On the statistical significance of the bulk flow measured by the Planck satellite

A recent analysis of data collected by the Planck satellite detected a net dipole at the location of X-ray selected galaxy clusters, corresponding to a large-scale bulk flow extending at least to z similar to 0.18, the median redshift of the cluster sample. The amplitude of this flow, as measured with Planck, is consistent with earlier findings based on data from the Wilkinson Microwave Anisotropy Probe (WMAP). However, the uncertainty assigned to the dipole by the Planck team is much larger than that found in the WMAP studies, leading the authors of the Planck study to conclude that the observed bulk flow is not statistically significant. Here, we show that two of the three implementations of random sampling used in the error analysis of the Planck study lead to systematic overestimates in the uncertainty of the measured dipole. Random simulations of the sky do not take into account that the actual realization of the sky leads to filtered data that have a 12% lower root-mean-square dispersion than the average simulation. Using rotations around the Galactic pole (the Z axis), increases the uncertainty of the X and Y components of the dipole and artificially reduces the significance of the dipole detection from 98-99% to less than 90% confidence. When either effect is taken into account, the corrected errors agree with those obtained using random distributions of clusters on Planck data, and the resulting statistical significance of the dipole measured by Planck is consistent with that of the WMAP results.