[1003.1073] The origin of the WMAP quadrupole

 Authors: Hao Liu, Ti-Pei Li Abstract: The cosmic microwave background (CMB) temperature maps from the Wilkinson Microwave Anisotropy Probe (WMAP) are of great importance for cosmology. After finding out significant systematics in official WMAP maps, we had developed our own map-making software independently of the WMAP team. The new maps produced from the WMAP raw data and our software are notably different to the official ones, and the power spectrum as well as the best-fit cosmological parameters are significantly different too. By revealing the inconsistency between the WMAP raw data and their official map, we pointed out that there must exist an unexpected problem in the WMAP map-making routine. Here we state that the trouble comes from the inaccuracy of antenna pointing direction caused by improper offset of the quaternion interpolation in the WMAP routine. The CMB quadrupole in the WMAP release can be generated from a differential dipole field which is completely determined by the spacecraft velocity and the antenna directions without using any CMB signal. After correcting the WMAP team's error, the CMB quadrupole component disappears. Therefore, the released WMAP CMB quadrupole is almost completely artificial and the real quadrupole of the CMB anisotropy should be near zero. Our finding is important for understanding the early universe. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Douglas Applegate
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Affiliation: Kavli Institute for Particle Astrophysics & Cosmology (KIPAC)

[1003.1073] The origin of the WMAP quadrupole

These authors have been quite busy reprocessing the WMAP data. I noticed that some of their last papers have also been posted on Cosmo Coffee for comment.

In this paper, the authors hit on a small, but they say crucial, difference between the official analysis and their analysis. Basically, the telescope pointing is off by half a pixel (interesting amount), and thus the quadrapole is mis-measured.

Putting aside the hard question of correctness, is it plausible that an incorrect model for the telescope pointing would result in a mis-measured quadrapole?

Boud Roukema
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Re: [1003.1073] The origin of the WMAP quadrupole

Douglas Applegate wrote: ... is it plausible that an incorrect
model for the telescope pointing would result in a mis-measured
Bennett et al 2003 arXiv:astro-ph/0302207 give 3.3mK for the dipole.

$\sin(7') * 3.3mK = 0.002 * 3.3mK = 6.7 \mu K$

Liu and Li say 10-20 $\mu K$, just slightly higher. Sounds close
enough to me for plausibility.

The direction of the expected error should vary as the direction of
observation varies, so it seems reasonable to me that it doesn't give
a simple offset detectable by the standard post-processing pipeline.
This gives plausibility of why nobody detected this by post-processing
tests.

Step-by-step tests presumably missed it because taking the middle
point of an interval sounds right. Liu and Li state that in fact,
it's wrong, because it's used as the start of an interpolation
interval, not as a mid-value. At least, that's how I interpret the
text. A Nature-letter-type paper prevents the authors from including
any serious details.
Douglas Applegate wrote:Putting aside the hard question of
correctness,
Figure 2-left is calculated using only the directional
information
from the time-ordered-data from the spacecraft, with
no CMB data except for the dipole direction (if I understand
correctly). See paragraph 2, page 4: "only the spacecraft attitude
information is used to compute d' ."
I have not checked this
calculation for correctness myself. I have also not checked the
quaternion directional representation and interpolation methods. But
these should presumably be computationally quite fast to calculate -
no reading in of CMB maps is necessary at all. So I would say that
reproducing Fig 2-left is not that hard.

Digging through the data pipeline papers, finding the quaternions and
the interpolation process, are probably also not that hard. It just
would take time for people not familiar enough with the papers.

Doing Fig 1-right-panel is what would presumably take a lot of work
for someone who has not already set up and tested the pipeline for
analysing the TOD. But Fig 2-left should IMHO be enough to establish
that another "conspiracy" has been found - an analysis error in
spacecraft pointing agrees surprisingly well with what has been
widely considered to be a low amplitude, but detected, CMB quadrupole.

Cosmological interpretation: the Polish relativist Leopold
Infeld would presumably have said "I told you so!" if he were still
alive. He seems to be the first person (Infeld 1949) to have predicted
the disappearance of fluctuation statistics on scales larger than the
size of the Universe if the Universe is a compact FLRW model in the
sense of Friedmann, Lemaitre and Robertson. [See e.g. Roukema 2010
1002.3528 and follow the references if you need an introduction
to observational and (very few) theoretical aspects of cosmic
topology. I was only recently alerted to Infeld's prior claim to the
low k (low l) cutoff argument, so I haven't yet referred to it in any
formal publication.]

i think that along with inhomogeneous universe exact (Krasi&#324;ski,
Célérier et al.) and averaging (Buchert et al.) approaches, the
Concordance Model is becoming more and more of a phenomenological
fit and less and less of a physical model.

Hao Liu
Posts: 10
Joined: August 22 2008
Affiliation: Institute of High Energy Physics

[1003.1073] The origin of the WMAP quadrupole

I'm Hao Liu, one of the authors of this paper. I'm glad to see such a long
comment on our work. Here are a few replies, and I hope they would be
Step-by-step tests presumably missed it because taking the middle
point of an interval sounds right. Liu and Li state that in fact,
it's wrong, because it's used as the start of an interpolation
interval, not as a mid-value. At least, that's how I interpret the
text. A Nature-letter-type paper prevents the authors from including
any serious details.
Actually, it's hard to say which offset setting is right without looking at the
final map. We just say that the WMAP setting is "a little oddly".
Figure 2-left is calculated using only the directional
information from the time-ordered-data from the spacecraft, with
no CMB data except for the dipole direction (if I understand
correctly). See paragraph 2, page 4: "only the spacecraft attitude
information is used to compute d' ." I have not checked this
calculation for correctness myself. I have also not checked the
quaternion directional representation and interpolation methods. But
these should presumably be computationally quite fast to calculate -
no reading in of CMB maps is necessary at all. So I would say that
reproducing Fig 2-left is not that hard.

Digging through the data pipeline papers, finding the quaternions and
the interpolation process, are probably also not that hard. It just
would take time for people not familiar enough with the papers.
To produce Figure 2-left is indeed much easier than making a real map,
but one still has to do a lot of things: read and understand the TOD,
interpolate the quaternion and compute the directions (because there is
no immediate direction information in the TOD), compute the differential
dipole, and write an iterative mapmaking routine...

In fact, we are willing to provide our source code to help those who want
to repeat and test this work. If anyone is interested in our code, please

Gil Holder
Posts: 27
Joined: September 25 2004
Affiliation: McGill University

[1003.1073] The origin of the WMAP quadrupole

I don't understand why WMAP would agree with COBE if this is just an interpolation effect. Did COBE use exactly the same scheme, even with a 20x bigger beam?

The numerology is also consistent with a (v/c)^2 effect: sin(7') is very close to v/c here. Is relativistic aberration included in converting from the spacecraft to the CMB frame? It isn't clear to me how that gives the right geometry for the observed quadrupole, though. I'm just throwing out ideas.

Boud Roukema
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Affiliation: Torun Centre for Astronomy, University of Nicolaus Copernicus
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Re: [1003.1073] The origin of the WMAP quadrupole

Gil Holder wrote:I don't understand why WMAP would agree with COBE ...

Because COBE4 not only agrees with WMAP, it also agrees with zero quadrupole. The error bars are big.

COBE4: Hinshaw et al. 1996 arXiv:astro-ph/9601058 Table 2. $Q_{rms}$ in $\mu K$ with 68% confidence intervals
• "31+53+90" (residual Galaxy emission not subtracted): $6.9^{+5.4}_{-2.7}$
• "correlated" (Galaxy templates subtracted): $10.0^{+6.5}_{-4.4}$
• "combination" (synchrotron and dust best fits subtracted; followed by internal linear combination): $7.6^{+6.2}_{-4.5}$
If we accept the linear combination map as the best estimate of the
cosmological signal, then we have only $7.6/4.5 = 1.7 \sigma$
detection of a positive quadrupole. So to rephrase the answer to your
puzzlement: COBE4 (combination map) did not significantly detect
any quadrupole above zero (despite early claims from COBE1).

Gil Holder
Posts: 27
Joined: September 25 2004
Affiliation: McGill University

[1003.1073] The origin of the WMAP quadrupole

I'm not sure the power spectrum is the place to be looking here. Shouldn't the direct WMAP-COBE comparison (e.g., fig 9 in WMAP1 Bennett et al) show this quadrupole? Maybe it is hidden in the color stretch in the WMAP paper, but it sure isn't obvious in their WMAP-COBE comparison. Could it really be true that no one has ever constructed a WMAP-COBE map and looked at the quadrupole? That shatters my faith in the thousand-monkeys model.

The WMAP version is at http://lambda.gsfc.nasa.gov/product/map ... _ppt_M.png

Hao Liu
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Joined: August 22 2008
Affiliation: Institute of High Energy Physics

[1003.1073] The origin of the WMAP quadrupole

In a direct WMAP-COBE compare, the quadrupole difference is completely overwhelmed by the WMAP small scale structures, because COBE can not see small scale things like WMAP.

I agree with Boud Roukema that the COBE quadrupole is not accurate enough for us to say it is "consistent" with the WMAP release. Just look at fig. 9 in the WMAP1 paper, Hinshaw et al.
http://lambda.gsfc.nasa.gov/product/map ... _PPT_M.png
It shows clearly that the error bar for COBE (black) for the lowest multipole is very big, especially, the lower end of the error bar is far below zero. Note that there is no cosmic variance in this figure, as the WMAP team said in the footnote: "we omit the cosmic variance band from the model curve in the figure"

Gil Holder
Posts: 27
Joined: September 25 2004
Affiliation: McGill University

[1003.1073] The origin of the WMAP quadrupole

Is the problem that COBE has too much 1/f for a good quadrupole measurement?

I can't see how the beam or pixel noise is a big problem there (less than 20 uK per 7 deg beam, so negligible for quadrupole), so I can't see how this has anything to do with WMAP being higher resolution or lower pixel noise (i.e., "small scale").

Douglas Applegate
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Joined: October 19 2007
Affiliation: Kavli Institute for Particle Astrophysics & Cosmology (KIPAC)

[1003.1073] The origin of the WMAP quadrupole

Hao Liu, thanks for chiming in to this discussion.

Have you spoken to the WMAP team about your findings? What is their take on the interpolation issue?

Boud Roukema
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Re: [1003.1073] The origin of the WMAP quadrupole

Boud Roukema wrote:COBE4: Hinshaw et al. 1996 arXiv:astro-ph/9601058 Table 2. $Q_{rms}$ in $\mu K$ with 68% confidence intervals
My error: I meant Table 1, not Table 2. I quoted the fourth column of Table 1 - this contains info only from $C_2$.
Gil Holder wrote:I'm not sure the power spectrum is the place to be looking here.
I agree - the numbers I quoted are not intended to contain info from higher $l$ values.

On the other hand, the text (paragraph "The fits to...") says that the error bars include both instrument noise and cosmic variance. What we really need for this discussion is an error margin that includes not only instrument noise, but also all other forms of measurement error, while excluding cosmic variance.

Kogut et al. 1996 arXiv:astro-ph/9601060 seem to give just what we need for this discussion: "The CMB quadrupole amplitude, after correction for Galactic emission, has amplitude $Q_{rms} = 10.7 \mu K$ with random uncertainty $3.6 \mu K$ and systematic uncertainty $7.1 \mu K$ from uncertainty in our knowledge of Galactic microwave emission." From Table 4, the linear combination $|b| > 20^\circ$ quadrupole is $7.1 \pm 4.2 \pm 7.1 \mu K$. The value in the abstract is the cross-correlation $|b| > 20^\circ$ result. In either case: no significant detection of the quadrupole.

On the third hand, the same two sets of $Q_{i=1...5}$ values (linear combination and cross-correlation methods, $|b|>20^\circ$) of Table 4 of Kogut et al. 1996 give the following quadrupole maps, if I've done them correctly. I used the basis functions in note a of Table 2 of Bennett et al. 1992. This is a Mercator projection, with the standard longitude convention (Galaxy Centre at centre, longitude increasing to left). The colours are similar to Liu and Li's plots.

linear combination map

cross-correlation map

These look like they match Liu & Li 2010 Figure 2-right (WMAP5 V+W quadrupole) rather well, despite being statistically insignificant.

I think this brings us back to Gil's concern:
Gil Holder wrote:I don't understand why WMAP would agree with COBE if this is just an interpolation effect. Did COBE use exactly the same scheme, even with a 20x bigger beam?
with the complication: how can COBE4 (Kogut et al 1996) and WMAP seem to (by eye) agree when the error bar on the former is so huge?

Hao Liu
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Joined: August 22 2008
Affiliation: Institute of High Energy Physics

Re: [1003.1073] The origin of the WMAP quadrupole

Douglas Applegate wrote:Hao Liu, thanks for chiming in to this discussion.

Have you spoken to the WMAP team about your findings? What is their take on the interpolation issue?
I have sent our article to Hinshaw early this week, but there is no response yet.
Anyway, I think its very easy for them to test our result, because the bifurcation point
has been exactly pointed out.

Hao Liu
Posts: 10
Joined: August 22 2008
Affiliation: Institute of High Energy Physics

[1003.1073] The origin of the WMAP quadrupole

As to Boud Roukema's result, by comparing our fig2-left and the COBE
Quadrupole presented by Boud Roukema in similar projection, we can
see that they are probably inconsistent:

Our fig2-left, plotted in similar projection to Boud Roukema's (Galaxy
Centre at centre, longitude increasing to left), the deep-blue region is

And Boud Roukema's images:

Many differences can be easily listed, e.g.:

In our figure, the left cold region is in the north hemisphere and the right
cold region is in the south; however, in Boud Roukema's images the case
is right the opposite.
Longitude for the right hot region is about -90 in Boud Roukema's,
The left cold region and the left hot region are roughly in the same
latitude in our figure, but apparently in significantly different latitudes in
Boud Roukema's. So do the right cold region and the right hot region...

So it seems that, even if we ignore the possible amplitude difference (as
stated by Boud Roukema, "The colours are similar to Liu and Li's plots",
thus it's apparent that the quadrupole in our fig2 is much weaker), the
COBE quadrupole is still inconsistent to WMAP. If the amplitude, direction,
and uncertainty are all considered, we have to say that the COBE
quadrupole doesn't seem to be consistent to WMAP.

Boud Roukema
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Affiliation: Torun Centre for Astronomy, University of Nicolaus Copernicus
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Re: [1003.1073] The origin of the WMAP quadrupole

Hao Liu wrote:So it seems that, even if we ignore the possible amplitude difference (as stated by Boud Roukema, "The colours are similar to Liu and Li's plots",
thus it's apparent that the quadrupole in our fig2 is much weaker), the
COBE quadrupole is still inconsistent to WMAP. If the amplitude, direction,
and uncertainty are all considered, we have to say that the COBE
quadrupole doesn't seem to be consistent to WMAP.
Thanks for the Mercator plot of the WMAP quadrupole. My comparison was
just by eye. I agree that the COBE and WMAP plots are not as similar as I
initially thought - the axes look like they're off by something like
40-50 degrees or so. That's consistent with COBE4 having a huge error
bar: the cosmological quadrupole according to COBE4 (Kogut et al 1996)
might be as big as 18 $\mu K$, or it might be close to zero,
and its maxima/minima might be aligned within 40-50 degrees of the
WMAP quadrupole. That's not a very strong argument in favour of the

Hao Liu
Posts: 10
Joined: August 22 2008
Affiliation: Institute of High Energy Physics

[1003.1073] The origin of the WMAP quadrupole

Our map-making software is now publicly available at:
http://cosmocoffee.info/viewtopic.php?p=4525#4525 or
http://dpc.aire.org.cn/data/wmap/090727 ... e_code/v1/.

We sincerely invite readers to check our software and our results.

henry couannier
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Joined: March 18 2010
Affiliation: Université de la méditerranée
Contact:

Re: [1003.1073] The origin of the WMAP quadrupole

I 'm quite confused about the implication of a low quadrupole because there have been many articles claiming that the low quadrupole published by WMAP was already very unlikely while WMAP in their last publication dedicated to the alleged anomalies explains that the low quadrupole is well within two sigmas. Arent they (the WMAP collaboration) going to say the same thing even for the reduced quadrupole of Liu Hao.

For instance, does the grey band due to the cosmic variance usually reported in the WMAP power spectra actually imply that the points are expected to fluctuate from each point to its neighbor with the 1 sigma deviation being given by this grey band. If so why should the l=3, 4, 5 multipoles be so closely aligned on the fitted curve as we see them on the WMAP spectra: where are the expected large fluctuations?

There is also a very large difference between the WMAP analysis that was applied to the lowest multipole in the first year data publication (which is also the Liu Hao analysis as far as i can understand, if we except the possible bug on the Doppler effects corrections) and the analysis applied to these multipoles in the three year publications.
In particular the octopole result changed very significantly. Why did they change their method for these multipoles only and why can the result be so different ?

thank you

Frederic H-C, a beginner in that field