# Specially processed maps

## Overview

## Lensing map

### Description

Here we present the minimum-variance (MV) lens reconstruction which forms the basis for the main results of P12_Lensing. 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], <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). RING format. It is obtained by convolving the lensing potential estimate $\hat{\phi}$ with the lensing response function $R_L^{\phi\phi}$. This map has been band-limited between multipoles $10 \le L \le 2048$.
- MASK
- This is a NSIDE = 2048 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). 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 $R_L^{\phi\phi}$.
- NLPP
- This column contains a sky-averaged estimate of the noise power spectrum of PHIBAR, $N_L^{\phi\phi}$. The noise is highly coloured. There is a weak dependence of the noise power spectrum with the local noise level of the map, discussed in Appendix A of P12_Lensing. Note that the noise power spectrum estimate here is not sufficiently accurate for a power spectrum analysis.

### Production process

The construction PHIBAR, RLPP and NLPP are described in detail in Sec. 2.1 of P12_Lensing. The response function $R_L^{\phi\phi}$ 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 sky maps.

### File names and format

A single file named

*COM_CompMap_Lensing_2048_R1.10.fits*

with two BINTABLE extensions containing the items described below.

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 |