Scale-dependent non-Gaussianities in the CMB data identified with Minkowski functionals and scaling indices

Abstract

We present further investigations of the Wilkinson Microwave Anisotropy Probe (WMAP) data by means of the Minkowski functionals and the scaling index method. In order to test for non-Gaussianities (NGs) with respect to scale-dependencies we use so-called surrogate maps, in which possible phase correlations of the Fourier phases of the original WMAP data and the simulations, respectively, are destroyed by applying a shuffling scheme to the maps. A statistical comparison of the original maps with the surrogate maps then allows to test for the existence of higher order correlations (HOCs) in the original maps, also and especially on well-defined Fourier modes.We calculate the σ-normalised deviation between the Minkowski functionals of original data and 500 surrogates for different hemispheres in the sky and find ecliptic hemispherical asymmetries between the northern and southern ecliptic sky. Using Minkowski functionals as an image analysis technique sensitive to HOCs we find deviations from Gaussianity in the WMAP data with an empirical probability p > 99.8% when considering the low-range with ∆ = [2, 20]. The analysis technique of the scaling indices leads to the same results for this interval with a slightly lower deviation but still at p > 99.8%. Although the underlying foreground reduction methods of the maps differ from each other, we find similar results for the WMAP seven-year ILC map and the WMAP seven-year (needlet-based) NILC map for deviations from Gaussianity in the low-range. Our results point once more to a cosmological nature of the signal. For a higher range with ∆ = [120, 300] the results differ between the two image analysis techniques and between the two maps which makes an intrinsic nature of the signal on this range less likely. When we decrease the size of the analysed sky regions for the low-study, we do not find signatures of NG in the northern ecliptic sky. In the south we find individual spots which show deviations from Gaussianity.In addition, we investigate non-Gaussian CMB simulations that depend on the f NL -parameter of the local type. These simulations with f local NL = [0, ±100, ±1000] cannot account for the detected signatures on the low-range.

Planck2013 results. XXIII. Isotropy and statistics of the CMB

“…The dashed (dotted) line indicates the 1 (3) σ significance level. the Planck data, consistent with those obtained previously with WMAP data (for comparison see Modest et al 2013). Figure 25 presents results that allow us to attempt to elucidate the origin of the detected asymmetry and its relationship to other anomalies.…”

“…Previous studies using these methods, based on the WMAP three-, five-and seven-year data (Räth et al 2009(Räth et al , 2011Rossmanith et al 2012;Modest et al 2013), showed significant evidence for intrinsic phase correlations at low values in the CMB. The signal was demonstrated to be robust with respect to the WMAP data release, to the component separation methods and to the selected test statistics.…”

Planck2015 results

“…MFs (Mecke et al 1994;Schmalzing & Buchert 1997;Schmalzing & Gorski 1998;Winitzki & Kosowsky 1998) are a measure of fields' local morphology used to constrain their stationarity, isotropy and Gaussianity. Mostly probing general NG in a frequentist fashion in two-dimensions on CMB maps (Eriksen et al 2004;Komatsu et al 2005;Modest et al 2013;Natoli et al 2010;Curto et al 2008) or three-dimensions on LSS data (Park et al 2005;Wiegand et al 2014), they have also been used to measure specific NG targets with Bayesian methods, such as f local NL (Hikage et al 2006(Hikage et al , 2008Ducout et al 2013;Planck Collaboration XXIV 2014), other bispectrum and trispectrum shapes (Hikage & Matsubara 2012) and topological defects (Planck Collaboration XXV 2014). New developments have been made recently, using needlets (Fantaye et al 2015), neural networks (Novaes et al 2015) or allowing scaledependent measurements (Munshi et al 2013).…”

Planck2013 results. XXIV. Constraints on primordial non-Gaussianity

“…MFs describe the morphological properties of the CMB field and can be used as generic estimators of NG Eriksen et al 2004;De Troia et al 2007;Hikage et al 2008;Curto et al 2008;Natoli et al 2010;Hikage & Matsubara 2012;Modest et al 2013). As they are sensitive to every order of NG, they can be used to constrain different bispectrum and trispectrum shapes (Hikage et al 2006(Hikage et al , 2008Hikage & Matsubara 2012).…”