Easily Interpretable Bulk Flows: Continuing Tension with the Standard Cosmological Model

We present an improved Minimal Variance (MV) method for using a radial peculiar velocity sample to estimate the average of the three-dimensional velocity field over a spherical volume, which leads to an easily interpretable bulk flow measurement. The only assumption required is that the velocity field is irrotational. The resulting bulk flow estimate is particularly insensitive to smaller scale flows. We also introduce a new constraint into the MV method that ensures that bulk flow estimates are independent of the value of the Hubble constant Ho; this is important given the tension between the locally measured Ho and that obtained from the cosmic background radiation observations. We apply our method to the \textit{CosmicFlows-3} catalogue and find that, while the bulk flows for shallower spheres are consistent with the standard cosmological model, there is some tension between the bulk flow in a spherical volume with radius 150\hmpc\ and its expectations; we find only a ∼2% chance of obtaining a bulk flow as large or larger in the standard cosmological model with \textit{Planck} parameters.