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The bulk flow, i.e. the dipole moment of the peculiar velocity field, is a sensitive probe of matter density fluctuations on very large scales. However, the peculiar velocity surveys for which the bulk flow has been calculated have non‐uniform spatial distributions of tracers, so that the bulk flow estimated does not correspond to that of a simple volume such as a sphere. Thus bulk flow estimates are generally not strictly comparable between surveys, even those whose effective depths are similar. In addition, the sparseness of typical surveys can lead to aliasing of small‐scale power into what is meant to be a probe of the largest scales. Here we introduce a new method of calculating bulk flow moments where velocities are weighted to give an optimal estimate of the bulk flow of an idealized survey, with the variance of the difference between the estimate and the actual flow being minimized. These ‘minimum variance’ estimates can be designed to estimate the bulk flow on a particular scale with minimal sensitivity to small‐scale power, and are comparable between surveys. We compile all major peculiar velocity surveys and apply this new method to them. We find that most surveys we studied are highly consistent with each other. Taken together the data suggest that the bulk flow within a Gaussian window of radius  50  h  −1  Mpc  is  407 ± 81 km s −1   toward   l = 287°± 9°,  b = 8°± 6° . The large‐scale bulk motion is consistent with predictions from the local density field. This indicates that there are significant density fluctuations on very large scales. A flow of this amplitude on such a large scale is not expected in the  WMAP 5 ( Wilkinson Microwave Anisotropy Probe ) normalized Λ cold dark matter cosmology, for which the predicted one‐dimensional rms velocity is  ∼110 km s −1  . The large amplitude of the observed bulk flow favours the upper values of the  WMAP  5 Ω m  h  2 –σ 8   error‐ellipse, but even the point at the top of the  WMAP 595 per cent confidence ellipse predicts a bulk flow which is too low compared to that observed at &gt;98 per cent confidence level.

Consistently large cosmic flows on scales of 100 h −1 Mpc : a challenge for the standard ΛCDM cosmology