We report on the results from two independent but complementary statistical analyses of the Wilkinson Microwave Anisotropy Probe (WMAP) first- year data, based on the power spectrum and N-point ...correlation functions. We focus on large and intermediate scales (larger than about 3 degree ) and compare the observed data against Monte Carlo ensembles with WMAP-like properties. In both analyses, we measure the amplitudes of the large-scale fluctuations on opposing hemispheres and study the ratio of the two amplitudes. The power- spectrum analysis shows that this ratio for WMAP, as measured along the axis of maximum asymmetry, is high at the 95%-99% level (depending on the particular multipole range included). The axis of maximum asymmetry of the WMAP data is weakly dependent on the multipole range under consideration but tends to lie close to the ecliptic axis. In the N-point correlation-function analysis, we focus on the northern and southern hemispheres defined in ecliptic coordinates, and we find that the ratio of the large-scale fluctuation amplitudes is high at the 98%-99% level. Furthermore, the results are stable with respect to choice of Galactic cut and also with respect to frequency band. A similar asymmetry is found in the COBE Differential Microwave Radiometer (DMR) map, and the axis of maximum asymmetry is close to the one found in the WMAP data.
ABSTRACT
We repeat and extend the analysis of Eriksen et al. and Hansen et al., testing the isotropy of the cosmic microwave background fluctuations. We find that the hemispherical power asymmetry ...previously reported for the largest scales ℓ = 2–40 extends to much smaller scales. In fact, for the full multipole range ℓ = 2–600, significantly more power is found in the hemisphere centered at (θ = 107° ± 10°, ϕ = 226° ± 10°) in galactic co-latitude and longitude than in the opposite hemisphere, consistent with the previously detected direction of asymmetry for ℓ = 2–40. We adopt a model selection test where the direction and amplitude of asymmetry, as well as the multipole range, are free parameters. A model with an asymmetric distribution of power for ℓ = 2–600 is found to be preferred over the isotropic model at the 0.4% significance level, taking into account the additional parameters required to describe it. A similar direction of asymmetry is found independently in all six subranges of 100 multipoles between ℓ = 2–600. None of our 9800 isotropic simulated maps show a similarly consistent direction of asymmetry over such a large multipole range. No known systematic effects or foregrounds are found to be able to explain the asymmetry.
We consider the issue of hemispherical power asymmetry in the third-year WMAP data, adopting a previously introduced modulation framework. Computing both frequentist probabilities and Bayesian ...evidences, we find that the model consisting of an isotropic CMB sky modulated by a dipole field gives a substantially better fit to the observations than the purely isotropic model, even when accounting for the larger prior volume. For the ILC map, the Bayesian log-evidence difference is similar to 1.8 in favor of the modulated model, and the raw improvement in maximum log likelihood is 6.1. The best-fit modulation dipole axis points toward (l, b) = (225 degree , -27 degree ), and the modulation amplitude is 0.114, in excellent agreement with the results from the first-year analyses. The frequentist probability of obtaining such a high modulation amplitude in an isotropic universe is similar to 1%. These results are not sensitive to data set or sky cut. Thus, the statistical evidence for a power asymmetry anomaly is both substantial and robust, although not decisive, for the currently available data. Increased sky coverage through better foreground handling and full-sky and high-sensitivity polarization maps may shed further light on this issue.
We study the Internal Linear Combination (ILC) method presented by the Wilkinson Microwave Anisotropy Probe (WMAP) science team, with the goal of determining whether it may be used for cosmological ...purposes, as a template- free alternative to existing foreground-correction methods. We conclude that the method does have the potential to do just that, but great care must be taken both in implementation and in a detailed understanding of limitations caused by residual foregrounds, which can still affect cosmological results. As a first step we demonstrate how to compute the ILC weights both accurately and efficiently by means of Lagrange multipliers, and we apply this method to the observed data to produce a new version of the ILC map. This map has 12% lower variance than the ILC map of the WMAP team, primarily because of less noise. Next we describe how to generate Monte Carlo simulations of the ILC map and find that these agree well with the observed map on angular scales up to l ~ 200, using a conservative sky cut. Finally we make two comments to the ongoing debates concerning the large-scale properties of the WMAP data. First, we note that the Galactic southeastern quadrant is associated with notably different ILC weights than the other three quadrants, possibly indicating a foreground-related anisotropy. Second, we study the properties of the quadrupole and octopole (amplitude, alignment, and planarity) and reproduce the previously reported results that the quadrupole and octopole are strongly aligned and that the octopole is moderately planar. Even more interestingly, we find that the l = 5 mode is spherically symmetric at about 3 capital sigma , and that the l = 6 mode is planar at the 2 capital sigma level. However, we also assess the impact of residual foregrounds on these statistics, and find that the ILC map is not clean enough to allow for cosmological conclusions. Alternative methods must be developed to study these issues further.
We propose a method for CMB component separation based on standard Bayesian parameter estimation techniques. We assume a parametric spectral model for each signal component and fit the corresponding ...parameters pixel by pixel in a two-stage process. First we fit for the full parameter set (e.g., component amplitudes and spectral indices) in low-resolution and high signal-to-noise ratio maps using MCMC, obtaining both best-fit values for each parameter and the associated uncertainty. The goodness of fit is approximated by a j super(2) statistic. Then we fix all nonlinear parameters at their low-resolution best-fit values and solve analytically for high-resolution component amplitude maps. This likelihood approach has many advantages: the fitted model may be chosen freely, and the method is therefore completely general; all assumptions are transparent; no restrictions on spatial variations of foreground properties are imposed; the results may be monitored by goodness-of-fit tests; and, most importantly, we obtain reliable error estimates on all estimated quantities. We apply the method to simulated Planck satellite and 6 year WMAP data based on realistic models and show that separation at the microkelvin level is indeed possible in these cases. We also outline how the foreground uncertainties may be rigorously propagated through to the CMB power spectrum and cosmological parameters using a Gibbs sampling technique.
The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte ...Carlo simulations, based on Gaussian fluctuations with the a priori best-fit running- index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton show no evidence for departures from the Gaussian hypothesis, the northern hemisphere genus has a Chi super(2) that is large at the 95% level for all scales. For the particular smoothing scale of 3 degree 40 FWHM it is larger than that found in 99.5% of the simulations. In addition, the WMAP genus for negative thresholds in the northern hemisphere has an amplitude that is larger than in the simulations with a significance of more than 3 capital sigma . On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 capital sigma level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter gamma is high at the 99% level in the northern Galactic hemisphere, while perfectly acceptable in the southern hemisphere. The results provide strong evidence for the presence of both non-Gaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data.
Context. Future weak lensing surveys, such as the Euclid mission, will attempt to measure the shapes of billions of galaxies in order to derive cosmological information. These surveys will attain ...very low levels of statistical error, and systematic errors must be extremely well controlled. In particular, the point spread function (PSF) must be estimated using stars in the field, and recovered with high accuracy. Aims. The aims of this paper are twofold. Firstly, we took steps toward a nonparametric method to address the issue of recovering the PSF field, namely that of finding the correct PSF at the position of any galaxy in the field, applicable to Euclid . Our approach relies solely on the data, as opposed to parametric methods that make use of our knowledge of the instrument. Secondly, we studied the impact of imperfect PSF models on the shape measurement of galaxies themselves, and whether common assumptions about this impact hold true in an Euclid scenario. Methods. We extended the recently proposed resolved components analysis approach, which performs super-resolution on a field of under-sampled observations of a spatially varying, image-valued function. We added a spatial interpolation component to the method, making it a true 2-dimensional PSF model. We compared our approach to PSFEx , then quantified the impact of PSF recovery errors on galaxy shape measurements through image simulations. Results. Our approach yields an improvement over PSFEx in terms of the PSF model and on observed galaxy shape errors, though it is at present far from reaching the required Euclid accuracy. We also find that the usual formalism used for the propagation of PSF model errors to weak lensing quantities no longer holds in the case of an Euclid -like PSF. In particular, different shape measurement approaches can react differently to the same PSF modeling errors.
We apply the recently defined multipole vector framework to the frequency-specific first-year WMAP sky maps, estimating the low-l multipole coefficients from the high-latitude sky by means of a power ...equalization filter. While most previous analyses of this type have considered only heavily processed (and foreground-contaminated) full-sky maps, the present approach allows for greater control of residual foregrounds and therefore potentially also for cosmologically important conclusions. The low-l spherical harmonic coefficients and corresponding multipole vectors are tabulated for easy reference. Using this formalism, we reassess a set of earlier claims of both cosmological and noncosmological low-l correlations on the basis of multipole vectors. First, we show that the apparent l = 3 and 8 correlation claimed by Copi and coworkers is present only in the heavily processed map produced by Tegmark and coworkers and must therefore be considered an artifact of that map. Second, the well-known quadrupole-octopole correlation is confirmed at the 99% significance level and shown to be robust with respect to frequency and sky cut. Previous claims are thus supported by our analysis. Finally, the low-l alignment with respect to the ecliptic claimed by Schwarz and coworkers is nominally confirmed in this analysis, but also shown to be very dependent on severe a posteriori choices. Indeed, we show that given the peculiar quadrupole-octopole arrangement, finding such a strong alignment with the ecliptic is not unusual.
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