Re: Question about inflation theory

Craig Markwardt wrote:
"Thomas Smid" <thomas.smid@xxxxxxxxx> writes:

The sign of the differences between A and B is irrelevant for the
angular power spectrum (or do you see any negative values there?). The
power spectra are obtained by means of a 'quadratic estimator' i.e. the
sign of T1-T2 doesn't matter (see
http://lambda.gsfc.nasa.gov/product/map/dr1/ang_power_spec.cfm ). The
power spectrum thus reflects directly the standard deviation
sqrt(2)*sigma.

No. You are confusing the *observable*, which is the time series that
measures the intensity difference between two WMAP receiver feeds, and
the *derived products* (the angular power spectra and cross
correlation functions).
The WMAP observable quite obviously is a signed value, since it
involves differencing two positive quantities. It is this difference
that is inherent to the WMAP hardware. The differences are also the
values used by Page et al (2003; see description of analysis therein).

Thus your original claims are erroneous. The "standard deviation" is
*not* the observable, and they contain no hidden bias.

We are discussing here only a 'derived product' i.e. the angular power
spectra. This is cleary independent of the sign of T1-T2 but depends
only on the absolute value which in turn is given by the standard
deviation of the signal as argued above.

As for the derived products (cross correlations and/or angular power
spectra), the beam profiles of all the feeds and their cross
correlations are of course handled in the analysis. I already
referred to Hinshaw, et al., (2003, ApJS, 148, 135) which describes
this process.

This paper is not relevant for the details of the beam profiles. You
have to look at L. Page et al, 2003, ApJS, 148, 39 (from which I took
the Fig. 4 on my page http://www.physicsmyths.org.uk/wmap.htm ). It is
clear from this that these beam profiles are for a single telescope (as
they have been obtained by the transit of an individual point source
(Jupiter)), but following my argument from above, they are not
appropriate for differences of identical noisy signals.

Thomas

.

Relevant Pages

  • Re: Question about inflation theory
    ... angular power spectrum. ... It was *you* who discussed the measured beam profiles, ... appropriate for differences of identical noisy signals. ...
    (sci.astro)
  • Re: Question about inflation theory
    ... angular power spectrum. ... It was *you* who discussed the measured beam profiles, ... power spectrum is *derived* from the sky measurements and beam ...
    (sci.astro)
  • Re: Question about inflation theory
    ... angular power spectrum. ... It was *you* who discussed the measured beam profiles, ... power spectrum is *derived* from the sky measurements and beam ...
    (sci.astro)
Quantcast