# Additional maps

## Overview

This section describes products that require special processing. Only one such product is available at this time; this section will be expanded with time as more products are added.

## Lensing map

### Description

Here we present the minimum-variance (MV) lens reconstruction which forms the basis for the main results of Planck-2013-XVII^{[1]}. This map is produced using a combination of the 143 and 217 GHz Planck maps on approximately 70% of the sky, and is the same map on which the Planck lensing likelihood is based.

We distribute:

- PHIBAR
- A (transfer-function convolved) map of the lensing potential, in NSIDE 2048 HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). RING format. It is obtained by convolving the lensing potential estimate [math]\hat{\phi}[/math] with the lensing response function [math]R_L^{\phi\phi}[/math]. This map has been band-limited between multipoles [math]10 \le L \le 2048[/math].
- MASK
- This is a NSIDE = 2048 HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). map, containing the analysis mask used in the lens reconstruction.
*Note*: the lensing map PHIBAR may take small but non-zero values inside the masked regions because it has been bandlimited. - RLPP
- This column contains the response function [math]R_L^{\phi\phi}[/math].
- NLPP
- This column contains a sky-averaged estimate of the noise power spectrum of PHIBAR, [math]N_L^{\phi\phi}[/math]. The noise is highly coloured. There is a dependence of the noise power spectrum on the local noise level of the map, discussed in Appendix A of Planck-2013-XVII
^{[1]}. Note that the noise power spectrum estimate here is not sufficiently accurate for a power spectrum analysis.

Also, the table below gives the lensing curl-mode power spectrum data used to produce Figure A2 of Planck-2013-XVII^{[1]}:

[math]L[/math]_{min} |
[math]L[/math]_{max} |
[math]{\hat{C}_L}^{\psi\psi} (L(L+1))^2/(2\pi)[/math] | [math] std({\hat{C}_L}^{\psi\psi}) (L(L+1))^2 /(2\pi)[/math] |
---|---|---|---|

2 | 7 | -13.6379 | 15.3409 |

8 | 20 | 6.0184 | 4.8881 |

21 | 39 | -1.0675 | 3.0940 |

40 | 65 | 0.6135 | 1.8474 |

66 | 100 | 1.5030 | 1.2696 |

101 | 144 | 1.3760 | 0.9950 |

145 | 198 | -1.2289 | 0.8286 |

199 | 263 | 1.1910 | 0.7001 |

264 | 338 | -0.6567 | 0.6197 |

339 | 425 | -0.8201 | 0.5235 |

426 | 525 | -0.7581 | 0.4850 |

526 | 637 | -0.3201 | 0.5134 |

638 | 762 | -0.1589 | 0.4073 |

763 | 901 | -0.6451 | 0.4044 |

902 | 1054 | 0.4910 | 0.3718 |

1055 | 1221 | -0.2186 | 0.3702 |

1222 | 1404 | -0.3295 | 0.4146 |

1405 | 1602 | -0.3647 | 0.4703 |

1603 | 1816 | -0.1060 | 0.5904 |

1817 | 2020 | -0.7887 | 0.8507 |

### Production process

The construction PHIBAR, RLPP and NLPP are described in detail in Sec. 2.1 of Planck-2013-XVII^{[1]}. The response function [math]R_L^{\phi\phi}[/math] here is analogous to the the beam transfer function in a CMBCosmic Microwave background temperature or polarization map. We have chosen to distribute this transfer-function convolved map rather than the normalized lens reconstruction as it is a significantly more localized function of the CMBCosmic Microwave background temperature map from which it is derived, and therefore more useful for cross-correlation studies.

### Inputs

This product is built from the 143 and 217 GHz Planck frequency maps, with 857GHz projected out as a dust template.
The analysis mask is constructed from a combination of thresholding in the 857GHz map (to remove the regions which are most contaminated by Galactic dust) and the Type2 CO map (to reduce contamination from CO lines at 217GHz). This is joined with a compact object mask synthesized from several Planck source catalogues, including the ERCSC, SZ and PCCS . The reconstruction was performed using the fiducial beam window functions B(l) from the HFI RIMO . Details of the procedure used to produce a lensing estimate from these inputs are given in Planck-2013-XVII^{[1]}.

### File names and format

A single file named

with two BINTABLE extensions containing the items described below.

For illustration, we show in the figures below the maps of the Wiener-filtered CMBCosmic Microwave background lensing potential in Galactic coordinates using orthographic projection. The reconstruction was bandpass filtered to [math]L \in [10, 2048][/math]. Note that the lensing reconstruction, while highly statistically significant, is still noise dominated for every individual mode, and is at best [math]S/N \simeq 0.7[/math] around [math]L = 30[/math].

1. EXTNAME = LENS-MAP
| ||||
---|---|---|---|---|

Column Name | Data Type | Units | Description | |

PHIBAR | Real*4 | none | Map of the lensing potential estimate, convolved with RLPP | |

MASK | Int | none | Region over which the lensing potential is reconstructed | |

Keyword | Data Type | Value | Description | |

PIXTYPE | string | HEALPIX | ||

COORDSYS | string | GALACTIC | Coordinate system | |

ORDERING | string | NESTED | Healpix ordering | |

NSIDE | Int*4 | 2048 | Healpix Nside | |

FIRSTPIX | Int*4 | 0 | ||

LASTPIX | Int*4 | 50331647 | ||

2. EXTNAME = TransFun
| ||||

Column Name | Data Type | Units | Description | |

RLPP | Real*4 | none | Response function | |

NLPP | Real*4 | none | Sky-averaged noise power spectrum estimate | |

Keyword | Data Type | Value | Description | |

L_MIN | Int*4 | 0 | First multipole | |

L_MAX | Int*4 | 2048 | Last multipole |

## IRAM Maps of the Crab nebula

Maps of the Crab nebula at 89.189 GHz (HCO+(1-0) transition) in both temperature and polarization, prodouced from observations performed at the IRAM 30m telescope from January 9th to January 12th 2009, are delivered as a tarball of 416 KB in the file

See README in the tarball for full details. These data were used in^{[2]}

## References

- ↑
^{1.0}^{1.1}^{1.2}^{1.3}^{1.4}^{1.5}**Planck 2013 results: Gravitational lensing by large-scale structure**, Planck Collaboration XVII, A&A, in press, (2014). - ↑
**Measurement of the Crab nebula polarization at 90 GHz as a calibrator for CMB experiments**, J. Aumont, L. Conversi, C. Thum, H. Wiesemeyer, E. Falgarone, J. F. Macías-Pérez, F. Piacentini, E. Pointecouteau, N. Ponthieu, J. L. Puget, C. Rosset, J. A. Tauber, M. Tristram, A&A,**514**, A70+, (2010).