Testing for Non‐Gaussianity in theWilkinson Microwave Anisotropy ProbeData: Minkowski Functionals and the Length of the Skeleton

Abstract

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, , 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 2 that is large at the 95% level for all scales. For the particular smoothing scale of 3N40 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 . On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter 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 nonGaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data. Subject headingg s: cosmic microwave background -cosmology: observations -methods: statistical

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).…”

Asymmetries in the angular distribution of the cosmic microwave background

“…Other anomalies were found in the WMAP data that were not expected according to the ΛCDM model either, such as the alignment between the quadrupole and octopole (e.g. Bielewicz et al 2004;Schwarz et al 2004;Copi et al 2004;de Oliveira-Costa et al 2004;Bielewicz et al 2005;Land & Magueijo 2005;Copi et al 2006;Abramo et al 2006;Frommert & Ensslin 2010;Gruppuso & Burigana 2010), the low quadrupole and octopole amplitudes (e.g., Mukherjee & Wang 2003;Ayata et al 2010;Cayon 2010;Cruz et al 2011), the north-south asymmetry (e.g., Eriksen et al 2004a;Hansen et al 2004a;Eriksen et al 2004b;Hansen et al 2004b;Donoghue et al 2005;Hoftuft et al 2009;Paci et al 2010;Pietrobon et al 2010;Vielva & Sanz 2010), the anomalous alignment of the CMB features toward the Ecliptic poles (e.g., Wiaux et al 2006;Vielva et al 2007), and the cold spot (e.g., Vielva et al 2004;Cruz et al 2005Cruz et al , 2007Vielva 2010).…”

Filaments in observed and mock galaxy catalogues

“…In order to describe the filamentary structure of continuous density fields, a skeleton method has been proposed and developed by Eriksen et al (2004) and Novikov et al (2006). The skeleton is determined by segments parallel to the gradient of the field, connecting saddle points to local maxima.…”

“…This is generally the case for most of the density-based approaches. The skeleton method was first applied for two-dimensional maps, an approach to study the cosmic microwave sky background (Eriksen et al 2004). The method was adapted for 3-D maps (Sousbie et al 2008a) and was applied to the Sloan Digital Sky Survey by Sousbie et al (2008b), providing by means of the length of the skeleton, a good distinguishing tool for the analysis of the filamentary structures.…”