A scaling index analysis of the Wilkinson Microwave Anisotropy Probe three-year data: signatures of non-Gaussianities and asymmetries in the cosmic microwave background

Abstract

Local scaling properties of the co‐added foreground‐cleaned three‐year Wilkinson Microwave Anisotropy Probe (WMAP) data are estimated using weighted scaling indices α. The scaling index method 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‐fitting Λ cold dark matter power spectrum and WMAP‐like beam and noise properties. Statistical quantities based on the scaling indices, namely the mean and standard deviation, a combination of both and probability‐based measures are determined. We find for most of the test statistics highly significant deviations from the Gaussian hypothesis. Using a very conservative χ2 statistics, which averages over all scales, we detect non‐Gaussianity for the full sky at a level of 97.3 per cent regarding the mean, 97.3 per cent for the standard deviation and 97.7 per cent for a combination of mean and standard deviation. For the Northern hemisphere, the signatures of non‐Gaussianities are more pronounced and we obtain 97.7 per cent (mean), 99.8 per cent (standard deviation) and 99.0 per cent (combination), whereas the Southern hemisphere is more consistent with Gaussianity [94.8 per cent (mean), 71.0 per cent (standard deviation) and 91.5 per cent (combination)]. These differences between Northern and Southern hemispheres induce 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 giving rise to highly significant signature for non‐Gaussianity in the spectrum of scaling indices P(α). 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 the presence of asymmetries in the WMAP three‐year data. More detailed band‐ and year‐wise analyses are needed to elucidate the origin of the detected anomalies. In either case the scaling indices provide powerful non‐linear statistics to analyse cosmic microwave background maps.

Planck2013 results. XXIII. Isotropy and statistics of the CMB

“…Indeed, the WMAP team (Spergel et al 2003) themselves initially proposed some intriguing discrepancies in the form of a lack of power on large angular scales, which was subsequently reconfirmed for the three-year data in Copi et al (2007). Further examples include an alignment of the low-order multipoles (Tegmark et al 2003;Schwarz et al 2004;Bielewicz et al 2005;Land & Magueijo 2005a), a north-south asymmetry in both power spectra (Eriksen et al 2004a;Hansen et al 2009) and various measures of non-Gaussianity (Eriksen et al 2004cRäth et al 2007a), parity asymmetry in the power spectrum corresponding to large angular scales (Kim & Naselsky 2010a), and a region of significant temperature decrement -the so-called cold spot (Vielva et al 2004;Cruz et al 2005).…”

A theory of a spot

“…[25]. The cold spot was also identified using other techniques: using more sophisticated wavelet techniques [26], steerable wavelets [27], needlets [28] and scalar indices [29]. On the other hand [30] argue that the spot is not statistically significant.…”

Characterizing black hole variability with nonlinear methods: the case of the X-ray Nova 4U 1543–47

“…4. The main difference between "normal" and weighted scaling index methods is that in the latter the cumulative number function is substituted by the weighted cumulative point distribution, where the weighting function can be any differentiable function (in our case a Gaussian function; see Räth et al 2007 for a detailed explanation of the WSIM).…”

“…Atmanspacher et al 1989) has been employed in a number of different fields because of its ability to discern underlying structure in noisy data. It has been successfully used for instance in medical science (see Morfill & Bunk 2001 for a brief review), in image analysis (e.g., Räth & Morfill 1997;Brinkmann et al 1999), in plasma physics (e.g., Ivlev et al 2008;Sütterlin et al 2009), and in cosmology (Räth et al , 2007. Recently, we have applied this method to well-sampled AGN light curves to look for signs of nonstationarity (Gliozzi et al 2002(Gliozzi et al , 2006.…”