A MEASUREMENT OF LARGE-SCALE PECULIAR VELOCITIES OF CLUSTERS OF GALAXIES: TECHNICAL DETAILS

This paper presents detailed analysis of large-scale peculiar motions derived from a sample of ∼700 X-ray clusters and cosmic microwave background (CMB) data obtained with WMAP. We use the kinematic Sunyaev-Zeldovich (KSZ) effect combining it into a cumulative statistic that preserves the bulk motion component with the noise integrated down. Such statistic is the dipole of CMB temperature fluctuations evaluated over the pixels of the cluster catalog. To remove the cosmological CMB fluctuations the maps are filtered with a Wiener-type filter in each of the eight WMAP channels (Q, V, W) that have negligible foreground component. Our findings are as follows. The thermal SZ (TSZ) component of the clusters is described well by the Navarro-Frenk-White profile expected if the hot gas traces the dark matter in the cluster potential wells. Such gas has X-ray temperature decreasing rapidly toward the cluster outskirts, which we demonstrate results in the decrease of the TSZ component as the aperture is increased to encompass the cluster outskirts. We then detect a statistically significant dipole in the CMB pixels at cluster positions. Arising exclusively at the cluster pixels, this dipole cannot originate from the foreground or instrument noise emissions and must be produced by the CMB photons that interacted with the hot intracluster gas via the SZ effect. The dipole remains as the monopole component, due to the TSZ effect, vanishes within the small statistical noise out to the maximal aperture where we still detect the TSZ component. We demonstrate with simulations that the mask and cross-talk effects are small for our catalog and contribute negligibly to the measurements. The measured dipole thus arises from the KSZ effect produced by the coherent large-scale bulk flow motion. The cosmological implications of the measurements are discussed by us in the 2008 work of Kashlinsky et al.