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Register a new userPhase analysis of the 1-year WMAP data and its application for the CMB foreground separation
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We present a new method based on phase analysis for the Galaxy and foreground component separation from the cosmic microwave background (CMB) signal. This method is based on a prevailing assumption that the phases of the underlying CMB signal should have no or little correlation with those of the foregrounds. This method takes into consideration all the phases of each multipole mode (l <= 50, -l <= m <=l) from the whole sky without galactic cut, masks or any dissection of the whole sky into disjoint regions. We use cross correlation of the phases to illustrate that significant correlations of the foregrounds manifest themselves in the phases of the WMAP 5 frequency bands, which are used for separation of the CMB from the signals. Our final phase-cleaned CMB map has the angular power spectrum in agreement with both the WMAP result and that from Tegmark, de Oliveira-Costa and Hamilton (TOH), the phases of our derived CMB signal, however, are slightly different from those of the WMAP Internal Linear Combination map and the TOH map.
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We present a detailed analysis on the phases of the WMAP foregrounds (synchrotron, free-free and dust emission) of the WMAP K-W bands in order to estimate the significance of the variation of the spectral indices at different components. We first extract the spectral-index varying signals by assuming that the invariant part among different frequency bands have 100% cross-correlation of phases. We then use the minimization of variance, which is normally used for extracting the CMB signals, to extract the frequency independent signals. Such a common signal in each foreground component could play a significant role for any kind of component separation methods, because the methods cannot discriminate frequency independent foregrounds and CMB.
We present an analysis of the foreground emission present in the WMAP 3-year data as determined by the method of Independent Component Analysis. We derived coupling coefficients between the WMAP data and foreground templates which are then used to infer the spectral behaviour for three foreground components -- synchrotron, anomalous dust-correlated emission and free-free. For the first two components, we find values consistent with previous results although slightly steeper. We confirm the inconsistency in the scaling between the Ha template and free-free emission at K- and Ka-bands where an electron temperature of ~ 4000 K is indicated. We also see evidence of significantly flatter spectral behaviour to higher frequencies than expected theoretically and previously noted by Dobler et al.(2008a), but only when analysing the Kp2 sky coverage. We further apply FASTICA iteratively, using data pre-cleaned using foreground templates scaled to the WMAP frequencies by coupling coefficients determined by a prior FASTICA analysis. This multi-frequency analysis allows us to determine the presence of residual foreground emission not traced by the templates. We confirm the existence of a component spatially distributed along the Galactic plane and particularly enhanced near the center (the WMAP haze). This emission is less extended when using the WMAP K-Ka data as the synchrotron template confirming that it can be considered a better template for foreground cleaning of the WMAP data. However its use complicates the physical interpretation of the nature of the foreground emission and residuals. since it contains a mixture of several, physically distinct emission mechanisms.
Using a Gibbs sampling algorithm for joint CMB estimation and component separation, we compute the large-scale CMB and foreground posteriors of the 3-yr WMAP temperature data. Our parametric data model includes the cosmological CMB signal and instrumental noise, a single power law foreground component with free amplitude and spectral index for each pixel, a thermal dust template with a single free overall amplitude, and free monopoles and dipoles at each frequency. This simple model yields a surprisingly good fit to the data over the full frequency range from 23 to 94 GHz. We obtain a new estimate of the CMB sky signal and power spectrum, and a new foreground model, including a measurement of the effective spectral index over the high-latitude sky. A particularly significant result is the detection of a common spurious offset in all frequency bands of ~ -13muK, as well as a dipole in the V-band data. Correcting for these is essential when determining the effective spectral index of the foregrounds. We find that our new foreground model is in good agreement with template-based model presented by the WMAP team, but not with their MEM reconstruction. We believe the latter may be at least partially compromised by the residual offsets and dipoles in the data. Fortunately, the CMB power spectrum is not significantly affected by these issues, as our new spectrum is in excellent agreement with that published by the WMAP team. The corresponding cosmological parameters are also virtually unchanged.
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.
We perform a blind multi-component analysis of the WMAP 1 year foreground cleaned maps using SMICA (Spectral Matching Independent Component Analysis). We provide a new estimate of the CMB power spectrum as well as the amplitude of the CMB anisotropies across frequency channels. We show that the CMB anisotropies are compatible with temperature fluctuations as expected from the standard paradigm. The analysis also allows us to identify and separate a weak residual galactic emission present significantly in the Q-band outside of the Kp2 mask limits, and mainly concentrated at low galactic latitudes. We produce a map of this residual component by Wiener filtering using estimated parameters. The level of contamination of CMB data by this component is compatible with the WMAP team estimation of foreground residual contamination. In addition, the multi-component analysis allows us to estimate jointly the power spectrum of unresolved point source emission.
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