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

Appleby, Stephen and Chingangbam, Pravabati and Park, Changbom and Hong, Sungwook E and Kim, Juhan and Ganesan, Vidhya (2018) Minkowski Tensors in Two Dimensions: Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields. In: ASTROPHYSICAL JOURNAL, 858 (2).

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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 x 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 lambda(1), lambda(2) for the matrix W-2(1,1) of each distinct connected region and hole and measure their mean shape using the ratio beta equivalent to <lambda(2)/lambda(1)>. We compare both W-2(1,1) and beta 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, beta 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.

Item Type:	Journal Article
Publication:	ASTROPHYSICAL JOURNAL
Publisher:	IOP PUBLISHING LTD, TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Additional Information:	Copy right for this article belong toIOP PUBLISHING LTD, TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	05 Jun 2018 15:45
Last Modified:	09 Oct 2018 15:44
URI:	http://eprints.iisc.ac.in/id/eprint/59956

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