Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Asymmetric Beams and CMB Statistical Anisotropy

Duncan Hanson, Antony Lewis, Anthony Challinor

TL;DR

This paper develops a harmonic-space framework to quantify how asymmetric instrumental beams induce statistical anisotropy in CMB maps and how such beam-induced covariance biases can be separated from primordial anisotropy using optimal quadratic maximum-likelihood estimators. By decomposing beam effects into spin-weighted components and expressing the anisotropic covariance through spin multipoles and bipolar harmonics, the authors construct estimators that can reconstruct the scan-strategy–weighted beam modes while correcting for mean-field biases. Applying the method to the WMAP quadrupolar modulation, they show that beam asymmetries can fully account for the observed anomaly, yielding tight limits on any residual primordial quadrupole modulation. The results provide a robust, generalizable toolkit for Planck and future polarization analyses, where accurate beam modeling and mean-field subtraction are essential for reliable anisotropy measurements.

Abstract

Beam asymmetries result in statistically-anisotropic cosmic microwave background (CMB) maps. Typically, they are studied for their effects on the CMB power spectrum, however they more closely mimic anisotropic effects such as gravitational lensing and primordial power asymmetry. We discuss tools for studying the effects of beam asymmetry on general quadratic estimators of anisotropy, analytically for full-sky observations as well as in the analysis of realistic data. We demonstrate this methodology in application to a recently-detected 9 sigma quadrupolar modulation effect in the WMAP data, showing that beams provide a complete and sufficient explanation for the anomaly.

Asymmetric Beams and CMB Statistical Anisotropy

TL;DR

This paper develops a harmonic-space framework to quantify how asymmetric instrumental beams induce statistical anisotropy in CMB maps and how such beam-induced covariance biases can be separated from primordial anisotropy using optimal quadratic maximum-likelihood estimators. By decomposing beam effects into spin-weighted components and expressing the anisotropic covariance through spin multipoles and bipolar harmonics, the authors construct estimators that can reconstruct the scan-strategy–weighted beam modes while correcting for mean-field biases. Applying the method to the WMAP quadrupolar modulation, they show that beam asymmetries can fully account for the observed anomaly, yielding tight limits on any residual primordial quadrupole modulation. The results provide a robust, generalizable toolkit for Planck and future polarization analyses, where accurate beam modeling and mean-field subtraction are essential for reliable anisotropy measurements.

Abstract

Beam asymmetries result in statistically-anisotropic cosmic microwave background (CMB) maps. Typically, they are studied for their effects on the CMB power spectrum, however they more closely mimic anisotropic effects such as gravitational lensing and primordial power asymmetry. We discuss tools for studying the effects of beam asymmetry on general quadratic estimators of anisotropy, analytically for full-sky observations as well as in the analysis of realistic data. We demonstrate this methodology in application to a recently-detected 9 sigma quadrupolar modulation effect in the WMAP data, showing that beams provide a complete and sufficient explanation for the anomaly.

Paper Structure

This paper contains 8 sections, 35 equations, 1 figure, 1 table.

Table of Contents

  1. Model
  2. Covariance
  3. Anisotropy Estimators
  4. Case Study: Primordial Power Asymmetry
  5. Conclusions
  6. Acknowledgements
  7. Toy Scan Strategy
  8. Beam asymmetries and power spectra

Figures (1)

  • Figure 1: Significance of the observed WMAP primordial-power-modulation quadrupole, with correction for beams, for the WMAP $V$-band foreground-reduced data, limited to $l_{\rm max}=1000$. This is essentially a beam-corrected version of Fig. 9 in Hanson:2009gu. The gray histograms are from the 500 simulations which are used to determine the estimator Fisher matrix and mean-field. The dashed vertical lines are for the observed data. Detailed interpretation is provided in the text.