## Residual dipole in 3-year WMAP maps

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### Residual dipole in 3-year WMAP maps

Significant gotcha for those working on the 3-year WMAP data, especially for foreground analysis: the 3-year Stokes I maps (both individual DA and band-averaged) contain a residual 'CMB' monopole and dipole. (NB: the single-year maps have large random monopoles, cf Jarosik et al 2006, sec 3.4.3).

The ILC map 'wmap_ilc_3yr_v2.fits' has both the monopole and dipole set to zero. But you can reconstruct them by re-generating the ILC map from the smoothed individual frequency maps using the weights listed by Hinshaw et al (or, with higher precision, in the header of 'wmap_ilc_rgn_defn_3yr_v2.fits').

Hence, subtracting the official ILC map from individual frequency maps leaves a monopole and dipole with the CMB spectrum in the data. Amplitude is about -11 uK for the monopole and approximately (x,y,z) = (-0.6, -8.4, 8.7) uK (Galactic) for the dipole. The latter is nearly parallel to the main dipole as it is essentially a residual calibration error. The effect is quite noticable in V band.

The zero level of the maps is said to be based on a cosec|b| fit to latitudes south of -15deg. In fact (i) this is after the ILC map WITH monopole and dipole has been subtracted and (ii) the fit is not over all pixels; excluding pixels inside Kp2 gives almost but not exactly consistent answers (this also applies to the 1-year analysis).

The ILC map supplied with the likelyhood code (bias_corrected_pass2_3yr_ilc.fits) still contains the residual monopole and dipole; this is the origin of the dipole found by Kate Land in another topic on this board (note that the image she supplied is actually (likelyhood ILC) minus (LAMBDA ILC) not the other way round).

Finally, in working this out I noticed the undocumented feature that in 'wmap_ilc_3yr_v2.fits' the bias correction has only been applied inside the Kp2 mask. Presumably someone felt that the correction is basically noise at high latitude. I can't tell whether the correction has been applied over the full sky in 'bias_corrected_pass2_3yr_ilc.fits' because there are certainly other differences between this and the LAMBDA version (e.g. this does explain the excess differences at the positions of planets).

regards,

Pier Stefano Corasaniti
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### Residual dipole in 3-year WMAP maps

that's very interesting, I wonder if this is specifically due to the fact that WMAP has observed the CMB sky in a "non-honogeneous" way. Something that has always puzzled me is this map from the Hinshaw et al. paper (2006),

which shows the number of independent observations per pixel in W-band in Galactic coordinates for year 1, 2 and 3. As one can see the satellite has spent more time observing near the ecliptic poles than in the plane of the ecliptic. Exactly where there can be contamination from zodiacal light as it can be seen from this IR-image of the sky
.
Can the "axis of evil" and the correlated orientation of the lowest multipoles be just such an effect?
Cheers

Pier Stefano

Hans Kristian Eriksen
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### Re: Residual dipole in 3-year WMAP maps

Pier Stefano Corasaniti wrote:Something that has always puzzled me is this map from the Hinshaw et al. paper (2006),
Actually, there's something else with these hit count maps that always has puzzled me -- why are there structures present parallel to the galactic plane in these maps..? It's not a big deal, but I never quite understood those features..
Pier Stefano Corasaniti wrote: Exactly where there can be contamination from zodiacal light as it can be seen from this IR-image of the sky.
Can the "axis of evil" and the correlated orientation of the lowest multipoles be just such an effect?
I strongly doubt it. First of all, the scanning strategy only affects modes with low signal-to-noise. If S/N > 100, one really doesn't care if one pixel has been observed twice as often as another one -- we know the value of the spherical harmonic mode anyway. So I feel very confident that all large-scale anomalies reported from the WMAP data are independent of the noise properties of WMAP. (Unless there are some weird unknown systematics, of course, but that also seems very unlikely for a number of reasons.)

Then there are foregrounds, and these are considerably trickier. You are pointing to the zodical light. In fact, we considered this with respect to the power asymmetry issue some time ago. However, it matches the observations very poorly. One clear issue is the fact that it is (almost) symmetrical around the ecliptic plane. Therefore it is very difficult to explain an hemispherical asymmetry. Also, the amplitude is much too weak to have any effect, at least according to the tests we did.

Of course, the power asymmetry is seen all the way up to l=40 in the first-year data, and is therefore more robust to such issues than a single- or few-l feature. However, even for the l=2, 3, 5, 6 anomalies, I think it's difficult to explain the observations with a model like this. One main point is that the symmetry axs of the l=2 and 3 multipoles points (nearly) towards the *ecliptic plane*, not the *poles*. Therefore you basically have two great circles that are perpendicular to eachother, and that doesn't match very well with this model. It would have been much more suspicious if the axis had pointed towards the poles, such that the features had been properly aligned.

Of course, foregrounds are always the main concern when it comes to non-Gaussian signatures, but it's not straightforward to come up with an ecliptical model that works properly, I think.

Ben Gold
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### Residual dipole in 3-year WMAP maps

Actually, there's something else with these hit count maps that always has puzzled me – why are there structures present parallel to the galactic plane in these maps..? It's not a big deal, but I never quite understood those features..
If you're talking about the large dark horizontal bands at either side of the image, I think those are relics of the symmetric pixel masking: when one side of the instrument is pointed at a very bright region of the galaxy, data from both sides is tossed out. Since the angle between the two sides of WMAP is greater than 90 degrees, it winds up looking like shadowy circles around the the point in the galactic plane 180 degrees from the bright spots. A bunch of circles in a row along the galactic plane (since the bright galaxy region is extended) overlap and make horizontal bands about 51 degrees off the galactic plane.

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### Residual dipole in 3-year WMAP maps

Update:
Monopole is -11.93 \mu K (thermodynamic)
Dipole = 11.82 \mu K, towards (l,b) = 259.47^\circ, 48.96^\circ

Zero levels appear to have been established by (a) subtracting the ILC including the above mono- and dipole (b) applying the Kp2 mask and rejecting points north of csc b = -4 (not b = -15) and (c) fitting to MEDIAN $\Delta T$ vs. csc|b| for bins of 0.1 in csc |b| (as in Fig. 7 of Bennett et al. 2003c). This gives zero intercept to within 0.2 \mu K at each band. The Bennett et al. figure certainly shows bin medians rather than means, contrary to the figure caption which says the data was "averaged".

However, closer inspection suggests that this dipole is not really in the CMB. It seems to predominantly come from the V band map, which appears with weight 2 in the ILC map. Hence, subtracting it leaves a residual dipole in every map, but with half the amplitude and the sign reversed at V band. Seen as a residual of the main CMB dipole, the amplitude is within the calibration uncertainty, so perhaps the best thing would be to fit for a residual dipole aligned with the CMB dipole, independently at each band, as part of the component separation process.