# Beam Window Functions

Beam window functions have computed with the Febecop Pipeline (as described there), and the QuickPol pipeline (see Hivon et al, 2017[1], and the Planck 2016 Likelihood paper[2]).

The beam window functions relate, over the full sky or over a masked sky, the angular power spectrum measured (in the absence of noise) on a map produced by a set of detectors , to the true underlying sky angular power spectrum (assumed to have isotropic statistical properties, as is the case for the CMB).

### QuickPol effective beam window functions

They are available in two forms:

• The beam window functions

such that




for X=T, E or B, and where is the pixel window function, which depends on the resolution parameter Nside (=2048 for Planck HFI maps). They are provided in FITS files, in a format compatible with HEALPix tools such as synfast and smoothing, as well as with PolSpice.

• Beam matrices ,

such that




for X,Y,X',Y'= T, E or B

### References

1. Hivon E., Mottet, S. & Ponthieu N., 2017 QuickPol: Fast calculation of effective beam matrices for CMB polarization A&A 598, A25, 2017A&A...598A..25H
2. Planck collaboration, 2018, Planck 2016 results. V. Legacy Power Spectra and Likelihoods

Cosmic Microwave background

(Planck) High Frequency Instrument

Flexible Image Transfer Specification