Planck 2013 results. IV. Low Frequency Instrument beams and window functions

TL;DR

This paper addresses accurate characterization of the Planck LFI beams and window functions to recover the intrinsic sky power spectrum $C_\ell$ from observed data via the beam window $W_\ell$. It combines in-flight Jupiter measurements with a tuned optical model (GRASP) to derive main-beams and sidelobes, then computes effective beams using FEBeCoP and two Monte Carlo window-function methods to quantify $W_\ell$. The study finds that total window-function uncertainties are ~2% at 30 GHz, ~1.2% at 44 GHz, and ~0.7% at 70 GHz around representative multipoles, with main-beam solid angles known to better than 0.2% and cross-polarization effects negligible. This work provides a robust framework for propagating beam uncertainties into cosmological parameter estimation (e.g., via Markov Chain Beam Randomization) and informs future data releases that will incorporate full in-band beam treatments.

Abstract

This paper presents the characterization of the in-flight beams, the beam window functions and the associated uncertainties for the Planck Low Frequency Instrument (LFI). Knowledge of the beam profiles is necessary for determining the transfer function to go from the observed to the actual sky anisotropy power spectrum. The main beam distortions affect the beam window function, complicating the reconstruction of the anisotropy power spectrum at high multipoles, whereas the sidelobes affect the low and intermediate multipoles. The in-flight assessment of the LFI main beams relies on the measurements performed during Jupiter observations. By stacking the data from multiple Jupiter transits, the main beam profiles are measured down to -20 dB at 30 and 44 GHz, and down to -25 dB at 70 GHz. The main beam solid angles are determined to better than 0.2% at each LFI frequency band. The Planck pre-launch optical model is conveniently tuned to characterize the main beams independently of any noise effects. This approach provides an optical model whose beams fully reproduce the measurements in the main beam region, but also allows a description of the beams at power levels lower than can be achieved by the Jupiter measurements themselves. The agreement between the simulated beams and the measured beams is better than 1% at each LFI frequency band. The simulated beams are used for the computation of the window functions for the effective beams. The error budget for the window functions is estimated from both main beam and sidelobe contributions, and accounts for the radiometer bandshapes. The total uncertainties in the effective beam window functions are: 2% and 1.2% at 30 and 44 GHz, respectively (at $\ell \approx 600$), and 0.7% at 70 GHz (at $\ell \approx 1000$).

Figures (24)

• Figure 1: Typical shape of a 30GHz beam (LFI27M). The plot shows the distinction between the main beam, near sidelobes and far sidelobes. The distinction between "near" and "far" sidelobes is of course arbitrary: their boundary is marked at 5$^\circ$. The peak of the spillover of the primary mirror is clearly visible, at an angle of roughly 90$^\circ$.
• Figure 2: Graphic representation of $\psi_{{\rm ell}}$ defined as the angle between the major axis of the fitted elliptical Gaussian beam and the x-axis of the main beam frame, (XY)$_{\rm{MB}}$, which is aligned with the main beam polarization direction. In the figure also the LOS frame is reported. The angle between the main beam polarization direction and the x-axis of the LOS frame is named $\psi_{{\rm uv}}$ and is described in planck2013-p02.
• Figure 3: Scanning beam profiles for both polarization arms, reconstructed from the first four Jupiter transits. The beams are plotted in contours of --3, --10, --20, and --25 dB from the peak at 70GHz (green), and --3, --10, --20 at 30GHz (blue) and 44GHz (pink).
• Figure 4: FWHM at 70 GHz (upper panel) and 30/44GHz (lower panel) for the four Jupiter scans (grey bars) and for the stacked beams (white bars), in which the four scans are considered together.
• Figure 5: Ellipticity at 70 GHz (upper panel) and 30/44GHz (lower panel) for the four Jupiter scans (grey bars) and for the stacked beams (white bars), in which the four scans are considered together.