# Map-making and photometric calibration

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## Introduction

This page will give an overview of the map-making and photometric calibration procedures used by the HFI(Planck) High Frequency Instrument DPCData Processing Center to build detector and frequency maps. This processing and its performances are described in Planck-2013-VI[1] and Planck-2013-VIII[2].

To build HFI(Planck) High Frequency Instrument maps, we use the destriping approximation, in which noise is assumed to decompose into two components : white noise plus low frequency drifts. Using the sky redundancy, the low frequency drifts are modelled as one constant, or offset, per pointing period. To speed up the ulterior processing we first build intermediate products, by taking advantage of redundancies : we average signal and detector orientation on healpix pixels visited during each fixed pointing period, which we call hereafter 'ring'. Detector's pointing are corrected for slow drifts and aberration (displacement on the sky indouced by the satellite's motion). This intermediate product is called HPR for healpix pixel ring. They have been constructed using the same map resolution as the final HFI(Planck) High Frequency Instrument products (corresponding to nside=2048). This new dataset is used as input in the following steps.

## 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.

### Dipole calibration (100 to 353 GHz)

For the 2013 data release, the calibrator for the CMBCosmic Microwave background frequency was the solar dipole, as measured by the WMAP team[3]. We use a two components template fitting procedure, performed for each detector independently, to determine ring by ring an estimation of the dipole gain. The two fitted components are the Solar dipole and a sky template. We used the PSMPlanck Sky Model for thermal dust emission at the detector's frequency as a first approximation of the sky template in pur early release. Using the HFI(Planck) High Frequency Instrument channel map as a template brings negligible change in the averaged gain, but reduces the systematic ring-to-ring dispersion of our estimation. We average these estimations over a subset of rings in the first survey (2000 to 6000) in which the dipole's amplitude is high enough with respect to that of the sky template, to get a single dipole gain per detector.

Several pieces of evidence led us to the conclusion that out bolometers presented apparent gain variation with time, after comparing the 3rd scan of the sky with the first one. This was later (mid-2012) explained by inequalities in the steps of the analog-to-digital converters (ADCanalog to digital converter) used in each bolometer's electronic chain. These devices had to be characterized using warm data after the end of the HFI(Planck) High Frequency Instrument observations. This process is still on-going (01/2012).

In the mean time we used an empiric correction, looking for a gain estimation and an offset per ring. This amounts to solve the non-linear equation :

where d is s the detector measurement, both S the sky signal, g the detector gain, O the offset (for ring no i) are the unknowns to be determined, and n the noise. We linearized this equation starting from the constant gain approximation, to get a measurement of the apparent time-varying gains for each bolometer independently. The limitations of this process are intrinsic signal variability from one observation to the other, like polarization or intra-pixel gradient. This procedure was thus only used for the 100 to 217 GHz detectors, for which the dipole signal is brighter and galactic signal (and polarization). A mask was used to removed the inner part of the Galactic plane.

### Higher frequency calibration (545 and 857 GHz)

We therefore finally derived the sub-mm channels' calibration for the 2013 Planck data release from the comparison of measurements of the Neptune and Uranus fluxes (with aperture photometry) with their expectations from the Moreno et al model of their atmospheres' emission. This procedure is justified, since for both planets, at the lower frequencies (100-353 Ghz), the fluxes we recover are in agreement within ~ +/-5\% with what is expected from the planet spectral model, and the HFI(Planck) High Frequency Instrument detector's band-passes.

We determined zero-level for the released maps is selected regions of the sky where dust emissions are low and well correlated with HI. We may thus estimate and subtract dust emissions using the Hi template, and CMBCosmic Microwave background from a Planck component separated template. The remaining astrophysical zero level is that of CIB. By imposing that the vele we find is equal to that of the CIB model of Bethermin et al, we may aset the sezo level of our maps.

## Building of maps

Using the photometric calibration parameters, we build maps in two steps :

• we determine the destriping offsets using the full mission data
• we build the maps, using these offsets, by inverting the photometric equation :

where d is the destriped and calibrated signal at the HPR level. Detector's data are combined with an inverse noise weights derived from each detector's NEPNoise Equivalent Power. Q and U maps are build whenever possible. We propagate the white noise by building the 3x3 (or 1x1 if only I is reconstructed) covariance matrices in each pixel. At each frequency we build maps combining all detectors and independent detector sets. We use the offsets build for the full mission for building maps for each scan survey and for the nominal mission duration. We also build maps from the two independent halves of each rings. Altogether, more than 6000 maps are built at each release.

HPR and Maps are built in galactic coordinates.

## Noise properties

Map noise properties can be evaluated using several methods, thanks to the high level of observation redundancies. We can use the maps built from the difference between the first and second half of each rings, or compare individual sky scans, of detector sets with each other.

Low resolution (nside = 8, 16, 32 ?) pixel-to-pixel noise covariance matrices are build using an analytic approach from the measured noise power spectra.

## Zodiacal light correction

At the highest Planck frequencies, zodiacal light emission is visible in a survey difference map:

857 GHz Survey 2 - Survey 1 Difference

This map is a difference between the 857 GHz Survey 2 map and the 857 GHz Survey 1 map. This difference effectively removes Galactic and other emissions which originate far from Planck. As the Solar elongation is different for measurements of the same point on the sky for the two surveys, we see zodiacal light emission, while all emission from further sources is removed. The zodiacal light emission follows the Ecliptic plane, which starts at the lower left of the image, then crosses the center of the plot towards the upper right. Note that the "arcs" at the top and bottom of the image are images of the Galactic center in the Far Sidelobes, which are discussed in the section below. Similar plots for other HFI(Planck) High Frequency Instrument frequencies, for maps both before and after removal, are shown here.

Zodiacal light emission is removed from the 353, 545 and 857 GHz channels. It is described in Planck-2013-VI[1], but a synopsis of the procedure is as follows:

• During each survey, a large fraction of the sky has observations which all fall within a week of each other. That is, during a single survey, most pixels are observed during a short, well-defined period. The contribution from zodiacal light emission to the total brightness seen, then, is well defined.
• We use the the COBE model of the zodiacal light emission to make predictions for this zodiacal light emission for those pixels observed over a span of one week or less, and use GRASP models of the beams to predict the emission from the galaxy given our sidelobes. The templates from the COBE model are shown here.
• We fit the survey difference maps with these model templates to estimate the emissivity of each zodi component and sidelobe at the Planck wavelengths. The results of these fits at each frequency are shown here.
• We reconstruct each ring of the the full mission using the combination of the COBE geometric model with the emissivities determined above and the sidelobe models.
• We remove the reconstruction above from each ring of data.
• We then make maps as described previously in this section. Maps with and without, as well as the differences between the two, are shown here. The survey differences before and after this removal are shown with and without zodical light emission removal here. The power spectra of what is removed from each map is shown here.

## Far SideLobes (FSL)

The far sidelobe correction for the highest frequency HFI(Planck) High Frequency Instrument channels is described in the section above. Note that this correction is not always used, as other, CMBCosmic Microwave background-specific, component separation methods have been more effective at removing the zodiacal light emission, though as this is done along with dust and other component removal, it is difficult to characterize the zodiacal light emission in this fashion.

Fit values for specific horns and surveys are show here

We have made estimates of the contamination of the far sidelobes at 143 GHz by taking the 143 GHz map, adding the dipole, and passing it through our simulator, using a GRASP calculation of the far sidelobes for the 143-1a detector as the beam. The resulting maps is

While there is one small region that might reach 20 micro-K (this happens when the secondary spillover overlaps with the Galactic center), most of the map is quite quiet. This is evidenced by the power spectrum of the above map, which is quite small.

## CO correction

The extraction of CO maps from HFI(Planck) High Frequency Instrument maps is described in detail in the Planck-2013-XIII[4]. The CO maps are produced by a combination of bolometer maps or frequency maps.

## Map validation

Several validations of HFI(Planck) High Frequency Instrument maps are described in Planck-2013-VI[1], largely based on the analysis of the differences between half ring maps.

ADCanalog to digital converter non-linearities induce significant differences (of order 1 micro-K_cmb) at low ell (<25) that are well reproduced by simulations including this effect.

These checks showed that at higher multipole, half ring map differences give an estimation of the noise level in the total map that is biased low of ~0.5%. This bias is introduced by the deglitching algorithm which uses the same, eventually biased, signal estimation for the two halves of each rings.

Further checks are presented in the Planck-2013-XV[5] and in Planck-2013-XXXI[6].

## References

1. Planck 2013 results: High Frequency Instrument Data Processing, Planck Collaboration 2013 VI, A&A, in press, (2014).
2. Planck 2013 results: HFI calibration and Map-making, Planck Collaboration 2013 VIII, A&A, in press, (2014).
3. Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results, G. Hinshaw, J. L. Weiland, R. S. Hill, N. Odegard, D. Larson, C. L. Bennett, J. Dunkley, B. Gold, M. R. Greason, N. Jarosik, E. Komatsu, M. R. Nolta, L. Page, D. N. Spergel, E. Wollack, M. Halpern, A. Kogut, M. Limon, S. S. Meyer, G. S. Tucker, E. L. Wright, ApJS, 180, 225-245, (2009).
4. Planck 2013 results: Galactic CO emission as seen by Planck, Planck Collaboration XIII, A&A, in press, (2014).
5. Planck 2013 results: CMB power spectra and likelihood, Planck Collaboration XV, A&A, in press, (2014).
6. Planck 2013 results: Consistency of the data, Planck Collaboration XXXI, In preparation, (2014).