**Decorrelation plots for foreground models**

Sept 14 2018, Clem Pryke

Most of the foreground models we are considering for PICO implement spatial variation of the spectral behavior at some level - this produces "decorrelation" - i.e. the sky pattern for a given foreground component changes as a function of frequency.
This potentially degrades the efficiency of the component separation algorithms.
In this post I look at the decorrelation of the dust and sync patterns by comparing cross-spectra to the
geometric mean of auto-spectra (the lower right panel of each plot).
We see that only the 98 and 99 (multi-layer and Vansyngel) models are significantly decorrelated in dust,
and none of them are significantly decorrelated in sync.

I take the power spectra using anafast and the soft edge mask shown below.
Since foreground do not have E>>B this should be adequate.

{{180914_fm.gif}}

To recap the models are:

  * 00=Toy Gaussian models for dust and sync with uniform amplitude over the sky at level appropriate for the BICEP/Keck patch (i.e. way too low for PICO large sky coverage).
  * 91=PySM a1d1f1s1 [[https://arxiv.org/abs/1608.02841 | arxiv/1608.02841]]
  * 92=PySM a2d4f1s3
  * 93=PySM a2d7f1s3
  * 96=Brandon's MHD model for dust and sync taken from /global/homes/b/bhensley/mhd_maps/maps_v1 on 180424
  * 98=MKD multilayer dust model as described in [[https://arxiv.org/pdf/1706.04162.pdf | arxiv/1706.04162]]. Since only dust is provided this is added to PySM a2f1s3 as per models 92 and 93.
  * 99=Vansyngel model as described in [[https://arxiv.org/abs/1611.02577 | arxiv/1611.02577]] with multi-frequency extension. This model provides both dust and sync (and no AME or free-free is added.)

So we have 7 models for dust and 5 for sync.

**Dust plots**

{{180914_f0.gif}}
{{180914_f1.gif}}
{{180914_f2.gif}}
{{180914_f3.gif}}
{{180914_f6.gif}}

Compare the below to fig 20 of [[https://arxiv.org/pdf/1706.04162.pdf]]
{{180914_f8.gif}}
{{180914_f9.gif}}

**Sync plots**

{{180914_f0s.gif}}
{{180914_f1s.gif}}
{{180914_f2s.gif}}
{{180914_f6s.gif}}
{{180914_f9s.gif}}