Skewness and kurtosis as indicators of non-Gaussianity in galactic foreground maps

Abstract

Observational cosmology is entering an era in which high precision will be required in both measurement and data analysis. Accuracy, however, can only be achieved with a thorough understanding of potential sources of contamination from foreground effects. Our primary focus will be on non-Gaussian effects in foregrounds. This issue will be crucial for coming experiments to determine B-mode polarization. We propose a novel method for investigating a data set in terms of skewness and kurtosis in locally defined regions that collectively cover the entire sky. The method is demonstrated on two sky maps: (i) the SMICA map of Cosmic Microwave Background fluctuations provided by the Planck Collaboration and (ii) a version of the Haslam map at 408 MHz that describes synchrotron radiation. We find that skewness and kurtosis can be evaluated in combination to reveal local physical information. In the present case, we demonstrate that the statistical properties of both maps in small local regions are predominantly Gaussian. This result was expected for the SMICA map. It is surprising that it also applies for the Haslam map given its evident large scale non-Gaussianity. The approach described here has a generality and flexibility that should make it useful in a variety of astrophysical and cosmological contexts.

Non-Gaussianity of diffuse Galactic synchrotron emission at 408 MHz

“…Our results indicate scales of 3 • (or 60), and in regions away from the Galactic plane, the statistics of the 408 MHz map is consistent with the Gaussian sky realisations. Our finding is consistent with the earlier results from Ben-David et al (2015b), who reported that the Gaussian approximation is valid for scales 3. • 7 away from the Galactic plane.…”

“…A number of methods for quantifying departure from Gaussianity have been suggested, e.g., Kullback-Leibler divergence (see Ben-David et al 2015a), higher order moments (skewness, kurtosis) (Ben-David et al 2015b;Contaldi et al 2000;Munshi et al 2013), and three-point correlation function (Chen & Szapudi 2005). One of the tools for analysing the statistical properties of smooth random fields are the Minkowski Functionals (Adler 1981;Tomita 1986).…”

Tensor Minkowski Functionals for random fields on the sphere

“…Non-Gaussianity of PLANCK foreground maps have been analyzed in [56]. As mentioned in the introduction, [23] used scalar MFs to detect the presence of residual Galactic foreground and point sources contamination in the WMAP data.…”

Statistical properties of polarized CMB foreground maps

“…In this work we would like to take a step back and investigate the statistical behavior of foregrounds in a general manner, independent of studies of specific CMB non-Gaussianities, in order to, among others, finally make connections to general issues in foreground removal methods. Also this has been of recent interest (Ben-David et al 2015;Rana et al 2018) regarding temperature maps of Galactic synchrotron radiation, which calls for similar studies of maps of polarization.…”

“…1. More detail on the computations and background information can be found in Ben-David et al (2015).…”