# Checking dust decorrelation in models d1/d4/d7 and hipdt

June 27 2017, Clem Pryke

Up to now we have made simulated maps using three different dust models and Raphael has re-analyzed them and shown unbiased recovery of r=0 and r=0.003. These three models are PySM d1 and d4 as described in the PySM paper arxiv/1608.02841, plus d7 which is a Hensley/Draine model (is it described in a paper anywhere?!).

These models all contain some spatial variation of the dust SED, and will therefore produce dust patterns which vary as function of observing frequency, and hence decorrelate between frequencies. Such a decorrelation effect will potentially bias the recovery of a cosmological signal and it is therefore critically important to model it at a realistic level. The problem of course is that the proper level is not well constrained by Planck data.

Planck Intermediate Paper XXX arxiv/1409.5738 looked for evidence of decorrelation by plotting the amplitude of the cross-spectrum 220x353 divided by the geometric mean of the corresponding auto spectra - i.e. 220x353/sqrt(220x220*353x353). Fig E.1 shows the result for various sky cuts and doesn't find any clear effect (reproduced below).

The power spectrum amplitude used in PIP XXX was effectively weighted to lower ell. Planck Intermediate Paper L arxiv/1606.07335 extended the analysis to probe for an ell dependent effect and shows modest evidence for decorrelation which increases with ell in Fig 2 (reproduced below). PIP L then goes on to show Fig 3 which is a plot of the decorrelation in the range 50<ell<160 as a function of sky cut (reproduced below). This is an alarming plot - it appears to show decorrelation which worsens when going to cleaner regions of sky. One can object that the points in this plot are all correlated with one another since the sky cuts are nested. However, I am told that the points are effectively independent since for each the region which dominates is the "bright ring around the edge" which is not common with the next innermost nested region. (This begs the question as to why to nest the regions at all...)

Taken at face value PIP L is suggesting that the cross-spectrum 220x353 is suppressed in the ell range we care about to as little as 0.8x the expectation in an undecorrelated dust model. The PySM maps which we have been working with for S4 don't have a 350GHz band so in the plots below I use the 85, 155, 220 and 270GHz bands to investigate the degree of decorrelation which is present in these models for the 3% apodization mask which we have been using for the 02 experiment definition. In the lower right panel of each group of 6 plots we see that all of these models contain negligible decorrelation. (The color code for the other five panels is 85x85=blue, 155x155=red, 220x220=green, 270x270=magenta.)

Tuhin Gosh and collaborators have formulated an astrophysics based model which is described in arxiv/1611.02418. Tuhin provided maps from this model at the S4 bands and made a posting in this logbook HI-based dust polarization model for r forecasts to describe them. This model comes in a decorrelated version and I am not clear whether this is described fully in the paper or posting. Regardless below is a plot analogous to the above for the maps which Tuhin has placed on NERSC for S4 use. We see that there is significant decorrelation (although perhaps still not as strong as PIP L suggests may be present on the real sky).

On June 30 Tuhin provided a replacement set of maps. These appear to have much lower decorrelation as shown in the plot below.