# Specially processed maps

## Contents

## Overview[edit]

## Lensing map[edit]

### Description[edit]

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 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 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[edit]

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 CMB 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 CMB temperature map from which it is derived, and therefore more useful for cross-correlation studies.

### Inputs[edit]

This product is built from the 143 and 217 GHz Planck sky maps.

### File names and format[edit]

A single file named *COM_CompMap_Lensing_2048_R1.10.fits* with two BINTABLE extensions containing the items described above.

Column Name | Data Type | Units | Description |
---|---|---|---|

1. EXTNAME = 'LENS-MAP' : Data columns | |||

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

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

Keywords | |||

PIXTYPE | HEALPIX | ||

COORDSYS | GALACTIC | Coordinate system | |

ORDERING | NESTED | Healpix ordering | |

NSIDE | 2048 | Healpix Nside | |

FIRSTPIX | 0 | ||

LASTPIX | 50331647 | ||

2. EXTNAME = 'TransFun' : Data columns | |||

RLPP | Real*4 | none | Response function (see above) |

NLPP | Real*4 | none | Sky-averaged noise power spectrum estimate (see above) |

Keywords | |||

L_MIN | 0 | ||

L_MAX | 2048 |

(Hierarchical Equal Area isoLatitude Pixelation of a sphere, <ref name="Template:Gorski2005">**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).

Cosmic Microwave background