Planck 2018 results
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Fig. B.1.


Characterization of the mean-field power spectrum and its components in our temperature-only reconstruction. The left-hand part shows the convergence-like power spectrum on large scales, while the right-hand part shows the deflection power spectrum on smaller scales. The blue line shows the total mean field as obtained from the SMICA FFP10 simulation set. Lines showing the contributions from statistical anisotropy of the mask (red), noise (orange), and the beam-convolved and pixelized CMB anisotropies (green) are plotted with rough 68% confidence regions shown shaded on the right panel (the uncertainty arises from the finite number of simulations used to estimate the mean fields). The mask mean field dominates at low multipoles and is barely distinguishable from the total on the left-hand plot. The orange and green curves were obtained from full-sky lensing reconstructions using idealized, statistically-isotropic CMB or noise components, respectively. The red curve was obtained by differencing the mean-field spectra on the full anisotropic simulations, with and without masking. Pixelization effects due to sub-pixel pointing offsets are expected to appear as an approximately white-noise lensing deflection component of amplitude 0.​​′05 (the brown line shows the prediction for the 217-GHz channel), and is clearly detected by cross-correlating the mean field to the sub-pixel deflection prediction (pink curve). The rise of the mean field at L ≃ 3000 originating in the noise maps is mostly a simulation artefact, sourced by nonlinearities in the data processing that cause slight correlations between the simulations (due to the fixed fiducial CMB and foregrounds used to make the noise simulations); the purple curve shows the lensing quadratic estimator applied to the empirical average of the noise simulations. The predicted mean field due to inhomogeneity of the variance of idealized uncorrelated pixel noise (grey curve, as derived from Eq. (B.1)) is much weaker on smaller scales and is only visible at low lensing multipoles in this figure.

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