24 Sep 2008 -
Kashlinsky *et al.* (2008) have claimed a detection of a
bulk flow in the motion of many distant X-ray emitting clusters of galaxies.
Unfortunately this paper and the
companion paper
have several errors so their conclusions cannot be trusted.
These errors include:

- An error of a factor of sqrt(4π/3) in the relation between
C
_{1}and the velocity, so the quoted effect should be divided by 2.05. Of course Kashlinsky*et al.*(2008) may have used a non-standard definition of C_{1}as well, but their papers are never clear on this point. - Inconsistent treatment of the WMAP beam function. In the ApJ Letter the beam response function is not used, while in the methods paper the model angular power spectrum is multiplied by the beam response function. Both of these treatments are wrong. The correct window function is the square of the beam response function.
- The Wiener filter formula used is peculiar. Normally one would
use

filter = noise/(cmb+noise),

but Kashlinsky uses

filter = (total-cmb)/total.

If total = cmb+noise these are equivalent, but actually the observed

total = cmb +/- cosmic variance + noise

and there are large cosmic variance fluctuations in the low order multipoles, so Kashlinsky's filter gives a map with large amplitude structure on large angular scales which can interact with the non-uniform catalog of clusters of galaxies to give a false dipole. - The functions G(ν) and H(ν) given by Kashlinsky
*et al.*are for Rayleigh-Jeans brightness temperatures, while WMAP gives Planck brightness temperatures. Thus H(ν) should be exactly one, and G(ν) should be just [x coth(x/2)-4]. - The sizes of the X-ray emitting clusters are determined in a way that depends on the noise in the observation. Thus there will be a systematic shift when better X-ray data is obtained instead of just a reduction in the uncertainty.
- Keisler (2009, ApJL, 707, 42) points out that Kashlinsky assumed that the CMB "noise" was independent from radiometer to radiometer in WMAP, but since all the WMAP channels view the same sky, this cosmic variance noise is totally correlated. This reduces the Kashlinsky result to less than 1σ in statistical signifcance, even using Kashlinsky's peculiar Wiener filter.
- Osborne
*et al.*(2011, ApJ, 737, 98) re-examine the dark flow using the correct Wiener filter, and find results that are 3 times more sensitive than the results Kashlinsky*et al.*obtained with their incorrect filter, and found no dark flow. - "Planck intermediate results. XIII. Constraints on peculiar velocities" uses the CMB data from Planck to show that "There is no detection of bulk flow".

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