocities with the SZ effect