CMB power spectrum estimation with non-circular beam and incomplete sky coverage

Abstract

Over the last decade, measurements of the CMB anisotropy has spearheaded the remarkable transition of cosmology into a precision science. However, addressing the systematic effects in the increasingly sensitive, high resolution, `full' sky measurements from different CMB experiments pose a stiff challenge. The analysis techniques must not only be computationally fast to contend with the huge size of the data, but, the higher sensitivity also limits the simplifying assumptions which can then be invoked to achieve the desired speed without compromising the final precision goals. While maximum likelihood is desirable, the enormous computational cost makes the suboptimal method of power spectrum estimation using Pseudo-C_l unavoidable for high resolution data. We provide a (semi)analytic framework to estimate bias in the power spectrum due to the effect of beam non-circularity and non-uniform sky coverage including incomplete/masked sky maps and scan strategy. The approach is perturbative in the distortion of the beam from non-circularity, allowing for rapid computations when the beam is mildly non-circular. We advocate that it is computationally advantageous to employ `soft' azimuthally apodized masks whose spherical harmonic transform die down fast with m. We numerically implement our method for non-rotating beams. We present preliminary estimates of the computational cost to evaluate the bias for the upcoming CMB anisotropy probes l_max~3000, with angular resolution comparable to the Planck surveyor mission. We further show that this implementation and estimate is applicable for rotating beams on equal declination scans and possibly can be extended to simple approximations to other scan strategies.

22 pages, 7 figures. Revised presentation to highlight significance of extended results. Matches version accepted to the MNRAS

References in corpus (39)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• Wilkinson Microwave Anisotropy Probe (WMAP) First Year Observations: TE Polarization
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• Cosmic Microwave Background Anisotropies
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Detection of Polarization in the Cosmic Microwave Background using DASI
• Detection of primordial non-Gaussianity (fNL) in the WMAP 3-year data at above 99.5% confidence
• Myths and Truths Concerning Estimation of Power Spectra
• Measuring Statistical isotropy of the CMB anisotropy
• DASI Three-Year Cosmic Microwave Background Polarization Results
• Cosmological Parameters from the 2003 flight of BOOMERANG
• The Pseudo-$C_l$ method: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
• A measurement of the polarization-temperature angular cross power spectrum of the Cosmic Microwave Background from the 2003 flight of BOOMERANG
• Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background
• CMB temperature and polarisation pseudo-Cl estimators and covariances
• The Age of the Universe and the Cosmological Constant Determined from Cosmic Microwave Background Anisotropy Measurements
• Statistical Isotropy of the Wilkinson Microwave Anisotropy Probe Data: A Bipolar Power Spectrum Analysis
• Testing Global Isotropy of Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Data: Temperature Analysis
• Hybrid Estimation of CMB Polarization Power Spectra
• A blind estimation of the power spectrum of CMB anisotropy from WMAP
• CMB anisotropy power spectrum using linear combinations of WMAP maps
• Fast, exact CMB power spectrum estimation for a certain class of observational strategies
• Statistical Isotropy of CMB Polarization Maps
• Elliptical Beams in CMB Temperature and Polarization Anisotropy Experiments: An Analytic Approach
• Analysis of cosmic microwave background data on an incomplete sky
• Window Function for Non-Circular Beam CMB Anisotropy Experiment
• Harmonic analysis of cosmic microwave background data I: ring reductions and point-source catalogue
• CMB power spectrum estimation using noncircular beams
• Harmonic analysis of cosmic microwave background data II: from ring-sets to the sky
• CMB Tomography: Reconstruction of Adiabatic Primordial Scalar Potential Using Temperature and Polarization Maps
• Fast Power Spectrum Estimation
• CMB Power Spectrum Estimation via Hierarchical Decomposition
• Galactic Foreground Constraints from the Python V Cosmic Microwave Background Anisotropy Data
• Cosmic Microwave Background Anisotropy Measurement From Python V
• Non-Circular beam correction to the CMB power spectrum

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