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Tensor Minkowski Functionals for random fields on the sphere

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dc.contributor.author Pravabati, C
dc.contributor.author Yogendran, K. P
dc.contributor.author Joby, P. K
dc.contributor.author Vidhya, G
dc.contributor.author Appleby, S
dc.contributor.author Park, C
dc.date.accessioned 2020-11-12T14:31:46Z
dc.date.available 2020-11-12T14:31:46Z
dc.date.issued 2017-12
dc.identifier.citation Journal of Cosmology and Astroparticle Physics, Vol. 2017, No. 12, 23 en_US
dc.identifier.issn 1475-7516
dc.identifier.uri http://prints.iiap.res.in/handle/2248/6927
dc.description Restricted Access © IOP Publishing https://doi.org/10.1088/1475-7516/2017/12/023 en_US
dc.description.abstract We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random field on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh fields. The results hold on flat as well as any curved space with affine 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 field. 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. en_US
dc.language.iso en en_US
dc.publisher IOP Publishing en_US
dc.subject CMBR theory en_US
dc.subject Cosmological parameters from CMBR en_US
dc.title Tensor Minkowski Functionals for random fields on the sphere en_US
dc.type Article en_US


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