Correlating Fourier phase information with real-space higher order statistics in CMB data

Abstract

We present a heuristic study on the correlations between harmonic space phase information and higher-order statistics. Using the spherical full-sky maps of the cosmic microwave background as an example, we demonstrate that known phase correlations at large spatial scales can gradually be diminished when subtracting a suitable best-fit (Bianchi-)template map of a given strength. The weaker phase correlations are attended by a vanishing signature of anisotropy when measuring the Minkowski functionals and scaling indices in real space with the aid of surrogate maps being free of phase correlations. Those investigations can open a new road to a better understanding of signatures of non-Gaussianities in complex spatial structures, especially by elucidating the meaning of Fourier phase correlations and their influence on higher-order statistics.