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Register a new userNon-Gaussian Signatures in the five-year WMAP data as identified with isotropic scaling indices
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We continue the analysis of non-Gaussianities in the CMB by means of the scaling index method (SIM, Raeth, Schuecker & Banday 2007) by applying this method on the 5-year WMAP data. We compare each of the results with 1000 Monte Carlo simulations mimicing the Gaussian properties of the best fit $Lambda CDM$-model. Based on the scaling indices, scale-dependent empirical probability distributions, moments of these distributions and $chi^2$-combinations of them are calculated, obtaining similar results as in the former analysis of the 3-year data: We derive evidence for non-Gaussianity with a probability of up to 97.3% for the mean when regarding the KQ75-masked full sky and summing up over all considered length scales by means of a diagonal $chi^2$-statistics. Looking at only the northern or southern hemisphere, we obtain up to 98.5% or 96.6%, respectively. For the standard deviation, these results appear as 95.6% for the full sky (99.7% north, 89.4% south) and for a $chi^2$-combination of both measurements as 97.4% (99.1% north, 95.5% south). By performing an analysis of rotated hemispheres, we detect an obvious asymmetry in the data. In addition to these investigations, we present a method of filling the mask with Gaussian noise to eliminate boundary effects caused by the mask. With the help of this technique, we identify several local features on the map, of which the most significant one turns out to be the well-known cold spot. When excluding all these spots from the analysis, the deviation from Gaussianity increases, which shows that the discovered local anomalies are not the reason of the global detection of non-Gaussianity, but actually were damping the deviations on average. Our analyses per band and per year suggest, however, that it is very unlikely that the detected anomalies are due to foreground effects.
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We present a model-independent investigation of the WMAP data with respect to scale- dependent non-Gaussianities (NGs) by employing the method of constrained randomization. For generating so-called surrogate maps a shuffling scheme is applied to the Fourier phases of the original data, which allows to test for the presence of higher order correlations (HOCs) on well-defined scales. Using scaling indices as test statistics we find highly significant signatures for non-Gaussianities when considering all scales. We test for NGs in the bands l = [2,20], l = [20,60], l = [60,120] and l = [120,300]. We find highly significant signatures for non-Gaussianities and ecliptic hemispherical asymmetries for l = [2, 20]. We also obtain highly significant deviations from Gaussianity for the band l = [120,300]. The result for the full l-range can be interpreted as a superposition of the signatures found in the bands l = [2, 20] and l = [120, 300]. We find remarkably similar results when analyzing different ILC-like maps. We perform a set of tests to investigate if the detected anomalies can be explained by systematics. While no test can convincingly rule out the intrinsic nature of the anomalies for the low l case, the ILC map making procedure and/or residual noise in the maps can also lead to NGs at small scales. Our investigations prove that there are phase correlations in the WMAP data of the CMB. In the absence of an explanation in terms of Galactic foregrounds or known systematic artefacts, the signatures at low l must so far be taken to be cosmological at high significance. These findings strongly disagree with predictions of isotropic cosmologies with single field slow roll inflation. The task is now to elucidate the origin of the phase correlations and to understand the physical processes leading to these scale-dependent non-Gaussianities - if systematics as cause for them must be ruled out.
(Abridged)Motivated by the recent results of Hansen et al. (2008) concerning a noticeable hemispherical power asymmetry in the WMAP data on small angular scales, we revisit the dipole modulated signal model introduced by Gordon et al. (2005). This model assumes that the true CMB signal consists of a Gaussian isotropic random field modulated by a dipole, and is characterized by an overall modulation amplitude, A, and a preferred direction, p. Previous analyses of this model has been restricted to very low resolution due to computational cost. In this paper, we double the angular resolution, and compute the full corresponding posterior distribution for the 5-year WMAP data. The results from our analysis are the following: The best-fit modulation amplitude for l <= 64 and the ILC data with the WMAP KQ85 sky cut is A=0.072 +/- 0.022, non-zero at 3.3sigma, and the preferred direction points toward Galactic coordinates (l,b) = (224 degree, -22 degree) +/- 24 degree. The corresponding results for l <~ 40 from earlier analyses was A = 0.11 +/- 0.04 and (l,b) = (225 degree,-27 degree). The statistical significance of a non-zero amplitude thus increases from 2.8sigma to 3.3sigma when increasing l_max from 40 to 64, and all results are consistent to within 1sigma. Similarly, the Bayesian log-evidence difference with respect to the isotropic model increases from Delta ln E = 1.8 to Delta ln E = 2.6, ranking as strong evidence on the Jeffreys scale. The raw best-fit log-likelihood difference increases from Delta ln L = 6.1 to Delta ln L = 7.3. Similar, and often slightly stronger, results are found for other data combinations. Thus, we find that the evidence for a dipole power distribution in the WMAP data increases with l in the 5-year WMAP data set, in agreement with the reports of Hansen et al. (2008).
In the recent years, non-Gaussianity and statistical isotropy of the Cosmic Microwave Background (CMB) was investigated with various statistical measures, first and foremost by means of the measurements of the WMAP satellite. In this Review, we focus on the analyses that were accomplished with a measure of local type, the so-called Scaling Index Method (SIM). The SIM is able to detect structural characteristics of a given data set, and has proven to be highly valuable in CMB analysis. It was used for comparing the data set with simulations as well as surrogates, which are full sky maps generated by randomisation of previously selected features of the original map. During these investigations, strong evidence for non-Gaussianities as well as asymmetries and local features could be detected. In combination with the surrogates approach, the SIM detected the highest significances for non-Gaussianity to date.
Local scaling properties of the co-added foreground-cleaned three-year Wilkinson Microwave Anisotropy Probe (WMAP) data are estimated using weighted scaling indices. The scaling index method (SIM) is - for the first time - adapted and applied to the case of spherical symmetric spatial data. The results are compared with 1000 Monte Carlo simulations based on Gaussian fluctuations with a best fit $Lambda$CDM power spectrum and WMAP-like beam and noise properties. Statistical quantities based on the scaling indices, namely the moments of the distribution and probability-based measures are determined. We find for most of the test statistics significant deviations from the Gaussian hypothesis. We find pronounced asymmetries, which can be interpreted as a global lack of structure in the northern hemisphere, which is consistent with previous findings. Furthermore, we detect a localized anomaly in the southern hemisphere, which gives rise to highly significant signature for non-Gaussianity in the spectrum of scaling indices. We identify this signature as the cold spot, which was also already detected in the first year WMAP data. Our results provide further evidence for both the presence of non-Gaussianities and asymmetries in the WMAP three-year data. More detailed bandand year-wise analyses are needed to elucidate the origin of the detected anomalies. In either case the scaling indices provide powerful nonlinear statistics to analyse CMB maps.
We constrain the amplitude of primordial non-Gaussianity in the CMB data taking into account the presence of foreground residuals in the maps. We generalise the needlet bispectrum estimator marginalizing over the amplitudes of thermal dust, free-free and synchrotron templates. We apply our procedure to WMAP 5 year data, finding fNL= 38pm 47 (1 sigma), while the analysis without marginalization provides fNL= 35pm 42. Splitting the marginalization over each foreground separately, we found that the estimates of fNL are positively cross correlated of 17%, 12% with the dust and synchrotron respectively, while a negative cross correlation of about -10% is found for the free-free component.
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