Morphological Measures of Non-Gaussianity in Cosmic Microwave Background Maps

We discuss the tests of non-Gaussianity in CMB maps using morphological statistics known as Minkowski functionals. As an example we test degree-scale cosmic microwave background (CMB) anisotropy for Gaussianity by studying the QMASK map that was obtained from combining the QMAP and Saskatoon data. We compute seven morphological functions M_i(ΔT), i = 1, ... ,7: six Minkowski functionals and the number of regions N_c at a hundred ΔT levels. We also introduce a new parameterization of the morphological functions M_i(A) in terms of the total area A of the excursion set. We show that the latter considerably decorrelates the morphological statistics and makes them more robust because they are less sensitive to the measurements at extreme levels. We compare these results with those from 1000 Gaussian Monte Carlo maps with the same sky coverage, noise properties, and power spectrum and conclude that the QMASK map is neither a very typical nor a very exceptional realization of a Gaussian field. At least about 20% of the 1000 Gaussian Monte Carlo maps differ more than the QMASK map from the mean morphological parameters of the Gaussian fields.