Anze Slosar wrote:
I don't like 100-200 bin: it makes \chi^2 horrible and it cannot possibly be a noise fluctuation, unless errors are badly underestimated. I think it is also quite difficult to come up with something that changes things on such large scales.
If it's any comfort, we don't like that bin either :-)
My best guess is that it's residual foregrounds leaking in from the Q-band. Diffuse foregrounds still have a significant impact at l~100, and the Q-band is not clean by any means. But one never knows. Another thing that may be worth checking out is the fact that the maps are cleaned with (smoothed) K-Ka as one of three templates. These are of course noisy, and since this noise contribution is the same for all channels in the yearly maps, it's not killed by the cross-correlation estimator. Don't know the magnitude of this effect yet, though..
\beta=-2 - is assuming this a good assumption? What happens if you put some sensible prior around \beta (say 2\pm0.5)? I would expect that faint sources are not the same population as sources so bright, that you can actually cut them out....
Certainly, the fact that WMAP (and we) use the same spectral index for both the resolved and the unresolved point sources is a quite bold assumption. I think the best justification for doing so is that it seems to work reasonably OK. But of course, there is still a ~2\sigma difference between the V and W-bands, so there may be something there. As always, more work is needed..
Poisson distribution: surely, there are some LSS effects in the unresolved sources; what authors do (I think) is to assume white noise for unresolved sources: instead you could do something like Limber between z=0 and 5, fit the amplitude on large scales and extrapolate to smaller scales - surely this would have been better than C_\ell = const?
Right. The justification for using a flat spectrum is simply that CMB experiments are rather insensitive, and therefore only pick up the brightest sources. In other words, the point sources are very sparsely sampled. And that pushes the effective spectrum towards a flat "white noise" spectrum. But in principle, there may certainly be clustering effects present, yes.
I think the main conclusion from all of this work is that current parameter constraints shouldn't be taken too literally, in the sense that 3\sigma detections really are 3\sigma detections. There is a reason why particle physicists operate with a 5\sigma criterion, and that's precisely because of unknown systematics. Of course, we like to think that CMB observations are both cleaner and simpler, but it's still a good idea to have these issues in mind, I think.