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New approaches to probing Minkowski functionals

Munshi, Dipak, Smidt, J., Cooray, A., Renzi, A., Heavens, A. and Coles, Peter 2013. New approaches to probing Minkowski functionals. Monthly Notices of the Royal Astronomical Society 434 (4) , pp. 2830-2855. 10.1093/mnras/stt1189

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We generalize the concept of the ordinary skew-spectrum to probe the effect of non-Gaussianity on the morphology of cosmic microwave background (CMB) maps in several domains: in real space (where they are commonly known as cumulant-correlators), and in harmonic and needlet bases. The essential aim is to retain more information than normally contained in these statistics, in order to assist in determining the source of any measured non-Gaussianity, in the same spirit as Munshi & Heavens skew-spectra were used to identify foreground contaminants to the CMB bispectrum in Planck data. Using a perturbative series to construct the Minkowski functionals (MFs), we provide a pseudo-C based approach in both harmonic and needlet representations to estimate these spectra in the presence of a mask and inhomogeneous noise. Assuming homogeneous noise, we present approximate expressions for error covariance for the purpose of joint estimation of these spectra. We present specific results for four different models of primordial non-Gaussianity local, equilateral, orthogonal and enfolded models, as well as non-Gaussianity caused by unsubtracted point sources. Closed form results of nextorder corrections to MFs too are obtained in terms of a quadruplet of kurt-spectra. We also use the method of modal decomposition of the bispectrum and trispectrum to reconstruct the MFs as an alternative method of reconstruction of morphological properties of CMB maps. Finally, we introduce the odd-parity skew-spectra to probe the odd-parity bispectrum and its impact on the morphology of the CMB sky. Although developed for the CMB, the generic results obtained here can be useful in other areas of cosmology.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Physics and Astronomy
Subjects: Q Science > QB Astronomy
Q Science > QC Physics
Uncontrolled Keywords: methods: analytical – methods: numerical – methods: statistical – cosmic background radiation – diffuse radiation – large-scale structure of Universe
Publisher: Oxford University Press (OUP): Policy P - Oxford Open Option A
ISSN: 0035-8711
Funders: STFC
Date of First Compliant Deposit: 18 July 2017
Date of Acceptance: 26 June 2013
Last Modified: 19 Oct 2019 03:42

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