Inconsistency in WMAP Data?
The two authors of these papers came to Caltech to talk about their work, but unfortunately I didn't know they were coming until they were already gone. In April they will be at UC Berkeley and they may return to Caltech late in April. So I may have more to say then.
I received a copy of the 2nd paper (
The origin of the WMAP quadrupole) the day before it was placed on arXiv and yesterday presented both papers in a journal club meeting of the
astrophysics group at JPL, including several members of the CMB community with experience on WMAP. We came quickly to the conclusion that the authors must be wrong, on deciding that their principle claim is too severe and could not have been overlooked by the WMAP team. See this 2nd paper, wherein we find the reason they claim the WMAP data are flawed ...
From the abstract:
"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."
From page 2:
"The difference between the resulting antenna directions from different interpolation offset settings is small, only ~7', just about a half-pixel in the WMAP resolution (with HEALPix resolution parameter Nside = 512)."
The authors might think that 7 arcminutes or 1/2 pixel is "small", but nobody in the room with me was prepared to tolerate such an idea. The spacecraft pointing is rigorously tested many times in the map making process, against point source catalogs with milliarcsecond accuracy and precision. In the map making process, rather than subtract foreground point sources (because it requires a
PSF fit), the source pixels are blanked out. Bright sources (and there are plenty of them) require more than one pixel to be blanked and an offset that large would mean the wrong pixels get blanked and point source artifacts will be created in the maps which would be obvious to anyone. These two considerations, the absence of point source artifacts in the maps, and the accuracy & precision of the pointing tests make an error so large as 7' too much to believe.
We believe the authors have probably made the mistake of misinterpreting the time ordered data (TOD) time flags. The antennae actually scan the sky in a complex pattern of overlapping ellipses which must then be interpreted as a map of the sky (see
WMAP Scan Strategy). The TOD are binned into 2 or 3 samples per beamwidth and each sample receives a time stamp from the digital electronics unit (I think; see
WMAP Receivers). The point is that the data are actually integrated over a window of time, but assigned an arbitrary time stamp that usually coincides with analog to digital conversion. In the map making routines the telescope pointing has to coincide with the time stamp on the TOD. This procedure is typical of any device that does not take an instantaneous measure, not just WMAP.
The authors here have concluded that the WMAP pointing error amounts to 1/2 sample, which is a suspicious number. At this point we must refer once again to the paper
Origin of the WMAP quadrupole:
From page 2:
"In order to reduce the data size roughly only one quaternion is recorded for each WMAP science frame, whereas each science frame contains 12-30 observations. Therefore, the quaternion data must be interpolated to determine the spacecraft attitude for each observation. To do the interpolating, the offset of each observation to the start of the frame must be used. For example, for the Q-band, there are 15 observations in one frame. Ordinarily, in such interpolation the recorded quaternion for the start of the frame is used as the starting value of the interpolation, and then 0.000, 0.066, ... , 0.933 are used as offsets for observation 1,2, ..., 15, respectively. But, oddly, the WMAP team take 0.033, 0.099, ..., 0.967 as the offsets."
We don't know what "ordinarily" is supposed to refer to in this context, but one might naively expect the time stamp to fall at the mid-point of the integration window instead of the endpoint. If by "ordinarily" the authors expect this, then they will be off by 1/2 frame in their timing, which is exactly what they claim to be the case, that WMAP is off by 1/2 frame in pointing. So it is likely that the WMAP offsets are in fact correct because they are properly using end-of-frame offsets instead of mid-frame offsets.
It is easy enough, in principle, to test this simply by testing the positions of cataloged point sources in the WMAP data. If they are not off by 7' then the authors here are wrong. It should be noted here that he authors are high energy physicists and experts in statistics & probability, but have no experience with spacecraft data or architecture. So this kind of mistake would not be out of the question for them. As far as I know, only one of their earlier papers has been submitted for publication (in Monthly Notices of the Royal Astronomical Society) but is still in the review process. Because of the long review process, the authors decided to place the rest of their papers on arXiv for community review.
That said, it still leaves open the questions raised in their first paper (
Inconsistency between WMAP Data and Released Map). While it was not difficult to disbelieve the reason cited in the 2nd paper for the claimed mismatch between TOD and map, it may still be the case that there is a mismatch for some other reason. It was not clear to us (though we did not look very hard) that the process of reconstructing TOD from the map will work they way they think it will work, because of the geometric complexity of the TOD compared to the map. We should also take note of another comment from the authors in the first paper ... "
It will be very helpful if the WMAP team can thoroughly re-check their map-making process to find out where and how the error occurs. But until now they have insisted that their result has no problem and have prevented to discuss it with us." So in fact the authors are not directly comparing their results with WMAP team results, but rather with results arrived at by Peter Freeman at Carnegie Mellon University (whom the authors credit & acknowledge in their 2nd paper). We felt that an inconsistency as large as claimed seems unlikely but arrived at no firm conclusion one way or another on that score.
Let us also not read more into the results then warranted. Suppose for the sake of argument that the authors are correct, and there does exist an inconsistency in the WMAP maps. Does this mean an end to standard cosmology? Not quite. First, keep in mind that COBE and WMAP arrive at mutually consistent results, using very different spacecraft, receivers, and map making routines. And we will soon be hearing from PLANCK, another entirely independent system, which has already scanned the entire sky, so we await developments there. Meanwhile, Liu & Li, at the conclusion of their 2nd paper tell us that ... "
If the epoch when the angular scale of 90 degrees exit the horizon is as early as before the reheating period when the primordial density perturbations had not occurred, we could detect no CMB quadrupole." Now this hinges on the validity of the reason given in their 2nd paper, which seems not likely. Nevertheless, in general, an inconsistency of the type suggested here, if valid, may lead to changes in cosmological parameters, and alter our perception of details in inflationary cosmology, but does not indicate an fatal flaw in standard concordance cosmology.
Finally, let me add the comment that a
quaternion is a 4x4 matrix that can be used to locate points on a sphere (like the sky, for instance) and avoid the singularities that normal polar coordinates will generate (see
Quaternion on Wikipedia or
Quaternion from Mathworld). And
HEALPix is a software package for pixelization of the surface of a sphere (which is not as easy to do as you might think).
