Systematic effect uncertainties

Overview

Known systematic effects in the Planck-LFI data can be divided into two broad categories: effects independent of the sky signal, which can be considered as additive or multiplicative spurious contributions to the measured timelines, and effects which are dependent on the sky and that cannot be considered independently from the observation strategy.

Here we report a brief summary of these effects, all the details can be found in Planck-2013-III and Planck-2015-A04.

Summary of uncertainties due to systematic effects

In this section we provide a top-level overview of the uncertainties due to systematic effects in the Planck-LFI CMB temperature maps and power spectra. Table 1 provides a list of these effects with short indications of their cause, strategies for removal and references to sections and/or papers where more information is found.

Table 1. List of known instrumental systematic effects in Planck LFI.

Effect	Source	Control/Removal	Reference
Effects independent of sky signal (T and P)
White noise correlation	Phase-switch imbalance	Diode weighting	Planck-2013-IIIPlanck-2015-A04
1/f noise	RF amplifiers	Pseudo-correlation and destriping	Planck-2013-IIIPlanck-2015-A04
Bias fluctuations	RF amplifiers, back-end electronics&	Pseudo-correlation and destriping	Planck-2015-A03
Thermal fluctuations	4-K, 20-K and 300-K thermal stages	Calibration, destriping	Planck-2015-A03
1-Hz spikes	Back-end electronics	Template fitting and removal	Planck-2015-A03
Effects dependent on sky signal (T and P)
Main beam ellipticity	Main beams	Accounted for in window function	Planck-2015-A03
Near sidelobes pickup	Optical response at angles 5° from the main beam	Masking of Galaxy and point sources	Planck-2015-A03
Far sidelobes pickup	Main and sub-reflector spillovers	Model sidelobes removed from timelines	Planck-2015-A03
Analogue-to-digital converter nonlinearity	Back-end analogue-to-digital converter	Template fitting and removal	Planck-2015-A03
Imperfect photometric calibration	Sidelobe pickup, radiometer noise temperature changes and other non-idealities	Calibration using the 4-K reference load voltage output	Planck-2015-A03
Pointing	Uncertainties in pointing reconstruction, thermal changes affecting focal plane geometry	Negligible impact anisotropy measurements	Planck-2015-A03
Effects specifically impacting polarization
Bandpass asymmetries	Differential orthomode transducer and receiver bandpass response	Spurious polarization removal	Planck-2015-A03
Polarization angle uncertainty	Uncertainty in the polarization angle in-flight measurement	Negligible impact	Planck-2015-A03
Orthomode transducer cross-polarization	Imperfect polarization separation	Negligible impact	Planck-2015-A03

The impact of 1/f noise has been assessed using half-ring noise maps normalized to the white noise estimate at each pixel (obtained from the white noise covariance matrix), so that a perfectly white noise map would be Gaussian and isotropic with unit variance. Deviations from unity trace the contribution of residual 1/f noise in the final maps, which ranges from 0.06% at 70 GHz to 2% at 30 GHz. Pixel uncertainties due to other systematic effects have been calculated on simulated maps degraded to N_side = 128 at 30 and 44 GHz and N_side = 256 at 70 GHz, in order to approximate the optical beam size. This downgrading has been applied in all cases that a systematic effect has been evaluated at map level.

In Table 2 we list the rms and the difference between the 99% and the 1% quantities in the pixel value distributions. For simplicity we refer to this difference as the "peak-to-peak" (p-p) difference, although it neglects outliers but effectively approximates the peak-to-peak variation of the effect on the map.

Table 2. Summary of systematic effects uncertainties on maps in μK_CMB units.

30 GHz

44 GHz

70 GHz

Angular power spectra have been obtained from full resolution (N_side = 1024) systematic effect maps at each frequency using the HEALPix Anafast routine . In Fig. 1 we show the power spectrum of the various effects compared with the Planck best-fit spectra and with the noise level coming from the half-ring difference maps.

Our assessment shows that the global impact of systematic effect uncertainties in the LFI do not limit either temperature or E-mode spectrum measurements.

Figure 1. Angular power spectra of the various systematic effects compared to the Planck beam-filtered temperature and polarization spectra. The thick dark-grey curve represents the total contribution. The dark-green dotted curve represent the contribution from far sidelobes that has been removed from the data and, therefore not considered in the total. The CMB TT and EE curves correspond to the Planck best-fit power spectra. The theoretical B-mode CMB spectrum assumes a tensor-to-scalar ratio r = 0.1, a tensor spectral index n_T=0 and has not been beam-filtered. Rows: 30, 44 and 70 GHz spectra. Columns: temperature, E-mode and B-mode spectra. .

Detailed description of the various effects

A detailed description of the impact of the various effects is conained in the paper Planck-2015-A04 and details will also be updated in this supplement.