Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2010-11-23
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
14 Pages, 5 Figures, Submitted to MNRAS
Scientific paper
Most studies of Non-Gaussianity (NG) in the CMB data rely on moment based approaches that depend on the study of bispectrum or its higher order analogs of multispectra. In contrast, the studies that use the Minkowski functionals (MF) depend on morphological characteristics of the observed fields. The two approaches are complementary. We show how the topological statistics such as MFs can be computed from real data sets in the presence of a mask and inhomogeneous noise by using methods for estimation of skew-spectrum. We exploit the fact that the computation of MF at the lowest order is equivalent to the estimation of three different skewness parameters. These one-point estimates are volume averages of third order statistics of fields that are constructed from the original data. Generalizing the concept of ordinary skew-spectra we define a sets of three different skew-spectra which specify the MFs at lowest order in non-Gaussianity and can probe them as a function of harmonic number. These spectra can also be studied independently to provide a valuable check for any cross-contamination from the secondaries or foreground sources. The Pseudo-C_l (PCL) approach is employed to estimate the generalized skew-spectra associated with the MFs in the presence of mask from noisy data. The variance for such estimators is analyzed. The results presented here are generic and can be useful in analyzing data from other projected surveys such as from the weak lensing surveys or from the future Sunyaev-Zel'dovich (SZ) surveys. Generalization to 3D can be done in a straight forward way which will be useful in quantifying the topology of galaxy distributions. We also go beyond the lowest order in skew-spectra and discuss the extraction of four generalized kurtosis and the corresponding kurt-spectra that are relevant in studying the next order corrections.
Cooray Asantha
Munshi Dipak
Smidt Joseph
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