3,965 research outputs found
Marginal distributions for cosmic variance limited CMB polarization data
We provide computationally convenient expressions for all marginal
distributions of the polarization CMB power spectrum distribution
P(C_l|sigma_l), where C_l = {C_l^TT, C_l^TE, C_l^EE, C_l^BB} denotes the set of
ensemble averaged polarization CMB power spectra, and sigma_l = {sigma_l^TT,
sigma_l^TE, sigma_l^EE, sigma_l^BB} the set of the realization specific
polarization CMB power spectra. This distribution describes the CMB power
spectrum posterior for cosmic variance limited data. The expressions derived
here are general, and may be useful in a wide range of applications. Two
specific applications are described in this paper. First, we employ the derived
distributions within the CMB Gibbs sampling framework, and demonstrate a new
conditional CMB power spectrum sampling algorithm that allows for different
binning schemes for each power spectrum. This is useful because most CMB
experiments have very different signal-to-noise ratios for temperature and
polarization. Second, we provide new Blackwell-Rao estimators for each of the
marginal polarization distributions, which are relevant to power spectrum and
likelihood estimation. Because these estimators represent marginals, they are
not affected by the exponential behaviour of the corresponding joint
expression, but converge quickly.Comment: 8 pages, 3 figures; minor adjustment, accepted for publication in
ApJ
The two-and three-point correlation functions of the polarized five-year WMAP sky maps
We present the two- and three-point real space correlation functions of the
five-year WMAP sky maps, and compare the observed functions to simulated LCDM
concordance model ensembles. In agreement with previously published results, we
find that the temperature correlation functions are consistent with
expectations. However, the pure polarization correlation functions are
acceptable only for the 33GHz band map; the 41, 61, and 94 GHz band correlation
functions all exhibit significant large-scale excess structures. Further, these
excess structures very closely match the correlation functions of the two
(synchrotron and dust) foreground templates used to correct the WMAP data for
galactic contamination, with a cross-correlation statistically significant at
the 2sigma-3sigma confidence level. The correlation is slightly stronger with
respect to the thermal dust template than with the synchrotron template.Comment: 10 pages, 5 figures, published in ApJ. v2: New title, minor changes
to appendix, and fixed some typos. v3: Matches version published in Ap
Point-Source Power in 3 Year Wilkinson Microwave Anisotropy Probe Data
Using a set of multifrequency cross spectra computed from the 3 year WMAP sky maps, we fit for the unresolved point-source contribution. For a white-noise power spectrum, we find a Q-band amplitude of A = 0.011 ± 0.001 μK^2 sr (antenna temperature), significantly smaller than the value of 0.017 ± 0.002 μK^2 sr used to correct the spectra in the WMAP release. Modifying the point-source correction in this way largely resolves the discrepancy that Eriksen et al. found between the WMAP V- and W-band power spectra. Correcting the co-added WMAP spectrum for both the low-l power excess due to a suboptimal likelihood approximation—also reported by Eriksen et al.—and the high-l power deficit due to oversubtracted point sources—presented in this Letter—we find that the net effect in terms of cosmological parameters is an ~0.7 σ shift in n_s to larger values. For the combination of WMAP, BOOMERANG, and ACBAR data, we find ns = 0.969 ± 0.016, lowering the significance of n_s ≠ 1 from ~2.7 σ to ~2.0 σ
A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data
We present a new Monte Carlo Markov Chain algorithm for CMB analysis in the
low signal-to-noise regime. This method builds on and complements the
previously described CMB Gibbs sampler, and effectively solves the low
signal-to-noise inefficiency problem of the direct Gibbs sampler. The new
algorithm is a simple Metropolis-Hastings sampler with a general proposal rule
for the power spectrum, C_l, followed by a particular deterministic rescaling
operation of the sky signal. The acceptance probability for this joint move
depends on the sky map only through the difference of chi-squared between the
original and proposed sky sample, which is close to unity in the low
signal-to-noise regime. The algorithm is completed by alternating this move
with a standard Gibbs move. Together, these two proposals constitute a
computationally efficient algorithm for mapping out the full joint CMB
posterior, both in the high and low signal-to-noise regimes.Comment: Submitted to Ap
Spatial variations in the spectral index of polarized synchrotron emission in the 9 yr WMAP sky maps
We estimate the spectral index, beta, of polarized synchrotron emission as
observed in the 9 yr WMAP sky maps using two methods, linear regression ("T-T
plot") and maximum likelihood. We partition the sky into 24 disjoint sky
regions, and evaluate the spectral index for all polarization angles between 0
deg and 85 deg in steps of 5. Averaging over polarization angles, we derive a
mean spectral index of beta_all-sky=-2.99+-0.01 in the frequency range of 23-33
GHz. We find that the synchrotron spectral index steepens by 0.14 from low to
high Galactic latitudes, in agreement with previous studies, with mean spectral
indices of beta_plane=-2.98+-0.01 and beta_high-lat=-3.12+-0.04. In addition,
we find a significant longitudinal variation along the Galactic plane with a
steeper spectral index toward the Galactic center and anticenter than toward
the Galactic spiral arms. This can be well modeled by an offset sinusoidal,
beta(l)=-2.85+0.17sin(2l-90). Finally, we study synchrotron emission in the
BICEP2 field, in an attempt to understand whether the claimed detection of
large-scale B-mode polarization could be explained in terms of synchrotron
contamination. Adopting a spectral index of beta=-3.12, typical for high
Galactic latitudes, we find that the most likely bias corresponds to about 2%
of the reported signal (r=0.003). The flattest index allowed by the data in
this region is beta=-2.5, and under the assumption of a straight power-law
frequency spectrum, we find that synchrotron emission can account for at most
20% of the reported BICEP2 signal.Comment: 11 pages, 9 figures, updated to match version published in Ap
CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator
We introduce a new CMB temperature likelihood approximation called the
Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by
transforming the observed marginal power spectrum distributions obtained by the
CMB Gibbs sampler into standard univariate Gaussians, and then approximate
their joint transformed distribution by a multivariate Gaussian. The method is
exact for full-sky coverage and uniform noise, and an excellent approximation
for sky cuts and scanning patterns relevant for modern satellite experiments
such as WMAP and Planck. A single evaluation of this estimator between l=2 and
200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space
likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires
~20 seconds. We apply this tool to the 5-year WMAP temperature data, and
re-estimate the angular temperature power spectrum, , and likelihood,
L(C_l), for l<=200, and derive new cosmological parameters for the standard
six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the
official WMAP spectrum, but we find slight differences in the derived
cosmological parameters. Most importantly, the spectral index of scalar
perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma
higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that
an exact likelihood treatment is required to higher l's than previously
believed, reinforcing and extending our conclusions from the 3-year WMAP
analysis. In that case, we found that the sub-optimal likelihood approximation
adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while
here we find that the same approximation between l=30 and 200 introduces a bias
of 0.6 sigma in n_s.Comment: 10 pages, 7 figures, submitted to Ap
Sensitivity and foreground modelling for large-scale CMB B-mode polarization satellite missions
The measurement of the large-scale B-mode polarization in the cosmic
microwave background (CMB) is a fundamental goal of future CMB experiments.
However, because of unprecedented sensitivity, future CMB experiments will be
much more sensitive to any imperfect modelling of the Galactic foreground
polarization in the reconstruction of the primordial B-mode signal. We compare
the sensitivity to B-modes of different concepts of CMB satellite missions
(LiteBIRD, COrE, COrE+, PRISM, EPIC, PIXIE) in the presence of Galactic
foregrounds. In particular, we quantify the impact on the tensor-to-scalar
parameter of incorrect foreground modelling in the component separation
process. Using Bayesian fitting and Gibbs sampling, we perform the separation
of the CMB and Galactic foreground B-modes. The recovered CMB B-mode power
spectrum is used to compute the likelihood distribution of the tensor-to-scalar
ratio. We focus the analysis to the very large angular scales that can be
probed only by CMB space missions, i.e. the Reionization bump, where primordial
B-modes dominate over spurious B-modes induced by gravitational lensing. We
find that fitting a single modified blackbody component for thermal dust where
the "real" sky consists of two dust components strongly bias the estimation of
the tensor-to-scalar ratio by more than 5{\sigma} for the most sensitive
experiments. Neglecting in the parametric model the curvature of the
synchrotron spectral index may bias the estimated tensor-to-scalar ratio by
more than 1{\sigma}. For sensitive CMB experiments, omitting in the foreground
modelling a 1% polarized spinning dust component may induce a non-negligible
bias in the estimated tensor-to-scalar ratio.Comment: 20 pages, 8 figures, 6 tables. Updated to match version accepted by
MNRA
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