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Minkowski Tensors in Two Dimensions: Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields

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dc.contributor.author Appleby, S
dc.contributor.author Pravabati, C
dc.contributor.author Park, C
dc.contributor.author Hong, S. E
dc.contributor.author Kim, J
dc.contributor.author Vidhya, G
dc.date.accessioned 2020-11-11T01:09:22Z
dc.date.available 2020-11-11T01:09:22Z
dc.date.issued 2018-05-10
dc.identifier.citation The Astrophysical Journal, Vol. 858:87, No. 2, 1-15 en_US
dc.identifier.issn 0004-637X
dc.identifier.uri http://prints.iiap.res.in/handle/2248/6823
dc.description Restricted Access © The American Astronomical Society; https://doi.org/10.3847/1538-4357/aabb53 en_US
dc.description.abstract We apply the Minkowski tensor statistics to two-dimensional slices of the three-dimensional matter density field. The Minkowski tensors are a set of functions that are sensitive to directionally dependent signals in the data and, furthermore, can be used to quantify the mean shape of density fields. We begin by reviewing the definition of Minkowski tensors and introducing a method of calculating them from a discretely sampled field. Focusing on the statistic ${W}_{2}^{1,1}$—a 2 × 2 matrix—we calculate its value for both the entire excursion set and individual connected regions and holes within the set. To study the morphology of structures within the excursion set, we calculate the eigenvalues λ 1, λ 2 for the matrix ${W}_{2}^{1,1}$ of each distinct connected region and hole and measure their mean shape using the ratio $\beta \equiv \langle {\lambda }_{2}/{\lambda }_{1}\rangle $. We compare both ${W}_{2}^{1,1}$ and β for a Gaussian field and a smoothed density field generated from the latest Horizon Run 4 cosmological simulation to study the effect of gravitational collapse on these functions. The global statistic ${W}_{2}^{1,1}$ is essentially independent of gravitational collapse, as the process maintains statistical isotropy. However, β is modified significantly, with overdensities becoming relatively more circular compared to underdensities at low redshifts. When applying the statistics to a redshift-space distorted density field, the matrix ${W}_{2}^{1,1}$ is no longer proportional to the identity matrix, and measurements of its diagonal elements can be used to probe the large-scale velocity field. en_US
dc.language.iso en en_US
dc.publisher IOP Publishing en_US
dc.subject Dark matter en_US
dc.subject Galaxies: evolution en_US
dc.subject Methods: statistical en_US
dc.title Minkowski Tensors in Two Dimensions: Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields en_US
dc.type Article en_US


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