MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets

Abstract

We describe a fast and accurate method for estimation of the cosmic microwave background (CMB) anisotropy angular power spectrum --- Monte Carlo Apodised Spherical Transform EstimatoR. Originally devised for use in the interpretation of the Boomerang experimental data, MASTER is both a computationally efficient method suitable for use with the currently available CMB data sets (already large in size, despite covering small fractions of the sky, and affected by inhomogeneous and correlated noise), and a very promising application for the analysis of very large future CMB satellite mission products.

Figures (2)

• Figure 1: Simulation of the Boom-LDB experiment and application of MASTER to extract the CMB angular power spectrum. The oval contour on the maps shows the ellipse (distorted by projection) within which the power spectrum is estimated (${f_{\rm sky}}=1.8\%$ of the sky). Top left panel: A random realisation of the CMB sky from the theoretical model described by the power spectrum shown in the top right panel (red line). Middle left panel: A noiseless map of the same region of the sky made from the TOD with actual Boom-LDB pointing and processed with the 100 mHz high-pass filter (see text). Bottom left panel: the difference between the two CMB sky maps shown above, which shows the component of the sky signal lost due to the combination of Boomerang scanning and data processing. Middle right panel: A simulation of the same Boomerang CMB sky map with the instrumental noise included. Bottom right panel: Integration time per pixel for the actual scanning of the Boom-LDB channel B150A; the average integration time is about 500s/Deg$^2$. Top right panel: The input power spectrum smoothed by the beam and pixel window function (red line); The average angular power spectrum of the instrumental noise (black line); The pseudo $C_\ell$-s directly measured on the sky map shown in the middle right panel and divided by ${f_{\rm sky}}$ (orange line); The binned MASTER estimate of the full sky power spectrum after removal of noise contribution and correction of the effect of the high pass filtering and mode-mode coupling (blue histogram).
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