# Dust delensing firstlook

(Alex writing)

Here I describe a first look at the impact of non-Gaussian dust on delensing. One possible concern is that a coupling between long- and short-scale modes can lead to a bias on delensing. To try to capture this we do the following (other suggestions are welcome):

1. For a simulated dust map (Q_dust, U_dust) we compute a reconstructed lensing map using a quadratic estimator, phi_dust ~ E_dust B_dust. The noise is set to 3 uK-arcmin, with [lmin , lmax] = [300,3000] for the reconstruction. We Weiner filter phi_dust according to the expected statistics for the CMB lensing field (C_phi / (C_phi + N_phi) )
2. We then perform lensing to get a B template: We take E_dust (which I Weiner filter, assuming the same noise level) and lens it according to phi_dust
3. We then compute the cross power spectrum of B_template with B_dust on large scales l < 300 (note these modes were not used in the phi reconstruction).

This sequence of steps is shown here: http://cita.utoronto.ca/~engelen/plots/Vansyngel_00036_series_TQU.pdf

• Slide 1: Original T, Q, U for this dust patch (One of 300+ 10x10 degree patches)
• Slide 2: Convergence (kappa) map from E_dust x B_dust
• Slide 3: Lensing potential (phi) map from E_dust x B_dust
• Slide 4: Weiner-filtered T and E; B set to zero
• Slide 5: Same as Slide 4, in T,Q,U basis
• Slide 6: After lensing (look closely for the action of lensing as you switch between slides 4 and 5)

A preliminary result is shown here:

Here are the results for the 300+ patches:

There are as many positive as negative points, so no evidence for a bias is seen.

Steps forward:

1. repeat for other sims -- we have a number of models with varying levels of EE / BB power
2. Other checks? Look at excess power (not just correlation with low-ell B_dust)