arXiv subjects

Pravabati Chingangbam

Publications and source records attributed to Pravabati Chingangbam.

At least 37 records · Page 2Linked to original sources

arXiv2021

The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map

Accurate component separation of full-sky maps in the radio and microwave frequencies, such as the cosmic microwave background (CMB), relies on a thorough understanding of the statistical properties of the Galactic foreground emissions. Using scalar Minkowski functionals and their tensorial generalization known as Minkowski tensors, we analyze the statistical properties of one of the major foreground components, namely the Galactic synchrotron given by the full sky 408 MHz Haslam map. We focus on understanding the nature of non-Gaussianity and statistical isotropy of the cooler regions of the map as a function of angular scale. We find that the overall level of the non-Gaussian deviations does decrease as more high emission regions are masked and as we go down to smaller scales, in agreement with the results obtained in earlier works. However, they remain significantly high, of order 3.3$σ$, at the smallest angular scales relevant for the Haslam map. We carry out a detailed examination of the non-Gaussian nature using the generalized skewness and kurtosis cumulants that arise in the perturbative expansion of Minkowski functionals for weakly non-Gaussian fields. We find that the leading sources of non-Gaussianity are the kurtosis terms which are considerably larger than the skewness terms at all angular scales. Further, for the cooler regions of the Haslam map, we find that the non-Gaussian deviations of the Minkowski functionals can be well explained by the perturbative expansion up to second-order (up to kurtosis terms), with first-order terms being sub-dominant. Lastly, we test the statistical isotropy of the Haslam map and find that it becomes increasingly more isotropic at smaller scales.

astro-ph.CO↗

arXiv2021

Application of Contour Minkowski Tensor and $\mathcal{D}$ Statistic to the Planck $E$-mode data

We test the statistical isotropy (SI) of the $E$-mode polarization of the Cosmic Microwave Background (CMB) radiation observed by the Planck satellite using two statistics, namely, the $α$ estimator that is derived from the contour Minkowski Tensor (CMT), and the Directional statistic ($\mathcal{D}$ statistic). The $α$ estimator obtained from the CMT provides information about the alignment of structures and can be used to infer statistical properties such as Gaussianity and SI of random fields. The $\mathcal{D}$ statistic is based on detecting preferred directionality shown by vectors defined by the field. We compute $α$ and $\mathcal{D}$ statistic for the low resolution component separated SMICA $E$-mode map of CMB polarization, and compare with the values calculated using FFP10 SMICA simulations. We find good agreement between the Planck data and SMICA simulations for both $α$ estimator and $\mathcal{D}$ statistic.

astro-ph.CO↗

arXiv2021

Prospects of constraining reionization model parameters using Minkowski tensors and Betti numbers

We explore the possibility of constraining model parameters of the Epoch of Reionization (EoR) from 21cm brightness temperature maps, using a combination of morphological descriptors constructed from the eigenvalues of the Contour Minkowski Tensor (CMT), Betti numbers (count of connected regions $n_{con}$ and holes $n_{hole}$) and the area of structures in the excursion set of the field. We use a three parameter model of EoR simulated using 21\textrm{cmFAST}, namely the ionizing efficiency of sources $ζ$, the minimum virial temperature $T_{vir}$ required for collapse into a halo and the maximum radius for ionizing radiation described by $R_{mfp}$. We performed a Bayesian analysis to recover model parameters for a mock 21cm image from SKA phase I at a redshift of $z=7.4$ corresponding to a mean neutral hydrogen fraction of $\mathrm{\bar x}_{HI} \simeq 0.5$. We find that in the absence of noise the average size of structures in the field with $x_{HI} \lesssim 0.5$ is smaller than regions with $x_{HI} \gtrsim 0.5$ and the structures are equally isotropic when $\mathrm{\bar x}_{HI}=0.5$ . We also find that in order to recover the input model to within $1-σ$ accuracy for a mock noisy image at a single frequency channel of $1~\mathrm{MHz}$, for an observation time $t_{obs}<2000~\mathrm{hrs}$, the noisy $δT_b$ map needs to be smoothed at a scale $R_s>9.5~\mathrm{Mpc}$. Finally we show that the systematic behaviour of the statistic as ionization progresses, enables us to obtain stringent constraints on $\mathrm{\bar x}_{HI}$ (with a coefficient of variation $\sim 0.05$ as compared to $\sim 0.1-0.2$ for model parameter constraints), thereby making these descriptors a promising statistic for constraining EoR model parameters and the ionization history of the universe.

astro-ph.CO↗

arXiv2021

Local patch analysis for testing statistical isotropy of the Planck convergence map

The small but measurable effect of weak gravitational lensing on the cosmic microwave background radiation provide information about the large-scale distribution of matter in the universe. We use the all sky distribution of matter, as represented by the {\em convergence map} that is inferred from CMB lensing measurement by Planck survey, to test the fundamental assumption of Statistical Isotropy (SI) of the universe. For the analysis we use the $α$ statistic that is devised from the contour Minkowski tensor, a tensorial generalization of the scalar Minkowski functional, the contour length. In essence, the $α$ statistic captures the ellipticity of isofield contours at any chosen threshold value of a smooth random field and provides a measure of anisotropy. The SI of the observed convergence map is tested against the suite of realistic simulations of the convergence map provided by the Planck collaboration. We first carry out a global analysis using the full sky data after applying the galactic and point sources mask. We find that the observed data is consistent with SI. Further we carry out a local search for departure from SI in small patches of the sky using $α$. This analysis reveals several sky patches which exhibit deviations from simulations with statistical significance higher than 95\% confidence level (CL). Our analysis indicates that the source of the anomalous behaviour of most of the outlier patches is inaccurate estimation of noise. We identify two outlier patches which exhibit anomalous behaviour originating from departure from SI at higher than 95\% CL. Most of the anomalous patches are found to be located roughly along the ecliptic plane or in proximity to the ecliptic poles.

astro-ph.CO↗

arXiv2020

A novel probe of bubble size statistics and time scales of the epoch of reionization using the contour Minkowski Tensor

We employ the rank-2 {\em contour} Minkowski Tensor in two dimensions to probe length and time scales of ionized bubbles during the epoch of reionization. We demonstrate that the eigenvalues of this tensor provide excellent probes of the distribution of the sizes of ionized bubbles, and from it the characteristic bubble sizes, at different redshifts. We show that ionized bubbles are not circular, and hence not spherical in three dimensions, as is often assumed for simplified analytic arguments. We quantify their shape anisotropy by using the ratio of the two eigenvalues. The shape parameter provides the characteristic time epochs when bubble mergers begin and end. Our method will be very useful to reconstruct the reionization history using data of the brightness temperature field.

astro-ph.CO↗

arXiv2020

Statistical Isotropy of the CMB E-mode signal

We test the statistical isotropy (SI) of the $E$-mode polarization of the cosmic microwave background (CMB) radiation observed by the Planck satellite using two statistics, namely, the contour Minkowski Tensor (CMT) and the Directional statistic ($\mathcal{D}$ statistic). The parameter $α$ obtained from the CMT provides information of the alignment of structures and can be used to infer statistical properties such as Gaussianity and SI of random fields. The $\mathcal{D}$ statistic is based on detecting preferred directionality shown by vectors defined by the field. These two tests are complementary to each other in terms of sensitivity at different angular scales. The CMT is sensitive towards small-scale information present in the CMB map while $\mathcal{D}$ statistic is more sensitive at large-scales. We compute $α$ and $\mathcal{D}$ statistic for the observed $E$-mode of CMB polarization, focusing on the SMICA maps, and compare with the values calculated using FFP10 SMICA simulations which contain both CMB and noise. We find good agreement between the observed data and simulations. Further, in order to specifically analyze the CMB signal in the data, we compare the values of the two statistics obtained from the observed Planck data with the values obtained from isotropic simulations having the same power spectrum, and from SMICA noise simulations. We find no statistically significant deviation from SI using the $α$ parameter. From $\mathcal{D}$ statistic we find that the data shows slight deviation from SI at large angular scales.

astro-ph.CO↗

arXiv2019

Morphology of CMB fields -- effect of weak gravitational lensing

We study the morphology of the cosmic microwave background temperature and polarization fields using the shape and alignment parameters, $β$ and $α$, that are constructed from the contour Minkowski tensor. The primary goal of our paper is to understand the effect of weak gravitational lensing on the morphology of the CMB fields. In order to isolate different physical effects that can be potentially confused with the effect of lensing, we first study the effect of varying the cosmology on $α$ and $β$, and show that they are relatively insensitive to variation of cosmological parameters. Next we analyze the signatures of hemispherical anisotropy, and show that information of such anisotropy in $α$ gets washed out at small angular scales and become pronounced only at large angular scales. For $β$ we find characteristic distortions which vary with the field threshold. We then study the effect of weak gravitational lensing using simulations of lensed temperature and $E$ and $B$ modes. We quantify the distortion induced in the fields across different angular scales. We find that lensing makes structures of all fields increasingly more anisotropic as we probe down to smaller scales. We find distinct behaviour of morphological distortions as a function of threshold for the different fields. The effect is small for temperature and $E$ mode, while it is significantly large for $B$ mode. Further, we find that lensing does not induce statistical anisotropy, as expected from the isotropic distribution of large scale structure of matter. We expect that the results obtained in this work will provide insights on the reconstruction of the lensing potential.

astro-ph.CO↗

arXiv2019

Ensemble Average of Three-Dimensional Minkowski Tensors of a Gaussian Random Field in Redshift Space

We present the ensemble expectation values for the translation invariant, rank-2 Minkowski tensors in three-dimensions, for a linearly redshift space distorted Gaussian random field. The Minkowski tensors $W^{0,2}_{1}$, $W^{0,2}_{2}$ are sensitive to global anisotropic signals present within a field, and by extracting these statistics from the low redshift matter density one can place constraints on the redshift space distortion parameter $β= f/b$. We begin by reviewing the calculation of the ensemble expectation values $\langle W^{0,2}_{1} \rangle$, $\langle W^{0,2}_{2} \rangle $ for isotropic, Gaussian random fields, then consider how these results are modified by the presence of a linearly anisotropic signal. Under the assumption that all fields remain Gaussian, we calculate the anisotropic correction due to redshift space distortion in a coordinate system aligned with the line of sight, finding inequality between the diagonal elements of $\langle W^{0,2}_{1} \rangle $, $\langle W^{0,2}_{2} \rangle $. The ratio of diagonal elements of these matrices provides a set of statistics that are sensitive only to the redshift space distortion parameter $β$. We estimate the Fisher information that can be extracted from the Minkowski tensors, and find $W^{0,2}_{1}$ is more sensitive to $β$ than $W^{0,2}_{2}$, and a measurement of $W^{0,2}_{1}$ accurate to $\sim 1\%$ can yield a $\sim 4\%$ constraint on $β$. Finally, we discuss the difference between using the matrix elements of the Minkowski tensors directly against measuring the eigenvalues. For the purposes of cosmological parameter estimation we advocate the use of the matrix elements, to avoid spurious anisotropic signals that can be generated by the eigenvalue decomposition.

astro-ph.CO↗

arXiv2019

Morphology of 21cm brightness temperature during the Epoch of Reioinization using Contour Minkowski Tensor

We use morphological descriptors, Betti numbers and Contour Minkowski Tensor (CMT) on 21cm brightness temperature excursion sets, to study the ionization and heating history of the intergalactic medium (IGM) during and before the Epoch of Reionization (EoR). The ratio of eigenvalues of the CMT denoted by $β$, gives shape information while it's trace gives the contour length of holes and connected regions. We simulate the matter density, neutral hydrogen fraction, spin temperature and brightness temperature field using the publicly available code 21cmFAST in a redshift range of $z=20.22$ to $z=6$. We study the redshift evolution of three quantities - the Betti number counts $N_{con,hole}$, the characteristic size $r^{ch}_{con,hole}$ and shape anisotropy parameter $β^{ch}_{con,hole}$ of connected regions and holes for these fields and investigate the different physical origins of their evolution. We make a qualitative comparison of different models of heating and ionization during the EoR. We obtain different regimes of morphological evolution of brightness temperature, depending upon how the shapes and sizes of connected regions and holes change with redshift for different astrophysical settings affecting the ionization and heating history of the IGM during and before the EoR. We find that the morphology of the brightness temperature field traces the morphology of ionized regions below a certain redshift value depending upon the model, where $Δr^{ch}_{hole}<10 \%$ and $Δβ^{ch}_{hole}<1 \%$ relative to the $x_{HI}$ field. This difference decreases with redshift. Therefore, the ionization history of the IGM can be reconstructed using the morphological description of $δT_b$ in real space.

astro-ph.CO↗

arXiv2018

Non-Gaussianity of diffuse Galactic synchrotron emission at 408 MHz

Diffuse Galactic emission at low frequencies is a major contaminant for studies of redshifted $21$ cm line studies. Removal of these foregrounds is essential for exploiting the signal from neutral hydrogen at high redshifts. Analysis of foregrounds and its characteristics is thus of utmost importance. It is customary to test efficacy of foreground removal techniques using simulated foregrounds. Most simulations assume that the distribution of the foreground signal is a Gaussian random field. In this work we test this assumption by computing the binned bispectrum for the all-sky $408$ MHz map. This is done by applying different brightness temperature ($T$) thresholds in order to assess whether the cooler parts of the sky have different characteristics. We find that regions with a low brightness temperature $T < 25$ K indeed have smaller departures from a Gaussian distribution. Therefore, these regions of the sky are ideal for future H{\sc i} intensity mapping surveys.

astro-ph.CO↗

arXiv2018

Search for anomalous alignments of structures in Planck data using Minkowski Tensors

Minkowski Tensors are tensorial generalizations of the scalar Minkowski Functionals. Due to their tensorial nature they contain additional morphological information of structures, in particular about shape and alignment, in comparison to the scalar Minkowski functionals. They have recently been used [29] to study the statistical isotropy of temperature and E mode data from the Planck satellite. The calculation in [29] relied on stereographic projection of the fields to extract the shape and alignment information. In this work, we calculate Minkowski Tensors directly on the sphere and compute the net alignment in the data, based on a recent work that extends the definition of Minkowski Tensors to random fields on curved spaces. This method circumvents numerical errors that can be introduced by the stereographic projection. We compare the resulting net alignment parameter values obtained from the frequency coadded CMB temperature data cleaned by the SMICA pipeline, to those obtained from simulations that include instrumental beam effects and residual foreground and noise. We find very good agreement between the two within $\approx$ 1$σ$ . We further compare the alignments obtained from the beam-convolved CMB maps at individual Planck frequencies to those in the corresponding simulations. We find no significant difference between observed data and simulations across all Planck frequencies, except for the 30 GHz channel. For the 30 GHz channel we find $\approx$ 2$σ$ difference between the data and the simulations. This mild disagreement most likely originates from inaccurate estimation of the instrumental beam at 30 GHz.

astro-ph.CO↗

arXiv2018

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

We apply the Minkowski Tensor statistics to two dimensional slices of the three dimensional 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 peaks. We begin by introducing our algorithm for constructing bounding perimeters around subsets of a two dimensional field, and reviewing the definition of Minkowski Tensors. Focusing on the translational invariant statistic $W^{1,1}_{2}$ - a $2 \times 2$ matrix - we calculate its eigenvalues for both the entire excursion set ($Λ_{1},Λ_{2}$) and for individual connected regions and holes within the set ($λ_{1},λ_{2}$). The ratio of eigenvalues $Λ_{2}/Λ_{1}$ informs us of the presence of global anisotropies in the data, and $\langle λ_{2}/λ_{1} \rangle$ is a measure of the mean shape of peaks and troughs in the density field. We study these quantities for a Gaussian field, then consider how they are modified by the effect of gravitational collapse using the latest Horizon Run 4 cosmological simulation. We find $Λ_{1,2}$ are essentially independent of gravitational collapse, as the process maintains statistical isotropy. However, the mean shape of peaks is modified significantly - overdensities become relatively more circular compared to underdensities of the same area. When applying the statistic to a redshift space distorted density field, we find a significant signal in the eigenvalues $Λ_{1,2}$, suggesting that they can be used to probe the large-scale velocity field.

astro-ph.CO↗

arXiv2018

Minkowski Tensors in Three Dimensions - Probing the Anisotropy Generated by Redshift Space Distortion

We apply the Minkowski tensor statistics to three dimensional Gaussian random fields. Minkowski tensors contain information regarding the orientation and shape of excursion sets, that is not present in the scalar Minkowski functionals. They can be used to quantify globally preferred directions, and additionally provide information on the mean shape of subsets of a field. This makes them ideal statistics to measure the anisotropic signal generated by redshift space distortion in the low redshift matter density field. We review the definition of the Minkowski tensor statistics in three dimensions, focusing on two coordinate invariant quantities $W^{0,2}_{1}$ and $W^{0,2}_{2}$. We calculate the ensemble average of these $3 \times 3$ matrices for an isotropic Gaussian random field, finding that they are proportional to products of the identity matrix and a corresponding scalar Minkowski functional. We show how to numerically reconstruct $W^{0,2}_{1}$ and $W^{0,2}_{2}$ from discretely sampled fields and apply our algorithm to isotropic Gaussian fields generated from a linear $Λ$CDM matter power spectrum. We then introduce anisotropy by applying a linear redshift space distortion operator to the matter density field, and find that both $W^{0,2}_{1}$ and $W^{0,2}_{2}$ exhibit a distinct signal characterised by inequality between their diagonal components. We discuss the physical origin of this signal and how it can be used to constrain the redshift space distortion parameter $Υ\equiv f/b$.

astro-ph.CO↗

arXiv2017

Tensor Minkowski Functionals for random fields on the sphere

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 obtain analytic expressions for the ensemble expectation values for the matrix elements of the tensor-valued Minkowski Functionals for isotropic Gaussian and Rayleigh fields. We elucidate the way in which the elements of the tensor Minkowski Functionals encode information about the nature and statistical isotropy (or departure from isotropy) of the field. We then implement our method to compute the tensor-valued Minkowski Functionals numerically and demonstrate how they encode statistical anisotropy and departure from Gaussianity by applying the method to maps of the Galactic foreground emissions from the PLANCK data.

astro-ph.CO↗

arXiv2017

On Minkowski Functionals of CMB polarization

CMB polarization data is usually analyzed using $E$ and $B$ modes because they are scalars quantities under rotations along the lines of sight and have distinct physical origins. We explore the possibility of using the Stokes parameters $Q$ and $U$ for complementary analysis and consistency checks in the context of searches for non-Gaussianity. We show that the Minkowski Functionals (MFs) of $Q,U$ are invariant under local rotations along the lines of sight even though $Q,U$ are spin-2 variables, for full sky analysis. The invariance does not hold for incomplete sky. For local type primordial non-Gaussianity, when we compare the non-Gaussian deviations of MFs for $Q,U$ to what is obtained for $E$ mode or temperature fluctuations, we find that the amplitude is about an order of magnitude lower and the shapes of the deviations are different. This finding can be useful in distinguishing local type non-Gaussianity from other origins of non-Gaussianity in the observed data. Lastly, we analyze the sensitivity of the amplitudes of the MFs for $Q$, $U$ and the number density of singularities of the total polarization intensity to the tensor-to-scalar ratio, $r$, and find that all of them decrease as $r$ increases.

astro-ph.CO↗

arXiv2016

Tensor Minkowski Functionals: first application to the CMB

Tensor Minkowski Functionals (TMFs) are tensorial generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze CMB maps. They encapsulate information about the shapes and the orientation of structures. We focus on one of the TMFs, namely $W_2^{1,1}$, which is the generalization of the genus. The ratio of the eigenvalues of the average of $W_2^{1,1}$ over all structures, $α$, encodes the net orientation; and the average of the ratios of the eigenvalues of $W_2^{1,1}$ for each structure, $β$, encodes the net anisotropy. We have developed a code that computes $W_2^{1,1}$, and from it $α$ and $β$, for a set of structures on the plane. We compute $α$ and $β$ as functions of threshold levels for simulated Gaussian and isotropic CMB fields. We obtain $α$ to be one for both temperature and $E$ mode, which means that we recover the input statistical isotropy of density fluctuations in the simulations. The level of net anisotropy of hotspots and coldspots in the CMB fields is quantified by $β\sim 0.62$. Then we compute $α$ and $β$ for data from PLANCK. We find that the temperature field agrees with the standard LCDM prediction of no net orientation within $3-σ$. However, we find that $E$ mode data shows a net orientation that deviates from the theoretical expectation at $14-σ$. The possible origin of this deviation may be instrumental effects or other sources and needs to be investigated further. For the net anisotropy we obtain values of $β$ for both temperature and $E$ mode that are consistent with the expectations from the standard LCDM simulations. Accurate measurements of $α$ and $β$ can be used to test the standard model of cosmology and to search for deviations from it.

astro-ph.CO↗

arXiv2016

Understanding Ghost Interference

The ghost interference observed for entangled photons is theoretically analyzed using wave-packet dynamics. It is shown that ghost interference is a combined effect of virtual double-slit creation due to entanglement, and quantum erasure of which-path information for the interfering photon. For the case where the two photons are of different color, it is shown that fringe width of the interfering photon depends not only on its own wavelength, but also on the wavelength of the other photon which it is entangled with.

quant-ph↗

arXiv2015

Constraint on noncommutative spacetime from PLANCK data

We constrain the energy scale of noncommutativity of spacetime using CMB data from PLANCK. We find that PLANCK data puts the lower bound on the noncommutativity energy scale to about 20 TeV, which is about a factor of two larger than a previous constraint that was obtained using data from WMAP, ACBAR and CBI. We further show that inclusion of data of $E$ mode of CMB polarization will not significantly change the constraint.

astro-ph.CO↗