Dark Flow Detected - Not!
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
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
C1 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 C1 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
filter = noise/(cmb+noise),
but Kashlinsky uses
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
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
- 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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© 2008-13 Edward
L. Wright. Last modified 21 Mar 2013