Re: Question about inflation theory

On 2006-04-12, Thomas Smid <thomas.smid@xxxxxxxxx> wrote:
It removes the noise bias only if it is statistically uncorrelated from
receiver to receiver i.e. for the internal receiver noise (that's the
assumption made in
http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/powspec/wmap_powspec.pdf
).

OK, we are agreed that method used removes the uncorrelated noise
bias.

It does not remove noise-like behaviour in the actual signal as this
is correlated in all receivers.

You have presented no evidence that there is noise that is correlated
in all the receivers. Significant effort was spent to ensure there was
not correlated noise.

If it would be uncorrelated, then,
according to your own admission, the auto- and cross-power spectra
would be different (which they are not according to Fig.6 in that
paper).

No, there could be a tiny correlated bias in the auto power
spectra. The fact that the auto power and cross power spectra are so
similar shows that IF any noise bias exists, then it is negligible.

The difference between the one year and three year maps is not noise,
indeed it is immediatly obvious, especially in the K and Ka band
images, that the differences majorly in the galactic plane.

In the V and W-bands (which are the most important ones for the angular
power spectra) there is no galactic emission at all visible in Fig. 3

Agreed, and the differences shown are much less than the 30 microK
differences in the K and Ka maps. The amplitude of the differences in
the V and W bands appear to my eye to be less than 10 microK, which
means they can't possibly account for the signal seen at l ~= 300.

As I said already, I am pretty sure that a power spectrum for the
(unsmoothed) difference map would prove my point that the second peak
is not a static feature.

If you are sure of this then demonstrate it. The maps are public
domain, and the HealPix software is freely available.

You are still missing the point here: due to the differential system
there is no proper signal but only one that has noise characteristics:

No, the presence of the dipole field means that most of the time the
temperatures are slightly different between the two fields of
view. That fact is actually used in some of the calibration.

if telescope 1 observes a temperature T1=T0+dT1 and telescope 2
T2=T0+dT2, then the difference signal is T1-T2=dT1-dT2 . If dT1 and dT2
vary randomly in space and time, then the mean of the absolute value of
dT1-dT1 i.e.

Since WMAP does not take the absolute value of the difference signal
your calculation is not relavent.

WMAP does not at any point in the data analysis take the square or the
absolute value of the difference signal. To do so would introduce a
bias, and they are well aware of that.

To calculate a power spectrum WMAP does a cross power analysis of one
signed map (of some stokes parameter) to a different image with
statistically independant noise characteristics.

As a double check, they do calculate an auto power spectrum, which
agrees with the cross power spectrum for l < 800 or so, but that
simply shows that any bias, if it exists, is small.

However, given the choice between doing science with a cross power or
an auto power spectrum, anyone would chose the cross power, because it
is bias free.

I am about to fly to Chile for a week of observing at Cero Tololo, so
I will not be able to respond with any regularity untill after April
21st.

.

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