Spatially Inhomogeneous Correlation Estimator for Temperature and Polarisation

by
Anthony Challinor (Astrophysics Group, Cavendish Lab, Cambridge, UK),
Gayoung Chon (LBL, Berkeley, USA),
Stéphane Colombi (Institut d'Astrophysique de Paris, France),
Eric Hivon (IPAC/Caltech, USA & IAP),
Simon Prunet (Univ. of Toronto, Canada & IAP),
István Szapudi (Institute for Astronomy, Hawaii, USA).

PolSpice (aka Spice) is a tool to statistically analyze Cosmic Microwave Background (CMB) data, as well as any other diffuse data pixelized on the sphere.

This Fortran90 program measures the 2 point auto (or cross-) correlation functions w(θ) and the angular auto- (or cross-) power spectra C(l) from one or (two) sky map(s) of Stokes parameters (intensity I and linear polarisation Q and U). It is based on the fast Spherical Harmonic Transforms allowed by isolatitude pixelisations such as Healpix [for N_pix pixels over the whole sky, and a C(l) computed up to l=l_max, PolSpice complexity scales like N_pix^1/2 l_max² instead of N_pix l_max²]. It corrects for the effects of the masks and can deal with inhomogeneous weights given to the pixels of the map. In the case of polarised data, the mixing of the E and B modes due to the cut sky and pixel weights can be corrected for to provide an unbiased estimate of the "magnetic" (B) component of the polarisation power spectrum. Most of the code is parallelized for shared memory (SMP) architecture using OpenMP.

 Main input files are the Healpix sky maps to analyse, and the pixel masks and weights if any. Those can be either in FITS binary format or in Planck internal I/O format/DMC database objects .
 Main input parameters are file names, and various options such as gaussian beam window correction, pixel window correction, noise substraction, angular range of the correlation functions and apodization angle.
 Output w(θ) and C(l) are plain text or FITS files or DMC objects.

Extra features:
 The maps can be either in RING or NESTED scheme. They can be in full-sky or cut-sky format.
 In the case of cross-correlation, the 2 maps being analyzed can have been observed with different beams, but should have the same pixel size and same coordinates; the mask and weighting scheme applied to each map can be different but should spatially overlap. A different pixel mask can be applied to the intensity and polarization components of the map(s).
 The best fit monopole and dipole can be regressed out of unmasked pixels before the analysis (since version 02-05-08)

More details on the theory can be found in
 Chon et al, 2004, MNRAS 350, 914
 Szapudi, Prunet & Colombi, 2001, ApJ 548, 115

Examples of PolSpice application to CMB data analysis:
 BICEP 2yr data analysis: paper (Chiang et al, 2009; arXiv:0906.1181), data product
 CMBPol Mission Concept Study: Prospects for polarized foreground removal (Dunkley et al, 2008; arXiv:0811.3915)

requirements for installation:
 Fortran90 compiler (some are available for free for Unix, Linux, MacOSX and Windows, such as gfortran and g95)
 recent Healpix Fortran90 library (2.10 or more)
 cfitsio library (also required by Healpix)