Understanding the non-Gaussian nature of Galactic foreground emissions towards small scales

Abstract

We present a unified, multi-scale study of non-Gaussianity of Galactic foreground emissions using Minkowski Functionals and generalized skewness-kurtosis parameters, focusing on the characterization of small-scale non-Gaussianity and its underlying physical origin. We find that all foreground components studied exhibit a remarkably universal non-Gaussian nature dominated by excess kurtosis, whose shape remains stable across angular scales despite large differences in emission physics. Focusing on thermal dust, we perform a detailed comparison between observed maps (GNILC and Planck 545 GHz) and dust model realizations (PySM and filament-based models) to assess the performance of state-of-the-art models in reproducing the observed non-Gaussian properties. At the global level, GNILC and PySM display closely matched kurtosis behavior over the angular scales where the GNILC reconstruction is reliable, while the filament-based model produces substantially weaker skewness and kurtosis signals. For PySM, however, a patch-based analysis reveals statistically significant regional variations, indicating that while the model reproduces the overall non-Gaussian amplitude and scale dependence, it does not fully capture the spatial variability of the observed kurtosis signal. Using simple PDF-based toy models, we demonstrate that the universal kurtosis signature arises from the combination of heavy-tailed one-point statistics and steep large-scale spatial correlations, while its detailed amplitude and scale dependence depend on the underlying foreground physics. These results identify excess kurtosis as a robust statistical fingerprint of Galactic foregrounds and provide a practical framework for validating small-scale foreground models for future CMB analyses.