Planck intermediate results. LIII. Detection of velocity dispersion from the kinetic Sunyaev-Zeldovich effect

Using the Planck full-mission data, we present a detection of the temperature (and therefore velocity) dispersion due to the kinetic Sunyaev-Zeldovich (kSZ) effect from clusters of galaxies. To suppress the primary CMB and instrumental noise we derive a matched filter and then convolve it with the Planck foreground-cleaned "{tt 2D-ILC,}" maps. By using the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we determine the normalized rms dispersion of the temperature fluctuations at the positions of clusters, finding that this shows excess variance compared with the noise expectation. We then build an unbiased statistical estimator of the signal, determining that the normalized mean temperature dispersion of $1526$ clusters caused by the kSZ effect is $langle left(Delta T/T right)^{2} rangle = (1.64 pm 0.48) times 10^{-11}$, which gives a detection at the $3.2,sigma$ level. We convert the temperature dispersion of uniform weight into a measurement of the line-of-sight velocity dispersion, by using estimates of the optical depth of each cluster (which introduces additional uncertainty into the estimate). We find that the velocity dispersion is $langle v^{2} rangle =(154,000 pm 72,000),({rm km,s^{-1}})^{2}$, which is consistent with findings from other large-scale structure studies, and provides direct evidence of statistical homogeneity on scales of $600,h^{-1}{rm Mpc}$. Our study shows the promise of using cross-correlations of the kSZ effect with large-scale structure in order to constrain the growth of structure.