# Mapmaking and photometric calibration

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## Introduction

This section will give an overview of the mapmaking and photometric calibration procedures used by the to build detector and frequency maps for the 2015 data release. They are described in Planck-2015-A08[1]. These have common elements with the tools used for the 2013 release that are described in Planck-2013-VI[2] and Planck-2013-VIII[3].

To build maps, we use the destriping approximation, in which noise is assumed to decompose into two components, namely 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 subsequent processing we first build intermediate products, by taking advantage of redundancies. We average signal and detector orientation on pixels visited during each fixed pointing period, which we call hereafter a "ring." The detector pointing is corrected for slow drifts and aberration (displacement on the sky induced by the satellite's motion). This intermediate product is called HPR for pixel ring." These have been constructed using the same map resolution as the final products (corresponding to Nside=2048). This new data set is used as input for 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 2015 data release, the channels were calibrated using the orbital dipole modulation. This time-variable anisotropy results from the motion of the spacecraft in the solar system, which is precisely known. Thus it provides an absolute calibrator for orbital missions. Its measurement is now used to calibrate data, thanks to the improvements in the time stability of the data brought by the nonlinearity corrections and a better characterization of the time response of the detectors.

Residual time response slow components are modelled as a dipole shifted by 90° in phase, whose amplitude is fitted bolometer per bolometer. To mitigate residual systematics, we perform a simultaneous fit of the detectors gains on the orbital dipole. This amounts to solving the nonlinear equation $\displaystyle{d\ =\ g_i.(S+D) + O_i + n}, \label{nlequat}$

where d is the detector measurement, D the total dipole component, n the (white) noise, and S the sky signal, g the detector gain, O the offset (for ring number i) are the unknowns to be determined. This is done by linearizing the above equation to look for gains and sky variations, and iterating by updating the approximate sky and gains.

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

We derived the sub-mm channels' calibration for the 2015 Planck data release from comparison of measurements of the Neptune and Uranus flux densities (using aperture photometry) with their expectations from the Moreno et al. model of their atmospheric emission. This procedure is justified, since for both planets, at the lower frequencies (100-353 GHz), the flux densities we recover are in agreement within approximately ±5% of what is expected from the planet spectral model, given the detector bandpasses.

### Zero levels

We determined zero-levels for the released maps in selected regions of the sky where dust emission is low and well-correlated with HI. We may thus estimate and subtract dust emission using the HI template, and using a Planck component-separated template. The remaining astrophysical zero level should be that of the CIB. By imposing that the level we find is equal to that of the CIB model of Béthermin et al., we thereby set the zero 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 for all detectors of a given frequency;
• we build the maps, using these offsets, by inverting the photometric equation

$\displaystyle{d_i = g(I^p+\eta [Q^p cos(2\psi_i) + U^p sin(2\psi_i)]) + n}. \label{photeq}$

Here d is the destriped and calibrated signal at the HPR level. The detector data are combined with inverse noise weights derived from each detector's . Q, and U maps are built whenever possible. We propagate the white noise by building the 3×3 (or 1×1 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 built for the full mission for constructing maps for each scan survey, year (combination of Surveys 1 and 2 or 3 and 4, respectively), and for the full, nominal mission duration and its two halves. We also build maps from the two independent halves of each ring. Altogether, more than 8000 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 observational redundancy. We can use the maps built from the differences between the first and second halves of each ring, or compare individual sky scans, years, half-mission or independent detector sets with each other. Some of these tests are described in Planck-2015-A08[1].

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

## Zodiacal light correction

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

2013 Release 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 emission that originates 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 centre of the plot towards the upper right. Note that the "arcs" at the top and bottom of the image are images of the Galactic centre in the far sidelobes, which are discussed in the section below. Similar plots for other frequencies, for maps both before and after zodiacal light removal, are shown here.

For the 2015 Planck release, zodiacal light emission is removed from all channels. The general procedure is described in Planck-2013-VI[2], but a synopsis of the procedure is as follows.

• During each survey, a large fraction of the sky has observations that 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 is then well defined.
• We use the the COBE model of the zodiacal light to make predictions for this emission for those pixels observed over a span of one week or less. 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 zodiacal light component at the Planck wavelengths. The results of these fits at each frequency are given in Planck-2015-A08[1].
• We reconstruct each ring of the the full mission using the combination of the COBE geometric model with the emissivities determined above.
• We remove the reconstruction above from each ring of data.
• We then make maps as described previously in this section.

## Far SideLobes (FSL)

Contrary to the 2013 Planck release, far sidelobes were not removed from the data for the 2015 Planck release. The change of the gain due to the neglect of the far sidelobes is calculated by fitting the dipole to full timeline simulations of the dipole convolved with the FSL. The correction factors applied to the data are 0.09 % at 100 GHz, 0.05 % at 143 GHz, 0.04 % at 217 GHz and negligible at 353 GHz. Corrections were not made at 545 and 857 GHz (see Planck-2015-A08[1] for details).

## CO maps

Carbon monoxide rotational transition line emission is present in all bands except for the 143-GHz channel. It is especially significant in the 100, 217, and 353 GHz channels (due to the 115GHz (1-0), 230GHz (2-1) and 345GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarized below) have been used to extract CO velocity-integrated emission maps from data and to generate the CO products. See Planck-2013-XIII[4] and Planck-2015-A10[5] for a full description.

• "Type 1" product: this is based on a single channel approach, using the fact that each CO

line has a slightly different transmission in each bolometer at a given frequency channel. From this, the J=1-0, J=2-1, and J=3-2 CO lines can be extracted independently. Since this approach is based on individual bolometer maps of a single channel, the resulting S/N is relatively low. The benefit, however, is that these maps do not suffer from contamination from other channels (as is the case for the other approaches) and are more reliable, especially in the Galactic plane.

• "Type 2" product: this product is obtained using a multi-frequency approach. Three

frequency channel maps are combined to extract the J=1-0 (using the 100, 143, and 353 GHz channels) and J=2-1 (using the 143, 217, and 353 GHz channels) CO maps. Since frequency maps are combined, the spectral behaviour of other foregrounds influences the result. The two Type 2 CO maps produced in this way have a higher S/N than the Type 1 maps, at the cost of a larger residual contamination from other diffuse foregrounds.

• "Type 3" product: no Type 3 product (as defined in 2013) has been produced for the

2015 release. Instead, this has been is superseded by a high-resolution CO(2-1) map (=7.5') produced by the Commander component separation pipeline. Note that low resolution (=1°) CO maps of the three lines have also been produced using Commander. See section 5 of Planck-2015-A10[5] for a complete description.

The 2015 Type 1 and Type 2 CO maps have been produced using the same procedure as for the 2013 results. Very similar to their 2013 counterparts, the 2015 maps benefit from an increased S/N due to the use of the full, rather than nominal, mission data.  Characteristics of the released maps are the following. We provide maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in KRJ km s-1 units. A conversion factor from this unit to the native unit of maps (K) is provided in the header of the data files and in the . Four maps are given per transition and per type:

• the signal map;
• the standard deviation map (same units as the signal);
• a null-test noise map (same units as the signal) with similar statistical properties, which is made out of half the difference of half-ring maps;
• a mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.

All products of a given type belong to a single file. Type 1 products have the native resolution. i.e.. approximately 10, 5, and 5 arcmin for the CO 1-0, 2-1, and 3-2 transitions, respectively. Type 2 products have a 15 arcmin resolution.  We refer the reader to section 5 of Planck-2015-A10[5] for a description and characteristics of the Commander CO products.

## Map validation

Several validations of maps are described in Planck-2015-A07[6] and in Planck-2015-A08[1].

Further checks are presented in the likelihood, parameters, component separation, and Commander papers.

## References

1. Planck 2015 results. VIII. High Frequency Instrument data processing: Calibration and maps, Planck Collaboration, 2016, A&A, 594, A8.
2. Planck 2013 results. VI. High Frequency Instrument Data Processing, Planck Collaboration, 2014, A&A, 571, A6
3. Planck 2013 results. VIII. HFI photometric calibration and Map-making, Planck Collaboration, 2014, A&A, 571, A8
4. Planck 2013 results. XIII. Galactic CO emission, Planck Collaboration, 2014, A&A, 571, A13
5. Planck 2015 results. X. Diffuse component separation: Foreground maps, Planck Collaboration, 2016, A&A, 594, A10.
6. Planck 2015 results. VII. High Frequency Instrument data processing: Time-ordered information and beam processing, Planck Collaboration, 2016, A&A, 594, A7.