Planck 2013 results. VII. HFI time response and beams

TL;DR

The paper delivers a rigorous framework to extract Planck HFI time response and scanning beams from on-orbit planetary data, computing accurate effective beam window functions $W_\ell^{\mathrm{eff}}$ for CMB analyses. The core methodology combines an improved time-response model (LFER4) with planet-based beam measurements, and advanced pixel- and harmonic-space tools (FEBeCoP, Quickbeam, FICSBell) to propagate errors via a low-dimensional eigenmode description. Key results include main-beam solid angles known to within $<0.5\%$, near sidelobes contributing $<10^{-3}$ of the solid angle, and an error budget on $W_\ell^{\mathrm{eff}}$ characterized by five eigenmodes; overall beam-window errors are below 1\% at 100 GHz up to $\ell\approx1500$ and below 0.5\% at 143 and 217 GHz up to $\ell\approx2000$. The work demonstrates robust cross-validation across methods and instruments, while detailing the residual systematic effects and guiding future releases with improved planet-based beam maps and a more complete near-sidelobe treatment. The resulting beam knowledge ensures unbiased CMB power spectrum recovery and provides a foundation for precise cosmological parameter estimation with Planck HFI data.

Abstract

This paper characterizes the effective beams,the effective beam window functions and the associated errors for the Planck HFI detectors. The effective beam is the angular response including the effect of the optics,detectors,data processing and the scan strategy. The window function is the representation of this beam in the harmonic domain which is required to recover an unbiased measurement of the CMB angular power spectrum. The HFI is a scanning instrument and its effective beams are the convolution of: (a) the optical response of the telescope and feeds;(b)the processing of the time-ordered data and deconvolution of the bolometric and electronic time response; and (c) the merging of several surveys to produce maps. The time response functions are measured using observations of Jupiter and Saturn and by minimizing survey difference residuals. The scanning beam is the post-deconvolution angular response of the instrument, and is characterized with observations of Mars. The main beam solid angles are determined to better than 0.5% at each HFI frequency band. Observations of Jupiter and Saturn limit near sidelobes (within 5deg) to about 0.1% of the total solid angle. Time response residuals remain as long tails in the scanning beams, but contribute less than 0.1% of the total. The bias and uncertainty in the beam products are estimated using ensembles of simulated planet observations that include the impact of instrumental noise and known systematic effects.The correlation structure of these ensembles is well-described by five error eigenmodes that are sub-dominant to sample variance and instrumental noise in the harmonic domain. A suite of consistency tests provide confidence that the error model represents a sufficient description of the data. The total error in the effective beam window functions is below 1% at 100GHz up to ell~1500$,and below 0.5% at 143 and 217GHz up to ~2000.

Figures (7)

• Figure 1: Data flow for fitting time response model parameters.
• Figure 2: Data flow for determining the HFI beams.
• Figure 3: Survey 2 minus Survey 1 residual close to the Galactic centre before (upper) and after (lower) fitting and deconvolving the low frequency part of the time response for bolometer 353-2. Remaining residuals are dominated by gain difference between the surveys due to ADC nonlinearity planck2013-p03f and artifacts of the different scanning directions (beam asymmetry) and pixel coverage survey to survey.
• Figure 4: 68%, 95%, and 99% likelihood contours for the long time constant $\tau_3$ and associated amplitude $a_3$ for a 545GHz bolometer (545-4) with (black) and without (red) zodiacal emission and far sidelobe removal. The square and cross indicate the maximum likelihood values.
• Figure 5: Survey 1 minus survey 2 residual for the 545GHz bolometers, averaged from Galactic longitude 0 through 20∘$^\circ$. The black curves show the Planck data, and red is a simulation.