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Title: Tensor Minkowski Functionals for random fields on the sphere
Authors: Pravabati, C
Yogendran, K. P
Joby, P. K
Vidhya, G
Appleby, S
Park, C
Keywords: CMBR theory;Cosmological parameters from CMBR
Issue Date: Dec-2017
Publisher: IOP Publishing
Citation: Journal of Cosmology and Astroparticle Physics, Vol. 2017, No. 12, 23
Abstract: We generalize the translation invariant tensor-valued Minkowski Functionals which are de ned on two-dimensional at space to the unit sphere. We apply them to level sets of random elds. The contours enclosing boundaries of level sets of random elds give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random eld on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh elds. The results hold on at as well as any curved space with a ne connection. We elucidate the way in which the matrix elements encode information about the Gaussian nature and statistical isotropy (or departure from isotropy) of the eld. Finally, we apply the method to maps of the Galactic foreground emissions from the 2015 PLANCK data and demonstrate their high level of statistical anisotropy and departure from Gaussianity.
Description: Restricted Access
ISSN: 1475-7516
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Appears in Collections:IIAP Publications

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