The fluctuations in the Cosmic Microwave Background ( CMB ) intensity due to the Sunyaev-Zeldovich ( 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 T _ { e } of the intracluster medium 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 \times 480 ^ { 3 } particles , of a cosmological volume 192 h ^ { -1 } Mpc on a side of a flat Cold Dark Matter model with \Omega _ { 0 } = 0.3 and \Omega _ { \Lambda } = 0.7 .
Our simulation includes radiative cooling , star formation and the effect of feedback and galactic winds from supernovae .
We find that ( 1 ) our simulated clusters reproduce the observed scaling relations between X-ray and SZ properties ; ( 2 ) bulk flows internal to the intracluster medium affect the velocity estimate by less than 200 km s ^ { -1 } in 93 per cent of the cases ; ( 3 ) using the X-ray emission weighted temperature , as an estimate of T _ { e } , 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 T _ { e } .
Thanks to the large size of our cluster samples , these results set a robust lower limit of \sim 200 km s ^ { -1 } to the systematic errors that will affect upcoming measures of cluster peculiar velocities with the SZ effect .