Measuring the Galaxy Cluster Bulk Flow from WMAP data

We have looked for bulk motions of galaxy clusters in the WMAP~7 year data. We isolate the kinetic Sunyaev-Zeldovich (SZ) signal by filtering the WMAP Q, V and W band maps with multi-frequency matched filters, that utilize the spatial properties of the kinetic SZ signal to optimize detection. We try two filters: a filter that has no spectral dependence, and a filter that utilizes the spectral properties of the kinetic and thermal SZ signals to remove the thermal SZ bias. We measure the monopole and dipole spherical harmonic coefficients of the kinetic SZ signal, as well as the $\ell=2-5$ modes, at the locations of 736 ROSAT observed galaxy clusters. We find no significant power in the kinetic SZ signal at these multipoles with either filter, consistent with the $\Lambda$CDM prediction. Our limits are a factor of ~ 3 more sensitive than the claimed bulk flow detection of~\citet{2009ApJ...691.1479K}. Using simulations we estimate that in maps filtered by our matched filter with no spectral dependence there is a thermal SZ dipole that would be mistakenly measured as a bulk motion of $\sim \! 2000-4000$ km/s. For the WMAP data the signal to noise ratio obtained with the unbiased filter is almost an order of magnitude lower.