Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?

Abstract

In this paper, we investigate the utility of Minkowski Functionals as a probe of cold/hot disk-like structures in the CMB. In order to construct an accurate estimator, we resolve a long-standing issue with the use of Minkowski Functionals as probes of the CMB sky -- namely that of systematic differences ("residuals") when numerical and analytical MF are compared. We show that such residuals are in fact by-products of binning, and not caused by pixelation or masking as originally thought. We then derive a map-independent estimator that encodes the effects of binning, applicable to beyond our present work. Using this residual-free estimator, we show that small disk-like effects (as claimed by Vielva et al.) can be detected only when a large sample of such maps are averaged over. In other words, our estimator is noise-dominated for small disk sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to the WMAP7 data to obtain a null result.

15 pages, 13 figures

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Cited by in corpus (25)

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• Determining the outcome of cosmic bubble collisions in full General Relativity
• Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski Functionals
• Limits on Second-Order Non-Gaussianity from Minkowski Functionals of WMAP Data
• Search for anomalous alignments of structures in Planck data using Minkowski Tensors
• Tensor Minkowski Functionals for random fields on the sphere
• Distinguishing general relativity and $f(R)$ gravity with the gravitational lensing Minkowski functionals
• Probing the statistical properties of CMB $B$-mode polarization through Minkowski Functionals
• Primordial non-Gaussian signatures in CMB polarization
• Residual foreground contamination in the WMAP data and bias in non-Gaussianity estimation
• Probing Primordial Non-Gaussianity with Weak Lensing Minkowski Functionals
• Effect of Mask Regions on Weak Lensing Statistics
• Cosmological constraints using Minkowski functionals from the first year data of the Hyper Suprime-Cam
• 3D cosmic shear: numerical challenges, 3D lensing random fields generation and Minkowski Functionals for cosmological inference
• Morphological Analysis of the Polarized Synchrotron Emission with WMAP and Planck
• The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map
• Probing CMB Cold Spot through Local Minkowski Functionals
• Minkowski Tensors in Redshift Space -- Beyond the Plane Parallel Approximation
• Morphology of CMB fields -- effect of weak gravitational lensing
• Local patch analysis for testing statistical isotropy of the Planck convergence map
• Joint Minkowski Functionals and Bispectrum Constraints on Non-Gaussianity in the CMB
• The geometrical meaning of statistical isotropy of smooth random fields in two dimensions
• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
• Anisotropic power spectrum and the observed low-l power in PLANCK CMB data