View source for Nongaussian dust in lensing



'''Alex writing -- all results are preliminary'''

One of the potential issues for CMB-S4 is the possibility of non-Gaussian foregrounds on the small scales that enter lensing reconstruction.  These could impact not only measures of lensing itself but also delensing.

Here, we describe an ongoing effort to detect / characterize a lensing bias from non-Gaussian dust on small scales.

Colin Hill and Susan Clark have provided a map of small-scale polarization using correlation with HI angles (and for the pol amplitude assuming a constant pol fraction). I (Alex) cut this map out into 10x10-deg chunks.

'''Fig 1.''' T map:

[[File:quickPlot_T.png|900px]]

'''Fig 2.''' Q map:


[[File:quickPlot_Q.png|900px]]


'''Fig 3.''' Power spectra — darker colors are at higher Galactic latitude:

[[File:DustPower.png|800px]]

'''Fig 4.''' Ratio of EE to BB power in each patch - not exactly 2:


[[File:RatioPower.png|500px]]

We run these maps through a 4-pt estimator to get the bias to the lensing autospectrum.  For each patch we subtract a piece from the disconnected trispectrum.  

'''Fig 5:''' Bias to lensing power spectrum:

[[File:KappaPowers.png|500px]]

'''Fig 6:''' Lensing bias vs. dust power for each patch:

[[File:DustAndKappaPowers.png|500px]]

# The power is very high in the EE and BB maps; we are working to understand the origin of this.  This is likely leading to a significant overestimate of the bias on the lensing which we need to quantify.
#We are currently doing a similar analysis on maps from Vansyngel et al http://adsabs.harvard.edu/abs/2016arXiv161102577V
#Note that the correlated delensing correction to low-ell B mode power arises from the same <EBEB> trispectrum (though with most weight falling on different quadrilaterals, some of which have zero weight here).  We have a strawperson plan for computing the impact on delensing:
## From these maps construct phi_dust ~ E_dust B_dust
## Perform lensing for B modes, B_template = E_dust . phi_dust (where . represents the lensing operator)
## Compute <B_dust B_template>

In addition to this correlated / non-Gaussian contribution to delensing (which may be a worry as it could cause a small, unknown bias), the increase in the reconstruction noise (due to excess foreground power) will also degrade the delensing performance. However, this is probably less of a worry, as it can be understood / absorbed in an increase of A_L more easily. We may have to bear it in mind, however, when considering very high delensing fractions.