Accurate estimation of angular power spectra for maps with correlated masks

Abstract

The widely used MASTER approach for angular power spectrum estimation was developed as a fast $C_{\ell }$ estimator on limited regions of the sky. This method expresses the power spectrum of a masked map ("pseudo-$C_{\ell }$") in terms of the power spectrum of the unmasked map (the true $C_{\ell }$) and that of the mask or weight map. However, it is often the case that the map and mask are correlated in some way, such as point source masks used in cosmic microwave background (CMB) analyses, which have nonzero correlation with CMB secondary anisotropy fields and other mm-wave sky signals. In such situations, the MASTER approach gives biased results, as it assumes that the unmasked map and mask have zero correlation. While such effects have been discussed before with regard to specific physical models, here we derive a completely general formalism for any case where the map and mask are correlated. We show that our result ("reMASTERed") reconstructs ensemble-averaged pseudo-$C_{\ell }$ to effectively exact precision, with significant improvements over traditional estimators for cases where the map and mask are correlated. In particular, we obtain an improvement in the mean absolute percent error from 30% with the MASTER result to essentially no error with the reMASTERed result for an integrated Sachs-Wolfe (ISW) field map with a mask built from the thresholded ISW field, and 10% to effectively zero for a Compton-$y$ map combined with an infrared source mask (the latter being directly relevant to actual data analysis). An important consequence of our result is that for maps with correlated masks it is no longer possible to invert a simple equation to obtain the true $C_{\ell }$ from the pseudo-$C_{\ell }$. Instead, our result necessitates the use of forward modeling from theory space into the observable domain of the pseudo-$C_{\ell }$. Our code is publicly available at https://github.com/kmsurrao/reMASTERed.

arXiv comment14+9 pages, 6+6 figures; matches the version accepted for publication in PRD (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.107.083521); code available at at https://github.com/kmsurrao/reMASTERed

References in corpus (52)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Herschel Space Observatory - An ESA facility for far-infrared and submillimetre astronomy
• The Simons Observatory: Science goals and forecasts
• Planck 2018 results. V. CMB power spectra and likelihoods
• Acoustic Signatures in the Primary Microwave Background Bispectrum
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background
• The Herschel Multi-tiered Extragalactic Survey: HerMES
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters
• Cosmology with cosmic shear observations: a review
• A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope
• A unified pseudo-$C_{\ell }$ framework
• How to measure CMB power spectra without losing information
• A Measurement of the Cosmic Microwave Background B-Mode Polarization Power Spectrum at Sub-Degree Scales with POLARBEAR
• Measurements of the E-Mode Polarization and Temperature-E-Mode Correlation of the CMB from SPT-3G 2018 Data
• Myths and Truths Concerning Estimation of Power Spectra
• The shape of primordial non-Gaussianity and the CMB bispectrum
• On the Cluster Physics of Sunyaev-Zel'dovich Surveys II: Deconstructing the Thermal SZ Power Spectrum
• Planck 2015 results. XXI. The integrated Sachs-Wolfe effect
• The Atacama Cosmology Telescope: A Measurement of the Cosmic Microwave Background Power Spectrum at 148 and 218 GHz from the 2008 Southern Survey
• HerMES: Cosmic Infrared Background Anisotropies and the Clustering of Dusty Star-Forming Galaxies
• Planck 2013 results. XVIII. Gravitational lensing-infrared background correlation
• Xspect, estimation of the angular power spectrum by computing cross-power spectra with analytical error bars
• Planck 2015 results. XXIII. The thermal Sunyaev-Zeldovich effect--cosmic infrared background correlation
• On the Origin of Near-Infrared Extragalactic Background Light Anisotropy
• The Websky Extragalactic CMB Simulations
• General CMB and Primordial Trispectrum Estimation
• The mass-Peak Patch algorithm for fast generation of deep all-sky dark matter halo catalogues and its N-Body validation
• Improved Models for Cosmic Infrared Background Anisotropies: New Constraints on the IR Galaxy Population
• Secondary anisotropies of the CMB
• Cosmology from the Thermal Sunyaev-Zel'dovich Power Spectrum: Primordial non-Gaussianity and Massive Neutrinos
• The integrated Sachs-Wolfe Effect -- Large Scale Structure Correlation
• A WISE measurement of the ISW effect
• Associating Fast Radio Bursts with Their Host Galaxies
• Cosmology Without Windows: Quadratic Estimators for the Galaxy Power Spectrum
• Modelling the correlation between the thermal Sunyaev Zel'dovich effect and the cosmic infrared background
• Cosmic shear power spectra in practice
• Cosmology Without Window Functions: Cubic Estimators for the Galaxy Bispectrum
• The Cosmic Thermal History Probed by Sunyaev-Zeldovich Effect Tomography
• Sharpening the Precision of the Sunyaev-Zel'dovich Power Spectrum
• The Atacama Cosmology Telescope: measuring radio galaxy bias through cross-correlation with lensing
• Integrated Sachs Wolfe Effect and Rees Sciama Effect
• Unbiased pseudo-Cl power spectrum estimation with mode projection
• The Atacama Cosmology Telescope: A Measurement of the Thermal Sunyaev-Zel'dovich Effect Using the Skewness of the CMB Temperature Distribution
• Radio Point Sources and the Thermal SZ Power Spectrum
• The Integrated Sachs Wolfe effect: unWISE and Planck constraints on Dynamical Dark Energy
• Measurement of the integrated Sachs-Wolfe effect using the AllWISE data release
• CMB lensing reconstruction biases from masking extragalactic sources
• Detection of WHIM in the Planck data using Stack First approach
• Impact of radio sources and cosmic infrared background on thermal Sunyaev-Zel'dovich - gravitational lensing cross correlation
• Lensed CMB power spectrum biases from masking extragalactic sources

Cited by in corpus (4)

• The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters
• Selecting samples of galaxies with fewer Fingers-of-God
• The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra
• On the impact of the galaxy window function on cosmological parameter estimation