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Register a new userBayesian component separation and CMB estimation for the 5-year WMAP temperature data
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Clive Dickinson PhD
Publication date
2009
fields
Physics
and research's language is
English
Authors
C. Dickinson
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A well-tested and validated Gibbs sampling code, that performs component separation and CMB power spectrum estimation, was applied to the {it WMAP} 5-yr data. Using a simple model consisting of CMB, noise, monopoles and dipoles, a ``per pixel low-frequency power-law (fitting for both amplitude and spectral index), and a thermal dust template with fixed spectral index, we found that the low-$ell$ ($ell < 50$) CMB power spectrum is in good agreement with the published {it WMAP}5 results. Residual monopoles and dipoles were found to be small ($lesssim 3 mu$K) or negligible in the 5-yr data. We comprehensively tested the assumptions that were made about the foregrounds (e.g. dust spectral index, power-law spectral index prior, templates), and found that the CMB power spectrum was insensitive to these choices. We confirm the asymmetry of power between the north and south ecliptic hemispheres, which appears to be robust against foreground modeling. The map of low frequency spectral indices indicates a steeper spectrum on average ($beta=-2.97pm0.21$) relative to those found at low ($sim$GHz) frequencies.
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We develop a new Bayesian method for estimating white noise levels in CMB sky maps, and apply this algorithm to the 5-year WMAP data. We assume that the amplitude of the noise RMS is scaled by a constant value, alpha, relative to a pre-specified noise level. We then derive the corresponding conditional density, P(alpha | s, Cl, d), which is subsequently integrated into a general CMB Gibbs sampler. We first verify our code by analyzing simulated data sets, and then apply the framework to the WMAP data. For the foreground-reduced 5-year WMAP sky maps and the nominal noise levels initially provided in the 5-year data release, we find that the posterior means typically range between alpha=1.005 +- 0.001 and alpha=1.010 +- 0.001 depending on differencing assembly, indicating that the noise level of these maps are biased low by 0.5-1.0%. The same problem is not observed for the uncorrected WMAP sky maps. After the preprint version of this letter appeared on astro-ph., the WMAP team has corrected the values presented on their web page, noting that the initially provided values were in fact estimates from the 3-year data release, not from the 5-year estimates. However, internally in their 5-year analysis the correct noise values were used, and no cosmological results are therefore compromised by this error. Thus, our method has already been demonstrated in practice to be both useful and accurate.
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