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      CMB multipole measurements in the presence of foregrounds

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          Abstract

          Most analysis of Cosmic Microwave Background spherical harmonic coefficients a_lm has focused on estimating the power spectrum C_l=<|a_lm|^2> rather than the coefficients themselves. We present a minimum-variance method for measuring a_lm given anisotropic noise, incomplete sky coverage and foreground contamination, and apply it to the WMAP data. Our method is shown to constitute lossless data compression in the sense that the widely used quadratic estimators of the power spectrum C_l can be computed directly from our a_lm-estimators. As the Galactic cut is increased, the error bars Delta-a_lm on low multipoles go from being dominated by foregrounds to being dominated by sample variance from other multipoles, with the intervening minimum defining the optimal cut. Applying our method to the WMAP quadrupole and octopole, we find that their previously reported "axis of evil" alignment appears to be rather robust to Galactic cut and foreground contamination.

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          Radical Compression of Cosmic Microwave Background Data

          Powerful constraints on theories can already be inferred from existing CMB anisotropy data. But performing an exact analysis of available data is a complicated task and may become prohibitively so for upcoming experiments with \gtrsim10^4 pixels. We present a method for approximating the likelihood that takes power spectrum constraints, e.g., ``band-powers'', as inputs. We identify a bias which results if one approximates the probability distribution of the band-power errors as Gaussian---as is the usual practice. This bias can be eliminated by using specific approximations to the non-Gaussian form for the distribution specified by three parameters (the maximum likelihood or mode, curvature or variance, and a third quantity). We advocate the calculation of this third quantity by experimenters, to be presented along with the maximum-likelihood band-power and variance. We use this non-Gaussian form to estimate the power spectrum of the CMB in eleven bands from multipole moment ell = 2 (the quadrupole) to ell=3000 from all published band-power data. We investigate the robustness of our power spectrum estimate to changes in these approximations as well as to selective editing of the data.
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            Foregrounds and Forecasts for the Cosmic Microwave Background

            One of the main challenges facing upcoming CMB experiments will be to distinguish the cosmological signal from foreground contamination. We present a comprehensive treatment of this problem and study how foregrounds degrade the accuracy with which the Boomerang, MAP and Planck experiments can measure cosmological parameters. Our foreground model includes not only the normalization, frequency dependence and scale dependence for each physical component, but also variations in frequency dependence across the sky. When estimating how accurately cosmological parameter can be measured, we include the important complication that foreground model parameters (we use about 500) must be simultaneously measured from the data as well. Our results are quite encouraging: despite all these complications, precision measurements of most cosmological parameters are degraded by less than a factor of 2 for our main foreground model and by less than a factor of 5 in our most pessimistic scenario. Parameters measured though large-angle polarization signals suffer more degradation: up to 5 in the main model and 25 in the pessimistic case. The foregrounds that are potentially most damaging and therefore most in need of further study are vibrating dust emission and point sources, especially those in the radio frequencies. It is well-known that E and B polarization contain valuable information about reionization and gravity waves, respectively. However, the cross-correlation between polarized and unpolarized foregrounds also deserves further study, as we find that it carries the bulk of the polarization information about most other cosmological parameters.
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              A method for subtracting foregrounds from multi-frequency CMB sky maps

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              An improved method for subtracting contaminants from Cosmic Microwave Background (CMB) sky maps is presented, and used to estimate how well future experiments will be able to recover the primordial CMB fluctuations. We find that the naive method of subtracting foregrounds (such as dust emission, synchrotron radiation, free-free-emission, unresolved point sources, etc) on a pixel by pixel basis can be improved by more than an order of magnitude by taking advantage of the correlation of the emission in neighboring pixels. The optimal multi-frequency subtraction method improves on simple pixel-by-pixel subtraction both by taking noise-levels into account, and by exploiting the fact that most contaminants have angular power spectra that differ substantially from that of the CMB. The results are natural to visualize in the two-dimensional plane with axes defined by multipole l and frequency v. We present a brief overview of the geography of this plane, showing the regions probed by various experiments and where we expect contaminants to dominate. We illustrate the method by estimating how well the proposed ESA COBRAS/SAMBA mission will be able to recover the CMB fluctuations against contaminating foregrounds.
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                Author and article information

                Journal
                14 March 2006
                2006-05-10
                Article
                10.1103/PhysRevD.74.023005
                astro-ph/0603369
                dd5b9fa8-0b80-45b5-9282-542973c304b0
                History
                Custom metadata
                Phys.Rev.D74:023005,2006
                3-year WMAP results added, TOH foreground-cleaned 3-year map available at http://space.mit.edu/home/tegmark/wmap.html . 15 PRD pages, 7 figs. More multipoles available electronically from the authors on request
                astro-ph

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