From top-hat masking to smooth transitions: P-filter and its application to polarized microwave sky maps

Abstract

In CMB science, the simplest idea to remove a contaminated sky region is to multiply the sky map with a mask that is 0 for the contaminated region and 1 elsewhere, which is also called a top-hat masking. Although it is easy to use, such top-hat masking is known to suffer from various leakage problems. Therefore, we want to extend the top-hat masking to a series of semi-analytic functions called the P-filters. Most importantly, the P-filters can seamlessly realize the core idea of masking in CMB science, and, meanwhile, guarantee continuity up to the first derivative everywhere. The P-filters can significantly reduce many leakage problems without additional cost, including the leakages due to low-, high-, and band-pass filtering, and the E-to-E, B-to-B, B-to-E, and E-to-B leakages. The workings of the P-filter are illustrated by using the WMAP and Planck polarization sky maps. By comparison to the corresponding WMAP/Planck masks, we show that the P-filter performs much better than top-hat masking, and meanwhile, has the potential to supersede the principal idea of masking in CMB science. Compared to mask apodization, the P-filter is ``outward'', that tends to make proper use of the region that was marked as 0; whereas apodization is ``inward'', that always kills more signal in the region marked as 1.

arXiv comment19 pages and 11 figures

References in corpus (17)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Planck 2013 results. I. Overview of products and scientific results
• An All-Sky Analysis of Polarization in the Microwave Background
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission
• A Joint Analysis of BICEP2/Keck Array and Planck Data
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Planck 2015 results. IX. Diffuse component separation: CMB maps
• Pseudo-$C_{\ell }$ estimators which do not mix E and B modes
• A needlet ILC analysis of WMAP 7-year data: estimation of CMB temperature map and power spectrum
• Polarised radio filaments outside the Galactic plane
• CMB Polarization Experiments
• Separating E and B types of polarization on an incomplete sky
• CMB E/B decomposition of incomplete sky: a pixel space approach
• Pure E and B polarization maps via Wiener filtering
• E and B families of the Stokes parameters in the polarized synchrotron and thermal dust foregrounds
• Optimal and fast E/B separation with a dual messenger field
• Fingerprint of Galactic Loop I on polarized microwave foregrounds

Cited by in corpus (1)

• Statistics of non-polarized points in the CMB polarization maps