Systematic effect uncertainties

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Overview[edit]

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[1].

Summary of uncertainties due to systematic effects[edit]

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

The impact of 1/[math]f[/math] noise has been assessed using half-ring noise maps normalised 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 at Nside = 128 at 30 and 44 GHz and Nside = 256 at 70 GHz in order to approximate the optical beam size. This downgrading has been applied in all cases a systematic effect has been evaluated at map level.

In Table 2 we list the r.m.s. and the difference between the 99% and the 1% quantities in the pixel value distributions. For simplicity we refer to this difference as 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 μKCMB.

30 GHz
44 GHz
70 GHz
Selection 263.png Selection 261.png Selection 262.png

Angular power spectra have been obtained from full resolution (Nside = 1024) systematic effect maps at each frequency using HEALPix Anafast [2]. In Fig. 1 we show how 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 effects uncertainties in the LFI do not limit either temperature or E-mode spectra measurements.

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Selection 265.png

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Figure 1. Angular power spectra of the various systematic effects compared to the Planck beam-filtered temperature and polarization spectra. The dark-gray thick 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 nT=0 and has not been beam-filtered. Rows: 30, 44 and 70 GHz spectra. Columns: temperature, E-mode and B-mode spectra. .


Effects independent of sky signal[edit]

Noise correlations and 1/f noise[edit]

TBW

Thermal effects[edit]

TBW


Bias fluctuations[edit]

TBW


1-Hz spikes[edit]

TBW


Main Beam Ellipticity[edit]

TBW

Near Sidelobes pickup[edit]

TBW

Effects dependent on sky signal[edit]

Sidelobe pick-up[edit]

TBW


ADC non linearity[edit]

TBW


Imperfect photometric calibration[edit]

Pointing effects[edit]

TBW


Polarization Angle Uncertainty[edit]

TBW

Ortho-Mode Transducer Cross-Polarization[edit]

TBW

References[edit]

  1. 1.01.11.2 Planck 2013 results. III. Low Frequency Instrument systematic uncertainties, Planck Collaboration, 2014, A&A, 571, A3
  2. HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere, K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, M. Bartelmann, ApJ, 622, 759-771, (2005).

(Planck) Low Frequency Instrument

Cosmic Microwave background

Data Processing Center

[LFI meaning]: absolute calibration refers to the 0th order calibration for each channel, 1 single number, while the relative calibration refers to the component of the calibration that varies pointing period by pointing period.

(Hierarchical Equal Area isoLatitude Pixelation of a sphere, <ref name="Template:Gorski2005">HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere, K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, M. Bartelmann, ApJ, 622, 759-771, (2005).

analog to digital converter