Flat-sky joint MAP lensing template for 06b simulations

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Marius Millea, March 6, 2020

True curved-sky MAP estimation with the CMBLensing.jl code is still under development. In the meantime, this page presents lensing templates built from the 06b simulations projected and analyzed on the flat-sky, ignoring the curvature and subtracting its impact via Monte-Carlo. This yields templates which are less optimal than they could (and will) be, but which still give a template which cleans more than twice the lensing B mode power as compared to the curved-sky QE. The absolute AL reached here with just 95Gz data is ~0.2. Once the analysis is updated to model sky curvature, it is expected to reach the target AL of 0.1. For now, these results serve as an intermediate but explicit demonstration of beyond-QE delensing on S4 sims.

Analysis details:

  • I compute the joint MAP in the lensed parameterization, i.e. the joint best-fit (f̃,ϕ) of the lensing posterior, where f̃ are the lensed E and B fields. The best-fit lensed B is the main data-product, and is what should be used in the r-estimation pipeline.
  • I use the 06b signal + noise simulations, without foregrounds for now.
  • I use data filtered to keep E on 30<ℓ<3000 and B on 200<ℓ<3000. T is not used.
  • I rotate and project the 06b maps to flat-sky 2048x2048 2' maps, and do the analysis there. The resulting lensed B can then be reprojected back to the sphere and used by the other pipelines (note, this last reprojection should be complete by the end of next week, but is not quite done yet). Note that the funny rotation I pick (see below) has no impact once reprojected back.
  • I assume spatially homogenous noise in the analyis. Since the noise is not actually homogenous, this imprints a mean-field, which can subtracted (along with the mean-field from mask and sky-curvature) using the Monte-Carlos.
  • Noise levels and beams are taken from the "Hi-res Ultra-deep Field" section of Expected_Survey_Performance_for_Science_Forecasting.
  • For the curious, the iterative maximization uses 15 steps and takes about 10 minutes to complete on one NERSC GPU.



Currently only the flat-sky maps are there. Reprojected Healpix fits files will appear this week.

Fig 1. A typical joint MAP.

These maps are exactly what comes out of the join MAP maximization, no other processing is necessary. The nature of the MAP solution is such that these are like a non-linear Wiener filter where low S/N is suppressed, which is nice since that's exactly what we want. The mean-field (due to masking, sky-curvature, and inhomogenous noise) in ϕ is visible by eye and present at some level in the other estimates too (although not visible), and can be subtracted via the Monte-Carlos.

Typical MAP.png

Fig 2. Cross-correlation coefficient

We can cross-correlate the lensed B template with the truth to assess how much delensing to expect. If the cross-correlation is ρ, then 1-ρ^2 is the AL residual lensing we expect to reach. Both quantities are show here, the top one can be compared with the similar plot for the QE. The bottom shows we reach AL~0.2. Hence, these may be useful intermediate templates while work is ongoing on the curved-sky version of something like this, which should get us to ~0.1.

Cross correlation.png