Secondary anisotropies in CMB, skew-spectra and Minkowski Functionals

Secondary contributions to the anisotropy of the cosmic microwave background (CMB), such as the integrated Sachs-Wolfe (ISW) effect, the thermal Sunyaev-Zel'dovich (tSZ) effect, and the effect of gravitational lensing, have distinctive non-Gaussian signatures, and full descriptions therefore require information beyond that contained in their power spectra. The Minkowski Functionals (MF) are well-known as tools for quantifying any departure from Gaussianity and are affected by noise and other sources of confusion in a different way from the usual methods based on higher-order moments or polyspectra, thus providing complementary tools for CMB analysis and cross-validation of results. In this paper we use the recently introduced skew-spectra associated with the MFs to probe the topology of CMB maps to probe the secondary non-Gaussianity as a function of beam smoothing in order to separate various contributions. We devise estimators for these spectra in the presence of realistic observational masks and present expressions for their covariance as a function of instrumental noise. Specific results are derived for the mixed ISW-lensing and tSZ-lensing bispectra as well as contamination due to point sources for noise levels that correspond to the Planck (143 GHz channel) and Experimental Probe of Inflationary Cosmology (EPIC; 150 GHz channel) experiments. The cumulative signal-to-noise ratio (S/N) for one-point generalized skewness parameters can reach an order of O(10) for Planck and two orders of magnitude higher for EPIC, i.e. O(10(3)). We also find that these three skew-spectra are correlated, having correlation coefficients r similar to 0.5-1.0; higher l modes are more strongly correlated. Although the values of S/N increase with decreasing noise, the triplets of skew-spectra that determine the MFs become more correlated; the S/N of lensing-induced skew-spectra are smaller compared to that of a frequency-cleaned tSZ map.