Systematic effect uncertainties
Known systematic effects in the Planck-LFI(Planck) Low Frequency Instrument 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.
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(Planck) Low Frequency Instrument CMBCosmic Microwave background 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.
|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[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.||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 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 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 μKCMBCosmic Microwave background units.
Angular power spectra have been obtained from full resolution (Nside = 1024) systematic effect maps at each frequency using the HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], <ref name="[[:Template:Gorski2005]]">[http://iopscience.iop.org/0004-637X/622/2/759/pdf/0004-637X_622_2_759.pdf '''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). 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(Planck) Low Frequency Instrument 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 CMBCosmic Microwave background TT and EE curves correspond to the Planck best-fit power spectra. The theoretical B-mode CMBCosmic Microwave background 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. .
Detailed description of the various effects
- Planck 2013 results. III. Low Frequency Instrument systematic uncertainties, Planck Collaboration, 2014, A&A, 571, A3
- Planck 2015 results. III. LFI systematics, Planck Collaboration, 2016, A&A, 594, A3.
- Planck 2015 results. II. LFI processing, Planck Collaboration, 2016, A&A, 594, A2.
- 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).