Checking BB purity in re-analysis II
June 30 2020, Clem Pryke
This posting is a follow up to Checking BB purity in re-analysis for alternate masks.
When starting to run BK style reanalysis of 06b sims I noticed very poor E/B purity. I traced this to requirements on the apodization mask when using the Kendrick Smith style Pure-B estimator which is implemented in the S2HAT library which we are currently using to do the spherical harmonic transforms. The default is to use the sky hit pattern used to generate the simulations as the apodization mask applied before spherical harmonic transform.
The hit patterns handed to us by Reijo in Deep_SAT_from_the_Pole had artifacts so before using them to generate the 06b sims in  I smoothed them with 0.5deg fwhm and then reimposed the same unobserved sky edge. (One can quibble with these decisions but that is what I did and the sims are now generated.) This results in a small step down to zero around the edge and it turns out the Kendrick style pure-B estimator performs very poorly in this case.
It turns out that by making very small changes to the hit pattern before using is as the apodization mask one can recover very good E/B purity. The plot below illustrates this. The upper left panel shows the hit pattern as used to generate the sims. In the lower two panels we see horizontal and vertical cross cuts through the center of the maps. The edge 2.5deg of the map is set to zero and then it is re-smoothed with a 1deg fwhm Gaussian. This results in the apodization mask in the upper right panel.
The plot below is an update to the previous posting Checking BB purity in re-analysis for alternate masks. It shows the the mean BB power in lensed and unlensed LCDM simulations. We see that for the 06b apodization mask shown above the E/B purity is excellent.